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1609 | 1609.08110_arXiv.txt | The hundreds of multiple planetary systems discovered by the \textit{Kepler} mission are typically observed to reside in close-in ($\lesssim0.5$ AU), low-eccentricity, and low-inclination orbits. We run N-body experiments to study the effect that unstable outer ($\gtrsim1$ AU) giant planets, whose end orbital configurations resemble those in the Radial Velocity population, have on these close-in multiple super-Earth systems. Our experiments show that the giant planets greatly reduce the multiplicity of the inner super-Earths and the surviving population can have large eccentricities ($e\gtrsim0.3$) and inclinations ($i\gtrsim20^\circ$) at levels that anti-correlate with multiplicity. Consequently, this model predicts the existence of a population of dynamically hot single-transiting planets with typical eccentricities and inclinations of $\sim 0.1-0.5$ and $\sim 10^\circ-40^\circ$. We show that these results can explain the following observations: (i) the recent eccentricity measurements of \textit{Kepler} super-Earths from transit durations; (ii) the tentative observation that single-transiting systems have a wider distribution of stellar obliquity angles compared to the multiple-transiting systems; (iii) the architecture of some eccentric super-Earths discovered by Radial Velocity surveys such as HD\,125612c. Future observations from \textit{TESS} will reveal many more dynamically hot single transiting planets, for which follow up Radial Velocity studies will be able to test our models and see whether they have outer giant planets. | \label{sec:intro} Originally launched in 2009, NASA's \textit{Kepler} mission \citep{Borucki2010} is responsible for the discovery of thousands of planetary candidates, including over 3000 confirmed planets (e.g., \citealt{Mullally2015,Burke2015,Morton2016}). Through monitoring periodic changes in brightness of light curves from stars (i.e. the ``transit method''), \textit{Kepler} is able to detect planets with radii on the order of 1 $\text{R}_{\oplus}$, although the majority of planets detected are so-called ``super-Earths'' or ``sub-Neptunes'' (with radii $\sim 1.2 - 3 \text{R}_{\oplus}$, \citealt{Burke2015}). Of the thousands of planetary systems discovered by \textit{Kepler} to date, $80\%$ are single-transit systems (i.e. only one planet is observed to transit), while the other $\sim20\%$ consist of 2-7 transiting planets (\citealt{Mullally2015}). The multi-transit planet systems in the \textit{Kepler} sample populate dynamically cold orbits with low eccentricities and mutual inclinations ($e,i_{\rm m}\ll1$). In particular, the eccentricities derived from transit timing variations (TTVs) are typically $\sim0.01$ \citep{Wl13}, while the transit durations of ensembles of multiple transiting planets can be well-fitted with a Rayleigh distribution (Equation \ref{eq:sigma_e}) with mean values of $\bar{e}\sim0.04$ \citep{VA15,xie16} and $\bar{i}_{\rm m}\simeq1-2^\circ$ \citep{FM2012,Fabrycky2014}. In contrast, the properties of the single-transit planet systems seem to be much less certain. \citet{Lissauer2011} first noted with preliminary {\em Kepler} data that when modeling the mutual inclination distribution as a Rayleigh function, they had difficulty reproducing the large observed ratio of single transiting systems to multiple transiting systems. This ``problem" was later on referred to as the ``\textit{Kepler} dichotomy'' in several other studies (\citealt{Johansen2012,HM13,Ballard2016}). A wide range of studies into this problem have been undertaken with varying degrees of success \citep[e.g.,][]{Johansen2012,Moriarty2015,Ballard2016,Dawson:2016}, but a consistent picture is still missing. This dichotomy might not only be reflected on the derived occurrences between single and multiple planetary systems, but there is tentative evidence, possibly related to the occurrences through the planetary mutual inclinations, that at least a fraction of the single transiting planets in \textit{Kepler} occupy dynamically hotter orbits. First, \citet{xie16} find that the best fit to the transit durations of single transiting planets is a single Rayleigh distribution with $\bar{e}\simeq0.3$. Second, by combining measurements of the star's rotation period, radius, and projected rotational velocity, \citet{MW14} found statistically significant evidence that multiple transiting systems to have lower stellar obliquity angles than their single transiting counterparts. This trend can be indicative of larger individual inclinations in the singles assuming that the initial invariable plane, where planets form, nearly coincides with the host star's equator. A dozen of these dynamically hot close-in super-Earth/Neptune systems have also been discovered in the Radial Velocity surveys, often with giant planets companion further out ($a>1\,AU$). As shown in Figure \ref{fig:observed}, these inner super-Earths (defined as $M\sin i<0.1 M_J$) can easily have reported eccentricity of about $\sim0.1-0.4$. For example, HD\,125612c ($P\sim4$\,day, $M\sin\,i\sim18\,M_{\oplus}$) was determined to have an eccentricity of $0.27\pm0.12$ \citep{LoCurto:2010}. In this paper, we put forth a connection between these dynamically ``hot" super-Earths and distant giant planets. We propose a scenario by which scattering between distant planets with properties drawn from Radial Velocity surveys can robustly introduce single, eccentric ($e\gtrsim0.3$) and inclined (stellar obliquity $\gtrsim20^\circ$) super-Earth systems, and therefore account for the observed differences between single- and multi-transit systems observed in \textit{Kepler} data. This paper will proceed as follows. In section \S\ref{sec:sims}, we will discuss the details of the code used to run the simulations, as well as the initial conditions chosen to explore the problem. Our results are presented in section \S\ref{sec:results}, including the effects of different populations and initial conditions used in the simulations. During the course of this work, many authors explored various interaction between giant planets and close-in super-Earths \citep[e.g.][]{Lai2016,GF16,hansen2016,MDJ16}. We discuss our result together with these works in section \S\ref{sec:discussion}, and our conclusions are presented in section \S\ref{sec:conclusion}. \begin{figure}[htbp!] \centering \includegraphics[width=\columnwidth]{observed_try3.pdf} \caption{Known planet systems (from exoplanets.org) with long period giant planets and close-in super-Earths ($M{\rm sin}i<0.1\,M_{J}$), color coded by the number of planets in the system. The super Earths (giant planets) are plotted with diamonds (circles), regardless of their period. The size of the markers are proportion to $M{\rm sin}i^{1/3}$. The planet systems we used in this figure including 55 Cnc \citep{Fischer:2008}, BD -08 2823 \citep{Hebrard:2010}, GJ\,832 \citep{Wittenmyer:2014}, GJ\,876 \citep{Correia:2010}, HD\,11964 \citep{Wright:2009}, HD\,125612 \citep{LoCurto:2010}, HD\,181433 \citep{Bouchy:2009}, HD\,190360 \citep{Courcol:2015}, HD\,215497 \citep{LoCurto:2010}, HD\,219828 \citep{Santos:2016}, HD\,47186 \citep{Bouchy:2009}, HIP\,57247 \citep{Fischer:2012}, Kepler-68 \citep{Marcy:2014}, Kepler-89 \citep{Weiss:2013}, and mu Ara \citep{Pepe:2007}. \label{fig:observed}} \end{figure} | \label{sec:conclusion} We run N-body experiments to study the effect that outer ($\gtrsim1$ AU) giant planet companions can have on the orbital configurations of close-in super-Earth multiple systems. We show that, the planet-planet scattering events that shapes the giant planets to have final orbital states that resemble those of the systems discovered by Radial Velocity surveys, can excite the eccentricity and inclination of the super-Earths. As a result, about half of the inner multiple systems are completely destroyed, with a fraction of the remaining systems have their multiplicity reduced, producing a population of dynamically hot single super-Earth systems. We predict these single super-Earths to have mean eccentricities of $\sim0.4$ and mean inclinations $\sim 30^\circ$. As the multiplicity increases, the systems have lower eccentricity and mutual inclinations. The obliquity distribution from this mechanism agrees with the tentative observation that single transiting systems have a wider distribution of stellar obliquity angles compared to the multiple transiting systems \citep{MW14}. | 16 | 9 | 1609.08110 |
1609 | 1609.08921_arXiv.txt | Calculations of atmospheric refraction are generally based on a simplified model of atmospheric density in the troposphere which assumes that the temperature decreases at a constant lapse rate $L$ from sea level up to a height $h_t\approx 11$ km, and that afterwards it remains constant. In this model, the ratio $T_o/L$, where $T_o$ is the temperature at the observer's location, determines the length scale in the calculations for altitudes $h\leq h_t$. But daily balloon measurements across the U.S.A. reveal that in some cases the air temperature actually increases from sea level up to a height $h_p$ of about one km, and only after reaching a plateau with temperature $T_o'$ at this height, it decreases at an {\it approximately} constant lapse rate.Hence, in such cases, the relevant length scale for atmospheric refraction calculations in the altitude range $h_p\leq h<h_t$ is $T_o'/L$, and the contribution for $h\leq h_p$ has to be calculated from actual measurements of air density in this range. Moreover, in three examples considered here, the temperature does not remain constant for $h_t \leq h$, but continues to decreases to a minimum at $h_m \approx 16$ km, and then increases at higher altitudes at a lower rate. Calculations of atmospheric refraction based on this atmospheric data is compared with the results of simplified models. | 16 | 9 | 1609.08921 |
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1609 | 1609.01800_arXiv.txt | We investigate the contentious issue of the presence, or lack thereof, of satellites mass segregation in galaxy groups using the Galaxy And Mass Assembly (GAMA) survey, the GALFORM semi-analytic and the EAGLE cosmological hydrodynamical simulation catalogues of galaxy groups. We select groups with halo mass $12 \leqslant \log(M_{\text{halo}}/h^{-1}M_\odot) <14.5$ and redshift $z \leqslant 0.32$ and probe the radial distribution of stellar mass out to twice the group virial radius. All the samples are carefully constructed to be complete in stellar mass at each redshift range and efforts are made to regularise the analysis for all the data. Our study shows negligible mass segregation in galaxy group environments with absolute gradients of $\lesssim0.08$ dex and also shows a lack of any redshift evolution. Moreover, we find that our results at least for the GAMA data are robust to different halo mass and group centre estimates. Furthermore, the EAGLE data allows us to probe much fainter luminosities ($r$-band magnitude of 22) as well as investigate the three-dimensional spatial distribution with intrinsic halo properties, beyond what the current observational data can offer. In both cases we find that the fainter EAGLE data show a very mild spatial mass segregation at $z \leqslant 0.22$, which is again not apparent at higher redshift. Interestingly, our results are in contrast to some earlier findings using the Sloan Digital Sky Survey. We investigate the source of the disagreement and suggest that subtle differences between the group finding algorithms could be the root cause. | Both theoretical modelling of galaxy formation and observations reveal that most of the stellar material in the Universe resides in groups of a few $10^{12} M_{\sun}$ and larger masses \citep[e.g.][etc]{1958ApJS....3..211A,1977ApJ...211..311R,1982ApJ...255..382H,1982ApJ...257..423H,1983ApJS...52...61G, 2000ARA&A..38..289M,2004MNRAS.348..866E,2006ApJS..167....1B,2007ApJ...671..153Y,2009ApJ...697.1842K,2011MNRAS.416.2640R,2013MNRAS.436..380N, 2014A&A...566A...1T,2014MNRAS.441.1270L,2015arXiv151105856S}. Moreover, it is known that galaxies residing in a group environment follow a very different evolutionary course compared to that of isolated systems \citep{1974Natur.252..111E,1984ApJ...281...95P}. Therefore, the group environment is clearly an important factor in understanding both structure formation and galaxy evolution at intermediate local mass densities. In current galaxy formation models, galaxies in the groups can be broadly classified in two categories: central galaxies and satellite galaxies \citep[e.g.][etc]{2005ApJ...633..791Z,2011MNRAS.410..417S}. Central galaxies are located near the centre of a parent dark matter halo. Under the current paradigm of hierarchical structure formation, the central galaxies of the subhalo that gets accreted to the dominant nearby halo are called satellites. Subsequently the accreted galaxies (satellites) are potentially quenched by environmental effects, such as gas stripping by ram-pressure \citep{1972ApJ...176....1G,2009MNRAS.399.2221B}, removal or reduction of hot/cold gas or even the stellar components of the satellite galaxy due to tidal stripping \citep{1996Natur.379..613M,2006PASP..118..517B}. Thus, to develop a viable theory of galaxy formation it is important to understand the processes that could influence the abundance and distribution of satellites in galaxy groups. A spatial distribution of stellar mass segregation in any dynamical system, ranging from globular clusters to galaxy groups and clusters, is an important indicator of their evolutionary history and dynamical friction time-scales. The sinking of heavier objects in a gravitational potential well of stellar \citep{1998MNRAS.295..691B} and galaxy \citep{1977MNRAS.179...33W,2004MNRAS.352L...1G,2005ApJ...619..193M} clusters has been repeatedly observed. Broadly, the mass segregation is known to be either primordial \citep{1997MNRAS.285..201B}, meaning clusters may form with the most massive galaxies concentrated near the centre, or dynamical \citep{Allison2009} caused by migration of the most massive galaxies into the centre of the cluster via relaxation. If dynamical friction in the group environment plays a dominant role, then the effect on the stellar mass distribution in galaxy groups should be detectable. Conversely, if there is an absence of spatial mass segregation in groups, it could possibly mean that the contribution of ongoing star formation in galaxies, or tidal stripping of satellite galaxies as they fall inward, or that the group is continually fed by new merging groups in a dominant process directing the distribution of the mass in groups. In other words, it means that the relaxation time of the galaxy groups is significantly longer than their crossing time. With the advent of large redshift surveys it has only recently become possible to study mass segregation in galaxy groups in great detail using the Sloan Digital Sky Survey (SDSS; \citealt{2000AJ....120.1579Y}) and zCOSMOS \citep{2012ApJ...753..121K}. Recently, \cite{2015MNRAS.448L...1R} showed the presence of mass segregation trends in SDSS, meaning satellites of higher masses are systematically concentrated close to the group-centre at all halo mass ranges. This is in close agreement with earlier studies using different data sets, for example, \citet[SDSS]{2008arXiv0805.0002V} and \citet[zCOSMOS]{2012A&A...539A..55P}. Similarly, \cite{2014MNRAS.443.2679B} also find some mass segregation, but at small group radii of $\lesssim 0.1$ times the virial radius. Simultaneously, there are also evidence to contradict the existence of mass segregations in galaxy groups. For example, \cite{2013MNRAS.434.3089Z} fail to observe strong mass segregation in X-ray selected groups up to $z\sim1.7$. However, they could not rule out that this might be due to a bias introduced by their sample selection. Similarly \cite{2012MNRAS.424..232W}, using galaxy group catalogues created from SDSS DR7, with a modified implementation of the group-finding algorithm in \cite{2007ApJ...671..153Y}, also find no evidence of mass segregation for satellites at any halo mass range. Despite this large body of work, there is little consensus on the presence or the strength of mass segregation in galaxy groups. On the theory side there have been analogous studies \citep[e.g.][etc]{2004MNRAS.348..333D,2005MNRAS.359.1537R,2016MNRAS.455..158V} that show the segregation of dark matter subhaloes in numerical simulations of various extents, but also see \cite{2004MNRAS.352..535D,2008MNRAS.391.1685S,2009ApJ...692..931L} for contradictory findings. In the future, it would be valuable to combine the theoretical work with the studies of satellites mass segregation in galaxy groups to better understand the galaxy-halo connection and the various physical processes, such as how galaxies populate haloes. In this work we aim to resolve the contentious issue of the presence or absence of mass segregation in galaxy groups. For this we investigate group catalogues from three types of data, observed: using the Galaxy and Mass Assembly survey (\gama; \citealt{2011MNRAS.413..971D,2015MNRAS.452.2087L}); semi-analytics: using the \gama\ lightcone mock catalogues (\gamamock; \citealt{2013MNRAS.429..556M} using the \cite{2014MNRAS.439..264G} variant of the \textsc{galform} semi-analytic model of galaxy formation \citep{2000MNRAS.319..168C,2015arXiv150908473L}), and cosmological hydrodynamical simulation: using the Evolution and Assembly of GaLaxies and their Environments (\eagle; \citealt{2015MNRAS.446..521S,2015arXiv151001320M}). In order to make the results from all the three data sets comparable, we homogenise the estimates of physical quantities such as group-centric distance, stellar mass and halo virial properties. Throughout the paper we assume a cosmological constant $\Omega_\Lambda=0.75$, matter density $\Omega_M=0.25$ and $h=H_0/(100$ kms$^{-1}$ Mpc$^{-1})$. Also, $\log$ stands for logarithm to the base 10, and $r$ and $R$ represent the spherical (3D) and projected (2D) radii respectively. For conciseness, we use the standard notation $($ and $]$ to denote open and closed intervals respectively. This paper is arranged as follows. In Section~\ref{sec:data}, we describe \gama, \gamamock\ and \eagle\ data, their corresponding group catalogues and the derivation of quantities relevant to our analysis. In Section~\ref{sec:result} we present our main results. In Section~\ref{sec:discussion} we provide a detailed comparison of our work with the available group catalogues of Sloan Digital Sky Survey (SDSS) data and also among different group catalogues of SDSS. Our findings are summarised in Section~\ref{sec:conclusion}. | \label{sec:conclusion} We investigate the controversial issue of the presence, or lack thereof, of mass segregation in galaxy groups. We provide a comprehensive study of the radial distribution of stellar mass of the satellite galaxies in galaxy groups for observations: the galaxy-redshift survey Galaxy and Mass Assembly (\gama); semi-analytics: the \gama\ lightcone mock catalogues (\gamamock) constructed using a model of galaxy formation by the GALFORM group, and cosmological hydrodynamical simulation: the Evolution and Assembly of GaLaxies and their Environments (\eagle). Overall, the absolute gradient of spatial mass segregation in galaxy groups is found to be insignificant ($\lesssim0.04$ dex). We find this to be consistent for all the three data sets at various halo mass ranges between $12 \leqslant \logmhalo <14.5$ and in the redshift range $0 \leqslant z \leqslant 0.32$. Analogous to the observed \gama\ data, we magnitude-limit both the synthetic data i.e. \gamamock\ and \eagle\ to $r<19.8$ mag, and carefully select stellar mass complete samples at given redshift intervals. We also find that the radial distributions of the stellar mass does not show any redshift evolution out to $z \leqslant 0.32$. In cases where we separate data into different redshift ranges the absolute gradients of spatial mass segregation trends were slightly larger $\lesssim0.08$ dex but consistent to zero given the uncertainties in the slope. Moreover, we find that our results at least for the \gama\ data are robust to different halo mass and group centre estimates. The \eagle\ data give us further insights by allowing us to probe fainter magnitude limit of $r_{\text{mag}}<22$ and also, to study the three-dimensional spatial distributions using the intrinsic stellar and virial masses. Except for the low redshift regime $z \leqslant 0.22$, even with the fainter magnitude limit of $r_{\text{mag}}<22$, we find that the \eagle\ data do not show any mass segregation in the halo mass range $12 \leqslant \logmhalo <14.5$ and out to $z \leqslant 0.75$. This remains the case for both the projected and intrinsic data alike. Intriguingly, the lack of mass segregation we observe is in contrast to what has recently been reported in \cite{2008arXiv0805.0002V, 2015MNRAS.448L...1R} with the SDSS group catalogues of \cite{2007ApJ...671..153Y}. We find that the magnitude of mass segregation seen in earlier works with SDSS group catalogues reduces when we replace their original luminosity based halo masses with dynamically inferred masses. As advocated in \cite{2015MNRAS.453.3848D}, the original estimates for halo masses from abundance matching could have propagated uncertainties from how \cite{2007ApJ...671..153Y} group catalogues are constructed. A subtle effect due to using halo based group finding instead of FoF based finding could also potentially result in observed mass segregation. Interestingly, our analysis based on the SDSS group catalogue of \cite{2015arXiv151105856S}, which uses a similar group-finder to \cite{2011MNRAS.416.2640R}, accompanied with implied dynamical halo masses, confirms the lack of significant evidence of mass segregation in low redshift galaxy groups. This is entirely consistent with our findings from \gama, \gamamock\ and \eagle\ group studies and with the conclusion of \cite{2012MNRAS.424..232W} using a revised SDSS group catalogue. The apparent lack of mass segregation in groups suggests that whatever processes might enhance the effect (e.g. dynamical friction, mergers etc) is sub-dominant compared to competing and masking processes (e.g. long time-scales, star-formation, quenching etc). | 16 | 9 | 1609.01800 |
1609 | 1609.06611_arXiv.txt | We present the results of a search for \HI\ 21-cm line emission from the circumstellar environments of four Galactic Cepheids (RS~Pup, X~Cyg, $\zeta$~Gem, and T~Mon) based on observations with the Karl G. Jansky Very Large Array. The observations were aimed at detecting gas associated with previous or ongoing mass loss. Near the long-period Cepheid T~Mon, we report the detection of a partial shell-like structure whose properties appear consistent with originating from an earlier epoch of Cepheid mass loss. At the distance of T~Mon, the nebula would have a mass (\HI+He) of $\sim0.5M_{\odot}$, or $\sim$6\% of the stellar mass. Assuming that one-third of the nebular mass comprises swept-up interstellar gas, we estimate an implied mass-loss rate of ${\dot M}\sim (0.6-2)\times10^{-5}~M_{\odot}$ yr$^{-1}$. No clear signatures of circumstellar emission were found toward $\zeta$~Gem, RS~Pup, or X~Cyg, although in each case, line-of-sight confusion compromised portions of the spectral band. For the undetected stars, we derive model-dependent $3\sigma$ upper limits on the mass-loss rates, averaged over their lifetimes on the instability strip, of $\lsim(0.3-6)\times10^{-6}~M_{\odot}$ yr$^{-1}$ and estimate the total amount of mass lost to be less than a few per cent of the stellar mass. | } \label{intro} Cepheid variables serve as fundamental calibrators of the cosmic distance scale, making these stars of vital importance to extragalactic astronomy and cosmology (Freedman et al. 2001; Di Benedetto 2013 and references therein). However, important gaps remain in our understanding of the physics and evolution of Cepheids. One of the most confounding puzzles is the decades-old problem known as the ``Cepheid mass discrepancy": mass estimates based on stellar evolution models are inconsistent with pulsation masses (derived from the mass-dependent Period-Luminosity relation) and with masses inferred from orbital dynamics (e.g., Christy 1968; Cox 1980; Pietrzy\'nski et al. 2010). Discrepancies of $\sim$10-20\% have persisted despite continued improvements in evolutionary models (e.g., Bono et al. 2002; Caputo et al. 2005; Keller \& Wood 2006; Neilson et al. 2011). Proposed solutions have included extra mixing, rotation, the need for better radiative opacities, and perhaps most importantly, {\em mass-loss} (e.g., Cox 1980; Bono et al. 2006; Neilson et al. 2011, 2012a, b). If mass loss is occurring during the Cepheid evolutionary phase, this could have important implications for the use of Cepheids as distance indicators, since the presence of circumstellar material may add scatter to inferred luminosities in the form of extra extinction in the visible and excess emission at IR wavelengths (Neilson et al. 2009; Gallenne et al. 2013; Schmidt 2015). Indeed, accounting for these effects may be key to resolving the discrepancy between the Hubble constant determination from Cepheids compared with that derived from Cosmic Microwave Background measurements (e.g., Riess et al. 2016). Mass loss on the instability strip would also impact other evolutionary stages of intermediate mass stars, including the relative lifetimes of the red and blue supergiant phases (e.g., Dohm-Palmer \& Skillman 2002), and the determination of what is the maximum initial mass of a star that will end its life as a white dwarf rather than a supernova. While Cepheid mass loss has been suspected for decades (see review by Cox 1980), the direct and unambiguous detection of escaped or outflowing material from Cepheids has proved to be challenging, leading to empirically estimated mass-loss rates (or upper limits) spanning several orders of magnitude (${\dot M}\lsim10^{-12}$ to $10^{-5}M_{\odot}$ yr$^{-1}$; McAlary \& Welch 1986; Welch \& Duric 1988; Deasy 1988; B\"ohm-Vitense \& Love 1994; Neilson et al. 2009). However, a series of recent studies has provided mounting evidence that not only is mass loss common for stars on the instability strip, but it typically occurs at rates high enough to significantly impact the star's evolutionary track. In a study based on {\it Spitzer} infrared (IR) imaging data, Marengo et al. (2010b) reported the discovery of a bow shock surrounding the Cepheid archetype $\delta$~Cephei ($\delta$~Cep), providing direct evidence for the existence of a stellar wind, and hence, ongoing mass loss at a rate of $\sim10^{-7}~M_{\odot}$ yr$^{-1}$. Extended IR emission was also detected with {\it Spitzer} around several other Cepheids by Barmby et al. (2011), including three stars with extended emission seen in multiple IR bands and four other stars with evidence for extended emission in at least one band. In addition, on scales closer to the star, near- and mid-IR interferometry have revealed what appear to be warm, dusty circumstellar envelopes on scales ranging from a few stellar radii (M\'erand et al. 2006; Kervella et al. 2006; Gallenne et al. 2013) to several hundred AU (Kervella et al. 2009). As noted by some authors (e.g., Schmidt 2015), observed IR excesses and extended IR emission are not necessarily a {\em direct} product of ongoing mass loss, particularly dusty mass loss. For example, in the case of $\delta$~Cep, the extended IR nebulosity may be somehow linked with the presence of a binary companion (Anderson et al. 2015), while in the case of RS~Pup, the vast circumstellar nebulosity may represent a pre-existing interstellar cloud (Kervella et al. 2009). However, in both of these cases, there is evidence that a stellar wind has had a role in {\em shaping} the IR-emitting material. Similarly, Marengo et al. (2010a) suggested that near-IR emission seen close to the star may result from shocked gas emission rather than dust. Nonetheless, the presence of this emission is consistent with a pulsationally-driven wind. Another line of evidence for Cepheid mass loss comes from the work of Neilson et al. (2012b), who analyzed the observed rates of period change, ${\dot P}$, for a sample of 200 Galactic Cepheids and compared the results to stellar evolution models. They found that models without mass loss could not reproduce the observed ${\dot P}$ trends. However, mass loss on the Cepheid instability strip at a mean rate ${\dot M}\sim 10^{-7}~M_{\odot}$ yr$^{-1}$ rectifies the models with observations. For the specific case of Polaris, Neilson et al. (2012a) concluded that a mass-loss rate of ${\dot M}\sim 10^{-6}~M_{\odot}$ yr$^{-1}$ is necessary to account for the secular period change of this star over the past $\sim$200 years. Because of the moderate temperatures of Cepheids ($\sim$5000-6000~K), their winds are expected to be predominantly neutral and atomic (Glassgold \& Huggins 1983), with at most, a modest ionized fraction (e.g., Engle et al. 2014). This makes the \HI\ 21-cm line a potentially powerful tracer of Cepheid outflows. Although contamination from interstellar \HI\ emission along the line-of-sight tends to be strong toward sources near the Galactic plane, the finite outflow velocity of the wind is expected in most cases to shift a portion of the circumstellar gas outside of the velocity range most strongly affected by line-of-sight emission. In addition, interferometers act as spatial filters against the largest scale components of the line-of-sight emission, which can aid in disentangling circumstellar signals from foreground and/or background signals (Bowers \& Knapp 1987; Matthews \& Reid 2007; Le~Bertre et al. 2012). Motivated by these factors, Matthews et al. (2012; hereafter M12) used the legacy Very Large Array to observe $\delta$~Cep in the \HI\ 21-cm line with the goal of searching for a gaseous counterpart to the stellar wind revealed by the {\it Spitzer} observations of Marengo et al. (2010b). Based on the \HI\ data, M12 reported the discovery of an extended \HI\ nebula ($\sim13'$, or 1~pc across) surrounding the position of $\delta$~Cep. This nebula exhibits a head-tail morphology, consistent with debris that was ejected from the star and subsequently sculpted by its interaction with the interstellar medium (ISM). M12 derived an outflow velocity for the wind of $V_{\rm o}\approx35.6\pm$1.2~\kms---the first ever directly measured from a Cepheid---and constrained the mass-loss rate to be ${\dot M}\approx (1.0\pm0.8)\times10^{-6}~M_{\odot}$ yr$^{-1}$. If similar \HI\ envelopes are present around other Cepheids, this would have profound implications for our understanding of these stars and our ability to constrain their mass-loss and evolutionary histories. For this reason, we have undertaken \HI\ imaging observations of a sample of four additional Galactic Cepheids using the upgraded Karl F. Jansky Very Large Array (VLA) of the National Radio Astronomy Observatory\footnote{The National Radio Astronomy Observatory is operated by Associated Universities, Inc., under cooperative agreement with the National Science Foundation.}. As described below, these observations have uncovered evidence for circumstellar material associated with one additional Cepheid and allow us to place limits on the mass of circumstellar material associated with the three remaining targets. | \subsection{Upper Limits on the Circumstellar \HI\ Mass and Mass-Loss Rates for the Undetected Stars\protect\label{upperlimits}} For the stars undetected in the \HI\ line, our new VLA observations allow us to place new limits on the presence of circumstellar debris that may have been shed by these Cepheids during periods of recent or ongoing mass loss. However, translating our measurements to quantitative upper limits that are useful for constraining the stellar mass-loss properties requires adopting some assumptions about the nature of Cepheid outflows---a topic on which we have very few empirical constraints. To our knowledge, $\delta$~Cep is only Cepheid with a directly measured outflow velocity ($V_{\rm o}\approx$35~\kms; M12). The value of $V_{\rm o}$ for $\delta$~Cep is noteworthy in that it is significantly lower than the escape speed from the star, consistent with a general trend of $V_{\rm o}<<V_{\rm esc}$ that has been seen in other types of supergiants (Reimers 1977; Holzer \& MacGregor 1985; Judge \& Stencel 1991). Indeed, Reimers (1977) found that for non-variable G and K supergiants, the stars roughly follow a relation of the form $V_{\rm o}\sim 1.6\times10^{-3} V_{\rm esc}^{2}$. This relationship also holds for stars of comparable spectral type in the sample of Judge \& Stencel (1991) and reasonably agrees with the measured outflow speed for $\delta$~Cep (M12), even though the underlying mass-loss mechanism may be quite different between pulsating and non-pulsating supergiants. Lacking any further constraints on $V_{\rm o}$ for Cepheids, we adopt the empirical relation of Reimers to estimate representative outflow velocities for our sample stars. These values are presented in Table~5. If we assume that the \HI\ linewidth for each star is approximately twice its outflow speed, we may now derive model-dependent limits on the quantity of circumstellar gas for the undetected stars. For $\zeta$~Gem, X~Cyg, and T~Mon, we use the RMS noise levels, $\sigma_{\rm RMS}$, from the uncontaminated portions of the naturally-weighted \HI\ data cubes in Table~4 to compute 3$\sigma$ upper limits to the velocity-integrated \HI\ flux density within a single synthesized beam centered on each of the undetected stars as $\int S dV < 3\sigma_{\rm RMS}\times (2V_{\rm o})$ Jy \kms. For RS~Pup, where the entire velocity range $V_{\star,\rm LSR}\pm V_{\rm o}$ is affected by confusion (see Figure~\ref{fig:RSPupspec}), we substitute for $\sigma_{\rm RMS}$ the term $\sigma_{\rm obs}=(\sigma^{2}_{\rm c}+\sigma^{2}_{\rm RMS})^{0.5}$, where $\sigma_{c}$=0.66~mJy beam$^{-1}$ is the additional confusion noise estimated from channels with velocities between $-25$ and $-10$~\kms. For optically thin emission, the aforementioned upper limits to the integrated flux density can be translated into 3$\sigma$ upper limits on the mass of \HI\ within the synthesized beam as $M_{\rm HI}<2.36\times10^{-7}d^{2}\int S dV~~M_{\odot}$, where $d$ is the adopted distance in pc (e.g., Roberts 1975). Results are given in column 4 of Table~5. Because the mass loss on the instability strip is expected to extend over tens of thousands of years or more, ejecta may be spread well beyond a single beam diameter---possible reaching a parsec or more from the star (see M12; Kervella et al. 2012; Section~\ref{TMon}). For each undetected star, we therefore also compute upper limits on the total \HI\ mass within a fiducial volume of radius 0.5~pc. The choice of this radius is arbitrary, but is useful for illustrative purposes. These resulting limits are given in column~7 of Table~5. To provide an estimate of the rate of recent or ongoing mass-loss for each star, we assume ${\dot M}< 1.4(M_{\rm HI}/t_{c})$. Here, the factor of 1.4 accounts for the mass of helium, and the fiducial timescale $t_{\rm c}$ is taken as $r_{c}/V_{o}$. We adopt as the characteristic radius, $r_{c}$, the geometric mean HWHM of the synthesized beam, projected to the distance of the star. Results are given in column~5 of Table~5. We include an upper limit for T~Mon, where \HI\ was detected offset from the stellar position, but not directly along the line-of-sight to the star (see Section~\ref{TMondisc}). To constrain the {\em mean} mass-loss rates of $\zeta$~Gem, RS~Pup, and X~Cyg during their entire Cepheid evolution, we combine the volume-averaged \HI\ mass limits computed above with estimates of the total time, $t_{i}$, that each of the stars have spent on the instability strip. We estimate $t_{i}$ based on the solar metallicity models of Bono et al. (2000, their Table~7). We assume that $\zeta$~Gem is on its second crossing of the instability strip, that RS~Pup and X~Cyg are on their third crossings, and that the total time spent on the instability strip is equal to the sum of the previous crossings, plus one-half the predicted duration of the current crossing. The resulting time-averaged mass-loss rates, $|{\dot M}|=1.4\left(M_{\rm HI}({\rm total})\right)/t_{i}$, are given in column~8 of Table~5. \subsection{Upper Limits Compared with Expected Values of ${\dot M}$} Based on recent studies of rates of period change, the mean mass-loss rate expected over the course of a Cepheid's lifetime is $\sim10^{-7}$ to $10^{-6}M_{\odot}$ yr$^{-1}$ (Neilson et al. 2011, 2012a, b). These values are comparable to the upper limits in column~8 of Table~5. The present non-detection of $\zeta$~Gem, X~Cyg, and RS~Pup in the \HI\ line is therefore not in contradiction with the findings from the period change studies, and suggests that deeper \HI\ observations may yet uncover mass-loss signatures. Furthermore, the mass-loss rate of Cepheids are not expected to be constant, but rather may vary by up to several orders of magnitude as the stars evolve along the instability strip (Neilson et al. 2011). This means that periods of intense mass loss ($\sim10^{-5}M_{\odot}$ yr$^{-1}$) may occur, particularly for longer period Cepheids ($P>$15~days; B\"ohm-Vitense \& Love 1994; Deasy 1988; Neilson \& Lester 2008). While the mechanism for generating such intense mass loss is unclear, it is worth noting that because the crossing time of the instability strip is relatively short for Cepheids with periods of $\sim$15-30 days ($<10^{5}$~yr; Bono et al. 2000) periods of intense mass-loss are likely to be required if stars in this period range (including X~Cyg and T~Mon) are to lose even a few per cent of their mass during the Cepheid phase (see Section~\ref{discrep}). For $\zeta$~Gem and RS~Pup, our present upper limits on the current mass-loss rates are inconsistent with mass loss of this magnitude during the past several thousand years, but for X~Cyg or T~Mon it cannot be excluded (see also Section~\ref{TMondisc}). \subsection{Constraints on the Role of Mass Loss for Solving the Mass Discrepancy\protect\label{discrep}} After scaling the upper limits to the circumstellar \HI\ mass within a 0.5~pc radius around each star (column~7 of Table~5) by a factor of 1.4 to correct for the mass of He, it is of interest to compare the resulting masses with the stellar masses from Table~1. We find that for the three undetected stars, our limits on the mass of circumstellar matter correspond to $\lsim$2-5\% of the stellar mass. While it is difficult to accurately estimate the mass discrepancy for any individual star owing to model uncertainties, statistically, discrepancies between pulsation and evolutionary masses average between 10-20\% (see Section~\ref{intro}). This tentatively suggests that for our sample stars, mass loss alone is unlikely to fully reconcile the mass discrepancy, although it could still account for a significant fraction of it. However, we stress that this conclusion is model-dependent. For example, if the \HI\ linewidths are smaller than we have assumed (e.g., as a result of deceleration of large-scale ejecta owing to interaction with the surrounding ISM), this could allow significant quantities of gas to be hidden by line-of-sight confusion (see e.g., Le~Bertre et al. 2012). Alternatively, if we have systematically underestimated the expected wind outflow velocities, the inferred upper limits would also increase. \subsection{Comparison to Past Results} A comparison between our new results and previous constraints on the mass-loss rate of T~Mon were described in Section~\ref{tmonimp}. Here we briefly compare our new results for the other three stars to earlier studies. \subsubsection{$\zeta$ Gem} For $\zeta$~Gem, Sasselov \& Lester (1994) reported evidence based on the \HeI~$\lambda$10830 line for the outflow of material in the upper chromosphere, albeit with velocities well below the escape speed (they found the mean \HeI\ line velocity to be blueshifted from the stellar velocity by 31~\kms). Ultraviolet spectroscopy by Schmidt \& Parsons (1984) and Deasy (1988) also revealed possible outflow signatures in the Mg~II~h and k line profiles of $\zeta$~Gem (see also Deasy \& Wayman 1986). In this case, two blueshifted components are seen with velocities comparable to the surface escape velocity ($\gsim-110$~\kms\ relative to the stellar systemic velocity). While it is unclear whether the large Mg~II~h and k velocities are reflective of the bulk outflow speed, as described in Section~\ref{zetaGem}, we find no statistically significant emission at comparable velocities in our \HI\ data. In any case, a wind resulting from mass-loss at a rate comparable to that estimated by Deasy (${\dot M}\sim10^{-10}~M_{\odot}$ yr$^{-1}$) would be several orders of magnitude below the detection limit of our \HI\ observations, although it is important to stress that Deasy's ${\dot M}$ value is a lower limit, since it does not take into account the continuous flow of matter from the upper atmosphere. \subsubsection{RS Pup} The recombination line study of Gallenne et al. (2011) provided evidence of a significant quantity of atomic hydrogen in the close environment of RS~Pup (i.e., on scales of $\sim1''$ or $\sim$1550~AU). Although our current spatial resolution is comparatively coarse, we are able to place a 3$\sigma$ upper limit on the mass of neutral atomic hydrogen within a radius of 38,000~AU from the star (i.e., one synthesized beam) of $<0.11~M_{\rm HI}$ (Table~5). Looking to larger scales, Kervella et al. (2012) found a mean radius of the RS~Pup reflection nebula to be \am{1}{8} ($\sim$0.8~pc for our adopted distance) based on the analysis of scattered light images, and they estimated the total quantity of gas plus dust within this volume to be $190~M_{\odot}$ (with an uncertainty of $\sim$40\%). The assumed dust fraction is 1\%. Despite the significant line-of-sight contamination in our RS~Pup data, such a large quantity of gas within a region spanning only a few arcminutes in spatial extent should have been readily detectable ($>5\sigma$) in our data at velocities blueshifted by $\gsim-10$~\kms\ from the stellar systemic velocity, even if it were only $\sim$1\% atomic. This suggests that either the nebula is predominantly molecular---consistent with the mean nucleon density of $\sim$2600 cm$^{-3}$ implied from the work of Kervella et al. (2012)--- or else that the atomic gas associated with the reflection nebula lies within the range of velocities where detection is hampered by line-of-sight contamination (cf. Figure~\ref{fig:RSPupspec}). Lastly, it is worth noting that several previous authors derived much more modest mass estimates for the nebula based on dust measurements in the IR [e.g., $\sim2.3M_{\odot}$ (McAlary \& Welch 1986); $\sim2.2M_{\odot}$ (Deasy 1988); $\sim$0.06 to $0.9M_{\odot}$; (Barmby et al. 2011)].\footnote{All of these estimates assume a gas-to-dust ratio of 100 and are scaled to our adopted distance.} However, in contrast to these other studies, the technique of measuring scattered light used by Kervella et al. probes additional dust content whose temperature is too low to directly emit in the IR. Based on {\it IRAS} data, Deasy (1988) previously estimated the mean rate of mass-loss from RS~Pup to be $\sim3\times10^{-6}~M_{\odot}$ yr$^{-1}$ (scaled to our adopted distance). However, based on the structure of the surrounding nebula, he argued that the mass-loss from this star is likely to be intermittent, with episodes of enhanced mass loss at rates as high as a few times $10^{-5}~M_{\odot}$ yr$^{-1}$. Our present upper limits on the mass-loss rate of RS~Pup (Table~5) appear to exclude ongoing mass loss of this magnitude. \subsubsection{X Cyg} Based on {\it IRAS} data, McAlary \& Welch (1986) noted a possible IR excess associated with X~Cyg. Barmby et al. (2011) also found tentative evidence for extended IR emission around this star in their {\it Spitzer} images. However, in neither case are the data sufficient to estimate a mass-loss rate, and to our knowledge, no empirical limits on the mass-loss rate of X~Cyg have been published to date. \begin{deluxetable*}{lcccccccc} \tabletypesize{\tiny} \tablewidth{0pc} \tablenum{5} \tablecaption{Derived Mass-Loss Properties for the Target Stars} \tablehead{ \colhead{Star} & \colhead{$V_{\rm esc}$} & \colhead{$V_{\rm o}$} & \colhead{$\int S dv$} & \colhead{$M_{\rm HI}$(beam)} & \colhead{${\dot M}$(current)} & \colhead{$M_{\rm HI}$(total)} & \colhead{$t_{i}$} & \colhead{$|{\dot M}|$}\\ \colhead{} & \colhead{(\kms)} & \colhead{(\kms)} & \colhead{(Jy km s$^{-1}$)} & \colhead{($M_{\odot}$)} & \colhead{($M_{\odot}$ yr$^{-1}$)} & \colhead{($M_{\odot}$)} & \colhead{($10^{4}$ yr)} & \colhead{($M_{\odot}$ yr$^{-1}$)}\\ \colhead{(1)} & \colhead{(2)} & \colhead{(3)} & \colhead{(4)} & \colhead{(5)} & \colhead{(6)} & \colhead{(7)} & \colhead{(8)} & \colhead{(9)} } \startdata $\zeta$~Gem & 183 & 54 & $<$0.35 & $<$0.012 & $<$1.9$\times10^{-5}$ & $<$0.102 & 4.0 & $<2.0\times10^{-6}$\\ RS Pup& 116 & 21 & $<$0.20 & $<$0.112 & $<1.9\times10^{-5}$ & $<$0.258 & 140. & $<2.6\times10^{-7}$\\ X~Cyg & 190 & 58 & $<$0.41 & $<$0.093 & $<$5.6$\times10^{-5}$ & $<$0.288 & 7.2 & $<5.6\times10^{-6}$ \\ T~Mon$^{*}$ &153 & 37 & $<$0.33 & $<$0.156 & $<4.2\times10^{-5}$ & 0.4 & 7.0 & $\sim6\times10^{-6}$\\ \enddata \tablenotetext{*}{For T~Mon, upper limits in columns 4-6 apply to {\em recent or ongoing} mass-loss, not to a period of mass loss associated with the formation of the nebula northeast of the star (see Sections~\ref{TMon} and \ref{TMondisc}).} \tablecomments{Explanation of columns: (1) star name; (2) escape velocity, assuming the stellar mass and radius from Table~1; (3) predicted wind outflow speed based on the relation $V_{\rm o}\approx 1.6\times10^{-3} V_{\rm esc}^{2}$ (Reimers 1977); (4) 3$\sigma$ upper limit on the integrated \HI\ flux density within a single synthesized beam centered on the star, assuming a rectangular line profile with a total linewidth of twice the estimated outflow velocity; (5) 3$\sigma$ upper limit on the \HI\ mass within a single synthesized beam centered on the star, using the integrated flux density from Column~4; (6) 3$\sigma$ upper limit on the current stellar mass-loss rate (see Section~\ref{upperlimits} and Section~\ref{TMondisc} for details); (7) total detected \HI\ mass (for T~Mon) or 3$\sigma$ upper limit on the \HI\ mass within a volume of radius 0.5~pc surrounding the star; (8) estimated time spent on the instability strip based on Bono et al. (2000; see text for details); (9) estimated mass-loss rate (or 3$\sigma$ upper limit), averaged over the lifetime of the star on the instability strip. } \end{deluxetable*} | 16 | 9 | 1609.06611 |
1609 | 1609.07617_arXiv.txt | HD 179070, ${\it aka}$ Kepler-21, is a ${\rm V}$ = 8.25 F6IV star and the brightest exoplanet host discovered by ${\it Kepler}$. An early detailed analysis by \cite{Howell2012} of the first thirteen months (Q0 -- Q5) of ${\it Kepler}$ light curves revealed transits of a planetary companion, Kepler-21b, with a radius of about 1.60 $\pm$ 0.04 ${\rm R_{\oplus}}$ and an orbital period of about 2.7857 days. However, they could not determine the mass of the planet from the initial radial velocity observations with Keck-HIRES, and were only able to impose a 2$\sigma$ upper limit of 10 ${\rm M_{\earth}}$. Here we present results from the analysis of 82 new radial velocity observations of this system obtained with HARPS-N, together with the existing 14 HIRES data points. We detect the Doppler signal of Kepler-21b with a radial velocity semi-amplitude ${\rm K}$ = 2.00 $\pm$ 0.65 ${\rm m~s^{-1}}$, which corresponds to a planetary mass of 5.1 $\pm$ 1.7 $\rm M_{\oplus}$. We also measure an improved radius for the planet of 1.639$^{\rm +0.019}_{\rm -0.015}$ $\rm R_{\oplus}$, in agreement with the radius reported by \cite{Howell2012}. We conclude that Kepler-21b, with a density of 6.4 $\pm$ 2.1 ${\rm g~cm^{-3}}$, belongs to the population of terrestrial planets with iron, magnesium silicate interiors, which have lost the majority of their envelope volatiles via stellar winds or gravitational escape. The radial velocity analysis presented in this paper serves as example of the type of analysis that will be necessary to confirm the masses of TESS small planet candidates. | Results from NASA's ${\it Kepler}$ Mission have revealed an abundance of planets smaller than 2 ${\rm R_{\earth}}$ with orbital periods less than 100 days \citep{Howard2012,Fressin2013,Dressing2013,Petigura2013a,Petigura2013b,ForemanMackey2014,Silburt2015,Dressing2015}. Although only a few of those planets have measured masses, and therefore densities, those measurements have started to unveil an interesting picture. Below a radius of about 1.6 ${\rm R_{\earth}}$ most planets are consistent with bare rocky compositions without any significant volatile envelopes \citep{Rogers2015}. Moreover, when considering only planets with masses measured with precisions better than 20$\%$ via radial velocities, planets with masses smaller than about 6 ${\rm M_{\earth}}$ appear to be rocky and have interiors composed mostly of iron and magnesium silicates in Earth-like abundances \citep[26$\%$ Fe, 74$\%$ ${\rm MgSiO_3}$, on average, based on][]{Zeng2016}, while planets more massive than about 7 ${\rm M_{\earth}}$ show a wider range of densities \citep{Dressing2015b,Gettel2016,Buchhave2016}. Such a dichotomy suggests the possible existence of mechanisms by which planets more massive than approximately 7 ${\rm M_{\earth}}$ in orbits of only a few days can retain significant volatile envelopes, while less massive planets lose all the material in their outer layers to a combination of the effect of stellar winds and atmospheric escape. However, despite the rapid observational progress on the determination of fundamental properties of low mass planets, some basic questions about the origin of this short-period rocky planet population are still not understood. Almost all of the confirmed rocky planets are on highly irradiated orbits, where they are bombarded by large amounts of ionizing EUV and X-ray radiation, which can drive a photo-evaporative wind from the atmosphere of the planet and over a planet's lifetime can remove a significant amount of mass from planets with volatiles envelopes \citep[e.~g.][]{Owen2012}. Several recent studies have shown that Kepler's short-period super-Earths and sub-Neptunes have likely been significantly sculpted by photo-evaporation \citep[e.~g.][]{Lopez2012,Lopez2013,Owen2013}, or else by some other comparable process like atmospheric erosion by impacts \citep[e.~g.][]{Inamdar2015,Schlichting2015}. Thus, while it is possible that the short-period rocky planets simply formed with their current Earth-like compositions, their low masses and highly irradiated orbits mean that they could also be the remnant cores of volatile-rich hot Neptunes which have lost their envelopes. Even considering all these scenarios, it is not clear why a transition between bare cores and planets with significant volatiles would occur at 1.6 $\rm R_{\earth}$. For example, recent precise mass measurements of planets with masses between 3 and 8 ${\rm M_{\earth}}$ and periods out to 17 days, via transit timing variations, reveal a wide range of densities for planets with masses near 5--6 ${\rm M_{\earth}}$, analogous to the situation for more massive planets \citep{JontofHutter2016}. The recently discovered Kepler-20b, with a mass of 9.7 ${\rm M_{\earth}}$, radius 1.9 $\rm R_{\earth}$, and a orbital period of 3.7 days appears to be a bare core \citep{Buchhave2016}. With the current sample of small planets with precise mass measurements it is not possible to establish whether stellar irradiation is the cause of the bare core to volatile rich envelopes transition. It is also not possible to discern whether the transition is abrupt or smooth \citep{Rogers2015}. We therefore need a larger number of precise mass measurements, especially around the apparent 1.6 $\rm R_{\earth}$ transition region. In this paper we report a new mass determination for Kepler-21b, a 5.1 $\pm$ 1.7 ${\rm M_{\earth}}$ super-Earth located near the apparent mass boundary between predominately volatile-poor super Earths and volatile-rich larger planets. Kepler-21b orbits the brightest exoplanet host star discovered by ${\it Kepler}$ (HD 179070, V = 8.25), which is also a slightly evolved F6IV star. An earlier study of this planet by \cite{Howell2012}, based on the first six quarters of ${\it Kepler}$ data (Q0--Q5), found a planet radius of 1.6 $\pm$ 0.04 $\rm R_{\earth}$, but could not determine the planetary mass because of the effect of the stellar variability on the radial velocity (RV) measurements. Our mass measurement comes from new radial velocity data collected with HARPS-N between 2014 and 2015, combined with the HIRES data from \cite{Howell2012} and fitted using Gaussian Processes regressions (GPs). In addition, we compute a new planetary radius from the complete ${\it Kepler}$ Q0-Q17 light curves, detrended from stellar variability using new time series analysis techniques. We describe the light curve and radial velocity analyses in Section 2. In Sections 3 and 4, we describe the light curve and radial velocity fits and their results. Finally, we discuss our findings and summarize our conclusions in Section 5. | We measure a mass for Kepler-21b of 5.1 $\pm$ 1.7 $\rm M_{\oplus}$ and derive a revised radius for the planet of 1.639$^{\rm +0.019}_{\rm -0.015}$ $\rm R_{\oplus}$, in agreement with the previous radius measurement of \cite{Howell2012}. Those parameters combined yield a density for this object of 6.4 $\pm$ 2.1 ${\rm g~cm^{-3}}$, which suggests a rocky composition. Figure~\ref{fig:massradius} shows theoretical mass-radius curves for planets composed of 100$\%$, 50$\%$, and 25$\%$ $\rm H_2O$, as well as rocky planets with 25$\%$, 50$\%$, and 100$\%$ $\rm Fe$ cores and the remaining mass in magnesium silicate mantles \citep{Zeng2016}. The figure also shows all the mass-radius measurements so far for exoplanets with masses less than 20 $M_{\oplus}$ and mass errors smaller than 20$\%$. The location of Kepler-21b in this diagram is consistent with a rocky composition. Kepler-21b fits within the group of 1--6 $\rm M_{\oplus}$ planets reported by \cite{Dressing2015b} as being well-described by the same fixed ratio of iron to magnesium silicate. The recently discovered Kepler-20b, with a mass of 9.7 $M_{\oplus}$ also fits in that group \citep{Buchhave2016}. Kepler-21b has also similar parameters to CoRoT-7b \citep{Barros2014,Haywood2014}. If the interior of Kepler-21b is differentiated, i.e. the $\rm Fe$ in the planet's interior has sunk to the center, while the lighter silicates remain in the mantle, we can use eq.~3 in \cite{Zeng2016} to estimate a core mass fraction (CMF) for this planet of 0.1 $\pm$ 0.3, which is, within the uncertainties, close to the CMF of 0.3 for Earth and Venus in the Solar System. Most of the uncertainty in this CMF estimate comes from the current error in the mass and refining the mass measurement would yield a more accurate CMF estimate. Rocky planets of the same composition and the same mass, one differentiated, one un-differentiated, will have almost identical radius, within 1-2$\%$ \citep{Zeng2013}, so at present we cannot distinguish between these two scenarios given the current uncertainty in the radius of Kepler-21b of 1.2$\%$. With an estimated equilibrium temperature of about 2000 K, the top few-hundred-kilometer-thick layer of Kepler-21b is expected to be molten. However, the silicate (rocky) mantle underneath is expected to be solid due to fact that the adiabat has shallower slope than the melting curve \citep{Zeng2016b,Stixrude2014}. The core of the planet is expected to be fully or partially molten. An interior structure calculation for Kepler-21b using the {\it Manipulate Planet} tool \citep{Zeng2016,Zeng2014,Zeng2013}, gives a central pressure for the planet of around 1200 ${\rm GPa}$. The pressure at the core-mantle boundary is estimated to be 800 ${\rm GPa}$. The density at the planet's center is estimated to be about 17 ${\rm g~cc^{-1}}$, so compared to the zero-pressure density of iron (7-8 ${\rm g~cc^{-1}}$), there appears to be significant compression in the core. The density of silicate at the core-mantle boundary of the planet is estimated to be about 8 ${\rm g~cc^{-1}}$. Kepler-21b orbits the brightest planet host star discovered by the ${\it Kepler}$ mission. The star is a slightly evolved F6IV subgiant, with intrinsic radial velocity variations up to about 10 ${\rm m~s^{-1}}$. With Gaussian Process regression, however, we can reconstruct the intrinsic stellar variability well enough to confidently extract radial velocity signals with amplitudes five times smaller than the stellar noise. The apparent brightness of Kepler-21 is similar to the bright targets to be observed by TESS and many of those targets will most likely have significant intrinsic radial velocity variability. Therefore, this study serves as example of the kind of radial velocity analysis that will be necessary to confirm the masses of TESS planet candidates. In particular, we emphasize the need for radial velocity observations with cadence tailored for each target, based on their stellar rotational period and active-region lifetimes to efficiently model the activity and extract the planetary doppler signal. Given the proximity of Kepler-21b to its host star and with a planetary surface temperature of about 2000K, it is unlikely that the planet has retained a significant amount of envelope volatiles. However, even though the atmosphere of the planet is expected to be tenuous, the brightness of the system may allow detection of atmospheric features in the UV, optical or infrared, either from space, with HST and JWST, or from the ground with upcoming large facilities. \begin{figure}[t] \centering \includegraphics[scale=0.45]{massradiusfinalupdated.pdf} \caption{Mass-Radius relation for planets with masses $<$ 20 $\rm M_{\oplus}$, measured with precisions better than 20$\%$. Circles indicate the planets with masses measured via RVs; triangles indicate planets with masses measured via TTVs \citep{Carter2012,JontofHutter2016}. The plot also includes Earth and Venus, for reference. The lines show models of different compositions, with solid lines indicating {\it single} composition planets (either $\rm H_2O$, $\rm MgSiO_3$, i.e. rock, or $\rm Fe$). The dashed and dotted lines indicate Mg-silicate planets with different amounts of $\rm H_2O$ and $\rm Fe$. The data points representing the planets are color-coded as a function of incident bolometric stellar flux (compared to the Earth) and equilibrium temperature (assuming circular orbit, uniform planetary surface temperature, and bond albedo A=0). For other A values, the temperature can be obtained by multiplying those values by a factor of $\rm (1-A)^{1/4}$, following the flux and temperature scale indicated in the upper-left corner of the diagram.} \label{fig:massradius} \end{figure} | 16 | 9 | 1609.07617 |
1609 | 1609.02204_arXiv.txt | We identify \numtot\ arc-shaped mid-infrared nebula in 24 $\mu$m {\it Spitzer Space Telescope} or 22 $\mu$m {\it Wide Field Infrared Explorer} surveys of the Galactic Plane as probable dusty interstellar bowshocks powered by early-type stars. About 20\% are visible at 8 $\mu$m or shorter mid-infrared wavelengths as well. The vast majority (\numnewhere) have no previous identification in the literature. These extended infrared sources are strongly concentrated near Galactic mid-Plane with an angular scale height of $\sim$0.6\degr. All host a symmetrically placed star implicated as the source of a stellar wind sweeping up interstellar material. These are candidate ``runaway'' stars potentially having high velocities in the reference frame of the local medium. Among the \numPM\ objects with measured proper motions, we find an unambiguous excess having velocity vectors aligned with the infrared morphology --- kinematic evidence that many of these are ``runaway'' stars with large peculiar motions responsible for the bowshock signature. We discuss a population of ``in-situ'' bowshocks ($\sim$\numFH\ objects) that face giant \hii\ regions where the relative motions between the star and ISM may be caused by bulk outflows from an overpressured bubble. We also identify $\sim$\numFB\ objects that face 8 $\mu$m bright-rimmed clouds and apparently constitute a sub-class of in-situ bowshocks where the stellar wind interacts with a photo-evaporative flow from an eroding molecular cloud interface (i.e., ``PEF bowshocks''). Orientations of the arcuate nebulae exhibit a correlation over small angular scales, indicating that external influences such as \HII\ regions are responsible for producing some bowshock nebulae. However, the vast majority of this sample appear to be isolated (\numI\ objects) from obvious external influences. | Stellar bowshock nebulae are arcuate structures created by the interaction between stellar winds and the surrounding interstellar medium (ISM) where the relative velocity between the two is supersonic \citep{vanBuren90, maclow91}. A shock front forms at the interface of the high speed stellar wind and the ambient interstellar medium. The swept up interstellar dust and gas ahead of the high-velocity star forms an arc-like feature preceding the peculiar motion of the star. This material is most clearly visible in the mid-infrared and sometimes in optical emission lines such as H$\alpha$ and \ion{O}{3} \citep{brown05,Meyer14, Meyer16}. Most bowshock nebulae are observed around high-velocity massive stars, but they have also been identified preceding high-velocity pulsars \citep{wang13}, red supergiants \citep{Noriega97}, and associated with proplyds in the Orion Nebula \citep{Bally98}. \citet{Wilkin96} derived an exact analytic solution for this interaction by balancing the ISM pressure and ram pressure of the stellar winds. Based on this model, \citet{comeron98,Meyer14,Meyer16} used computer simulations to demonstrate that stable bowshocks can be formed for a variety of interaction scenarios over a range of relative velocities, ISM densities, and stellar wind momentum fluxes. A significant proportion (10$\pm$25\%) of early-type stars reside outside of stellar clusters \citet{gies86}. Because of their short main-sequence lifetimes these stars, known as runaway stars, must be moving at high peculiar velocities, typically \textgreater30 \kms\ \citep{gies86}. \citet{stone91} found that O and B type stars (OB stars) comprise 50\% of all runaway stars, and these OB runaways are dominated by O type stars (12:1). Two general scenarios that generate runaway stars have been proposed: close dynamical interactions of either single stars \citep{poveda67} or binary-binary interactions \citep{spitzer80}, and ejection from close binary systems when the more evolved member undergoes a core-collapse supernova \citep[CCSN;][]{zwicky57, blaauw61}. \citet{poveda67} analytically simulated the dynamical interactions of small clusters of 5--6 50 \msun\ stars and found that 2--17\% of these stars were ejected from the cluster with velocities in excess of 35 \kms. \citet{kroupa01} concluded that dynamical few-body ejections of OB stars likely occur in the first $\lesssim$1 Myr of the cluster's history before the radiation of the OB stars expels the mass-dominant gas component of the cluster, causing the cluster to expand. \citet{leonard91} simulated binary-binary gravitational interactions and found a maximum ejection velocity of 700 \kms\ for 60 \msun\ stars and 1400 \kms\ for 1--4 \msun\ stars. Though the initial multiplicity fraction of OB stars is unknown, studies have shown that the fraction is likely higher than 60\% in stellar clusters, meaning that at least 75--90\% of massive stars are in a multiple system and have the potential to participate in few-body interactions \citep{garcia01,sana12,kiminki12,kobul14}. \citet{zwicky57} first proposed that stars that form in close binary systems could be ejected when one of the components explodes as a supernova. \citet{zheng15} hydrodynamically simulated the effects of asymmetric CCSN in close binary systems and determined that the less-evolved companion could survive with minimal disruption and be ejected at runaway velocities. \citet{fryer98} used Monte Carlo simulations to determine the necessary impulse to account for the observed velocity distribution of pulsars and found by extension that the necessary forces could accelerate the surviving OB companions to velocities up to 100 km s$^{-1}$. \citet{tauris15} expanded upon this work with new simulations and found that early-type B stars (10 \msun) could be accelerated up to $\sim$320 \kms\ under ideal conditions with increasing maximum velocities for lower mass stars (up to $\sim$1050 \kms\ for a 0.90 \msun\ star). It is likely that both few-body interactions and supernovae in binary systems combine to generate the observed population of runaway stars. Using Hipparcos proper motions \citet{hoogerwerf00} traced the motions of two known runaway stars, AE Aur and $\mu$ Col (O9.5V and O9.5B/B0, moving in opposite directions at 100 \kms) to a common origin $\sim$2.5 million years ago near the location of the binary pair $\iota$ Ori. They proposed that the two runaways may have been ejected in a binary-binary interaction. \citet{Gvaramadze13} identified two O-type runaways that may have been ejected from the star cluster NGC~3603 in a single star-binary interaction when the single star captured one binary member and ejected the other with both systems being accelerated to high peculiar velocities relative to the cluster. The new binary system later merged into the single 'blue straggler' star observed. \citet{hoogerwerf00} used Hipparcos proper motions to trace $\zeta$ Oph and the pulsar J1932+1059 back to the same region of the Upper Scorpius star forming region $\sim$1 Myr ago, which could indicate that the two were once members of a common binary prior to the supernova creating the pulsar. \citet{hoogerwerf01} identified eight additional binary-binary and 16 binary-supernova ejection candidates by extrapolating their proper motions. A fraction of the ejected stars in the \citet{zheng15} simulations accreted material from the CCSN, and these simulations predict that atmospheric chemical enrichments may be observable in the runaway stars if mixing is inefficient. Several runaway stars \citep{blaauw93,Gvaramadze09} have been observed with significant $\alpha$-element enrichment, consistent with this prediction. Hybrids of these ejection scenarios may also be possible. \citet{pflamm10} suggested that a two-step scenario involving a dynamically ejected binary pair could accelerate a single runaway star following a CCSN. Because of the two kicks accelerating the star in this scenario, the star's observed proper motion vector may not point back to a cluster. \citet{wit05} examined a sample of known runaway stars and found that 4$\pm$2\% do not have proper motions that can be extrapolated back to a known cluster or association. Hypervelocity stars (HVSs) are a special class of runaway stars with extremely high space velocities, typically defined as being greater than 400 \kms\ \citep{kenyon08}. \citet{hills88, hills91} first predicted hypervelocity stars when modelling the close interaction of binary star systems with a supermassive black hole (SMBH), which produced stars with velocities in excess of 1000 km s$^{-1}$. \citet{yu03} proposed two additional mechanisms: gravitational interaction between a pair of single stars with a extreme mass ratio or stellar acceleration by a binary SMBH system. However, they predicted that the HVS generation rate by single star interactions is likely low enough to be undetectable due to the extremely small impact parameter required. \citet{brown05} reported the discovery of the first HVS in the Galactic Halo, SDSS J090745.0+024507, a main sequence B star \citep{fuentes06} which remains the fastest observed HVS with a Heliocentric radial velocity of 831.1$\pm$5.7 \kms\ \citep{brown14}. \citet{brown14} assembled the most complete catalog of HVSs with 24 confirmed objects and several additional candidates. Several simulations \citep{brown05,Meyer14, Meyer16} have demonstrated that it is unlikely that HVSs can support visible bowshock nebulae due to their high velocities inhibiting the accumulation of material in the leading shock. Two general classes of bowshock nebulae are generally recognized: those supported by runaway stars, and ``in-situ'' bowshocks supported by a star overrun by an outflow of hot gas from a star-forming or \ion{H}{2} region. \citet{gull79} used optical emission line imaging to catalog the first bowshock nebulae which appeared as ``distorted interstellar bubbles''. These nebulae were observed around the prototypical runaway $\zeta$ Oph and around the star LL Ori situated in an outflow from $\theta^1$ Ori in the Orion Nebula. \citet{Povich08} cataloged six arcuate nebulae around the star-forming regions M~17 and RCW~49 and identified these in-situ shocks as a distinct class. The associated physics of these in-situ shocks are similar to runaway bowshocks when considered within the rest frame of the stellar source. Using 60 $\mu$m images from the Infrared Astronomical Satellite ($IRAS$) \citep{IRAS} \citet{vanBuren88} compiled the first catalog of bowshock nebulae. A more complete sample gathered from $IRAS$ images found a total of 58 bowshock nebula candidates around 188 runaway OB stars \citep{vanBuren95}. Subsequent re-analysis of $IRAS$ all-sky images concluded only 19 of the 58 candidate were bowshock nebulae with 2 additional questionable candidates \citep{Noriega97}. The increased angular resolution of infrared surveys conducted by the Spitzer Space Telescope ($SST$) and Wide-Field Infrared Survey Explorer ($WISE$) \citep{Wright10}, enabled the identification of small collections of bowshock nebulae in both the LMC \citep{Gvaramadze10} and SMC \citep{Gvaramadze11A}, generated by stars ejected from the star-forming regions NGC 6611 \citep{Gvaramadze08}, Cygnus OB2 \citep{kobul10}, NGC 6357 \citep{Gvaramadze11C}, NGC 3603 \citep{Gvaramadze13}, and Carina Nebula \citep{Sexton15}, and powered by high-mass X-ray binaries \citep{Gvaramadze11B}, pulsars \citep{wang13}, red \citep{Noriega97, cox12, Gvaramadze14A} and blue \citep{Gvaramadze14B} supergiants, and the A-type star $\delta$ Vel \citep{gaspar08}. \citet{Peri12, Peri15} conducted the most extensive search to date for bowshock nebulae and runaway stars by examining $WISE$ archival images in the vicinity of several hundred runaway star candidates identified by \citet{tetzlaff10}. The most recent release of their E-BOSS (Extensive Bow Shock Survey) catalog \citep{Peri15} contains a compilation of 73 bowshock nebulae candidates found in their visual search and those previously identified in the literature. Based on their work, it appears that 5--10\% of runaway stars support bowshock nebulae, though some earlier studies have suggested higher rates of $\sim$15\% \citep{vanBuren95} or as high as $\sim$30\% \citep{vanBuren88}. The present paper is the first in a series presenting and analyzing a new catalog of candidate bowshock nebulae. Our group has taken the opposite approach of the E-BOSS survey \citep{Peri12, Peri15} by conducting a comprehensive visual inspection of existing space-based infrared surveys to identify candidate bowshock nebulae and runaway stars along the Galactic mid-Plane. In this paper, we report the identification of 708 candidate bowshock nebulae, 659 of which have not been previously identified in the literature. This catalog constitutes the largest collection of bowshock nebula candidates by an order of magnitude. In \citet{chick16}, we present the results of spectroscopic follow-up of nearly 100 targets, that $>$95\% of these infrared-selected stellar sources are, in fact, early-type massive stars, and that infrared nebular morphology alone is enough to select massive stars with confidence. In Section 2, we discuss the selection process and space-based infrared datasets used for identifying candidate nebulae. Section 3 presents the archival infrared images of our candidates and discusses the demographics of our sample including the sky distribution, proper motions, and their surrounding environments. We summarize our results in Section 4. | We have compiled the largest collection to date of candidate stellar bowshock nebulae selected on the basis of mid-IR morphology at 24 or 22 $\mu$m from \sst\ and $WISE$ sky surveys of the Galactic Plane. The vast majority --- \numnewhere\ of the \numtot\ objects --- are identified here for the first time. A minority of objects ($\sim$19\%) appear at 8 $\mu$m or shorter wavelengths as well, indicating a population of very small hot dust grains within the swept-up nebula, or possibly a PAH contribution. While the infrared images alone do not demonstrate that the tabulated objects are necessarily shocks, the preponderance of ancillary evidence, including proper motions and spectral classifications of the host stars, strongly suggests that this is the best interpretation for the majority of objects. On further investigation, some of the objects may turn out to be other phenomena, such as asymmetric dust shells around evolved stars. The distribution of these objects on the sky is tightly confined to the Galactic mid-Plane, consistent with their production by massive stars which have strong stellar winds. Proper motions of the central stars, where known, indicate a clear excess of objects having velocity vectors aligned with the symmetry axis of the infrared nebula. This is consistent with their production by a population of massive runaway stars. While the majority of the candidate bowshock nebulae and their central stars lie in relatively isolated environments, a substantial subset ($\sim$20\%) either face giant \hii\ regions or face bright-rimmed clouds. These may, respectively, constitute two classes of ``in-situ'' bowshocks where either an external flow overruns the star or ``photoevaporative flow'' bowshocks where a stellar wind interacts with material evaporating from a nearby molecular cloud skin. The correlation of bowshock orientations on angular scales of $\lesssim$10\arcmin\ provides evidence that local environmental phenomena, such as outflows from star forming regions, produce the relative motions between a nearby massive star and the ISM that generate the bowshock nebulae. Table~\ref{bigtable.tab} and the Appendix of \numtot\ stellar bowshock candidates may be used to further investigate the origins of runaway stars, phenomena associated with large-scale outflows of gas from star forming regions, and the physics of massive star winds. Additional scrutiny of existing infrared surveys could be expected to find a few additional bowshock candidates, especially at higher Galactic latitudes not covered by our search. However, we expect the yield to be small as the areal density of bowshocks within the \sst\ Plane surveys drops rapidly with latitude. In a forthcoming series of papers we will present an analysis of the characteristics of this comprehensive bowshocks sample, including their spectral types, binarity, distances, spectral energy distributions, and local environments. | 16 | 9 | 1609.02204 |
1609 | 1609.05612_arXiv.txt | \begin{description} \item[Background] The synthesis of heavy, proton rich isotopes in the astrophysical $\gamma$ process proceeds through photodisintegration reactions. For the improved understanding of the process, the rates of the involved nuclear reactions must be known. The reaction $^{128}$Ba($\gamma$,$\alpha$)$^{124}$Xe was found to affect the abundance of the $p$ nucleus $^{124}$Xe in previous rate variation studies. \item[Purpose] Since the stellar rate for this reaction cannot be determined by a measurement directly, the aim of the present work was to measure the cross section of the inverse $^{124}$Xe($\alpha$,$\gamma$)$^{128}$Ba reaction and to compare the results with statistical model predictions used in astrophysical networks. Modified nuclear input can then be used to provide an improved stellar reaction rate. Of great importance is the fact that data below the \ran\ threshold was obtained. Studying simultaneously the $^{124}$Xe($\alpha$,n)$^{127}$Ba reaction channel at higher energy allowed to further identify the source of a discrepancy between data and prediction. \item[Method] The $^{124}$Xe($\alpha$,$\gamma$)$^{128}$Ba and $^{124}$Xe($\alpha$,n)$^{127}$Ba cross sections were measured with the activation method using a thin window $^{124}$Xe gas cell and an $\alpha$ beam from a cyclotron accelerator. The studied energy range was between E$_\alpha$\,=\,11 and 15 MeV close above the astrophysically relevant energy range. \item[Results] The obtained cross sections are compared with Hauser-Feshbach statistical model calculations. The experimental cross sections are smaller than standard predictions previously used in astrophysical calculations. As dominating source of the difference, the theoretical $\alpha$ width was identified. The experimental data suggest an $\alpha$ width lower by at least a factor of 0.125 in the astrophysically important energy range. \item[Conclusions] An upper limit for the $^{128}$Ba($\gamma$,$\alpha$)$^{124}$Xe stellar rate was inferred from our measurement. The impact of this rate and lower rates was studied in two different models for core-collapse supernova explosions of 25 $M_\odot$ stars. A significant contribution to the $^{124}$Xe abundance via this reaction path would only be possible when the rate was increased above the previous standard value. Since the experimental data rule this out, they also demonstrate the closure of this production path. \end{description} | \label{sec:intro} The chemical elements in the upper half of the periodic table represent only a tiny fraction of matter building up our universe. The reason for the rarity of these heavy elements is that they are produced in stars in subsidiary processes, not in the ones powering the star. It has been shown that these processes involve neutron-induced reactions that build the heavy elements from the Iron group up to Uranium. Two distinct processes, characterized by neutron density and duration, have been identified: the slow and the rapid neutron-capture process, also called $s$- and $r$ process, respectively \cite{ctt,thi11,kap11,arn07}. Some of the most neutron deficient isotopes of the heavy elements, moreover, are even less abundant than the more neutron-rich ones. These stable isotopes on the proton rich side of the valley of stability between $^{74}$Se and $^{196}$Hg are the so-called $p$ isotopes. They are not produced in any of the neutron capture processes and their isotopic abundances are typically only 0.1\,--\,1\,\% of that of their more neutron-rich neighbours. Owing to their rareness and the fact that no heavy element has a dominant $p$ isotope, their existence is identified so far only in the Solar System. We have no information on their abundance in other stars. Regardless of their rarity, the existence of $p$ isotopes requires an explanation of their production processes and sites. To date, there is no unique and generally accepted process which could explain the abundances of \textit{all} $p$ nuclei. Several possible astrophysical production sites are suggested and also contributions from several mechanisms are considered. For reviews, see \cite{arn03,rau13} and references therein. Perhaps the most important process which contributes to the synthesis of $p$ isotopes is the so-called $\gamma$ process which converts heavy, neutron-rich species into $p$ isotopes through photodisintegration reactions \cite{rau13}. In the reaction network of a $\gamma$-process model the \rgn\ reactions, which drive the material toward the proton rich side, play the key role. On the proton rich side, \rgp\ and \rga\ reactions start to compete with the \rgn\ reactions and influence the resulting abundances of $p$ isotopes or their $\beta$-decay progenitors. Although recent years have seen significant progress in modeling the $\gamma$ process in massive stars \cite{rau13,rayet95,rau02,haya08}, no good reproduction of abundances across the measured range has been achieved by the models, yet. Especially severe differences can be found between calculated and observed abundances in certain mass regions, like around the Mo-Ru isotopes or at mass numbers around 150. The failure of the models can in part be attributed to the nuclear physics input, especially in the region $A\approx 150$. For the light $p$ nuclides, thermonuclear supernovae with enhanced $s$-process seeds in binary systems have been suggested as a promising alternative \cite{howmey,kusa11,tra11,tra15}. Lacking experimental data in the relevant mass and energy range, the rates of reactions are taken from theoretical calculations based on the Hauser-Feshbach statistical model. An experimental check of the theoretical cross sections is therefore important to examine one possible reason of the deficiencies. This need triggered huge experimental work in the last decade on studying reactions relevant for the $\gamma$ process (see the references in the review paper \cite{rau13} and some of the most recent studies \cite{har13,net13,qui13,sim13,spy13,net14,kis14,gyu14,gyu14b,yal15,gur15,kis15,net15,sim15,qui15,net15b,naq15,har16}). Owing to the size of a $\gamma$-process network which involves thousands of reactions, it is difficult to identify a key reaction which should be the target of experimental investigations. Sensitivity studies, however, have been carried out to point out those reactions to which $\gamma$-process models are especially sensitive, i.e., the $\gamma$-process flow and therefore the resulting abundance of certain $p$ isotopes depend strongly on the rate of these reactions. The two, currently available sensitivity studies \cite{rau06,rap06} come up with lists of key reactions largely different from each other. This is due to the different approaches adopted. While the study by \cite{rap06} collectively varied groups of reactions to find their impact on final $p$ abundances, the paper by \cite{rau06} identified nuclides where predicted \rgn\, \rgp\, and/or \rga\ rates are close and thus a change in either rate would affect deflections of the $\gamma$-process path. There are only few reactions which are identified as being important in both studies, the $^{128}$Ba($\gamma$,$\alpha$)$^{124}$Xe reaction being among them. Earlier experiments have shown that in the case of \rag\ reactions the discrepancy between experimental and calculated cross sections (used to obtain reaction rates) can easily be as much as a factor of three, or even an order of magnitude. Therefore, the experimental study of the identified key reaction is of high importance. Instead of directly studying photodisintegration reactions, a cross section measurement of the reverse reaction, i.e., particle capture, is usually preferred. Technically, it is much easier to measure a charged particle capture cross section than a $\gamma$ induced one. Moreover, the effect of the thermally populated excited states of nuclei in the hot stellar plasma is much more pronounced in the case of $\gamma$-induced reactions than for captures \cite{rau13,rau12,rau13supp,rauadv}. Thus, a measurement in the direction of the capture reaction provides more relevant astrophysical information compared to the study of the $\gamma$-induced reaction itself. The aim of the present work is therefore the measurement of the \xeag\ cross section. Nevertheless, reactions on nuclei in excited states are particularly important at the high plasma temperatures encountered in the $\gamma$ process also for captures. Therefore, a measurement of laboratory ground-state (g.s.) cross sections cannot fully constrain the stellar reaction rate but a comparison to the calculated g.s.\ cross sections allows to perform an important test of the prediction. This paper is organized as follows. Section \ref{sec:invesreac} provides some further details about the investigated reactions. The experimental technique is described in Sec.\ \ref{sec:exp}. The results are presented and discussed in Sec.\ \ref{sec:results} while conclusions and a summary are given in Sec.\ \ref{sec:conclusions}. | \label{sec:conclusions} The reaction cross sections of \xeag\ and \xean\ were measured close to the \ran\ threshold using the activation method. It was found that the experimental cross sections for both reactions are smaller than the ones predicted by the reaction model which has been used in previous $\gamma$-process studies. This is in line with the findings of previous \rag\ and \ran\ experiments on other $p$ nuclei, which also showed smaller cross sections than predicted (see \cite{net13, kis14, yal15} and references in \cite{ERCRep}). Although the covered energy range is slightly above the astrophysically relevant energies, it is possible to evaluate the astrophysical impact of the measurement. The \rag\ cross section below the threshold can be taken as an upper limit for the calculation of the astrophysically relevant $^{128}$Ba\rga\ reaction rate. Since the new rate is already below the $^{128}$Ba\rgn\ rate, it was possible to show that this reaction path cannot contribute significantly to the synthesis of the $p$ nucleus $^{124}$Xe. A further reduction of the $^{128}$Ba\rga\ rate does not change this conclusion. It can be affected, however, by modified $^{128}$Ba\rgn\ and $^{128}$Ba\rgp\ rates. The values of these rates used in current astrophysical simulations are still based on theoretical predictions by \cite{adndt00,SMARAGD}. An experimental investigation of the respective \rng\ and \rpg\ cross sections close to the astrophysically relevant energy window would be desirable. Unfortunately, this proves to be very difficult because both $^{127}$Ba and $^{127}$Cs are unstable and any measurements will have to await further technical development. | 16 | 9 | 1609.05612 |
1609 | 1609.02518_arXiv.txt | {} {Our aim is to characterize the conditions in the closest interstellar cloud.} {We analyze interstellar absorption features in the full UV spectrum of the nearby (d = 24 pc) B8 IVn star alpha Leo (Regulus) obtained at high resolution and high S/N by the HST ASTRAL Treasury program. We derive column densities for many key atomic species and interpret their partial ionizations. } { The gas in front of alpha Leo exhibits two absorption components, one of which coincides in velocity with the local interstellar cloud (LIC) that surrounds the Sun. The second, smaller, component is shifted by +5.6 km/s relative to the main component, in agreement with results for other lines of sight in this region of the sky. The excitation of the C II fine-structure levels and the ratio of Mg I to Mg II reveal a temperature T = 6500 (+750,-600)K and electron density n(e) = 0.11 (+0.025,-0.03)\cmc. Our investigation of the ionization balance of all the available species indicates that about 1/3 of the hydrogen atoms are ionized and that metals are significantly depleted onto grains. We infer that N(H I) = 1.9 (+0.9,-0.6)\,10$^{18}$\cmc, which indicates that this partly neutral gas occupies only 2 to 8 pc (about 13\%) of the space toward the star, with the remaining volume presumably being filled with a hot gas that emits soft X-rays. We do not detect any absorption features from the highly ionized species that could be produced in an interface between the warm medium and the surrounding hot gas. Finally, the radial velocity of the LIC agrees with that of the Local Leo Cold Cloud, indicating that they may be physically related. } {} | \subsection{General motivation} Beginning with findings from the {\it Copernicus\/} satellite \citep{Spitzer.Jenkins1975}, studies of ultraviolet absorption features appearing in the spectra of hot, rapidly rotating stars have yielded fundamental insights on the compositions and physical characters of different phases of the interstellar medium \citep{Savage.Sembach1996}, along with the processes that influence them. With the exception of white dwarf stars and stars with spectral types A and cooler, nearly all of the targets are so distant that their sight lines traverse regions with characteristics that are substantially different from one another. As a consequence, the interstellar absorption features usually reveal a heterogeneous mix of the imprints of many different regions, which can only be separated by chance offsets in radial velocities. Nearby stars offer an opportunity to explore a less cluttered situation, but they have the drawback that they represent only one or a few regions with very similar properties. Even so, recent investigations of nearby environment have been very useful in revealing its dynamics \citep{Redfield.Linsky2008,Gry.Jenkins2014}, gas-phase composition \citep{Lehner2003,Redfield.Linsky2004a}, ionization state \citep{Jenkins2000}, temperature, and turbulent velocities \citep{Redfield.Linsky2004b}. In addition, \cite{Oegerle2005}, \cite{Savage.Lehner2006}, and \cite{Barstow2010} have found evidence for the presence of a very hot medium in some nearby locations. A review of many findings on the local medium has been presented by \cite{Frisch.Redfield.Slavin2011}. The earlier UV studies of the local environment had to contend with some difficulties. White dwarf stars were once thought to have featureless spectra that could cleanly show interstellar lines, but subsequent investigations have revealed unexpectedly high metal abundances in the atmospheres of these narrow-line stars caused by radiative levitation \citep{Barstow2003} and pollution by the infall of circumstellar matter \citep{Rafikov.Garmilla2012,Barstow2014}. These atmospheric metal-line features, along with ones arising from circumstellar matter, can create serious confusion when attempting to discern interstellar features \citep{Lallement2011}, but in a small percentage of cases the interstellar absorptions can be separated from the photospheric or circumstellar contributions \citep{Barstow2010}. For cool stars, a different problem emerges. Here, interstellar absorption features must be viewed on top of chromospheric emission features, a problem which forces one to have a good understanding of the shapes of the underlying emission profiles. O and B type stars whose stellar features are broadened by rotation represent ideal targets for interstellar absorption line studies. This paper focuses on the UV spectrum of one such star, \aleo\ (Regulus), a bright (V~=~1.40) B8\,IVn star that was recently observed in a 230-orbit HST Cycle 21 Treasury Program (program ID = 13346, T.~R.~Ayres, PI) called the Advanced Spectral Library II: Hot Stars (ASTRAL). This observing program produced atlases of high resolution, complete UV spectra of 21 diverse early-type stars. Our target $\alpha$~Leo at a distance of 24\,pc is the nearest B-type main sequence or giant star in the sky. Its strong brightness in the ultraviolet and its high projected rotational velocity ($v\sin i=353\,\kms$) make it an ideal target for investigating the local medium. As we discuss in later sections of this paper, the spectrum of this star reveals important details on the density and degree of ionization of hydrogen atoms, the gas-phase abundances of certain elements, the temperature of the gas, along with the filling factor along the sight line for constituents that we can detect. Finally, at the Galactic coordinates $\ell=226.4\degree$, $b=+48.9\degree$, \aleo\ samples a portion of the sky that has not been well sampled at close distances \citep{Gry.Jenkins2014,Malamut2014}. \subsection{Our local environment} In broadest terms, the Sun is located in a specially rarefied region of the Galaxy. It is situated in a small, diffuse ($n_\mathrm{H~I} = 0.05-0.3$ cm$^{-3}$), warm medium, which itself is embedded in an irregularly shaped cavity of about 100~pc radius \citep{Welsh2010,Lallement2014}. This cavity is called the Local Bubble. It is almost devoid of neutral gas and is probably filled mostly with a hot ($T\sim 10^6$ to $10^7$\,K) tenuous, collisionally ionized gas that emits soft X-rays \citep{Williamson1974,McCammon.Sanders1990,Snowden1997,Snowden2014}. It is generally recognized that the Local Interstellar Cloud (LIC) that surrounds our heliospheric environment is partly ionized to a level $n_e/n_{\rm H} \sim 0.5$ by the ambient EUV and X-ray radiation field that arises from stars \citep{Vallerga1998} and the surrounding hot gas \citep{Slavin.Frisch2008}. In accord with previous findings by \cite{Redfield.Linsky2004b}, we will show that the temperature of the gas is $T\sim 7000\,$K, which is one of the stable phases that arises from the bifurcation due to the Field (1965) thermal instability \citep{Wolfire2003}. The magnetic field at distances greater than 1000\,AU from the Sun has a strength of about $3\mu$G and is directed toward $\ell=26.1\degree$, $b=49.5\degree$, according to an interpretation of results from the {\it Interstellar Boundary Explorer\/} (IBEX) by \cite{Zirnstein2016}. The magnetic direction thus makes an angle of about 79 \degree\ with respect to the direction toward \aleo. The distance to the boundary between the LIC and the surrounding hot medium is not well determined, but it is probably of order 10\,pc \citep{Frisch.Redfield.Slavin2011,Gry.Jenkins2014}. It is therefore very likely that the sight line to \aleo\ penetrates this boundary. In principle, UV spectroscopic data should help us to understand the nature of this boundary: is it a conduction front where evaporation or condensation of warm gas is occurring \citep{Cowie.McKee1977,McKee.Cowie1977,Ballet1986,Slavin1989,Borkowski1990,Dalton.Balbus1993}? Alternatively, could it be a turbulent mixing layer (TML), where, as the name implies, the existence of any shear in velocity between the phases creates instabilities and mechanically induced chaotic interactions \citep{Begelman.Fabian1990,Slavin1993,Kwak.Shelton2010}? Observers have attempted to identify these processes chiefly by analyzing interstellar absorption features of ions that are most abundant at intermediate temperatures, such as Si~IV, C~IV, N~V and O~VI, and then comparing their column density ratios with the theoretical predictions \citep{Spitzer1996,Sembach1997,Zsargo2003,Indebetouw.Shull2004a,Indebetouw.Shull2004b,Lehner2011,Wakker2012}. Such studies have been conducted over very long sight lines, where multiple interfaces may be found. Also, the signatures from interfaces possibly could be mixed with contributions from radiatively cooling gases. Papers that report these results give us information on the relative importance of different cases, but they tell us nothing about what happens within any single interface. Inside the Local Bubble, there are a few isolated, dense clouds \citep{Magnani1985,Begum2010}. One such cloud attracted the attention of \cite{Verschuur1969} and was studied further by \cite{Verschuur.Knapp1971} because it had an unusually low 21-cm spin temperature and a low velocity dispersion. This cloud covering 22~$\deg^2$ in the Leo constellation and later estimated to be at a distance between 11 and 40 pc away from us was investigated using optical absorption features by \cite{Meyer2006} and in further detail by \cite{Peek2011}, who named the cloud the Local Leo Cold Cloud (LLCC). The upper limit to its distance of 40 pc was established by \citep{Meyer2006}, who detected narrow Na I features toward two stars beyond the LLCC located at distances slightly over 40 pc. From HST STIS spectroscopy of stars behind this cloud, \cite{Meyer2012} analyzed the excitation of the fine-structure levels of C~I and came to the remarkable conclusion that this cloud had an internal thermal pressure $p/k \approx 60,000\,{\rm cm}^{- 3}\,$ K, which is considerably higher than estimates of $p/k \leq 10,000\,{\rm cm}^{-3}\,$K for the low density material inside the Local Bubble \citep{Jenkins2002,Jenkins2009,Frisch.Redfield.Slavin2011,Snowden2014}. From its extraordinarily high thermal pressure and low 21-cm spin temperatures [13 to 22 K \citep{Heiles.Troland2003}], this cloud presents an anomaly in the very diffuse context of the Local Bubble. Another interesting feature of this cloud is that it appears to coincide with a long string of other dense clouds that stretches across 80\degree\ in the sky \citep{Haud2010}. Our target \aleo\ is separated in projection by only about 4\degree\ from the LLCC. In fact, \cite{Peek2011} claimed that the very weak Ca II absorption feature in the spectrum of \aleo\ arises from the outermost portions of the LLCC, and therefore proposed that the LLCC distance upper limit be determined by the distance to the star \aleo. However we argue later that this component is likely to be produced by the local interstellar cloud surrounding the Sun. | } { We have analyzed the ultraviolet absorption spectrum of the nearby star \aleo\ to characterize the interstellar medium in its line of sight, and in particular the warm diffuse interstellar cloud surrounding the Sun. \\ - The strongest of the two velocity components coincides with the predictions for the local interstellar cloud (LIC) detected in all directions around the Sun, according to the picture proposed by Gry.Jenkins (2014). The second, smaller, component exhibits a velocity shift of +5.4\,\kms\ relative to the main component, in agreement with shifts observed in other lines of sight in this region of the sky. \\ - By performing profile fitting on the spectra, we derive column density intervals or upper limits for 18 atoms or ions (Table~\ref{tab:results}). The LIC contains about 75 \% of the total matter in the line of sight and the distribution between both components does not vary significantly from element to element. \\ - The temperature $T$ and the electron density $n(e)$ are derived by combining the measurements of the fine-structure level excitation of C~II and the ionization equilibrium of Mg~I and Mg~II. \\ - After estimating the local interstellar radiation field in the UV, extreme UV, and X-ray domains (Fig.~\ref{fig:ISRF}) and considering all possible ionizing and recombination processes, we study the ionization balance of all elements and create a model that describes consistently the partial ionization of the gas. Two free parameters in this model are (1) the amount of shielding of this radiation by neutral hydrogen and helium and (2) the volume density of hydrogen. \\ - The total (neutral plus ionized) amount of hydrogen $N({\rm H_{tot}})$ is derived from the sum of the \NI\ and \NII\ column densities. \\ - The densities of neutral and ionized hydrogen, and hence $N({\rm H~I})$, result from our model for the photoionization of hydrogen and our knowledge of $n(e)$. \\ - The ionization fractions of all elements follow from our model (Table~\ref{tbl:ion_fractions}), and their comparisons with the observations provide a measure of the depletion of metals in the gas phase. \\ -Table~\ref{tab:LIC} summarizes the characteristics derived from this analysis for the warm interstellar matter in the \aleo\ sight line. \begin{table}[h] \caption{Characteristics of the warm interstellar gas in the line of sight of \aleo\ \label{tab:LIC}} \begin{tabular}{ll} \hline $N({\rm H_{tot}})$ (\cms) & 2.83\,$^{+1.18}_{-0.69}\,10^{18}$\\[4pt] $N$(\HI) (\cms) & 1.9\,$^{+0.9}_{-0.6}$\,10$^{18}$\\[4pt] $n({\rm H_{tot}})$ (cm$^{-3}$) & $0.30\,^{+0.10}_{-0.13}$\\[4pt] $n$(\HI) (cm$^{-3}$)& $0.20\,^{+0.08}_{-0.10}$ \\[4pt] $n(e)$ (cm$^{-3}$)& 0.11\,$^{+0.025}_{-0.03}$\\[4pt] $T$ (K) & 6500\,$^{+750}_{-600}$\\[4pt] Pressure log$(p/k)$ & 3.42\,$^{+0.12}_{-0.22}$\\[4pt] Path length (pc)& 3\,$^{+5}_{-1}$\\[4pt] ioniz. fraction $\chi$ & 0.33\,$^{+0.09}_{-0.06}$\\[4pt] depletion strength$^a$ $F_*$ & 0.6\\ \hline $^a$ {\footnotesize in the sense defined by Jenkins (2009)} \end{tabular} \end{table} With the exception of the temperatures and the electron densities that we derived for each of the velocity components, the analysis has been done for the combination of the two components. Nevertheless since we have shown that the conditions in both components are likely to be identical, the densities and the ionization ratios found for them are likely to apply to just the LIC alone. \\ - From the neutral hydrogen column and volume densities we derive a filling factor of only 13\% for the warm gas, the remaining space is probably filled with hot, soft-X-ray emitting gas, in agreement with measurements of the diffuse soft X-ray background radiation. \\ - We do not detect any absorption features in the highly ionized species that could be produced in the interfaces between the warm clouds and the surrounding hot gas, possibly because of the reduction of thermal conduction due to the alignment of the magnetic field with the surface of the conduction front. On the other hand, an extra component of hot neutral hydrogen, required to fit the Lyman $\alpha$ absorption feature, may turn out to be the best interface signature. \\ - This sight-line is particularly interesting because it is close to a nearby cold cloud called the Local Leo Cold Cloud (LLCC) discovered by \cite{Meyer2006}. We show that the Ca~II absorption that had been invoked to set a new upper limit of 24 pc for the distance of LLCC is actually fully consistent with just the LIC absorption. Therefore, the LLCC upper limit remains 42 pc and this reconciles the LLCC distance with the estimated path length of the measured X-ray emission from the foreground hot gas in the Local Bubble, which places the LLCC at a distance of 33.5 $\pm 11.3 \, pc$. \\ - We note the remarkable velocity coincidence between the LIC and the LLCC. We also note that in the hypothesis that the LIC has a patchy structure, with diffuse warm gas alternating with hot gas along the line of sight, the LIC could reach as far as the distance of the LLCC and the two clouds may be physically related. | 16 | 9 | 1609.02518 |
1609 | 1609.02497_arXiv.txt | { Extragalactic radio sources have been classified into two classes, Fanaroff-Riley I and II, which differ in morphology and radio power. Strongly emitting sources belong to the edge-brightened FR~II class, and weakly emitting sources to the edge-darkened FR~I class. The origin of this dichotomy is not yet fully understood. Numerical simulations are successful in generating FR~II morphologies, but they fail to reproduce the diffuse structure of FR~Is. }{ By means of hydro-dynamical 3D simulations of supersonic jets, we investigatehow the displayed morphologies depend on the jet parameters. Bow shocks and Mach disks at the jet head, which are probably responsible for the hot spots in the FR~II sources, disappear for a jet kinetic power ${\cal L}_{\mathrm kin} \lesssim 10^{43}$ erg s$^{-1}$. This threshold compares favorably with the luminosity at which the FR~I/FR~II transition is observed. }{ The problem is addressed by numerical means carrying out 3D HD simulations of supersonic jets that propagate in a non-homogeneous medium with the ambient temperature that increases with distance from the jet origin, which maintains constant pressure. }{ The jet energy in the lower power sources, instead of being deposited at the terminal shock, is gradually dissipated by the turbulence. The jets spread out while propagating, and they smoothly decelerate while mixing with the ambient medium and produce the plumes characteristic of FR~I objects. }{ Three-dimensionality is an essential ingredient to explore the FR~I evolution because { the properties of turbulence in two and three dimensions are very different, since there is no energy cascade to small scales in two dimensions, and two-dimensional simulations with the same parameters lead to FRII-like behavior}. } | Extragalactic radio sources have been classified into two categories \citep{FR74} based upon their radio morphology: a first class of objects, named Fanaroff-Riley I (FR~I), which is preferentially found in rich clusters and hosted by weak-lined galaxies, shows jet-dominated emission and two-sided jets at the kiloparsec scale that smoothly extend into the intracluster medium, where they form large-scale plumes or tails of diffuse radio emission. The second class, named Fanaroff-Riley II (FR~II, or classical doubles), found in poorer environments and hosted by strong emission-line galaxies, presents lobe-dominated emission and one-sided jets at the kpc scale that abruptly terminate into hot-spots of emission. In addition to morphology, FR~I and FR~II radio sources have been distinguished based on power: objects below $\sim 10^{25} h_ {70}^2$ W Hz$^{-1}$ str$^{-1}$ at 178 MHz were typically found to be FR~I sources. A perhaps more illuminating criterion was found by \citet{Ledl96}, who plotted the radio luminosity at $1.4$ GHz against the optical absolute magnitude of the host galaxy: they found the bordering line of FR~I to FR~II regions to correlate as $L_R \propto L_{opt}^{1.7} $, that is, in a luminous galaxy more radio power is required to form a FR~II radio source. This correlation is important since it can be interpreted as an indication that the environment may play a crucial role in determining the source structure. Furthermore, a class of hybrid sources has been discovered that shows FR~I structure on one side of the radio source and FR~II morphology on the other \citep{gopal00}. These arguments describe the basic question of the origin of the FR~I and FR~II dichotomy, whether the shapes are intrinsic or moulded by the environment \citep{gopal00, wold07, kawa09, Mass03}. Recent studies based on the cross correlation of wide-area optical and radio surveys \citep{best12} unveiled yet another class of compact radio-galaxies representing the majority of the local radio-loud AGN population. Because they lack the prominent extended radio structures characteristic of the other FR classes, they were dubbed FR~0 \citep{baldi09, baldi10b, sadler14, baldi15}. Nonetheless, FR~0s often show radio jets, but they extend only a few kpc at most \citep{baldi15}. This suggests that in most radio-loud AGN, the jets fail to propagate to (or become too faint to be detected at) radii exceeding the size of their host. The distorted, diffuse, and plume-like morphologies of FR~I sources led researchers to model them as turbulent flows \citep{Bicknell84, Bicknell86, Komissarov90a, Komissarov90b, DeYoung93}, while the characteristics of FR~II, such as their linear structure and the hot-spots at the jet termination, are associated with hypersonic flows. The difference in morphology between the two classes therefore reflects a difference in how the jet energy is dissipated during jet propagation: in the first case, the jet gradually dissipates its energy and is characterized by entrainment of the ambient material, while in the second case, the jet retains its velocity and dumps all its energy at its termination, forming the observed hot-spots. While the dynamics of jets with high Mach number has been widely studied by means of numerical simulations in 2D and 3D by, for example, \citet{MBF96}, \citet{zanni03}, \citet{hard13}, \citet{hard14}, 3D simulations of transonic jets have been carried out following the evolution of instabilities to turbulence \citep{bass95, hardee95, loken97, bodo98}, and simulations of turbulent jets that include the jet head propagation are { limited to \citet{Nawaz14, Nawaz16}, who investigated the properties of the jet in Hydra A. With this paper, we therefore intend to start a systematic study of these flows}. We perform three-dimensional simulations of the propagation of jets with low Mach number in a stratified medium, which is meant to model the interstellar-intracluster transition. In this first paper we perform hydrodynamic simulations and neglect the effects of the magnetic field. An important point to consider is that both FR~I and FR~II radio sources show evidence of relativistic flows at the parsec scale, and therefore a deceleration to sub-relativistic velocities must occur in FR~Is between the inner region and the {kiloparsec} scale \citep{gg94, gg01, laing14}. Several models have been proposed for the deceleration mechanism \citep{Bicknell94, Bicknell95, Komissarov94, Bowman96, DeYoung05} and numerical simulations of these processes have been performed \citep{Perucho07, rossi08, Tchekhovskoy16}. In this paper, however, we assume that the deceleration has already taken place, and we consider a scale where the jet is non-relativistic. Moreover, we stress that to study the transition to turbulence and the turbulent structure of these flows, it is essential to perform the simulations in three dimensions. The behavior of 2D jets with the same physical parameters is completely different from their 3D counterparts. The plan of the paper is the following: in Sect. \ref{sec:theory} we describe the numerical setup and show the equations we solve, Sect. \ref{sec:obs} outlines the observational framework and constrains the physical parameters, and in Sect. \ref{sec:results} we present and discuss the obtained results. The conclusions are drawn in Sect. \ref{sec:conclusions}. | \label{sec:conclusions} We have performed three-dimensional numerical simulations of turbulent jets, which generate morphologies typical of FR~I radio sources. The jet propagates in a stratified medium that is meant to model the interstellar intracluster transition. FR~I radiosources are known to be relativistic at the parsec scale, therefore a deceleration to sub-relativistic velocities must occur between this scale and the kiloparsec scale. In this paper we did not model the deceleration process, but we assumed that deceleration already occurred and considered scales where the jet is sub-relativistic. { We did not consider buoyancy effects, by not taking into account the galaxy gravitational potential, but they are expected to be negligible up to the distances reached by the jet head in our simulations (of about ten kpc), while they may become more relevant at lager distances, as the head further slows down.} In this first analysis we also neglected the effect of the magnetic field. The parameters governing the jet evolution are therefore the Mach number $M$ and the initial jet-to-ambient density ratio $\eta$, which, by constraining the values of the external density and temperature through observational data, can be combined to give the jet kinetic power. The estimated jet kinetic power of the transition between FR~I and FR~II is $10^{43}$ erg s$^{-1}$ , and we investigated a series of cases below this threshold. These low-power cases have $M = 4$ and different values of density ratio, and they all give rise to turbulent structures typical of FR~I sources. The jet power, instead of being completely deposited at the termination through a series of terminal shocks, as in FR~II sources, is gradually dissipated by the turbulence. We showed that three-dimensionality is an essential ingredient for the occurrence of the transition to turbulence. Two-dimensional simulations with the same parameters lead to FR~II like behavior with energy dissipation concentrated at the jet termination. Increasing the Mach number to $40$ and consequently the kinetic power well above the FR~I - FR~II threshold, we obviously recover well-collimated jets that dump all their energy at the termination shocks. At intermediate Mach numbers ($M=10$), with a kinetic power around the transition value, we find characteristics typical of FR~II sources, even though the energy deposition at the jet termination starts to become more gradual and the morphology acquires some of the FR~I properties. The simulations presented show that in FR~Is the jet energy is transferred to the ISM in part inducing, through entrainment, a global low-velocity outflow; the remaining power is instead dissipated through acoustic waves. The energy released by active nuclei is thought to play a fundamental role in the evolution of their host galaxies \citep{fabian12}; in particular, in radio-loud AGN, the kinetic energy carried by their jets is transferred to the surrounding medium, which leads to the so-called radio-mode feedback. The FR~I jets, although of lower power with respect to those of FR~IIs, are extremely important from the point of view of feedback. This is because the FR~I jets remain confined within the central regions of the host over longer timescales (and possibly for their whole lifetime) which exceeds 10$^7$ years for our reference case B. Furthermore, the entire host is affected by the radio-mode feedback, while in more powerful radiosources a smaller volume (immediately surrounding the jets) is involved. Finally, as a result of the steep radio luminosity function (e.g. \citealt{mauch07}), the less powerful FR~I radio sources are much more common than the FR~II, and they are then (potentially) able to affect the general evolution of massive elliptical galaxies. Clearly, further simulations are required to quantitatively assess the effects of feedback in FR~Is. | 16 | 9 | 1609.02497 |
1609 | 1609.09099_arXiv.txt | The frequency of Galactic stellar encounters the Solar system experienced depends on the local density and velocity dispersion along the orbit of the Sun in the Milky Way galaxy. We aim at determining the effect of the radial migration of the solar orbit on the rate of stellar encounters. As a first step we integrate the orbit of the Sun backwards in time in an analytical potential of the Milky Way. We use the present-day phase-space coordinates of the Sun, according to the measured uncertainties. The resulting orbits are inserted in an N-body simulation of the Galaxy, where the stellar velocity dispersion is calculated at each position along the orbit of the Sun. We compute the rate of Galactic stellar encounters by employing three different solar orbits \,---\,migrating from the inner disk, without any substantial migration, and migrating from the outer disk. We find that the rate for encounters within $4\times10^5$\,AU from the Sun is about 21, 39 and 63\,Myr$^{-1}$, respectively. The stronger encounters establish the outer limit of the so-called parking zone, which is the region in the plane of the orbital eccentricities and semi-major axes where the planetesimals of the Solar system have been perturbed only by interactions with stars belonging to the Sun's birth cluster. We estimate the outer edge of the parking zone at semi-major axes of 250--1300\,AU (the outward and inward migrating orbits reaching the smallest and largest values, respectively), which is one order of magnitude smaller than the determination made by \cite{portegies15}. We further discuss the effect of stellar encounters on the stability of the hypothetical Planet~9. | \label{Sect:introd3} To explain the constant rate of observed new long period comets, \citet{oort} suggested that more than $10^{11}$ icy bodies orbit the Sun with aphelia of $5$--$15\times10^4$~AU, and isotropically distributed inclinations of their orbital planes. The comets are delivered to the inner Solar system from the cloud due to perturbation by the Galactic tide and passing stars (see for example \citealp{rickman14} or \citealp{2015SSRv..197..191D} for summaries), and the interstellar medium such as the giant molecular clouds \citep[e.g.][]{1985AJ.....90.1548H,1996A&A...308..988B,2009CoSka..39...85J,2008CoSka..38...33J}. The Galactic tide has a stronger overall effect when averaged over long time scales \citep[for example][]{heisler86}. The effect of the encounters is stochastic and helps to keep the Oort cloud isotropic \citep[e.g.][and references therein]{kaib11}. The two mechanisms act together and combine in a non-linear way \citep{rickman08,2011Icar..214..334F}. The orbit of the Sun in the Galaxy determines the intensity of the gravitational tides the Solar System was exposed to, as well as the number of stars around the Sun that could pass close enough to perturb the Oort cloud. \citet{kaib11} investigated the effect of encounters with the field stars and that of the Galactic tides on the Oort cloud, considering the so-called radial migration effect on the orbit of the Sun \citep[see e.g][for a more detailed description]{sellwood,roskar, minchev10, martinezb14}. They simulated the Oort cloud around the Sun, adopting possible solar orbits from the simulation of a Milky Way-like galaxy of \citet{roskar}, including those that experienced no migration and those that experienced strong radial migration (some of their solar analogues get as close as $2$~kpc from the Galactic centre or as far as $13$~kpc). Kaib and collaborators found that the present-day structure of the Oort Cloud strongly depends on the Sun's orbital history, in particular on its minimum past Galactocentric distance. The inner edge of the Oort cloud shows a similar dependence (on the orbital history of the Sun) and it is also influenced by the effect of strong encounters between the Sun and other stars. With the increasing amount of precise astrometric and radial velocity data for the stars in the solar neighborhood, several studies have focused on the identification of stars that passed close to the Solar system in the recent past, or will pass close by in the future \citep[][]{mamajek, bailer15, dubinsky15}. \citet{mamajek} identified the star that is currently known to have made the closest approach to the Sun --- the so called Scholz's star that passed the Solar System at $0.25^{+0.11}_{-0.07}$\,pc. Additionally, \citet{2015MNRAS.454.3267F} studied the effect of recent and future stellar encounters on the flux of the long period comets. They carried out simulations of the Oort cloud, considering perturbations by the identified encounters and a constant Galactic field at the current solar Galactocentric radius, and kept track of the flux of long-period comets injected into the inner Solar system as a consequence of the encounters. Unlike \citet{kaib11}, \citet{2015MNRAS.454.3267F} focused only on the effect of the actually observed perturbers. They conclude that past encounters in their sample explain about 5\% of the currently observed long period comets and they suggest that the Solar system experienced more strong, as yet unidentified, encounters. \cite{portegies15} discuss the effect of the stellar encounter history on the structure of the system of planetesimals surrounding the Sun. They considered encounters with stars in the Sun's birth cluster (early on in the history of the Sun) and encounters with field stars that occur as the Sun orbits in the Galaxy. The encounters with the field stars set the outer edge of the so called Parking zone of the Solar system \citep{portegies15}. The parking zone is defined as a region in the plane of semi-major axis and eccentricity of objects orbiting the Sun that have been perturbed by the parental star cluster but not by the planets or the Galactic perturbations. The orbits located in the parking zone maintain a record of the interaction of the Solar system with stars belonging to the Sun's birth cluster. Therefore, these orbits carry information that can constrain the natal environment of the Sun. Recently, \citet{jilkova15} argued that a population of observed planetesimals with semi-major axes $>150$\,au and perihelia $>30$\,au, would live in the parking zone of the Solar system. They also found that such a population might have been captured from a debris disc of another star during a close flyby that happened in the Sun's birth cluster. The outer edge of the parking zone is defined by the strongest encounter the Solar system experienced after it left its birth cluster. The strength of the encounter is measured by the perturbation of semi-major axes and eccentricity of the bodies in their orbit around the Sun. \citet{portegies15} used the impulse approximation \citep{rickman76} to estimate the effect and defined the outer edge of the Solar system's parking zone as corresponding to the perturbation caused by the Scholz's star \citep{mamajek}. However, stronger encounters might have happened in the past, as the Sun orbited in the Galactic disc. These encounters would alter the outer edge of the Solar system's parking zone moving it closer to the Sun. The perturbation strength of the stellar encounters depends on the characteristics of the close encounters with field stars --- the mass of the other star, its closest approach and relative velocity. Similar to Scholz's star, the parameters of some of the recent close encounters can be derived from the observed data \citep[for example][]{2015MNRAS.454.3267F, dubinsky15}. Estimates of the number and strength of past encounters are difficult to make because of the large uncertainties in the Galactic environment where the Sun has been moving since it left its birth cluster. These uncertainties are due to the unknown evolution of the Galactic potential (leading to uncertainties in the Sun's past orbit), which is in turn related to the unknown (population dependent) density and velocity dispersion of the Milky Way stars along the Sun's orbit. \cite{garcia01} studied the recent encounter history of the Sun by integrating its orbit in an analytical Milky Way potential together with 595 stars from the Hipparcos catalogue in order to identify recent and near future encounters. In addition they estimated the encounter frequency for the Sun in its present environment by considering the velocity dispersions and number densities of different types of stars. \cite{rickman08} simulated the stellar encounters by assuming random encounter times (for a fixed number of encounters) over 5 billion years and using velocity dispersions for 13 different types of stars (different masses), with relative encounter frequencies for these types taken from \cite{garcia01}. An alternative approach based on a numerical model of the Milky Way was taken by \cite{kaib11}. The orbits of solar analogues in this model were extracted from a simulation of a Milky Way-like galaxy and then the encounters were simulated by tracking the stellar number density and velocity dispersion along the orbit and then generating random encounters by starting stars at random orientations $1$~pc from the Sun. The encounter velocities were generated using the recipe by \cite{rickman08}. In this paper we aim to improve the determination of the outer edge of the Solar system's parking zone by determining the number of stellar encounters experienced by the Sun along its orbit. We compute the number of encounters by employing the largest Milky Way simulation to date, which contains 51 billion particles, divided over a central bulge, a disk and a dark matter halo \citep[][]{bedorf}. This Galaxy model is used to estimate the velocity dispersion of the stars encountered by the Sun along its orbit. To achieve this we integrate the Sun's orbit back in time using an analytical potential for the Milky Way. The orbit of the Sun is then inserted in a snapshot of the particle simulation and the velocity dispersion of the disk stars is estimated at each position. We employ three different orbits of the Sun (no radial migration, migration inward, migration outward) and use the resulting estimates of the encounter frequencies along each of these orbits to discuss the implications for the location of the outer edge of the Solar system's parking zone. We also discuss the effect of such encounters on the stability of the orbit of the so-called Planet 9. The presence of this object was predicted by \citet{BB16} in the outer Solar system to explain the clustering of the orbital elements of the distant Kuiper Belt Objects (KBOs). According to the updated simulations of \cite{2016ApJ...824L..23B}, Planet 9 has a mass of 5--20\,M$_\oplus$; an eccentricity of $\sim 0.2$--0.8, semi-major axis of $\sim 500$--1050\,AU and perihelion distance of $\sim150$--350\,AU. This paper is organized as follows: In Sect.\ \ref{sect:gal_model} we explain the Galaxy model and we show three possible orbital histories of the Sun. In Sect.\ \ref{sect:nenc} we determine the number of encounters along each of these solar orbits. From this estimate, we generate a set of stellar encounters with random mass, encounter distance and velocity. In Sect.\ \ref{sect:stability} we find the stellar encounters that produce the strongest perturbation of objects orbiting the Sun. These encounters are used to estimate the outer edge of the Solar system's parking zone. In Sect. \ref{sect:discussion3} we discuss the effects of such encounters on the stability of the orbit of Planet 9. We also mention the limitations of our computations and the improvements that could be made in future studies. In Sect. \ref{sect:summary} we summarize. | \label{sect:summary} We estimate the number of Galactic stellar encounters the Sun may have experienced in the past, along its orbit through the Galaxy. We aim to improve the previous estimates of the outer edge of the Solar system's parking zone made by \cite{portegies15}. The parking zone is the region in the plane of the eccentricity and semi-major axis where objects orbiting the Sun have been perturbed by stars belonging to the Sun's birth cluster but not by the planets or by Galactic perturbations. As a consequence, the orbits of objects located in the parking zone maintain a record of the interaction of the Solar system with the so called solar siblings \citep{portegies09}. These orbits carry information that can constrain the natal environment of the Sun. We investigate the orbital history of the Sun by using an analytical potential containing a bar and spiral arms to model the Galaxy. In this potential we integrate the orbit of the Sun back in time during $4.6$~Gyr. Since we include the uncertainties in the present-day phase-space coordinates of the Sun, we obtain a collection of possible orbital histories. Here we study three different orbits, depending on the migration experienced by the Sun namely: migration inwards, no migration and migration outwards. The Galactic stellar encounters are estimated for each of these orbits. We compute the number of stellar encounters ($n_\mathrm{enc}$) by calculating the frequency of stellar passages experienced by the Sun along its orbit. This frequency is determined by computing the number density and the stellar velocity dispersion along the orbit of the Sun. We found that $n_\mathrm{enc}= 9.3\times10^4, 28.2\times10^4$ and $17.5\times10^4$ for the orbits with inward migration, outward migration and no migration respectively. We use these estimates to generate a sample of $n_\mathrm{enc}$ random stellar encounters with certain time of occurrence (\tenc); mass (\menc); pericenter distance (\renc) and velocity (\venc). By looking at the distribution of stellar encounters in the space of \menc, \venc\ and \renc , we found that most of the stellar encounters experienced by the Sun have been with low-mass stars (\menc $< 1$~M$_\odot$) with velocities of $20$-$100$~kms$^{-1}$. We calculate the the outer edge of the Solar system's parking zone using the impulse approximation \citep{rickman76}. For each solar orbit, we calculate the outer edge for 1000 different sets of encounters. The actual outer edge of the Solar system's parking zone is determined such that the number of encounters along the orbit resulting in smaller $a_{\mathrm{PZ}}(e)$ is $n_\mathrm{enc}=1$. The parking zone is then located at about 250--700, 450--950, and 600--1300\,AU (Fig.~\ref{fig:pz}) for the orbits with migration outwards, no migration, and migration inwards, respectively. Therefore, the orbital history of the Sun is important to establish the outer edge of the parking zone. From Fig.~\ref{fig:pz} it is also clear that the Sun has experienced stronger stellar encounters than those with the Scholz's star. As a consequence, the location of the outer edge of the parking zone is closer to the Sun than the previous estimates made by \cite{portegies15} and is comparable to the border between the inner and outer Oort cloud. Regardless of the migration of the solar orbit, we find that objects in the Solar system with semi-major axis smaller than about 200~AU have not been perturbed by encounters with field stars. However, depending on the migration of the solar orbit, it is possible that the inner Oort cloud (including Sedna) has been perturbed. We further discuss the effect of the stellar encounters on the stability of the orbit of a hypothetical Planet 9 (P9). According to the orbital parameters of P9, this object is located in the same region as the outer edge of the parking zone. This means that there was at least one encounter along the solar orbit that could have changed the aphelion velocity of P9 by $100\%$. | 16 | 9 | 1609.09099 |
1609 | 1609.07573_arXiv.txt | To obtain the most accurate pulse arrival times from radio pulsars, it is necessary to correct or mitigate the effects of the propagation of radio waves through the warm and ionised interstellar medium. We examine both the strength of propagation effects associated with large-scale electron-density variations and the methodology used to estimate infinite-frequency arrival times. Using simulations of two-dimensional phase-varying screens, we assess the strength and non-stationarity of timing perturbations associated with large-scale density variations. We identify additional contributions to arrival times that are stochastic in both radio frequency and time and therefore not amenable to correction solely using times of arrival. We attribute this to the frequency dependence of the trajectories of the propagating radio waves. We find that this limits the efficacy of low-frequency (metre-wavelength) observations. Incorporating low-frequency pulsar observations into precision timing campaigns is increasingly problematic for pulsars with larger dispersion measures. | The pulsar-timing technique has enabled many studies fundamental to physics and astrophysics, including precise tests of general relativity \cite[][]{1975ApJ...195L..51H,2006Sci...314...97K}, constraints on the equation of state of dense nuclear matter \cite[][]{2007PhR...442..109L,2010Natur.467.1081D}, and the discovery of the first planetary mass objects outside of the solar system \cite[][]{1992Natur.355..145W}. One possible application of the pulsar-timing technique is the detection of gravitational waves (GWs) and the characterisation of GW-emitting sources. GWs passing through the solar neighbourhood manifest as variations in arrival times in an array of (MSPs) \cite[a pulsar timing array, PTA; ][]{1979ApJ...234.1100D,1983ApJ...265L..39H,1990ApJ...361..300F} that have a quadrupolar correlation on the sky. PTAs are sensitive to gravitational waves with periods ranging from $1$~month to $20$~yr (frequencies between $\approx 2$ and $400$~nHz), with the band constrained by the observing cadence and total timing-campaign duration. The strongest gravitational-wave signal in the PTA observing band is predicted to be a stochastic background associated with merging massive black holes \cite[][]{2003ApJ...583..616J,2010arXiv1001.3161S,2012ApJ...761...84R}. This background imparts a red-noise signal in the TOAs\footnote{In power spectrum analysis, a red noise signal has more power at lower fluctuation frequencies and is therefore strongly correlated between observations.}. This is in contrast with white signals that are uncorrelated between observations. The root mean squared (rms) amplitude of the background in the residual TOAs is predicted to be $\lesssim 20$~ns over a $5$~year observing span (\citealt{sc2010}, henceforth referred to as Paper I). It is currently expected that $20$~to~$100$ MSPs, with timing precision between $\approx 10$ and $100$~ns level are required to significantly detect gravitational radiation (\citealt[][]{2005ApJ...625L.123J}, Paper I, \citealt[][]{2012ApJ...750...89C}, \citealt{2013CQGra..30v4015S}). Constraints on the amplitude of the background indicate that PTAs are sensitive to GWBs at astrophysically plausible levels \cite[][]{2013Sci...342..334S} and are already in tension with some models of Galaxy-black hole coevolution % \cite[][]{2015Sci...349..1522S, 2016ApJ...821...13A} To reach the required precision for detecting GWs, it is necessary to identify and correct for many perturbations to the TOAs. These perturbations are incorporated into sophisticated algorithms that incorporate maximum-likelihood or Bayesian approaches. Some of these perturbations are deterministic in time, independent of observing frequency, and hence can be parameterized and directly modelled \cite[][]{2006MNRAS.372.1549E} or marginalized analytically \cite[][]{2014MNRAS.437.3004L}. For example, the perturbation associated with the secular spin down of the pulsar is modelled through the inclusion of a quadratic polynomial in the timing model. Other perturbations exist that are stochastic in time but have a known frequency dependence and can be corrected or constrained using multi-frequency observations. These are associated with refraction and diffraction of radio waves in the ionised interstellar (ISM), interplanetary, and ionopsheric media. In this paper, we focus on understanding propagation delays associated with the ISM. Uncorrected perturbations contribute an additional error to TOAs and degrade the sensitivity of a PTA to GWs. It is of particular interest to identify and correct red-noise perturbations because these more severely affect the sensitivity of a PTA to a stochastic gravitational wave background than white noise (Paper I). As part of the effort to detect GWs with pulsars, we are assessing stochastic perturbations to pulsar TOAs in PTA observations. In Paper I, we estimated the levels of intrinsic spin noise in MSPs. Based on the levels of timing noise in the more slowly spinning and rotationally unstable canonical pulsars, and two MSPs that exhibit timing noise, we concluded that for many MSPs, spin noise is present at levels comparable to the GWB with similar temporal variability. In \cite{cs2010} (henceforth referred to as Paper II) we comprehensively assessed the stochastic perturbations to TOAs employing a physical model for TOAs. One set of perturbations discussed in Paper II is associated with the propagation of radio waves through the ISM. As the radio emission travels from the pulsar to the Earth, it is refracted by the warm ionised electrons (as shown in Figure \ref{fig:geometry}), and the pulse TOA is retarded relative to the expected TOA in vacuum. This delay varies with time because the sampled region of the ISM changes as the pulsar-Earth line of sight (LOS) changes due to relative motion of the Earth and the pulsar through the Galaxy. The effects of interstellar propagation can be partially mitigated though identification and removal of radio frequency dependent perturbations to the TOAs, because the strength of refraction and hence the magnitude of the TOA perturbation is strongly chromatic. This is in contrast with other astrophysically interesting phenomena, such as gravitational radiation, that impart achromatic perturbations. Multi-frequency mitigation methods are at present only minimally applied in precision-timing observations. It is usually assumed that chromatic variability in pulse TOAs is associated entirely with the change in the total electron content (the dispersion measure, DM) of the LOS through the interstellar medium\footnote{The interplanetary medium and the ionosphere also contribute to the DM. However the contributions are small, do not significantly refract and diffract pulsar radiation at wavelengths of interest, and are therefore not considered here.}, and the TOA is proportional to the DM and the inverse square of observing frequency. When the DM is larger, the pulses arrive slightly later, and vice-versa. This effect is usually assumed to be completely deterministic in frequency; under this assumption TOAs can be corrected by observing at only two frequencies. For the nearby MSPs currently incorporated in PTAs observed at typical observing frequencies, DM variation delays have an rms amplitude of many microseconds. Indeed correcting for DM variations has been identified as crucial to the success of PTAs \cite[][]{2007MNRAS.378..493Y,2013ApJ...762...94D,2013MNRAS.429.2161K,2014MNRAS.441.2831L}. The approximation that the ISM is smooth is poor. It is well known that the electron plasma density fluctuations in the ISM cover a wide variety of length scales \cite[][]{1995ApJ...443..209A} and that they cause multi-path propagation of the pulsar signal \cite[][]{1968Natur.218..920S,1969Natur.221..158R,1990ARAA..28..561R}. Thus, in addition to the DM delay, scattering effects must also be considered (\citealt{1984Natur.307..527A}, \citealt{1990ApJ...364..123F}; \citealt{1991ApJ...366L..33H}; \citealt{2010arXiv1005.4914C}, henceforth referred to as C10; Paper II). In this paper, we examine some of the propagation effects associated with diffraction and refraction in the interstellar medium. We extend on previous studies of refractive propagation effects. \cite{1990ApJ...364..123F} investigated propagation effects using a one-dimensional screen. They suggested that there were likely significant perturbations to the pulse TOA associated with geometric path length variations that would not be corrected using the simple DM-correction technique. \cite{1991ApJ...366L..33H} extended this analysis to a two-dimensional screen. Both of these studies were conducted when there were only a few known MSPs and timing precision was much poorer. A re-examination of propagation effects is warranted because of the increase in the number of known MSPs and the improvement in timing precision. \cite{2016ApJ...817...16C} investigated the mis-estimation of TOAs due to incorrect DM estimates. They modelled the frequency-dependent screen-averaged DM and found that when RF bandwidths exceeded an octave in frequency range, $ \gtrsim 100$~ns timing errors are introduced. In a more restrictive model, \cite{2015ApJ...801..130L} investigated the effects of non-contemporaneous multi-frequency observations on correcting for DM variations, and found that for widely separated observing epochs, the imprecision of DM correction would limit timing precision for the best pulsar at the levels required to detection gravitational waves. We quantitatively assess the efficacy of several mitigation strategies relevant to PTAs and other long-term timing observations. This study is complementary to the study presented in C10, which focused on diffractive effects that cause variations in TOAs on short time scales. Due to computational limitations associated with fully diffractive simulations (discussed below) C10 only discussed wave propagation in a narrow frequency band. Here we take a complementary approach and focus on effects associated with time and size scales comparable to and larger than refractive scales, enabling us to study the effects of large-scale variations over a wide range of frequencies ($>15:1$ bandwidth). Our findings are presented as followed: In Section \ref{sec:analytic_delays}, we discuss the relationship between the pulse perturbation and the image brightness that is the basis of our analysis. In Section \ref{sec:refractive_screens}, a refractive screen model for wave propagation is motivated and an approximation for the image intensity is presented. In Section \ref{sec:ref_pert}, the TOA perturbations from the refractive screen are discussed. In Section \ref{sec:simuls}, a series of simulations conducted to investigate refractive perturbations are presented. The details of the simulations are presented in the Appendix. In Section \ref{sec:mitigate}, mitigation strategies are described. In Section \ref{sec:future_studies}, we discuss future observations that can confirm the presence of these effects and simulations that guide their analysis. In Section \ref{sec:conclusions}, we summarise our findings and motivate future studies that complement this work. Throughout this paper we use {\em frequency} in two distinct ways. Observing radio frequency (RF) is denoted as $\nu$. Fluctuation frequency, which is the conjugate variable to time in the spectral analyses of a time series, is denoted as $f$. \begin{figure} \begin{center} \includegraphics[scale=0.4]{geometry2d_2a.eps} \\ \caption{ \label{fig:geometry} {\em Panel a:} Propagation delay geometry. Observed TOAs are corrected to the solar system barycentre (circle S), assuming that the radio waves propagate along a direct LOS from the pulsar (circle P) to the Earth (circle E). The coordinate system orientation is labelled in the upper left corner of the panel. In this analysis, scattering is assumed to be constrained to a thin screen located a distance $sD$ from the Earth along the pulsar earth LOS, where $D$ is the pulsar-Earth distance. At the screen distance, the centre of the tube is offset from the direct LOS by an angle $\theta_r$ and has a width $\theta_d$. The location of the tube, projected on the screen can also be characterised by an image intensity $B(\bm{\theta})$. {\em Panels b-d:} Schematic diagrams of the emitted pulse shape ({\em Panel b}), pulse broadening function $p(\tau,\nu)$ ({\em Panel c}), and observed pulse shape ({\em Panel d}), as a function of pulse phase $\phi = t/P$, where t is the residual time and $P$ is the pulse period. } \end{center} \end{figure} | \label{sec:conclusions} Without mitigation, the propagation of radio pulses through the ISM may impede usage of the highest precision pulsar timing observations for fundamental measurements, including those intending to detect gravitational waves. We have assessed the strength of dispersive and refractive interstellar propagation effects on precision pulsar timing observations by simulating TOA perturbations caused by frequency-dependent phase-changing screens. We then investigated techniques to determine the infinite frequency time of arrival $t_\infty$ using a variety of scattering screen and observing configurations. Our main findings are as follows: 1. The ISM induces TOA perturbations that stochastically vary in time, and both deterministically and stochastically vary in radio frequency. Through simulation, we have analysed their strengths and temporal variability. None of the effects have the steep power spectrum predicted for the GWB, with most showing correlations on week to month time scales. 2. Multi-frequency observations can be used to correct propagation effects to a certain extent. For some nearby, weakly scattered pulsars, sub-$10$~ns rms residuals can be achieved when correcting only for $\nu^{-2}$ perturbations. For other more distant pulsars, correcting for both $\nu^{-2}$ and $\nu^{-6}$ terms produces corrected time series with a higher degree of stationarity. 3. Optimal observing strategies are highly LOS dependent: The strengths of the terms depend on the strength and structure of the scattering screen. As a result, observation and correction strategies need to be tailored to individual pulsars. For fixed scattering strength, square law media induce larger and more non-stationary fluctuations in the corrected time series than Kolmogorov media. 4. The best observing strategy depends on the strength of the propagation effects relative to other noise sources: When the total observing bandwidth is increased, TOA perturbations become less correlated and correction becomes less effective. When the total observing bandwidth is narrow, higher order corrections cannot be resolved from the frequency dependent terms. 5. Corrected time series contain propagation errors associated with perturbations that vary stochastically with frequency. Even though these effects may be at levels smaller than the white noise, they affect the sensitivity of a PTA to GWs. This is further discussed in the context of a measurement model for GW detection (Paper I; \citealt[][]{2012ApJ...750...89C}). We find that the greatest benefit comes from down-weighting low frequency TOAs due to the frequency-dependent stochasticity of the arrival times. There is mounting evidence that effects like these are present in MSP observations. Recent analysis indicates that the effects of scattering are contributing excess red noise in observations of the millisecond pulsar J1643$-$1224 \cite[][]{iptanoise}. At low frequency ($700-800$~MHz) the pulsar shows stochastic arrival-time variations (in excess of DM variations) with a shallow red-noise spectrum and a strength that is proportional to the pulse broadening time. Observations with the PPTA project show that the highest-precision pulsars show excess noise at the lowest observing frequency \cite{2015Sci...349..1522S}. It is unclear if the noise is instrumental or astrophysical. If it is astrophysical it could be associated with effects like the ones simulated here. | 16 | 9 | 1609.07573 |
1609 | 1609.02998_arXiv.txt | Numerical simulations have consistently shown that the reconnection rate in certain collisionless regimes can be fast, on the order of $0.1 {v_A}{B_u}$, where $v_A$ and ${B_u}$ are the Alfv{\'e}n speed and the reconnecting magnetic field upstream of the ion diffusion region. This particular value has been reported in myriad numerical simulations under disparate conditions. However, despite decades of research, the reasons underpinning this specific value remain mysterious. Here, we present an overview of this problem and discuss the conditions under which the ``0.1 value'' is attained. Furthermore, we explain why this problem should be interpreted in terms of the ion diffusion region length. | Magnetic reconnection is a fundamental plasma process that occurs in a wide variety of laboratory, space, and astrophysical plasmas. Its definition is meaningful in plasmas that are almost ideal, i.e., in those cases where magnetic field lines ``move'' with the plasma in the vast majority of the domain, while the breaking of the magnetic field line connectivity occurs only in very localized diffusion regions. This reconnection process can enable a rapid conversion of magnetic energy into thermal, supra-thermal, and bulk kinetic energy. As such, magnetic reconnection is believed to play a key role in many of the most striking and energetic phenomena such as sawtooth crashes, magnetospheric substorms, coronal mass ejections, stellar and gamma-ray flares \citep[]{Tajima1997,Kulsrud2005,Yamada2010}. In order to explain the magnetic energy conversion rates associated with these phenomena, it is essential to know the rate at which magnetic reconnection occurs. The reconnection rate quantifies the temporal rate of change of magnetic flux that undergoes the reconnection process. When the system under consideration is translationally invariant in one direction, the reconnection rate can be expressed as \begin{equation}\label{} \frac{{d\Phi}}{{dt}} = \frac{d}{{dt}}\int_S {{\vec B} \cdot d{\vec S}} = \oint_{\partial S} {\vec E \cdot d\vec l} = \int_{X{\rm{-line}}} {{E_z}dl} \, . \end{equation} Here, $\Phi$ is the magnetic flux through the surface $S$ bounded by the contour $\partial S$ encompassing the $X$-line. An $X$-line is the projection of an hyperbolic point for the magnetic field along the ignorable direction. Therefore, the reconnection rate is a measure of the rate at which magnetic flux is transported across the $X$-line. In a more general three-dimensional case, the evaluation of the reconnection rate is more subtle. A general approach \citep[]{Hesse2005} would be to quantify the reconnection rate as \begin{equation}\label{Rec_Hesse} \frac{{d\Phi}}{{dt}} = \max \left( {\int {{E_\parallel }ds} } \right) \, , \end{equation} where $s$ represents the parametrization of the magnetic field lines, and the integral has to be performed over all field lines passing through the non-ideal region (where $E_\parallel = \vec E \cdot \vec B/ | {\vec B} | \neq 0$). The measure (\ref{Rec_Hesse}) is an attractive choice for quantifying the reconnection rate, but there are some caveats associated with it. Indeed, there could be some ambiguity related to the field line integration of $E_\parallel$, as in regions where magnetic field lines are stochastic \citep[]{Borgogno2005}, or it may be not possible to distinguish between reconnection and simple diffusion \citep[]{Huang2014}. In addition, this measure can be applied only in the presence of a non-vanishing magnetic field. If this is not the case, the reconnection rate may be calculated by combining the line integrals of $E_\parallel$ along magnetic separators \citep[]{Greene1988,LauFinn1990,Wilmot2011}, which are magnetic field lines connecting two null points (i.e., points at which $|{\vec B}|=0$). As this brief discussion may suggest, a completely general and practical measure of the reconnection rate is still lacking, and indeed it constitutes an important ongoing area of research (see, for example, the discussion given by \citet[]{Dorelli2008} in the context of the Earth's magnetosphere.) The problem of determining the reconnection rate of a magnetic reconnection process dates back to the 1950's. At that time, the astrophysical community was trying to understand if magnetic reconnection could have served as the mechanism underlying solar flares, which are bursts of high-energy radiation from the Sun's atmosphere that strongly affect the space weather surrounding the Earth. A simple resistive magnetohydrodynamic (MHD) model of magnetic field line merging was proposed by \citet[]{Sweet}, and then, with the contribution of \citet[]{Parker}, the reconnection rate was evaluated. They considered a quasi-stationary reconnection process occurring within a two-dimensional current sheet. Then, assuming an incompressible flow, the normalized reconnection rate (per unit length) can be shown to be \begin{equation}\label{eq1} \frac{1}{{{v_A}B_{u}}} \frac{{d{\Phi}}}{{dt}} \sim S^{-1/2} (1 + P_m)^{1/4} \, . \end{equation} In this formula, $S := v_A L/\eta$ and $P_m := \nu/\eta$ are the Lundquist number and the magnetic Prandtl number, respectively. As usual, $\eta$ indicates the magnetic diffusivity and $\nu$ the kinematic viscosity. The Lundquist number is evaluated using the current sheet half-length $L$ and the Alfv{\'e}n speed $v_A = B_u {\left( {{\mu _0}\rho } \right)^{-1/2}}$, where $B_u$ is the reversing magnetic field upstream of the current sheet. In reality, Eq. (\ref{eq1}) is not exactly the Sweet-Parker formula for the reconnection rate, but represents its generalization to account for plasma viscosity \citep[]{Park1984}. The Sweet-Parker model of reconnection is faster than simple diffusion, but for very large $S$ systems, such as those found in most space and astrophysical environments, it is far too slow to explain the observed fast energy release rates. In order to bypass this limitation, \citet[]{Petschek1964} proposed a different model in which a relatively short reconnection layer acts as a source for two pairs of slow mode shocks, allowing for much faster reconnection rates. This model was subsequently generalized by \citet[]{Priest1986}, who put forward a wider family of ``almost-uniform models'' that include Petschek's model as a special case. However, these models have not been supported by numerical simulations \citep[]{Biskamp1986}, which have shown that Petschek-like configurations cannot be sustained in the context of MHD with constant resistivity. Petschek's mechanism can occur within the resistive-MHD framework if the plasma resistivity increases sharply in the reconnection layer \citep[]{Kulsrud2001,Kulsrud2011}, but the difficulties in firmly establishing the nature and details of such anomalous resistivity have led the scientific community to look for other alternatives. An important advance occurred when \citet[]{BHYR_2009}, and later \citet[]{Cassak2009}, showed that the predictions of the Sweet-Parker model break down for large $S$ values because of the occurrence of the plasmoid instability \citep[]{Biskamp1986,Tajima1997,Loureiro2007,Comisso2016,Comisso2016B}. In the high-Lundquist number regime, the reconnection process in the nonlinear regime becomes strongly time-dependent due to the continuous formation, merging, and ejection of plasmoids. An estimation of the time-averaged reconnection rate in this regime was proposed by \citet[]{Huang2010}, as well as by \citet[]{Uzdensky2010}, and it has been generalized to account for plasma viscosity as \citep[]{Comisso2015,Comisso2016} \begin{equation}\label{eq2} \frac{1}{{{v_A}{B_u}}}\left\langle {\frac{{d{\Phi}}}{{dt}}} \right\rangle \sim 10^{-2} {(1 + P_m)^{-1/2}} \, , \end{equation} where $\left\langle \ldots \right\rangle$ denotes time-average. This formula shows that, for high-Lundquist numbers, the (time-averaged) reconnection rate becomes independent of the Lundquist number (but not the magnetic Prandtl number) and much higher than the Sweet-Parker rate for very large $S$-values. Other MHD models of reconnection have also been investigated. In particular, since the pioneering work by \citet[]{Matthaeus1986}, turbulence effects have been shown to produce a distribution of reconnection sites that is capable of increasing the global reconnection rate \citep[]{Servidio2009}. The impact of turbulence and the plasmoid instability on the reconnection rate has caused a rethinking of magnetic reconnection in MHD plasmas. However, in many situations the current layers that form reach scales at which two fluid/kinetic effects become important. In all these cases, an MHD description fails to reproduce accurately the physics of the reconnection process, and two fluid and kinetic effects must be considered. For the aforementioned reasons, a complementary path in investigating fast magnetic reconnection has been pursued at least since the 1990's by means of numerical simulations of Hall MHD, two-fluid and kinetic models. Several research groups have shown that collisionless effects were able to strongly speed up the reconnection process \citep[]{Aydemir1992,OttPor1993,Wang1993,Mandt1994,Biskamp1995,Kleva1995,MaBhatta1996,Shay1999,Grasso1999,Birn_2001,Porcelli2002}. In particular, numerical simulations consistently demonstrated that the reconnection rate in certain collisionless regimes becomes \begin{equation}\label{eq3} \frac{1}{{{v_A}B_{u}}} \frac{{d{\Phi}}}{{dt}} \sim 0.1 \, , \end{equation} a value that is compatible with many observations and experiments \citep[]{Yamada2010}, meaning that collisionless effects may be crucial to explain many magnetic reconnection phenomena. Note that even here (and in the following) we have considered the reconnection rate per unit length in the out-of-plane direction, whereas $v_A$ and $B_u$ are evaluated upstream of the ion diffusion region, which can be seen as the region where ${E_z} + {({{\vec v}_i} \times \vec B)_z} \ne 0$. Although the relation (\ref{eq3}) was found to be valid only in the steady-state limit, or in the vicinity of the peak reconnection rate, it was nevertheless surprising to discover that ${({v_A}{B_u})^{ - 1}}d\Phi /dt$ seemed to be unaffected by the microphysics and macrophysics of specific models. This intriguing result led \citet[]{Shay1999} to speculate that the aforementioned value could be universal. Such a conjecture stimulated a long debate in the plasma physics and astrophysics communities - one that continues to this day. \emph{Is the reconnection rate value of $0.1$ truly universal?} \emph{What are the physical reasons of this particular value?} In order to explain the fast reconnection rates observed in numerical simulations, \citet[]{Shay1999} brought forward an argument by \citet[]{Mandt1994}, who proposed that fast magnetic reconnection is enabled by the presence of fast dispersive waves. These waves would speed up the reconnection process by giving rise to the development of a Petschek-type outflow configuration. In contrast, the absence of dispersive waves would lead to an extended Sweet-Parker-type layer, forcing collisionless reconnection to be slow in large systems \citep[]{Rogers2001}. This argument, however, was found not to be true. Indeed, numerical simulations have shown that fast magnetic reconnection also occurs in electron-positron plasmas, which do not support fast dispersive waves \citep[]{Bessho2005,DaugKar2007,Chacon2008,Zenitani2008}. More recently, \citet[]{Liu_2014}, as well as \citet[]{Stanier2015}, have reconsidered this argument and have shown that, in an electron-ion plasma, fast reconnection is also manifested in the strongly magnetized limit (where fast dispersive waves are suppressed) defined by $\beta := 2{\mu_0}{n_0}{k_B}(T_e + T_i)/B^2 \ll {m_e}/{m_i}$ and $B_{u}^2 \ll ({m_e}/{m_i}){B^2}$. While several works have shown that fast dispersive waves are not required for fast magnetic reconnection, they have also confirmed that the maximum/steady-state reconnection rate satisfies Eq. (\ref{eq1}) \citep[e.g.,][]{DaugKar2007,Liu_2014,Stanier2015}. There are also some works that have argued against the $\sim 0.1$ value of the maximum/steady-state reconnection rate \citep[e.g.,][]{Porcelli2002,Fitzpatrick2004,Bhatta2005,Andres2016}. In light of the subtlety of the problem, we shall elucidate the conditions under which one should expect a maximum/steady-state reconnection rate $\sim 0.1$. We will also present some thoughts on this apparent commonality of the reconnection rate, which still remain a mystery, and constitutes an important unsolved problem in magnetic reconnection theory. We refer to this problem as the ``$0.1$ problem''. | 16 | 9 | 1609.02998 |
|
1609 | 1609.02951_arXiv.txt | We present a multi-wavelength study of the unidentified \textit{Fermi} object, 3FGL J0212.1+5320. Within the 95\% error ellipse, \textit{Chandra} detects a bright X-ray source {(i.e., ${F_\mathrm{{0.5-7keV}}=1.4\times10^{-12}}$\flux)}, which has a low-mass optical counterpart ($M\lesssim0.4M_\sun$ and $T\sim6000$K). A clear ellipsoidal modulation is shown in optical/infrared at 20.87 hours. The gamma-ray properties of 3FGL J0212.1+5320 are all consistent with that of a millisecond pulsar, {suggesting} that it is a $\gamma$-ray redback millisecond pulsar binary with a low-mass companion filling $\gtrapprox$ 64\% of the \textit{Roche}-lobe. {If confirmed, it will be a redback binary with one of the longest orbital periods known. } Spectroscopic data taken in 2015 from the \textit{Lijiang} observatory show no evidence of strong emission lines, revealing {that} the accretion is currently inactive {(the rotation-powered pulsar state)}. {This is consistent with the low X-ray luminosities (${L_X\approx10^{32}}$\lum) and the possible X-ray modulation seen by \textit{Chandra} and \textit{Swift}. Considering that the X-ray luminosity and the {high} X-ray-to-$\gamma$-ray flux ratio {(8\%)} are both comparable} to that of the two known $\gamma$-ray transitional millisecond pulsars, {we suspect that} 3FGL J0212.1+5320 could be a {potential} target to search for future transition to the accretion active state. \\ | Progenitors of millisecond pulsars (MSPs), though not yet fully understood, are believed to be {neutron stars} in low-mass X-ray binaries (LMXBs). According to the recycling scenario \citep{1982Natur.300..728A}, {the neutron stars} are spun up through accretion from the late-type companions (if any) to ultimately evolve into MSPs. Through the so-called \textit{LMXB Case A} channel \citep{2011ASPC..447..285T}, a compact binary (i.e., orbital period $<$ 1 day) consisting of a MSP and a very low-mass companion (which was striped by the neutron star and/or partially ``evaporated'' by the energetic pulsar wind/$\gamma$-rays; \citealt{2013ApJ...775...27C}) remains at the very end phase of such an evolution, known as black widow (BW; companion mass: $<0.1M_\odot$) or redback (RB; companion mass: $\sim$0.1--0.4 $M_\odot$) binaries. A few RBs, known as transitional MSPs, have already shown remarkable transition(s) between the LMXB state and the radio pulsar state in optical, X-rays, and{/or} $\gamma$-rays {(i.e., M28I; \citealt{2013Natur.501..517P}, PSR J1023+0038; \citealt{2009Sci...324.1411A,2014ApJ...781L...3P}, and PSR J1227$-$4853; \citealt{2015ApJ...800L..12R})}, clearly indicating the close relationship between LMXBs and radio MSPs. BW/RBs are interesting objects, not to mention the fascinating theoretical interpretation of multi-wavelength observations for individual studies (e.g., the keV-to-GeV emission models of PSR J1023+0038 in different states; \citealt{2014ApJ...797..111L,2015ApJ...807...33P}). They also provide crucial information {on} the long-term accretion history. {In particular, BWs are the key to uncover how the companions are finally eliminated, after which isolated MSPs are formed \citep{1988Natur.334..227V}. } As MSPs are powerful $\gamma$-ray sources with strong GeV magnetospheric radiations (e.g., from the outer gap, the slot gap, or the polar cap; \citealt{1986ApJ...300..500C,2003ApJ...588..430M,1975ApJ...196...51R}) and/or the inverse-Compton $\gamma$-ray emissions of the pulsar wind nebulae when the accretion is active \citep{2014ApJ...785..131T,2014ApJ...797..111L}, many of them should have been detected by \textit{Fermi}-LAT as a class of unidentified \textit{Fermi} object (UFO), the second-largest population detected by \textit{Fermi}-LAT \citep{2015ApJS..218...23A}. Although not all the UFOs are MSPs (in fact many of them are thought to be AGNs, the largest source class in the catalog), good BW/RBs candidates can be selected based on the $\gamma$-ray spectral curvatures and the $\gamma$-ray variabilities \citep{2012arXiv1205.3089R,2012ApJ...747L...3K,2014ApJ...794L..22K,2015ApJ...809...68H} and confirmed their pulsar natures by detecting the radio/$\gamma$-ray pulsations. Thanks to the \textit{Fermi} Pulsar Search Consortium (PSC), a great success has been achieved in discovering new pulsars through ``blind'' searches {for} coherent pulsations in radio and $\gamma$-rays \citep{2012arXiv1205.3089R}, and {the known BW and RB populations have been greatly extended in recent years. } {Alternatively, multi-wavelength studies of UFOs are the secondary way to search for BW/RBs MSP candidates. }In most of the cases, X-ray follow-ups are the key to narrow down the source location, allowing identification of the optical counterparts. {Once the optical counterpart is identified}, time-series optical observations can test the BW/RB identity by searching for the orbital modulation on timescale of hours produced by pulsar irradiation on the companion and/or ellipsoidal variation. Through this multi-wavelength technique, several UFOs, for examples, 2FGL J1311.7$-$3429/PSR J1311$-$3430 \citep{2012Sci...338.1314P}, 1FGL J1417.7$-$4407/PSR J1417$-$4402 (not a canonical BW/RB system; \citealt{2015ApJ...804L..12S,2016ApJ...820....6C}), and 1FGL J2339.7$-$0531/PSR J2339$-$0533 \citep{2012ApJ...747L...3K,2015ApJ...807...18P} have been identified as MSP binaries and some of them have been {confirmed by the detection of millisecond radio/$\gamma$-ray pulsations}, proving the validity of the method. In this paper, we report the discovery of a $\gamma$-ray-emitting {RB candidate}, 3FGL J0212.1+5320. In the following sections, we present multi-wavelength studies using the optical imaging/spectroscopic data from the \textit{Lijiang} \citep{2015RAA....15..918F}, \textit{Lulin}, and Michigan State University (MSU) observatories, the \textit{Chandra} X-ray data, and the \textit{Fermi}-LAT third source catalog (3FGL; \citealt{2015ApJS..218...23A}). Discussions will be given in the last section. | We presented a multi-wavelength study of 3FGL J0212.1+5320 and found that {a RB MSP} binary as its physical nature can naturally explain the entire data set. The X/$\gamma$-ray spectral properties and the hourly-timescale orbital period are very similar to that of many known RBs (Table \ref{tab:rbs}), revealing the first hint of 3FGL J0212.1+5320 as a RB candidate. {The inferred primary star's masses from the best-fit ELC models are $1.5-2.2\,M_\sun$ that are consistent with that of a neutron star, though they are only indicative estimates.} An hourly variability is seen in the \textit{Swift}/\textit{Chandra} joint lightcurve and it could be an orbital modulation, however, uncertainly. If the modulation is genuine, it could be caused by an intrabinary shock emission, {through \textit{Doppler} boosting with a pulsar-wrapping shock geometry \citep{2014ApJ...797..111L} or partial occultation by the companion \citep{2011ApJ...742...97B}}. All the observational evidence is pointing to the conclusion of 3FGL J0212.1+5320 as a newly-discovered RB system. {A bright optical counterpart (could be one of the brightest known for RBs) has been identified with a clear orbital modulation at 20.87 hours}. We do not see an obvious non-uniform radiation heating to contribute {to} the orbital modulation and therefore the companion is probably not completely tidally locked. This may imply 3FGL J0212.1+5320 as a very young MSP system. According to \cite{1977A&A....57..383Z}, the synchronization timescale of such a close binary is approximately $t_\mathrm{sync}\sim10^4\,((1+q_i)/2)^2(P_i/\mathrm{1\,day})^4$~years (equation 6.1 of \citealt{1977A&A....57..383Z}), where $q_i$ and $P_i$ are the initial mass ratio and orbital period, respectively\footnote{The equation presented here is slightly different from the one in \citealt{1977A&A....57..383Z} because of the different definitions of the mass ratios. }. Assuming an initial mass ratio of $q_i=2.8$ (i.e., $m_{1,i}=1.4M_\sun$ and $m_{2,i}=0.5M_\sun$)\footnote{The initial masses are both poorly known due to the highly uncertain accretion and ablation processes, and thus the {values} are merely estimated within reasonable ranges. }, $P_i\approx13$d gives $t_\mathrm{sync}\gtrsim10^9$ years and $P_i\approx4$d gives $t_\mathrm{sync}\gtrsim10^7$ years. We took the calculated timescales for 3FGL J0212.1+5320 as lower limits because the orbital widening by the ablation from the pulsar \citep{2013ApJ...775...27C}, that would extend the synchronization process, was not considered in Zahn's work. In the case of $t_\mathrm{sync}\gtrsim10^7$ years, the initial orbital period is actually close to the estimated value of PSR J2129$-$0429 (i.e., $P_i\approx2.5$d; \citealt{2016ApJ...816...74B}), which has a long orbital period of $P=15.2$h, comparable to 3FGL J0212.1+5320's. Obviously, a young age of 3FGL J0212.1+5320 (i.e., in the order of 10 Myr) would be a self-consistent explanation for the data. In fact, $\sim10$ Myr old MSPs are rare but not impossible. For example, PSR J1823$-$3021A, one of the youngest MSPs known, has a characteristic age of 25 Myr \citep{2011Sci...334.1107F}. {Searching for the radio/X-/$\gamma$-ray pulsations of 3FGL J0212.1+5320 and computing the characteristic age would be useful to investigate the speculation. } Despite no heating effect seen, it is still highly likely that the companion is uniformly irradiated by the X/$\gamma$-rays from the pulsar, {resulting in a higher} surface temperature than a $\sim0.4\,M_\sun$ star should have. As the companion mass is no longer the only dominant factor to determine the surface temperature, the assumption of $m_2\sim0.4M_\sun$ (see \S \ref{sec:lijiang}) could be overestimated. Considering the fact that all the fitting results indicate a lighter $m_2$, $m_2\lesssim0.4M_\sun$ would be more reasonable. As the companion has a temperature {close to that of the Sun}, it is convenient to use the solar $R$-band absolute magnitude (i.e., $R=4.42$~mag; \citealt{1998gaas.book.....B}) to infer the distance of 3FGL J0212.1+5320. From the ELC model fits, the size of the companion is about $R_c\approx1\,R_\sun$. After a proper scaling, the inferred distance is about $d\approx0.8$~kpc leading to an X-ray luminosity of $L_X\approx10^{32}$\lum, which is relatively high among the known X-ray RBs in the \textit{pulsar state} (when radio pulsations can be detected and $L_X\sim10^{31}-4\times10^{32}$\lum; \citealt{2014ApJ...795...72L}). {Since} a high X-ray luminosity (i.e., $L_X\gtrapprox10^{32}$\lum) in the pulsar state is a common feature of all three known transitional MSPs (tMSPs; i.e., PSR J1023+0038, PSR J1227$-$4853, and M28I), it has been suggested by \cite{2014ApJ...795...72L} that $L_X\gtrapprox10^{32}$ is possibly a consequence of a stronger interaction between the pulsar and the companion, and therefore the higher X-ray luminosity could be a signature of a RB binary developing a strong accretion for the transition. {One possibility is that the companion of a pre-transition (to the LMXB state) system has a stronger wind {(i.e, a stronger inflow to the pulsar; see \citealt{2014ApJ...785..131T} and \citealt{2014ApJ...797..111L} for the interpretation of a varying stellar wind as the transition trigger for PSR J1023+0038)}, which powers a stronger intrabinary shock X-ray emission.} Based on the X-ray luminosity, two bright systems, PSR J2215+5135 ($L_X=1.3\times10^{32}$\lum) and PSR J1723-2837 ($L_X=2.4\times10^{32}$\lum; see Table \ref{tab:rbs} for their $\gamma$/X-ray properties), have been suggested by \cite{2014ApJ...795...72L} to be {potential targets for state transitions in the near future}. 3FGL J0212.1+5320 could be the third member of the group. In addition, we also examined the X-ray-to-$\gamma$-ray flux ratios of some known RBs and found that the flux ratios of the tMSPs (i.e., $\gg 1$\%) are significantly larger than that of the ``normal'' RBs (i.e., $\lesssim1$\%). 3FGL J0212.1+5320 has a ratio of $7.9$\% that is consistent with the tMSP ones. {One of the two prospective tMSP candidates, PSR J1723$-$2837, also has a large ratio of 13\% (Table \ref{tab:rbs}). } {Certainly, the speculation is not mature and should not be taken conclusively. However, it is still worth paying attention to the X-ray activity of 3FGL J0212.1+5320 for any future transition.} Even if it is not exhibiting any transition in the near future, 3FGL J0212.1+5320 could be one of the brightest RBs in X-rays and certainly is one of the best sources {for studying} the X-ray emissions of RBs. No previous attempt of radio pulsation blind search for 3FGL J0212.1+5320 has been found in the literature \citep{2011ApJ...727L..16R,2012MNRAS.422.1294G,2015ApJ...810...85C}. In fact, the system is likely radio-faint as no radio counterpart can be found in the 1.4 GHz NRAO/VLA Sky Survey (NVSS), of which the detection limit is $\sim2.5$ mJy {(\citealt{1998AJ....115.1693C}; Note: most of the radio MSPs found by targeting \textit{Fermi}-LAT sources have flux densities much lower than 2.5 mJy at 1.4 GHz; \citealt{2012arXiv1205.3089R})}. Nevertheless, a GBT observation is being planned for searching for radio coherent pulsations. {Hopefully, this extreme RB MSP (i.e., high X-ray luminosity, bright optical companion, long orbital period, and potentially young age) can be confirmed soon. } {After the submission of this paper, we became aware of a similar work by \cite{2016arXiv160902232L}, in which results including the measured orbital period, the radial velocity curve of the companion, the \textit{Chandra} spectral analysis, and the redback MSP nature interpretation are consistent with ours. In particular, they have sampled a much better radial velocity curve, which would be very helpful in searching the radio/$\gamma$-ray pulsations in the future. } | 16 | 9 | 1609.02951 |
1609 | 1609.09044_arXiv.txt | { We study non-perturbatively the effect of the deflection angle on the BAO wiggles of the matter power spectrum in real space. We show that from redshift $z\sim2$ this introduces a dispersion of roughly $1 \ \text{Mpc}$ at BAO scale, which corresponds approximately to a $1\%$ effect. The lensing effect induced by the deflection angle, which is completely geometrical and survey independent, smears out the BAO wiggles. The effect on the power spectrum amplitude at BAO scale is about $0.1 \%$ for $z\sim2$ and $0.2 \%$ for $z\sim4$. We compare the smoothing effects induced by the lensing potential and non-linear structure formation, showing that the two effects become comparable at $z \sim 4$, while the lensing effect dominates for sources at higher redshifts. We note that this effect is not accounted through BAO reconstruction techniques. } | \label{sec:intro} All cosmological observations are performed by detecting photons that have traveled along our past light cone. Therefore they do not only carry information about the density and the velocity fields of the sources, but they are also contaminated by the geometrical effects induced by the matter distribution along the line of sight. Photons traveling in a clumpy universe are affected, to first order in perturbation theory, by cosmic magnification, integrated Sachs-Wolfe (ISW) and Shapiro time-delay effects. For different cosmological probes some of these effects have been already detected, see e.g.~\cite{Ade:2015zua, Ade:2015dva, Scranton:2005ci}. Recently, motivated by the ultra-large scales that will be probed by future surveys, several works~\cite{Yoo:2009,Yoo:2010,Bonvin:2011bg,Challinor:2011bk} have derived a description of galaxy clustering in a relativistic framework. It has been shown that the leading correction to the matter power spectrum, beyond redshift space distortion, arises from the cosmic magnification, see e.g.~\cite{Scranton:2005ci} for a detection and \cite{sachs,Bartelmann:1994ye,Dolag:1997yt,Sanz:1997pw} for the first theoretical predictions. Other relativistic effects have been shown to be negligible with a single tracer analysis~\cite{Yoo:2012se, Yoo:2013zga, Alonso:2015uua}, while multi-tracer techniques~\cite{Seljak:2009} may lead to a detection with future surveys~\cite{Yoo:2012se, Bonvin:2013ogt,Alonso:2015sfa, Fonseca:2015laa, Irsic:2015nla, Gaztanaga:2015jrs,Bonvin:2015kuc}. In galaxy surveys, cosmic magnification affects the number density by changing the solid angle $d\Omega$. At the same time, since galaxy surveys are limited in flux magnitude, some faint galaxies might be enough magnified to be detected and vice-versa. The latter effect is called magnification bias and its amplitude is determined by the slope of the luminosity function. Therefore its amplitude and relevance are survey dependent. This introduces some additional systematics which have to be carefully treated. Several works have already shown its importance for (future) galaxy surveys, see e.g.~\cite{DiDio:2013sea, Montanari:2015rga, Alonso:2015sfa, Cardona:2016qxn,DiDio:2016ykq}. It is well known that the Cosmic Microwave Background (CMB) is not affected by cosmic magnification. Indeed the change in the solid angle $d\Omega$ is exactly compensated by the change in the observed flux, due to surface brightness conservation. The lensing of CMB arises from the deflection angle effect, see the Ref.~\cite{Lewis:2006fu} for a detailed review about CMB lensing. This is a second order effect, but it is amplified being coherently summed along the line of sight, introducing a deflection of few arc minutes. Relativistic number counts beyond linear order have been recently computed~\cite{Yoo:2014sfa,Bertacca:2014dra,DiDio:2014lka,Nielsen:2016ldx} and they include lensing terms due to the deflection angle. These effects have been computed for the tree level bispectrum~\cite{DiDio:2015bua}. As shown in~\cite{DiDio:2015bua}, this contribution is not affected by the slope of the luminosity function (i.e.~magnification bias). At the two-point statistics, the deflection angle effect appears only at higher orders in perturbation theory. Therefore, even if a galaxy catalog is characterized by a luminosity function that compensates the cosmic magnification contribution through the magnification bias, the deflection angle still induces a non-vanishing lensing effect on the observable. In this work we compute, non-perturbatively in the deflection angle, the amplitude of this effect on the Baryonic Acoustic Oscillation (BAO) wiggles of the matter power spectrum in real space. A similar calculation has been already performed for the 2-point correlation function~\cite{Dodelson:2008qc}, while in the CMB framework, an analog calculation has been first done in~\cite{Seljak:1995ve} for the angular power spectrum. Starting from the results of~\cite{Dodelson:2008qc}, we compute the lensed matter power spectrum. We show that the deflection angle smears the BAO wiggles and its effect grows with redshift, becoming larger than the smoothing effect induced by non-linear structure formation for sources at high redshift. We remark that our derivation applies also for 21cm power spectrum, see e.g.~\cite{Mandel:2005xh}. The paper is organized as follows. In Sec.~\ref{sec:deflaction_angle} we define and compute the linear deflection angle, while in Sec.~\ref{sec:PK} we derive the lensed matter power spectrum in real space and we show the smoothing effect on the BAO wiggles. In Sec.~\ref{sec:comparison} we compare the smoothing effect induced by the lensing potential and the non-linear dynamics of gravity. In Sec.~\ref{sec:conclusions} we draw our conclusions. In Appendix~\ref{app:LSS_NG} we compute the corrections induced by the non-Gaussianity of the gravitational potential at late time. In Appendix~\ref{app:a} we present an analog derivation in terms of the redshift dependent angular power spectra, which are well-adapted to include relativistic corrections~\cite{Challinor:2011bk,Bonvin:2011bg}, and we show the amplitude of the correlation between the galaxy number counts and the lensing potential, induced at the linear level by cosmic magnification and magnification bias. All the numerical results shown in the paper are derived with the following cosmological parameters: $h=0.704$, $\Omega_\text{cdm} = 0.226$, $\Omega_\text{b} = 0.045 $, and vanishing curvature. The primordial curvature power spectrum is characterized by $\sigma_8 = 0.81$, the pivot scale $k_\text{pivot} = 0.05 \ \text{Mpc}^{-1}$, the spectral index $n_s = 0.967$ and no running. The matter and the lensing potential power spectra are computed with {\sc class}\footnote{\url{http://class-code.net}}~\cite{Lesgourgues:2011re,Blas:2011rf}. | \label{sec:conclusions} In this work we have studied the smoothing effect on BAO wiggles induced on the matter power spectrum in real space by the lensing potential. The smoothing effect has been computed non-perturbatively, under the assumption that the lensing potential obeys Gaussian statistics. We also have estimated the corrections induced by the non-Gaussian nature of the gravitational potential, showing that it induces a very small effect at the relevant redshifts. We found that lensing introduces a smearing effect with a dispersion of about $1 \ \text{Mpc}$ at BAO scale for sources at redshift $z\sim 2$ or larger. This corresponds to roughly a $1\%$ effect at BAO scale and it is approximately a factor 2 below the lensing effect on the CMB perturbations. It also introduces a minimal resolution, which can be improved only by knowing the lensing potential and by de-lensing the matter power spectrum. By comparing with a no-wiggle power spectrum we have shown the effect on the BAO wiggles. In particular, the lensing potential reduces the amplitude of BAO wiggles, by affecting the matter power spectrum of about $0.1 \%$ at $z\sim 2$ and $0.2 \%$ at $z\sim 4$. For sources at larger redshifts the suppression is even larger. We remind that our results apply also for 21cm matter power spectrum. We have finally compared the smoothing effects on BAO wiggles induced by lensing and by non-linear structure formation. While at low redshift the non-linear dynamics of gravity leads to the dominant smearing effect on the BAO wiggles, the two effects become comparable at $z\sim 4$ and at larger redshifts the lensing effect dominates over the non-linearities. So, if on one hand, sources at high redshift are less affected by non-linearities, on the other hand, they are more sensitive to the smearing effect due to the lensing potential. In the literature lensing effects on LSS observables have been studied in terms of the cosmic magnification. Contrarily to the deflection angle, which we have studied in this work, cosmic magnification enters at first order in perturbation theory. Different works have quantified the amplitude of this effect and stressed its importance for future surveys. Nevertheless, its amplitude depends on the galaxy and magnification biases. Hence its effect can be degenerated with these terms. Whereas, the deflection angle is a purely geometrical effect and it is not degenerate with any bias factors, but it is sensitive only to the metric perturbations through the lensing potential. | 16 | 9 | 1609.09044 |
1609 | 1609.00679_arXiv.txt | We present new high-resolution chemical-abundance analyses for the well-known high proper-motion subdwarfs \g12\ and \g37, based on very high signal-to-noise spectra ($S/N \sim 700/1$) with resolving power $R \sim 95,000$. These high-quality data enable the first {\it reliable} determination of the carbon abundances for these two stars; we classify them as carbon-enhanced metal-poor (CEMP) stars based on their carbonicities, which both exceed [C/Fe] $= +1.0$. They are sub-classified as CEMP-no Group-II stars, based on their location in the Yoon-Beers diagram of absolute carbon abundance, $A$(C) vs. [Fe/H], as well as on the conventional diagnostic [Ba/Fe]. The relatively low absolute carbon abundances of CEMP-no stars, in combination with the high effective temperatures of these two stars (\teff\ $\sim 6500$~K) weakens their CH molecular features to the point that accurate carbon abundances can only be estimated from spectra with very high $S/N$. A comparison of the observed abundance patterns with the predicted yields from massive, metal-free supernova models reduces the inferred progenitor masses by factors of $\sim$ 2-3, and explosion energies by factors of $\sim$ 10-15, compared to those derived using previously claimed carbon abundance estimates. There are certainly many more warm CEMP-no stars near the halo main-sequence turnoff that have been overlooked in past studies, directly impacting the derived frequencies of CEMP-no stars as a function of metallicity, a probe that provides important constraints on Galactic chemical evolution models, the initial mass function in the early Universe, and first-star nucleosynthesis. | \label{intro} The basic cosmological framework suggesting that the chemical evolution of the Universe is a continuous process of nucleosynthesis and mixing of subsequent stellar generations has been in place since the work of \citet{hoyle1954}. In this scenario, the long-lived, low-mass extremely metal-poor \citep[EMP; \metal\footnote{\abund{A}{B} = $log(N_X/{}N_Y) _{\star} - \log(N_X/{}N_Y) _{\odot}$, where $N$ is the number density of atoms of elements $X$ and $Y$ in the star ($\star$) and the Sun ($\odot$), respectively.}~$<-3.0$, e.g.,][]{beers2005,frebel2015} stars observed today were formed from gas that was polluted by the nucleosynthesis products of previous generations of (likely massive) stars, also known as Population III (Pop III). The proposed existence of massive Pop III stars is not new \citep[e.g., ][]{puget1980}; the first comparison between the theoretical yields of Pop III stars and observed elemental abundances of very metal-poor stars was made by \citet{nomoto1999}. Since then, there has been significant advances in our understanding of the underlying physics of first-generation stars, and different classes of models are able to well-reproduce observations of EMP stars in the Galaxy \citep[see][for a brief summary]{placco2016}. Despite the fact that the elemental-yield predictions of first-star nucleosynthesis differ somewhat between various authors, they all agree that the light element carbon plays a central role at early times. Indeed, the majority of the long-lived relics of the chemical evolution in the early Universe are expected to be heavy-metal deficient, but carbon enhanced \citep{frebel2007b}. Such stars, which once were considered an {\it{Astrophysical Enigma}} by \citet{bidelman1956}\footnote{The author states ``{\it{The spectra of these objects show extremely strong absorption features due to CH, and considerably weaker lines of neutral metals than do the typical carbon stars.}}''}, today are known as carbon-enhanced metal-poor (CEMP) stars, following recognition of their existence at the lowest metallicities by \citet{beers1992}. Although carbon-enhanced Solar-metallicity stars were first identified almost 75 years ago \citep{keenan1942}, the majority of early spectral catalogs contained only cooler (\teff~$< 4500$~K) carbon stars with strong molecular features \citep{kamijo1959}. One of the first attempts to determine carbon abundances for warmer (\teff$> 5500$~K), low-metallicity stars came some twenty years later \citep{peterson1978}. This study only considered stars of relatively higher metallicity (\metal~$>-2.3$), since few stars were known below this abundance at the time. Nevertheless, it showed that, even when the carbon abundance ratio relative to iron \citep[carbonicity;][]{placco2011} of a given star is high (\cfe~$>+1.0$), the CH molecular features around 4300\,{\AA}\ can be quite weak at these temperatures, present at less than 2\% of the continuum level for \teff\ = 6500~K. As a result, reliable carbonicity determinations for warm stars are biased towards relatively bright stars, where the $S/N$ required to detect such small deviations from the continuum can be obtained with reasonable integration times. \begin{deluxetable*}{lrrrrrrrrrr}[!ht] \tablewidth{40pc} \tabletypesize{\small} \tablecaption{Final Abundance Estimates for \protect\g12\ and \protect\g37. \label{abfinal}} \tablehead{ && \multicolumn{4}{c}{\g12} & & \multicolumn{4}{c}{\g37} \\ \cline{3-6} \cline{8-11} Ion & $\log\epsilon_{\odot}$\,(X) & $\log\epsilon$\,(X) & $\mbox{[X/H]}$ & $\mbox{[X/Fe]}$ & $\sigma$ & & $\log\epsilon$\,(X) & $\mbox{[X/H]}$ & $\mbox{[X/Fe]}$ & $\sigma$ } \startdata \ion{Li}{1} & 1.05 & 2.36 & $+$1.31 & $+$4.59 & 0.04 && 2.25 & $+$1.20 & $+$4.31 & 0.03 \\ C (CH) & 8.43 & 6.21 & $-$2.22 & $+$1.07 & 0.05 && 6.44 & $-$1.99 & $+$1.12 & 0.05 \\ \ion{O }{1} & 8.69 & 6.58 & $-$2.11 & $+$1.17 & 0.07 && 6.59 & $-$2.10 & $+$1.00 & 0.03 \\ \ion{Na}{1} & 6.24 & 2.87 & $-$3.37 & $-$0.09 & 0.03 && 2.92 & $-$3.32 & $-$0.21 & 0.03 \\ \ion{Mg}{1} & 7.60 & 4.79 & $-$2.80 & $+$0.48 & 0.07 && 4.87 & $-$2.73 & $+$0.38 & 0.07 \\ \ion{Al}{1} & 6.45 & 2.56 & $-$3.90 & $-$0.61 & 0.05 && 2.63 & $-$3.82 & $-$0.71 & 0.05 \\ \ion{Si}{1} & 7.51 & 4.06 & $-$3.45 & $-$0.16 & 0.04 && 4.11 & $-$3.40 & $-$0.29 & 0.03 \\ \ion{Ca}{1} & 6.34 & 3.56 & $-$2.78 & $+$0.50 & 0.03 && 3.64 & $-$2.70 & $+$0.41 & 0.03 \\ \ion{Sc}{2} & 3.15 & 0.03 & $-$3.12 & $+$0.17 & 0.06 && 0.20 & $-$2.95 & $+$0.15 & 0.05 \\ \ion{Ti}{1} & 4.95 & 2.40 & $-$2.55 & $+$0.74 & 0.05 && 2.53 & $-$2.42 & $+$0.69 & 0.04 \\ \ion{Ti}{2} & 4.95 & 2.19 & $-$2.76 & $+$0.52 & 0.09 && 2.34 & $-$2.61 & $+$0.50 & 0.07 \\ \ion{Cr}{1} & 5.64 & 2.27 & $-$3.37 & $-$0.09 & 0.05 && 2.50 & $-$3.14 & $-$0.03 & 0.04 \\ \ion{Mn}{1} & 5.43 & 1.50 & $-$3.93 & $-$0.65 & 0.05 && 1.77 & $-$3.66 & $-$0.55 & 0.04 \\ \ion{Fe}{1} & 7.50 & 4.21 & $-$3.29 & 0.00 & 0.04 && 4.39 & $-$3.11 & 0.00 & 0.03 \\ \ion{Fe}{2} & 7.50 & 4.26 & $-$3.24 & $+$0.05 & 0.06 && 4.45 & $-$3.05 & $+$0.05 & 0.04 \\ \ion{Co}{1} & 4.99 & 2.10 & $-$2.89 & $+$0.40 & 0.05 && 2.23 & $-$2.76 & $+$0.35 & 0.05 \\ \ion{Ni}{1} & 6.22 & 2.95 & $-$3.27 & $+$0.02 & 0.03 && 3.17 & $-$3.05 & $+$0.06 & 0.02 \\ \ion{Zn}{1} & 4.56 & 1.80 & $-$2.76 & $+$0.52 & 0.03 && 1.92 & $-$2.64 & $+$0.47 & 0.02 \\ \ion{Sr}{2} & 2.87 & $-$0.34 & $-$3.21 & $+$0.07 & 0.06 && $-$0.19 & $-$3.06 & $+$0.05 & 0.04 \\ \ion{Ba}{2} & 2.18 & $-$1.17 & $-$3.35 & $-$0.07 & 0.06 && $-$1.28 & $-$3.46 & $-$0.36 & 0.04 \enddata \end{deluxetable*} The recognition that carbon-enhanced stars occur with higher frequency at lower metallicities extends back over two decades \citep[e.g.,][and references therein]{beers1992}. Subsequent observations of metal-poor stars using medium- and high-resolution spectroscopy has confirmed that the fractions of CEMP stars increases from $\sim 15-20$\% for \metal~$ < -2.0$ to more than 80\% for \metal~$ < -4.0$ \citep{lee2013, placco2014c}, prima facia observational evidence that carbon is an important contributor to the chemical evolution of the early Universe. Among the various sub-classes of CEMP stars \citep{beers2005}, the CEMP-no stars (which exhibit no enhancements in their neutron-capture elements, e.g., \xfe{Ba} $ < 0.0$) are believed to have formed from gas polluted by the nucleosynthesis products of massive stars, perhaps including Pop III progenitors. Even though the low abundances of neutron-capture elements (such as Ba) is a feature of such stars, it has been recently suggested by \citet{yoon2016}, building on the work of \citet{spite2013} and \citet{bonifacio2015}, that the absolute carbon abundance ($A$(C) $ = \log\,\epsilon $(C)) is a sufficient (and likely more fundamental) criterion to distinguish CEMP-no stars from the far more populous sub-class of CEMP-$s$ stars (where the carbon enhancement arises due to mass transfer from a binary asymptotic giant-branch stellar companion). This new criterion is particularly useful for warmer CEMP stars, where measurement of [Ba/Fe] can prove challenging. In this paper, we present the first confirmation that the well-studied subdwarfs \g12\ and \g37\ are in fact CEMP-no stars. Even though these stars have been considered by numerous previous authors, accurate determinations of their carbon abundances was limited by the quality of the available spectra. It is highly likely that other warm low-metallicity stars have been incorrectly classified as ``carbon-normal,'' a deficiency that must be addressed in the future. This paper is outlined as follows: Section~\ref{secobs} describes the spectroscopic data used in this work, and presents the elemental-abundance estimates obtained for \g12\ and \g37\ from our very high-quality data. Section~\ref{disc} considers the consequences of properly classifying warm CEMP-no stars on our understanding the nature of their progenitors, and on the derived CEMP fractions as a function of metallicity. Our conclusions are provided in Section~\ref{final}. | \label{final} In this letter we have provided conclusive evidence that the well-known and extensively studied EMP subdwarfs \g12\ and \g37\ are in fact CEMP-no Group-II stars, based on high-resolution, extremely high signal-to-noise data from KECK/HIRES. Both are members of the outer-halo population and are single stars, properties that have been demonstrated to be associated with CEMP-no stars \citep{carollo2014,hansen2016}. Many more examples of warm CEMP-no stars near the halo main-sequence turnoff that have been previously claimed as carbon-normal stars are likely to be found in future investigations. We have also shown that under-estimates of the carbon abundances for such stars can have large affects on the inferred progenitor masses and explosion energies of CEMP-no stars. Future studies of the frequencies of CEMP-no stars as a function of metallicity will need to consider this result as well; existing frequency estimates based on samples including stars with effective temperatures $\gtrsim 5750$~K likely under-estimate the true fractions of CEMP-no stars. | 16 | 9 | 1609.00679 |
1609 | 1609.00023_arXiv.txt | We present a population study of the star formation history of $1244$ Type 2 AGN host galaxies, compared to $6107$ inactive galaxies. A Bayesian method is used to determine individual galaxy star formation histories, which are then collated to visualise the distribution for {\Rfive quenching and quenched galaxies within} each population. We find evidence for {\Rfive some of} the Type 2 AGN host galaxies having undergone a rapid drop in their star formation rate within the last 2 Gyr. AGN feedback is therefore important at least for this population of galaxies. This result is not seen for the {\Rfive quenching and quenched} inactive galaxies whose star formation histories are dominated by the effects of downsizing at earlier epochs, a secondary effect for the AGN host galaxies. We show that histories of rapid quenching cannot account fully for the quenching of all the star formation in a galaxy's lifetime across the population of {\Rfive quenched} AGN host galaxies, and that histories of slower quenching, attributed to secular (non-violent) evolution, are also key in their evolution. This is in agreement with recent results showing both merger-driven and non-merger processes are contributing to the co-evolution of galaxies and supermassive black holes. The availability of gas in the reservoirs of a galaxy, and its ability to be replenished, appear to be the key drivers behind this co-evolution. \\ \\{\bf Keywords:} galaxies: evolution $-$ galaxies: statistics $-$ galaxies: active $-$ galaxies: Seyfert $-$ galaxies: photometry | The nature of the observed co-evolution of galaxies and their central supermassive black holes \citep{Mag98, MH03, HR04} and the effects of AGN feedback on galaxies are two of the most important open issues in galaxy evolution. AGN feedback was first suggested as a mechanism for regulating star formation in simulations \citep{SR98, Croton06, Bower06, Somer08} and indirect evidence has been observed for both positive and negative feedback in various systems (see the comprehensive review from \citealt{Fab06}). The strongest observational evidence for AGN feedback in a population is that the largest fraction of AGN are found in the green valley \citep{CB08, Hickox09, Sch2010}, suggesting some link between AGN activity and the process of quenching which moves a galaxy from the blue cloud to the red sequence. However, concrete statistical evidence for the effect of AGN feedback on the host galaxy population has so far been elusive. \begin{figure*} \includegraphics[width=\textwidth]{fig1.pdf} \caption{Randomly selected SDSS \emph{gri} composite images from the sample of $1,244$ Type 2 AGN in a redshift range $0.04 < z < 0.05$. The galaxies are ordered from least to most featured according to their debiased `disc or featured' vote fraction, $p_d$ (see \citealt{GZ2}). The scale for each image is $0.099~\rm{arcsec/pixel}$.} \label{mosaic} \end{figure*} Here we present a large observational population study of the {\Rfive star formation histories (SFH)} of Type 2 AGN host galaxies. We use a new Bayesian method \citep{Sme2015} to effectively determine the most probable SFH of a galaxy, modelled with two parameters, time of quenching, $t_q$, and exponential rate, $\tau$, given the observed near ultra-violet (NUV) and optical colours. {\changed This builds on the work of \citet{Martin07} and \citet{Sch2014}, but improves significantly on previous techniques. We} aim to determine the following: (i) Are galaxies currently hosting an AGN undergoing quenching? (ii) If so, when and at what rate does this quenching occur? (iii) Is this quenching occurring at different times and rates compared to a control sample of inactive galaxies? The zero points of all magnitudes are in the AB system. Where necessary, we adopt the WMAP Seven-Year Cosmology (Jarosik et al. 2011) with $(\Omega_m , ~\Omega_\Lambda , ~h) = (0.26, 0.73, 0.71)$. | \label{dis} The differences between the {\secondchange population density distributions} of the \textsc{agn-host} and \textsc{inactive} populations reveal that an AGN can have a significant effect on the SFH of its host galaxy. Both recent, rapid quenching and early, slow quenching are observed in the {\secondchange population density} {\Rfive within} the \textsc{agn-host} population. {\changed There are minimal differences between the smooth and disc weighted distributions of the quenching parameters {\Rfive within} the \textsc{agn-host} population. This is agreement with the conclusions of \citet*{Kauff03b} who found that the structural properties of AGN hosts depend very little on AGN power. } The difference between the \textsc{agn-host} and \textsc{inactive} {\secondchange population distributions} in Figure~\ref{rate} for the rate of quenching, $\tau$, tells a story of gas reservoirs. The {\secondchange density distribution} for higher mass \textsc{agn-host} galaxies is dominated by slow, early quenching implying another mechanism is responsible for the cessation of star formation {\Rfive within} {\Rfour a proportion of} these high mass galaxies prior to the triggering of the current AGN. This preference for slow evolution timescales follows from the ideas of previously isolated discs evolving slowly by the Kennicutt-Schmidt \citep{Schmidt59, Kennicutt97} law which can then undergo an interaction or merger to reinvigorate star formation, feed the central black hole and trigger an AGN \citep{Varela04, Em15}. These galaxies would need a large enough gas reservoir to fuel both SF throughout their lifetimes and the recent AGN. These high mass galaxies also play host to the most luminous AGN (mean $\log (L[OIII] ~[\rm{erg}~s^{-1}]) \sim 41.6$) and so this SFH challenges the usual explanation for the co-evolution of luminous black holes and their host galaxies driven by merger growth. Quenching at early times is also observed {\Rfive within} a subsample of the \textsc{inactive} population, where the {\secondchange density} for the quenching time is roughly constant until recent times where the distribution drops off. {\changed This drop-off occurs at earlier times with increasing mass with a significant lack of quenching occurring at early times for low mass \textsc{inactive} galaxies} (right panels Figure~\ref{time}). This is evidence of downsizing {\Rfive within} the \textsc{inactive} galaxy population whereby stars in massive galaxies form first and quench early \citep{Cowie96, Thomas10}. {\Rfour Some of the} most massive \textsc{agn-host} galaxies also show a preference for earlier quenching (bottom left panel Figure~\ref{time}) occurring at slow rates; we speculate that this is also due to the effects of downsizing rather than being caused by the current AGN. This earlier evolution would first form a slowly `dying' or `dead' galaxy typical of massive elliptical galaxies which can then have a recent infall of gas either through a minor merger, galaxy interaction or environmental change, triggering further star formation and feeding the central black hole, triggering an AGN \citep{Kav14}. In turn this AGN can then quench the recent boost in star formation. This track is similar to the evolution history proposed for blue ellipticals \citep{Kav13, McIntosh14, Haines15}. This SFH would then give rise to the distribution seen {\Rfive within} the high mass \textsc{agn-host} population for both time and rate parameters. These recently triggered AGN in both massive disc and smooth galaxies do not have have the ability to impact the SF across the entirety of a high mass galaxy in a deep gravitational potential \citep{Ish12, Zinn13}. This leads to the lower peak for recent, rapid quenching {\Rfive within} the high mass \textsc{agn-host} population for both morphologies. Conversely, rapid quenching, possibly caused by the AGN itself through negative feedback, is the most dominant history {\Rfive within} the low mass \textsc{agn-host} population with lower gravitational potentials from which gas may be more readily expelled or heated \citep{Torbra09}. \cite{Torbra09} model the effects of jet-induced AGN feedback on a typical early type (i.e. smooth) galaxy {\changed and observe a drastic suppression of star formation on a timescale of $\sim 3 ~\rm{Myr}$. Comparing their synthetic colours with observed colours of SDSS elliptical galaxies, they} find the time between the current galaxy age, $t_\mathrm{gal}$ and the time that the feedback began, $t_\mathrm{AGN}$, peaks at $t_\mathrm{gal} - t_\mathrm{AGN} \sim 0.85 ~\rm{Gyr}$. This agrees with the location of the peak in Figure~\ref{time} for low mass galaxies {\Rfive which have undergone quenching}, where the difference between the peak of the {\secondchange distribution} and the average age of the population ({\secondchange galaxy age is calculated as the age of the Universe at the observed redshift}, by assuming all galaxies form at $t=0$) is $\sim0.83 ~\rm{Gyr}$. This implies that this SFH dominated by recent quenching is caused directly by negative AGN feedback. {\changed However, there still remains the possibility that the AGN is merely a consequence of an alternative quenching mechanism. This idea is supported by simulations showing that the exhaustion of gas by a merger fuelled starburst could cause such a rapid quench in star formation and in turn also trigger an AGN \citep{Croton06, Wild09, Snyder11, Hayward14}. \citet{Yesuf14} also showed that AGN are more commonly hosted by post starburst galaxies, with the peak AGN activity appearing $\geq 200 \pm 100 ~\rm{Myr}$ after the starburst. Such a SFH is not accounted for in the models presented here, however this scenario is still consistent with the results presented in this paper; that AGN which are \emph{currently} active have been detected in host galaxies $\sim 1~\rm{Gyr}$ after the onset of quenching.} This rapid quenching is particularly dominant for low-to-medium mass smooth galaxies. \cite{Sme2015} suggest that incredibly rapid quenching rates could be attributed to mergers of galaxies in conjunction with AGN feedback, which are thought to be responsible for creating the most massive smooth galaxies \citep{Con03, SdMH05, Hopkins08}. This dominance of rapid quenching across the smooth \textsc{agn-host} population supports the idea that a merger, having caused a morphological transformation to a smooth galaxy, can also trigger an AGN, causing feedback and cessation of star formation (\citealt{Sanders88}). {\Rfive Within} the medium mass \textsc{agn-host} population we see a bimodal distribution between these two quenching histories, highlighting the strength of this method which is capable of detecting such variation in the SFHs {\Rfive within} a population of galaxies. {\Rfive Indeed not all galaxies in the \textsc{agn-host} and \textsc{inactive} samples are quenching, as seen in Figure \ref{cmdsfms}, with a significant proportion of both the \textsc{agn-host} and \textsc{inactive} samples lying on the star forming sequence. A galaxy can therefore still maintain star formation whilst hosting an AGN. The results presented in Section \ref{results} only reflect the trends for galaxies that have undergone or are currently undergoing quenching within a population and can therefore be accurately fit by an exponentially declining SFH. This prevalence of star forming AGN host galaxies, combined with the results above allows us to consider that either: (i) the AGN are the cause of the rapid quenching observed but only in gas-poor host galaxies where they can have a large impact, (ii) the AGN are a consequence of another quenching mechanism but can also be triggered by other means which do not cause quenching, or (iii) the SFR of a galaxy can recover post-quench and return to the star forming sequence after a few Gyr (see recent simulations by \citealt{Pontzen16}). Further investigation will therefore be required to determine the nature of this quenching.} \\ \\ We have used morphological classifications from the Galaxy Zoo 2 project to determine the morphology-dependent SFHs of a population of $1,244$ Type 2 Seyfert AGN host galaxies, in comparison to an inactive galaxy population, via a {\secondchange partially} Bayesian analysis of an exponentially declining SFH model. We determined the {\secondchange population distribution} for the quenching onset time, $t_q$, and exponential quenching rate, $\tau$, and find clear differences in the {\secondchange distributions}, between inactive and AGN host galaxy populations. We have demonstrated a clear dependence on a galaxy currently hosting an AGN and its {\Rfive SFH for those galaxies which have undergone or are undergoing quenching}. There is strong evidence for downsizing in massive inactive galaxies, which appears as a secondary effect in AGN host galaxies. The dominant mechanism for {\Rfive quenched and quenching} galaxies currently hosting an AGN is for rapid quenching which has occurred very recently. This result demonstrates the importance of AGN feedback {\Rfive within} the host galaxy population, in driving the evolution of galaxies across the colour-magnitude diagram. | 16 | 9 | 1609.00023 |
1609 | 1609.07435_arXiv.txt | We present optical and near-infrared spectroscopy of WISEA J061543.91$-$124726.8, which we rediscovered as a high motion object in the AllWISE survey. The spectra of this object are unusual; while the red optical ($\lambda >$ 7,000 \AA) and near-infrared spectra exhibit characteristic TiO, VO, and H$_{2}$O bands of a late-M dwarf, the blue portion of its optical spectrum shows a significant excess of emission relative to late-M type templates. The excess emission is relatively featureless, with the exception of a prominent and very broad Na I D doublet. We find that no single, ordinary star can reproduce these spectral characteristics. The most likely explanation is an unresolved binary system of an M7 dwarf and a cool white dwarf. The flux of a cool white dwarf drops in the optical red and near-infrared, due to collision-induced absorption, thus allowing the flux of a late-M dwarf to show through. This scenario, however, does not explain the Na D feature, which is unlike that of any known white dwarf, but which could perhaps be explained via unusual abundance or pressure conditions. | The study and census of our Solar neighborhood is important to advance our understanding of low mass stars and brown dwarfs, which are the most numerous known objects in the Galaxy. As such they shed light on the low-end of the initial mass function, and on star formation efficiency. The search for our nearest neighbors lets us study objects in great detail, because they are the closest, brightest objects of their class. The detailed study of late-type dwarfs, brown dwarfs, subdwarfs, and white dwarfs has historically relied on the identification of objects based on their optical through mid-infrared colors. These studies have been enhanced by recent surveys for high proper motion objects, because these surveys have no color bias, and can therefore identify objects with unusual characteristics not found through color-based searches. The object 2MASS J06154357$-$1247221 = WISEA J061543.91$-$124726.8, which we henceforth designate WISEA 0615$-$1247, was originally discovered as a high proper motion star by L\'{e}pine (2008) and designated by him as PM I06157$-$1247 in a re-analysis of southern hemisphere digitized sky surveys. L\'{e}pine (2008) finds proper motion components for WISEA 0615$-$1247 of $\mu_{\alpha} =$ 452 $\pm$ 10 mas\, yr$^{-1}$, and $\mu_{\delta} = -$421 $\pm$ 10 mas\, yr$^{-1}$ from measurements spanning an epoch range of 39.2 years (see Table 1). The object was rediscovered by Kirkpatrick et al.\ (2014) due to its high motion in the AllWISE Data Release of the Wide-Field Infrared Survey Explorer ({\it WISE}; Wright et al.\ 2010). The colors of the object, namely $J - K_{s} =$ 0.937 $\pm$ 0.058 mag, from the Two Micron All-Sky Survey (2MASS; Skrutskie 1997), and $J - W2 =$ 1.685 $\pm$ 0.040 mag (from 2MASS $J$ and the {\it WISE} 4.6 $\mu$m bandpass $W2$; see Table 1), are shown as the red symbol in Figure~\ref{fig1}. This figure compares these colors with those of 47,936 high motion sources (Kirkpatrick et al.\ 2014, 2016). WISEA 0615$-$1247 lies $\sim$ 0.2 mag below or blueward in $J - K_{s}$ color relative to the normal sequence of field objects, possibly hinting at a cool subdwarf nature. Early-L subdwarfs have colors $J - W2$ ranging from 1.1 to 1.8 mag, and $J - K_{s}$ on average 0.23 mag below the normal sequence of field objects (see Figure 7 in Kirkpatrick et al.\ 2016). The suggested sub-dwarf classification of the object is similar to that by L\'{e}pine (2008), based on the reduced proper motion of the object in the $V$ bandpass. In order to elucidate the nature of the object, we obtained optical and near-infrared spectroscopy. The spectrum, as discussed below, proved to be unique. We propose a binary scenario that we believe best explains the observed data, although it invokes a cool white dwarf companion unlike any heretofore cataloged. | We propose that WISEA 0615$-$1247 is an unresolved binary consisting of an M7 dwarf and a cool white dwarf, the latter having an SED unlike any other cool white dwarf currently known. We speculate that the cool white dwarf produces the observed Na I D absorption feature, if Na abundance is high, and if pressure broadening is less than in other known cool white dwarfs. Additional studies of this fascinating system are warranted, including an accurate trigonometric parallax measurement. \clearpage | 16 | 9 | 1609.07435 |
1609 | 1609.01739_arXiv.txt | We use the \eagle\ cosmological hydrodynamic simulation suite to study the specific angular momentum of galaxies, $j$, with the aims of (i) investigating the physical causes behind the wide range of $j$ at fixed mass and (ii) examining whether simple, theoretical models can explain the seemingly complex and non-linear nature of the evolution of $j$. We find that $j$ of the stars, $j_{\rm stars}$, and baryons, $j_{\rm bar}$, are strongly correlated with stellar and baryon mass, respectively, with the scatter being highly correlated with morphological proxies such as gas fraction, stellar concentration, (u-r) intrinsic colour, stellar age and the ratio of circular velocity to velocity dispersion. We compare with available observations at $z=0$ and find excellent agreement. We find that $j_{\rm bar}$ follows the theoretical expectation of an isothermal collapsing halo under conservation of specific angular momentum to within $\approx 50$\%, while the subsample of rotation-supported galaxies are equally well described by a simple model in which the disk angular momentum is just enough to maintain marginally stable disks. We extracted evolutionary tracks of the stellar spin parameter of \eagle\ galaxies and found that the fate of their $j_{\rm stars}$ at $z=0$ depends sensitively on their star formation and merger histories. From these tracks, we identified two distinct physical channels behind low $j_{\rm stars}$ galaxies at $z=0$: (i) galaxy mergers, and (ii) early star formation quenching. The latter can produce galaxies with low $j_{\rm stars}$ and early-type morphologies even in the absence of mergers. | The formation of galaxies can be a highly non-linear process, with many physical mechanisms interacting simultaneously (see reviews by \citealt{Baugh06,Benson10b}). Notwithstanding all that potential complexity, early studies of galaxy formation stressed the importance of three quantities to describe galaxies: mass, $M$, angular momentum, $J$, and energy, $E$ \citep{Peebles69,Doroshkevich70,Fall80,White84}; or alternatively, one can define the specific angular momentum, $j\equiv J/M$, which contains information on the scale length and rotational velocity of systems. It is therefore intuitive to expect the relation between $j$ and $M$ to contain fundamental information.% Studies such as \citet{Fall80}, \citet{White91}, \citet{Catelan96a} and \citet{Mo98}, showed that many properties of galaxies, such as flat rotation curves, and the Tully-Fisher relation could be obtained in the Cold Dark Matter (CDM) framework if $j$ of baryons is similar to that of the halo and is conserved in the process of disk formation (although conservation does not need to be strict, but within a factor of $\approx 2$; \citealt{Fall83}). The situation is of course different for the mass and energy of galaxies, which can vary significantly throughout their evolution due to accretion, star formation and dissipative processes, such as galaxy mergers. Theoretical models of how $j$ of halos evolves in a CDM universe predict $j\propto \lambda\,M^{2/3}$, where $\lambda$ is the spin parameter of the halo (e.g. \citealt{White84}; \citealt{Catelan96a}; \citealt{Mo98}). If $j$ of baryons is conserved throughout the formation of galaxies, then a similar relation should apply to galaxies. These models generally assume that halos collapse as their spherical overdensity reaches a threshold value, and in that sense neglect mergers. Due to the dissipative nature of the latter, one would expect significant changes in the relation between $j$ and $M$ of halos and galaxies \citep{Zavala08,Sales12,Romanowsky12}. Hydrodynamic simulations used to suffer from catastrophic loss of angular momentum, producing galaxies that were too compact and too low $j$ compared to observations \citep{Steinmetz99,Navarro00}. This problem was solved by improving the spatial resolution and including efficient feedback (e.g. \citealt{Kaufmann07}; \citealt{Zavala08}; \citealt{Governato10}; \citealt{Guedes11}; \citealt{Danovich15}). A new generation of simulations have immensely improved in spatial resolution, volume and sophistication of the sub-grid physics included, allowing the study of angular momentum loss in galaxies statistically. For example, simulations such as \eagle\ \citep{Schaye14}, Illustris \citep{Vogelsberger14} and Horizon-AGN \citep{Dubois14} achieve spatial resolutions of $\approx 700\,\rm pc$ (physical units), volumes of $(100\,\rm Mpc)^3$, and include models for metal cooling, star formation and stellar and active galactic nucleus (AGN) feedback. These simulations contain thousands of galaxies with stellar masses $>10^{10}\,\rm M_{\odot}$. Observationally, \citet{Fall83} presented the first study of the relation between $j$ of the stellar component, $j_{\rm stars}$, and stellar mass. \citet{Fall83} found that both spiral and elliptical galaxies follow a relation that is close to $j\propto M^{2/3}$, but with spiral galaxies having a normalisation $\approx 5$ times larger than elliptical galaxies. Recently, this was extended by \citet{Romanowsky12} and \citet{Fall13} in a sample of $\approx 100$ galaxies. These studies confirmed that the power-law index of the relation was close to $2/3$ for their entire galaxy population and that ellipticals galaxies had significantly lower $j$ than spiral galaxies at a given mass. \citet{Obreschkow14b} presented the most accurate measurements of $j$ in the stellar, neutral gas and total baryon components of galaxies out to large radii ($\approx 10$ times the disk scale length) in a sample of $16$ late-type galaxies of the HI Nearby Galaxy Survey (THINGS; \citealt{Walter08}) and found (i) galaxies follow a relation close to $j_{\rm stars} \propto M^{2/3}_{\rm stars}$ and $j_{\rm bar} \propto M^{2/3}_{\rm bar}$, where $M_{\rm stars}$, $M_{\rm bar}$ and $j_{\rm bar}$ are the stellar mass, baryon mass (stars plus neutral gas) and baryon specific angular momentum respectively, (2) the scatter in the $j_{\rm bar}$-$M_{\rm bar}$ and $j_{\rm stars}$-$M_{\rm stars}$ relations is strongly correlated with the bulge-to-total stellar mass ratio and the neutral gas fraction (neutral mass divided by baryon mass; $f_{\rm gas, neutral}$). By fixing the bulge-to-total stellar mass ratio, \citet{Obreschkow14b} found that $j_{\rm bar} \propto M_{\rm bar}$. Using the \citet{Toomre64} stability model, surface density of the gas in galaxies and a flat exponential disk, \citet{Obreschkow16} found that the atomic gas fraction in galaxies is $\propto (j_{\rm bar}/M_{\rm bar})^{1.12}$. \citet{Obreschkow14b} argued that under the assumption that bulges in spiral galaxies form through disk instabilities, one could understand the relation between $j_{\rm stars}$, stellar mass and bulge-to-total stellar mass ratio from the model above. \citet{Stevens16}, using a semi-analytic model, showed that disk instabilities play a major role in regulating the $j_{\rm stars}-M_{\rm stars}$ sequence for spiral galaxies, consistent with the picture of \citet{Obreschkow14b}. To measure $j$ accurately in galaxies, requires spatially resolved kinematic information. The pioneering work of the SAURON \citep{Bacon01} and ATLAS$^{\rm 3D}$ \citep{Cappellari11} surveys, on samples of galaxies that comprised $260$ early-type galaxies in total, showed that the stellar kinematics and distributions of stars are not strongly correlated, and thus morphology is not necessarily a good indicator of the dynamics of galaxies \citep{Krajnovic13}. Based on these surveys, \citet{Emsellem07,Emsellem11} coined the terms {\it slow} and {\it fast} rotators, and proposed the $\lambda_{\rm R}$ parameter, which measures how rotationally or dispersion-dominated a galaxy is and is closely connected to $j_{\rm stars}$, as a new, improved scheme to classify galaxies. \citet{Naab14} showed later that such a classification is also applicable for galaxies in hydrodynamic simulations. Unfortunately, accurate measurements of $j$ have only been presented for a few hundred galaxies. The future, however, is bright: the advent of integral field spectroscopy (IFS) and the new generation of radio and millimeter telescopes promises a revolution in the field. Currently, the Sydney-AAO Multi-object Integral field spectrograph (SAMI; \citealt{Croom12}) survey is observing $\approx 3,200$ galaxies for which resolved kinematics will be available \citep{Bryant15}. Similarly, high-resolution radio telescopes, such as the Square Kilometre Array (SKA), promise to collect information that would allow the measurement of $j$ for few thousand galaxies during its first years \citep{Obreschkow15b}, truly revolutionising our understanding of the build-up of angular momentum in galaxies. \citet{Cortese16} presented the first measurements of the $j_{\rm stars}$-$M_{\rm stars}$ relation for $297$ galaxies in SAMI, and found that, for the entire sample and for a relation of the form $j_{\rm stars}\propto M^{\alpha}_{\rm stars}$, $\alpha\approx 0.7$, close to the theoretical expectation of $2/3$, but when studied in subsamples of different morphological types $\alpha$ varies from $0.69$ for elliptical galaxies to $0.97$ for spiral galaxies. Cortese et al. found that the dispersion of the $j_{\rm stars}-M_{\rm stars}$ relation is correlated with morphological proxies such as S\'ersic index and light concentration. These new results have not yet been examined in simulations. In this paper we explore two long-standing open questions of how $j$ evolves in galaxies: (i) how does $j$ depend with mass, and what are the most relevant secondary galaxy properties, and (ii) how well do simple, theoretical models explain the evolution of $j$ in a complex, non-linear hydrodynamical simulations. In our opinion, \eagle\ is the ideal testbed for this experiment due to the spatial resolution achieved, the large volume that allows us to statistically assess these relations and also the growing amount of evidence that the simulation produces a realistic galaxy population. For instance, \eagle\ reproduces well the relations between star formation rate (SFR) and stellar mass (\citealt{Furlong14}; \citealt{Schaye14}), the colour bi-modality of galaxies (\citealt{Trayford15,Trayford16}), the molecular and atomic gas fractions as a function of stellar mass (\citealt{Lagos15}; \citealt{Bahe15}; \citealt{Crain16}), and the co-evolution of stellar mass, SFR and gas \citep{Lagos15b}. So far, simulations have been used to test theoretical models for the evolution of angular momentum. For instance, \citet{Zavala15} presented a study of the build-up of angular momentum of the stars, cold gas and dark matter in \eagle, and showed that disks form mainly after the {\it turnaround} epoch (epoch of maximum expansion of halos, after which they collapse into virialised structures, approximately conserving specific angular momentum) while bulges formed before turnaround, explaining why bulges have much lower $j$. \citet{Zavala15} also compared the $j_{\rm stars}$-$M_{\rm stars}$ relation for \eagle\ galaxies at $z=0$ with the observations of \citet{Romanowsky12} and found general agreement. \citet{Teklu15} and \citet{Pedrosa15} also found that that the positions of galaxies in the $j_{\rm stars}$-$M_{\rm stars}$ relation is correlated with the bulge-to-total stellar mass ratio in the Magneticum and Fornax simulations, respectively. Similarly, \citet{Genel15} presented an analysis of the effect of baryon processes on the $j_{\rm stars}$-$M_{\rm stars}$ relation in the Illustris simulation and confirmed previous results that feedback is a key process preventing catastrophic angular momentum loss. Here we investigate several galaxy properties that have been theoretically and/or empirically proposed to be relevant for the relationship between $j$ and mass in \eagle, and extend previous work by exploring a larger parameter space of galaxy properties that could determine the positions of galaxies in the $j$-mass relation of different baryonic components of galaxies. We also perform the most, to our knowledge, comprehensive comparison between hydrodynamic simulations and observations of $j$ to date. This paper is organised as follows. In $\S$~\ref{EagleSec} we give a brief overview of the simulation, and describe how the dynamic and kinematic properties of galaxies used in this paper are calculated. In $\S$~\ref{theoryback} we give a theoretical background that we then use to interpret our results. In $\S$~\ref{jz0sec} we explore the dependence of $j$ on galaxy properties at $z=0$ and present a comprehensive comparison with observations. {In $\S$~\ref{StructureEvolution} we analyse in detail the evolution of $j$ of the different baryonic components of galaxies, and identify average evolutionary tracks of $j_{\rm stars}/M^{2/3}_{\rm stars}$.} Here we also compare the evolution of $j$ in \eagle\ with simple, theoretical models to study how closely these models can reproduce the trends seen in \eagle. We discuss our results and present our conclusions in $\S$~\ref{ConcluSec}. In Appendix~\ref{ConvTests} we present `weak' and `strong' convergence tests (terms introduced by \citealt{Schaye14}), and in Appendix~\ref{ScalingRelations} we present additional scaling relations between the specific angular momentum of stars and baryons and other galaxy properties. | We presented a comprehensive study of how $j$ of the stellar, baryon and neutral gas components of galaxies, depend on galaxy properties using the \eagle\ hydrodynamic simulation. Our main findings are: \begin{itemize} \item In the redshift range studied, $0\le z\le3$, galaxies having higher neutral gas fractions, lower stellar concentrations, younger stellar ages, bluer $\rm (u^*-r^*)$ colours and higher $V_{\rm rot}/\sigma_{\rm stars}$ have higher $j_{\rm stars}$ and $j_{\rm bar}$ overall. All the properties above are widely used as proxies for the morphologies of galaxies, and thus we can comfortably conclude that late-type galaxies in \eagle\ have higher $j_{\rm stars}$ and $j_{\rm bar}$ than early-type galaxies, as observed. \item We compare with $z=0$ observations and find that the trends seen in the $j$-mass plane reported by \citet{Romanowsky12}, \citet{Obreschkow14b}, \citet{Cortese16} and measured here for the ATLAS$^{\rm 3D}$ survey, with stellar concentration, neutral gas fraction and $\lambda_{\rm R}$, are all also present in \eagle\ in a way that resembles the observations very closely. These trends show that galaxies with lower $\lambda_{\rm R}$, lower gas fractions and higher stellar concentrations, generally have lower $j_{\rm stars}$ and $j_{\rm bar}$ at fixed stellar and baryon mass, respectively. Again, the trends above are present regardless of the apertures used to measure $j$. \item $j$ scales with mass roughly as $j\propto M^{2/3}$ for both the stellar and total baryon components of galaxies. This is the case for all galaxies with $M_{\rm stars}>10^9\,\rm M_{\odot}$ at $0\le z\le 3$. In the case of the neutral gas we find a different scaling closer to $j_{\rm neutral}\propto M^{1/3}_{\rm neutral}$, which we attribute to the close relation between $j_{\rm neutral}$ and $j$ of the entire halo \citep{Zavala15} and the poor correlation between the neutral gas content of galaxies and the halo properties. \item We identified two generic tracks for the evolution of the stellar spin parameter, $\lambda^{\prime}_{\rm stars}\equiv j_{\rm stars}(r_{50})/M^{2/3}_{\rm stars}$, depending on whether most of stars formed before or after turnaround (which occurs at $z\approx 0.85$ for galaxies that at $z=0$ have $M_{\rm stars}>10^{9.5}\,\rm M_{\odot}$). In the absence of mergers, galaxies older than $9\,\rm Gyr$ (i.e. most stars formed before turnaround) show little evolution in their $j_{\rm stars}/M^{2/3}_{\rm stars}$, while younger ones show a constant $\lambda^{\prime}_{\rm stars}$ until $z\approx 1.2$, and then increase as $\lambda^{\prime}_{\rm stars}\propto a$. Mergers reduce $\lambda^{\prime}_{\rm stars}$ by factors of $\approx 2-3$, on average, in galaxies older than $9\,\rm Gyr$, and the index of the scaling between $\lambda^{\prime}_{\rm stars}$ and the scale factor to $\approx 0.4$ in younger galaxies. {We find that these tracks are the result of two effects: (i) the evolution of the total $j_{\rm stars}$ of galaxies, and (ii) its radial distribution, which suffers significant rearrangements in the inner regions of galaxies at $z\lesssim 1$.} {Regardless of the aperture in which $j_{\rm stars}$ is measured}, two distinct channels leading to low $j_{\rm stars}$ in galaxies at $z=0$ are identified: (i) galaxy mergers, and (ii) early formation of most of the stars in a galaxy. \item We explore the validity of two simple, theoretical models presented in the literature that follow the evolution of $j$ in galaxies using \eagle. We find that on average \eagle\ galaxies follow the predictions of an isothermal collapsing halo with negligible angular momentum losses within a factor of $\approx 2$. These results are interesting, as it helps validating some of the assumptions that go into the semi-analytic modelling technique to determine $j$ and sizes of galaxies (e.g. \citealt{White91,Kauffmann93,Cole00}), at least as a net effect of the galaxy formation process. We also test the model of \citet{Obreschkow16}, in which the stability of disks is governed by the disk's angular momentum. In this model, $f_{\rm atom}\propto (j_{\rm bar}/M_{\rm bar})^{1.12}$. {We find that this model can reproduce the evolution of $j_{\rm bar}$ to within $50$\% at $z\lesssim 2$}, but only of \eagle\ galaxies that are rotationally-supported. \end{itemize} {One of the most important predictions that we presented here is the evolution of $j_{\rm stars}(r_{50})$ in passive and active galaxies, and the evolutionary tracks of $\lambda^{\prime}_{\rm stars}$.} The advent of high quality IFS instruments and experiments such as the SKA, discussed in $\S$~$1$, will open the window to measure $j$ at redshifts higher than $0$, and to increase the number of galaxies with accurate measurements of $j$ by one to two orders of magnitude. They will be key to study the co-evolution of the quantities addressed here and test our \eagle predictions. | 16 | 9 | 1609.01739 |
1609 | 1609.03350_arXiv.txt | The GeV-range spectra of blazars are shaped not only by non-thermal emission processes internal to the relativistic jet but also by external pair-production absorption on the thermal emission of the accretion disc and the broad-line region (BLR). For the first time, we compute here the pair-production opacities in the GeV range produced by a realistic BLR accounting for the radial stratification and radiation anisotropy. Using photoionization modelling with the \cloudy\ code, we calculate a series of BLR models of different sizes, geometries, cloud densities, column densities and metallicities. The strongest emission features in the model BLR are Ly$\alpha$ and \ion{He}{II}\,Ly$\alpha$. Contribution of recombination continua is smaller, especially for hydrogen, because Ly continuum is efficiently trapped inside the large optical depth BLR clouds and converted to Lyman emission lines and higher-order recombination continua. The largest effects on the gamma-ray opacity are produced by the BLR geometry and localization of the gamma-ray source. We show that when the gamma-ray source moves further from the central source, all the absorption details move to higher energies and the overall level of absorption drops because of decreasing incidence angles between the gamma-rays and BLR photons. The observed positions of the spectral breaks can be used to measure the geometry and the location of the gamma-ray emitting region relative to the BLR. Strong dependence on geometry means that the soft photons dominating the pair-production opacity may be actually produced by a different population of BLR clouds than the bulk of the observed broad line emission. | Some gamma-ray source may be also bright at softer energies, so that this soft radiation becomes a source of opacity for the gamma-rays through photon-photon electron-positron pair production. In particular, radiation from the infrared to the EUV band (0.1--100~eV) contributes to the opacity in the 1--10$^3$~GeV range. This may be important for accreting black holes with gamma-ray emitting jets, both in close binary systems and in active galactic nuclei (AGN) as well as for pulsars with high-mass companions. Here we consider in detail the case of flat spectrum radio quasars (FSRQ), which are not only bright non-thermal sources from radio to gamma-ray energies but also powerful emitters of thermal optical/UV/EUV radiation. In this spectral range, isotropic (unbeamed) emission of a bright AGN is dominated by the so-called big blue bump (BBB) with a maximum around 1000\AA. Emission of the BBB is continual, but considerable part of the radiation comes in broad components of emission lines. Unlike the broad-band emission, the broad emission lines and recombination edges may produce relatively sharp spectral details in gamma-ray absorption. In particular, the strong Ly$\alpha$ line should create a spectral break at the threshold energy of about 25~GeV. Observational data hint that such absorption details do indeed exist. The spectra of FSRQ and bright (low-synchrotron-peak) BL\,Lacs obtained by the Large Area Telescope onboard of the {\it Fermi Gamma-ray Space Telescope} ({\it Fermi}/LAT) in the 0.1\div30~GeV energy range reveal strong deviations from any smooth (single power-law or log-normal) spectral model \citep{fermi10, PS10,tanaka11,SP11,SP14}. Unlike the fainter BL\,Lac objects lacking observable disc and line emission, a nearly power-law spectrum observed in FSRQs in the $\lesssim 1$~GeV range cannot be extrapolated to energies higher than several GeV. The spectral slope becomes steeper near a break energy of about several GeV. Qualitatively such details are well explained by pair-production opacity created by individual bright spectral lines and sharp spectral edges \citep{PS10,SP14} in the far and extreme UV range. Such spectral details are naturally produced by the BLR responsible for the broad components of emission lines. The best candidates for absorption at several GeV are the \ion{He}{ii}~Ly$\alpha$ line and Lyman recombination continuum (LyC). Hydrogen Ly$\alpha$ and LyC emission should contribute at $\sim 20\div 30\GeV$. However, because of the lack of photons above 20 GeV, it is challenging to judge about spectral shape at these energies. The positions and even the existence of the breaks at several GeV have been questioned \citep{Harris}. Some of the originally detected sharp features are likely the artefacts of the {\it Fermi}/LAT Pass 6 response function, but still some breaks are significantly detected in the redshift-corrected stacked spectra of blazars as well as in the spectra of individual bright sources in the Pass 7 data \citep{SP14}. The BLR is composed of dense ($n_{\rm H}\sim 10^{9}\div 10^{13}\cmc$) clumpy photoionized gas moving nearly chaotically at random velocities close to virial. The physical conditions in BLR are constrained by relative line intensities (see \citet{osterbrock}, sections 13.6 and 14.5, and references therein). BLR gas is often viewed as some sort of a wind produced by the accretion disc (see \citealt{botorff97} and references therein) though there is strong observational evidence for inward-directed motions in BLRs \citep{doro12, grier13}. The BLR size measured through reverberation mapping depends on the quasar UV luminosity $L_{\rm UV}$ as $R_{\rm BLR,17}\sim 1\times L_{\rm UV, 45}^{1/2}$\citep{kaspi07}.\footnote{Here and below we use notation $Q=10^x Q_x$ in cgs units. } To reproduce the observed BLR spectra, individual clouds should be optically thick to Lyman continuum and the Lyman series lines. This means that the emission of BLR clumps should be highly anisotropic, and the inward- and outward-directed diffuse continua should differ considerably \citep{anisofer}. The typical density of BLR photons within the BLR is $n_{\rm ph,BLR}\approx 10^9\cmc$ independently of the luminosity. Here we assumed that 10 per cent of quasar luminosity is reprocessed in the BLR to photons of average energy 10 eV. The photon density is uncertain by an order of magnitude, because of the uncertainties on the BLR radius determined using different emission lines \citep{PW99,MS12}. The gamma-ray radiation is believed to be produced by the relativistic jet and, therefore, is highly beamed in the direction of the jet propagation. In quasars, this radiation would propagate through the radiation field of the accretion disc, BLR and the dusty torus. While the photon density around quasar is dominated by the accretion disc, it is not the dominant source of gamma-ray opacity, as this radiation streams along the jet basically in the same direction as the gamma-rays leading to a strong reduction of the interaction rate. On the other hand, the BLR photons, distributed more or less isotropically, collide with the beamed gamma-rays at much larger angles and, therefore, provide a much high opacity. For a gamma-ray source well inside a BLR and photons above 30~GeV, we can estimate the maximal optical depth created by the BLR emission (mostly by Ly $\alpha$) as $\tau_{\gamma\gamma} \sim 0.2 \sigma_{\rm T} n_{\rm ph,BLR} R_{\rm BLR} \sim (1\div 100) L_{\rm UV, 45}^{1/2}$. The first attempts to compute the gamma-ray opacity were made by \citet{liu_bai06} and \citet{Reimer07}, who considered sources of all observed broad lines distributed inside a spherical BLR shell. It is known, however, that lines of different ionization are produced at very different distances from the central source \citep{PW99} and the gamma-ray opacity strongly depends on the local BLR UV spectrum which cannot be directly observed because of the internal as well as external absorption. This justifies the attempts to use photoionization models to predict the local BLR spectrum and, consequently, the gamma-ray absorption. Such modelling was made by \citet{tavecchio08} using \cloudy\ (the latest release of this photoionization code is described in \citealt{cloudy13}) and by \citet{PS10} using \xstar\ (see \citealt{xstar}). \citet{tavecchio12} have noticed a strong dependence of the gamma-ray opacity on the BLR geometry, within a framework of a single thin spherical shell (or its fraction). Similar conclusions were reached by \citet{LeiWang14PASJ} who considered the sources of the observed line emission. In this paper, we compute for the first time the photon-photon pair-production absorption through a realistic BLR. We consider an axisymmetric model for the anisotropically emitting, radially-stratified BLR of different geometries. In Section~\ref{sec:model}, the \cloudy\ BLR model is introduced. In Section~\ref{sec:tau}, we describe the calculation of the gamma-ray absorption. Results are given in Section~\ref{sec:res} and discussed in Section~\ref{sec:disc}. | In this work we have considered the optical depths to pair production that a realistic BLR should produce. Certain simplifications were used such as uniform density within individual BLR clouds and uniform distribution of the clouds themselves within the volume they occupy. We took into account the geometry effects introducing an opening angle of the BLR distribution in space, and also anisotropic emission pattern of individual clouds, that should emit mostly backwards in the most prominent emission lines. The structure, physical conditions and the outcoming spectra of the BLR clouds were calculated using the photoionization code \cloudy. As many BLR show signatures of super-solar metallicity, we also calculated one model with a metallicity ten times solar. High metallicity increases the intensity of the soft X-ray metal lines, especially \ion{C}{V}$\lambda$40.7. The opacity growth with energy in the 1$\div$100\GeV\ range becomes generally steeper. We find that the main effect of geometry is upon the positions of spectral details in the absorption spectrum. The key quantity is the maximal incidence angle cosine $\mu_{\max} $. Moving the spectral breaks to higher energies makes the opacity in the relevant GeV range much smaller, sometimes by several orders of magnitude, if the geometry is changed from a complete sphere to a thin disc. At the same time, the optical depth at harder energies $E\gtrsim 100\GeV$ remains practically independent of energy and close to the maximal possible. { Strong dependence on the incidence angle makes the gamma-ray opacity extremely sensitive to the position of the gamma-ray source as well as of the sources of soft photons. Most of the broad line radiation produced below the gamma-ray source (at $R\lesssim H$) remains invisible for the GeV-range photons. Therefore, the average BLR spectrum can not be used to predict the positions and strengths of the absorption edges. Instead, the absorption may be dominated by the radiation of a small part of the BLR located favourably with respect to the gamma-ray emission site. } | 16 | 9 | 1609.03350 |
1609 | 1609.01952_arXiv.txt | {} {Future astrophysics and cosmic microwave background space missions operating in the far-infrared to millimetre part of the spectrum will require very large arrays of ultra-sensitive detectors in combination with high multiplexing factors and efficient low-noise and low-power readout systems. We have developed a demonstrator system suitable for such applications.} {The system combines a 961 pixel imaging array based upon Microwave Kinetic Inductance Detectors (MKIDs) with a readout system capable of reading out all pixels simultaneously with only one readout cable pair and a single cryogenic amplifier. We evaluate, in a representative environment, the system performance in terms of sensitivity, dynamic range, optical efficiency, cosmic ray rejection, pixel-pixel crosstalk and overall yield at at an observation centre frequency of 850 GHz and 20\% fractional bandwidth.} {The overall system has an excellent sensitivity, with an average detector sensitivity $\mathrm{<NEP_{det}>=3\times10^{-19}\;\WHz}$ measured using a thermal calibration source. At a loading power per pixel of 50fW we demonstrate white, photon noise limited detector noise down to 300 mHz. The dynamic range would allow the detection of $\sim$ 1 Jy bright sources within the field of view without tuning the readout of the detectors. The expected dead time due to cosmic ray interactions, when operated in an L2 or a similar far-Earth orbit, is found to be $<$4\%. Additionally, the achieved pixel yield is 83\% and the crosstalk between the pixels is $<$-30dB.} {This demonstrates that MKID technology can provide multiplexing ratios on the order of a 1000 with state-of-the-art single pixel performance, and that the technology is now mature enough to be considered for future space based observatories and experiments.} | About half the energy generated in the Universe since the Big Bang, from stellar radiation and accretion processes, comes to us in the far infrared (FIR) and sub-mm spectral range (0.03 - 1 mm) \citep{Dole2006}. Access to this spectral range is therefore essential for astrophysics and cosmology as it allows us to gain understanding of cold, distant, and dust enshrouded objects, many of which are completely invisible in other spectral ranges. Unfortunately observations are very difficult: the Earth's atmosphere is opaque over a large fraction of this spectral range, thus requiring observations from space. To reach the natural astrophysical backgrounds an observatory with an actively cooled telescope is required for a large fraction of the FIR spectral range in combination with background limited detectors. The required photon noise limited sensitivity of the detectors, NEP$_{ph}$, depends on the power absorbed per pixel in the instrument and ranges from NEP$_{ph}$$\sim$5$\times 10^{-18} \WHz$ for cosmic microwave background (CMB) instrument to NEP$_{ph}$$\sim$1$\times 10^{-20} \WHz$ for a grating spectrometer on an observatory with a 5-K telescope. For most space missions the total pixel count needed will be $\mathrm{\sim10^4}$. The combination of sensitivity and pixel count presents a major challenge for future detector systems. Recent experiments using thermal calibration sources have shown that it is possible to reach, or at least approach, the required detector sensitivities with a number of different technologies. Examples are Quantum Capacitance Detectors (QCD's)\citep{Echternach2013}, Transition Edge Sensors (TES's) \citep{Suzuki2016,Audley2016}, small-volume hot-electron bolometers \citep{Karasik2011} and Microwave Kinetic Inductance Detectors (MKIDs) \citep{Visser2014}. MKIDs, pioneered by \citet{Day2003}, are in essence superconducting resonant circuits designed to efficiently absorb radiation. They offer an attractive option to construct a large imaging system due to their intrinsic ease of using frequency division multiplexing at microwave frequencies, which allows many pixels to be read out using a single readout line. MKIDs have been operated successfully at millimetre wavelengths on the IRAM 30 m telescope \citep{NIKA2010,Nika22016} and at near infrared/optical wavelengths at Palomar \citep{Strader2013}. \begin{table*} \caption{The detector requirements for the various mission concepts discussed in the text.} % \label{table:1} % \centering % \begin{tabular}{l c c c c c c} % \hline\hline % & $\lambda$ & $P_{det}$ & $NEP_{ph}$ & $P_{det}$ for 1 Jy & Time constant & 1/f knee\\ & ($\mum$) & (fW) & $\mathrm (10^{-19}\WHz)$ & (fW) & (msec.) & (Hz)\\ \hline % \textbf{Double Fourier interferometer} & 25 - 50 & 0.029 & 6.1 &4.6 & 0.2 & 1 \\ 2 3m $\diameter$ 5 K telescopes & 50 - 100 & 0.022 & 3.7 &2.3 & & \\ 0.5$\lambda$/D pixels & 100 - 200 & 0.018 & 2.4 &1.2 & & \\ & 200 - 400 & 0.83 & 10 &0.58 & & \\ \hline \textbf{Single dish Broadband camera} & 30 & 0.053 & 8.5 &30 & 30 & 0.1 \\ 3m $\diameter$ 5 K telescope & 60 & 0.043 & 5.2 &15 & & \\ 0.5$\lambda$/D pixels & 120 & 0.030 & 3.3 &7.4 & & \\ $\lambda/\Delta\lambda$=3 & 240 & 0.041 & 2.6 &3.7 & & \\ & 400 & 0.27 & 5.2 &2.2 & & \\ \hline \textbf{Single dish Broadband camera} & 30 & 0.053 & 8.5 &120 & 30 & 0.1 \\ 10m $\diameter$ 25 K telescope & 60 & 0.88 & 24 &60 & & \\ 0.5$\lambda$/D pixels & 120 & 24 & 89 &30 & &\\ $\lambda/\Delta\lambda$=3 & 240 & 77 & 113 &15 & &\\ & 400 & 89 & 93 &8.9 & & \\ \hline \textbf{Single dish Grating spectrometer} & 30 & 9.1$\times 10^{-5}$ & 0.35 &0.052 & 100 & 0.1 \\ 3m $\diameter$ 5 K telescope & 60 & 7.1$\times 10^{-5}$ & 0.22 &0.026 & & \\ 0.5$\lambda$/D pixels & 120 & 5.2$\times 10^{-5}$ & 0.13 &0.013 & & \\ $\lambda/\Delta\lambda$=1000 & 240 & 6.9$\times 10^{-5}$ & 0.11 &0.0065 & & \\ & 400 & 4.8$\times 10^{-5}$ & 0.22 &0.039 & & \\ \hline \textbf{Single dish Grating spectrometer} & 30 & 9.1$\times 10^{-5}$ & 0.35 &0.21 & 100 & 0.1 \\ 10m $\diameter$ 25 K telescope & 60 & 1.5$\times 10^{-4}$ & 1.0 &0.1 & & \\ 0.5$\lambda$/D pixels & 120 & 0.044 & 3.3 &0.052 & &\\ $\lambda/\Delta\lambda$=1000 & 240 & 0.13 & 2.6 &0.026 & & \\ & 400 & 0.15 & 5.2 &0.016 & & \\ \hline \textbf{CMB experiment} & 400 & 120 & 111 &0.57 & 5 & 0.1 \\ 2 m $\diameter$ 30 K telescope & 600 & 110 & 85 &0.38 & & \\ 1$\lambda$/D pixels & 900 & 96 & 65 &0.25 & & \\ $\lambda/\Delta\lambda$=3 & 1400 & 107 & 54 &0.16 & &\\ & 2000 & 123 & 50 &0.11 & &\\ & 3000 & 129 & 41 &0.076 & & \\ \hline % \hline \end{tabular} \tablefoot{ On top of the requirements listed in the table, all detector systems have the common requirements of: i) a cosmic ray dead time $<$20\% and ii) a pixel-pixel crosstalk (after data de-correlation) $<$-30 dB. Additionally all instruments will require on the order of several $\mathrm{10^4}$ of pixels. } \end{table*} However, up to now there has been no demonstration of a large scale detector system with sufficient sensitivity for operation in space. In this paper we report on the design, fabrication and evaluation of a kilo-pixel imaging system designed for future space-born FIR observatories that is based on a large array of MKIDs in combination with a dedicated readout system. The paper is organised as follows: We present in Section \ref{Sec:DetReq} a summary of the generic requirements for near- and far-future missions in the FIR and sub-mm from which we derive a set of specifications for the detector system discussed in the remainder of the text. In Section \ref{Sec:DetDes} we describe the design and fabrication of the detector array, in Section \ref{Sec:ExpSys} the experimental system and readout electronics, and in Section \ref{Sec:Exp} we describe the experimental results: We have performed a set of dedicated tests measuring i) optical efficiency, ii) sensitivity, iii) dynamic range, iv) pixel-to-pixel crosstalk, v) noise spectral dependence, vi) sensitivity to cosmic rays, and vii) pixel yield. We discuss in Section \ref{Sec:Dis} the measured results and discuss briefly the outlook for using a MKID system in a space based observatory and end with our concluding remarks in Section\ref{Sec:Con}. | \label{Sec:Con} We have demonstrated an MKID-based imaging system consisting of a 961 pixel MKID array that is read out using a single readout system and one pair of readout cables. The readout requires one low noise amplifier operating at $\sim$4K with a power dissipation of a few mW. This demonstrator represent a major step forward in FIR detector technology, especially in terms of multiplexing capabilities in combination with a very high sensitivity. It fulfils many generic requirements for future space based observatories. The detector array operates in a 20\% bandwidth around 850 GHz. The sensitivity obtained with a thermal calibration source is given by $\mathrm{<NEP_{det}>=3\times10^{-19}\WHz}$ with an aperture efficiency of 0.58, which represents 73\% of he theoretical limit for a single mode system. Furthermore we achieve 83\% yield, low crosstalk ($<$-30dB) and a dynamic range of $10^5$, enabling measurement of sources of close to 1 Jy for most applications. Additionally the detector array is hardened against cosmic ray interaction with an expected loss of integration time of less that 4\% when operated in L2. This proves that MKID technology is now sufficiently mature for consideration in future space based observatories. | 16 | 9 | 1609.01952 |
1609 | 1609.02576_arXiv.txt | HD 11112 is an old, Sun-like star that has a long-term radial velocity (RV) trend indicative of a massive companion on a wide orbit. Here we present direct images of the source responsible for the trend using the Magellan Adaptive Optics system. We detect the object (HD 11112B) at a separation of 2\fasec 2 (100 AU) at multiple wavelengths spanning 0.6-4 \microns ~and show that it is most likely a gravitationally-bound cool white dwarf. Modeling its spectral energy distribution (SED) suggests that its mass is 0.9-1.1 \msun, which corresponds to very high-eccentricity, near edge-on orbits from Markov chain Monte Carlo analysis of the RV and imaging data together. The total age of the white dwarf is $>2\sigma$ discrepant with that of the primary star under most assumptions. The problem can be resolved if the white dwarf progenitor was initially a double white dwarf binary that then merged into the observed high-mass white dwarf. HD 11112B is a unique and intriguing benchmark object that can be used to calibrate atmospheric and evolutionary models of cool white dwarfs and should thus continue to be monitored by RV and direct imaging over the coming years. | \label{sec:intro} Direct imaging and Doppler spectroscopy are complementary techniques for characterizing planetary systems. The former can detect young, massive companions on wide orbits, while the latter is most sensitive to massive companions orbiting close to their typically old, chromospherically-quiet host stars. The combination of the two techniques has now been exploited in several large programs: the NACO-SDI survey \citep{jenkinsrvimaging}, the TRENDS survey \citep{crepptrends1,crepptrends2,crepptrends3,crepptrends4,crepptrends5,crepptrends6}, the Friends of Hot Jupiters survey \citep{friendsofhotjupiters1,friendsofhotjupiters2}, and the Subaru/HiCIAO survey \citep{subarutrends}. In addition to these, for the past few years we have been executing our own survey, MagAO Imaging of Long-period Objects (MILO), which uses the superb visible and near-infrared (NIR) imaging capabilities of the Magellan adaptive optics (MagAO; \citealt{lairdtrapezium}) system in combination with precision radial velocities (RVs) to discover and characterize wide companions. In our first paper, we described the discovery and characterization of a benchmark mid-M dwarf (HD 7449B) that is likely to be inducing Kozai oscillations on a very nearby gas giant planet (HD 7449Ab) \citep{milo1}. In this paper, we present the discovery and characterization of a faint white dwarf orbiting the Sun-like star HD 11112. This star, located 45.3$^{+1.2}_{-1.1}$ pc away \citep{updatedhip}, has a spectral type of \about G2 (ranging from G0-G4; \citealt{sptypesbook,evans,bidelman}), is metal-rich ($[Fe/H] = 0.20\pm 0.06$, \citealt{bensby}), is thought to be old (\about 4-8 Gyr; \citealt{valenti,bensby,ghezziages,holmberg,ramirezlithium,feltzing}) based on its chromospheric activity and kinematics, and is likely evolving off the main sequence. The star has been monitored for the past 17 years by the Anglo-Australian Telescope (AAT) UCLES spectrometer, revealing a long-term linear trend indicative of a massive companion on a wide orbit. In Section 2, we describe our high-contrast imaging and Doppler spectroscopy observations and data reduction. In Section 3, we present our astrometry and photometry of the directly imaged companion, model its spectral energy distribution (SED) using cool white dwarf model atmospheres, and constrain its mass via analysis of the RVs. In Section 4, we summarize and discuss the nature of this puzzling companion based on all the information at hand on the system. | In this work, we have shown that the HD 11112 system is a binary consisting of a Sun-like evolving G dwarf and a secondary white dwarf. SED modeling suggests that the white dwarf is cool ($T_{eff} < 10,000 K$) and has a mass of \about 0.9-1.1 \msun. These physical properties correspond to cooling ages ranging from \about 2.4-4 Gyr (Table \ref{tab:models}). The SED mass falls in the tail of the posterior mass distribution from our RV analysis, corresponding to a 25$\%$ chance the mass is $>$ 0.9 \msun. However, white dwarf models have been shown to be robust and have been calibrated on objects like HD 11112B with accurate parallaxes (e.g., see \citealt{wdcalibrations}). Therefore it seems very plausible that we have found a rather unusual high-mass white dwarf, which is statistically rare in and of itself (white dwarf mass distribution in the solar neighborhood being peaked at \about 0.6-0.7 \msun; \citealt{wdcalibrations,wdmasses,nearbywhitedwarfs}). In addition, we have to reconcile the apparent age discrepancy with the primary star (age = 7.2$^{+0.78}_{-1.2}$ Gyr). Assuming a 50$\%$ C/O core composition, the white dwarf cooling age is at best $2.4\sigma$ smaller than the primary's age. The only way to reconcile this discrepancy is to assume an (unlikely, see Section \ref{sec:sed}) 100$\%$ C core. In this case, the cooling age is 3.58$^{+2.38}_{-1.63}$ Gyr and marginally consistent at the 1.4$\sigma$ level. However, this corresponds to model fits to the epoch 1 data, which were of much poorer quality than the epoch 2 data. If we restrict ourselves to the epoch 2 data alone, then for a 100$\%$ C core, the age discrepancy is at best at the 2.3$\sigma$ level. One way to reconcile the age discrepancy is if there was a \textit{delay} in HD 11112B's evolution to the white dwarf phase. This could be achieved if HD 11112B was originally a close binary (and the HD 11112 system was therefore a hierarchical triple system). The two stars could have spent several Gyr on the main sequence and then either (1) merged into a single, high-mass blue straggler that then evolved into the observed white dwarf or (2) evolved separately into two low-mass white dwarfs that then merged into the observed high-mass white dwarf. An example of such a system was recently discovered by \cite{wdmerger}, where the ``delayed" white dwarf has a final mass of \about 0.85 \msun. We can infer some properties of the binary progenitors based on the age constraints from the primary and the observed white dwarf. The total age of the system is \about 7 Gyr (from the primary), and the cooling age of the white dwarf (assumed to have mass of \about 1 \msun) is at most \about 4 Gyr. The white dwarf progenitor would have a mass of \about 5 \msun ~\citep{williamswdprogenitors} and live on the main sequence for \about 125 Myr \citep{massivestarages}. Therefore the process that produced the white dwarf progenitor has \about 2.9 Gyr of evolution to account for (if the progenitor is a single star; otherwise 3 Gyr to account for). During a merger of two main sequence stars, only a few percent of the total input mass is lost \citep{mergermass}. Thus we can take the white dwarf single-star progenitor mass as an upper limit on the total pre-merger mass. If the two stars in the binary are identical, they would have masses \about 2.5 \msun ~and each live on the main sequence for \about 765 Myr, far short of the required 2.9 Gyr. In fact, in order for the two identical main sequence stars to merge after 2.9 Gyr, the pair would have to each be \about 1.6 \msun ~for a total of 3.2 \msun, which is far short of the expected 5 \msun ~white dwarf progenitor mass. We are thus left with three possible scenarios. (1) one star in the binary has mass $\lesssim$ 1.6 \msun, the other star is more massive and evolves into a white dwarf first, and then the white dwarf merges and is absorbed into the other star after \about 3 Gyr. Unfortunately, the total merged mass (even for a white dwarf with mass = 1.4 \msun) would still fall short of the required 5 \msun ~progenitor, so this scenario seems unlikely. (2) The same formation happens as in (1), except that the white dwarf accretes material from the lower-mass main sequence star after it evolves off the main sequence. The binary would become a cataclysmic variable whose final fate could be completely self-destructive, so this scenario seems unfavorable. (3) Both stars in the binary evolve into white dwarfs and then merge into a more massive white dwarf. While white dwarf mergers often result in supernova explosions \citep{wdmergerfates}, two low-mass (total mass $<$ 1.4 \msun) white dwarfs can merge into a more massive white dwarf as long as dynamic carbon burning does not occur during the merger phase \citep{massivewdmerger}. In fact, this is the favored scenario to explain most of the massive white dwarfs in the solar neighborhood \citep{nearbywhitedwarfs}. For HD 11112, the timing works out as long as the two white dwarfs each had masses $\lesssim$ 0.55 \msun, which correspond to progenitor main sequence lifetimes of \about 3 Gyr. In order to evolve into two white dwarfs and merge in this timeframe, the binary would have to shrink to an orbital period of \about 5 hours. This would naturally happen if the pair had undergone common envelope evolution due to dynamical friction with Roche lobe material from both stars. After reaching such a small orbit, it would continue to decay and merge in \about 3 Gyr \citep{orbitaldecay}. This seems like the most plausible explanation for the peculiarities of HD 11112B. This would appear to resolve the puzzling nature of HD 11112B. The only other similar benchmark white dwarf (HD 114174B, likewise detected by both RV and direct imaging, \citealt{crepptrends3}), is also discrepant with its primary star's age \citep{lbtwd}. In this case, the white dwarf cooling age is actually \textit{larger} than the primary's age and so may be more difficult to explain. Benchmark objects like HD 114174B and HD 11112B are perhaps the best candidates for testing white dwarf models because they have been resolved, they have measured ages via their primaries, and their orbital motions and their RVs can be used to constrain their masses with continued monitoring over time. Given the intriguing nature of HD 11112B, the HD 11112 system warrants further study. At $>$ 2\asec ~separation, \textit{GAIA} should provide high-quality astrometric data to help refine the orbit \citep{gaiaplanets}, though the object should be moving very slowly due to its likely large orbit and high eccentricity (Fig. \ref{fig:massplots}). The companion should also be easily detected by extreme AO systems like GPI \citep{gpi} and SPHERE \citep{sphere}, which would help not only with astrometric and photometric monitoring, but also potentially with finer characterization of the object via spectroscopy or polarization. | 16 | 9 | 1609.02576 |
1609 | 1609.07954_arXiv.txt | There have been extraordinary advances in our knowledge of asymptotic giant branch (AGB) stars over the last decade. On the observational side Spitzer, Herschel and ALMA in particular have provided access to the wavelength ranges in which these stars and their associated dust and molecular shells emit most of their energy. Interferometry has enabled convection cells to be resolved and has highlighted the role of binary interactions in the mass-loss process from these huge stars. At the same time theoretical advances give us a better understanding of element formation, 3D models of convection, and new insight into the properties of grains produced in the very extended circumstellar environments (see invited presentation by H\"ofner to the main meeting). Nucleosynthesis models are making testable predictions and population synthesis models are reproducing many of the characteristics of highly evolved stars, for the first time (see invited presentation by Karakas to the main meeting). In this two day splinter session we covered some of the recent observational and theoretical advances in the understanding of AGB stars and red supergiants (RSG), as well as touching on many aspects that remain puzzling. We nominally divided the two days so that on the first we focused on the star itself, and discuss pulsation, convection, surface magnetic fields etc.; while on the second we examined the circumstellar environment, dust formation, binary interactions etc. In practice the star and its environment are so closely linked that there is considerable overlap in the topics discussed in the two sessions. | 16 | 9 | 1609.07954 |
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1609 | 1609.09664_arXiv.txt | {We compute the non-thermal emissions produced by relativistic particles accelerated by the AGN-driven shocks in \textsc{NGC 1068}, and we compare the model predictions with the observed $\gamma$-ray and radio spectra . The former is contributed by pion decay, inverse Compton scattering, and bremsstrahlung, while the latter is produced by synchrotron radiation. We derive the $\gamma$-ray and radio emissions by assuming the standard acceleration theory, and we discuss how our results compare with those corresponding to other commonly assumed sources of $\gamma$-ray and radio emissions, like Supernova remnants (SNR) or AGN jets. We find that the AGN-driven shocks observed in the circumnuclear molecular disk of such a galaxy provide a contribution to the $\gamma$-ray emission comparable to that provided by the starburst activity when standard particle acceleration efficiencies are assumed, while they can yield the whole $\gamma$-ray emission only when the parameters describing the acceleration efficiency and the proton coupling with the molecular gas are tuned to values larger than those assumed in standard, SNR-driven shocks. We discuss the range of acceleration efficiencies (for protons and electrons) and of proton calorimetric fractions required to account for the observed $\gamma$-ray emission in the AGN outflow model. \\ We further compare the neutrino flux expected in our model with constraints from current experiments, and we provide predictions for the detections by the upcoming KM3NeT neutrino telescope. This analysis strongly motivates observations of \textsc{NGC 1068} at $ \gtrsim $ TeV energies with current and future Cherenkov telescopes in order to gain insight into the nature of the $\gamma$-rays source. | \textsc{NGC 1068} is the brightest, closest and best studied Seyfert 2 galaxy. The discovery of its Seyfert 1 nucleus in polarized light led \cite{Antonucci85} to propose the AGN unification model. In its central region this source exhibits both starburst and AGN activities. Interferometric observations in the millimetre (mm) band identified a circumnuclear disk (CND) $ \sim $200 pc in radius, surrounded by a $ \sim $2 kpc starburst ring connected to the CND by a bar. In X-rays, the spectrum is dominated by reflection components of the primary AGN radiation by Compton thick material (i.e. with column density $N_H>1.5 \times 10^{24}$ cm$^{-2}$), and in particular by a strong K$\alpha$ iron line (EW$ \simeq $1 , \citealt{Matt04}). Recently \cite{Marinucci16} detected a transient flux excess at energies above 20 keV that can be explained by a temporary decrease of $N_H$ along the line of sight. This event allows to unveil the primary AGN emission and to infer an intrinsic 2-10 keV luminosity of L$_X=7\times 10^{43}$ erg/s (corresponding to bolometric luminosity L$_{AGN}\simeq 2.1\times 10^{45}$ erg/s, \citealt{Marconi04}). \\ \textsc{NGC 1068} is a strong $\gamma$-ray emitter. It is the brightest of the few non-blazar galaxies detected by the {\it Fermi Gamma-ray space telescope} and with the flattest $\gamma$-ray spectrum \citep{Ackermann12}. Models assuming that the $\gamma$-ray emission is entirely due to starburst activity failed to reproduce the observed spectrum \citep{Yoast14, Eichmann15}. This suggests an alternative/complementary origin for the $\gamma$-ray emission (see e.g. \citealt{Lenain10}).\\ Interestingly, sub-mm interferometry of molecular lines in the CND strongly suggests the existence of a giant, AGN-driven outflow which extends to $ \sim $100 pc scale with velocity of $ \sim $ (100-200) km/s \citep{Krips11, Garcia14}. This outflow can induce shocks in the CND, which, in turn, can accelerate relativistic particles with an efficiency that may exceed that in Supernova remnant (SNR) and could leave observational signatures in different electromagnetic bands \citep{FGQ12,Nims15}. In addition to primary accelerated electrons, the decay of neutral pions created by collisions between relativistic protons accelerated by the AGN shocks with ambient protons may produce a significant $\gamma$-ray emission. This hadronic $\gamma$-ray emission is mostly favored as the dominat component of the $\gamma$-ray spectrum at energies above $ \simeq $100 MeV. At lower energies leptonic processes like inverse Compton (IC) scattering and non-thermal bremsstrahlung can significantly contribute to the $\gamma$-ray emission. The same electrons responsible for IC and bremsstrahlung emission spiraling in interstellar magnetic fields radiate synchrotron emission in the radio continuum. The interpretation of the radio emission as a by-product of the AGN-driven outflow activity could in part explain the deviation of \textsc{NGC 1068} from the observed correlation between the radio and far infrared (FIR) luminosities of star forming galaxies. The FIR-radio correlation spans over five orders of magnitude in luminosity, from dwarf galaxies to starburst galaxies \citep{Condon91,Yun01} and has been explained in terms of FIR emission related to dust heated by young massive stars, and radio emission associated to relativistic electrons accelerated in SNR. NGC1068 is observed to have about four times larger radio luminosity than expected from the radio-FIR correlation \citep{Yun01}.\\ Radio emission from AGN-driven outflows can also explain the strong correlation between the kinematics of the ionized gas emission and the radio luminosity observed in obscured radio-quiet quasars at $z\lesssim$1 \citep{Zakamska14}.\\ In this picture, the $\gamma$-ray and radio luminosities are determined by the energy supplied to relativistic protons and electrons at the shock. In this paper we examine if the kinetic power of the AGN-driven outflow observed in \textsc{NGC 1068} can account for the observed $\gamma$-ray and radio luminosities.\\ The paper is organized as follows. An overview of the observational data, including our {\it Fermi} Large Area Telescope (LAT) data analysis, is given in Section \ref{CND}. The physical processes involved in the cosmic-ray (CR) particle energy distributions and the non-thermal emission produced by accelerated particles are described in Section \ref{model} . In Section \ref{results} we present our results, discussion and conclusion follow in Section \ref{discussion} and \ref{conclusions}. \\ Throughout the paper, we use a vacuum-dominated cosmological model with $\Omega_m$=0.3, $\Omega_{\lambda}$=0.7, and $H_0$=70 km s$^{-1}$ Mpc$^{-1}$; and we adopt a distance to \textsc{NGC 1068} of 14.4 Mpc, so that 1$^{\arcsec}\simeq$70 pc. | We compute the non-thermal emissions produced by CR particles accelerated in the shocks produced by the galactic AGN-driven outflow observed in \textsc{NGC 1068}. We find that, within the standard acceleration theory, the predicted $\gamma$-ray spectrum is lower than the observed data by a factor of $ \sim $2 at energies $ E\gtrsim $1 GeV, and by a factor of $ \sim $10 at $ E\simeq $0.1 GeV. This contribution to the $\gamma$-ray emission is comparable to that provided by the starburst activity \citep{Yoast14, Eichmann15}. \\ The analysis presented in this paper indicates that the $\gamma$-ray emission from \textsc{NGC 1068} is either entirely produced by leptonic processes - as proposed in the AGN jet model by \cite{Lenain10} - or by processes with acceleration efficiencies of protons and electrons larger than those commonly assumed in SNR-driven shocks. The latter interpretation requires either a substantial revision of the standard acceleration theory, or the condition that AGN-driven shocks are substantially different from those powered by SNR.\\ The AGN outflow model proposed in this paper can be directly tested by present and forthcoming instruments. The observation of \textsc{NGC 1068} at TeV energies with present and next generation Cherenkov telescopes could provide stringent constraints on CR acceleration models in active galaxies by the detection of a high-energy cut-off in the $\gamma$-ray spectrum. Moreover, in the next future the CTA spatial resolution of $ \sim $ 3 arcmin at energies $E=$(1-10) TeV might distinguish between point-like and extended $\gamma$-ray emission. In case of extended emission, the determination of the centroid will allow to determine if it originates from the nucleus or from the more extended starburst ring.\\ Another way to directly test the AGN outflow model is to look for neutrino signal. The fluxes predicted by this model indicate that the neutrino signal from \textsc{NGC 1068} may be detectable by the next generation neutrino telescope KM3NeT, which, thanks to the improved angular resolution compared to the current neutrino detectors, will allow to constrain effectively the possible astrophysical sources of high energy neutrino events. The AGN outflow model can also be indirectly tested. A potential test is to determine the CR ionization rate of the molecular medium in the CND. In fact, an enhanced molecular ionization of the CND gas could be an indication that the $\gamma$-ray emission has an hadronic component. Molecular line surveys toward the nucleus of \textsc{NGC 1068} at ALMA resolution are therefore necessary to properly determine the chemical and physical properties of the CND gas.\\ Finally, the large efficiencies required to accelerate protons and electrons in the AGN outflow model imply a large production of CR particles. An immediate consequence is that weaker magnetic fields are required to produce the observed synchrotron emission in the radio continuum. \\ \begin{figure*}[h!] \begin{center} \includegraphics[width=8.5 cm]{fig3a.pdf} \includegraphics[width=9 cm]{fig3b.pdf} \caption{Left: neutrino spectra for \textsc{NGC 1068}. Muon neutrino flux (dotted line), electron neutrino flux (dashed line), total neutrino flux (solid line). The neutrino fluxes expected from the models in figure \ref{bestfit} are shown with black, blue, and magenta lines. Right: IceCube effective area (red line), ANATARES effective area (blue line), muon neutrino KM3NeT effective area (magenta dotted line), and electron neutrino KM3NeT effective area (magenta dashed line).} \label{neutrino_flux} \end{center} \end{figure*} \begin{figure*}[h!] \begin{center} \includegraphics[width=18 cm]{fig4.pdf} \caption{Aitoff projection of the IceCube neutrinos in Galactic coordinate system. Red numbered points represent the location of each neutrino event and the surrounding circular areas show the respective median angular error (which includes systematic uncertainties). Black squares are local galaxies with $v \leqslant$1200 km s$^{-1}$ and IRAS 100 $\mu$m flux $\geqslant$50 Jy. Blue crossed squares indicate galaxies in the 3FGL catalogue \citep{Acero15}. \textsc{NGC 1068} is located at the lower left part of the map in correspondence of the neutrino ID 1.} \label{icecube_events} \end{center} \end{figure*} | 16 | 9 | 1609.09664 |
1609 | 1609.09722_arXiv.txt | {Absolute photoionisation cross sections for the Cl$^+$ ion in its ground and the metastable states; $3s^2 3p^4\; ^3P_{2,1,0}$, and $3s^2 3p^4\; ^1D_2,\; ^1S_0$, were measured recently at the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory using the merged beams photon-ion technique at an photon energy resolution of 15 meV in the energy range 19 -- 28 eV. These measurements are compared with large-scale Dirac Coulomb {\it R}-matrix calculations in the same energy range. Photoionisation of this sulphur-like chlorine ion is characterized by multiple Rydberg series of autoionizing resonances superimposed on a direct photoionisation continuum. A wealth of resonance features observed in the experimental spectra are spectroscopically assigned and their resonance parameters tabulated and compared with the recent measurements. Metastable fractions in the parent ion beam are determined from the present study. Theoretical resonance energies and quantum defects of the prominent Rydberg series $3s^2 3p^3 nd$, identified in the spectra as $3p \rightarrow nd$ transitions are compared with the available measurements made on this element. Weaker Rydberg series $3s^2 3p^3 ns$, identified as $3p \rightarrow ns$ transitions and window resonances $3s3p^4 (^4P)np$ features, due to $3s \rightarrow np$ transitions are also found in the spectra.} | In astrophysics, abundances calculations are based on available atomic data that often are insufficient to make definite identifications of spectroscopic lines \citep{Cardelli1993}. In planetary nebulae, the known emission lines are used to identify a characteristic element resulting from the process of nucleosynthesis in stars \citep{sharpee2007,sterling2007}. The study of photoionisation of sulphur-like ions is of considerable interest because of its abundance in space and the interstellar medium. As previously indicated by Hern\'{a}ndez and co-workers \citep{Hernandez2015} there is a wealth of astrophysical applications for this Cl II ion \citep{Cartlidge2012,Sylwester2011,Neufeld2012,Moomey2012}. Sulphur-like chemistry is also of importance in theoretical studies of interstellar shocks \citep{Pineau1986}. Photoabsorption and photoionisation processess in the vacuum ultraviolet (VUV) region play an important role in determining solar and stellar opacities \citep{Kohl1973,Dupree1978,Lombardi1981}. The Cl II ion is an important basis for atmospheric and astrophysical models. Determining accurate abundances for sulphur-like chlorine is of great importance in understanding extragalactic H II regions \citep{Garnett1989} and emission lines of Cl II in the optical spectra of planetary nebulae NGC 6741 and IC 5117 \citep{Keenan2003}. Cl II emission lines have also been seen in the spectra of the Io torus \citep{Schneider2000} and by the far-ultraviolet spectroscopic explorer (FUSE) \citep{Feldman2001}. In the present study, we use a fully relativistic Dirac Coulomb $R$-matrix approximation \citep{norrington1987,norrington1991,norrington2004,grant2007} to interpret and analyze resonance features found in recent high resolution measurements obtained at the ALS \citep{Hernandez2015}. In our work we give a detailed interpretation and understanding of the atomic processes involved for single-photon ionization of Cl II forming Cl III. The interaction of a single photon with a Cl II ion comprises contributions from both direct ionization and excitation of autoionizing resonances \citep{berko1979}. Direct electron ejection processes relevant to the total cross section for single ionization of the Cl$^{+}$ ion in its ground configuration include, \begin{equation} h\nu + {\rm Cl}^{+}({3s^2 3p^4\,\,{^3P} }) \rightarrow \left\{ \begin{array} {l} {\rm Cl}^{2+}({3s^2 3p^3 }) + e^- \\ {\rm Cl}^{2+}({3s 3p^4 }) + e^- . \end{array} \right. \end{equation} Indirect ionization of Cl$^{+}$ levels within the $^3P$ ground term may proceed via resonance formation \begin{equation} h\nu + {\rm Cl}^{+}({3s^2 3p^4}\,\, {^3P}_J) \rightarrow \left\{ \begin{array} {l} {\rm Cl}^{+}({3s^2 3p^3} n\ell \,\, {^3L}_{J' }) \\ {\rm Cl}^{+}({3s 3p^4} n\ell' \,\, {^3L}_{J' }) \end{array} \right. \end{equation} (where, $n\ell$= $ns$ or $nd$, and $n\ell'$=$np$), with subsequent decay by emission of a single electron \begin{equation} {\rm Cl}^{+}({^3L}_{J' }) \rightarrow {\rm Cl}^{2+} + e^-, \end{equation} where $L$ is the total orbital momentum quantum number and $J'$ the total angular momentum quantum number of the intermediate resonant state. Selection rules for electric dipole transitions require that $J' = J$ or $J'=J\pm1$. Similar types of atomic processes occur for the case where this Cl$^+$ ion is in the excited metastable states, $3s^2 3p^4\,\,^1D_2,{\rm or}\, ^1S_0$. On the experimental side, measurements of the photoionisation spectrum for this ion have been reported on recently \citep{Hernandez2015}. Detailed high-resolution measurements were carried out at an energy resolution of 15 meV full width half maximum (FWHM) using synchrotron radiation at the Advanced Light Source (ALS) in Berkeley, California, for the photon energies in the region 19 - 27.8 eV. Absolute values for the cross section were reported on for the photoionisation of the $^3P_{2,1,0}$ states of the $3s^2 3p^4\; ^3P$ configuration in this sulphur-like ion, for photon energies in the energy region 23.38 - 27.8 eV, and for the metastable states $3s^2 3p^4\; ^1D_2,\; ^1S_0$ for photon energies, 19.5 - 27.8 eV. Resonance features observed in the corresponding experimental spectra were analyzed and discussed but no attempt was made to assign and identify the resonance series \citep{Hernandez2015}. On the theoretical side, previous photoionisation cross-section calculations of this ion to the author's knowledge have been rather limited \citep{Opacity1995}. We note that accurate transition probabilities \citep{fischer1977,cowan1981,fischer1997} and $f$-values between levels of a system are good indicators of the quality of target wavefunctions used in subsequent cross sections calculations. For electron impact excitation (EIE) of the Cl$^{2+}$ (Cl III) ion, calculations have been reported on using the intermediate coupling approximation by Sossah and Tayal \citep{Sossah2012} within the {\it R}-matrix method \citep{Burke1975,Burke2011} although no resonance features were reported. Radiative data for chlorine and its ions has also been reported on by Berrington and Nakazaki \citep{Berrington2002} based on {\it R}-matrix calculations performed in $LS$-coupling as no data currently exists in the Opacity Project database \citep{Opacity1995}. The limited high quality data available for the Cl$^+$ ion is one of the major motivating factors for the present investigations. Identification of the Rydberg resonance series in spectra, in particular the window resonances is another major motivation factor. Understanding the interplay and interaction between the direct and indirect photoionisation processes help us understand and interpret the underlying physics. Furthermore, benchmarking the present large-scale cross section calculations on this ion against available high-resolution experimental results, is essential as it provides further confidence in the data for use in various laboratory and astrophysical plasma applications. The layout of this paper is as follows. In Section 2 we outline the theoretical methods employed in our work. Section 3 presents the theoretical results from the DARC photoionisation cross and the resonance analysis. Section 4 presents a comparison between the available experimental measurements \citep{Hernandez2015} and the theoretical cross section results for singly ionized atomic chlorine ground and metastable terms [Cl$^+$ ($3s^2 3p^4\; ^3P_{2,1,0}$ ) and Cl$^+$ ($3s^2 3p^4 \; ^1D_2,\; ^1S_0$ )] in the photon energy range from 19 - 28 eV. Section 5 gives a brief discussion of our results in comparison to the available measurements \citep{Hernandez2015}. Finally in Section 6 we give a summary of our findings from our theoretical work. \begin{figure*} \centering \includegraphics[width=\textwidth]{Figure1} \caption{\label{all} (colour online) Theoretical cross sections from the 512 level DARC calculations for the sulphur-like chlorine ion in the $3s^23p^4\; ^3P_{2,1,0}$, $3s^23p^4\; ^1D_2$, and $3s^23p^4\; ^1S_0$ initial states convoluted with a Gaussian profile of 15 meV. Single photoionisation cross sections of the sulphur-like chlorine ion as a function of energy over the photon energy from thresholds to and energy region just above the Cl$^{2+}$($3s3p^4\; ^4P$) threshold, illustrating strong resonance features in the spectra. (a) $3s^23p^4\; ^3P_2$, (b) $3s^23p^4\; ^3P_1$, (c) $3s^23p^4\; ^3P_0$, (d) $3s^23p^4\; ^3P$ level averaged, (e) metastable $3s^23p^4\; ^1D_2$ and (f) metastable $3s^23p^4\; ^1S_0$ cross sections. The corresponding series limits $E_{\infty}$ of Equation (2) for the window resonances converging to the $3s3p^4\; ^4P$ threshold is indicated by vertical lines. } \end{figure*} | Large-scale Dirac Coulomb {\it R}-matrix (DARC) photoionisation cross section calculations have been carried for the singly ionised chlorine ion for the $3s^23p^4\; ^3P_{2,1,0}$, $3s^23p^4\; ^1D_2$ and $3s^23p^4\; ^1S_0$ initial states in the energy range 19 - 28 eV. For a physical understanding of the atomic processes taking place, we analyze the autoionizing resonance features found in the spectra. Strong Rydberg series of the type $3s^23p^3nd$ along with much weaker series of the form $3s^23p^3ns$ are found in the respective photoionisation spectra. All these resonance series are analyzed, compared and contrasted with recently reported high resolution measurements made at the ALS and spectroscoptically assigned. Excellent agreement of the present theoretical photoionisation cross sections with recent ALS measurements \citep{Hernandez2015} is found. This essential benchmarking of the theoretical work against high-resolution measurements provides confidence in the data for applications. | 16 | 9 | 1609.09722 |
1609 | 1609.00329_arXiv.txt | The photospheric spatial distribution of the main magnetic polarities of bipolar active regions (ARs) presents during their emergence deformations are known as magnetic tongues. They are attributed to the presence of twist in the toroidal magnetic flux-tubes that form the ARs. The aim of this article is to study the twist of newly emerged ARs from the evolution of magnetic tongues observed in photospheric line-of-sight magnetograms. We apply the procedure described by Poisson et al. (2015, \textit{Solar Phys.} \textbf{290}, 727) to ARs observed over the full Solar Cycle 23 and the beginning of Cycle 24. Our results show that the hemispherical rule obtained using the tongues as a proxy of the twist has a weak sign-dominance (53\,\% in the southern hemisphere and 58\,\% in the northern hemisphere). By defining the variation of the tongue angle, we characterize the strength of the magnetic tongues during different phases of the AR emergence. We find that there is a tendency of the tongues to be stronger during the beginning of the emergence and to become weaker as the AR reaches its maximum magnetic flux. We compare this evolution with the emergence of a toroidal flux-rope model with non-uniform twist. The variety of evolution of the tongues in the analyzed ARs can only be reproduced when using a broad range of twist profiles, in particular having a large variety of twist gradient in the direction vertical to the photosphere. Although the analytical model used is a special case, selected to minimize the complexity of the problem, the results obtained set new observational constraints to theoretical models of flux-rope emergence that form bipolar ARs. | \label{sec:Introduction} The study of the solar-cycle properties is the basis for understanding how the solar dynamo produces and amplifies the magnetic field in the solar interior. In the last five decades, several models have proposed a dynamo mechanism located at the bottom of the convective zone (CZ). In this scenario, the magnetic flux at the base of the CZ is amplified and distorted by differential rotation and convection and, finally, it is destabilized by a buoyant-instability process. Magnetohydrodynamic (MHD) numerical simulations show the way that this instability creates coherent magnetic-tubes that rise from the deep layers of the CZ and manifest as the emergence of solar active regions (ARs) observed at photospheric heights \citep{Fan09r}. An important prediction of these simulations is that the emerging structures should form twisted flux tubes or flux ropes (FR) in order to maintain their consistency during the transit through the turbulent CZ. In this view, ARs are the consequence of the emergence of FRs. Other mechanisms, however, have been proposed to explain the formation of ARs (see \citet{Cheung14} and references therein). There is much observational evidence of twist in ARs \citep[\ie\ sunspot whorls, non-potentia\-lity of coronal loops, prominences, X-ray sigmoids; see the review of ][]{Pevtsov14}. ARs with complex magnetic-field distribution, associated with highly twisted FRs, are more productive in terms of flares and coronal mass ejections (CMEs) due to the amount of free magnetic energy and helicity stored in their structures \citep{Kusano04,Liu08,Tziotziou12,Szajko13}. The tendency of magnetic helicity to have a different sign in each solar hemispheres was first proposed by Hale from the evidence of vortical patterns in the chromospheric fibrils surrounding the ARs sunspots \citep{Hale25}. According to this ``hemispherical rule'', there is a predominancy of positive (negative) helicity in the southern (northern) hemisphere. The strength of the rule has been tested using several estimations of the magnetic and current helicity \citep{Bao00,LaBonte07,Pevtsov08,Liu14}. However, a wide range of variation is observed in the rule, \eg\, it is weaker for ARs ($\approx 60$\,\% -- 70\,\%) than for quiescent filaments \citep[$\approx 80$\,\%;][]{Wang13,Pevtsov14}. The significant scatter exhibited by the hemispheric rule implies that turbulence in the convection zone may play an important role in the generation of the observed chirality trends \citep{Longcope98,Nandy06}. \citet{Lopez-Fuentes00} reported a proxy of the twist associated with the deformation of the magnetic polarities observed in line-of-sight magnetograms. These observed features, called magnetic tongues (or tails), are produced by the azimuthal field component of the emerging FR projected on the line-of-sight. The magnetic-flux distribution due to the magnetic tongues is directly related to the sign of the twist in an emerging AR, so the deformation or elongation of the magnetic polarities can be used as a proxy for the sign of the helicity. \citet{Luoni11} computed the elongation of the AR polarities and the evolution of the polarity inversion line (PIL) to characterize the strength of the magnetic tongues. They found that the twist sign inferred from the observed magnetic tongues is consistent with the helicity sign deduced from other proxies (photospheric-helicity flux, sheared coronal loops, sigmoids, flare ribbons, and/or the associated magnetic cloud). \citet{Poisson15} introduced a systematic method to quantify the effect of the magnetic tongues by studying the PIL evolution during the emergence of ARs. This less user-dependent procedure consists in the systematic computation of a linear approximation of the PIL in between the strong magnetic polarities. This is done by minimizing the opposite-sign magnetic-flux component on each side of the computed PIL (see \sect{Characterizing}). From the acute angle between the computed PIL and the line orthogonal to the AR bipole axis [$\tau$] we estimated the average number of turns in the sub-photospheric emerging flux rope, assuming that it can be represented by a uniformly twisted half torus. We found that the number of turns [$\Nt$] is typically below unity; then, sub-photospheric flux-ropes have in general a low amount of twist. In a more recent article \citet{Poisson16} compared $\Nt$ with the twist of simple bipolar ARs calculated from linear force-free field extrapolations of their line-of-sight (LOS) magnetic field to the corona. The signs of the twist obtained with both methods are consistent. Moreover, we found a linear relation between $\Nt$ computed at the photospheric level from the tongues and the number of turns obtained from coronal field modeling. In this article, we use the procedure described by \citet{Poisson15} to explore the properties of the twist of emerging ARs during a complete solar cycle. Our main aim is to search for any dependence of the parameters (\ie\ $\Nt$, $\tau$) characterizing magnetic tongues on the different phases of the cycle and to expand the previous results to a larger statistical sample. Moreover, we quantify the strength of the tongues in the different stages of the AR emergence. This provides further information about how the twist is distributed in the FR. In \sect{Observations}, we describe the data used and the selected sample of ARs. We also define the procedure to derive the tongue characteristics. In \sect{Properties}, we study the properties of the magnetic tongues; in particular, along the solar cycle. In \sect{FRmodel}, we compare the evolution of the PIL angle during an AR emergence with the emergence of a FR model that we develop to interpret the variety in the evolution of the magnetic tongues. In particular, we show that a broad range of twist profiles is required to interpret the observations. Finally, in \sect{Conclusions}, we summarize our results and conclude. | \label{sec:Conclusions} We analyze the emergence phase of bipolar ARs using photospheric line-of-sight magnetograms during Solar Cycle 23 and the beginning of Cycle 24. To have clearer results we select bipolar ARs whose emergence occurred around the central meridian. Our selection included 187 ARs in a temporal range of 13 years. At least 80\,\% of the studied ARs present clear observable elongations of their magnetic polarities, or tongues, during more than $50$\,\% of their emergence time (when the background flux or any disturbing extra flux was not high enough to affect significantly the magnetic tongues). We apply the method described by \citet{Poisson15} to define the mean PIL inclinations of the bipolar ARs. This method defines the tongue angle [$\tauc$] that characterizes the twist of emerging flux-ropes (FRs) producing ARs. The method has proven to be efficient in reducing the large amount of data (more than 4000 line-of-sight magnetograms) to a few parameters that characterize the tongue evolution of the ARs. We define the mean and maximum values of $\tauc$, $\taucMean$, and $\taucMax$, during the full emergence period. Both $\taucMean$ and $\taucMax$ have only a weak sign dominance in each solar hemisphere (53 and 58 \% of dominance); so, as in previous studies involving young ARs \citep[\eg\ ][]{Pevtsov14}, the hemispherical rule is weak. We also study the variation of $\tauc$ during the full emergence, being $\Deltauc$ its total change. We find no relation between the observed tongue characteristics [$\taucMean, \taucMax, \Deltauc$] and the different periods of the solar cycle. The same happens for the amount of magnetic flux, size of the magnetic polarities, latitude, emergence rate, {\it etc.}. Therefore, the helicity in the studied ARs must be generated independently from other FR properties. A striking result is that the total change of $\tauc$ [$\Deltauc$] has a Gaussian distribution with an added very narrow peak at the position of its mean value (\fig{histo-dtc}). After comparing the results derived from observations with those of a FR model, we propose that this distribution could be the result of large convective cells having a differential effect between the top and bottom part of the FR cross-section. This would imply a variation of the local twist {\it per} unit length along the FR axis, as traced by the evolution of $\tauc$ during the FR emergence. More generally, we can summarize the magnetic-tongue evolution during an AR emergence with three main parameters: the mean tongue angle [$\taucMean$] and its total change, $\Delta \tau_{\rm c}$, as well as the tilt change [$\Delphic$] during the full emergence phase. The distribution of the main characteristics of the magnetic tongues [$\taucMean$, $\Delta \tau_{\rm c}$, and $\Delphic $] can be reproduced by the simple analytical model of \append{model}, which extends the previous uniformly twisted model \citep{Luoni11}. $\taucMean$ is predominantly affected by the amount of twist and its sign corresponds to the magnetic-helicity sign \citep{Luoni11}. $\Deltauc$ and $\Delphic $ are broadly distributed according to the twist magnitude and its distribution within the FR, as follows. We search for the minimal model, \ie\ the one with the lowest number of free parameters, that can reproduce the main characteristics of the observations. The main parameters of the model are its axial twist [$\Nto$: the number of turns for a half torus], and two dimensionless parameters [$h$ and $g$] that characterize the twist distribution. We set the constraint of no reversal for both the azimuthal- and axial-field components within the FR model to avoid the presence of parasitic polarities with unobserved characteristics in the synthetic magnetograms. Within these limits, the scan of the three main parameters of the model [$\Nto$, $h$ and $g$] allows us to describe the observed variety of emerging ARs (\fig{correl(Dtilt,DTc)}). This constrains the type of FRs that form isolated bipolar ARs, as well as it challenges dynamo and transport models to create such a large variety of FRs. However, we cannot define the twist magnitude and its profile independently from the magnetic-tongue evolution since there is an overlap in the observable consequences of twist magnitude and profile (\ie\ changing $\Nto$ and $h$ cover a common portion of the parameter space, see \fig{correl(Dtilt,DTc)}). We can still claim that uniformly twisted flux tubes are not enough to interpret the observations and that profiles with less twist at the periphery ($h<0$) are required to explain a significant part of the present AR observations. The simplicity of the analytical model, with no force balance, arising from a special treatment of the divergence-free property of the field and assumed functions for $\Nt(\rho)$ and $\asy(\theta)$, allows us to do a complete scan over the limits of the free parameters with small computational effort. However, it is obvious from the acquired results, as detailed in \sect{Interpretation} and in the conclusions of this article, that a more realistic numerical model with proper full treatment of the equations and relevant forces is necessary to fully explain the properties of bipolar ARs, as the chosen simple analytical model fails to explain 38\,\% of the selected AR sample. Even more unexpected is the fact that the variety of emerging-AR properties is reproduced only if a large gradient of the axial magnetic field is present or, equivalently, that the FR is differentially twisted at the top and bottom parts of its apex. As far as we know, such twist gradient and its variation have never been reported by numerical simulations of emergence and its origin is unknown. One possibility is that it is produced during the magnetic-field storage that occurs below the photosphere before the undulatory instability leads to the emergence of the main FR broken into smaller flux tubes. A differential effect of flow divergence between the top and bottom parts of the FR apex, due to the flow motion in a large convective cell, could be at the origin of the observed variety of tongue evolutions during AR emergence. This process needs to be tested using numerical simulations, before any firm conclusions can be achieved. \begin{figure} \centerline{\includegraphics[width=\textwidth,clip=]{fig-sketch_FR_magneto} } \caption{Model of a twisted flux tube having a half-torus shape with a main radius $R$ and a center located at $z=-d$ below the photospheric level ($z=0$). The twist is positive and uniform ($\Nt =0.5$ turn in half a torus, $h=g=0$ in \eqs{Nt}{Bphi}). The photospheric magnetogram of $B_{\rm z}$ is shown with isocontours and color levels as for observations (\fig{example}) and the superposed brown ellipses (continuous/dashed lines) show the intersection of the FR with $z=-d$ and $z=0$. The torus is outlined for a minor radius $\rho$. The red line is an example of a magnetic-field line (drawn with an enhanced twist by a factor $\approx 6$ to better outline the FR structure). $\phi$ and $\theta$ are the angular coordinates along and around the axis, respectively.} \label{fig:torus} \end{figure} \begin{acks} SOHO is a project of international cooperation between ESA and NASA. MP, MLF, and CHM acknowledge financial support from grants PICT 2012-0973 (ANPCyT), PIP 2012-01-403 (CONICET), and UBACyT 20020130100321 (UBA). MLF and CHM are members of the Carrera del Investigador Cient\'{\i}fico of the Consejo Nacional de Investigaciones Cient\'{\i}ficas y T\'ecnicas (CONICET) of Argentina. MP is a CONICET Fellow. \end{acks} | 16 | 9 | 1609.00329 |
1609 | 1609.05210_arXiv.txt | We report on the results from a large observational campaign on the bare Seyfert galaxy \ark, jointly carried out in 2014 with \xmm, \chandra, and \nustar. The fortunate line of sight to this source, devoid of any significant absorbing material, provides an incomparably clean view to the nuclear regions of an active galaxy. Here we focus on the analysis of the iron fluorescence features, which form a composite emission pattern in the 6--7 keV band. The prominent \ka line from neutral iron at 6.4 keV is resolved in the \chandra High-Energy Transmission Grating spectrum to a full-width at half maximum of 4700$^{+2700}_{-1500}$ \kms, consistent with an origin from the optical broad-line region. Excess components are detected on both sides of the narrow \ka line: the red one (6.0--6.3 keV) clearly varies in strength in about one year, and hints at the presence of a broad, mildly asymmetric line from the accretion disk; the blue one (6.5--7.0 keV), instead, is likely a blend of different contributions, and appears to be constant when integrated over long enough exposures. However, the \fek excess emission map computed over the 7.5 days of the \xmm monitoring shows that both the red and the blue features are actually highly variable on timescales of $\sim$\,10--15 hours, suggesting that they might arise from short-lived hotspots on the disk surface, located within a few tens of gravitational radii from the central supermassive black hole and possibly illuminated by magnetic reconnection events. Any alternative explanation would still require a highly dynamic, inhomogeneous disk/coronal system, involving clumpiness and/or instability. | About four decades have passed since a crude shape of the X-ray continuum from active galactic nuclei (AGNs) was first revealed (e.g., Ives et al. 1976; Mushotzky et al. 1980), yet the origin of the main spectral components that have been progressively brought out is still largely unclear. The primary X-ray emission, usually described by a power law with high-energy ($\ga$\,100 keV) cutoff, is thought to stem from inverse Compton scattering of ultraviolet (UV) disk photons in a coronal region of hot electrons (e.g., Haardt \& Maraschi 1993). The nature of this corona and of its coupling with the disk, however, remains unknown. Neither do widely accepted explanations exist for the soft (Done et al. 2012; Vasudevan et al. 2014) or hard X-ray excesses (Risaliti et al. 2013; Miller \& Turner 2013), or the broad iron fluorescence lines at $\sim$\,5--7 keV (Tanaka et al. 1995; Inoue \& Matsumoto 2003). In fact, intricate absorption by neutral and/or ionized gas along the line of sight can reproduce any sort of spectral curvature or deviation from the power-law continuum. The unique potential of X-ray observations as a means of probing the immediate surroundings of an accreting supermassive black hole (SMBH) is therefore best exploited in the so-called \textit{bare} active galaxies, where any obscuration effect is negligible. The nearby ($z \simeq 0.0327$; Osterbrock \& Phillips 1977) Seyfert galaxy \ark is arguably the most remarkable object in the bare AGN subclass. It is the X-ray brightest source of this type ($f_\rmn{0.3-10\,keV} \sim f_\rmn{14-195\,keV} \sim 7 \times 10^{-11}$ \fluxcgs; this work; Baumgartner et al. 2013), and it offers the cleanest view to the central engine. Early high-resolution data taken with the Reflection Grating Spectrometer (RGS) onboard \xmm posed stringent constraints on the presence of any warm absorber, whose column density would be at least an order of magnitude lower than found in a typical Seyfert 1 (Vaughan et al. 2004). Moreover, no evidence for UV absorption emerges from the \textit{Hubble Space Telescope} spectrum (Crenshaw et al. 1999). Since it is not affected by any significant foreground screen, the observed X-ray emission of \ark can thus be regarded as representative of the intrinsic high-energy output of an AGN, and of the physical processes associated with the inner accretion flow, such as Comptonization and/or relativistic reflection. \ark displays all the X-ray spectral traits expected for an unobscured, radiatively efficient SMBH, namely a smooth soft excess below 2 keV, an iron K-shell line complex possibly including a broad and skewed component, and a Compton reflection hump peaking at about 30 keV (e.g., Nardini et al. 2011). The soft excess has always been noticeable in \ark since the first X-ray observations (Brandt et al. 1993), but its featureless appearance is compatible with several interpretations, the most relevant of which invoke either the Comptonization of the seed UV photons in the warm disk atmosphere, or the blurring of the soft X-ray reflection-line forest in the strong gravity regime. The broad iron line and the Compton hump are even more puzzling, since their relative intensity apparently decreased in a recent (2013), combined observation with \xmm and \nustar, when the source was found to be two times fainter than usual (Matt et al. 2014). In order to address these open issues and shed new light on the intrinsic X-ray emission of AGNs, \ark was the target of an extensive campaign carried out in 2014 March, consisting of an \xmm long look ($\sim$\,650 ks, or 7.5 days) with joint high-resolution view of the iron-K band with the \chandra High-Energy Transmission Grating (PI: D. Porquet), plus a simultaneous \nustar observation. Here we focus on the properties of the iron K-shell emission features, which can be studied in great detail thanks to the unprecedented depth of the new data sets. The paper is organized as follows: in Section~2 we introduce the various observations and provide the basic information on the data reduction, while Section~3 concerns the analysis of the time-averaged spectra. Section~4 deals with the subsequent discovery of the short-term variability of iron fluorescence. These results and their possible implications on the physics of the X-ray corona are further discussed in Section~5, and conclusions are drawn in Section~6. The consequences of the soft X-ray, grating spectra on the bare character of \ark are the subject of a companion paper (Reeves et al. 2016), while the broadband analysis of the \xmm and \nustar observations, and the modeling of the optical to hard X-ray spectral energy distribution will be presented in a forthcoming work (D. Porquet et al. 2016, in preparation). | We have presented the analysis of the composite emission spectrum due to iron K-shell fluorescence in the local Seyfert galaxy \ark, the nearest and brightest example of a bare AGN, based on a large 2014 campaign consisting of simultaneous \xmm, \chandra/HETG, and \nustar observations. Overall, \ark displays a broad and irregular emission-line complex in the 6--7 keV energy range, where the main feature corresponds to the \ka transition in neutral iron around 6.4 keV. Its profile is well resolved by the \chandra grating to a FWHM of $\sim$\,4700 \kms, consistent with the typical velocity broadening of the optical broad-line region. The narrow \fei \ka accounts for less than one half of the total line emission over this band, though. The residuals take the shape of a red wing down to $\sim$\,6 keV and of a blue plateau across 6.7 keV, connecting to a second, apparent feature centered just below 7 keV. Energy, equivalent width, and variability rule out an interpretation of the red excess as the Compton shoulder of the main, 6.4-keV \ka line. The wing's strength reached a maximum during a 2007 \suzaku observation, dropped by a factor of $\sim$\,2--3 following a low-flux state of the X-ray source in 2013, and then recovered one year later. This behavior suggests the presence of a \fek reflection component from the accretion disk. Indeed, a model including two narrow ($\sigma \simeq 40$ eV) lines at 6.40 and 6.98 keV plus a mildly distorted relativistic disk line successfully reproduces the entire \fek emission complex in \ark over the different epochs. From the time-averaged spectra alone the intensity of the former pair would seem approximately constant, as might be expected for BLR gas, only sensitive to the average continuum over long timescales. The 7-keV narrow feature would thus be (mistakenly) identified with the \fexxvi \ka, possibly blended with the neutral \kb. Some additional fluctuations around 6.4--6.5 keV could be ascribed to the elusive broad component, which is responsible for most of the short-term spectral changes. The disk-line parameters point to an origin in a moderate relativistic regime, at a few/several tens of gravitational radii of distance from the central black hole. Rather than a disk truncation, this likely implies that the main X-ray corona, if extended, smooths out any reflection from the inner disk. Diffuse flares associated with magnetic reconnection events might be involved instead to efficiently illuminate the line-emitting regions further out. Such a conjecture is supported by the \fek excess emission map obtained from the 2014 \xmm monitoring, which covered four consecutive satellite orbits for a span of 7.5 days. This shows that both the red wing and the bulk of the 6.5--7 keV excess (encompassing also the tentative, BLR-like \fexxvi line) undergo significant intensity variations in about $\sim$\,30--50 ks (i.e., 10--15 hours), and that they are substantially uncorrelated with each other. The broad \fek emission feature detected in \ark could then be the superposition of several different peaks arising from short-lived, yet continuously generated orbiting hotspots on the accretion disk surface. Perhaps similar observable effects could be produced also as a result of clumpiness in the corona and/or density inhomogeneities in the disk, provided that these are highly dynamic. Future X-ray observatories like \athena (Nandra et al. 2013) will afford the higher energy resolution and larger effective area in the 6--7 keV band that are needed to reveal any fine structures in the observed \fek profile and to perform a proper time-resolved spectral analysis, so disentangling the various BLR and disk contributions and tracing the evolution of the putative hotspots. Thanks to its bare nature, \ark stands out as the most promising source to study the accretion disk/X-ray corona system in AGNs, and its possible flaring, transient components. \vspace*{0.5cm} \noindent The authors would like to thank the anonymous referee for their useful comments that helped improving the clarity of this paper. EN is supported by the UK Science and Technology Facilities Council under grant ST/M001040/1. DP acknowledges financial support from the French Programme National Hautes Energies (PNHE) and the EU 7th Framework Programme FP7 (2013--2017) under grant agreement number 312789. JNR acknowledges support from \chandra grant number GO4-15092X and NASA grant NNX15AF12G. AL acknowledges support from the UK STFC. The results presented in this paper are based on data obtained with the \chandra \textit{X-ray Observatory}; \xmm, an ESA science mission with instruments and contributions directly funded by ESA member states and NASA; and \suzaku, a collaborative mission between the space agency of Japan (JAXA) and NASA. We have made use of software provided by the \chandra \textit{X-ray Center} (CXC) in the application package \textsc{ciao}. The figures were generated using \texttt{matplotlib} (Hunter 2007), a \textsc{python} library for publication of quality graphics. \appendix | 16 | 9 | 1609.05210 |
1609 | 1609.06739_arXiv.txt | We investigate observable cosmological aspects of sterile neutrino dark matter produced via the freeze-in mechanism. The study is performed in a framework that admits many cosmologically interesting variations: high temperature production via annihilation processes from higher dimensional operators or low temperature production from decays of a scalar, with the decaying scalar in or out of equilibrium with the thermal bath, in supersymmetric or non-supersymmetric setups, thus allowing us to both extract generic properties and highlight features unique to particular variations. We find that while such sterile neutrinos are generally compatible with all cosmological constraints, interesting scenarios can arise where dark matter is cold, warm, or hot, has nontrivial momentum distributions, or provides contributions to the effective number of relativistic degrees of freedom $N_{\text{eff}}$ during Big Bang nucleosynthesis large enough to be probed by future measurements. | \label{sec:introduction} A sterile neutrino is a well-motivated and widely studied dark matter (DM) candidate. The traditional candidate, studied within the Neutrino Minimal Standard Model ($\nu$MSM) \cite{Asaka:2005an,Asaka:2005pn,Asaka:2006nq}, has a keV scale mass, where its mixing with the active neutrinos is appropriate for both producing the correct (warm) dark matter relic abundance through the Dodelson-Widrow (DW) mechanism \cite{Dodelson:1993je} and making it sufficiently long lived. However, this nonzero mixing also results in decays producing a monochromatic gamma ray line, which is constrained by X-ray measurements \cite{Boyarsky:2006fg,Boyarsky:2006ag, Boyarsky:2005us,Boyarsky:2007ay,Boyarsky:2007ge}, while the warm nature of DM from DW production disrupts small scale structure formation, which is constrained by Lyman-$\alpha$ measurements \cite{Seljak:2006qw, Asaka:2006nq, Boyarsky:2008xj}. The combination of these two constraints now rule out DW as a viable production mechanism for sterile neutrino dark matter (see, e.g. \cite{Horiuchi:2013noa} for a recent summary). Several alternate production mechanisms that circumvent these bounds to various degrees exist in the literature \cite{Shi:1998km,Boyarsky:2008mt,Nemevsek:2012cd,Asaka:2006ek,Asaka:2006nq,Bezrukov:2009th,Patwardhan:2015kga,Shuve:2014doa,Khalil:2008kp,Lello:2014yha,Falkowski:2011xh,Biswas:2016bfo}. The Shi-Fuller mechanism \cite{Shi:1998km} produces a colder population but requires fine-tuned parameters to ensure resonant production, and might still be incompatible with structure formation \cite{Horiuchi:2015qri,Schneider:2016uqi}. Thermal freeze-out with additional interactions, followed by appropriate entropy dilution, can result in the correct relic abundance \cite{Bezrukov:2009th,Nemevsek:2012cd,Patwardhan:2015kga}, but faces strong constraints from Big Bang nucleosynthesis \cite{King:2012wg}. One mechanism that is particularly successful and employed widely is sterile neutrino dark matter production through the freeze-in mechanism \cite{Chung:1998rq, Hall:2009bx} via a feeble coupling to some particle beyond the Standard Model present in the early universe. This can be realized in several motivated frameworks: this particle could be the inflaton \cite{Shaposhnikov:2006xi}, a heavy higgs in an extended Higgs sector \cite{Petraki:2007gq,Kusenko:2006rh,McDonald:1993ex,Yaguna:2011qn,Merle:2013wta,Adulpravitchai:2014xna,Kang:2014cia}, a scalar that breaks a symmetry that the sterile neutrinos might be charged under \cite{Roland:2014vba,Roland:2015yoa,Heurtier:2016iac}, a charged scalar motivated by leptogenesis \cite{Frigerio:2014ifa}, the radion in warped extra dimension models \cite{Kadota:2007mv}, or pseudo-Dirac neutrinos \cite{Abada:2014zra}; for a recent review of various scenarios that admit freeze-in of sterile neutrino dark matter, see Ref.\,\cite{Shakya:2015xnx}. Such scenarios carry the dual virtues of a colder sterile neutrino population compared to DW as well as not relying on any mixing with the active neutrinos for production, thereby alleviating the tension with Lyman-$\alpha$ and X-ray measurements. \footnote{It should be clarified that DW is technically also a freeze-in mechanism; in this paper, freeze-in will be understood to refer to production mechanisms that do not involve active-sterile mixing.} The phenomenological signatures of sterile neutrino dark matter from such freeze-in scenarios are in stark contrast to those from DW production. In the latter framework, the ``smoking gun" signature is a monochromatic X-ray line from the loop level decay into an active neutrino and a single photon, induced by the mixing between active and sterile neutrinos required for DW production. In the freeze-in scenario, this mixing angle can be arbitrarily small, and there is essentially no direct coupling between the sterile neutrino dark matter candidate and the Standard Model particles; hence no signals arising from such active-sterile mixing that characterize sterile neutrino dark matter from DW, such as astrophysical signatures in gamma rays or direct production in searches for neutral leptons in laboratory experiments \cite{PIENU:2011aa,Bergsma:1985is,Ruchayskiy:2011aa,Bernardi:1985ny,Bernardi:1987ek,Vaitaitis:1999wq}, are expected. The most promising observable imprints are instead of a cosmological nature: the phase space distribution of sterile neutrinos from freeze-in is distinct from that arising from DW, and can lead to possible deviations in free-streaming lengths of warm dark matter or the dark radiation content of the universe during Big Bang nucleosynthesis (BBN) or cosmic microwave background (CMB) decoupling. Although the exact properties depend on the details of the underlying model, given that such cosmological imprints offer the most direct probes of sterile neutrino dark matter from freeze-in, it is worth studying such features in greater detail in a broad framework. The purpose of this paper is to investigate such potentially observable cosmological aspects of sterile neutrino dark matter. We perform this study in a specific model, based on Ref.\,\cite{Roland:2014vba}, which admits many cosmologically interesting variations: production can occur via annihilation processes from higher dimensional operators that are active at the highest temperatures (referred to as ultraviolet (UV) freeze-in), or from decays of a scalar, which occur at lower temperatures (infrared (IR) freeze-in); the scalar producing the dark matter population can be taken to be in or out of equilibrium with the thermal bath; moreover, both supersymmetric and non-supersymmetric setups can be considered. The framework therefore covers a diverse range of possibilities, allowing us to both extract generic properties and highlight features unique to particular variations. Similar studies have been performed in previous work in the literature \cite{Merle:2015oja,Petraki:2007gq}, but in a more constrained framework of a keV scale sterile neutrino with IR production only in a non-supersymmetric setup. The paper is organized as follows. Section \ref{sec:model} outlines the theoretical framework and the various scenarios that we investigate in this paper. Section \ref{sec:formalism} describes the formalism employed in our calculations, covering the topics of Boltzmann equations, entropy dilution, the various observables of interest, and the simplifying assumptions made in our formalism. Results of our calculations are presented for various scenarios in Section \ref{sec:results}. We conclude by summarizing our main results in Section \ref{sec:summary}. Details of the Boltzmann equations and related collision terms used to derive our results are presented in Appendix \ref{sec:Collision}. | \label{sec:summary} In this paper, we have investigated cosmological aspects of light ( $\lsim$ GeV scale) sterile neutrino dark matter produced from the freeze-in mechanism. Given that such a dark matter candidate interacts feebly with the SM and thus has no promising indirect or direct search strategies, such cosmological aspects represent the most phenomenologically interesting features of such a candidate. While previous papers have performed similar studies in more restricted setups, we perform this study in a comprehensive framework that includes many interesting variations: production from a scalar in or out of equilibrium with the thermal bath in the early universe, via UV or IR freeze-in, and with or without supersymmetry. Under this broad approach, we find many novel features that were missed by earlier studies. Our findings can be summarized as follows: \begin{itemize} \item Relic density: The relic abundance required to explain all of dark matter can be achieved in all scenarios considered. Production can occur dominantly through UV freeze-in, IR freeze-in from decays of the scalar $\phi$ in or out of equilibrium with the SM bath, or through decays of a sterile sneutrino in supersymmetric setups; more generally, any combination of these processes can also result in the observed relic density. \item Free-streaming length: We find that sterile neutrino dark matter produced via freeze-in can be cold, warm, or hot, depending on the dominant production mechanism and choice of parameters. Dark matter from UV production or decay of $\phi$ in equilibrium with the thermal bath is generally cold (Scenario I), while late out of equilibrium decay of $\phi$ or the sterile sneutrino $\tilde{N}_1$ can result in warm or hot dark matter (Scenarios II, III, IV). Such scenarios can be of great interest from the point of view of structure formation. \item Phase space distribution: Given the interplay of multiple production mechanisms for dark matter, its momentum distribution can be extremely varied and nontrivial. UV and IR freeze-in produce dark matter with slightly different momentum distributions (Fig.\,\ref{fig:uvirps}); likewise, dark matter produced from decays of $\phi$ (in or out of equilibrium) and $\tilde{N}_1$ can have significantly different distributions if the times and energy scales of decay are very different (see Fig.\,\ref{fig:s4ps}). Note that such distributions are possible only because the $N_1$ abundance freezes in and only has feeble SM and self interactions, hence different components produced from different mechanisms do not mix but maintain their individual phase space distributions. Such features are not present in the traditionally studied dark matter candidates that freeze out of equilibrium. \item Contributions to $\Delta N_{\rm eff}$ during BBN: Extremely energetic dark matter particles in the early universe can mimic dark radiation, contributing to the effective number of relativistic degrees of freedom $\Delta N_{\rm eff}$. For GeV scale sterile neutrinos, we find that such contributions are more likely at BBN than CMB since they redshift and become non-relativistic at later times. We find that $\Delta N_{\rm eff}$ is generally restricted to negligible values ($\lsim 10^{-4}$) by free-streaming length constraints if $N_1$ makes up all of dark matter ($\eg$ Fig.\,\ref{fig:FSNeffPlot}). However, free-streaming constraints can be circumvented if $N_1$ makes up only a subdominant fraction (\,$\lsim 1\%$\,) of dark matter, and in this case we find that $\Delta N_{\rm eff}\sim\mathcal{O}(0.1)$ can indeed be realized consistent with all other constraints (see Fig.\,\ref{fig:s4NeffPlot}). \end{itemize} Finally, while we performed the above study in a specific framework, so that many of the quantitative results are model-dependent, we emphasize that the general features discussed here represent the most observable aspects of frozen in sterile neutrinos, and are more broadly applicable to any framework that has such a candidate. \medskip \textit{Acknowledgements: }We thank James D. Wells for collaboration in the early stages of the project, and for valuable discussions and suggestions on the manuscript. The authors are supported in part by the DoE under grants DE-SC0007859 and DE-SC0011719. This work was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1066293. | 16 | 9 | 1609.06739 |
1609 | 1609.09406.txt | {}{}{}{}{} % 5 {} token are mandatory \abstract % context heading (optional) % {} leave it empty if necessary {Pre-stellar cores within molecular clouds provide the very initial conditions in which stars are formed. FeSt\,1-457 is a prototypical starless core and the most chemically evolved among those isolated, embedded in the most pristine part of the Pipe nebula, the bowl.} % aims heading (mandatory) {We use the IRAM 30m telescope and the PdBI to study the chemical and physical properties of the starless core FeSt\,1-457 (Core 109) in the Pipe nebula.} % methods heading (mandatory) {We fit the hyperfine structure of the N$_2$H$^+$ (1$-$0) IRAM 30m data. This allow us to measure with high precision the velocity field, line widths and opacity and derive the excitation temperature and column density in the core. We use a modified Bonnor-Ebert sphere model adding a temperature gradient towards the center to fit the 1.2 mm continuum emission and visual extinction maps. Using this model, we estimate the abundances of the N$_2$H$^+$ and the rest of molecular lines detected in the 30 GHz wide line survey performed at 3 mm with IRAM 30m using ARTIST software.} % results heading (mandatory) {The core presents a rich chemistry with emission from early (C$_3$H$_2$, HCN, CS) and late-time molecules (e.g., N$_2$H$^+$), with a clear chemical spatial differentiation for nitrogen (centrally peaked), oxygen (peaking to the southwest) and sulphurated molecules (peaking to the east). For most of the molecules detected (HCN, HCO$^+$, CH$_3$OH, CS, SO, $^{13}$CO and C$^{18}$O), abundances are best fitted with three values, presenting a clear decrease of abundance of at least 1 or 2 orders of magnitude towards the center of the core. The Bonnor-Ebert analysis indicates the core is gravitationally unstable and the magnetic field is not strong enough to avoid the collapse.} % conclusions heading (optional), leave it empty if necessary {Depletion of molecules onto the dust grains occurs at the interior of the core, where dust grain growth and dust depolarization also occurs. This suggests that these properties may be related. On the other hand, some molecules exhibit asymmetries in their integrated emission maps, which appear to be correlated with a previously reported submillimetre polarization asymmetry. These asymmetries could be due to a stronger interstellar radiation field in the western side of the core.} %We present N$_2$H$^+$ (1$-$0) single-dish and interferometric high spectral resolution observations and a 30 GHz wide line survey at 3 mm towards the starless core FeSt\,1-457, located in the `bowl' region of the Pipe nebula. The core presents a clear southwest-northeast velocity gradient and a very rich chemistry of early and late-time molecules. It also shows a clear chemical differentiation for nitrogen, oxygen and sulphurated molecules. A modified Bonnor-Ebert sphere model adding a temperature gradient towards the center was used to fit the 1.2 mm continuum emission and visual extinction maps. Using the modified Bonnor-Ebert model, we estimated the abundances of the detected molecules using a radiative transfer code which revealed depletion of about 1 or 2 orders of magnitude for several molecules (HCN, HCO$^+$, CH$_3$OH, CS, SO, $^{13}$CO and C$^{18}$O), at a common radius of $\la55$ arcsec. The depletion occurs at a similar density, $\sim5\times10^4$~cm$^{-3}$, where dust grain growth and dust depolarization also occurs. This suggests that these properties may be related. However, N$_2$H$^+$, HC$_3$N and C$_3$H$_2$ show an almost constant abundance and the abundance of {\bf HNC and} NH$_2$D increases in the inner region of the core. Finally, some molecules exhibit asymmetries in their integrated emission maps, which appear to be correlated with a previously reported submillimetre polarization asymmetry. These asymmetries could be due to a stronger interstellar radiation field in the western side of the core. | Pre-stellar cores within molecular clouds constitute the stage previous to the star formation process. They provide the very initial conditions in which stars are formed. They are typically cold ($\le10$ K) with temperature gradients decreasing towards the center \citep[e.g.,][]{Ruoskanen11,Wilcock12,Launhardt13}, and densities $>10^4$ cm$^{-3}$, with a chemistry affected by molecular freeze-out onto dust grains \citep[e.g.,][]{Tafalla02,Marsh14}. Their physical structure can be well explained through a Bonnor-Ebert profile \citep{Bonnor56,Ebert55}, i.e., the profile corresponding to an isothermal gas sphere in hydrostatic equilibrium \citep[e.g.,][]{Evans01,Kandori05,Roy14}. However, their density and temperature gradient structures are still under debate \citep[e.g.,][]{Sipila11,Hardegree-Ullman13} and the implications of heavy molecular depletion on other physical properties, such as dust grain properties and polarization, are not clear. FeSt\,1-457 \citep{FeSt84}, also known as Core 109 in \citet{Lombardi06} catalogue, is a prototypical starless core, as previous studies have shown that this core is quiescent with no IRAS nor Spitzer Space Telescope point sources associated \citep{Forbrich09,Forbrich15,Ascenso13}. Indeed, the internal luminosity, estimated using the non-detection from the 70 $\mu$m Herschel\footnote{Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.} image ($3\times\mathrm{rms}=0.02$ Jy pixel$^{-1}$) and using the relation between the 70 $\mu$m flux and the internal luminosity \citep{Dunham08}, is L$_\mathrm{int}<0.004$ L$_\odot$. It is also the most chemically evolved starless core among those isolated, embedded in the most pristine part of the Pipe nebula, the bowl, at a distance of 145 pc \citep{AlvesFranco07}. \citet{Frau15} suggest the presence of two filaments with north-south and east-west directions colliding along the northwest-southeast direction at the bowl region, just where FeSt\,1-457 is located. %(no IRAS nor Spitzer Space Telescope point sources associated). As there is a tight correlation between the 70 $\mu$m flux and the internal luminosity of a protostar \citep{Dunham08}, we used the non-detection from the 70 $\mu$m Herschel image ($3\times\mathrm{rms}=0.02$ Jy pixel$^{-1}$ and the relation given in eq. (2) of \citet{Dunham08} to estimate an upper limit for the internal luminosity of L$_\mathrm{int}<0.004$ L$_\odot$ %(using the non-detection from the 70 $\mu$m Herschel\footnote{\bf Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.} image \citep[$3\times\mathrm{rms}=0.02$ Jy pixel$^{-1}$) and the relation given in eq. (2) of][]{Dunham08}.with no IRAS nor Spitzer Space Telescope point sources associated. The internal luminosity upper limit, estimated from the 70 ?m Herschel1 image (3 ? rms = 0.02 Jy pixel?1), and using the relation between 70 ?m flux and internal luminosity (Dunham et al. 2008), is Lint < 0.004 L?. is a prototypical starless core, as previous studies have shown that this core is quiescent with no IRAS nor Spitzer Space Telescope point sources associated (Forbirch et al. 2009, 2013; Ascenso et al. 2013). Indeed, the internal luminosity, estimated using the non-detection from the 70 ?m Herschel1 image \citet{Frau12a} carried out a 15 GHz bandwidth molecular survey at 3 mm towards FeSt\,1-457 with the Institute of Millimeter Radioastronomy (IRAM) 30m telescope. They find a rich chemistry (specially compared with most of the other Pipe starless cores): many lines are detected from early- (C$_3$H$_2$, HCN, CS, C$^{34}$S and CN) and late-time (N$_2$H$^+$, N$_2$D$^+$ and DCO$^+$) molecules, suggesting that FeSt\,1-457 is an evolved starless core. \citet{Aguti07} observed the 3 mm lines of N$_2$H$^+$, HCO$^+$, CS and C$^{18}$O with the IRAM 30m. They find evidence of CO and HCO$^+$ depletion in the center of the core. However, the N$_2$H$^+$ ($1-0$) may be undepleted to depths of $\la40$ mag of visual extinction. FeSt\,1-457 has a mass of $\sim4$ M$_\odot$ \citep{Frau10,Roman-Zuniga10}, quasi spherical and compact structure and shows signs of gravitational instability \citep{Kandori05,Frau10}. \citet{Aguti07} find that FeSt\,1-457 might be pulsating, based on expansions of the outer layers. However, their Jeans mass measurement is compatible with the mass of the core and they propose a quasi-stable state near hydrodynamic equilibrium. The core is embedded in a magnetised medium \citep{Alves08,Alves14,Franco10}, which suggests that the magnetic field could be a source of external support. \citet{Alves14}, in a multi scale polarization study towards FeSt\,1-457, find a polarization `hole' for radii $\la55$ arcsec which they propose to be the result of loss of grain alignment with the magnetic field due to the lack of an internal source of radiation. %In this work we present N$_2$H$^+$ (1$-$0) observations towards the FeSt\,1-457 starless core obtained with the IRAM 30m and Plateau de Bure Interferometer (PdBI) telescopes\footnote{IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).}. We also present maps of the molecular lines detected at 3 mm within a frequency range spanning 30 GHz obtained with the IRAM 30m which allowed us to perform a detailed study of the abundance radial profiles and to relate them to the known grain growth and depolarization in the center. In this work we study the starless core FeSt\,1-457 through N$_2$H$^+$ (1$-$0) observations obtained with the IRAM 30m and Plateau de Bure Interferometer (PdBI) telescopes\footnote{IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).}. N$_2$H$^+$ is known to be a very good tracer of the densest inner parts of dense cores as it is not expected to be depleted until densities >$10^5$ cm$^{-3}$ \citep[e.g.,][]{Bergin07}. In addition, we present mapping information of 15 molecular lines detected at 3 mm within a frequency range spanning 30 GHz obtained with the IRAM 30m which allowed us also to perform a detailed study of the abundance radial profiles and to relate them to the known grain growth and depolarization in the center. %-------------------------------------------------------------------- | We have used the IRAM 30m telescope and the PdBI to study the chemical and physical properties of the starless core FeSt\,1-457 (Core 109) in the Pipe nebula. Our main conclusions are as follows: \begin{enumerate} \item We fit the hyperfine structure of the N$_2$H$^+$ (1$-$0) IRAM 30m data. This allows to measure with high precision the velocity field and line widths in the core. The N$_2$H$^+$ emission shows a clear southwest-northeast velocity gradient of 1.78 km s$^{-1}$ pc$^{-1}$, and larger line widths (0.3 km s$^{-1}$) at the southwest part of the map. The typical line widths are $0.17-0.23$ km s$^{-1}$. The column density map presents an arc-structure around the the 1.2 mm dust continuum peak. \item Combining both IRAM 30m and PdBI N$_2$H$^+$ (1$-$0) data we can resolve the arc-like structure hinted at the single dish map. \item The core presents a rich chemistry with emission from early (C$_3$H$_2$, HCN, CS) and late-time molecules (e.g., N$_2$H$^+$), with a clear chemical spatial differentiation for nitrogen (centrally peaked), oxygen (peaking to the southwest) and sulphurated molecules (peaking to the east). \item The chemical difference in the core could be due to an external UV radiation field penetrating into the core from the (south)west which could be also affecting the polarization properties. This implies that the core should be close to the edge of the molecular cloud. \item FeSt\,1-457 is well fitted with a Bonnor-Ebert sphere model and introducing a temperature gradient decreasing towards the center from 12 to 6 K. We found the core is gravitationally unstable and that the magnetic field is not enough to stop the collapse. \item We have analyzed the abundances of the molecular lines using the ARTIST software. For most of the molecules detected (HCN, HCO$^+$, CH$_3$OH, CS, SO, $^{13}$CO and C$^{18}$O), abundances are best fitted with three values, presenting a clear decrease of abundance of at least 1 or 2 orders of magnitude towards the inner region of the core. This is consistent with chemical models of starless cores, that show that there is a significant depletion of molecules onto the dust grains. On the other hand, N$_2$H$^+$, HC$_3$N and C$_3$H$_2$ are well fitted with a constant abundance throughout the core and the abundance of HNC and NH$_2$D increases in the inner region of the core (at radius $\la55$ arcsec). %radius $\la55$ arcsec, corresponding to densities $>5\times10^4$ cm$^{-3}$. \end{enumerate} Finally, we have seen that depletion of molecules onto the dust grains, grain growth and depolarization take place at the inner region of the core. This strongly suggests that these properties could be correlated in FeSt\,1-457. %within a very similar radius ($\sim8000$ au) corresponding to densities $>5\times10^4$ cm$^{-3}$ and temperatures between $11-12$ K. | 16 | 9 | 1609.09406 |
1609 | 1609.04020_arXiv.txt | We present the first robust detection of \HI\ 21 cm emission in the blue compact galaxy Haro 11 using the 100m Robert C. Byrd Green Bank Telescope (GBT). Haro 11 is a luminous blue compact galaxy with emission in both Lyman Alpha and the Lyman continuum. We detect (5.1 \pom\ 0.7 $\times$10$^8$) \msun\ of \HI\ gas at an assumed distance of 88 Mpc, making this galaxy \HI\ deficient compared to other local galaxies with similar optical properties. Given this small \HI\ mass, Haro 11 has an elevated M$_{H2}$/M$_{HI}$ ratio and a very low gas fraction compared to most local galaxies, and contains twice as much mass in ionized hydrogen as in neutral hydrogen. The \HI\ emission has a linewidth of 71 \kms\ and is offset 60 \kms\ redward of the optical line center. It is undergoing a starburst after a recent merger which has elevated the star formation rate, and will deplete the gas supply in $<$ 0.2 Gyr. Although this starburst has elevated the SFR compared to galaxies with similar \HI\ masses and linewidths, Haro 11 matches a trend of lower gas fractions toward higher star formation rates and is below the general trend of increasing \HI\ mass with increasing luminosity. Taken together, our results paint Haro 11 as a standard low-mass galaxy that is undergoing an unusually efficient star formation episode. | \label{sec:intro} Haro 11 is a luminous blue compact galaxy (LBCG), a class of very bright and blue galaxies with intense star formation. Rare in the local universe \citep{Werk:2004de}, these LBCGs are typically gas rich \citep{Garland:2004ec} and likely form from merger events \citep{Ostlin:2001ch, Bekki:2008jt}. Haro 11 is a powerful emitter across the electromagnetic spectrum. It is classified as a Luminous InfraRed Galaxy (LIRG) with an infrared luminosity of $>$ 10$^{11}$L$_{\odot}$, and shows signs of strong star formation likely due to a recent merger \citep{Bergvall:2000tg, Ostlin:1999cl, Ostlin:2015tc}. Haro 11 also shows emission in \lya\ from some of its star forming regions \citep{Hayes:2007hk} and is one of a few currently known Lyman continuum emitting galaxies in the local universe \citep{Bergvall:2006ib, Leitet:2013cw}. The detection of \lya\ in emission in Haro 11 is particularly interesting. \lya\ is an energetic star formation tracer that, in theory, can probe the stellar processing in the early epochs of the universe. In practice, this line suffers from strong resonance scattering, uncertain extinction properties, and the fact that it is unobservable from the ground due to atmospheric absorption. The scattering and extinction process is further complicated by a number of confounding factors. Dust content and properties alone cannot explain the observed extinction of \lya\ (e.g. \citealt{1996ApJ...466..831G, Atek:2009hra}); instead, trends are apparent between the neutral gas content and geometry \citep{2004ApJ...608..768C, 1998A&A...334...11K}. Super bubbles formed after star formation episodes can clear a path for escaping \lya\ photons by shifting \HI\ atoms into a different rest frame \citep{1998astro.ph..9096K, TenorioTagle:1999bx}. \lya\ photons can also scatter while avoiding dust grains and spread into large halos \citep{2013ApJ...765L..27H, Hayes:2015wy}. Many of these hypotheses are now being tested by targeted observations using the Hubble Space Telescope \citep[HST;][]{Wofford:2013hg, Ostlin:2014vk}. In particular, the Lyman Alpha Reference Sample \citep[LARS;][]{Ostlin:2014vk, Hayes:2014jv, Pardy:2014ir, Guaita:2015kr, RiveraThorsen:2015ct} targeted 14 low-z potential \lya\ emitters based on their ultraviolet luminosities and \halpha\ equivalent widths. Initial observations of the LARS galaxies with the HST were followed up with multi-wavelength observations of the gas and dust content, including neutral hydrogen in absorption \citep{RiveraThorsen:2015ct} and emission \citep{Pardy:2014ir}. Combining observations of \lya\ and \HI\ emissions allow for direct comparisons and testing of the scattering effects at work. When combined with a dust tracer like \halpha/\hbeta, this technique can also probe the extinction effects at work \citep{Hayes:2014jv}. Given its proximity and star formation intensity, Haro 11 is a prime candidate for studies of \lya\ radiative transfer. The galaxy has three primary star forming knots A, B, and C \citep[see \autoref{fig:Haro11Img};][]{Vader:1993fk, 2003ApJ...597..263K, Adamo:2010jv}. One of these knots, knot C, shows \lya\ emission, while the other two show absorption. This is striking because knots C and B have very similar dust content and extinction values \citep{Atek:2008hn}. Further complicating matters, knot B has a stronger outflow of interstellar gas, yet no sign of \lya\ emission \citep{Sandberg:2013hw}. Haro 11's ISM properties have been extensively studied. \citet{Cormier:2014il} studied the molecular gas content of Haro 11 using both CO gas and IR dust emission. That work found a total H$_2$ mass of between 2.5$\times$10$^8$ and 3.6$\times$10$^9$ depending on the tracer used. \citet{James:2013ia} used a variety of metallicity tracers to find a range of metallicities across the star forming knots from 12 + log(O/H) = 8.25 \pom\ 0.15 and Z/Z$_{\odot}$ = 0.35 in Knot B, down to 8.09 \pom\ 0.23 (Z/Z$_{\odot}$ = 0.24) in Knot A, and 7.80 \pom\ 0.13 (Z/Z$_{\odot}$ = 0.12) in Knot C. Yet, to date there has been no direct detection of 21 cm emission for Haro 11. \citet{Bergvall:2000tg} first placed an upper limit on \HI\ emission of $\le$ 10$^8$ \msun. \HI\ was then seen in absorption by \citet{MacHattie:2014ipa}, giving a mass range of (3-10)$\times 10^8$ \msun, with an upper limit on the emission of M$_{HI} \le 1.7 \times 10^9$\msun. This absorption measurement assumed a spin temperature between 91 and 200 K in the optically thin regime. In this paper we present the first robust detection of the \HI\ spectral line in emission. In \autoref{sec:obs} we discuss the observations and data reduction. In \autoref{sec:results} and \autoref{sec:discussion} we present the results and interpret them in the context of LARS and other \lya\ emitters. \begin{figure}[h] % \centering \includegraphics[width=3.5in]{Haro11Adamofig1.pdf} \caption{HST image of Haro 11 and its three primary star-forming knots. Figure from \citet{Adamo:2010jv}. Knot C is the only knot with \lya\ emission, even though it shares very similar dust content with knot B \citep{Atek:2008hn}, which also has a stronger outflow of interstellar gas \citep{Sandberg:2013hw}.} \label{fig:Haro11Img} \end{figure} Throughout this paper we assume a value of H$_0$ = 70.2 \pom\ 1.4 \kms\ Mpc$^{-1}$ \citep{2011ApJS..192...18K}. | \label{conclusions} Haro 11 is a local starburst galaxy undergoing a major merger of two dwarf galaxies \citep{Ostlin:1999cl, Ostlin:2015tc}. It has long been known to be a local \lya-emitter, but until now has only had upper limits placed on its cold gas content. Our main contribution is the first robust detection of \HI\ gas in emission from this blue compact galaxy consistent with previous upper limits \citep{Bergvall:2000tg, MacHattie:2014ipa}. We find a dearth of \HI\ gas and a linewidth at 50\% of maximum that is smaller relative to other local starburst and LARS galaxies \citep{Ostlin:2014vk, Hayes:2014jv, Pardy:2014ir}. Given the small \HI\ mass, Haro 11 has an elevated M$_{H2}$/M$_{HI}$ ratio and a very low gas fraction compared to most local galaxies. Much of the hydrogen that remains has been heated during the merger process. \citet{Bergvall:2002ea} derived a mass of 10 \pom\ 1 $\times$10$^8$\msun\ for the ionized hydrogen, twice as much as in neutral hydrogen. Haro 11 is undergoing an unusually efficient star formation episode, and matches a trend of lower gas fractions toward higher star formation rates and shares \HI\ properties with galaxies of similar B-band magnitude. Haro 11 is a known merging galaxy, which could explain the presence of tidal arms and complicated ISM kinematics. Two other merging local \lya-emitters ESO\,338$-$IG\,004 (Tol\,1924$-$416) and IRAS 08339+6517 were studied by \citet{2004ApJ...608..768C} who found extended neutral gas connecting the main galaxy and companions. The processes that govern \lya\ transport are complicated, but most often thought to involve the bulk motion of \HI\ gas \citep{Hayes:2015wy}. Mapping the \HI\ gas in emission across Haro 11 will be the only way to test these hypotheses, but this task remains a challenge for the current generation of radio telescopes. As we move to the high resolution \HI\ era with the Square Kilometer Array (SKA), Haro 11 will be an excellent nearby target to probe the complicated coupling to cold neutral gas and \lya\ propagation. Probing the three distinct star formation knots will reveal processes at work in enabling \lya\ escape. | 16 | 9 | 1609.04020 |
1609 | 1609.04399_arXiv.txt | Observations suggest that there is a significant fraction of O-stars in the field of the Milky Way that appear to have formed in isolation or in low mass clusters ($<$100~$M_\odot$). The existence of these high-mass stars that apparently formed in the field challenges the generally accepted paradigm, which requires star formation to occur in clustered environments. In order to understand the physical conditions for the formation of these stars, it is necessary to observe isolated high-mass stars while they are still forming. With the \emph{Hubble~Space~Telescope}, we observe the seven most isolated massive ($>$8~$M_\odot$) young stellar objects (MYSOs) in the Large~Magellanic~Cloud (LMC). The observations show that while these MYSOs are remote from other MYSOs, OB associations, and even from known giant molecular clouds, they are actually not isolated at all. Imaging reveals $\sim$100 to several hundred pre--main-sequence (PMS) stars in the vicinity of each MYSO. These previously undetected PMS stars form prominent compact clusters around the MYSOs, and in most cases they are also distributed sparsely across the observed regions. Contrary to what previous high-mass field star studies show, these observations suggest that high-mass stars may not be able to form in clusters with masses less than 100~$M_\odot$. If these MYSOs are indeed the best candidates for isolated high-mass star formation, then the lack of isolation is at odds with random sampling of the IMF. Moreover, while isolated MYSOs may not exist, we find evidence that isolated clusters containing O-stars can exist, which in itself is rare. | \label{sec:intro} Approximately 20~percent of the Galactic main sequence O-stars are isolated field stars \citep[e.g.,][]{Mason1998}. After correcting for clustered environments and runaways, only \mbox{4\,--\,10}~percent of all O-stars appear to be truly isolated \citep[e.g.,][]{deWit2004,deWit2005,Zinnecker2007}. Isolated field O-stars are also suggested to account for 20\,to\,30\,percent of the high-mass stellar populations in star-forming galaxies \citep{Oey2004}. The existence of these stars is perplexing when one considers two theoretical expectations: 1) the relation between the maximum stellar mass and the hosting-cluster mass excludes O-stars from forming in clusters with masses $\leq$ 250~M$_\sun$ \citep[e.g.,][]{Weidner2006}, and 2) the maximum stellar mass is set by the high-mass end of a fully-populated stellar initial mass function \citep[IMF;][]{OeyClarke2005}. In favor of {\em in situ} formation, Monte Carlo simulations of a randomly sampled IMF suggest that ``isolated'' O-stars are likely formed in clusters with numerous unseen lower-mass stars \citep{Parker2007}, while contrary to being formed {\em in situ}, field O-type stars are proposed to be explained as runaway stars that are difficult to trace back to their original cluster or are remnants of clusters that have undergone significant dissolution \citep[e.g.,][]{Pflamm2010, Gvaramadze2012}. According to the generally accepted paradigm of star formation, stars typically form in giant molecular clouds (GMCs). \citet{Lamb2010} presented a \emph{Hubble Space Telescope} (\emph{HST}) study on isolated high-mass stars for eight main sequence OB-stars in the Small Magellanic Cloud (SMC). With a detection limit of 1 M$_\sun$, these authors found that two stars are runaways, three are in small clusters, and the remaining three appear to be isolated. Furthermore, two of these isolated OB stars are in \ion{H}{2} regions without bow-shocks, increasing the likelihood that they are in their natal environment. \cite{Oey2013} identified in the SMC 14 additional field OB stars with symmetric dense \ion{H}{2} regions around them, minimizing the likelihood that these objects have transverse runaway velocities. All stars are confirmed spectroscopically to be strong candidates for field high-mass stars that formed in situ \citep{Lamb2015}. Given that the main sequence lifetime of these particular O-stars is about an order of magnitude shorter than that of a GMC \citep[$\sim$20--40 Myr in the Local Group,][]{Kawamura2009,Miura2012}, these observations suggest that high-mass star formation may not require GMCs. Therefore, the fact that some O-stars may form in isolation allows for a new and interesting probe of high-mass star formation. \begin{figure*}[t!] \begin{center} \includegraphics[scale=0.55,angle=90]{fig01.pdf} \caption{H$\alpha$ image (with no background subtraction) of the LMC from the Magellanic Cloud Emission Line Survey \citep{SmithMCELS1999}. As indicated in the legend, small green $\times$'s are known stars in OB associations from \citet{Lucke1970}, magenta large $\times$'s are MYSOs observed with $HST$ presented in this paper, large red filled circles are MYSOs identified in GC09, small black empty black circles are sources which were confirmed to be MYSOs in \citet{Seale2009}, and orange, yellow, and blue empty circles are definite, probable, and possible YSOs, respectively, as categorized in GC09. The cyan contours show the CO(1--0) from MAGMA \citep{Wong2011} and indicate locations of GMCs. The cyan border indicates the entire LMC NANTEN \citep{Fukui2008} CO(1--0) survey. The MYSOs observed with $HST$ are numbered, corresponding to the following names: (1) 045403.62--671618.5, (2) 050941.94--712742.1, (3) 051906.69--682137.4, (4) 052124.90-660412.9, (5) 053244.25--693005.7, (6) 053342.15--684602.8, and (7) 053431.46--683513.9. \label{LMC_YSOs} } \end{center} \end{figure*} If high-mass field stars represent a population of stars that previously formed in isolation, there should be many high-mass stars that are currently forming in isolation. Specifically, considering that there are thousands of stars with $M>$10\,M$_\sun$ that are currently in the accretion phase in the Galaxy \citep{Zinnecker2007}, and it has been proposed that 4--10\% of O-stars are formed in isolation, the Galaxy should contain 100s of isolated high-mass stars under formation. However, convincing evidence of isolated field stars that are currently in the accretion phase is lacking. The only investigation of such a candidate is that of the compact star-forming region N33 in the SMC, reported by \cite{Selier2011}. These authors did not find any traces of a stellar clustering around the region on scales $\gsim$\,3\,pc, while on smaller scales a marginal concentration of faint stellar sources was discovered clustered around a high-mass O6.5-O7 main-sequence star. As pointed out by \citet{Bressert2012}, the term ``isolated high-mass star formation'' can be unclear. Specifically, these authors suggested three possible criteria that may suggest a high-mass star is \emph{not} isolated: 1) a high-mass star is forming with other high-mass stars in a molecular cloud; 2) the formation of a high-mass star may be triggered by another high-mass star; and 3) a high-mass star was gravitationally bound (within $\sim$3 pc) with another high-mass star sometime in the past. \citet{Bressert2012} were specifically interested in criterion 3, the least restrictive of the criteria, and found 15 candidates in the 30~Doradus region that may satisfy this criterion. This study is more concerned with the most restrictive of the criteria, criterion 1, and therefore it is more akin to the investigations of field O-stars by \citet{deWit2004,deWit2005} and \citet{Zinnecker2007}, who suggested that 4--10\% of all Galactic O-stars are not runaways, but formed in isolation. Our analysis also focuses in particular on high-mass stars at early stages of their formation. During its formation, the high-mass star will typically reach the main-sequence (i.e., commencing hydrogen fusion) while still accreting \citep[e.g.,][]{YorkeSonnhalter2002,Zinnecker2007}. Since the term ``protostar" is typically reserved for pre--main-sequence (PMS) stars, we use the term young stellar object (YSO) for embedded sources. Indeed, the massive YSOs (MYSOs) targeted in this study are associated with ionized gas and are embedded \citep{Seale2009}, and thus are on the main sequence and are likely still accreting. While observations of high-mass star forming regions can be studied at the highest resolution in our Galaxy, surveys of these regions have complications. Distances are typically measured kinematically and have high uncertainties -- especially since there is an ambiguity of assigning the velocity to a ``near arm'' distance or a ``far arm'' distance. Moreover, the Galaxy has high extinction and confusion along the line of sight, which causes significant difficulty in assigning which emission is happening at which distance. Therefore, it is very challenging to analyze Galactic emission at GMC-scales around MYSOs and to create unbiased and uniform surveys for high-mass star formation in the Galaxy. The Large Magellanic Cloud (LMC), being one of the nearest galaxies to the Milky Way, mitigates most of these problems, and therefore it is an ideal laboratory for uniform surveys of high-mass star formation. Specifically, all sources are at a similar distance of about 50~kpc \citep[][$\sim$0.25~pc per arcsecond]{Feast1999} and the nearly face-on orientation and low extinction allows for large regions to be studied unambiguously. Due to the observational advantages over the Galaxy, the entire LMC has been targeted by large surveys (e.g., \emph{Spitzer}, \citealt{Meixner2006}; \emph{Herschel}, \citealt{Meixner2013}). Based on the first criterion for isolation proposed by \citet{Bressert2012}, a high-mass star forms in isolation if it is not member of an OB association or of a runaway population. This criterion extended to MYSOs requests that the isolated source should be forming away from an OB association, as well as of any GMC. The close connection between GMCs and high-mass star formation was confirmed by \citet{Wong2011} in the LMC, where the more CO luminous GMCs are found more likely to contain MYSOs. Using $Spitzer$ observations, \citet[][hereafter GC09]{GC09} constructed one of the best, carefully-selected samples of MYSOs across the entirety of the LMC. Specifically, they compiled a catalog of 248 best MYSO candidates. \citet{CG08} found that 85\% of these MYSOs are in GMCs and 65\% are in OB associations. Only 7\% of the MYSOs are outside of both GMCs and OB associations, comparable to the amount of Galactic O-stars that appear to be isolated, non-runaway field stars. \begin{figure}[t!] \begin{center} \includegraphics[scale=0.5]{fig02.pdf} \caption{ Ground-based H$\alpha$ images (no continuum subtraction) in inverted grayscale illustrates that the seven isolated MYSO targets have central H$\alpha$ regions. North is up and east is left. Observations were taken with the MOSAIC2 camera on the Blanco 4~m telescope; see \citet{Stephens2014} for details of the observations. The field-of-view for each panel is 150$\arcsec$ (37.5~pc) on a side. The \citet{GC09} position is marked with an open cross. MYSO numbering is the same as Figure\,\ref{LMC_YSOs}. \label{Halpha} } \end{center} \end{figure} We employed \emph{HST} to follow up on seven of the sources identified in \citet{CG08} since they are the best candidates for isolated MYSOs in the LMC. This sample is selected based upon the fact that within 80\,pc (see Section\,\ref{ssel}), none of the sources are associated with (i) other MYSOs, (ii) OB associations, or (iii) any GMC. In all cases ground-based H$\alpha$ observations show that these MYSOs are affiliated with non-elongated, small \ion{H}{2} regions and therefore are unlikely to be part of a runaway population. We acquired WFC3 observations in the F656N, F555W, F814W, F110W, and F160W bands to examine the interstellar environment and determine the surrounding stellar populations down to $\sim$\,0.7\,M$_\sun$. The exquisite resolution of \emph{HST} immediately demonstrated in the reduced images that in fact none of the sources is single and therefore actually isolated. Instead, they are all associated with prominent stellar clusterings around them. % In this paper we present our observations for the search of ongoing isolated high-mass star formation in the LMC and describe the data reduction and point spread function (PSF) photometry applied. We present the analysis of the data for these seven MYSOs in order to characterize in depth the natal environments of high-mass stars that appear as forming in isolation and to constrain more accurately the definition of isolated high-mass star formation. In Section\,\ref{ssandobs}, we describe our source selection of the seven MYSOs, the Mopra and \emph{HST} observations, and the \emph{HST} photometry. In Section\,\ref{section3}, we characterize the isolation of each target in our sample. In Section\,\ref{identPMS} and \ref{s:clusanl}, we identify the stellar populations associated to these seven MYSOs and characterize their clustering behavior through the entire \emph{HST} fields. Finally, in Section\,\ref{discussion} we discuss our findings in the general context of the phenomenon of isolated high-mass star formation. | A galaxy-wide search throughout the entire LMC shows that there are very few MYSOs that are forming outside of GMCs and not near other MYSOs or OB associations, i.e., they form in apparent isolation. Based on an ancillary set of imaging data from both {\em Spitzer} and ground-based telescopes, we constructed from typical star formation indicators a dataset of MYSOs that are considered to be the best candidates for forming in isolation. These sources are confirmed MYSOs with {\em Spitzer} IRS spectroscopy, and they emit enough ionizing photons to produce \ion{H}{2} regions around them, confirmed with H$\alpha$ imaging. They are also more than 80\,pc away from any other MYSO \citep{GC09}, OB association star \citep{Lucke1970}, or GMC \citep{Fukui2008,Wong2011}. Our \emph{HST} follow-up observations clearly demonstrate that while these MYSOs appear to be in isolated environments, they are actually surrounded by a plethora of PMS stars. Our clustering analysis of these stars shows that all MYSOs are members of compact clusters. Six of the regions have significant sub-structure, with the PMS stars being both sparsely distributed and in the compact clusters. These stellar alignments appear to be the signatures of the parental molecular cloud, which is presently undetected by CO surveys. A seventh analyzed MYSO (\sthree) was found to be surrounded by a single isolated compact low-mass stellar cluster with no other stellar distribution being associated with it, indicating that the parental cloud of this object did not produce stars in a dispersed fashion. Moreover, \sthree\ contains no known clusters within 60~pc \citep{Bica2008}. Such an isolated cluster containing an O-star is a rare occurrence in the context of high-mass star formation. The observed population of isolated field O-stars that are expected to form in situ \citep[e.g.,][]{deWit2004,Lamb2010,Oey2013,Lamb2015} are often considered to be a phenomenon of random sampling of the IMF, which allows O-stars to form in relative isolation \citep[i.e., in clusters $<$100~$M_\odot$ with no other star $>$10~$M_\odot$][]{Parker2007}. In other words, in situ O-stars forming in a cluster of mass $<$100~$M_\odot$ is rare but not impossible. However, while the previous confirmations of isolated high-mass star formation among field main-sequence O-type stars (after correcting for runaways) provide evidence of {\em in situ} formation, they do not provide information on the {\em environment} where formation took place; radiation and winds from the high-mass star and dynamical events may have erased the signatures of the parental gas and the clustering around the O-star. We investigate isolated high-mass star formation at a much earlier stage, i.e., the embedded MYSO stage. Based on our selection criteria, we have selected the best candidates for in situ, isolated high-mass star formation. We find cluster masses about these MYSOs to be larger than 100~$M_\odot$, suggesting that these MYSOs are not as isolated as typical field O-stars. While we cannot entirely rule out random or optimal sampling of the IMF, we suggest that a randomly sampled IMF should find that significantly less than 5\% of LMC MYSOs are isolated. With the present study we demonstrate that the investigation of the phenomenon referred to as ``isolated high-mass star formation'' requires the investigation of sources at earlier stages of their formation, such as MYSOs, which should still be embedded in their natal environments. Our investigation is the only observational study \citep[apart from that presented by][]{Selier2011} that approaches the issue strictly from this perspective. Based on our findings we argue that panchromatic high-resolution observations in the vicinity of apparently isolated MYSOs (and not main-sequence stars) will allow a better understanding of the conditions and the parameters that set the stage for high-mass stars to form in isolation. % | 16 | 9 | 1609.04399 |
1609 | 1609.04485_arXiv.txt | We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed. | The de Broglie-Bohm pilot-wave formulation of quantum theory \cite{deB28,BV09,B52a,B52b,Holl93} provides a generalisation of the quantum formalism, in which probabilities may differ from those predicted by the usual Born rule \cite{AV91a,AV91b,AV92,AV96,AV01,PV06}. The Born rule applies only to a statistical state of quantum equilibrium, which may be understood as arising from a process of dynamical relaxation or `quantum relaxation' (analogous to thermal relaxation) \cite{AV91a,AV92,AV01,VW05,EC06,TRV12,SC12,ACV14}. Quantum nonequilibrium may have existed in the early universe \cite{AV91a,AV91b,AV92,AV96,AV01,AV09}, in which case violations of the Born rule could leave discernible traces in the cosmic microwave background (CMB) \cite{AV07,AV10,CV13,CV15,AV15,CV16} and perhaps even survive until today for certain relic cosmological particles \cite{AV01,AV07,AV08,UV15,UV16}. Our current understanding of these cosmological scenarios depends, however, on our understanding of quantum relaxation -- which remains incomplete in some important respects. In particular, the effect of small perturbations has not been considered. As we shall see, from a cosmological point of view it is important to establish what the effect of small perturbations might be, in particular over long timescales. In pilot-wave theory, a system has a definite configuration $q(t)$ which evolves in time according to a law of motion for its velocity, where $\dot {q}\equiv dq/dt$ is determined by the wave function $\psi(q,t)$. Here $\psi$ satisfies the usual Schr\"{o}dinger equation $i\partial\psi/\partial t=\hat {H}\psi$ (taking $\hbar=1$). For standard Hamiltonians, $\dot{q}$ is proportional to the gradient $\partial_{q}S$ of the phase $S$ of $\psi$. More generally, $\dot{q}=j/|\psi|^{2}$ where $j=j\left[ \psi\right] =j(q,t)$ is the Schr\"{o}dinger current \cite{SV08}. The `pilot wave' $\psi$ guides the motion of an individual system and in principle has no connection with probability. For an ensemble of systems with the same wave function, we may consider an arbitrary initial distribution $\rho(q,0)$ (at $t=0$) of configurations $q(0)$. By construction, the time evolution $\rho(q,t)$ will obey the continuity equation% \begin{equation} \frac{\partial\rho}{\partial t}+\partial_{q}\cdot\left( \rho\dot{q}\right) =0\ . \end{equation} Because $\left\vert \psi\right\vert ^{2}$ obeys the same equation, an initial distribution $\rho(q,0)=\left\vert \psi(q,0)\right\vert ^{2}$ will evolve into $\rho(q,t)=\left\vert \psi(q,t)\right\vert ^{2}$. In this equilibrium state, probabilities match the Born rule and pilot-wave theory reproduces the usual predictions of quantum theory \cite{B52a,B52b}. But we may just as well consider nonequilibrium distributions $\rho(q,0)\neq\left\vert \psi (q,0)\right\vert ^{2}$, opening up the possibility of a new and wider physics with violations of the Born rule and new phenomena outside the domain of conventional quantum physics \cite{AV91a,AV91b,AV92,AV96,AV01,AV02,AV07,AV08,AV08a,AV09,AV10,AVPwtMw,PV06}. Quantum relaxation to the equilibrium state $\rho=\left\vert \psi\right\vert ^{2}$ may be quantified by a coarse-grained $H$-function% \begin{equation} \bar{H}=\int dq\ \bar{\rho}\ln(\bar{\rho}/\overline{\left\vert \psi\right\vert ^{2}})\ , \end{equation} where $\bar{\rho}$, $\overline{\left\vert \psi\right\vert ^{2}}$ are obtained by coarse-graining $\rho$, $\left\vert \psi\right\vert ^{2}$ respectively. This obeys a coarse-graining $H$-theorem $\bar{H}(t)\leq\bar{H}(0)$ (if the initial state has no fine-grained micro-structure) \cite{AV91a,AV92,AV01}. The minimum $\bar{H}=0$ corresponds to equilibrium $\bar{\rho}=\overline {\left\vert \psi\right\vert ^{2}}$. While this provides some understanding of how equilibrium is approached, the extent of relaxation depends on the system and on the initial conditions. For two-dimensional systems with wave functions that are evenly-weighted superpositions of energy eigenstates, extensive numerical studies have shown that initial nonequilibrium distributions $\rho$ (with no fine-grained micro-structure) rapidly approach $\left\vert \psi\right\vert ^{2}$ on a coarse-grained level \cite{AV92,AV01,VW05,TRV12,SC12}, with $\bar{H}(t)$ decaying approximately exponentially with time \cite{VW05,TRV12}. In these examples, the wave function is periodic in time and the simulations were carried out up to one period $T$. More recently, such simulations were extended to longer timescales (up to $50T$) \cite{ACV14}. It was found that, for some initial wave functions (with certain choices of initial phases), the decay of $\bar{H}(t)$ saturates to a small but non-zero residue -- signalling an incomplete relaxation. This was shown to occur when a significant fraction of the trajectories remain confined to sub-regions and do not explore the full support of $\left\vert \psi\right\vert ^{2}$. The numerical evidence indicated that such confinement (and the associated incomplete relaxation) is less likely to occur for larger numbers of superposed energy states \cite{ACV14}. These conclusions are consistent with earlier examples studied by Colin \cite{SC12} and by Contopoulos \textit{et al}. \cite{CDE12}, in which limited relaxation -- and an associated confinement of trajectories -- was found for some initial wave functions with only three or four energy states. Previous studies of quantum relaxation have mostly focussed on a coarse-graining approach for isolated systems \cite{AV91a,AV92,AV01}, modelled on the analogous classical discussion \cite{Tol, Dav}.\footnote{An exception is an early paper by Bohm \cite{B53}, which considered an ensemble of two-level molecules subject to random external collisions and argued that the molecules would relax to equilibrium.} In this paper we consider instead the effect of small perturbations, in particular over very long timescales (of order $10^{3}T$). This is of interest in its own right, as well as for cosmological reasons. Consider a system with an unperturbed wave function $\psi$, which generates an unperturbed velocity field $\dot{q}$ and unperturbed trajectories $q(t)$. The system might be subjected to small external perturbations, which in a first approximation we may model as perturbations to the classical potential of the system. The system will then have a perturbed wave function $\psi^{\prime}$ which is close to $\psi$, and a perturbed velocity field $\dot{q}^{\prime}$ which we expect to be close to $\dot{q}$. Will the perturbed trajectories $q^{\prime}(t)$ remain close to $q(t)$? One might expect that even a small difference in the velocity field, acting over sufficiently long periods of time, would yield perturbed trajectories $q^{\prime}(t)$ which deviate greatly from $q(t)$. For example, one might consider a two-dimensional harmonic oscillator with configuration $q=(q_{1},q_{2})$ whose unperturbed wave function is simply the ground state, $\psi(q_{1},q_{2},t)=\phi_{0}(q_{1}% )\phi_{0}(q_{2})e^{-iE_{0}t}$, where $\phi_{0}(q_{1})\phi_{0}(q_{2})$ is a real Gaussian and $E_{0}$ is the ground-state energy. Because the phase $S=\operatorname{Im}\ln\psi$ is independent of position, the unperturbed velocity field $\dot{q}$ vanishes everywhere and all unperturbed trajectories are static. There can be no relaxation, nor indeed any evolution at all of the unperturbed density $\rho$. Any initial nonequilibrium distribution $\rho(q_{1},q_{2},0)\neq\left\vert \phi_{0}(q_{1})\phi_{0}(q_{2})\right\vert ^{2}$ will remain the same. Now let us consider a perturbed wave function $\psi^{\prime}$ that differs from $\psi$ by the addition of excited states $\phi_{m}(q_{1})\phi_{n}(q_{2})$ with small amplitudes $\epsilon_{mn}$. For small $\epsilon_{mn}$ the perturbed velocity field $\dot{q}^{\prime}$ will be small but generally non-zero. The question is: over arbitrarily long times, will the perturbed trajectories $q^{\prime}(t)$ remain confined to small sub-regions of the support of $\left\vert \phi_{0}(q_{1})\phi_{0}% (q_{2})\right\vert ^{2}$ or will they wander over larger regions and possibly over the bulk of the support of $\left\vert \phi_{0}(q_{1})\phi_{0}% (q_{2})\right\vert ^{2}$? In the former case, there could be no relaxation even over arbitrarily long times. In the latter case, relaxation could occur. Indeed, in the latter case it might seem plausible that, no matter how small $\epsilon_{mn}$ may be, over sufficiently long timescales the perturbed distribution $\rho^{\prime}(q_{1},q_{2},t)$ could approach $\left\vert \phi_{0}(q_{1})\phi_{0}(q_{2})\right\vert ^{2}$ to arbitrary accuracy (where $\left\vert \phi_{0}(q_{1})\phi_{0}(q_{2})\right\vert ^{2}$ coincides with equilibrium as $\epsilon_{mn}\rightarrow0$). The question, then, is whether small perturbations are generally ineffective for relaxation or whether they might conceivably drive systems to equilibrium over sufficiently long times. Cosmologically, the effect of perturbations over long timescales could be important for several reasons. According to inflationary cosmology, the temperature anisotropies in the CMB were seeded by primordial quantum fluctuations of a scalar field whose quantum state was approximately a vacuum (the Bunch-Davies vacuum) \cite{LL00,Muk05,PU09}. It has been shown that de Broglie-Bohm trajectories for field amplitudes in the Bunch-Davies vacuum are too trivial to allow relaxation \cite{AV07,AV10}. On this basis it was concluded that, if quantum nonequilibrium existed at the beginning of inflation, then it would persist throughout the inflationary phase and potentially leave an observable imprint in the CMB today. However, strictly speaking this conclusion depends on the implicit assumption that (unavoidable) small corrections to the Bunch-Davies vacuum can be neglected in the sense that they will not generate relaxation during the inflationary era. Similarly, a cosmological scenario has been developed according to which quantum relaxation occurred during a pre-inflationary (radiation-dominated) phase \cite{AV07,AV10,CV13,CV15,AV15,CV16}. It was shown that during such a phase relaxation proceeds efficiently at short wavelengths but is suppressed at long wavelengths, resulting in a distinctive signature of quantum nonequilibrium at the beginning of inflation -- which is then imprinted at later times in the CMB.\footnote{Specifically, the signature amounts to a primordial power deficit at long wavelengths with a specific (inverse-tangent) dependence on wavenumber $k$ \cite{CV15,CV16}. A large-scale power deficit has in fact been reported in the \textit{Planck} data \cite{PlanckXV-2013,Planck15-XI-PowerSpec}, though the extent to which it matches our prediction is still being evaluated \cite{VVP16}.} The resulting predictions for the CMB depend, however, on the assertion that there will be no significant relaxation during inflation itself, an assertion which again depends on the implicit assumption that small corrections to the Bunch-Davies vacuum may be ignored. Finally, a scenario has also been developed according to which, for certain particles created in the early universe, any nonequilibrium carried by them could conceivably survive (or partially survive) to the present \cite{UV15}. But such a scenario would fail if small perturbations caused the particles to relax over very long timescales. Indeed, if small perturbations do cause relaxation over long timescales it would be exceedingly difficult to have any hope at all of discovering relic nonequilibrium today. To discuss these cosmological matters quantitatively, it suffices to consider a free (minimally-coupled) massless scalar field $\phi$ on expanding flat space with scale factor $a(t)$. Here $t$ is standard cosmological time and physical wavelengths are proportional to $a(t)$. In Fourier space we have field components $\phi_{\mathbf{k}}(t)$ which may be written in terms of their real and imaginary parts, $\phi_{\mathbf{k}}=\frac{\sqrt{V}}{(2\pi)^{3/2}% }\left( q_{\mathbf{k}1}+iq_{\mathbf{k}2}\right) $ (where $V$ is a normalisation volume). The field Hamiltonian then becomes a sum $H=\sum _{\mathbf{k}r}H_{\mathbf{k}r}$, where $H_{\mathbf{k}r}$ ($r=1,2$) is mathematically the Hamiltonian of a harmonic oscillator with mass $m=a^{3}$ and angular frequency $\omega=k/a$ \cite{AV07,AV08,AV10}. If we consider an unentangled mode $\mathbf{k}$, we have an independent dynamics with a wave function $\psi=\psi(q_{1},q_{2},t)$ (dropping the index $\mathbf{k}$) that satisfies the Schr\"{o}dinger equation% \begin{equation} i\frac{\partial\psi}{\partial t}=\sum_{r=1,\ 2}\left( -\frac{1}{2m}% \partial_{r}^{2}+\frac{1}{2}m\omega^{2}q_{r}^{2}\right) \psi \end{equation} (with $\partial_{r}\equiv\partial/\partial q_{r}$). The pilot-wave equation of motion for the actual configuration $(q_{1},q_{2})$ then reads% \begin{equation} \dot{q}_{r}=\frac{1}{m}\operatorname{Im}\frac{\partial_{r}\psi}{\psi }\label{deB}% \end{equation} and an arbitrary marginal distribution $\rho=\rho(q_{1},q_{2},t)$ will then evolve according to the continuity equation% \begin{equation} \frac{\partial\rho}{\partial t}+\sum_{r=1,\ 2}\partial_{r}\left( \rho\frac {1}{m}\operatorname{Im}\frac{\partial_{r}\psi}{\psi}\right) =0\ . \end{equation} These equations are just those of pilot-wave dynamics for a two-dimensional harmonic oscillator with (time-dependent) mass $m=a^{3}$ and angular frequency $\omega=k/a$. It may be shown that the resulting time evolution is mathematically equivalent to that of an ordinary harmonic oscillator (with constant mass and angular frequency) but with the time parameter replaced by a `retarded time' that depends on $k$ \cite{CV13}. It is found, in particular, that relaxation is suppressed\ at long (super-Hubble) wavelengths while proceeding efficiently at short (sub-Hubble) wavelengths \cite{AV08,CV13,CV15}. Thus cosmological relaxation for a single field mode may be discussed in terms of relaxation for a standard oscillator. By studying the effect of small perturbations on relaxation for a simple two-dimensional harmonic oscillator, then, we may draw conclusions that have application to cosmology. In Section 2 we present our model, which is obtained simply by setting $m=1$ in the equation of motion (\ref{deB}) (for $r=1,2$). This defines our dynamics of trajectories for a two-dimensional harmonic oscillator, with constant mass and constant angular frequency and with a given wave function. We shall take $\psi$ to be the ground state with small perturbations of amplitude $\epsilon_{mn}$ coming from the lowest excited states $\phi_{m}(q_{1})\phi _{n}(q_{2})$. In Section 3 we discuss our method, where two different techniques are applied to infer the extent of relaxation in the long-time limit, using samples of trajectories evolved over long times. In Section 4 we then study numerically the behaviour of a sample of trajectories over very long timescales, in particular we consider how their behaviour changes as the perturbations become smaller. As we shall see, for sufficiently small perturbations the trajectories become highly confined, and neighboring trajectories are confined to almost the same regions, even over very long timescales -- from which we conclude (tentatively, given our numerical evidence) that small perturbations do not cause relaxation. Cosmological implications are briefly discussed in Section 5, where we draw our conclusions. | Our numerical results provide evidence that small perturbations will not, in fact, cause significant relaxation -- not even over arbitrarily long timescales. In the examples we have studied, the system trajectories are confined to sub-regions of the support of $|\psi|^2$. Furthermore, neighboring initial points generate trajectories that are confined to essentially the same sub-regions. Such behavior precludes relaxation. We have restricted ourselves to the harmonic oscillator, which as we explained in Section 1 provides a testing ground applicable to high-energy field theory in the early universe. In future work it would be of interest to consider other systems, as well as to develop an analytical understanding of the results (for which the methods of ref. \cite{CDE12} may prove useful). From the point of view of a general understanding of relaxation, our results suggest that in de Broglie-Bohm theory quantum equilibrium cannot be understood as arising from the effects of small perturbations only, not even in the long-time limit. Since all systems we know of have a long and violent astrophysical history (ultimately stretching back to the big bang), their current obedience to the Born rule may nevertheless be understood in terms of the efficient relaxation found in previous simulations (at least at the sub-Hubble wavelengths relevant to laboratory physics) for wave functions with significant contributions from a range of energy states. As regards cosmology, our results point to the following conclusions. Firstly, the implicit assumption made in refs. \cite{AV07,AV10,CV13,CV15,AV15,CV16} is justified: small corrections to the Bunch-Davies vacuum during inflation are unlikely to cause significant relaxation, and so the derived predictions for the CMB still stand (for the assumed scenario with a pre-inflationary period). Secondly, relic nonequilibrium particles from the early universe surviving to the present day remains a possibility at least in principle (albeit a rather remote one for other reasons, as discussed in ref. \cite{UV15}). | 16 | 9 | 1609.04485 |
1609 | 1609.06952_arXiv.txt | We present a multi-wavelength temporal analysis of the blazar 3C 454.3 during the high $\gamma$-ray active period from May-December, 2014. Except for X-rays, the period is well sampled at near-infrared (NIR)-optical by the \emph{SMARTS} facility and the source is detected continuously on daily timescale in the \emph{Fermi}-LAT $\gamma$-ray band. The source exhibits diverse levels of variability with many flaring/active states in the continuously sampled $\gamma$-ray light curve which are also reflected in the NIR-optical light curves and the sparsely sampled X-ray light curve by the \emph{Swift}-XRT. Multi-band correlation analysis of this continuous segment during different activity periods shows a change of state from no lags between IR and $\gamma$-ray, optical and $\gamma$-ray, and IR and optical to a state where $\gamma$-ray lags the IR/optical by $\sim$3 days. The results are consistent with the previous studies of the same during various $\gamma$-ray flaring and active episodes of the source. This consistency, in turn, suggests an extended localized emission region with almost similar conditions during various $\gamma$-ray activity states. On the other hand, the delay of $\gamma$-ray with respect to IR/optical and a trend similar to IR/optical in X-rays along with strong broadband correlations favor magnetic field related origin with X-ray and $\gamma$-ray being inverse Comptonized of IR/optical photons and external radiation field, respectively. | \label{sec:intro} Blazars are jetted active galactic nuclei (AGNs) with relativistic jets align at close angles to observer's line of sight. They are characterized by a highly variable, predominantly non-thermal continuum emission spanning the entire accessible electromagnetic spectrum with a significant polarization at radio-to-optical wavelengths, and superluminal features in high-resolution radio imaging \citep{2013AJ....146..120L}. In the temporal domain, flux variability is seen on all timescales ranging from minutes to years and is believed to be a manifestation of Doppler boosting associated with the close alignment of the relativistic jet with the line of sight. Traditionally, blazars have been classified as BL Lacertae objects (BL Lacs) and flat spectrum radio quasars (FSRQs) based on the absence and presence of prominent broad emission lines in their optical-ultraviolet spectra \citep{1995PASP..107..803U}. Despite a wide range of variability in energy and time domains, blazars spectral energy distributions (SEDs) exhibit a characteristic broad double-hump profile \citep{1998MNRAS.299..433F, 2016arXiv160403856M}. The low energy hump peaks between infra-red (IR) to ultraviolet(UV)/X-rays, and is widely accepted to be due to synchrotron emission from relativistic non-thermal electrons in the jet. The emission at high energy hump which peaks at $\gamma$-ray energies is still unclear and, is well reproduced by both leptonic and/or hadronic non-thermal processes \citep[e.g.][] {2013ApJ...768...54B, 2015MmSAI..86...13D}. In the leptonic models, the high energy emission originates as a result of inverse Compton (IC) scattering \citep[e.g.][]{2014Natur.515..376G} of ambient photons which can be synchrotron photons and/or photons external to the jet, like photons from the broad-line region (BLR), torus photons and/or Cosmic Microwave Background (CMB) photons. The hadronic models, on the other hand, attribute it to the interactions of relativistic protons in the jet with the magnetic field \citep[proton synchrotron,][]{2001APh....15..121M} and/or with the soft radiation field \citep[photo-pion cascade,][]{1992A&A...253L..21M}. Understanding the nature of variability in Blazars has eluded the researchers over the years. Generally attributed to relativistic shocks and/or magnetic reconnection processes, it differs from source-to-source, and even during different activity states of a source. Furthermore, its highly energy dependent manifestation across the electromagnetic (EM) spectrum makes it complex to decipher. This makes multi-wavelength spectral and temporal study of blazars emission one of the potential tools to probe and understand the physical conditions/processes responsible for its energy dependent variability within the compact unresolvable sites \citep[e.g.][]{2014ApJ...796...61K}. The correlations between different wavelengths carry an imprint of dynamics of interplay between energization and losses and hence, their relative dominance in different energy bands. 3C 454.3, located at the redshift of $\rm z = 0.859$ is a bright and a highly variable FSRQ first detected at $\gamma$-ray energies ($> 100$ MeV) by the \emph{EGRET} telescope onboard the CGRO \citep{1993ApJ...407L..41H}. The source has been studied extensively at different wavelengths over the last two decades. However, only after 2005 activity which was seen in all the accessible window of the electromagnetic spectrum \citep{2006A&A...453..817V, 2006A&A...456..911G, 2006A&A...449L..21P}, that it became one of the targets of coordinated multi-wavelength studies. 3C 454.3 has been extremely active FSRQ at $\gamma$-ray energies since 2007 as seen by \emph{AGILE} \citep{2010ApJ...718..455S} as well as the scanning $\gamma$-ray observatory \emph{Fermi}-LAT post its launch in 2008. Many extraordinary $\gamma$-ray activities in terms of spectral and temporal variations \citep{2010ApJ...721.1383A, 2011ApJ...733L..26A, 2015arXiv151102280B} have been reported with counterparts in other parts of the electromagnetic spectrum. The coordinated follow-ups during many of these high $\gamma$-ray activity periods have revealed diversity and complexity of emission processes in the source. The \emph{AGILE} 2007 multi-wavelength campaign observed a correlated optical and $\gamma$-ray variation with no lags during the November \citep{2009ApJ...690.1018V}, but found a possible $\lesssim 1$ day lag with $\gamma$-ray lagging the optical during the December observations \citep{2009ApJ...707.1115D}. A more extensive multi-wavelength campaign led by \emph{AGILE} over 18 months found almost simultaneous peaks in different energy bands with a delay of less than a day \citep{2010ApJ...712..405V}, consistent with its previous finding. Similarly, the multi-wavelength observation during \emph{Fermi}-LAT operation by \citet{2009ApJ...697L..81B} for the period of August to December 2008 revealed an excellent correlation between the IR, optical, UV, and gamma-ray light curves with a time lag of less than one day but no correlation between X-ray flux with either of these EM bands. A similar result was found for another multi-wavelength data set compiled by \citet{2012ApJ...756...13B} for the period of June 2008 to December 2010 showing excellent correlations between the IR, optical, and $\gamma$-rays with a time lag of less than a day, while \citet{2012ApJ...758...72W} have found near-simultaneous variations in millimeter, far-IR and $\gamma$-rays with $\gamma$-ray lagging IR (160 $\rm \mu m$) by $1\pm0.5$ days for November 2010 - January 2011 period. On the other hand, a study by \citet{2012AJ....143...23G} for November- December 2009, has found a lag of $\sim 4.5$ days with $\gamma$-ray leading optical, but neither being correlated with X-rays. Thus, the broadband emission during various $\gamma$-ray activity states seems to have recurring features despite widely different variability amplitudes in both flux and time domains. The well sampled simultaneous/contemporaneous data set generated by the coordinated follow-ups across the EM spectrum by the ground and space based observatories in response to the \emph{Fermi}-LAT triggers have, thus, opened a window for systematic exploration of various characteristics associated with particular sources \citep[e.g.][]{2016ApJ...822L..13K}, thereby providing insights and constraints on the rich physics of the relativistic jets, emission region etc. Here, we present correlation analysis of multi-wavelength data during a $\gamma$-ray active period between May-December, 2014, when the source $\gamma$-ray fluxs over daily timescale were $\rm\gtrsim 10^{-6}~ ph~ cm^{-2}~ s^{-1}$ and was followed in other electromagnetic bands. The source exhibited high $\gamma$-ray variability of different levels which were also noticed in X-rays and NIR-optical bands. The paper is organized into five sections with the next section presenting the details of data resources and associated reduction processes. Section 3 presents the temporal analysis technique and results, followed by discussion and implications in Section 4. We finally conclude in Section 5. | \label{sec:conclude} We performed a correlation analysis of multi-wavelength emission from 3C 454.3 during a high $\gamma$-ray activity period from May 13 - December 24, 2014, which is also noticed in other energy bands. The study performed over an almost continuous segment of data shows a highly correlated variation, almost simultaneous across the electromagnetic spectrum supporting a co-spatial emission, thereby strongly favoring leptonic origin scenarios. Interestingly, the correlation during this period changes from no lags between IR/optical-$\gamma$-ray to a lag of $\sim$ 3 days with IR/optical leading the $\gamma$-ray suggesting a change in magnetic field configuration/strength and/or a declining external field as the likely process driving the emission.The similarity of results with previous studies also suggests that the physical conditions remain more or less similar during different flaring events with amplitude and durations of flares being mainly governed by the size and particle/magnetic-energy density respectively. PK's work at University of Sao Paulo (IAG-USP) is supported by the FAPESP Grant No. 2015/13933-0. Most of the work was done while PK was in IUCAA. ACG's work is partially supported by Chinese Academy of Sciences (CAS) President's International Fellowship Initiative (PIFI) Grant No. 2016VMB073. This research has made use of data, software and web tools of High Energy Astrophysics Science Archive Research Center (HEASARC), maintained by NASA's Goddard Space Flight Center and an up-to-date SMARTS optical/near-infrared light curves available at www.astro.yale.edu/smarts/glast/home.php. | 16 | 9 | 1609.06952 |
1609 | 1609.03570_arXiv.txt | When modelling inflaton fluctuations as a free quantum scalar field, the initial vacuum is conventionally imposed at the infinite past. This is called the Bunch-Davies (BD) vacuum. If however an asymptotically Minkowskian past does not exist, this requires modifications. We derive corrections to the scalar spectral index $n_s$ and the tensor tilt $n_t$ descending from arbitrary mixed states or from explicit non-BD initial conditions. The former may stem from some pre-inflationary background and can redshift away whereas the latter are induced by a timelike hypersurface parametrising a physical cut-off. In both cases, we find that corrections scale in parts or fully as $\mathcal O(\epsilon)$ where $\epsilon$ is the first slow-roll parameter. The precise observational footprint is hence dependent on the model driving inflation. Further, we show how the inflationary consistency relation is altered. We thus provide an analytic handle on possible high scale or pre-inflationary physics. | Cosmic inflation \cite{Linde:1983gd, Starobinsky:1980te} has been well established as the leading paradigm to describe the physics of the early universe. Besides solving the horizon and flatness problem, inflation is furthermore predictive as it provides a mechanism \cite{Mukhanov:1990me} seeding structure formation which is in astonishing agreement with recent observations \cite{Bennett:2012zja, Ade:2015lrj, Ade:2015tva}. Typically, inflation is taken to be realised by a scalar field with a nearly shift-symmetric potential thus mimicking the equation of state of a cosmological constant. The shift symmetry is broken by a minimum in which the field may settle, hence inducing a graceful exit. Inducing the primordial density perturbation then comes naturally once promoting the inflaton field to a quantum operator. Precisely, the inflaton is decomposed into a classical background field evolving as determined by its potential, and a fluctuating part that is described as a massless quantum scalar field. The equation of motion for the free field then follows from the interplay of the perturbed stress-energy tensor of the inflaton field with the perturbed part of the linearised Einstein tensor. It has the form of that of a harmonic oscillator with time dependent mass. When taking the limit of the infinite past, the simple harmonic oscillator is recovered and one may impose a Minkowski vacuum as a boundary condition for the fluctuation; this is called the Bunch-Davies vacuum \cite{Bunch:1978yq}, and is the conventional procedure whenever an expanding spacetime is asymptotically Minkowskian at the infinite past. However, problems can arise when questioning the accessibility of the infinite past, or more generally, a Minkowskian limit at some past infinity. A prominent criticism of the standard procedure outlined above was coined the trans-Planckian problem \cite{Anderson:2000wx, Niemeyer:2000eh, Brandenberger:2000wr, Martin:2000xs, Hui:2001ce, Niemeyer:2001qe, Kaloper:2002uj, Burgess:2002ub, Brandenberger:2002hs, Danielsson:2002qh, Danielsson:2002kx, Bergstrom:2002yd, Kaloper:2002cs, Goldstein:2002fc, Easther:2002xe, Chung:2003wn, Kaloper:2003nv, Burgess:2003hw, Alberghi:2003am, Martin:2003kp, Ashoorioon:2005ep, Meerburg:2010rp, Kundu:2011sg, Brandenberger:2012aj, Kundu:2013gha, Aravind:2016bnx, Shukla:2016bnu}, and questioned whether or not scales from below the Planck length $l_P$ could leave a signature in the cosmic microwave background (CMB) when stretched across the (event) horizon during inflation. A true consensus was never reached. In this paper, we revisit some of the original considerations and argue that whenever the infinite past is not accessible, the BD vacuum may not be imposed. Instead, one has to resort to mixed states as vacua, so called $\alpha$-vacua \cite{Allen:1985ux,Mottola:1984ar,Danielsson:2002mb}, which have recently been rediscovered in \cite{Handley:2016ods}. While these are commonly thought to be ill behaved, they nevertheless provide a possible handle on imposing a vacuum at some finite past. Allowing yet unknown physics to settle the debate about the consistency of such vacua, we derive corrections to the inflationary observables $n_s$ and $n_t$ induced by arbitrary mixed states or non-BD initial conditions. Considering arbitrary mixed states, we find that the correction to the inflationary indices depends on the spectrum of mixed states; namely on the coefficient $|B_k|$ of the negative frequency contribution to the solution of the equation of motion for a mode $k$. It reads \begin{equation}\label{1} \delta n_{s,t}\sim 2\epsilon_V |B_k|^2-\frac{d|B_k|^2}{d\ln k} \thinspace . \end{equation} Assuming non-BD initial conditions, one finds oscillatory corrections \begin{equation}\label{2} \delta n_{s,t}\sim \epsilon_V\cos\left(\frac{2\Lambda}{H_{infl}}\exp{(\epsilon_V\thinspace N_e)}\right) \thinspace , \end{equation} where $N_e\leq 0$ is the number of remaining e-folds, $H_{infl}$ is the inflationary energy scale and $\Lambda$ is the physical momentum cut-off where the initial vacuum is imposed. The rest of the paper is structured as follows; we begin with a short review of field operators in time dependent backgrounds and establish our notation. Following a quick discussion of the relevant equation of motion for inflationary fluctuations, we discuss Bunch-Davies and non-BD initial conditions and highlight which scenario requires which choice of vacuum. In the main part, we first derive corrections to $n_s$ and $n_t$ from mixed states and continue to study the explicit example of corrections induced from $\alpha$-vacua. We conclude in section \ref{conclusions}. | \label{conclusions} In this work, we studied the phenomenology of arbitrary mixed states and non-BD initial conditions. Evaluating expressions for the inflationary observables \eqref{indicies} with the corrected spectra \eqref{spectrumwithcorrection}, \eqref{deltas} and \eqref{deltat}, we found corrections $\delta n_{s,t}$ scaling partly as $\mathcal O(\epsilon_V)$ in the case of arbitrary mixed states and being oscillatory with an amplitude of $\mathcal O(\epsilon_V)$ in the case of non-BD initial conditions. Results \eqref{1} and \eqref{2} thus provide an analytic handle on possible high scale corrections to inflationary observables. Reflecting on the theoretical motivation for this study, mixed states may be caused by non-slow-roll pre-inflationary backgrounds as described in e.g.\ \cite{Cicoli:2014bja}. There, the duration of inflation is taken to be just the required one, i.e.\ inflation does not last much longer than $|N_{CMB}|$. Concretely, assuming a non-slow-roll and asymptotically Minkowskian background before inflation can in principle induce non-zero Bogolubov coefficients for the inflaton fluctuations (provided the inflaton field already quantum fluctuates before inflation) which hence can induce the comoving excitations described above. Further, $\alpha$-vacua display several shortcomings. However, it seems that the conventional BD vacuum may only consistently be imposed at the infinite past. Postulating that an asymptotically Minkowskian background at some past infinity is not accessible then renders the standard procedure inconsistent. This could e.g.\ be the case if one assumes the inflationary phase to be without a predecessor, i.e.\ that inflation is indeed the first period in the universe when QFT and GR become applicable in their respective regimes. A consistent formulation of initial conditions, or more generally QFT on curved backgrounds, will surely require a full theory of quantum gravity. | 16 | 9 | 1609.03570 |
1609 | 1609.07287_arXiv.txt | We present a new method for tracing the evolution of BCGs from $z\sim 2$ to $z\sim 0$. We conclude on the basis of semi-analytical models that the best method to select BCG progenitors at $z\sim 2$ is a hybrid environmental density and stellar mass ranking approach. Ultimately we are able to retrieve 45\% of BCG progenitors. We apply this method on the CANDELS UDS data to construct a progenitor sample at high redshift. We furthermore populate the comparisons in local universe by using SDSS data with statistically likely contamination to ensure a fair comparison between high and low redshifts. Using these samples we demonstrate that the BCG sizes have grown by a factor of $\sim 3.2$ since $z\sim 2$, and BCG progenitors are mainly late-type galaxies, exhibiting less concentrated profiles than their early-type local counterparts. We find that BCG progenitors have more disturbed morphologies. In contrast, local BCGs have much smoother profiles. Moreover, we find that the stellar masses of BCGs have grown by a factor of $\sim 2.5$ since $z\sim 2$, and the SFR of BCG progenitors has a median value of 13.5 $M_\odot$yr$^{-1}$, much higher than their quiescent local descendants. We demonstrate that over $z=1-2$ star formation and merging contribute equally to BCG mass growth. However, merging plays a dominant role in BCG assembly at $z \lesssim 1$. We also find that BCG progenitors at high-$z$ are not significantly different from other galaxies of similar mass at the same epoch. This suggests that the processes which differentiate BCGs from normal massive elliptical galaxies must occur at $z \lesssim 2$. | Brightest cluster galaxies (BCGs) are the most luminous and massive galaxies in local universe. They reside at the bottom of the gravitational potential well of galaxy clusters, and are surrounded by a population of satellite galaxies. The special regions they reside in, and the unique properties they exhibit (e.g., distinct structures and morphologies, very high stellar masses) set them apart from the general galaxy population. Their origin and evolution also tightly link with the evolution of their host clusters and provide direct information on the history of large-scale structures in Universe (e.g., \citealt{Conroy07}). Even though much attention has been dedicated to the study of BCG formation and evolution, understanding when these most massive galaxies formed and how they evolve with time are still controversial issues. Early N-body simulations studying BCG formation through merging in a cold matter (CDM) cosmology, find that BCG growth through early merging of few massive galaxies dominates over late-time accretion of many smaller systems (e.g., \citealt{Dubinski98}). The modern context of BCG assembly through hierarchical growth within networks of dark matter halos is now well established. For example, by using nine high-resolution dark matter-only simulations of galaxy clusters in a $\Lambda$CDM universe, \citet{Laporte13} claim that BCGs can grow mainly through dissipationless dry mergers of quiescent galaxies from $z = 2$ to the present day, producing BCG light profiles and stellar mass growth in good agreement with observations. However, pure N-body models ignore mechanisms such as gas cooling and star formation in BCG evolution which are also likely important processes. Taking into account hydrodynamical processes such as infalling gas and AGN feedback, recent semi-analytic models (SAMs) suggest that the stellar component of today's BCGs was initially formed through the collapse of cooling gas or gas-rich mergers at high redshift, and consequently BCGs continued to grow, but assemble substantially very late ($50$\% of the final mass is assembled at $z \lesssim 0.5$) through dissipationless processes such as dry mergers of satellite galaxies (\citealt{DeLB07}; \citealt{Naab09}; \citealt{Laporte12}). This two-phase evolution for BCG growth successfully reproduces many observations, however, it has been questioned by a number of studies which find a much slower stellar mass growth in BCGs at $z\lesssim 1$ in observations (e.g., \citealt{Whiley08}; \citealt{Collins09}; \citealt{Lin13}; \citealt{Zhang15}). More observational studies of BCGs at higher redshifts will help to constrain these models and give us a better idea of their evolution. To understand how BCGs evolved and assembled their stellar masses, and which mechanisms drive these changes, it is important to properly connect today's BCGs to their progenitors at earlier times observationally. This requires the non-trivial task of linking BCG descendants with their progenitors through cosmic time, which in turn requires assumptions for how BCGs evolve. At lower redshift ($z\lesssim 1-1.5$), BCG progenitor-descendant pairs are selected by an empirical approach through constructing a sample based on finding distant clusters, and using the correlation between BCG stellar mass and cluster mass. Employing this method, many studies have characterized the assembly of BCGs at $z \lesssim 1$. \citet{Lidman12} demonstrated that BCGs have grown by a factor of $1.8$ between $z = 0.2-0.9$. While \citet{Lin13} found a similar growth such that the stellar mass of BCGs increases by a factor of $\sim 2.3$ since $z \sim 1.4$. \citet{Shankar15} claimed an increase of a factor $\sim 2-3$ in BCG mean stellar mass, and $\sim 2.5-4$ factor increase in BCG mean effective radius, since $z \sim 1$. \citet{Zhang15} showed a BCGs mass growth by a factor of $\sim 2$ since $z \sim 1.2$ using a similar approach. However, the techniques for linking local BCGs and their progenitors at $z \lesssim 1$ are difficult to apply at higher redshifts ($z \gtrsim 1.5$). On the one hand, it is difficult to identify clusters/proto-clusters at early times. On the other hand, it is also difficult to define BCG progenitors in high-$z$ clusters since the main progenitor may not be the most luminous/massive galaxy as the low-z BCGs. Nonetheless, a number of studies have been carried out to explore the build-up of massive galaxies up to $z\sim 3$. Among the solutions for linking galaxies at different redshifts, matching galaxy progenitors and descendants at a constant number density has been demonstrated to be a considerably improved approach for tracking the evolution of galaxies (e.g., \citealt{Leja13}; \citealt{Mundy15}). By applying this method, \citet{vanDokkum10} claim a mass growth of a factor of $\sim 2$, and a size growth of a factor of $\sim 4$ for massive galaxies since $z = 2$. \citet{Ownsworth14}, using a variety of number density selections with $n\leqslant 1\times10^{-4}$Mpc$^{-3}$ at $0.3 < z < 3$, find that about 75\% of the total stellar mass in massive galaxies at $z = 0.3$ is created at $z < 3$, and the sizes of massive galaxy progenitors is a factor of 1.8 smaller than local early-type galaxies of similar mass. \citet{Marchesini14} investigate ultra-massive galaxy evolution by using progenitors from $z = 3$ which are selected with both a fixed cumulative number density and an evolving number density. They find that the stellar content of ultra-massive galaxies have grown by a factor of $2-3.6$ since $z =3$. However, these systems are not necessarily BCGs, and a clear correspondence between massive galaxies and BCGs at high redshifts ($z \gtrsim 1.5$) is still lacking. In order to obtain better perspective of BCG assembly, it is critical to identify the progenitors of BCGs at $z \gtrsim 1.5$, and to explore their mass and structural evolution. Mergers are potentially a significant process in BCG formation, as they are predicted to be a major mechanism in the hierarchical picture of galaxy formation. Apart from the dominant role of minor mergers in BCG mass assembly at low redshift (e.g., \citealt{Burke15}), observations suggest that at high redshifts BCG evolution is also largely driven by mergers through both major and minor events (e.g., \citealt{Lidman13}; \citealt{Burke13}). Since mergers closely relate to the environmental density around galaxies, in this paper, we propose a method to identify BCG progenitors at $z \sim 2$, which depends on galaxy local densities as well as galaxy stellar masses. We first examine the effectiveness of our method using simulation data, and then apply this method on the observational data of the CANDELS UDS survey. Our method to probe BCG progenitors at $z \gtrsim 1.5$ is easier, since it avoids the difficulty of identifying clusters at high redshifts. Comparing high-$z$ BCG progenitors with their local SDSS descendants, we study the evolution of BCG structure, morphology, stellar mass and star formation since $z\sim 2$, and discuss the implied formation processes for BCGs. The rest of this paper is organized as follows. In Section ~\ref{sec:data_and_technique}, we present the observational data employed in this work. We also introduce necessary quantities which will be used in selecting our BCG progenitors and for comparing BCG properties in this section. The description and simulation tests of our selection of BCG progenitors are presented in Section~\ref{sec:progselect}. Although the BCG progenitors selected by our method are contaminated by non-BCG progenitors, in Section~\ref{sec:contam_effect}, we demonstrate that our selected progenitors sample, and their local descendants, can be used to trace BCG evolution since $z\sim 2$. We then describe our results of BCG assembly in Section~\ref{sec:results}. In Section~\ref{sec:discussion} we first discuss the possible mechanisms for BCG evolution implied by our results, and then we compare our results with other studies of BCG evolution at $z \lesssim 1$ as well as massive galaxy growth since $z\sim 2$. Finally, we summarise our results in Section~\ref{sec:summary}. Throughout this paper we have adopted the $\Lambda$CDM cosmology with $\Omega_m=0.3$, $\Omega_\Lambda=0.7$, and $H_0=70$ km s$^{-1}$ Mpc$^{-1}$. | \label{sec:discussion} \subsection{Mechanisms driving BCG mass growth} \label{sec:discuss_mechanism} The processes that increase the stellar masses and sizes of massive galaxies are still an open question. There are two primary mechanisms: star formation and merging. Mergers are important since massive galaxies very likely form through the merging together of smaller galaxies in the hierarchical picture of galaxy formation. Star formation is also essential for massive galaxies in building up stellar mass, particularly at high redshifts where massive galaxies experience a much higher SFR than in the local universe (e.g., \citealt{vanDokkum04}; \citealt{Papovich06}; \citealt{Ownsworth12}). In this section, we will discuss the contribution of these two processes to the evolution of BCGs and their importance at different epochs. Our study shows that BCG progenitors at $z\sim 2$ have a relatively high SFR, and a large fraction of them have either close companions or an asymmetric and distorted morphology. These results suggest that both star formation and (major) mergers may be key mechanisms in BCG evolution at $z \sim 2$. Here we carry out a simple estimate to determine how much these two mechanisms contribute to the BCG mass growth at high redshift. Note that the in-situ stellar mass of BCG progenitors at $z\sim 2$ already accounts for $\sim 40$\% of the total mass of BCGs at $z\sim 0$. With the assumption that the SFR of our BCG progenitors is constant over $z=1-2$, and taking into account the $0.4$ dex uncertainty in SFR from contaminants, the mass increase during this period via star formation is $0.07 - 0.18M_{*,\rm z=0}$ where $M_{*,\rm z=0}$ is the stellar mass of BCGs at $z\sim 0$. On the other hand, we estimate the possible BCG mass growth through mergers by employing the major merger rate for massive galaxies at high redshifts. \citet{Conselice08} use the CAS parameters (structural concentration, asymmetry and clumpiness) to estimate major merger rates for galaxies at $1<z<3$. Since the median redshift of our BCG progenitors is $z\sim 2$ and 80\% of them have stellar mass less than $10^{11} M_\odot$, we use their major merger rate for galaxies with stellar masses $>10^{10}M_\odot$ at $z=2$. Assuming the major merger rate is constant over $z=1-2$, we find that BCG mass growth is about $0.12 M_{*,\rm z=0}$ through major mergers. A similar mass increase is found by employing the major merger rate of \citet{Hopkins10}, such that for $z=2$ massive galaxies ($M_* > 10^{10}M_\odot$) $0.09 M_{*,\rm z=0}$ is built up through merging with other objects whose mass ratios are $>1/3$. The star formation and major mergers thus seem to contribute equally to BCG mass build-up at high redshifts. Our results show that the local BCGs are quite quiescent, where the mass added via star formation is only $0.2 M_\odot$ per year on average. Since the SFR of massive galaxies decreases quickly with cosmic time (e.g., \citealt{Daddi07}; \citealt{vanDokkum10}; \citealt{Ownsworth12}; \citealt{Ownsworth14}), the contribution from star formation to BCG mass growth since $z\sim 1$ should be very small. By using state-of-the-art, cosmological, semi-empirical models, \citet{BuchanShankar16} show that star formation cannot explain the full evolution of massive galaxies, and massive galaxies could have indeed assembled most of their final masses via late mergers. Observationally, by studying the number of mergers onto BCGs, as well as the mass ratio of infalling companions, \citet{Burke13} find that both major and minor mergers are common at $z\sim 1$, and cause a significant BCG mass growth. At much lower redshifts, some observational studies conclude that minor mergers dominate mass growth, and the rarity of major mergers (e.g., \citealt{Liu09}; \citealt{EP12}). Others point out that some BCGs continue to grow through major mergers at $z\sim 0$. Nevertheless, merger (either major or minor) is the dominant process at $z\lesssim 1$. \subsection{Links with BCG evolution at $z<1$} In this work, we extend the observational study of BCG structural evolution and mass growth to $z \sim 2$. In observations, BCG size evolution has been explored at $z<1$. By tracing host halo masses to link BCG progenitors and descendants, \citet{Shankar15} suggest a noticeable increase in BCG mean effective radius by a factor of $\gtrsim 2.5$ since $z\sim 1$. By comparing local WINGS BCGs with high-$z$ $HST$ BCGs whose host clusters span the same range of X-ray luminosity, \citet{Ascaso11} claim a BCG size growth of a factor of $\sim 2$ within the last 6 Gyr (since $z\sim 0.6$). These results indicate that about 60\% of the size growth of local BCGs has occurred at $z\lesssim1$. Considering the size increase in our study (by a factor of 3.2 from $z\sim 2$ ), it seems that BCG size increases only moderately during $z=1-2$. Galaxy shape also reveals important information on galaxy evolution. We find that the \sersic\ index $n$ of BCGs has a clear evolution, such that BCG progenitors are consistent with \sersic\ late-type galaxies at $z\sim 2$, which evolve into local BCGs as early-type galaxies. Moreover, the morphology of our BCG progenitors indicates that a fraction of them are undergoing morphological transformations at $z\sim 2$ through merging, or will undergo mergers at $z<2$. However, at $z<1$, \citet{Ascaso11} find that the shape of BCGs has not changed significantly after $z\sim 0.6$. Since the single \sersic\ model mainly represents the shape of the central bulge, it probably implies that the morphological transformation of BCG bulges is still going on at $z\sim 2$, and is complete before $z\sim 0.6$, during which mergers may play an important role. After that the size and mass growth is focused on the outer regions of BCGs. More observational studies on the shape evolution of BCGs are needed during $z=0 - 1$ to determine if this scenario is likely. Moreover, many studies explore the build-up of BCG stellar mass at $z\lesssim 1-1.5$ in observations. Some of them claim that there is little change in BCG mass since $z\sim 1$ (\citealt{BCM00}; \citealt{Whiley08}; \citealt{Collins09}). In contrast, other papers (e.g., \citealt{Lidman12}; \citealt{Lin13}; \citealt{Shankar15}; \citealt{Zhang15}) find a generally consistent BCG mass growth by a factor of $\sim 2$ over $z=0-1$. In Section~\ref{sec:discuss_mechanism}, we did a simple estimation of BCG mass growth from $z\sim 2$ to $z\sim 1$, reporting that, in this period, at most 18\% of the total mass of local BCGs will be added through star formation, and $\sim 12$\% via major mergers. Since SFR and major merger rate decrease with cosmic time (e.g., \citealt{Bridge10}; \citealt{Bluck12}; \citealt{Ownsworth14}), this mass growth is more likely an upper limit. Considering the stellar mass BCG progenitors already have at $z\sim 2$ ($\sim 40$\% of the total mass of local BCGs), our estimate shows that by $z\sim 1$ the BCG stellar mass will be no more than 70\% of the total mass at $z=0$, suggesting that there has to be an additional mass build-up in BCGs after $z\sim 1$. The BCG mass will increase by a factor of no less than $\sim 1.4$ from $z\sim 1$ to $z\sim 0$. Although we discuss the BCG evolution by combining our work over $z=0\sim 2$ with other studies at $z\lesssim 1$, it is dangerous to do so since the BCG progenitor selections we use are different. Homogeneous BCG data over large range of redshift from future observations is necessary for better understanding the BCG evolution since high redshifts. \subsection{Comparison with massive galaxy evolution} Many studies have examined the properties of massive galaxies at high redshifts, broadening our understanding of massive galaxy evolution over a large redshift range. Here we compare our results on BCGs with the evolution of massive galaxies over $z=0 - 2$. Since constant number density is applied in our study, the comparison is carried out with papers which also use constant number density to trace massive galaxies at different redshifts. \citet{vanDokkum10} study the growth of massive galaxies from $z=2$ using a fixed number density selection of $2 \times 10^{-4}$ Mpc$^{-3}$. They find that at this number density the stellar mass of galaxies has increased by a factor of $\sim 2$, and size has grown by a factor of $\sim 4$ since $z=2$. They verify that their results are not sensitive to the exact number density by repeating key parts of the analysis for a number density of $1 \times 10^{-4}$ Mpc$^{-3}$. \citet{Ownsworth14} study the growth of massive galaxies from $z=3$ by adopting a fixed number density of $ \sim 10^{-4}$ Mpc$^{-3}$, similar to the one used in this paper. Their results show that the stellar mass of galaxies at $z\sim 0.3$ is $\sim 2.5$ times larger than their progenitors at $z\sim 2$, and the size of massive galaxies increases by a factor of $\sim 2.3$ by comparing the average galaxy size within the redshift bin $0.3<z<0.5$ with the bin at $2.0<z<2.5$. Compared with BCG stellar mass growth (a factor of $\sim 2.5$) and size growth (by a factor of $\sim 3.2$), the evolution of massive galaxies appears similar to the BCG evolution from $z\sim2$. Specifically, at high redshift, we examine whether our selected BCG progenitors have different properties from normal massive galaxies which are in the same redshift and stellar mass range. The normal massive galaxies are selected from the CANDELS UDS catalogue whose redshifts and stellar masses have a similar distribution as our 38 selected BCG progenitors. We find that our BCG progenitors are very similar to the normal massive galaxies in many properties such as structure, morphology, and SFR/sSFR. This implies that the BCG progenitors do not show any specific differences with other massive galaxies at $z\sim 2$. Since local BCGs are different from the control samples of local non-BCGs which match in stellar mass, redshift and colour (see L07), BCG progenitors must experience some specific mechanism(s) at $z \lesssim 2$ (probably more minor mergers) which results in the specific properties of BCGs at $z\sim 0$. These mechanisms are likely responsible for the characteristic cD envelope observed in many local BCGs (\citealt{Zhao15a,Zhao15b}). In this paper, we carry out a study of BCG evolution beyond $z=1$ to explore how structure, morphology and stellar mass of BCGs vary with cosmic time since $z\sim 2$. By proposing a BCG progenitor selection which identifies BCG progenitors as the most massive galaxies in the densest local environments, we select our BCG progenitor sample at $z\sim 2$ from the CANDELS UDS data. Testing our method in simulations we find that 45\% of our selected progenitors are true BCG progenitors. Although the high-$z$ progenitors selected by our method are a mixed sample of BCG and non-BCG progenitors, the properties of our high-$z$ progenitors can be used to trace BCG evolution because they are similar to the properties of the pure BCG progenitors within the sample. We use a constant number density of $10^{-4.06} h^3$Mpc$^{-3}$ to select our samples. At this density the descendants of the high-$z$ selected sample are taken from the SDSS DR7 galaxy catalogue. To ensure the galaxy sample at $z\sim 0$ are the descendants of our selected progenitors, based on simulations, we construct a local mixed sample which contains 38\% BCGs and 62\% non-BCGs. We demonstrate through several methods that the contamination from non-BCGs and non-BCG progenitors do not erase the intrinsic BCG evolution. Comparing properties between our high-$z$ BCG progenitors and their local descendants, we find a clear BCG evolution since $z\sim 2$ in structure, morphology and stellar mass. Our major results on BCG evolution at $z \lesssim 3$ are: \begin{itemize} \item At $z\sim 2$, less than 50\% of the most massive galaxies in the densest environments are the true BCG progenitors. \item Although the environmental density is not a strong tracer, the method we propose to identify BCG progenitors at $z\sim 2$ can be applied to observational data to derive BCG evolution since they have similar properties to the pure BCG progenitors. \item The size of BCGs has grown by a factor of $\sim 3.2$ since $z\sim 2$. The BCG progenitor profiles are mainly \sersic\ late-type galaxies with median \sersic\ index of $n=2.3$, while their local BCG descendants are early-type galaxies whose median \sersic\ index is $n=4.5$. \item The residual images after subtracting single \sersic\ fits illustrate that BCG progenitors at $z\sim 2$ are more distorted, whereas the local BCGs have smoother profiles. This difference in morphology is verified quantitatively by \rff \ measures, such that BCG progenitors have larger \rff \ values than their local counterparts. About $32$\% of BCG progenitors at $z\sim 2$ are undergoing mergers, or will undergo mergers at $z<2$. \item The stellar mass of BCGs has grown by a factor of $\sim 2.5$ since $z\sim 2$. The average SFR of BCG progenitors at $z\sim 2$ is still relatively high, at $13.5$ $M_\odot$ yr$^{-1}$. In contrast, their local descendants are very quiescent, with an average SFR of only $ 0.2$ $M_\odot$ yr$^{-1}$. We find that over the $z=1 - 2$ period, star formation and merging contribute approximately equally to BCG mass growth. However, since the SFR decreases with time, merging must play a more important role in BCG assembly at $z\lesssim1$. \item We find that BCG progenitors at high-$z$ are not significantly different than other galaxies of similar mass at the same redshift range. This suggests that the processes which differentiate BCGs from normal massive elliptical galaxies must occur at $z \lesssim 2$. \end{itemize} | 16 | 9 | 1609.07287 |
1609 | 1609.06720.txt | We present the analysis of the first circumbinary planet microlensing event, OGLE-2007-BLG-349. This event has a strong planetary signal that is best fit with a mass ratio of $q \approx 3.4\times10^{-4}$, but there is an additional signal due to an additional lens mass, either another planet or another star. We find acceptable light curve fits with two classes of models: 2-planet models (with a single host star) and circumbinary planet models. The light curve also reveals a significant microlensing parallax effect, which constrains the mass of the lens system to be $M_L \approx 0.7 \msun$. Hubble Space Telescope images resolve the lens and source stars from their neighbors and indicate excess flux due to the star(s) in the lens system. This is consistent with the predicted flux from the circumbinary models, where the lens mass is shared between two stars, but there is not enough flux to be consistent with the 2-planet, 1-star models. So, only the circumbinary models are consistent with the HST data. They indicate a planet of mass $m_c = 80\pm 13\,\mearth$, orbiting a pair of M-dwarfs with masses of $M_A = 0.41\pm 0.07\msun$ and $M_B = 0.30\pm 0.07\msun$, which makes this the lowest mass circumbinary planet system known. The ratio of the separation between the planet and the center-of-mass to the separations of the two stars is $\sim 40$, so unlike most of the circumbinary planets found by Kepler, the planet does not orbit near the stability limit. | \label{sec-intro} One of the main features of the observational study of extrasolar planets has been the continuing stream of surprise observational discoveries. These include planets orbiting a pulsar \citep{pulsar_planets}, hot Jupiters \citep{51peg}, systems of short period, low-density planets in tightly packed orbits \citep{lissauer_kep11}, and circumbinary planets \citep{doyle11} close to the stability limit. Circumbinary planets and planets in close binary systems are very difficult to detect with the radial velocity method, but Kepler has proved quite adept at finding such systems \citep{doyle11,welch12,welch15,orosz12,kostov13,kostov14,kostov16}. Gravitational microlensing \citep{bennett_rev,gaudi_araa} has demonstrated the ability to detect such systems \citep{mps-97blg41,gould14,poleski14,udalski15} (either circumbinary planets or planets orbiting one member of a relatively close binary). Two of these claimed microlensing planets in binary systems have turned out to be incorrect, MACHO-97-BLG-41 \citep{mps-97blg41,albrow-97blg41,jung13} and OGLE-2013-BLG-0723 \citep{udalski15,han_ob130723}, but this is largely an issue that can be addressed by greater care in event modeling. These events still help to establish the sensitivity of the microlensing method to planets in close binary systems, because in each case, the light curve measurements do definitively distinguish between the triple-lens, planetary models, and the close binary models without a planet. In this paper, we present the first circumbinary planet found by microlensing, OGLE-2007-BLG-349L(AB)c\footnote{Our designation for this event corrects an apparent inconsistency in the naming of planets in binary systems by using a unique letter for each mass in the system, following the convention for planets orbiting single stars.}. The signal for this event is dominated by the microlensing effect of a Saturn mass ratio planet, but the very central part of the planetary binary lens light curve does not fit the data. As we show in Section~\ref{sec-lc}, the light curve can be fit by models with an additional lens mass, either another planet or another star. However, the light curve data does not tell us which of these models is correct. Nevertheless, the light curve does reveal finite source effects and a microlensing parallax signal that allow us to determine the lens system mass, as we discuss in Section~\ref{sec-lensprop}. In Section~\ref{sec-HST}, we present Hubble Space Telescope (HST) observations of the OGLE-2007-BLG-349 lens system and source star. These observations clearly indicate excess flux at the position of the source, which is consistent with the circumbinary models but not the two-planet models. If the stellar mass of the lens system is divided into two masses, then it is substantially fainter ($\sim 1.6\,$mag) in the $I$-band than a single host star would be. And it is only such a faint lens system that is consistent with the HST images, and so it is the HST observations that select the circumbinary model over the two-planet models. In Section~\ref{sec-HSTmod}, we add the lens brightness constraint to our light curve modeling in order to confirm this conclusion, and we find that two-planet models with an extremely faint host star (presumably a white dwarf) do better than the best two-planet models with a main sequence host star. But, these models are still substantially worse than the circumbinary models, so they are excluded. We consider adaptive optics observations of the source and lens stars in Section~\ref{sec-NACO}, and we find that these observations provide marginal support for the circumbinary interpretation of this light curve. Finally, in Section~\ref{sec-conclude}, we discuss the implications of this discovery for our understanding of the properties of exoplanets. | \label{sec-conclude} In the previous section, we have established that although the OGLE-2007-BLG-349 light curve can be explained by models with one star and two planets, it is only the circumbinary planet models that can explain both the light curve and the HST observations. So, the system consists of two host stars, OGLE-2007-BLG-349LA and OGLE-2007-BLG-349LB, orbited by a planet somewhat less massive than Saturn. Although it was the first circumbinary planet to be observed, aside from a planet orbiting a neutron star-white dwarf system \citep{ford00,sig03}, it was not the first circumbinary planet to be published, as 10 circumbinary planets \citep{doyle11,welch15,kostov16} have been discovered by the Kepler mission. \begin{figure} \vspace{-0.2cm} \epsscale{0.8} \plotone{circumbinary.pdf} \caption{Comparison of host star masses and orbital separations for the known circumbinary planet systems. The filled circles show the orbital separations of the host stars, while the orbital separations of the planets from the stellar centers of mass are marked with ``x"s. The vertical bars on each line indicate the approximate stability limit. The red region gives the typical Einstein radius as a function of mass and the light red region gives the approximate range of planetary microlens sensitivity. \label{fig-circumbin}} \end{figure} One puzzle with the circumbinary planets discovered in the Kepler data is that most of them are located quite close to the stability limit \citep{holman99}, as shown in Figure~\ref{fig-circumbin}. That is, if they were moved to orbits with slightly smaller semi-major axes, they would quickly become dynamically unstable. \citet{holman99} find that circular, coplanar circumbinary orbits become unstable within $a_c \simeq (2.28\pm 0.01) + (3.8\pm 0.3)e + (1.7\pm 0.1)e^2$, where $e$ is the eccentricity of the binary orbit and $a_c$ is measured in units of the stellar binary semi-major axis. Our modeling has enforced a circular orbit for the stellar binary, so it is sensible to assume a low eccentricity. Also, if the stellar binary orbit does have a significant eccentricity, then it is likely that the semi-major axis is smaller than the mean values listed in Table~\ref{tab-pparam}, because stars spend most of their time in an eccentric orbit at separations larger than the semi-major axis. So, the consideration of stellar binary orbits with significant eccentricity is not likely to significantly increase the maximum stellar separation, which is closely related to the stability constraint. So, we assume $e \approx 0.1$, and this yields $a_c = 2.7$. The median semi-major axis of the OGLE-2007-BLG-349LAB binary is $a \simeq 0.080\,$AU from Table~\ref{tab-pparam}, and the median three-dimensional separation between stellar center-of-mass and the OGLE-2007-BLG-349L(AB)c planet is $\sim 3.2\,$AU. Therefore, we estimate the planet orbits at $\sim 15a_c$. This compares to most of the Kepler circumbinary planets that orbit at $< 2a_c$, and the widest orbit Kepler circumbinary planet \citep{kostov16} that orbits at $7a_c$. The expected orbital period for the OGLE-2007-BLG-349L(AB)c planet is $\sim 7\,$years assuming a host system mass of $0.71\,\msun$ and a semi-major axis of $3.2\,$AU, so such a system could not have been detected by Kepler. The only Kepler planet with a comparable separation is Kepler-1647b. It orbits a star system that is three times more massive than the OGLE-2007-BLG-349L host star system, which implies a period short enough to allow for its detection with two transit episodes during Kepler observations. We expect that Kepler's detection efficiency for such systems is quite low, so such systems might be quite common. The fact that the first circumbinary planet found by microlensing has an orbital separation well beyond the stability limit adds modest support to the idea that circumbinary planets far beyond the stability limit are quite common. This would imply that circumbinary planets probably form in the outer disk, relatively far from the orbital stability limit \citep{kley14,bromley15,silsbee15} instead of in situ \citep{meschiari14}. In principle, this new microlensing discovery could provide strong evidence that circumbinary planets are substantially more common far from the stability limit than close to the stability limit \citep{luhn16}. Microlensing is most sensitive to both planets and stellar companions at separations close to the Einstein radius. However, for event OGLE-2007-BLG-349, the ratio of the two-dimensional separation between the planet and stellar center-of-mass to the separation between the two stars is 42. Such a large ratio was only detectable because of the very high magnification of this event, but circumbinary planets with a smaller separation ratio should be detectable for a much larger class of lower-magnification events. The fact that no other circumbinary planets have been found by microlensing might be considered to imply that circumbinary planets with smaller separation ratios are more rare. However, there is circumstantial evidence suggesting that we may be inefficient at identifying such events in our data. Unlike the transit method, microlensing is sensitive to planets beyond the snow line, \citep{lecar_snowline,kennedy_snowline}, so OGLE-2007-BLG-349L(AB)c is the first circumbinary planet beyond the snow line. \citet{gould14} presented another two-star plus one planet event, OGLE-2013-BLG-0341, which was interpreted as a wide binary with a planet orbiting one of the two stars, although there are circumbinary models with very similar light curves. This was also a high magnification event with the signal dominated by the stellar binary instead of by the planet (like OGLE-2007-BLG-349). However, the lens-source alignment was such that the source crossed a planetary caustic feature prior to reaching high magnification. This made it obvious that the lens system included a planet, but we were very lucky to have this planetary feature detected. And the analysis showed that the planet was required to fit the data even if the low-magnification planetary feature was not seen. This suggests that there should be many more two-star plus one planet events in the data that we have already collected, but that we are not efficient at finding planetary signals in events that are dominated by stellar binary microlensing features. Hence, we recommend a systematic search for planetary signals in the light curves of strong stellar binary events. If a large population of circumbinary planets are found, it will add to the $\sim 10$\% frequency of circumbinary planets found in short period orbits \citep{armstrong14}. Circumbinary planetary systems can be quite efficient at ejecting planets \citep{sutherland16,smullen16}, so they could contribute to the large population of rogue planets found by microlensing \citep{sumi11}. | 16 | 9 | 1609.06720 |
1609 | 1609.07308_arXiv.txt | With the help of 3D AMR hydrodynamical simulations we aim at understanding G2's nature, recent evolution and fate in the coming years. By exploring the possible parameter space of the diffuse cloud scenario, we find that a starting point within the disc of young stars is favoured by the observations, which may hint at G2 being the result of stellar wind interactions. | \cite[Gillessen et al. (2012)]{Gillessen_12} discovered a fast moving object within the range of the S-star cluster close to Sgr A*. VLT NACO images show the object in L'-band, but not in K-band, indicating that it is a dusty, ionised gas cloud. The spatially resolved ionised gas emission (especially in the Brackett-$\gamma$ line) monitored with the SINFONI instrument allows to accurately constrain the orbit around Sgr A* to be highly eccentric (e=0.98) with a peri-centre passage at a distance of 2400 Schwarzschild radii. The cloud has a mass of 3 earth masses and an orbital period of 400 years. The tidal interaction with the central black hole is clearly visible in the developing gradients in observed position-velocity (PV) diagrams \cite[(Gillessen et al., 2013a, 2013b)]{Gillessen_13a,Gillessen_13b}. An overlay of the PV diagrams of the years 2004 to 2014 shows that G2, a second cloud G1 and the {\it tail} might form a stream of gas \cite[(Pfuhl et al., 2015)]{Pfuhl_15}. | By directly comparing our simulated position-velocity (PV) diagrams for various starting times (in pressure equilibrium) along the orbit (upper row in Fig.~2) with the observed ones (residuals in second row in Fig.~2), we find better correspondence for models with a starting time close to apo-centre of the best-fit G2 orbit, as inferred from a reduced $\chi^2$ analysis. This might indicate a formation scenario due to stellar wind interaction within the disc of young stars \cite[(Calder\'{o}n et al., 2016)]{Calderon_16} or G2's origin from a gas streamer. Brackett-$\gamma$ light curves for these simulations show a (partly physical) mixing plateau and are roughly in agreement with the data. Similarly good overall agreement is found for the {\it Compact Source Scenario} (see conference contribution by Alessandro Ballone). However, in the latter scenario, the source leaves G2 behind in approximately 5 years from now and forms a separate cloud, allowing us to distinguish the two scenarios. \begin{figure} \begin{center} \includegraphics[width=0.8\textwidth]{dens_evol.pdf} \caption{Density distributions showing the evolution from a spherical cloud to a thin filamentary structure: (a) compression due to increasing ambient pressure and ram pressure, (b) tidal interaction and (c) accretion towards Sgr~A* in a nozzle-like accretion stream. Adapted from \cite[Schartmann et al. (2015)]{Schartmann_15}.} \label{fig1} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics[width=0.75\textwidth]{pvcomparison_somesim.pdf} \caption{Simulated PV diagrams (upper row) for various starting times of the clouds (as annotated in the upper left corner) and the normalized residual arrays after directly comparing them to the 2012 observed PV diagrams (lower row). The blue curve corresponds to G2's nominal orbit. A starting point of the clouds close to peri-centre gives the best adaptation of the data. Taken from \cite[Schartmann et al. (2015)]{Schartmann_15}.} \label{fig2} \end{center} \end{figure} | 16 | 9 | 1609.07308 |
1609 | 1609.09375.txt | We study analytically and experimentally \change{certain} symplectic and time-reversible $N$-body integrators which employ a Kepler solver for each pair-wise interaction, \change{including} the method of \citeauthor{HernandezBertschinger2015}. Owing to the Kepler solver, these methods treat close two-body interactions correctly, while close three-body encounters contribute to the truncation error at second order and above. The second-order errors can be corrected to obtain a fourth-order scheme with little computational overhead. We generalise this map to an integrator which employs a Kepler solver only for selected interactions and yet retains fourth-order accuracy without backward steps. In this case, however, two-body encounters not treated via a Kepler solver contribute to the truncation error. | The gravitational $N$-body problem has been studied ever since Newton first wrote down his universal gravitational law of attraction. The $N$-body problem appears often in dynamical astronomy, for example planetary systems, stellar associations, star clusters, galaxies, dark matter haloes, and even the universe as a whole can be modelled to good approximation as $N$-body problems \citep{HeggieHut2003}, although other, typically less accurate, alternative models are possible in some cases. No analytic solutions to the $N$-body problem exist for $N>2$, except for few cases \change{without practical relevance,} such as the five families of solutions found by \cite{Euler1767} and \cite{Lagrange1772}, and numerical integration is required instead. If the $N$-body method is used to model a collision-less system (where two-body encounters are dynamically unimportant), encounters between the simulation particles introduce relaxation into the model not present in the actual system. These artificial effects can be reduced \change{(but not eliminated)} by softening the gravitational inter-particle forces at small distances \change{\citep{DehnenRead2011}}, which in turn significantly simplifies the $N$-body dynamics and allows the use of comparatively simple integration techniques, such as the leapfrog integrator \citep{Stoermer1907, Verlet1967}\footnote{The leapfrog integrator has been independently discovered several times, and \change{was implicitly used by \cite[][figure for theorem I in book I]{Newton1687} as later discovered by Verlet himself \citep*{HairerLubichWanner2006}}.}. Here, we are instead concerned with the collisional $N$-body problem, which emerges for example when modelling the planetary systems including our own, planetesimals in a circum-stellar disc, or a globular cluster. In this case, the accurate long-term time integration of the unsoftened gravitational forces poses a formidable problem. Here `long term' means several Lyapunov times or when a conventional integrator becomes unreliable due to accumulation of truncation errors, whichever is shorter. A major problem arises from the dynamical stiffness of these systems in the sense that the relevant time scales differ by orders of magnitude: already a simple elliptic or hyperbolic orbit poses problems for numerical integration owing to the large variation of angular speed, i.e.\ of the local orbital time scale. Since the $N$-body problem comprises a Hamiltonian system, symplectic, or more broadly geometric, numerical time integration\footnote{A symplectic integrator advances the system by a canonical map which is close to that of the actual Hamiltonian. As a consequence, the geometric structure of phase space and the Poincar\'{e} invariants are exactly preserved. Many symplectic integrators also \change{exactly} conserve all first integrals, except for the Hamiltonian, which tends to have bounded error.} \citep*{HairerLubichWanner2006} provides a useful framework for the $N$-body problem. Unfortunately, symplectic integration has not been widely implemented for the study of the collisional $N$-body problem. Switching methods, which change between different symplectic integrators, have been proposed for the of study single-star planetary systems \citep*{Chambers1999, KvaernoLeimkuhler2000, DuncanLevisonLee1998}. Unfortunately, tests indicate these methods may break time-reversibility and symplecticity \citep{Hernandez2016}. Another possibility to deal with the varying time-scales is to transform to another time variable \citep[Sundman transform, see][]{LeimkuhlerReich2004} and apply a symplectic method in the resulting extended system \citep{PretoTremaine1999, MikkolaTanikawa1999}, \change{but} such methods cannot be efficient for $N\gg2$. An alternative to exactly symplectic integrators are time-reversible geometric integration methods, which share many desirable properties with symplectic integrators \citep{HairerLubichWanner2006}. When modelling globular clusters, a common such integration method is the implicit fourth-order Hermite integrator \citep{Makino1991}, which requires an iterative solution, but in practice often only one iteration is used, violating exact time symmetry. Even when iterating to convergence, the efficient adaptation of individual discrete step sizes cannot be reconciled with exact time symmetry (Dehnen 2016, in preparation). \cite*{KokuboYoshinagaMakino1998} argue that this is tolerable if only few step-size changes occur, such as in planetary systems with only near-circular orbits. \cite*{HutMakinoMcMillan1995} proposed a symmetrisation procedure for any integrator and \cite{MakinoEtAl2006} extended this procedure to adaptation of individual particle step sizes. However, the resulting method involves the solution of a large implicit system of equations requiring an excessive amount of computational effort and has not been used in practice. Because of these complications, contemporary methods for the integration of planetary systems employ a fixed global time step. A recent progress was the introduction of a symplectic and time-reversible map which treats close two-body encounters exactly \citep{HernandezBertschinger2015} and is efficient for planetary-system integration \citep{Hernandez2016}. In this present study, we show that the integrator \change{of \citeauthor{HernandezBertschinger2015}} is \change{still only} second-order accurate, but can be made fourth-order accurate with relatively little additional computational effort. We also discuss the option to treat only selected pair-wise interactions exactly (to improve efficiency) and yet keep the overall integration accuracy at fourth order. This paper is organised as follows. Section~\ref{sec:prelim} reviews background concepts on symplectic integration and re-analyses the popular leapfrog (St{\o}rmer-Verlet) integrator, Section~\ref{sec:kepler} discusses \change{the integrator of \citeauthor{HernandezBertschinger2015}}, introduces its fourth-order extension, and presents some numerical tests. Integrators which use a Kepler solver selectively are considered in Section~\ref{sec:mix}, including our novel fourth-order hybrid integrator. The appendices provide some detailed calculations and discuss implementation details. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | We have analysed novel symplectic and time reversible integrators for collisional $N$-body problems, where close encounters play an important role in driving the dynamics. These encounters render collisional $N$-body problems much harder than collision-less dynamics and are the main stumbling block for efficient time integration. Most symplectic integrators which have been applied to collisional dynamics in the past are only second-order accurate and generally handle close encounters inaccurately. A promising approach to overcome this hurdle is the usage of a Kepler solver to deal with close encounters \citep{GoncalvesFerrariEtAl2014}. \cite{HernandezBertschinger2015} have demonstrated how to use this approach to build a symplectic and time-reversible integrator (HB15 \change{or [DB]$^2$ in our nomenclature}). We provide theoretical justification for the success of HB15 and \change{some} related methods: terms of the error Hamiltonian that originate from close two-body encounters are eliminated at all orders. This leaves only close encounters of three or more particles to contribute to the truncation error. The lowest-order error Hamiltonian of the resulting integration methods can be expressed as the nested Poisson bracket $\{\{T,V\},V\}$ of kinetic and potential energies excluding terms of the form $\{\{T,V_{\!\ij}\},V_{\!\ij}\}$, which account for two-body encounters and are eliminated owing to the Kepler solver ($V_{\!\ij}$ denotes the potential energy arising form the gravitational interaction of particles $i$ and $j$, see equation~\ref{eq:T,V}). Since $T$ is quadratic in the momenta and $V$ a function of the positions only, the term $\{\{T,V\},V\}$ itself depends only on the particle positions. As a consequence, this terms acts like a potential energy and is integrable. Thus, the associated truncation error can be corrected in a symplectic way and with little extra cost (compared to the solutions of the Kepler problems), resulting in the fourth-order symplectic and time-reversible integrator \change{[DB]$^2_4$} presented in Section~\ref{sec:HB15:4}. The usage of a Kepler solver may be restricted to a sub-set $\mathcal{S}$ of all pair-wise particle interactions \citep{Hernandez2016}, when the terms $\{\{T,V_{\!\ij}\},V_{\!\ij}\}$ and $\{\{V_{\!\ij},T\},T\}$ from interactions $(i,j)\not{\in}\mathcal{S}$ contribute to the error Hamiltonian. This may be tolerable if such interactions are never close (for example, those between the gas giant planets in the Solar system). However, these terms can also be eliminated in a different way, namely using the method of \cite{Chin1997} which cancels $\{\{V_{\!\ij},T\},T\}$ and integrates $\{\{T,V_{\!\ij}\},V_{\!\ij}\}$ without the need for backward steps (as opposed to the fourth-order symplectic method of \citealt{Yoshida1990}), \change{resulting} in the new symplectic integrator \change{`DH16' of equation~\eqref{eq:map:[KDBK]^2_4}}. \change{This map} is a hybrid between the fourth-order forward method of \cite{Chin1997} and our fourth-order extension \change{[DB]$^2_4$} of HB15\change{, which is its limiting case when all particle pairs are in set $\mathcal{S}$}. Various tests and efficiency comparisons of the maps we discuss are presented. As our tests revealed, the novel fourth-order integrators are generally more efficient than previous methods when high accuracy is demanded. However, they still suffer inaccuracies, in particular in some chaotic systems. For a chaotic restricted three-body exchange orbit test \change{and a $N=1024$ cluster simulation} \change{our} fourth-order integrator \change{DH16 with all particle pairs treated with a Kepler solver} performed similarly to \change{the second-order methods} HB15 \change{or (for the cluster simulation only) \textsc{sakura} of \citeauthor{GoncalvesFerrariEtAl2014}, which also used a Kepler solver for each particle pair although in a way that destroys symplecticity and reversibility}. \change{The dynamics of} these \change{systems is} likely dominated by three-body encounters, and the only way to increase the accuracy in such situations appears some form of \change{adaption either of the} time stepping \change{or of the set $\mathcal{S}$ of particle pairs for which a Kepler solver is used. These methods change from one surrogate Hamiltonian to another and may lose symplecticity but retain time reversibility.} We plan to explore \change{these ideas} in the future. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | 16 | 9 | 1609.09375 |
1609 | 1609.01718_arXiv.txt | The predicted abundance and properties of the low-mass substructures embedded inside larger dark matter haloes differ sharply among alternative dark matter models. Too small to host galaxies themselves, these subhaloes may still be detected via gravitational lensing, or via perturbations of the Milky Way's globular cluster streams and its stellar disk. Here we use the \apostle cosmological simulations to predict the abundance and the spatial and velocity distributions of subhaloes in the range $10^{6.5}-10^{8.5}\Ms$ inside haloes of mass $\sim10^{12} \Ms$ in $\Lambda$CDM. Although these subhaloes are themselves devoid of baryons, we find that baryonic effects are important. Compared to corresponding dark matter only simulations, the loss of baryons from subhaloes and stronger tidal disruption due to the presence of baryons near the centre of the main halo, reduce the number of subhaloes by $\sim 1/4$ to $1/2$, independently of subhalo mass, but increasingly towards the host halo centre. We also find that subhaloes have non-Maxwellian orbital velocity distributions, with centrally rising velocity anisotropy and positive velocity bias which reduces the number of low-velocity subhaloes, particularly near the halo centre. We parameterise the predicted population of subhaloes in terms of mass, galactocentric distance, and velocities. We discuss implications of our results for the prospects of detecting dark matter substructures and for possible inferences about the nature of dark matter. | \label{sec:Introduction} While the $\Lambda$ Cold Dark Matter (hereafter $\Lambda$CDM) model explains many large scale observations, from the anisotropy of the microwave background radiation \citep[e.g.][]{Wright-1992} to the distribution of galaxies in the cosmic web \citep{Davis-1985}, inferences about the particle nature of dark matter or its possible (self)-interactions require observations require observations on far smaller scales. Warm Dark Matter (WDM) particles, such as sterile neutrinos with masses of a few keV, have free-streaming scales of less than 100 kpc, and differ from CDM in terms of the halo mass functions at mass scales on the order of $10^9 \Ms$ and below \citep[e.g.][]{Avila-Reese-2001, Bose-2016}, while weak self-interactions would produce shallow cores of the order of several kpc in the centre of dark matter haloes \citep[e.g.][]{Spergel-2000}. In principle, there is no shortage of observations that probe these small scales. They include the structures seen in the Lyman-$\alpha$ forest \citep[e.g.][]{Croft-2002, Viel-2013}, the abundance of dwarf galaxies in deep HI surveys \citep{Tikhonov-2009, Papastergis-2011}, and the abundance \citep[e.g.][]{Klypin-1999, Boylan-Kolchin-2011, Lovell-2012, Kennedy-2014} as well as internal kinematics that probe the density profiles \citep[e.g.][]{Walker-2011, Strigari-2014} of Local Group dwarf galaxies. While these studies have progressively narrowed the parameter space of viable dark matter candidates, inferences about the non-baryonic nature of dark matter from observations of the Universe's baryonic components are inherently limited by uncertainties in our understanding of complex astrophysical processes, such as radiative hydrodynamics, gas cooling, star formation, metal-enrichment, stellar winds, supernova and AGN feedback, and cosmic reionisation. For simple number counts, the effects of baryons in suppressing the formation of dwarf galaxies in CDM can be degenerate with the effects of warm dark matter \citep[e.g.][]{Sawala-2013}. As of 2016, a plethora of studies have also offered baryonic solutions to the various problems for $\Lambda$CDM that had previously been identified in Dark Matter Only (hereafter DMO) simulations \citep[e.g.][]{Okamoto-2008, Governato-2010, Zolotov-2012, Brooks-2013, Arraki-2014, Chan-2015, Sawala-2015, Dutton-2016}. In addition, in the $\Lambda$CDM cosmological model, the majority of low-mass substructures which would most easily discriminate between different dark-matter models are predicted to be completely dark \citep{Bullock-2000, Benson-2002, Okamoto-2008, Sawala-2016a, Ocvirk-2015}, and hence unobservable through starlight. Fortunately, alternative methods exist that can reveal small structures and substructures purely through their gravitational effect and detect even pure dark matter haloes, thereby potentially breaking the degeneracy with baryonic physics: \begin{itemize} \item Gravitational lensing directly probes the projected mass distribution in and around galaxies and can reveal their luminous and non-luminous components. Weak gravitational lensing has confirmed the existence of massive dark haloes surrounding galaxies down to Milky-Way scales, or masses of $\sim 10^{12}\Ms$ \citep[e.g.][]{Mandelbaum-2006}. While these provide strong evidence for the existence of non-baryonic dark matter, they cannot distinguish between different currently viable models of cold, warm or self-interacting dark matter that deviate on mass scales below $\sim10^{9}\Ms$. However, much lower masses, down to $\sim 10^6\Ms$, may be probed through strong gravitational lensing, either via flux-ratio anomalies \citep[e.g.][]{Mao-1998, Xu-2009, Xu-2015}, or detectable perturbations of observed Einstein rings by substructures in the lens itself or along the line of sight \citep{Mao-1998, Metcalf-2001, Dalal-2002, Vegetti-2012, Vegetti-2014}. On these scales, different dark matter models may be clearly distinguished, provided that the expected abundances and distributions of substructures for different models can be reliably predicted. \item Gaps in stellar streams originating from the tidal disruption of either globular clusters or dwarf galaxies can also provide evidence for substructures. In particular, globular cluster streams in the Milky Way, such as Palomar-5 (hereafter Pal-5, discovered by \citealt{Odenkirchen-2001}) and GD-1 (discovered by \citealt{Grillmair-2006}) can be stretched out over many kiloparsecs along their orbit while conserving their phase-space volume. Compared to dwarf galaxies, globular clusters have much lower internal velocity dispersions resulting in much narrower streams, making them very sensitive tracers both of the Galactic potential, and of perturbations by low-mass substructures \citep[e.g.][]{Ibata-2002, Carlberg-2013}. Based on the \vialactea DMO simulations, \cite{Yoon-2011} have calculated the interaction frequency of the Pal-5 stream with dark substructures during its assumed lifetime of 550 Myrs; they predicted $\sim 20$ direct encounters with subhaloes of $10^6-10^7\Ms$, and $\sim 5$ with subhaloes above $10^7\Ms$. \cite{Erkal-2015a, Erkal-2015b} have computed the properties of predicted gaps in streams such as Pal-5 and GD-1 in $\Lambda$CDM. They show that the improved photometry, greater depth, and more precise radial velocity and proper motion measurements of upcoming surveys such as Gaia \citep{Perryman-2001, Gaia-2012}, DES \citep{DES-2005} and LSST \citep{LSST-2009} should allow a characterisation of perturbers in terms of mass, concentration, impact time, and 3D velocity, for subhaloes above $10^7\Ms$, albeit with an irreducible degeneracy between mass and velocity. Recently, \cite{Bovy-2016} have used the density data of Pal-5 to infer the number of subhaloes in the mass range $M = 10^{6.5} - 10^{9} \Ms$ inside the central 20 kpc of the Milky Way to be $10^{+11}_{-6}$. However, they also noted the uncertainty due to unaccounted baryonic effects, and due to the required assumptions in the subhalo velocity distribution. \item The cold thin stellar disk of the Milky Way is another sensitive probe of the interactions with orbiting low-mass substructures. Satellite substructures passing through the Milky Way disk are expected to cause small but detectable changes in both the radial and vertical velocity distribution of stars in the disk, resulting in a thickening of the thin disk \citep[e.g.][]{Toth-1992, Quinn-1993, Navarro-1994, Walker-1996, Sellwood-1998, Benson-2004, Kazantzidis-2008}. The thinness and long-term stability of the Milky Way stellar disk could thus potentially put strong limits on the number of allowed massive dark substructures in the vicinity of the disk, and recent work by \cite{Feldmann-2015} suggest that the expected increase in the vertical velocity dispersion of disk stars due to the impact of dark substructures should be detectable with Gaia. However, the vertical heating and thickening of the disk by dark substructures are severely reduced in simulations that include dissipational gas physics. The inclusion of gas reduces disk heating mainly through two mechanisms: the absorption of kinetic impact energy by the gas and/or the formation of a new thin stellar disk that can recontract heated stars towards the disk plane \citep[e.g.][]{ Stewart-2009, Hopkins-2009, Moster-2010}. \end{itemize} While the above phenomena have a gravitational origin, they still fall short of providing a complete census of dark matter substructures. Instead, inferences about dark matter models based on the number of detected perturbations must be made statistically, and in each case, require an accurate prediction of the abundance, properties and distribution of dark matter substructures inside the central $\sim 10-20$~kpc of galaxy or group-sized dark matter haloes. Previous work has relied on very high resolution DMO simulations, such as \vialactea \citep{Diemand-2007} and \aquarius \citep{Springel-2008}. These have shown that tidal stripping reduces the mass fraction of dark matter contained in self-bound substructures towards the halo centre \citep[e.g.][]{Springel-2008}. It has also been argued that the presence of a stellar disk and adiabatic contraction of the halo can lead to enhanced tidal disruption of substructures. Based on DMO simulations with an additional massive disk-like potential, \cite{Donghia-2010} quantified the disruption of substructures through tidal stripping due to the smooth halo, tidal stirring near pericentre, and ``disk shocking'' by the passage of a substructure through the dense stellar disk. For their parameters, this led to a depletion of substructures by up to a factor of 3 for a subhaloes of mass $10^{7}\Ms$. Similarly, \cite{Yurin-2015} imposed a less massive disk inside a DMO simulation, and found a reduction in subhalo abundance by a factor of 2 in the centre. In addition to the enhanced tidal disruption studied by these authors, the loss of baryons reduces the masses and abundances of low-mass subhaloes relative to DMO simulations \citep{Sawala-2013, Schaller-2015, Sawala-2015}. While earlier work has focussed on the haloes of star-forming dwarf galaxies, here we use high resolution simulations which capture the full baryonic effects to explore the extent to which baryonic physics can change the abundance of even completely dark substructures deeply inside the MW halo, and discuss possible implications for the detection of substructures through lensing, stream gaps, and disk heating. This paper is organised as follows: in Section~\ref{sec:methods} we briefly describe the simulations used in this work, the selection of haloes and substructures, and the reconstruction of orbits. In Section~\ref{sec:results} we discuss how baryons affect the abundance and distribution of substructures inside dark matter haloes, as a function of satellite mass, galactocentric radius, and time. In Section~\ref{sec:dynamics} we examine the subhalo energy, angular momenta, orbital velocity profiles and orbital anisotropy, and, in Section~\ref{sec:velocities} we describe the non-Maxwellian subhalo velocity distributions. We discuss the implications of our results for different observables in Section~\ref{sec:observables}, and conclude with a summary in Section~\ref{sec:conclusion}. Additional details about the orbital interpolation and a comparison of the measured velocity distributions to standard Maxwellian fits are given in the Appendix. | \label{sec:conclusion} We have studied how baryonic effects can change the abundance of substructures in the mass range M$=10^{6.5}-10^{8.5}\Ms$ inside Milky Way mass haloes of M$_{200}\sim10^{12}\Ms$ over a lookback time of up to 5 Gyr. We find that the abundance of subhaloes, independently of subhalo mass, is reduced in hydrodynamic simulations of the same host halo compared to their DMO counterpart. The depletion increases towards the halo centre: at $r > 50$~kpc, the number of subhaloes in the hydrodynamic simulations is above $3/4$ of that in the DMO counterparts, dropping to $\sim 1/2$ at $r<10$~kpc. While baryonic effects of this magnitude clearly need to be taken into account for accurate predictions, they do not impede the detection of dark substructures through stream gaps, disk heating, or lensing. Purely in terms of substructure abundance, \cite{Donghia-2010} found a stronger reduction, with the subhalo number reduced to $1/3$relative to the original DMO simulation at $10^{7}\Ms$ by the effects of the stellar disk alone. This is due in part to the much higher disk mass ($10\%$ of M$_{96}$, or $\sim 14\%$ of M$_{200}$) that they assumed. They also reported a significant subhalo mass dependence, with $1/2$ of subhaloes remaining at $10^9\Ms$, while we find a nearly constant factor. One possible explanation for this may be numerical resolution: while we limit our study to subhaloes with more than 50 particles, the lower resolution in \cite{Donghia-2010} means that $10^7\Ms$ subhaloes only contain $\sim 20$ particles. The central galaxies in our four simulations have stellar masses in the range $(1.2-2.8)\times 10^{10}\Ms$, somewhat below the range of $\sim5\ \pm 1 \times 10^{10} \Ms $ commonly assumed for the Milky Way \citep[e.g.][]{Flynn-2006, Bovy-2013}. For a greater stellar mass, we would expect some of the baryonic effects to increase, although we note that the decline in subhalo abundance relative to DMO simulations is due not only to the presence of the stellar component, but also to the contraction of the halo itself, as well as to the almost complete loss of baryons from low-mass haloes by reionisation and ram-pressure stripping. The processes that lead to a relative underdensity of subhaloes near the centre also give rise to a positive velocity bias and rising anisotropy of subhalo orbits, two effects we find enhanced in the hydrodynamic simulation. Furthermore, we find that the velocity distribution of substructures near the halo centre cannot be assumed to be Maxwellian. The preferential disruption of strongly bound subhaloes leads to velocity distributions with far fewer low-velocity subhaloes than commonly assumed, and while the few surviving low-velocity subhaloes near the halo centre have more circular orbits, the overall subhalo population near the centre is dominated by high-velocity subhaloes on highly radial orbits. This impacts both the total number and the strength of detectable substructure interactions. | 16 | 9 | 1609.01718 |
1609 | 1609.06624_arXiv.txt | Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations. | Cosmological perturbation theory (in the following, Standard Perturbation Theory, SPT), as a tool to describe the evolution of structures in the universe has been discussed for a long time \cite{PT,JK06}. It provides a clear improvement with respect to linear theory on the range of scales of the Baryonic Acoustic Oscillations (BAO), but it fails to reach the percent accuracy needed to compare theories and data from present and future surveys. The problem is particularly urgent at small redshifts ($z\alt 2$) and small scales ($k\agt 0.1\;{\mathrm{h/Mpc}}$). Considering higher and higher loop orders in SPT does not lead to an improvement in this regime, as the perturbative expansion seems to converge at most only asymptotically \cite{Blas:2013aba}. The ultimate reason for the SPT failure is its inability to describe short (UV) scales, and their coupling to the intermediate scales relevant for cosmological observations. Numerical studies on the impact of modifications of the initial conditions at UV scales on the late time nonlinear power spectrum (PS) show evidence of a ``screening'' effect which is completely missed by SPT \cite{Little:1991py, 2014arXiv1411.2970N}. The UV failure of SPT is expected, as it neglects from the start all the effects -- such as shell crossing and virialization-- which cannot be described within the pressureless perfect fluid approximation. In order to deal with these UV shortcomings of SPT, modified schemes such as coarse-grained perturbation theory \cite{Pietroni:2011iz, Manzotti:2014loa}, or effective field theory \cite{Baumann:2010tm, Carrasco:2012cv, Blas:2015tla, Floerchinger:2016hja}, have been proposed. At the opposite end of the spectrum, large scale (IR) modes, are also known to play an important role. Bulk matter flows coherent on $O(10 \, {\mathrm{Mpc/h}})$ scales are responsible for the widening of the BAO peak in the correlation function, and the failure of taking them into account would hinder the use of this feature a standard ruler. A quantity which is very IR sensitive is the cross-correlator of the matter field at different times, or the closely related ``propagator". This quantity is not observable in practice, as observations are confined on the past-light cone, but is nonetheless measurable in simulations by cross-correlating different snapshots and, as we will see, provides powerful tests on the IR performance of a given approximation scheme. At each SPT order one can identify the subset of leading contributions to the propagator. The perturbative series of this subset is convergent, and can be analytically summed. In the limit in which only very long modes are taken into account, this summation coincides with the Zel'dovich approximation \cite{RPTb}. This observation is at the basis of approximation schemes such as Renormalized Perturbation Theory (RPT) \cite{RPTa}, Multi-Point-Propagator expansion \cite{Bernardeau:2008fa}, or Time-Flow equations \cite{Anselmi:2010fs, Anselmi:2012cn}, in which these leading IR contributions are summed at all orders, while the SPT expansion for the remaining ones is truncated at some finite order. In what follows, we will refer to all such methods as ``RPT-like summations". Notice that, as will be clear in what follows, also the Lagrangian resummation scheme of \cite{Matsubara07} belongs to this class of methods. The problem with RPT-like summations is that they violate Extended Galilean Invariance (GI) \cite{Turb_Pope}, that is, the invariance with respect to uniform, but time-dependent, boosts of the matter field. A consequence of this symmetry is that the effect of very long IR motions on a equal-time correlation function should vanish, as it can be reabsorbed in a change of frame \cite{Scoccimarro:1995if}. More quantitatively, we will consider a properly defined ``response function" and we will see that IR modes at a wavenumber $q$ should decouple as $O(q^3/k^3)$, where $k\gg q$ is the scale at which the equal time PS is computed. RPT-like summations fail this test, and generically exhibit a spurious $O(q/k)$ dependence. This is caused by a lack of cancellations between the IR effects that are resummed at all orders and the remaining ones, which are taken into account only up to a fixed order. Once the IR modes are integrated over, the spurious terms typically behave as powers of $k^2 \sigma_{IR}^2$ (where $\sigma_{IR}^2$ is the rms of the displacements induced by the IR modes), and therefore affect the PS in the UV, namely at large $k$-scales. In this paper we address the question of how to quantify the effects of this IR-UV problem in RPT-like summations, how to cure it, and how to formulate summation schemes which are IR safe from the start. Since our primary goal will be to single out the IR sector while leaving out the UV for a future work, we are not looking for extremely accurate results. We aim at analyzing the problem on general grounds and at identifying common features of the possible solutions. We will start with a general discussion on the IR effects on correlation functions at intermediate scales. Using the methods of \cite{Peloso:2013zw}, where exact consistency relations were obtained from GI, we will derive the general structure of the IR effects both for the equal-time and the non-equal time PS. Then we will employ the Zel'dovich approximation as a non-linear -- but analytically manageable -- benchmark to study the emergence of spurious IR effects in RPT like summations, and to envisage possible solutions. As we will see, a general feature of GI safe resummations is the dependence on a new scale, which becomes less and less relevant as the order of the truncation is increased. We will introduce a family of resummation schemes parameterised by such scale, which interpolates between SPT on one extreme and RPT on the opposite one, and we will see that RPT appears as the only pathological (from the point of view of GI) member of the family. Then, in order to deal with the real dynamics, we will focus on time-flow equations, like the Time Renormalization Group (TRG) of \cite{Pietroni08}, or the ones discussed in \cite{Anselmi:2010fs, Anselmi:2012cn}, clarifying the relation between the two and showing how to introduce the IR effects only partially captured by the TRG in the approximation schemes discussed so far in the literature. Before closing this introduction, we recall that other GI resummation schemes have been proposed, such as the eRPT of \cite{Anselmi:2012cn, Peloso:2013zw} or the methods of \cite{Senatore:2014via,Baldauf:2015xfa,Blas:2016sfa}. As for the methods discussed in this paper, also these IR-safe resummation introduce an arbitrary scale. The paper is organised as follows. In Sect.~\ref{formalism} we recall the main equations, introduce our formalism, and clarify the relation between the TRG approach of \cite{Pietroni08} and the time-flow equations of \cite{Anselmi:2010fs, Anselmi:2012cn}, in Sect.~\ref{LRfun} we discuss the linear response function, as the appropriate tool to discuss mode-mode coupling, in Sect.~\ref{ZeldS} we use the Zel'dovich approximation as a benchmark to discuss IR issues and their solutions, in Sect.~\ref{TRGs} we apply the methods developed in the previous section to the real dynamics, using time-flow equations as a tool to resum SPT contributions at all orders. Finally, in Sect.~\ref{conclusions} we give our conclusions. | \label{conclusions} In this work we studied the invariance under uniform, but time-dependent, boosts (GI, in short) of computational schemes for the large scale structures in the universe. Many resummation schemes that aim for an improvment over standard perturbation theory break GI, and are therefore affected by a spurious IR-UV connection. For instance, the computation of the PS at a scale $k$ is affected by long velocity modes at scales $\bar p \alt k$, through terms depending on $k^2 \bar \sigma(\bar p)^2$, with $\sigma(\bar p)^2$ the velocity dispersion of the long modes. The effect of mode-mode coupling can be studied through response functions. In this work we studied the linear response of the nonlinear PS, $P (k;\eta,\etap)$, evaluated at a scale $k$, to changes of the initial conditions at a much larger scale $q^{-1} \gg k^{-1}$, namely $K \left( k, q;\eta,\etap \right) \propto q \, \frac{\delta P \left( k;\eta,\etap \right)}{\delta P^0 \left( q \right)}$. By using the consistency relations of \cite{Peloso:2013zw}, we found that GI demands that~\footnote{This relation is for the density-density power spectrum; see eq. (\ref{lrffullIR}) for correlators that involve also the velocity gradient.} \begin{equation} \!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\! K (k,q;\eta,\etap) = - \frac{1}{3} \frac{1}{(2 \pi)^2} k^2 q \,\left(e^\eta-e^{\etap}\right)^2\, P (k;\eta,\etap) + O(q^3) \;\; , \;\; q \ll k \,. \label{LRF-IR-conclusions} \end{equation} The $O(q)$ coefficient in front of the fully nonlinear PS is protected by GI, and is therefore not renormalized at any order in SPT and even beyond that, when shell-crossing or virialization occurs. At equal times, $\eta=\etap$, it vanishes, and we are left with $O(q^3)$ terms whose coefficients are left undetermined by GI. Therefore, the strictest tests of GI for a given approximation scheme are obtained by considering non-equal time correlation functions. We have seen that the Zel'dovich PS passes the test fully, while SPT does it only up to the perturbative order of the calculation, which is the case of its poor performance on the propagator, see Fig.~\ref{fig:propagator}, or in accounting for the widening of the BAO peak. Non GI approximation schemes are characterized by having extra $O(q)$ terms, which can even be non-vanishing in the equal time limit. The coefficients of these terms can be used to tailor a counterterm which, when added to the original PS, gives an improved one with the correct behavior for the linear response function, and a better convergence to the full result, see for instance eq.~\re{Zeld-improved}. The arbitrariness of the coefficient of the $O(q^3)$ term reflects the fact that there are many possible GI approximation schemes: Eulerian PT, Lagrangian PT, eRPT \cite{Anselmi:2012cn, Peloso:2013zw}, Time-Sliced PT \cite{Blas:2016sfa}, IR resummed effective field theory \cite{Senatore:2014via}, and so on, all of which satisfy eq.~\re{LRF-IR-conclusions}, and differ precisely on that coefficient. This, effectively, translates in a dependence of the result - at a finite order in the given approximation scheme - on some new scale. This dependence vanishes by increasing the truncation order to infinity, in which limit all the different schemes should converge to the same result (at least as far as the IR effects are concerned). In this sense, the $\bar p$ scale introduced in this paper (as well as the detailed momentum dependence of the cutoff function in eq.~\re{sigma-bar}) ``mimics'' the scheme dependence of finite order results in different GI approximation schemes. We have introduced a family of approximation schemes parameterized by $\bar p$, from SPT (for ${\bar p} = \infty$, so that there is no resummation) to the physical range ${\bar p} \la k$, which avoids the spurious effects from modes of scales with $q \ll k$. We have also seen that RPT-like resummations correspond to the special value $\bar p = 0$, which singles out the only non GI scheme in the family parameterized by $\bar p$. After discussing the GI issue in the Zel'dovich approximation, we moved to the exact dynamics (still in the single stream approximation). We focused on the Time-flow equations, like the TRG approach \cite{Pietroni08} or the equations discussed in \cite{Anselmi:2010fs,Anselmi:2012cn}, clarifying the relation between the two (see eqs. \re{TRGPS} and \re{eq-PS-neq-exact}). We derived GI TRG equations which incorporate IR resummations and match to finite order SPT at small $k$'s. In Figure \ref{TRG} we show that, even limiting the matching to SPT to 1-loop order, setting the cut-off scale ${\bar p} \la k$ approximates the exact power spectrum (provided in this case by N-body simulation) significantly better than the original TRG and the plain one-loop SPT. The Time-Flow equations that we have introduced can be solved analytically in the $\Lambda$CDM case, as we have done. Moreover, they provide a convenient approach for cosmologies that are characterized by a scale-dependent growth factor, as for instance in the case of massive neutrinos \cite{LMPR09}, in which these equations can be easily solved numerically. The main goal of this work was to discuss on general grounds how to incorporate IR effects in a resummation scheme and to show how maintaining GI can improve their accuracy. We explicitly verified this up to four loop level in the Zel'dovich approximation, and up to one loop level in the exact case (in single stream approximation). Once the IR sector is fixed, our TRG equations can be further improved by considering mode-mode coupling at higher loops, and by including UV effects, as for instance in the coarse-grained approach of \cite{Pietroni:2011iz, Manzotti:2014loa}. We plan to come back to this in a future publication. | 16 | 9 | 1609.06624 |
1609 | 1609.03147_arXiv.txt | This paper explores the application of Probabilistic Neural Network (PNN), Support Vector Machine (SVM) and k-means clustering as tools for automated classification of massive stellar spectra. The data set consists of a set of stellar spectra associated with the Sloan Digital Sky Survey (SDSS) SEGUE-1 and SEGUE-2, which consists of 400,000 data from 3850 to 8900 \AA~with 3646 data points each. We investigate the application of principal components analysis (PCA) to reducing the dimensionality of data set to 280, 400 and 700 components.We show that PNN can give fairly accurate spectral type classifications $\sigma_{RMS}=1.752$, $\sigma_{RMS}=1.538$ and $\sigma_{RMS}=1.391$ and K-means can classify these spectra with an accuracy of $\sigma_{RMS}=1.812$, $\sigma_{RMS}=1.731$ and $\sigma_{RMS}=1.654$ and SVM with the accuracy of $\sigma_{RMS}=1.795$, $\sigma_{RMS}=1.674$ and $\sigma_{RMS}=1.529$ across the 280, 400 and 700 components, respectively. By using K-means the classification of the spectra renders 38 major classes. Furthermore, by comparing the results we noticed that PNN is more successful than K-means and SVM in automated classification. \\ | Over the past decades, stellar population has increased because of large spectroscopic surveys such as RAdial Velocity Experiment (RAVE) \citep{b1} or the Sloan Digital Sky Survey (SDSS) \citep{b2}. Visual classification of flooded data stream by human experts is often subjective and needs extensive effort which is very time consuming. Automated classification using different statistical modeling can easily be implemented for very large numbers of these spectra.\\ Classification of stellar spectra requires a model which is based on stars information and detail of analysis. The MK classification of stellar spectra \citep{b3,b4} has long been an important tool in astrophysics which is still in use today. \\ A reliable stellar spectral classification pipeline is necessary to automatically exploit these data sets. Developing an automated data analysis tool is of great challenge with the coming future instruments and the astronomers show fair attention towards these techniques which gives a very fast and reliable way of data analysis. There are many kinds of techniques for the classification of astronomical data such as Support Vector Machine (SVM), Probabilistic Neural Networks (PNN), Self-Organizing Map (SOM), Expert System and K-means. We choose PNN which is a kind of multilayer neural network model and K-means clustering for their fast and efficient implementation and also SVM algorithm. \\ The efficiency of artificial neural networks in spectral classification is addressed in previous works such as; \citet{b5, b6,b7}, \citet{b8}, \citet{b9}, \citet{b10}, \citet{b11}, and \cite{b11-2}. Also the K-Means classification of spectra is used for different astrophysical contexts in these papers; \citet{b12,b13}, \citet{b14}, \citet{b15,b16}, and \cite {b17}. The performance of SVM can be found in \citet{b29}, \citet{b30} and \citet{b31}. \\ We also show how the use of principal component analysis (PCA) can greatly compress the spectra and reduce the dimensionality of the data. Moreover, using PCA leads to a faster processing of ANN algorithm, as the dimension of data (spectrum) is reduced, and it reduces the complexity of the neural network and hence improves the classification accuracy.\\ This paper is organized as follows: Sects. 2 and 3 describe the data sets used in this study, their preprocessing and reduction procedure, Sect. 4 presents different classification methods implemented in this work, while Sect. 5 discusses our results. | We have classified a set of 400000 stellar spectra with PNN, SVM and K-means algorithm. The PCA showed that the efficient dimension of the spectra is about 700 components. We have shown that we can achieve classification errors of 1.391, 1.529 and 1.715 for our best principal component (700 pc) using PNN, SVM and K-means respectively. These algorithms have been able to correctly classify approximately 80\% of the data set. As is summarized in Table \ref {17}, PNN and SVM have a better performance, i.e. lower RMS error, than the K-means algorithm for all feature sizes. PNN is marginally better than SVM for a relatively small feature size of 280 but as the feature size grows to 700, PNN shows a better performance than SVM.\\ | 16 | 9 | 1609.03147 |
1609 | 1609.08580_arXiv.txt | Motivated by the projectable Horava--Lifshitz model/mimetic matter scenario, we consider a particular modification of standard gravity, which manifests as an imperfect low pressure fluid. While practically indistinguishable from a collection of non-relativistic weakly interacting particles on cosmological scales, it leaves drastically different signatures in the Solar system. The main effect stems from gravitational focusing of the flow of {\it Imperfect Dark Matter} passing near the Sun. This entails strong amplification of Imperfect Dark Matter energy density compared to its average value in the surrounding halo. The enhancement is many orders of magnitude larger than in the case of Cold Dark Matter, provoking deviations of the metric in the second order in the Newtonian potential. Effects of gravitational focusing are prominent enough to substantially affect the planetary dynamics. Using the existing bound on the PPN parameter $\beta_{PPN}$, we deduce a stringent constraint on the unique constant of the model. | Despite successes of General Relativity (GR)~\cite{Willbook, Will:2014kxa}, it appears to be incomplete in both high and low energy limits. First, GR is not perturbatively renormalizable and, consequently, loses its predictive power at distances of the order of the Planckian size, $l_{Pl} \sim 10^{-33}~\mbox{cm}$. To retain predictivity at those and smaller scales, one should replace GR by some ultraviolet complete theory {\it a la} superstrings. The 'infrared' problem stems from the existence of Dark Energy,---we yet do not know the physics behind the small $\Lambda$-constant. Another low energy phenomenon, which is less commonly viewed as challenge for GR, is Dark Matter (DM). While it could be relatively simply explained in some extensions of the Standard Model, only gravitational manifestations of DM have been identified so far. Therefore, it may be well a product of gravity modification. We will entertain this possibility in the present paper. We will be interested in the model of gravity described by the following action~\cite{Chamseddine:2014vna, Capela:2014xta, Mirzagholi:2014ifa}, \begin{equation} \label{action} S= -\frac{1}{16\pi G} \int d^4 x \sqrt{-g} R+\int d^4 x \sqrt{-g} \left[\frac{\Sigma}{2} \left( g^{\mu \nu} \partial_{\mu} \varphi \partial_{\nu} \varphi-1 \right)+\frac{\chi}{2} (\square \varphi )^2 \right] \; , \end{equation} (hereafter, we assume the mostly negative signature of the metric). The first term on the r.h.s. here describes the Einstein--Hilbert action; $G \equiv \frac{1}{M^2_{Pl}}$ is the gravitational constant, and $M_{Pl}$ is the Planck mass. The other two stand for what one calls {Imperfect Dark Matter} (IDM). In the limit of vanishing dimensionful constant $\chi$\footnote{In Ref.~\cite{Mirzagholi:2014ifa}, the parameter $\chi$ was promoted to a function of the field $\varphi$. This was proved crucial for generating the required amount of IDM in the early Universe (the issue analogous to getting the correct relic abundance of DM in the CDM framework). On the other hand, the slight dependence on the field $\varphi$ is completely irrelevant for the discussion of the present paper, where we focus on the Solar system scales.}, IDM reduces to a pressureless perfect fluid, with the fields $\Sigma$ and $\varphi$ playing the role of its energy density and velocity potential, respectively. Switching on the higher derivative term renders the fluid slightly imperfect~\cite{Mirzagholi:2014ifa} (hence, the name) and equips it with a non-zero sound speed $c_s \sim \frac{\sqrt{\chi}}{M_{Pl}}$~\cite{Chamseddine:2014vna}. In what follows, we assume no direct coupling between IDM fields and the standard matter fields. This guarantees that IDM may constitute the invisible matter in the Universe, at least for not large values of $c_s$. In the synchronous gauge, a homogeneous solution for the field $\varphi$ takes a simple form, \begin{equation} \label{synchr} {\bar \varphi}=t \; . \end{equation} So, it serves as the time parametrization. Note an unconventional dimensionality $-1$ of the scalar $\varphi$. Existence of the preferred frame, i.e., the one, where the background value of the field ${\varphi}$ is given by Eq.~\eqref{synchr}, implies dynamical Lorentz violation in the model~\eqref{action}. In this regard, it is akin to the Einstein--Aether theory~\cite{Jacobson:2000xp}\footnote{For this reason, the model~\eqref{action} is referred to as the 'scalar Einstein--Aether' in Ref.~\cite{Haghani:2014ita}.}. The latter, however, deals with a unit 4-vector field $u_{\mu}$ rather than with the 4-gradient of a scalar. This distinction produces drastically different dynamics in the two models. Particularities of the cosmological evolution in the scenario~\eqref{action} have been considered in Refs.~\cite{Capela:2014xta, Mirzagholi:2014ifa, Ramazanov:2015pha}. The main effect stems from non-zero sound speed~\cite{Chamseddine:2014vna}. Namely, the formation of objects with the size smaller than the sound speed horizon is suppressed compared to the predictions of Cold DM (CDM). Consequently, one risks to strongly affect the bottom-up picture of the structure formation for sufficiently large values of the parameter $\chi$. In Ref.~\cite{Capela:2014xta}, this observation was used to set the bound, \begin{equation} \label{limitstructure} \frac{\chi}{M^2_{Pl}} \lesssim 10^{-10} \; . \end{equation} For much smaller values of the parameter $\chi$, IDM is indistinguishable from CDM at the cosmological level. On the other hand, given values saturating the bound in Eq.~\eqref{limitstructure}, the behavior of IDM shares some similarities with the Warm DM. Let us briefly discuss the quantum features of the model~\eqref{action}. Compared to GR, it propagates three degrees of freedom: the standard ones associated with two polarizations of the helicity-2 graviton, and the scalar potential $\Psi$, which is now a dynamical field~\cite{Horava:2009uw, Sotiriou:2009gy, Sotiriou:2009bx, Koyama:2009hc, Blas:2010hb, Ramazanov:2016xhp}\footnote{These references deal with the projectable Horava--Lifshitz model, which nevertheless reproduces the action~\eqref{action} in the certain limit. See the discussion below.}. The extra degree of freedom $\Psi$ exhibits gradient/ghost instabilities for negative/positive values of the parameter $\chi$. This, however, does not invalidate the model immediately. Indeed, those pathologies are not particularly dangerous provided that there is a sufficiently low Lorentz-violating cutoff on the spatial momenta of the modes of the field $\Psi$~\cite{Cline:2003gs, Rubakov:2008nh}. That cutoff is associated with the scale of yet unknown UV completion of the model or the strong coupling scale. In the version with gradient instabilities ($\chi <0$), however, this cutoff turns out to be extremely low~\cite{Blas:2010hb}, $\Lambda \ll (0.1~\mbox{mm})^{-1}$. The latter contradicts the tests of gravity extending from the sub-mm distances to the Solar system scales. On the other hand, the ghost unstable branch of the model ($\chi >0$) allows for the cutoff scale $\Lambda$ as large as $\Lambda \sim 10$ TeV. Assuming that the strong coupling and UV scales are of the same order, this bound implies the constraint on the parameter $\chi$~\cite{Ramazanov:2016xhp}, \begin{equation} \label{micros} \frac{\chi}{M^2_{Pl}} \lesssim 10^{-20} \; . \end{equation} For larger values of the constant $\chi$, the vacuum decay with photons and ghosts in the final state is too fast, what leads to the conflict with measured fluxes of the gamma- and X-ray emission~\cite{Sreekumar:1997un}. One interesting way of UV completing the action~\eqref{action} is suggested in the context of the projectable Horava--Lifshitz model~\cite{Horava:2009uw}. The latter postulates a non-uniform transformation of time and spatial coordinates under the scaling. This has a dramatic effect on the ultraviolet behaviour of gravitons resulting into the strong distortion of their dispersion relation, $\omega^2 \sim {\bf p}^6$. Consequently, there are less divergences in the graviton loop integrals, what eventually leads to the (power counting) renormalizability of gravity~\cite{Horava:2009uw, Barvinsky:2015kil}. While the Horava--Lifshitz model is manifestly non-relativistic, it allows for the covariant description by introducing the St$\ddot{\mbox{u}}$ckelberg field $\varphi$ dubbed khronon. Then, its infrared limit exactly takes the form~\eqref{action}~\cite{Blas:2010hb, Blas:2009yd}. It is thus not a surprise that DM has been identified in this context~\cite{Mukohyama:2009mz}. In particular, the term with the Lagrange multiplier ensures the projectablility condition, which eliminates the pathological mode otherwise present at low momenta~\cite{Blas:2009yd, Charmousis:2009tc}\footnote{Alternative ways to tackle the pathological mode, not invoking for the projectability condition, are possible and have been proposed in Refs.~\cite{Blas:2009qj, Horava:2010zj}.}. The parameter $\chi$ is generically non-zero\footnote{The notation $\chi$ may be inconvenient for those familiar with Horava--Lifshitz gravity. There one deals with the parameter $\lambda$, which appears in front of the term $\sim K^2$ (the trace of the extrinsic curvature tensor squared) in the ADM formulation of the model. The two are related to each other by $\chi=\frac{1-\lambda}{8\pi G}$.}, and is supposed to follow the renormalization group flow towards the 'GR point' $\chi =0$. Embedding the model~\eqref{action} into the Horava--Lifshitz gravity is not without problems, though. The reason is that UV operators modifying the dispersion relation of the gravitons are not capable of curing ghost instabilities. Hence, the only way to stabilize the catastrophic vacuum decay is to assume that the model enters a putative strong coupling phase. This severely obstructs the main objective of the Horava's proposal---perturbative renormalization of gravity. Recently, the action~\eqref{action} has been rediscovered in a completely different framework of the mimetic matter~\cite{Chamseddine:2014vna, Chamseddine:2013kea}. There one deals with a non-invertible conformal transformation of the metric~\cite{Deruelle:2014zza}, \begin{equation} \nonumber \tilde{g}_{\mu \nu}=A(\varphi, X) g_{\mu \nu} +B(\varphi, X) \partial_{\mu} \varphi \partial_{\nu} \varphi \; , \end{equation} where $A$ and $B$ are the arbitrary functions of the scalar $\varphi$ and $X \equiv g_{\mu \nu} \partial^{\mu} \varphi \partial^{\nu} \varphi$. Performing this transformation on the standard Einstein--Hilbert action, one does not reproduce GR, but rather GR supplemented by a perfect pressureless fluid dubbed mimetic DM. Equivalently, the latter can be introduced by making use of the Lagrange multiplier as in Eq.~\eqref{action}, i.e., without directly referring to the disformally transformed metric~\cite{Golovnev:2013jxa, Hammer:2015pcx}. The higher derivative term is absent in the original formulation of the mimetic matter scenario. Nevertheless, that extension does not affect the main idea underlying the scenario, and even appears to be the only viable option for a number of phenomenological issues~\cite{Chamseddine:2014vna, Capela:2014xta}\footnote{Different extensions have been considered in Refs.~\cite{Chamseddine:2014vna, Arroja:2015wpa, Arroja:2015yvd}. The former equips the field $\varphi$ with some potential $V(\varphi)$. In this way, one manages to mimic fairly arbitrary cosmological evolution. In Refs.~\cite{Arroja:2015wpa, Arroja:2015yvd}, the mimetic matter scenario has been extended by means of the Horndeski higher derivative terms.}. In the present paper, we do not assume any particular gravitational framework behind the model~\eqref{action}. Neither, we are interested in its cosmological or microscopic manifestations. Our main focus here is the intermediate range of scales: Solar system. Surprisingly, this yields limits, which are many orders of magnitude stronger than those obtained from the structure formation considerations. Moreover, our discussion does not assume that IDM gives the dominant contribution to the invisible matter in the Universe (namely, IDM may constitute only its tiny fraction). The behavior of IDM in the Solar system shares some features (but not all) with CDM. Let us briefly summarize the main effect. The Sun moves relative to the cosmic microwave background and Milky Way rest frames with the speed $v \simeq 10^{-3}$. Naturally, the preferred frame is associated with one of those. An observer in the Solar system sees a flow of IDM. Affected by the gravitational potential of the Sun, the flow focuses downstream from the Sun forming a caustic. This part of the story parallels to that of CDM. In the latter case, however, gravitational focusing is a rather moderate effect introducing a few percent correction to the annual modulation of the flux of DM particles passing through the Earth~\cite{Danby, Danby1, Griest:1987vc, Sikivie:2002bj, Belotsky1, Belotsky2, Lee:2013wza, Patla:2013vza}. The things are different in the IDM scenario. The reason is the higher derivative structure of its action~\eqref{action}. The term $\sim \chi (\square \varphi )^2$ serves as a powerful source of the IDM energy density $\Sigma$. Recall that IDM is not coupled directly to the standard matter, but only gravitationally. Therefore, the amplification of the field $\Sigma$ has no consequences for particle experiment facilities. On the flipside, the field $\Sigma$ backreacts on the space-time geometry causing distortion of the metric. This is the main effect identified in the present paper\footnote{On the contrary, in the case of CDM the distortion of the metric is a negligible effect, while the predictions for the particle exxperiments can be sensisble.}. As in the case of CDM, it is particularly prominent in the direction opposite to the velocity of the Sun ${\bf v}$, where IDM is mainly accumulated. Borrowing terminology of Ref.~\cite{Dubovsky:2004qe}, astrophysical objects moving relative to the preferred frame~\eqref{synchr} leave 'star tracks' behind them. Remarkably, in the IDM scenario, deviations from the GR metric emerge only in the second order in the Newtonian potential. This is in a sharp contrast to the predictions of other models, which deal with preferred frame effects~\cite{Blas:2010hb, Foster:2005dk, Blas:2014aca}. In our case, the latter manifest via the spatial dependence of coefficients measuring quadratic corrections to the GR metric. Such a correction does not exactly follow the standard parametrized post-Newtonian (PPN) approach, where analogous coefficients are assumed to be constant. In particular, the parameter $\beta$ akin to the PPN one $\beta_{PPN}$, deviates from unity by $\beta -1\simeq \frac{4\pi \chi}{M^2_{Pl} v^4} \cdot \frac{1}{\theta^4}$, where $\theta$ is the angle between the line of sight of the observer on the Sun and the direction $-{\bf v}$. Ignoring $\theta$-dependence here, we convert bounds on $\beta_{PPN}$ following from the studies of the Mercury perihelion precession into the limit on the theory constant $\chi$. The resulting constraint is quite stringent: $\chi/M^2_{Pl} \lesssim 10^{-18}$, which is only two orders of magnitude weaker than the limit~\eqref{micros} inferred from the microscopic physics considerations. Notably, this is a conservative constraint, since neglecting the $\theta$-dependence we underestimate the actual effect due to gravitational focusing. The remainder of the paper is as follows. In Section~2, we deduce equations of motion following from the action~\eqref{action}. We discuss the main assumptions and approximations used to study the dynamics of IDM in Section~3. For the sake of convenience, there we also outline the main formulae describing the IDM profile in the Solar system, as well as the induced metric corrections. Derivation of those results is explained in Sections~4 and~5, where we restrict to the linear and quadratic order analysis in the Newtonian potential, respectively. In Section~4, we also identify the narrow region of space, where the perturbative description of IDM breaks down. We assess metric perturbations in this region in Section~6. The reader interested in the final results, may skip Sections 4-6 and go directly to Section 7, where we contrast our predictions for metric perturbations to the observational bounds, and derive the constraint on the theory constant $\chi$. | 16 | 9 | 1609.08580 |
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1609 | 1609.00764_arXiv.txt | We review the uncertainties in high-z star-formation rate (SFR) measures and the constraints that one obtains from high-z gamma-ray burst (GRB) rates on them. We show that at the present time, the GRB rates per unit star-formation at $z>3$ are higher than at lower redshift. There could be a multitude of reasons for this: a stellar metallicity bias for GRB production, a top-heavy initial mass function (IMF) and/or missing a significant fraction of star-formation in field galaxy surveys due to incompleteness, surface brightness limitations and cosmic variance. We also compare metallicity predictions made using a hierarchical model of cosmic chemical evolution based on two recently proposed SFRs, one based on the observed galaxy luminosity function at high redshift and one based on the GRB rate and find that within the considerable scatter in metal abundance measures, they both are consistent with the data. Analyzing the ensemble of different measurements together, we conclude that despite metallicity biases, GRBs may be a less biased probe of star-formation at $z>3$ than at $z<2$. There is likely to be a common origin to the high GRB rate per unit star-formation and the high observed Lyman-continuum production rate in high redshift galaxies and that this may be due to a relative overabundance of stars with mass $>$25\,M$_{\sun}$ which are likely GRB progenitors. We also find that to reconcile these measurements with the Thomson scattering cross section of cosmic microwave background (CMB) photons measured by Planck, the escape fraction of Lyman-continuum photons from galaxies must be low, about $\sim$15\% or less and that the clumping factor of the IGM is likely to be small, $\sim$3. Finally, we demonstrate that GRBs are unique probes of metallicity evolution in low-mass galaxy samples and that GRB hosts likely lost a significant fraction of metals to the intergalactic medium (IGM) due to feedback processes such as stellar winds and supernovae. | Measuring the evolution of the co-moving star-formation rate density (SFRD) with redshift has been one of the major goals of galaxy evolution studies. Primary tracers of star-formation include the rest-frame ultraviolet continuum, the mid-infrared through sub-millimeter continuum from thermal dust emission, 1.4 GHz and 30 GHz radio emission which traces the synchrotron and free-free components respectively and nebular lines (e.g. H$\alpha$ and H$\beta$). Each of these tracers have different systematics associated with them. Ultraviolet wavelengths are affected by dust attenuation and also require uncertain extrapolations for the faint end of the galaxy luminosity function. Mid-infrared and sub-millimeter tracers are biased towards the bright end of the galaxy luminosity function and suffer from AGN contamination. Current radio surveys are insensitive to all but extreme, ultra-luminous galaxies. Nebular lines are powerful but require extensive spectroscopic follow-up which is limited to the bright end of the LF. Furthermore, they too suffer from attenuation and stellar absorption which needs to be corrected for. The goal has motivated a multitude of deep surveys; they have been undertaken at visible/ultraviolet (UV) wavelengths with {\it Hubble}, in the mid- and far-infrared with {\it ISO}, {\it Spitzer}, {\it Herschel} and more recently {\it ALMA} and also with narrow-band filters and grisms (e.g. {\it Hubble}/WFC3 and NICMOS) to detect strong nebular emission lines. These surveys have resulted in a generally broad agreement whereby the SFR rises from redshift 0, peaks at $z\sim1-2$ and declines with increasing redshift out to $z\sim10$. Our understanding of this has been based on observations of the bright end of the luminosity function with significant assumptions needed to extrapolate to the faint end and to derive a co-moving star-formation rate density. For example, the UV SFR measurements are sensitive down to few times 10$^{8}$\,L$_{\sun}$ while the mid- and far-infrared surveys only detect galaxies down to 10$^{11}$\,L$_{\sun}$. As a result, it is unclear how much attenuation correction, if any, is required at the faint end of the galaxy LF and whether even the slope of the faint-end of the galaxy LF is robustly constrained. This is particularly true at the epoch of reionization at $z>6$, where considerable uncertainties exist at both the bright end of the ultraviolet luminosity function and the faint end. Although 1000s of candidate galaxies have been detected out to $z\sim10$, these have been through deep, pencil-beam surveys or through observations of galaxies lensed by foreground clusters, both of which trace relatively small comoving volumes at the redshifts of interest. Since these surveys are done with 4\,arcmin$^{2}$ instrumental fields of view, there is the issue of cosmic variance. A comparison with semi-analytical models indicate that similar fields of view could show as much as a factor of 3 scatter in luminosity density at $z>6$, depending on the large scale structure. Long-duration GRBs\footnote{Throughout this paper, we refer to long-duration GRBs whose gamma-ray emission typically lasts $>$2s and has a soft spectrum with hardness ratios of $\sim$0.5 compared to the short GRBs which last $<$2s, have hardness ratios of $\sim$1.0 and that are thought to arise from merging double-degenerate systems.}, since they are thought to be the evolutionary end-states of massive stars, are an alternate technique for tracing the comoving SFRD \citep{Wijers, Blain2000, bromm2002a,daigne06b, ishida11}. Provided the selection effects associated with GRBs can be understood, measuring the co-moving rate density of GRBs and/or comparing the properties of their host galaxies with field galaxies populations can allow a calibration of GRBs as a star-formation rate metric. With rates of $\sim1$/day, they are quite abundant with the biggest limitation arising in identification and spectroscopic follow-up of the afterglow \citep[e.g][]{Kruhler}. In addition, since GRB afterglows are bright, the spectroscopic follow-up detects absorption by metal lines that arise both in the host galaxy and in the intervening IGM. This would hopefully allow the characterization of star-forming environments in distant galaxies, and their evolution with redshift, which is otherwise a challenge. However, the question remains whether GRBs are unbiased tracers of star-formation. Are there metallicity/luminosity biases in the kinds of galaxies that GRBs occur in? Are there environment biases in the sense that GRBs only occur in stars with large angular momentum \citep{WoosleyHeger}? Although accurate answers to these questions are unclear at the present time, in this article, we review the current state of using GRB rates as a star-formation rate metric and outline possible ways forward. | In this summary, we have highlighted the complementary role that GRBs can play to field galaxy surveys in constraining the star-formation rate density at high-z. The GRB rate per unit star-formation derived from field galaxy surveys appears to be increasing with increasing redshift. This may be due to a top-heavy IMF which increases the fraction of massive stars for a particular UV luminosity density. Alternately, a metallicity bias for GRBs whereby galaxies above roughly solar metallicity are inefficient GRB producers could explain this observational result. Since a larger fraction of star-formation at low-z takes place in such galaxies, than at high-z, if the GRB rate per unit low-metallicity-star-formation is constant, a normalization between the GRB and total SFR at low redshift would result in the apparent GRB rate per unit total star-formation rate increasing with increasing redshift. A large contribution from faint/dusty galaxies below the detection limit of field galaxy surveys could also explain the observed trend but is disfavored based on the sparsity of dust obscured high-z galaxies in current surveys. While the Thomson scattering optical depth of CMB photons ($\tau$) could help constrain the high-z SFR, it too is plagued by both measurement uncertainty and the uncertainty in the escape fraction of ionizing photons from galaxies. However, the ensemble of current data favor the high SFR (assuming a conversion from far-ultraviolet luminosity density to SFR using a Salpeter IMF) inferred from GRB measurements, a high ionizing photon production rate probably due to a top-heavy IMF, a low escape fraction of $\sim$10-15\% and a low clumping factor for the IGM. Future breakthroughs in high-z star-formation will come from detecting significant populations of GRBs at $z>4-10$ with existing missions such as {\it Swift} and future missions such as SVOM and targeting them through multi-wavelength spectroscopy. This would yield a better measurement of the luminosity and metallicity distribution of high-z GRB hosts which can robustly discriminate between these scenarios and provide insights into galactic feedback processes at the low-mass end. Better measurements of high-z GRB rates and $\tau$ could also provide a unique constraint into the escape fraction of ionizing photons at $z\sim6$. Finally, improved GRB progenitor models which provide greater insights on the role of magnetic torques, angular momentum and metallicity of massive stars in the formation of GRBs will also help reduce the scatter in the mapping of GRB rates to star-formation rates. | 16 | 9 | 1609.00764 |
1609 | 1609.07372_arXiv.txt | {ANTARES is currently the largest neutrino telescope operating in the Northern Hemisphere, aiming at the detection of high-energy neutrinos from astrophysical sources. Neutrino telescopes constantly monitor at least one complete hemisphere of the sky, and are thus well-suited to detect neutrinos produced in transient astrophysical sources. A time-dependent search has been applied to a list of 33~X-ray binaries undergoing high flaring activities in satellite data (RXTE/ASM, MAXI and Swift/BAT) and during hardness transition states in the~2008--2012 period. The background originating from interactions of charged cosmic rays in the Earth's atmosphere is drastically reduced by requiring a directional and temporal coincidence with astrophysical phenomena. The results of this search are presented together with comparisons between the neutrino flux upper limits and the neutrino flux predictions from astrophysical models. The neutrino flux upper limits resulting from this search limit the jet parameter space for some astrophysical models.} \begin{document} | X-ray binaries are binary systems composed of a compact object (neutron star (NS) or stellar mass black hole (BH) candidate) and a companion non-degenerate star. Due to the strong gravitational attraction, matter expelled from the companion is accreted by the compact object. Depending on the mass of the companion star and the process of matter accretion, X-ray binaries are separated into two classes: Low-Mass X-ray Binaries (LMXB) which contain an evolved companion star of spectral class later than B transferring matter to the compact object through Roche lobe overflows; and High-Mass X-ray Binaries (HMXB) consisting of a massive O or B star developing intense stellar winds, a fraction of which is accreted by the compact object. While some of these objects are seen as persistent sources, most of them exhibit occasional outbursts, making them transient sources, in particular in the radio and X-ray domains. Recent detections of GeV--TeV gamma-ray signals from some X-ray binaries confirm that they can produce outflows containing particles accelerated away from the compact object up to relativistic speeds~\cite{bib:Tavani2009}. At the moment, it is not clear whether the high-energy particle acceleration is a common process occurring in X-ray binaries but observed only in some systems with preferred (geometrical) characteristics with respect to the line of sight, or whether it is powered by a different mechanism at work only in some specific systems. The theoretical mechanisms of gamma-ray production from X-ray binaries generally assume (very-) high-energy photon emission from the interaction of a relativistic outflow from the compact object with the wind and radiation emitted by the companion star. The outflow can take different shapes. In microquasars~\cite{bib:MirabelRodriguez1994} the high-energy emission is due to accretion energy released in the form of a collimated relativistic jets, detected in the radio domain through synchrotron emission. On the contrary, in other binary systems, high-energy emission can occur in a wide-angle shocked region, at the interface between pulsar and stellar winds~\cite{bib:Dubus2013}. They are probably the sites of effective acceleration of particles (electrons and/or protons) to multi-TeV energies but the nature of the high-energy emission is still unknown, and leptonic or hadronic origin is still debated nowadays~\cite{bib:Vila2010,bib:Vila2013, bib:Pepe2015}. Even if a rich variety of binary systems seems to be cosmic accelerators, some major issues are still open: are jets a common feature of X-ray binary systems? What is the particle acceleration mechanism at work in these systems? Is it unique? Constraining the jet composition and its baryonic content will help answering these questions. Indeed, the jet composition should be affected by the outflow-launching processes. For instance, jets powered by an accretion disk are likely to contain baryons~\cite{bib:BlandfordPayne1982} while jets which get their power from black hole spin are expected to be purely leptonic~\cite{bib:DiazTrigo2013}. Up to now, a hadronic component has been identified in only two X-ray binaries (SS 433 and 4U 1630-472)~\cite{bib:Migliari2002,bib:DiazTrigo2013} while a population of cold baryons present in the relativistic jet of Cyg\,X\texttt{-}1 has been proposed~\cite{bib:Heinz2006}. Hadronic models of jet interactions with the winds of massive stars were developed these last decades. The dominant hadronic contributions are expected from the photo-hadronic (p-$\gamma$) interactions between relativistic protons and synchrotron photons in the jet or coming from external sources ~\cite{bib:Levinson2001, bib:Distefano2002}), and from the hadronic (p-p) interactions between relativistic protons from the jet and thermal protons from the stellar wind~\cite{bib:Romero2003, bib:Christiansen2006,bib:Torres2007,bib:Vieyro2012}. In the absence of a jet, neutrinos can be produced through p-p processes between the accelerated protons in the the rotation-driven relativistic wind from the young neutron star and the circumstellar disk in the case of Be type stars~\cite{bib:NeronovRibordy2009,bib:Sahakyan2014}. The detection of high-energy neutrinos from an X-ray binary system would definitively confirm the presence of relativistic protons in the outflow, and thus further constrain the particle acceleration mechanism. The ANTARES Collaboration completed the construction of a neutrino telescope in the Mediterranean Sea with the connection of its twelfth detector line in May 2008~\cite{bib:Antares}. The telescope is located 20 km off the Southern coast of France (42$^\circ$48'N, 6$^\circ$10'E), at a depth of 2475 m. In the ANTARES telescope, events are primarily detected by observing the Cherenkov light induced by relativistic muons in the darkness of the deep sea. Owing to their low interaction probablility, only neutrinos have the ability to cross the Earth. Therefore, an upgoing muon is an unambiguous signature of a neutrino interaction close to the detector. To distinguish astrophysical neutrino events from background events (muons and neutrinos) generated in the atmosphere, energy and direction reconstructions have been used in several searches~\cite{bib:PointSource,bib:Diffuse}. To improve the signal-to-noise discrimination, the arrival time information can be used to significantly reduce the effective background~\cite{bib:MDP}. In this paper, the results of a time-dependent search for cosmic neutrino sources using the ANTARES data taken from~2008 to~2012 is presented. This extends a previous ANTARES analysis~\cite{bib:AntaresMicroQ} where only six sources and the first three years of data-taking were considered. It is also complementary to a previous IceCube transient analysis~\cite{bib:IceCube2015} which considered few X-ray binary systems. However, the ANTARES location in the northern hemisphere, and its lower neutrino energy threshold in comparison with IceCube, make it well-suited to study neutrino emission from such galactic sources. Neutrino emission has been searched-for during outburst periods of X-ray binaries characterised by the variability of their soft and hard X-ray flux density~\cite{bib:Remillard}. Jet emission, probably linked to particle acceleration and thus potential neutrino emission, usually occurs during periods of high levels of hard X-ray flux density (called hard states) and during transition periods (intermediate states) between a hard state and a soft state. Sections~2 and~3 present the selection of outburst periods selection from X-ray light curves, during hard and intermediate states respectively. Section~4 details the statistical approach used to perform the analysis, while results are provided and discussed in Section~5. Conclusions are drawn in Section~6. | This paper discusses the time-dependent search for neutrinos from X-ray binaries using the data taken with the full ANTARES detector between 2008 and 2012. This search has been applied to a list of 33 XRB sources, 8 of them during hardness transition periods. The search did not result in a statistically significant excess above the expected background from atmospheric neutrino and muon events. The most significant correlation during X-ray flares is found for the source GX\,1\texttt{+}4, for which 3 neutrino candidate events were detected in time/spatial coincidence with X-ray emission. However, the post-trial probability is 72\%, thus compatible with background fluctuations. A comparison with predictions from several models shows that for some sources, the upper limits start to constrain the parameter space of the expectations from hadronic jet emission models. Therefore, with additional data from ANTARES and with the order of magnitude sensitivity improvement expected from the next generation neutrino telescope, KM3NeT~\cite{bib:KM3NET}, the prospects for future searches for neutrino emission from X-ray binaries are very promising. | 16 | 9 | 1609.07372 |
1609 | 1609.05377_arXiv.txt | { Ultra-compact high velocity clouds (UCHVCs) were identified in the Arecibo Legacy Fast ALFA (ALFALFA) \hi\ survey as potential gas-bearing dark matter halos. Here we present higher resolution neutral hydrogen (\hi) observations of twelve UCHVCS with the Westerbork Synthesis Radio Telescope (WSRT). The UCHVCs were selected based on a combination of size, isolation, large recessional velocity and high column density as the best candidate dark matter halos. The WSRT data were tapered to image the UCHVCs at 210\arcsec\ (comparable to the Arecibo resolution) and 105\arcsec\ angular resolution. In a comparison of the single-dish to interferometer data, we find that the integrated line flux recovered in the WSRT observations is generally comparable to that from the single-dish ALFALFA data. In addition, any structure seen in the ALFALFA data is reproduced in the WSRT maps at the same angular resolution. At 210\arcsec\ resolution all the sources are generally compact with a smooth \hi\ morphology, as expected from their identification as UCHVCs. At the higher angular resolution, a majority of the sources break into small clumps contained in a diffuse envelope. These UCHVCs also have no ordered velocity motion and are most likely Galactic halo clouds. We identify two UCHVCs, AGC\,198606 and AGC\,249525, as excellent galaxy candidates based on maintaining a smooth \hi\ morphology at higher angular resolution and showing ordered velocity motion consistent with rotation. A third source, AGC\,249565, lies between these two populations in properties and is a possible galaxy candidate. If interpreted as gas-bearing dark matter halos, the three candidate galaxies have rotation velocities of $8-15$ \kms, \hi\ masses of $0.6-50 \times 10^{5}$ \msun, \hi\ radii of $0.3 - 2$ kpc, and dynamical masses of $2-20 \times 10^7$ \msun\ for a range of plausible distances. These are the UCHVCs with the highest column density values in the ALFALFA \hi\ data and we suggest this is the best way to identify further candidates. } | Studying the properties of the smallest galaxies is important both for testing $\Lambda$CDM and understanding galaxy formation. $\Lambda$CDM does an excellent job of describing large scale structure and the distribution of massive galaxies \citepads[e.g.,][]{2014Natur.509..177V}. However, on small scales, there are tensions between observations of dwarf galaxies and predictions from simulations for both field dwarf galaxies and satellite dwarf galaxies in the Milky Way (MW). These tensions include the total number count of expected galaxies \citepads[e.g., the "missing satellites problem" in the Local Group;][] {1993MNRAS.264..201K,1999ApJ...522...82K,1999ApJ...524L..19M,2010ApJ...723.1359M,2011ApJ...739...38P}; which dark matter halos host galaxies \citepads[e.g., the "too big too fail" problem;][]{2012MNRAS.422.1203B,2015A&A...574A.113P}; and the structure of those dark matter halos \citepads[e.g., the "cusp-core" problem;][]{2008AJ....136.2648D,2011ApJ...742...20W}. Much work exists to suggest that these differences can be reconciled by the proper inclusion of baryonic physics in simulations \citepads[e.g.,][]{2011AJ....142...24O,2015MNRAS.454.2092O,2016MNRAS.457.1931S,2016arXiv160205957W}. However, much of the relevant physics is implemented at the sub-grid level, and simulations of dwarf galaxies are sensitive to (at least some of) these parameters \citepads[e.g.,][]{2010ApJ...710..408B,2013MNRAS.432.1989S,2016MNRAS.458..912V}, and results between various simulations do not necessarily agree \citepads[e.g., the existence of a \mstar-$M_{halo}$ relation at low masses,][]{2015MNRAS.448.2941S,2015MNRAS.454.2092O,2015MNRAS.453.1305W}. Part of the issue may be resolution; as the resolution of simulations increases, typically the lowest mass galaxy that can form in the simulation also decreases \citepads{2006MNRAS.371..401H,2015MNRAS.453.1305W}. The existence of extremely low-mass galaxies that have a significant reservoir of neutral hydrogen (\hi) also challenges our understanding of how the smallest galaxies form and evolve. How have these galaxies maintained their gas reservoir given the multitude of baryonic processes that can disrupt it? The most extreme example is Leo T; this galaxy has an \hi\ mass of only $2.8 \times 10^5$ \msun\ and a stellar mass of $1.05 \times 10^5$ \msun\ \citepads{2008MNRAS.384..535R,2012ApJ...748...88W}. The recent discovery of Leo P demonstrates that there are more low-mass gas-dominated systems to be discovered. Leo P has an \hi\ mass of $8.1 \times 10^5$ and a stellar mass of $5.6 \times 10^5$ \msun\ \citepads{2015ApJ...812..158M}. Both systems are very faint optically; Leo T is on the edge of detection for the Sloan Digital Sky Survey \citepads[SDSS,][]{2010AdAst2010E...8K}, and Leo P was originally identified as an \hi\ source \citepads{2013AJ....146...15G}. This highlights a parameter space for \hi\ surveys for understanding the smallest galaxies. Galaxies similar to Leo T or Leo P but that lie at larger distances or have had slightly different star formation histories (e.g., less recent star formation) might be missed by optical surveys but detected in blind \hi\ surveys. To this end, \citetads{2010ApJ...708L..22G} presented the idea that ultra-compact high velocity clouds (UCHVCs) in the Arecibo Legacy Fast ALFA (ALFALFA) \hi\ survey may be gas in dark matter halos with a stellar counterpart not detectable in extant optical surveys. \citetads[][hereafter A13]{2013ApJ...768...77A} built on this work, presenting a catalog of sources with specific selection criteria for the 40\% complete ALFALFA survey. Similarly, \citetads{2012ApJ...758...44S} presented a catalog of compact \hi\ clouds from GALFA \hi\ survey, highlighting those that were potentially good galaxy candidates. These catalogs represent an excellent starting point for identifying potential gas-bearing dark matter halos in the local universe, and theoretical models suggest they contain good candidates \citepads[e.g.,][]{2013ApJ...777..119F}. However, without stellar counterparts there are no direct distances to these clouds and they may be local clouds of gas that arise from various Galactic processes. Determining which single-dish \hi\ properties of these clouds are the best predictor that a system is a good candidate to be gas in a dark matter halo, rather than a local \hi\ cloud, is critical for making the most use of expensive follow-up observations. The most straightforward approach for understanding the nature of the UCHVCs would be to detect an optical counterpart, constraining the distance to the system and identifying it as a bona-fide galaxy. Previous work has shown that stellar counterparts for UCHVCs appear to be rare and correspond to more distant, massive systems with typical \hi\ masses of $\sim 10^7$ \msun\ \citepads{2015A&A...575A.126B,2015ApJ...806...95S}. However, \citetads{2015ApJ...811...35J} identified a tentative optical counterpart for one UCHVC, AGC\,198606, at a distance of 383 kpc. This distance is consistent with the hypothesis that this UCHVC is a companion to Leo T, located only 1.2\dg\ and 17 \kms\ away. At this distance, AGC\, 198606 has an \hi\ mass of $5\times10^5$ \msun, comparable to that of Leo T, while its stellar mass is an order of magnitude lower. The lack of definitive stellar counterparts to date may indicate that UCHVCs representing gas-bearing dark matter halos are rare. Alternatively, it could also be a result of these systems having intrinsically faint stellar counterparts; in the case above, AGC\,198606 has \mhi/\mstar $>40$. The ability to better distinguish the best candidates could help address which of these scenarios is dominant. Previous work with high velocity clouds (HVCs), and especially compact HVCs (previously proposed as "dark" galaxies), has shown that higher resolution \hi\ imaging can be used to constrain the nature of these systems and to address whether they are Galactic or extragalactic \citepads[e.g.,][]{2002A&A...391...67D,2004A&A...426L...9B,2005A&A...436..101W,2014A&A...563A..99F}. Hence we present resolved \hi\ observations with the Westerbork Synthesis Radio Telescope (WSRT) data for twelve UCHVCs in order to help address their nature. The sources are drawn from a catalog of UCHVCs following the selection criteria of \citetalias{2013ApJ...768...77A} but including expanded sky coverage of the ALFALFA \hi\ survey. Importantly, the restriction that $| v_{LSR} | > 120$ \kms\ was relaxed so that clouds close to Galactic \hi\ velocities that were otherwise good candidates are included. The sources were selected to represent the best potential galaxy candidates on the basis of various properties: high average column density, as those systems with the highest density of gas and potential for star formation; small angular size, for the systems most consistent with being distant objects; isolation, as the objects least likely to be part of a larger Galactic HVC complex; and large recessional velocity, as it is difficult to explain in a Galactic fountain model. Every cloud was selected for at least one of these criterion; a few fulfilled multiple criteria. The goal is to determine which, if any, of these criteria are most important for identifying the best candidate galaxies. In Section 2 we present the ALFALFA \hi\ properties and the WSRT \hi\ data for the twelve UCHVCs observed. In Section 3, we compare the ALFALFA and WSRT \hi\ properties. In Section 4 we discuss the nature of the UCHVCs, how to identify the best galaxy candidates, and the properties of the galaxy candidates. We summarize our results in Section 5. The Appendix contains a full presentation of the data products for all the UCHVCs. \begin{table*} \footnotesize \caption{ALFALFA \hi\ properties} \label{tab:hi_alfalfa} \centering \begin{tabular}{lllllllll} \hline \hline HVC name & AGC & R.A.+Dec. & cz & \w50 & $\bar a$ & $S_{HI}$ & $M_{HI}$ & $\log \bar N_{HI}$ \\ & & J2000 & \kms & \kms & \arcmin & Jy \kms & \msun & atoms cm$^{-2}$ \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) &(9)\\ \hline HVC214.76+42.45+44 & 198606\tablefootmark{1,2} & 093005.4+163956 & 51 & 26 (1) & 12.2 & 17.44 (0.05) & 6.61 & 19.71\\ HVC204.88+44.86+147 & 198511\tablefootmark{2,3} & 093013.2+241217 & 152 & 15 (1) & 7.0 & 0.73 (0.03) & 5.24 & 18.81\\ HVC205.83+45.14+173 & 198683 & 093208.0+233752 & 178 & 19 (1) & 10.4 & 0.88 (0.04) & 5.32 & 18.56\\ HVC217.77+58.67+96 & 208747\tablefootmark{2} & 103706.6+203058 & 98 & 23 (1) & 10.9 & 2.74 (0.05) & 5.81 & 19.0\\ HVC212.68+62.39+64 & 208753 & 104932.4+235638 & 65 & 23 (1) & 12.7 & 3.95 (0.07) & 5.97 & 19.03\\ HVC230.27+71.10+76 & 219663 & 113429.7+201249 & 74 & 17 (1) & 7.2 & 0.75 (0.03) & 5.25 & 18.8\\ HVC235.38+74.79+195 & 219656\tablefootmark{2} & 115124.3+203220 & 192 & 21 (1) & 7.5 & 0.88 (0.04) & 5.32 & 18.84\\ HVC271.57+79.03+248 & 229326\tablefootmark{2} & 122734.7+173823 & 242 & 23 (8) & 7.8 & 0.77 (0.04) & 5.26 & 18.74\\ HVC276.53+79.84+255 & 229327\tablefootmark{2} & 123231.6+175721 & 249 & 19 (1) & 11.1 & 0.9 (0.05) & 5.33 & 18.51\\ HVC028.09+71.87-142 & 249393\tablefootmark{2,3} & 141054.9+241210 & -155 & 38 (2) & 12.7 & 1.02 (0.07) & 5.38 & 18.44\\ HVC011.76+67.89+60 & 249525\tablefootmark{2} & 141750.1+173252 & 48 & 24 (7) & 8.5 & 6.36 (0.04) & 6.18 & 19.59\\ HVC015.96+63.90+44 & 249565 & 143557.6+171004 & 30 & 18 (1) & 7.5 & 1.76 (0.04) & 5.62 & 19.14\\ \hline \end{tabular} \tablefoot{ \tablefootmark{1}{Previously published in \citetads{2015A&A...573L...3A}.} \tablefootmark{2}{Previously published in \citetads{2016MNRAS.457.4393J}.} \tablefootmark{3}{Previously published in \citetads{2013ApJ...768...77A}. Table columns are as follows: \begin{itemize} \item Col. 1: The HVC name of the source following the traditional convention of galactic coordinates at the nominal cloud center and the \vlsr\ of the cloud, for example HVC214.76+42.45+44 has $l=$214.76\dg, $b=$42.45, and \vlsr = 44 \kms. \item Col. 2: Identification number in the Arecibo General Catalog (AGC), an internal database maintained by MH and RG. This identifier allows for easy cross--reference with the ALFALFA survey catalogs. Generally, we will use this identifier for the UCHVCs for brevity. Footnotes in this column indicate references for previously published UCHVCs. \item Col. 3: Equatorial coordinates of the \hi\ centroid, epoch J2000. \item Col. 4: Recessional velocity in the heliocentric frame. \item Col. 5: \hi\ line full width at half maximum with estimated measurement error in brackets. \item Col. 6: Average angular diameter at the half-flux level, $\bar a$, computed as the geometric mean of the major and minor axes of the half-power ellipse: $\sqrt{ab}$. \item Col. 7: Flux density integral in Jy \kms\ with measurement error in brackets \item Col. 8: $\log$ of the \hi\ mass for an {\it assumed} distance of 1 Mpc in units of \msun \item Col. 9: $\log$ of the representative column density, $\bar N_{HI}$, in units of atoms cm$^{-2}$ \end{itemize} } } \end{table*} | \subsection{The nature of the UCHVCs}\label{sec:nature} The WSRT observations reveal that the UCHVCs fall into two categories: likely Galactic halo clouds and potential galaxy candidates. These two source populations are distinguished from each other based on a combination of \hi\ morphology and kinematics. All the sources show a smooth \hi\ morphology in the 210\arcsec\ resolution data; this is consistent with their selection as UCHVCs from the ALFALFA data. The first set of sources, likely Galactic halo clouds, are distinguished by a lack of ordered velocity motion at all spatial resolutions and breaking into clumps of low column density \hi\ contained in a much more diffuse envelope in the 105\arcsec\ resolution data. This is consistent with previous observations of (compact) HVCs, and the likely explanation for these sources is that they are clouds of \hi\ in the halo of the MW at typical distances of a 100 kpc \citepads[e.g.,][]{2001A&A...370L..26B,2002A&A...391...67D,2005A&A...432..937W}. In contrast, the potential galaxy candidates have ordered velocity motion at all angular resolutions and a smooth \hi\ morphology in the 105\arcsec\ resolution data. The potential galaxy candidates also have higher column density values, allowing them to be imaged at 60\arcsec\ resolution, where they maintain the smooth \hi\ morphology and ordered velocity motion. Figure \ref{fig:examplesources} illustrates the comparison between the 210\arcsec\ and 105\arcsec\ resolution data for an example likely Galactic halo cloud and one of the potential galaxy candidates. \begin{figure*} \centering \includegraphics[keepaspectratio,width=\linewidth]{example_sources.png} \caption{Velocity fields with \hi\ column density contours of AGC\,249525 (left) and AGC\,229326 (right) at 210\arcsec\ (top) and 105\arcsec\ (bottom) resolution. AGC\,249525 is representative of the potential galaxy candidates and AGC\,229326 of the likely Galactic halo clouds. The column density contours for AGC\,249525 for the 210\arcsec\ and 105\arcsec\ data are [4, 6, 8, 15, 25, 35] and [9, 15, 20, 30, 40] $\times 10^{18}$ atoms cm$^{-2}$. For AGC\,229326 the column density levels are [2.5, 3.5, 5, 6] and [7, 9, 10] $\times 10^{18}$ atoms cm$^{-2}$.} \label{fig:examplesources} \end{figure*} The \hi\ column density, velocity field, and velocity dispersion maps and the position-velocity slices used to determine the nature of the UCHVCs are presented in Appendix \ref{sec:sources}. We determined that three sources are potential galaxy candidates. The remainder of the UCHVCs are considered likely Galactic halo clouds. The two sources from this work included in \citetads{2015A&A...575A.126B} and \citetads{2015ApJ...806...95S}, AGC\,198511 and AGC\,249393, show the morphology and lack of ordered velocity motion that is typical of Galactic halo clouds. This is consistent with the fact that these sources have no detected optical counterparts, down to strict limits \citepads{2016A&A...591A..56B}. AGC\,198606 (also presented as a galaxy candidate in \citetads{2015A&A...573L...3A}) and AGC\,249525 are excellent galaxy candidates with a smooth \hi\ morphology and evidence for ordered velocity motion at all spatial resolutions considered. AGC\,249565 is a possible galaxy candidate, but the evidence for its ordered velocity motion is weaker, especially at higher angular resolution, and it may break into \hi\ clumps in a more diffuse envelope in the 60\arcsec\ resolution data, although this could be a S/N limitation. The ordered velocity motion is key for classifying a UCHVC as a galaxy candidate, and in Figure \ref{fig:pvslices} we show the position-velocity slices for all three galaxy candidates to illustrate their ordered velocity motion. \begin{figure*} \centering \includegraphics[keepaspectratio,width=\linewidth,clip=true,trim=2cm 2cm 2cm 2cm]{candidate_pvslices.png} \caption{Position-velocity slices along the direction of ordered motion for the three galaxy candidates at 210\arcsec, 105\arcsec\, and 60\arcsec\ resolution (top to bottom). From left to right the sources are AGC\,198606, AGC\,249525, and AGC\,249565. The contours start at 2 $\times$ rms of the data cube and increase by $\sqrt{2}$; negative contours with the same spacing are also shown. The solid horizontal black lines indicate the extent of velocity motion, and the dashed vertical lines indicate the spatial extent over which it occurs.} \label{fig:pvslices} \end{figure*} \subsection{Identifying galaxy candidates} The goal of this work is to identify \hi\ clouds that are good candidates to represent (nearly) starless gas in dark matter halos. In Section \ref{sec:nature}, we determined that AGC\,198606 and AGC\,249525 were excellent candidates to represent gas in dark matter halos while AGC\,249565 was a potential third candidate. The majority of the UCHVCs (9/12) lack any kinematic structure and show a \hi\ morphology at higher angular resolutions that is consistent with local Galactic halo clouds. This is not surprising as there are many potential formation mechanisms for HVCs and the majority of them are Galactic processes. An important step is to identify the \hi\ properties by which the best galaxy candidates may be recognized. The targets were selected for WSRT observations on the basis of four criteria: isolation, compact size, large recessional velocity, or large average column density. The three potential galaxy candidates were not selected for observations based on their size or isolation. While they are relatively compact and isolated, they are not distinguished from the rest of the UCHVC population by these two criteria. Instead, they are most clearly distinguished by having high column densities, as can be seen in Figure \ref{fig:nhi}. In fact, the two best candidates, AGC\,198606 and AGC\,249525, have column densities higher than any source included in \citetalias{2013ApJ...768...77A}. While the peak column densities for these sources are higher than the other UCHVCs at all resolutions, their peak column density increases by less from the 210\arcsec\ to 105\arcsec\ data (right panel of Figure \ref{fig:nhi}). This is consistent with their morphology in that the UCHVCs with the largest changes in peak column densities are those that show the most clumpiness at higher angular resolution. Figure \ref{fig:histcandsvel} shows the recessional velocities for all the candidates and the \citetalias{2013ApJ...768...77A} sample in two different frames: helicoentric ($cz$), and Galactic standard of rest ($v_{GSR}$). Contrary to our expectations when selecting targets, the highest recessional velocity targets are not the best candidate galaxy candidates. Instead, the best candidates are those at low recessional velocity, with the three best candidates having $|v_{LSR}| < 120$ \kms, outside the original selection selection criteria of \citetalias{2013ApJ...768...77A}. It is worth noting that Leo T has a low recessional velocity ($cz=35$ \kms), and we indicate its position in Figure \ref{fig:histcandsvel}. The picture that the best candidate galaxies are at low recessional velocities is consistent with theoretical work by \citetads{2014MNRAS.438.2578G}. They find that never-accreted halos (the most likely to be overlooked gas-rich dwarf galaxies) in Local Group analogs are most likely to have radial velocities relative to their host galaxy with an amplitude $<$ 150 \kms\ (e.g., $|v_{GSR}|<150$ \kms). This is in contrast to the work of \citetads{2015ApJ...808..136D} who find that \hi\ clouds distinguished as velocity outliers are most likely to have a GALEX counterpart. However these are systems with apparent stellar counterparts and likely lie at larger distances within the Local Volume, rather than nearby in the Local Group. \begin{figure*} \centering \includegraphics[keepaspectratio,width=\linewidth]{hist_cands_vel.png} \caption{ Distribution of velocities in heliocentric and Galactic standard of rest frames for the \citetalias{2013ApJ...768...77A} UCHVCs and the UCHVCs of this work, with the good galaxy candidates highlighted in yellow.} \label{fig:histcandsvel} \end{figure*} Overall, the clearest distinguishing feature of the best galaxy candidates is their high column density (albeit still low for galaxies). They also tend to be small, isolated and at low velocity, but none of those criteria are sufficient to identify the best candidates. The fact that the best candidates are at low recessional velocities means that identifying these sources will be strongly complicated by the presence of the Galactic \hi\ foreground. \subsection{Properties of galaxy candidates}\label{sec:gal} In this section, we assume AGC\,198606, AGC\,249525, and AGC\,249565 do in fact represent gas in dark matter halos and examine what their properties would be. The strongest evidence that these three systems potentially represent gas in dark matter halos is the ordered velocity motion, which can be interpreted as rotation of the gas. The extent of this velocity motion is indicated in the position-velocity slices in Figure \ref{fig:pvslices} and is in total 25, 15, and 10 \kms\ for AGC\,198606, AGC\,259525, and AGC\,249565. The magnitude of the velocity motion was determined to represent the global bulk velocity of the gas; gas exists at velocities beyond the extents indicated in Figure \ref{fig:pvslices} due to the dispersion of the gas about the global bulk velocity. In order to interpret the bulk velocity motion as a rotation velocity, the inclination of the system must be taken into account. For each candidate, a column density level at which the velocity motion could be reliably traced in both the 210\arcsec\ and 105\arcsec\ data was empirically determined. This physical extent is shown in Figure \ref{fig:pvslices} by the vertical dashed lines. Due to lower sensitivity to low column density emission, the 60\arcsec\ data typically does not trace the velocity motion to the same spatial extent as the 210\arcsec\ and 105\arcsec\ data. The axial ratio of each system was found by fitting an ellipse at this spatial extent to both the 105\arcsec\ and 210\arcsec\ data. For converting to an inclination, these systems are assumed to be thick disks with an intrinsic axial ratio of 0.6 \citepads{2010MNRAS.404L..60R}; changing the assumed intrinsic axial ratio by 10\% changes the derived inclination angles by a similar amount. For AGC\,198606, the velocity motion is reliably traced to the $2\times10^{19}$ atoms cm$^{-2}$ level. The fitted ellipse has a major axis of 12\arcmin\ $\pm$ 1\arcmin\ and the axial ratio is 0.75, which corresponds to an inclination of 56\dg. The corresponding rotation velocity is $15^{+4}_{-1}$ \kms, where the errors correspond to a 10\% uncertainty on the axial ratio. For AGC\,249525 the $1.5 \times 10^{19}$ atoms cm$^{-2}$ level was used, which has a major axis of 7.5\arcmin\ $\pm$ 0.1\arcmin\ and an axial ratio of 0.91, corresponding to an inclination of 30\dg. Then the rotation velocity is 15$_{-2}^{+6}$ \kms. And for AGC\,249565 the extent of the velocity motion was seen to the $1 \times10^{19}$ atoms cm$^{-2}$ level. This source shows the very unusual behavior that it has a larger major axis at this level in the 105\arcsec\ data than the 210\arcsec\ data. We take the major axis of 5.6\arcmin\ $\pm$ 0.1\arcmin\ from the 210\arcsec\ data as the extent for this source. The axial ratio is 0.86 and the rotation velocity is 8$^{+4}_{-2}$ \kms. The accuracy of these values is limited by the determination of the velocity extent, assumption that the velocity gradient represents rotation, and the assumed inclination of the system. This is particularly problematic for AGC\,249525 as its axial ratio is close to unity and small changes in the fitted axial ratio greatly impact the final rotation velocity. These velocity values are comparable to those seen in other low mass dwarf galaxies, such as Leo P, Pisces A and B, and the SHIELD galaxies \citepads{2014AJ....148...35B,2016A&A...587L...3C,McNichols}. These rotation velocities can be used to constrain the dynamical mass of the systems. These systems have low rotation velocities, on the order of their velocity dispersion. Thus, we follow \citetads{1996ApJS..105..269H} and explicitly include the dynamical support of velocity dispersion of the gas when calculating the dynamical mass within a given radius: \be M_{dyn} =2.325 \times 10^5 \,M_{\odot} \,\frac{V_{rot}^2 + 3\sigma_z^2}{\mathrm{km^2 \,s^{-2}}} \, \Bigg(\frac{r}{\mathrm{kpc}}\Bigg). \ee We take representative velocity dispersion values from the moment two maps. For AGC\,198606 this is 9 \kms, and for AGC\,249525 and AGC\,249565 this is 7 \kms. In order to calculate the dynamical mass or understand any of the other intrinsic properties of these systems, a distance is necessary. The most straight-forward way to obtain a distance is to detect a stellar counterpart. All three of these systems lie out side the $\alpha.40$ footprint and so are not considered in the works of \citetads{2015A&A...575A.126B} and \citetads{2015ApJ...806...95S}. In \citetads{2015A&A...573L...3A} we argued that due to its small separation in position and velocity space from Leo T that AGC\,198606 is likely located at a similar distance. In subsequent work, \citetads{2015ApJ...811...35J} found a tentative stellar counterpart (92\% confidence) at a distance of 383 kpc, consistent with AGC\,189606 being physically associated with Leo T. Using the slightly higher \hi\ integrated flux density value of this work, the \hi\ mass at a distance of 383 kpc is $5.3 \times 10^5$ \msun, and the system is extremely \hi\ dominated, with \mhi/\mstar $>50$. We can use a similar philosophy to try and constrain the distances to AGC\,249525 and AGC\,249565. These two sources are located 4.3\dg\ from each other so we consider their potential neighbors together. Within 10\dg\ and 200 \kms\ there are three galaxies: Bootes I at distance of 66 kpc \citepads{2006ApJ...653L.109D}, Bootes II at a distance of 46 kpc \citepads{2009ApJ...690..453K}, and UGC\,9128 at a distance of 2.27 Mpc \citepads{2013AJ....146...86T}. Given the observed morphological segregation in the Local Group \citepads{2014ApJ...795L...5S}, these systems are unlikely to be associated with Bootes I and II, but could be associated with UGC\,9128. Thus we can adopt 2 Mpc as a representative upper distance for these two sources. As a representative lower distance, we take 0.4 Mpc, the distance of Leo T and AGC\,198606. \begin{table*} \footnotesize \caption{Properties of galaxy candidates} \label{tab:galprops} \centering \begin{tabular}{lllllll} \hline \hline Name & Distance & \mhi & $v_{rot}$ & $r_{HI}$ & \mdyn & \mhi/\mdyn \\ & Mpc & $10^5$ \msun & \kms & kpc &$10^7$ \msun \\ (1) &(2) &(3) &(4) &(5) &(6) &(7)\\ \hline AGC\,198606\tablefootmark{a} & 0.383 & $5.3$ & 15$^{+4}_{-1}$ & 0.66 & $7$& 0.008 \\ AGC\,249525\tablefootmark{b} & $0.4-2$ & $1.9-48$ & 15$^{+6}_{-2}$ & 0.44 --2.2 & $4-20$ &$0.005-0.02$ \\ AGC\,249565\tablefootmark{c} & $0.4-2$ & $0.64-16$ & 8$^{+4}_{-2}$ & 0.33 -- 1.6 &$ 2-8$ &$0.003-0.02$ \\ \hline Leo T\tablefootmark{d} & 0.42 &2.8 &-- &0.3 & 0.33 &0.085 \\ Leo P\tablefootmark{e} & 1.62 & 8.1 & 15 & 0.5 & 2.5 & 0.032\\ \hline \end{tabular} \tablefoot{ \tablefoottext{a}{\hi\ extent measured at the $2 \times 10^{19}$ atoms cm$^{-2}$ level.} \tablefoottext{b}{\hi\ extent measured at the $1.5 \times 10^{19}$ atoms cm$^{-2}$ level.} \tablefoottext{c}{\hi\ extent measured at the $1 \times 10^{19}$ atoms cm$^{-2}$ level.} \tablefoottext{d}{Values from \citetads{2008MNRAS.384..535R}.} \tablefoottext{e}{Values from \citetads{2014AJ....148...35B} and \citetads{2015ApJ...812..158M}.} Table columns are as follows: \begin{itemize} \item Col. 1: Name of the system \item Col. 2: Known distance, or range of plausible distances, in Mpc \item Col. 3: \hi\ mass in units of $10^5$ \msun \item Col. 4: Rotation velocity in \kms \item Col. 5: \hi\ radius in kpc. For the UCHVCs this is the extent to which the velocity motion can be reliably traced in the 210\arcsec\ and 105\arcsec\ data. \item Col. 6: Dynamical mass in units of $10^7$ \msun, derived as described in the text above. \item Col. 7: The ratio of \hi\ mass to dynamical mass. \end{itemize} } \end{table*} Table \ref{tab:galprops} summarizes the properties of these sources for the relevant distances, with Leo T and Leo P given for reference. AGC\,198606 is physically bigger than Leo T and Leo P (albeit measured at a much lower column density level) while its \hi\ mass is intermediate between the two galaxies. Its rotational velocity is similar to that of Leo P but its dynamical mass is larger due to its larger physical size. AGC\,249525 has an \hi\ mass slightly smaller than Leo T and an \hi\ size between that of Leo T and Leo P at the lower bound of the distance range considered for it. Its rotational velocity is comparable to Leo P and it has a similar dynamical mass. At the upper end of the distance range considered, AGC\,249525 is much larger than Leo T and Leo P in terms of \hi\ mass, \hi\ size, and dynamical mass. At its closest plausible distance, AGC\,249565 has a quarter of the \hi\ mass of Leo T but a similar \hi\ size. At its furthest considered distance, AGC\,249525 has twice the \hi\ mass of Leo P and three times the \hi\ extent. These three candidate galaxies are distinguished from Leo T, Leo P and other low mass galaxies by the extremes of their baryonic component: they have a minimal stellar component, are extremely dark matter dominated, and have extremely low peak column densities. AGC\,198606 has a tentative stellar component with a mass of only $\sim 10^4$ \msun\ \citepads{2015ApJ...811...35J}; AGC\,249525 and AGC\,249565 have no known stellar counterpart. For all distances considered for AGC\,198606, AGC\,249525 and AGC\,249565, they are extremely dark matter dominated objects, with \mhi/\mdyn $\le$ 0.02 in all cases. This is lower than the \mhi/\mdyn\ value of Leo P, where the stellar population also contributes significantly to the total baryon mass ($M_{bary}$/\mdyn $=$ 0.05). The peak column densities of these three candidates with a 60\arcsec\ beam (0.1 kpc at 400 kpc or 0.6 kpc at 2 Mpc) are $4-6 \times 10^{19}$ atoms cm$^{-2}$. The least resolved SHIELD galaxies have a physical resolution of $\sim 0.6$ kpc but their peak column densities are almost an order of magnitude higher \citep{Teich}. The left panel of Figure \ref{fig:btf} places these three candidate galaxies in the context of the baryonic Tully-Fisher relation (BTFR), a tight observed correlation between the baryonic mass of a galaxy and its maximum rotational velocity. We show the relation of \citetads{2012AJ....143...40M} along with the galaxies used in that work. We also include the SHIELD galaxies and Leo P for an extension to lower masses \citepads{2014AJ....148...35B, McNichols}. The three candidate galaxies of this work are placed on this relation using the rotation velocities derived in this work and with baryonic masses consisting of only a neutral gas component (the \hi\ mass multiplied by a 1.33 correction factor to account for Helium). For AGC\,198606 we use the distance from \citetads{2015ApJ...811...35J} of $383\pm10$ kpc and include the uncertainty in the neutral gas mass of 10\% (based on the uncertainty of the WSRT integrated flux) in the vertical error bars; the potential stellar component is neglected as it negligible compared to the gas mass. For AGC\,249525 and AGC\,249565, we use a representative distance of 1 Mpc and the vertical errors bars indicate the range of distances considered, $0.4-2$ Mpc. These three candidate galaxies are consistent with extending the BTFR to lower rotation velocities. AGC\,198606 and AGC\,249525 occupy the same region as Leo P and AGC\,249565 extends the relation to even lower rotation velocities. In order to test the significance of the three candidate galaxies lying on the BTFR, in the right panel of Figure \ref{fig:btf} we place all the UCHVCs on the BTFR based on their single-dish ALFALFA \hi\ properties. The baryonic mass is the \hi\ mass for an assumed distance of 1 Mpc multiplied by a correction factor of 1.33 to account for Helium, and $v_{rot}$ is approximated as $\sqrt{3}\sigma$, where $\sigma$ is the line-of-sight velocity dispersion of the gas based on the $W_{50}$ value. The general UCHVC population occupies a region of parameter space below the BTFR. Interestingly, the candidate galaxies are among the sources that scatter closest the BTFR based on single-dish properties. \begin{figure*} \centering \includegraphics[width=\linewidth,keepaspectratio]{btf.png} \caption{Left: AGC\,198606, AGC\,249525 and AGC\,249565 (the three galaxy candidates) shown on the Baryonic Tully-Fisher relation (BTFR) of \citetads{2012AJ....143...40M} with Leo P and the SHIELD galaxies \citepads{2014AJ....148...35B, McNichols} shown for extension to low rotational velocities. Right: UCHVCs of \citetalias{2013ApJ...768...77A} (open circles) and this work (open symbols, same colors and shapes as in Figures \ref{fig:fluxrecov} and \ref{fig:nhi}) shown on the BTFR based on their single-dish ALFALFA properties. The galaxy candidates are shown based on their rotation velocities derived in this work.} \label{fig:btf} \end{figure*} \subsection{Implications for future surveys} In line with previous work, these observations highlight the power of resolved \hi\ observations for addressing questions as to the nature of (ultra-) compact HVCs and whether they can represent gas in dark matter halos \citepads[e.g.,][]{2002A&A...391...67D,2004A&A...426L...9B,2005A&A...432..937W,2005A&A...436..101W}. Of the twelve clouds identified in the single-dish ALFALFA survey, the higher angular resolution WSRT observations show that only three of the objects are potential candidates to represent gas in dark matter halos. With future large-field surveys planned with interferometers (e.g., Apertif and ASKAP), many more of these objects will be detected and immediately distinguished as galaxy candidates. If AGC\,198606, AGC\,249525, and AGC\,249565 do indeed represent what we might expect for gas-rich (nearly) starless galaxies in the Local Universe, we can use them as guides for how to find more of these objects in future surveys. Importantly, while they are the highest column density objects studied here, their peak column densities are lower than that typically found in low mass galaxies by an order of magnitude. In order to robustly detect and image these objects in future surveys, a special handling of the data with strong angular smoothing will be called for. | 16 | 9 | 1609.05377 |
1609 | 1609.02557_arXiv.txt | Both the three-dimensional density of red clump giants and the gas kinematics in the inner Galaxy indicate that the pattern speed of the Galactic bar could be much lower than previously estimated. Here, we show that such slow bar models are unable to reproduce the bimodality observed in local stellar velocity space. We do so by computing the response of stars in the Solar neighbourhood to the gravitational potential of slow and fast bars, in terms of their perturbed distribution function in action-angle space up to second order, as well as by identifying resonantly trapped orbits. We also check that the bimodality is unlikely to be produced through perturbations from spiral arms, and conclude that, contrary to gas kinematics, local stellar kinematics still favour a fast bar in the Milky Way, with a pattern speed of the order of almost twice (and no less than 1.8 times) the circular frequency at the Sun's position. This leaves open the question of the nature of the long flat extension of the bar in the Milky Way. | \label{sect:intro} The Milky Way is a barred galaxy. This conclusion can be readily established from the gas kinematics in the inner Galaxy \citep[e.g.,][]{deVaucouleurs1964,Binney1991}, as well as from near-infrared photometry \citep{Binney1997}. Nevertheless, and rather surprisingly, the structural parameters of the Milky Way bar, in particular its strength, orientation and pattern speed, are still very poorly constrained. Almost two decades ago, based on photometry and gas kinematics arguments, a consensus emerged for a fast bar with corotation (CR) around $\sim 3.5$~kpc \citep[e.g.,][]{Binney1997,Bissantz2003}, i.e. a perturbation pattern speed $\Omb \approx 1.9 \, \Omega_0$ where $\Omega_0$ is the local rotational frequency at the Sun's radius $R_0$, and an angle between the bar major axis and the Galactic centre-Sun direction of $\phib \sim 25\degree$. This pattern speed would place the Sun just outside the outer Lindblad resonance (OLR) of the bar, and the kinematical signature associated with this position indeed appears to be present in the stellar phase-space distribution in the Solar neighbourhood \citep[e.g.,][see also \Sec{sect:bim}]{Dehnen1999,Dehnen2000,Famaey2005,Minchev2007,Bovy2010,Quillen2011}, as well as possibly in large-scale stellar velocity fluctuations \citep{Monari2014,Bovy2015}. However, from the photometric point of view, the situation has recently changed quite dramatically, since \cite{WeggGerhard2013} and \cite{Wegg2015} measured the three--dimensional density of red clump giants in the inner Galaxy by combining various recent photometric surveys. They concluded that the Milky Way contains a central box/peanut bulge \citep{Combes1990,Athanassoula2005} which is the vertical extension of a longer, flatter bar, oriented at an angle of $\phib \sim 27\degree$ from the Galactic centre-Sun direction, but reaching out to a radius $\Rb \sim 5$~kpc. Since the bar cannot physically extend beyond its corotation, this limits the pattern speed of the bar. Simulated bars are usually rather shorter than their corotation, and indeed by constructing dynamical models reproducing this new bar density as well as the stellar kinematics from the BRAVA survey, the pattern speed was estimated to be of the order of $\Omb \approx \Omega_0$ \citep{Portail2015} placing the bar corotation very near to the Sun. Two independent subsequent re-analyses of gas kinematics in the inner Galaxy by \cite{Sormani2015} and \cite{Li2016} then favored slightly higher pattern speeds, of the order of $\Omb \approx 1.45 \, \Omega_0$ and $\Omb \approx 1.2 \, \Omega_0$ respectively, but both still much lower than the older estimate $\Omb \approx 1.9 \, \Omega_0$. Given this state of affairs, we now study in the present contribution the effect of such low pattern speeds on stellar kinematics in the Solar neighbourhood, which was previously considered a strong argument in favor of a fast bar. In \Sec{sect:bim}, we briefly review the characteristic observational signatures of non-axisymmetries in the Solar neighbourhood, and more specifically the prominent Hercules moving group in velocity space. We then review in \Sec{sec:analytical} the expected theoretical form \citep[][hereafter M16]{Monari2016} of the first order response of the phase-space distribution function (DF) in the presence of non-axisymmetric potential perturbations. We then extend this analysis up to second order, and also identify the location of resonantly trapped orbits in local velocity space. We subsequently confront the predictions to observations in the case of bars with low (\Sec{sect:low}) and high (\Sec{sect:high}) pattern speed. Conclusions are drawn in \Sec{sect:concl}. | \label{sect:concl} We presented the first application of the formalism developed in M16 to calculate, through perturbation theory, the effects of a non-axisymmetric gravitational disturbance on an initially axisymmetric DF, $f_0(\bJ)$, describing the phase-space density of stars in a collisionless stellar system (i.e., governed by the collisionless Boltzmann equation). We extended the M16 formalism to second order (Section~3), and concentrated on the effects of the Galactic bar on the DF in the Solar neighbourhood. We checked whether a slow bar with pattern speed $\Omega_0 \lesssim \Omb \lesssim 1.45 \Omega_0$ could reproduce the observed bimodality of local velocity space. We concluded that no feature in our modelled local velocity space could account for the observed bimodality (Section~4). We checked whether second order effects, or the additional effects of spiral arms, could help, and did not find any configuration reproducing the bimodality. A fast bar with $\Omb \approx 1.9 \, \Omega_0$, on the other hand, explains it nicely (Section~5). \cite{BlandHGerhard} fixed their final value of the bar's pattern speed at $\Omb= (1.48\pm0.31)\Omega_0$. Here we estimated that, if Hercules is created by the bar's OLR, the pattern speed of the bar cannot be less than $\Omb\approx1.8\Omega_0$ to be compatible with the measured density peaks of the Hercules moving group. In Section~3.3.3 and in all our figures, we also identified the regions of resonant trapping in phase-space. This trapping should affect the actual density of stars in the trapped zone compared to the analytical models presented here, but does not strongly affect the general distortion of phase-space itself, as numerical particle test simulations with adiabatic growth of the bar \citep[e.g.,][]{Monari2014} give the same result as our fast bar models for the {\it shape} of the bimodality in local velocity space. We note that, while such forward test-particle simulations can serve as benchmarks to test analytical models like those presented here (see M16), they do not allow to directly fit the data. Actually, the main motivation of models based on analytical DFs is that they will indeed allow to fit the data directly, with a few fitting parameters in the perturbing potential as well as in the axisymmetric DF, by performing a maximum-likelihood estimate of these parameters based on actual kinematical data for a large set of individual stars. However, in order to perform such a fully quantitative fit, our method will have to be extended to better treat the DF for resonantly trapped orbits. This will be the topic of a forthcoming paper. Concerning the bimodality, let us also note that we did not try every possible spiral arm configuration here, and cannot yet strictly exclude that a similar structure as the locally observed bimodality could be the result of spirals. Our results are generally in line with the N-body simulations of \citet{Quillen2011} in which velocity distributions created from regions just outside the bar's OLR more closely resembled that seen in the solar neighbourhood. Nevertheless, close inspection of the velocity distributions at other radii in these simulations reveal spiral-related features which also slightly resemble the Hercules stream, albeit at angles to the bar which do not correspond to the present orientation of the bar in the Milky Way. Also, \citet{Grand2014} showed that the outward radial migrators behind their corotating spiral arms display lower-$v$ and negative-$u$ velocity (see their Fig.~4), hence providing a possible explanation which will have to be inspected closely in the future. In any case, the future DR2 and DR3 data releases from Gaia \citep{Gaia} should allow a detailed investigation of phase-space structure outside of the Solar neighbourhood, at different Galactic radii and azimuths, and test our present conclusions about the pattern speed of the bar, since any possible spiral-related features in velocity space would not follow the same evolution at different radii and azimuths. Such a test might actually already be possible by combining the Gaia DR1 with existing spectroscopic surveys. We also note that the metallicity patterns in local stellar velocity space seem to also support our fast bar models (Antoja et al. 2016, in preparation). The three--dimensional density of red clump giants in the inner Galaxy nevertheless clearly indicate the existence of a long, flat structure, oriented at an angle of $\phib \sim 27\degree$ from the Galactic centre-Sun direction and reaching out to a radius $\sim 5$~kpc. The most natural explanation would be that this structure is not a long bar but rather a loosely wound spiral coupled to the end of the bar. If it has a pattern speed only somewhat smaller than the central bar, it could be a good candidate to explain the observed double-peak aspect of the Hercules stream, which is not reproduced even in our fast bar models. On the other hand, it is known that small nuclear bars with faster pattern speed than the main bar can be long-lived in numerical simulations including a gaseous component, even without resonance overlaps or mode coupling, if star formation remains moderately active in the region of the nuclear bar \citep[e.g.,][]{Wozniak2015}. However, we are not aware of any simulation reproducing a stable long bar with lower pattern speed than its central counterpart and similar in size to the structure observed in the inner 5~kpc of the Milky Way (hence about twice the disc scale-length). We would thus {\it a priori} favour a loosely wound spiral structure to explain the photometric observations. | 16 | 9 | 1609.02557 |
1609 | 1609.06718_arXiv.txt | Recent ALMA observations unveiled the structure of CO gas in the 23 Myr-old $\beta$ Pictoris planetary system, a component that has been discovered in many similarly young debris disks. We here present ALMA CO J=2-1 observations, at an improved spectro-spatial resolution and sensitivity compared to previous CO J=3-2 observations. We find that 1) the CO clump is radially broad, favouring the resonant migration over the giant impact scenario for its dynamical origin, 2) the CO disk is vertically tilted compared to the main dust disk, at an angle consistent with the scattered light warp. We then use position-velocity diagrams to trace Keplerian radii in the orbital plane of the disk. Assuming a perfectly edge-on geometry, this shows a CO scale height increasing with radius as $R^{0.75}$, and an electron density (derived from CO line ratios through NLTE analysis) in agreement with thermodynamical models. Furthermore, we show how observations of optically thin line ratios can solve the primordial versus secondary origin dichotomy in gas-bearing debris disks. As shown for $\beta$ Pictoris, subthermal (NLTE) CO excitation is symptomatic of H$_2$ densities that are insufficient to shield CO from photodissociation over the system's lifetime. This means that replenishment from exocometary volatiles must be taking place, proving the secondary origin of the disk. In this scenario, assuming steady state production/destruction of CO gas, we derive the CO+CO$_2$ ice abundance by mass in $\beta$ Pic's exocomets to be at most $\sim$6\%, consistent with comets in our own Solar System and in the coeval HD181327 system. | The circumstellar environment of $\beta$ Pictoris, a nearby \citep[$19.44\pm0.05$ pc,][]{vanLeeuwen2007}, young \citep[$23\pm3$ Myr,][]{Mamajek2014} main sequence A6 star \citep{Gray2006}, has been a continuous source of discoveries since more than three decades ago, when first circumstellar gas through optical absorption lines \citep{Slettebak1975} and then dust through an infrared excess from IRAS \citep{Aumann1985} were discovered. Its edge-on geometry was unveiled soon after through the first resolved image of a circumstellar dust disk \citep{Smith1984}, and explained the observed circumstellar gas absorption lines \citep{Hobbs1985}. Later, it was understood that to maintain the low levels of dust present in many nearby main sequence stars such as $\beta$ Pictoris, a replenishment mechanism is needed \citep{Backman1993}. This need for replenishment of second generation dust sets the physical definition of a \textit{debris disk}, and represents the fundamental difference with primordial protoplanetary disks, where the presence of large amounts of gas means the dust does not need replenishment \citep[e.g.][]{Wyatt2015}. Considered one of the archetypes of debris disks, the presence of gas has given $\beta$ Pictoris particular attention. The observed atomic absorption lines were seen to have both a stable component, at a radial velocity similar to that of the star, and a variable component, seen at different radial velocities \citep[e.g.][]{Slettebak1983, Kondo1985, Lagrange1987}. The latter feature was attributed to evaporating cometary bodies approaching the star on eccentric orbits \citep{Ferlet1987, Beust1990, Kiefer2014}. In addition, \textit{Hubble Space Telescope} (HST) observations showed that the gas composition is rather peculiar, with an extreme overabundance of carbon compared to other elements. This carbon acts as a braking agent and explains how the observed metallic gas levels can be maintained through braking against stellar radiation pressure \citep{Roberge2006, Fernandez2006}. Though generally absorption studies against the stellar continuum are the most sensitive, they are limited in that they only probe the gas column along the line of sight to the star. Recent studies have therefore been focusing on emission lines, which on the other hand can be used to trace the overall morphology of the gas disk. Firstly resolved observations of metallic atoms in the optical/UV \citep{Olofsson2001, Brandeker2004, Nilsson2012}, and subsequently observations of ionised carbon and oxygen in the far-IR \citep{Cataldi2014, Kral2016a} showed that the bulk of the atomic gas does not originate from the infalling cometary bodies at a few stellar radii, but from a more extended gas disk in Keplerian rotation at several tens of AU around the central star. Molecular gas has been more difficult to detect, with only upper limits on H$_2$ and OH \citep{Martin-Zaidi2008, Vidal-Madjar1994}. The presence of CO gas along the line of sight to the star was first marginally detected in absorption by the \textit{International Ultraviolet Explorer} \citep{Deleuil1993} and then confirmed through HST observations \citep[e.g.][]{Vidal-Madjar1994, Roberge2000}. However, detection of its rotational transitions at millimetre wavelengths proved impossible with single dish telescopes, despite very long integration times \citep{Liseau1998}. It is only through recent interferometric observations with the Atacama Large Millimeter/sub-millimeter Array (ALMA), bringing a drastic improvement in sensitivity and angular resolution, that detection of the J=3-2 transition at 345 GHz has been made possible \citep{Dent2014}. The data revealed for the first time the spatial distribution of CO, presenting a clump of emission at 85 AU on the SW side of the disk, which is co-located with both a radial peak in the dust millimetre emission and a SW dust clump similarly observed at mid-IR wavelengths \citep{Telesco2005}. This was interpreted as evidence for a common production location for both second-generation debris dust and second-generation CO. The clumpy azimuthal structure was then attributed to enhanced collision rates between icy bodies at specific azimuthal locations, which could be the dynamical evidence of either a giant impact between Mars-sized bodies \citep{Jackson2014} or the migration of a yet unseen planet sweeping icy planetesimals into resonance \citep{Wyatt2003, Wyatt2006}. We here present new ALMA follow-up observations of the $\beta$ Pictoris system. In this work, we focus on CO J=2-1 emission at 230 GHz, observed at an improved sensitivity and spatial resolution of $\sim5.5$ AU, and analyse it together with archival 345 GHz ALMA observations of the J=3-2 transition. We postpone the analysis of the dust continuum and upper limits on SiO emission as the subject of forthcoming work. In Section \ref{sect:obs}, we describe the observations, calibration and imaging procedures, whereas in Section \ref{sect:res} we analyse the radial, vertical and azimuthal structure of both CO transitions as well as the ratio between the two. In Section \ref{sect:mod}, we model the resolved line ratios using the non-local thermodynamic equilibrium methods developed in \citet{Matra2015}, showing how they can be used to probe undetectable species in the disk such as electrons and H$_2$, and measure the mass and optical thickness of CO gas. Finally, in Section \ref{sect:disc}, we discuss how our analysis impacts the current understanding of gas in the $\beta$ Pictoris system itself as well as other gas-bearing debris disks. \section[]{Observations} \label{sect:obs} \subsection{ALMA Band 6} We observed the $\beta$ Pictoris disk with ALMA during its Cycle 2 (project code 2012.1.00142.S) using band 6 receivers. Observations were performed using both the 12-m array and the Atacama Compact Array (ACA). The 12-m observations were carried out in two antenna configurations; for the most compact one, observed in December 2013, a mosaic strategy was used with two pointings at $\pm$5$\arcsec$ from the stellar location along the disk midplane, whereas for the most extended one, observed in August 2015, a single-pointing strategy was adopted. ACA observations were also carried out in single-pointing mode during October 2013. The on-source times were 28, 114 and 50 minutes respectively for the 12-m (compact and extended) and ACA observations. The spectral setup of the correlator consisted of four spectral windows; of these, two were centred around 218.5 and 232.5 GHz and set in time division mode (TDM) to achieve maximum bandwidth ($\sim$2 GHz each) for continuum observations. The remaining two were set in frequency division mode (FDM) to target the $^{12}$CO J=2-1 line (at rest frequency 230.538 GHz) and the SiO J=5-4 line (at 217.105 GHz) with a channel spacing of 244.141 and 488.281 kHz, respectively. The corresponding velocity resolutions are 0.64 and 1.35 km/s (after Hanning smoothing). Across all observations, either Uranus, Ganymede or J0519-454 were used as amplitude calibrators, whereas J0519-4546 was used as phase calibrator and either J0538-4405 or J0334-4008 as bandpass calibrators. The data calibration was carried out using the CASA software version 4.3.0, including appropriate weighting between different observations and/or array configurations. We note that the flux calibration is estimated to be accurate within 10\% (ALMA Cycle 2 Technical Handbook). The calibrated visibilities from the ACA and the 12-m datasets (covering baselines from 9 to 1574 m) were then concatenated, achieving a u-v coverage which gives us sensitivity to structure on scales between 0\farcs3 and 27\arcsec. To image the CO line, we first subtracted the continuum from the combined visibility dataset using the \textit{uvcontsub} task within CASA. Then, we imaged velocity channels within $\pm$10 km/s from the radial velocity of the star \citep[20.0$\pm$0.7 km/s in the heliocentric reference frame,][]{Gontcharov2006} using the CLEAN algorithm \citep{Hogbom1974}. Natural weighting of the visibilities was applied, resulting in a synthesised beam of size 0\farcs30$\times$0\farcs26 and position angle (PA, East of North) of -83\fdg9, corresponding to 5.8$\times$5.1 AU at the known distance to the system. As one of the main goals of this work is to directly compare this new Band 6 CO J=2-1 dataset with the archival CO J=3-2 Band 7 dataset, we also produced a final CO J=2-1 data cube at the degraded spatial and spectral resolution of the archival J=3-2 dataset; details of the procedure are described in Appendix \ref{app:3}. \subsection{ALMA Band 7} In addition to the new Band 6 observations, we retrieved archival ALMA Band 7 CO J=3-2 data obtained within Cycle 0 (project code 2011.0.00087.S), which are described in \citet{Dent2014}. In summary, a two-point mosaic strategy analogous to the Band 6 compact configuration observations was applied, although without use of the ACA (baselines ranging from 16 to 382 m). For consistency, we repeated the data reduction and imaging procedure the same way as done for the Band 6 data, using the same version of CASA. This resulted in a final synthesised beam of size 0\farcs69$\times$0\farcs55 (13.4$\times$10.7 AU) and PA 65\fdg4, with a channel width of 488.281 kHz (corresponding to a 0.85 km/s resolution at 345.796 GHz). As for the Band 6 dataset, the uncertainty in the flux calibration is estimated to be 10\% (ALMA Cycle 0 Technical Handbook). \begin{figure*} \begin{subfigure}{0.95\textwidth} \vspace{-5mm} \hspace{-15mm} \includegraphics*[scale=1.0]{bPic_CO21_mom0_fullres.pdf} \vspace{-5mm} \end{subfigure} \\ \begin{subfigure}{0.95\textwidth} \vspace{-34mm} \hspace{-15mm} \includegraphics*[scale=1.0]{bPic_CO32_mom0_fullpixsize.pdf} \vspace{-10mm} \end{subfigure} \caption{CO J=2-1 and J=3-2 spectrally integrated (moment-0) CLEAN images of the $\beta$ Pic disk, at their original synthesized resolution (natural weighting). The images have been rotated by the position angle of the main disk observed in scattered light (29.3$^{\circ}$). This way, we can define the $x_{\rm sky}$ axis as the direction along the disk on-sky midplane (positive towards the SW), and the $y_{\rm sky}$ axis as the direction perpendicular to it (positive towards the NW). The origin of the axis is set to the stellar location, and the restoring beam is shown as the yellow ellipse in the bottom left corner.} \label{fig:mom0} \end{figure*} \section[]{Results} \label{sect:res} Fig.\ \ref{fig:mom0} shows CO J=2-1 and J=3-2 moment-0 CLEAN images of the $\beta$ Pictoris disk at their original spatial resolution, obtained by spectrally integrating over heliocentric velocities between 14 and 26 km/s ($\pm 6$ km/s in the reference frame of the star). The 1-$\sigma$ noise levels on the moment-0 images are 2.7 and 24 $\times$10$^{-23}$ W m$^{-2}$ beam$^{-1}$ (or 3.5 and 21 mJy km/s), respectively, yielding a peak detection of CO integrated line emission at a SNR per beam of 17 and 21 for the 2-1 and 3-2 transitions, respectively. The total line flux was measured on the primary-beam-corrected moment-0 images by spatially integrating over a region that contains all significant disk emission, but small enough to avoid significant noise contamination. The integrated fluxes measured are $(3.5\pm0.4) \times10^{-20}$ W m$^{-2}$ for the J=2-1 transition, and $(6.7\pm0.7) \times 10^{-20}$ W m$^{-2}$ for the J=3-2 transition, indicating an integrated 3-2/2-1 line ratio of $1.9\pm0.3$. Absolute errors on integrated line fluxes take into account both the noise level in the moment-0 images and the flux calibration uncertainty; we then summed the relative errors on both fluxes in quadrature (under the assumption that they are Gaussian in nature) to obtain the uncertainty on the line ratio. \subsection{Spectrally-integrated radial structure} \begin{figure} \begin{subfigure}{0.45\textwidth} \hspace{-4mm} \includegraphics*[scale=0.27]{radprofspy.pdf} \vspace{-5mm} \end{subfigure} \caption{Radial distribution of CO line flux obtained from spatially integrating the moment-0 images in Fig.\ \ref{fig:mom0} along the perpendicular to the main disk midplane $y_{\rm sky}$, where $\left|y_{\rm sky}\right|<20$ AU. In order to highlight differences in the projected radial structure between the two datasets, the profile for each image was normalised to its maximum.} \label{fig:mom0prof} \end{figure} In Fig.\ \ref{fig:mom0prof} we present the radial profile of CO emission along the $\beta$ Pic disk midplane ($x_{\rm sky}$ axis in Fig.\ \ref{fig:mom0}). This was derived from the moment-0 images by vertically integrating disk emission from pixels within $\pm$20 AU from the midplane (i.e. with $\left|y_{\rm sky}\right|<20$ AU). The J=2-1 dataset confirms the presence of a clump of CO on the SW side of the disk \citep[previously discovered in J=3-2 by][]{Dent2014} at a projected separation of 60 AU from the star, and faint J=2-1 emission detected out to larger distances on the NE side than J=3-2 emission, which will become even clearer when looking at the CO velocity structure (Sect. \ref{sect:velstruct}). This is attributable to both the lower sensitivity of the Band 7 dataset, but also to an intrinsic decrease in the J=3-2/J=2-1 line ratio at increasing disk radii. \subsection{Spectrally-integrated vertical structure} \label{vertstruct} \begin{figure*} \begin{subfigure}{0.45\textwidth} \vspace{-3mm} \hspace{-9mm} \includegraphics[scale=0.44]{profwidth21_mcmc.pdf} \vspace{-2mm} \end{subfigure} \begin{subfigure}{0.45\textwidth} \vspace{-3mm} \hspace{-2mm} \includegraphics[scale=0.44]{profwidth32_mcmc.pdf} \vspace{-2mm} \end{subfigure} \\ \begin{subfigure}{0.45\textwidth} \vspace{-3mm} \hspace{-7mm} \includegraphics[scale=0.43]{vertprof_21_mcmc.pdf} \vspace{-2mm} \end{subfigure} \begin{subfigure}{0.45\textwidth} \vspace{-3mm} \hspace{0mm} \includegraphics[scale=0.43]{vertprof_32_mcmc.pdf} \vspace{-2mm} \end{subfigure} \\ \begin{subfigure}{0.45\textwidth} \vspace{-10mm} \hspace{-7mm} \includegraphics*[scale=0.43]{stdev_21_mcmc.pdf} \vspace{-2mm} \end{subfigure} \begin{subfigure}{0.45\textwidth} \vspace{-10mm} \hspace{0mm} \includegraphics*[scale=0.43]{stdev_32_mcmc.pdf} \vspace{-2mm} \end{subfigure} \caption{Vertical structure of the CO disk for the J=2-1 line (blue, left column) and the J=3-2 line (red, right column), from the moment-0 images (Fig. \ref{fig:mom0}). \textit{Top:} Fitting procedure to the disk's vertical emission profiles as a function of distance along the midplane. Coloured lines represent the measured flux as a function of distance along the vertical ($y_{\rm sky}$) axis for different midplane locations $x_{\rm sky}$. The black dashed lines are the best-fits derived, whereas the green dashed lines (as well as the filled ellipses) represent the instrumental resolution, centred on the best-fit Gaussian peaks $y_{\rm obs}$. \textit{Centre:} Disk spine, i.e. the vertical offset of Gaussian fits $y_{\rm obs}$ from the top panel as a function of midplane location $x_{\rm sky}$. The green crosses represent the same spine derived for the dust emission from HST observations \citep{Apai2015}. \textit{Bottom:} Scale height $H$ as a function of distance along the midplane, derived from the standard deviation $\sigma_{\rm obs}$ of best-fit Gaussians in the top panel.} \label{fig:vertprofs} \end{figure*} In order to probe the vertical structure in the disk, we analyse its \textit{spine}, which we define as the locus of the centres of best-fit vertical Gaussians measured at different locations along the disk midplane. We remind the reader that the disk images shown in Fig.\ \ref{fig:mom0} have been rotated by the position angle (PA) of the main disk observed in scattered light, corresponding to 29\fdg3$^{+0.2}_{-0.3}$ \citep{Lagrange2012}. In scattered light, this differs from the PA of the inner part of the disk, which appears tilted when compared to the main disk observed in the outer regions \citep[e.g.][]{Apai2015}. Fig.\ \ref{fig:vertprofs} (top row) illustrates the procedure employed. We apply vertical cuts in the $y_{\rm sky}$ direction for each location $x_{\rm sky}$ along the midplane where emission greater than 5$\sigma$ is detected. The measured (normalised) flux versus $y_{\rm sky}$ is shown as red and blue solid lines. The green dashed Gaussian profiles have width equal to the FWHM of the restoring beam projected onto the $y_{\rm sky}$ direction (11.4 and 5.7 AU for J=3-2 and J=2-1, respectively), and indicate that the disk is resolved vertically for both CO lines. We then employ 1D Gaussians to fit the vertical profiles and obtain the observed best-fit vertical location of the Gaussian peak, which we define as $y_{\rm obs}$ (see fitting procedure and error determination in Appendix \ref{app:2}). Repeating the process at several midplane locations yields the locus of vertical Gaussian centres $y_{\rm obs}$ at different $x_{\rm sky}$ locations, i.e. the disk spine. This appears significantly tilted with respect to the PA of the main disk midplane, presenting an extra anticlockwise rotation \citep[as was noted by][]{Dent2014} by a tilt angle dPA. The latter is similar to the tilt angle observed for the scattered light inner disk \citep[$\sim$4$^{\circ}$,][]{Apai2015}, and is most pronounced at the location of the clump. Accurate measurement of the true warp angle from this sky-projected tilt is challenging. To begin with, the disk spines derived from both CO and scattered light are not well represented by a straight line, meaning that measurement of the sky-projected tilt itself is highly sensitive to the disk radii between which the straight line is drawn. Secondly, even assuming a perfectly edge-on disk, there is no reason to believe that the warp axis lies in the plane of the sky; any azimuthal displacement of the warp axis in the orbital plane would cause a substantial difference between the true warp angle and the observed projected sky tilt. To further investigate any potential azimuthal dependence on this tilt, we repeat the same analysis as a function of radial velocity in Sect. \ref{sect: structedgeon}. As well as the vertical displacement from the midplane, the same Gaussian fits on the moment-0 images yield vertical standard deviations $\sigma_{\rm obs}$ as a function of midplane location. Assuming that the disk is edge-on and that its true vertical structure can be represented by a Gaussian (of standard deviation defined as the scale height $H$), we can derive $H$ by simply deconvolving $\sigma_{\rm obs}$ by the observed instrumental resolution projected along the vertical axis, i.e. $H=\sqrt{\sigma_{\rm obs}^2 -\sigma_{\rm res}^2}$. The resulting scale height as a function of midplane location is shown in the bottom row of Fig. \ref{fig:vertprofs}. Given the near edge-on geometry of the disk, its rather flat appearance is unsurprising, as the scale height observed on-sky at any midplane location will tend to trace the scale height at the disk's orbital outer radius. As such, in Sect. \ref{sect: structedgeon} we add the velocity information from the data cube to retrieve the scale height dependence on the orbital radius and explore its relation to the disk temperature. \subsection{Velocity information} \label{sect:velstruct} In order to understand the 3D gas disk kinematics and extract its vertical and azimuthal structure, we analyse the CO dataset through position-velocity (PV) diagrams, i.e. maps of different quantities as a function of both position along the disk midplane ($x_{\rm sky}$ axis in Fig. \ref{fig:mom0}) and radial velocity $v_{\rm rad}$. In particular, we aim to link the $\left(x_{\rm sky}, v_{\rm rad}\right)$ PV location in these diagrams to a $\left(x,y\right)$ location in the orbital plane of the disk. This can be done for a given inclination $i$ if we assume that the gas disk is infinitely thin vertically and in Keplerian rotation (see Appendix \ref{app:1} for details). In Sect. \ref{sect: structedgeon}, we begin by analysing the sky-projected vertical structure along $y_{\rm sky}$ in PV space to derive constraints on the disk vertical and azimuthal structure, assuming a perfectly edge-on disk ($i=90^{\circ}$). In Sect. \ref{sect: structnonedgeon}, on the other hand, we interpret the same sky-projected vertical structure along $y_{\rm sky}$ in PV space purely as azimuthal structure for a disk close to, but not perfectly edge-on ($i<90^{\circ}$). Finally, in Sect. \ref{sect:reslinerat} we carry out a PV diagram comparison between the new CO J=2-1 and the archival J=3-2 dataset. \subsubsection{CO 3D structure in the edge-on assumption} \label{sect: structedgeon} In Fig.\ \ref{fig:pvs}, we show PV diagrams of CO J=3-2 and J=2-1 line flux obtained by integrating emission vertically (i.e. along the $y_{\rm sky}$ axis in Fig. \ref{fig:mom0}) within 20 AU above and below the disk midplane, including all significant disk emission. The spectro-spatial resolution is given by the projection of the restoring beam along the disk midplane $x_{\rm sky}$, combined with the velocity resolution along $v_{\rm rad}$. \begin{figure} \begin{subfigure}{0.47\textwidth} \vspace{-8mm} \hspace{-15mm} \includegraphics*[scale=0.56]{bPic_CO21_pv_fullres.pdf} \vspace{0mm} \end{subfigure} \\ \begin{subfigure}{0.47\textwidth} \vspace{-23.8mm} \hspace{-15mm} \includegraphics*[scale=0.56]{bPic_CO32_pv_fullpixsize.pdf} \vspace{0.0mm} \end{subfigure} \vspace{-7mm} \caption{Position-velocity (PV) diagrams of the $\beta$ Pic disk, showing CO intensity as a function of position along the disk on-sky midplane $x_{\rm sky}$ and radial velocity $v_{\rm rad}$ for each of the two transitions observed. The black asterisk represents the stellar position, while the solid white curves are the maximum radial velocity observable in an edge-on Keplerian disk around a 1.75 M$_{\odot}$ star. The yellow rectangle in the bottom left corner represents the spectro-spatial resolution. The dashed white lines represent different radii $R$ in the orbital plane of the disk, assuming Keplerian rotation (see Appendix \ref{app:1}).} \label{fig:pvs} \end{figure} The two CO transitions show similar PV structure, consistent with a near edge-on gas disk in Keplerian rotation around a 1.75 M$_{\odot}$ star \citep{Crifo1997}. Diagonal lines on the diagrams represent different radii $R$ in the orbital plane of the disk (Appendix \ref{app:1}), which we here assume to be perfectly edge-on; we can use this to constrain the disk's radial extent in the orbital plane to between $\sim$50 and $\sim$220 AU. For both transitions, two flux enhancements are observed; one in the resolved SW clump, approaching us at a velocity $v_{\rm rad}$ between 3 and 4 km/s and sky-projected midplane location $x_{\rm sky}$ between 60 and 90 AU. The other enhancement, less pronounced, is found around the projected stellar location and radial velocity $\left(x_{\rm sky},v_{\rm rad}\right)\sim\left(0,0\right)$. As the latter is not observed towards the star in the moment-0 images, it is likely due to the larger disk volume per velocity channel probed at low compared to higher radial velocities. Another difference lies in the NE side of the disk, where there is a clear deficit of J=3-2 compared to J=2-1 emission at large radii and low radial velocities (Fig.\ \ref{fig:pvs}). This suggests that J=2-1 emission is detected extending further out in the disk on the NE side compared to J=3-2 emission. As mentioned above (again, see Appendix \ref{app:1} for details), for a disk in circular Keplerian rotation, each PV location (i.e. each $\left(x_{\rm sky},v_{\rm rad}\right)$ \textit{spaxel}) in the diagram corresponds to a radius $R$ and hence an $\left(x,\pm y\right)$ location in the orbital plane of the disk. The degeneracy in the sign of $y$, however, means that each spaxel traces two orbital locations, $\left(x, +y\right)$ and $\left(x, -y\right)$. Thus, we do not know how much flux belongs to either of the two locations; we only know that the sum of the two fluxes must equal that of the original spaxel. This leads to an infinite number of possible deprojections; Fig.\ \ref{fig:deprojectpvs} shows the two that are most likely physically plausible, as justified by dynamical models \citep[see Sect. \ref{sect:rescl} and][]{Dent2014}. We obtained these by placing \textit{all} of the spaxel emission in the NE side (negative $x_{\rm sky}$) at $-y$ (i.e. in front of the sky plane) and that in the SW (positive $x_{\rm sky}$) at either $+y$ (i.e. behind the sky plane, left column in Fig.\ \ref{fig:deprojectpvs}) or $-y$ (right column in Fig.\ \ref{fig:deprojectpvs}). The direction of rotation is known to be clockwise from the sign of the observed radial velocity. The central $\pm$30 AU from the star are masked as our spectro-spatial resolution is not sufficient to determine orbital locations accurately. \begin{figure*} \begin{subfigure}{0.45\textwidth} \vspace{-7mm} \hspace{-17mm} \includegraphics*[scale=0.52]{imdeconvolvedpv1_21} \vspace{-2mm} \end{subfigure} \begin{subfigure}{0.45\textwidth} \vspace{-7mm} \hspace{-3mm} \includegraphics*[scale=0.52]{imdeconvolvedpv3_21} \vspace{-2mm} \end{subfigure} \\ \begin{subfigure}{0.45\textwidth} \vspace{-18.5mm} \hspace{-17mm} \includegraphics*[scale=0.52]{imdeconvolvedpv1_32} \vspace{-2mm} \end{subfigure} \begin{subfigure}{0.45\textwidth} \vspace{-18.5mm} \hspace{-3mm} \includegraphics*[scale=0.52]{imdeconvolvedpv3_32} \vspace{-2mm} \end{subfigure} \vspace{-3mm} \caption{CO emission in the $\left(x, y\right)$ orbital plane of the disk, derived from the $\left(x_{\rm sky}, v_{\rm rad}\right)$ information in the PV diagrams for the J=2-1 transition (top) and for the J=3-2 transition (bottom), under the assumption of a perfectly edge-on disk. The two columns represent two plausible deprojections of the PV diagrams, justified by the dynamical scenarios proposed in \citet{Dent2014}. The asterisk represents the location of the star, with the inner and outer dashed circles representing deprojected radii of 50 and 220 AU. The 'fishbone' appearance is caused by the finite velocity resolution of the dataset, with any radial velocity tracing a characteristic curve in the displayed $\left(x, y\right)$ space. The central $\pm$30 AU have been masked due to all $y$ locations approaching zero radial velocity along the line of sight to the star, rendering the deprojection highly degenerate.} \label{fig:deprojectpvs} \end{figure*} These deprojected images of CO J=3-2 and J=2-1 line emission reveal the azimuthal structure of the disk; on the SW side, the clump peaks at $\phi\sim\pm32^{\circ}$ (measured from the positive $x_{\rm sky}$ direction), with a tail of emission extending to either the front or the back of the star along the line of sight direction. Depending on the system configuration, emission on the NE side can be interpreted either as the continuation of the tail originating from the SW clump (right column), or as a separate dimmer clump at $\phi\sim+212^{\circ}$ with its own tail also extending into the line of sight to the star (left column). In Section \ref{vertstruct} we analysed the spectrally-integrated disk vertical structure along $y_{\rm sky}$ as a function of position along the disk midplane $x_{\rm sky}$. Given our velocity information, however, it is more insightful to measure the disk spine and width separately for each of the radial velocities $v_{\rm rad}$ at which the disk is detected, using the same procedure as outlined in Appendix \ref{app:2}. This yields a measurement of the sky-projected scale height $H$ and of the disk vertical offset from the main disk midplane $y_{\rm obs}$ as a function of position along the midplane $x_{\rm sky}$ and radial velocity $v_{\rm rad}$. In other words, we obtain a PV diagram (shown for the J=2-1 transition in Fig. \ref{fig:pvvert}). \begin{figure} \begin{subfigure}{0.47\textwidth} \vspace{-2mm} \hspace{-12mm} \includegraphics*[scale=0.35]{vertoffsPV.png} \vspace{0mm} \end{subfigure} \\ \begin{subfigure}{0.47\textwidth} \vspace{-13mm} \hspace{-12mm} \includegraphics*[scale=0.35]{scaleheightPV.png} \vspace{0.0mm} \end{subfigure} \vspace{-5mm} \caption{Position-velocity diagrams of both the CO J=2-1 disk vertical offset $y_{\rm obs}$ with respect to the main dust disk (\textit{top}) and of the disk scale height $H$ (\textit{bottom}), for an assumed perfectly edge-on disk. These measurements were obtained through Gaussian fitting of measured fluxes along cuts perpendicular to the disk midplane (as displayed in Fig. \ref{fig:vertprofs}) repeated for each radial velocity channel.} \label{fig:pvvert} \end{figure} The anti-clockwise tilt (dPA=PA$_{\rm obs}$-PA$_{\rm main\ disk}$) observed in the moment-0 images (Fig. \ref{fig:vertprofs}) is also present throughout the radial velocity channels, with CO at negative radial velocities (SW) being vertically displaced above CO at positive velocities (NE). Some substructure is observed, with an enhanced vertical displacement at low radial velocities (hence large orbital radii) on the NE side, and a decreased displacement at high radial velocities (hence small orbital radii) on the SW side. In addition, a positive vertical offset of disk emission along the line of sight to the star (enhanced at positive velocities) is present. These local features are marginally significant at the typical 0.5-1 AU 1$\sigma$ uncertainty on vertical offsets in each spaxel; their interpretation in terms of a putative 3D warp structure requires detailed dynamical modelling, and is beyond the scope of this work. The scale height also presents significant PV structure in the form of a gradient from low values at high radial velocities to high values at lower radial velocities (Fig. \ref{fig:pvvert}, bottom). For the assumed perfectly edge-on configuration, and given that assuming Keplerian rotation different diagonal lines represent different orbital radii, this gradient is representative of an increase in the disk scale height as a function of orbital radius. Indeed, if we assign an orbital radius $R$ to each PV location (Appendix \ref{app:1}) and assume the disk scale height to be azimuthally symmetric, in Fig. \ref{fig:vert1D} (top) we show that the scale height $H$ scales as \begin{equation} H=7.0^{+0.6}_{-0.6} \times \left(\frac{R}{85 \rm AU}\right)^{0.75^{+0.02}_{-0.02}}. \end{equation} The error bars (1$\sigma$) in Fig. \ref{fig:vert1D} (top) represent the uncertainty in the derivation of both the scale height $H$ and the orbital radius $R$. The error on the scale height was calculated from MCMC fits as described in Appendix \ref{app:2}, whereas the error on the orbital radius $R$ was propagated from the uncertainty on the PV location (assumed to be equal to the size of a spaxel). Assuming the CO disk to be vertically isothermal and in hydrostatic equilibrium, the scale height can then be used to trace the disk temperature at a certain orbital radius through $T=\frac{GM_{\ast}\mu}{kN_A} \frac{H^2}{R^3}$, where $G$ is the gravitational constant, $M_{\ast}$ is the mass of the star, $\mu$ is the mean molecular mass of the gas, $k$ is Boltzmann's constant, and $N_A$ is Avogadro's number. We here assume the gas to be dominated by the carbon and oxygen atoms released from CO photodissociation, giving a mean molecular mass $\mu=14$ (see Sect. \ref{sect:atomdom}). \begin{figure} \begin{subfigure}{0.47\textwidth} \vspace{-2mm} \hspace{-2mm} \includegraphics*[scale=0.29]{scaleheightvsrad.png} \vspace{0mm} \end{subfigure} \\ \begin{subfigure}{0.47\textwidth} \vspace{-11.7mm} \hspace{-2mm} \includegraphics*[scale=0.29]{tempvsrad.png} \vspace{0.0mm} \end{subfigure} \vspace{-5mm} \caption{\textit{Top:} Measured dependence of the CO disk scale height on orbital radius, derived from the PV diagrams in Fig. \ref{fig:pvvert} (bottom) assuming Keplerian rotation. Each point corresponds to a spaxel in the J=2-1 PV diagram. \textit{Bottom:} Radial dependence of the temperature derived from the scale height under the assumption of a vertically isothermal disk. In both plots, the red lines are constructed by randomly picking 1000 values of our fitting parameters (intercept and slope in log-log space) from their joint posterior probability distribution. The best-fit power law coefficients are displayed in the top right of the diagrams, with their respective 1$\sigma$ uncertainties. The blue lines represent model predictions by \citet{Kral2016a}.} \label{fig:vert1D} \end{figure} We can then use our measured dependence of the scale height on radius to derive the radial dependence of the gas temperature in the $\beta$ Pic disk (Fig. \ref{fig:vert1D}, bottom). This decreases as a function of radius, scaling as \begin{equation} T=\left(2.1^{+0.4}_{-0.4} \times 10^{2}\right) \times \left(\frac{R}{85 \rm AU}\right)^{-1.58} \end{equation} where $T$ is in K and $R$ is in AU. No temperature increase/decrease is seen at the clump location compared to the rest of the disk, which is in line with the expectation that the CO, after release, should quickly collide and couple to the rest of the atomic disk (again, see discussion in Sect. \ref{sect:atomdom}). \subsubsection{CO 3D structure for a non-edge-on configuration} \label{sect: structnonedgeon} In the previous section, we neglected a potential deviation of the disk inclination from perfectly edge-on, which has been proposed before through modelling observations of optical and near-IR scattered light from the dust disk \citep[e.g.][]{Ahmic2009, Milli2014}. If the disk is inclined from edge-on, the vertical structure becomes coupled with the azimuthal structure. On one hand, this means that our derivation of the disk scale height and temperature in the previous section may be in part biased by the edge-on assumption. On the other hand, we can interpret the vertical displacement $y_{\rm obs}$ of the disk from the midplane (i.e. the disk spine) purely as an effect of azimuthal structure seen at an inclination $i<90^{\circ}$. Using the observed vertical displacement $y_{\rm obs}$ measured at each PV location $\left(x_{\rm sky},v_{\rm rad}\right)$ (see Fig. \ref{fig:pvvert} top) we can determine whether CO emission originates in front or behind the plane of the sky (i.e. at $+$ or $-y$ in Fig. \ref{fig:deprojectpvs}). This is because for a given orbit, characterised here by its inclination from face-on $i$ and its on-sky tilt angle dPA, an on-sky location $\left(x_{\rm sky, orb}, +y_{\rm sky, orb}\right)$ at radial velocity $v_{\rm rad}$ will correspond to either orbital location $\left(x, +y\right)$ behind the sky plane or $\left(x, -y\right)$ in front of the sky plane. Then, in the presence of a $\pm y$ asymmetry in the orbital plane of the disk, the flux contribution from the two on-sky vertical locations $+y_{\rm sky, orb}$ and $-y_{\rm sky, orb}$ will differ and the vertical centroid $y_{\rm obs}$ of the CO emission will be displaced from the midplane. As described in Appendix \ref{app:4}, we use this vertical displacement to infer the level of CO emission originating from $\left(x_{\rm sky, orb}, +y_{\rm sky, orb}\right)$ as opposed to $\left(x_{\rm sky, orb}, -y_{\rm sky, orb}\right)$ in the sky plane. A degeneracy remains in that we do not know which between $+y_{\rm sky, orb}$ and $-y_{\rm sky, orb}$ is in front or behind the plane of the sky. This may be solved using scattered light imaging, since material in front of the star will appear brighter than behind the star, owing to the phase function of the grains being peaked towards and hence favouring forward-scattering angles \citep[e.g.][]{Milli2015}. For $\beta$ Pictoris, scattered light emission above the midplane is seen to be brighter than below the midplane \citep[e.g.][]{Golimowski2006}; that suggests that dust at $+y_{\rm sky}$ lies preferentially in front of the star, whereas dust at $-y_{\rm sky}$ is located behind the star. However, this does not take into account that in the presence of an azimuthal asymmetry there may be an excess of material above the midplane, which would affect the above argument by leading us into interpreting the observed flux excess as a phase function effect. As the method produces a model data cube for a given orbit, we can compare different orbits and hence find how well different $\left(i, \rm dPA\right)$ combinations fit the data (see Appendix \ref{app:4} and $\chi^2$ map in Fig. \ref{fig:chisqmap}). We note once again that this approach does not take into account any intrinsic disk vertical structure (and in particular its dependence on orbital radius) nor any uncertainty in the determination of the vertical displacement $y_{\rm obs}$ from the on-sky midplane. Keeping this in mind, we find that the formal best-fit (i.e. the $\chi^2$ minimum) is at $i\sim88^{\circ}$ and dPA $\sim3^{\circ}$, though we consider all inclinations $\geq86^{\circ}$ and on-sky tilt angles $\leq5^{\circ}$ to provide reasonable fits. \begin{figure} \begin{subfigure}{0.45\textwidth} \vspace{-2mm} \hspace{-2mm} \includegraphics*[scale=0.40]{newdeproj_i88_extrapa3_noshift.pdf} \end{subfigure} \\ \begin{subfigure}{0.45\textwidth} \vspace{-0mm} \hspace{-2mm} \includegraphics*[scale=0.40]{newdeproj_i86_extrapa0_noshift.pdf} \end{subfigure} \caption{Face-on deprojection of CO disk emission, derived from the velocity information in the PV diagrams for the J=2-1 transition, for two cases of disk inclination $i$ and on-sky tilt angle dPA. Flux at each $x$ location has been divided between + and -$y$ locations in the orbital plane displayed here using the vertical displacement $y_{\rm obs}$ of disk emission in the plane of the sky (Fig. \ref{fig:pvvert}, top), using the method described in Appendix \ref{app:4}. Though the $\left(i,\rm dPA\right)$ choice for the deprojection in the top panel is formally the best-fitting in the framework of our simple model (see main text for details), the image in the bottom panel reproduces well the expected morphology from resonant trapping of planetesimals due to an outward migrating planet.} \label{fig:extradeproj} \end{figure} Of course, for any choice of $\left(i, \rm dPA\right)$, we can use our method to produce a map of emission in the orbital plane of the disk, as we now have determined what fraction of emission belongs to $+y$ and to $-y$ for a given $x$. Fig. \ref{fig:extradeproj} shows two examples, for our formal best-fit orbit ($i=88^{\circ}$, dPA = $3^{\circ}$) and in the case of a lower inclination ($i=86^{\circ}$) and no on-sky tilt (dPA $=0^{\circ}$). We report two main findings: \begin{itemize} \item The majority of the flux from the CO clump on the SW side of the disk is located above the sky-projected disk midplane for any reasonable choice of $i$ ($\geq 86$) and dPA ($<5^{\circ}$). This confirms that the flux in the sky-projected clump does originate from a physical clump, located either behind or ahead of the sky plane (due to the aforementioned degeneracy). \item The disk deprojection obtained for a lower inclination of $86^{\circ}$ and no dPA qualitatively reproduces well the resonance sweeping scenario proposed in \citet{Dent2014} and based on previous work by \citet{Wyatt2003, Wyatt2006}, with two clumps on opposite sides of the star and their respective trailing tails (see discussion in Sect. \ref{sect:rescl}). Further 3D modelling taking into account at the same time the disk vertical and azimuthal structure as well as its geometry is needed to rule out or confirm this possibility. \end{itemize} \subsubsection{CO 3-2/2-1 line ratio} \label{sect:reslinerat} In order to better investigate morphological differences between the two transitions, we combined the J=2-1 and J=3-2 PV diagrams to obtain line ratios in each position-velocity spaxel. As such ratios can be extreme in noise-dominated regions, we facilitate visualisation by only displaying ratios in spaxels where either CO J=3-2 and J=2-1 emission is over 4$\sigma$ (where $\sigma$ is the RMS noise level measured in each PV diagram). A detection at 3-2 but only an upper limit at 2-1 will then lead to a lower limit on the line ratio, and conversely a detection at 2-1 but not at 3-2 will lead to an upper limit on the ratio. Such line ratio PV diagram is shown in Fig.\ \ref{fig:pvratios} (left), with the corresponding uncertainty diagram in Fig.\ \ref{fig:pvratios} (right). At each spaxel, the uncertainty is the quadratic sum of the relative errors on the flux for the two original PV diagrams, where these are given by the RMS levels. We here do not take into account the 10\% flux calibration error on each dataset, since we are here most interested in the presence of gradients rather than in the absolute value of the ratios. \begin{figure*} \begin{subfigure}{0.45\textwidth} \hspace{-24mm} \includegraphics*[scale=0.57]{ratio_imcopv_sav.pdf} \vspace{0mm} \end{subfigure} \begin{subfigure}{0.45\textwidth} \hspace{-8mm} \includegraphics*[scale=0.57]{ratio_imcopverr_sav.pdf} \vspace{0mm} \end{subfigure} \vspace{-5mm} \caption{\textit{Left:} CO J=3-2/J=2-1 line ratio position-velocity diagram of the $\beta$ Pic disk. Only spaxels where \textit{either} CO transition is detected (at $\ge$4 $\sigma$) are shown; downward arrows indicate spaxels where only the J=2-1 transition was detected. The white asterisk represents the stellar position and velocity, while the solid white curves are the maximum radial velocity observable in an edge-on Keplerian disk around a 1.75 M$_{\odot}$ star. The yellow rectangle in the bottom left corner represents the spectro-spatial resolution. \textit{Right:} Percentage error map of the line ratio PV diagram, where this can only be quantified in spaxels where \textit{both} transitions are detected.} \label{fig:pvratios} \end{figure*} The line ratio PV diagram shows a noticeably different structure to the flux PV diagrams for the individual transitions in Fig.\ \ref{fig:pvs}. In particular, the line ratio shows no evidence of the CO clump nor the NE/SW asymmetry. On the other hand, it shows a significant gradient where the line ratio is seen increasing from low values at low radial velocities to high values at high radial velocities, for any given on-sky midplane location. On the NE side, where individual line fluxes are generally dimmer than in the SW side (see Fig.\ \ref{fig:pvs}), this causes a non-detection of the 3-2 line at low velocities (as illustrated through the upper limits on the ratios). This then explains the differences between the two lines that were already apparent from the individual moment-0 images and PV diagrams (Fig.\ \ref{fig:mom0} and \ref{fig:pvs}), with 2-1 emission lying at larger projected radii than the 3-2 line on the NE side of the disk. The physical significance of this gradient is explored through modelling in Sect. \ref{sect:mod} below. \section[]{Line ratio modelling} \label{sect:mod} Through detailed analysis of resolved ALMA CO J=3-2 and CO J=2-1 line observations, we unveiled the radial, vertical and azimuthal structure of CO line emission in the $\beta$ Pictoris disk. Under the assumption that the system is viewed perfectly edge-on, we interpreted the scale height observed as a function of orbital radius to give us an estimate for the temperature of the gas and its radial dependence. We then relaxed the edge-on assumption and interpreted the observed vertical structure as solely caused by azimuthal structure, in order to break the degeneracy in deprojecting PV diagrams to the disk orbital plane. Finally, we analysed the CO 3-2/2-1 line ratio PV diagram and discovered a significant gradient with the ratio increasing with radial velocity at any given midplane location. In this section, we aim to use the non-local thermodynamic equilibrium (NLTE) analysis of CO excitation developed in \citet{Matra2015} to interpret these line observations (particularly resolved line ratios) in terms of the physical conditions, origin and mass of CO in the $\beta$ Pic disk. \subsection{Second generation: NLTE line ratios as a probe for electron densities} \label{modelec} We begin by assuming CO line emission to be optically thin at the wavelengths of the observed transitions, and double-check this assumption later in Sect. \ref{sect:optthick}. In this regime, CO excitation and hence line ratios are only dependent on the kinetic temperature $T_{\rm k}$ and the collisional partner density $n_{\rm coll}$, for the known external millimetre radiation field $J_{\nu}$ at the frequency of the transitions in question. In a scenario where the gas is of second-generation origin, the dominant collisional partners for which collisional rates are available are electrons, which originate from the photoionisation of atoms created by rapid CO photodissociation. In the absence of H$_2$, electrons are more efficient colliders than H$_2$O \citep{Matra2015}, but also \ion{H}{I}, since the latter, despite being potentially $\sim$6 times more abundant than electrons \citep{Kral2016a}, is on average a much less efficient collider. For example, collisional de-excitation of a CO molecule from rotational level 3 to 2, for the given \ion{H}{I}/e$^-$ abundance of 6 happens at a rate that is $(\gamma_{3-2, \ion{H}{I}} n_{\ion{H}{I}}) / (\gamma_{3-2, e^-} n_{\rm e^-}) \sim 50$ times faster for electron collisions than for \ion{H}{I} collisions\footnote{Collisional rate coefficients $\gamma$ were obtained from \citet{Dickinson1975} for electrons and from \citet{Walker2015} for \ion{H}{I}}. Nonetheless, it is useful to keep in mind that other less dominant species may contribute to observed CO collisional excitation, which implies that the electron densities probed here should strictly speaking be considered upper limits. \begin{figure} \begin{subfigure}{0.47\textwidth} \vspace{-4mm} \hspace{-5mm} \includegraphics*[scale=0.45]{ratiotkncollelect.pdf} \vspace{0.0mm} \end{subfigure} \\ \begin{subfigure}{0.47\textwidth} \vspace{-4.7mm} \hspace{-5mm} \includegraphics*[scale=0.45]{ratiotkncollH2.pdf} \vspace{0.0mm} \end{subfigure} \vspace{-4mm} \caption{Colour maps of the J=3-2/2-1 line ratio expected in an optically thin disk as a function of the density of the dominant collider species and the kinetic temperature of the gas. The dominant collider species is electrons in a secondary origin scenario (top), and H$_2$ in a primordial origin scenario (bottom). Contours represent minimum and $90^{\rm th}$ percentile values observed in our ratio PV diagram (Fig.\ \ref{fig:pvratios})} \vspace{-6 mm} \label{fig:ratiotkncoll} \end{figure} Fig. \ref{fig:ratiotkncoll} (top) shows the J=3-2 / J=2-1 line ratios expected for CO that is excited by collisions with electrons and by millimetre radiation from the cosmic microwave background (CMB, which dominates over the dust continuum for low CO transitions), as a function of the electron density $n_{\rm e^-}$ and the gas kinetic temperature $T_{\rm k}$. Each ratio traces a line in $\left(T_{\rm k}, n_{\rm e^-}\right)$ space, since these are the only free parameters. For $n_{\rm e^-}$, we explore the parameter space between 10$^{-1}$ and 10$^{6}$ cm$^{-3}$, encompassing the transition between the two limiting excitation regimes \citep[LTE and radiation-dominated,][]{Matra2015}. For the kinetic temperature of the gas, we probe a broad range of $T_{\rm k}$ between 5 and 2000 K to illustrate the behaviour of the line ratios. Its true value depends on the detailed balance between local heating and cooling processes in the gas disk. Our temperature estimates from the CO scale height (Sect. \ref{sect: structedgeon}) suggest values between 40 and a few hundred K between 50 and 200 AU, whereas detailed thermodynamical modelling of the disk suggests values between 30 and 80K at the same radii \citep{Kral2016a}. In any case, we expect the gas kinetic temperature to be above a few tens of K throughout the disk. These predictions can then be compared with our measurements, tracing lines overplotted on Fig. \ref{fig:ratiotkncoll} (top). Above kinetic temperatures of $\sim$30 K, the vast majority (up to $\sim$90$^{\rm th}$ percentile) of the line ratios observed in the $\beta$ Pic disk (from spaxel values in Fig. \ref{fig:pvratios}) are very good probes of the electron density, being largely independent of the choice of kinetic temperature. On the other hand, if the electron densities were high enough for CO to reach local thermodynamic equilibrium (LTE, right edge of the colour map), the line ratios would be higher and become solely dependent on the kinetic temperature. While a unique solution for $T_{\rm k}$ and $n_{\rm e^-}$ is only obtainable with two (or more) line ratios, our measurements can confidently constrain the electron density in the disk to around $10^2$-$10^3$ cm$^{-3}$. This allows us to attribute the gradient of increasing CO line ratio with radial velocity observed in the PV diagrams (Fig. \ref{fig:pvratios}, left) to the electron density distribution in the disk. Since we want to measure the electron density as robustly as possible, we mask the highest 10\% of the line ratios (i.e. those above 3.80), which arise preferentially from high-noise regions of the PV diagram, and have a stronger kinetic temperature dependence. For the remaining line ratios, this temperature dependence is much weaker, so any assumption we make is not going to affect the result significantly. As such, we assume the temperature radial profile predicted by \citet{Kral2016a}, i.e. a power law with slope of $-0.8$, normalised to a value of 80 K at 50 AU. Using the temperature radial profile derived from our scale height measurement in Fig. \ref{fig:vert1D} (bottom) yields analogous results. Each location in the PV diagram traces a certain orbital radius within the disk (Appendix \ref{app:1}). This way, we can solve for the radial dependence of the electron density, which is shown in Fig.\ \ref{fig:neradial}, left. The uncertainty on $n_{\rm e^-}$ was propagated from that of the line ratio, assuming a perfectly known $T_{\rm k}$ from the models; the uncertainty on the radius, on the other hand, was calculated from the uncertainty in the $\left(x_{\rm sky}, v_{\rm rad}\right)$ location within a spaxel in the PV diagram. Since we are most interested in the radial dependence rather than on the absolute value of the electron density, we have not included sources of systematic error that may shift $all$ of the observational points in our plot (e.g. an error on $M_{\ast}$ or $i$ may cause an overall shift in the radial direction, whereas the ALMA flux calibration systematic may cause an overall shift in the $n_{\rm e^-}$ direction). \begin{figure*} \begin{subfigure}{0.45\textwidth} \hspace{-10mm} \includegraphics*[scale=0.40]{nevsrad.pdf} \vspace{-3mm} \end{subfigure} \begin{subfigure}{0.45\textwidth} \hspace{-0mm} \includegraphics*[scale=0.40]{nevsradH2.pdf} \vspace{-6.5mm} \end{subfigure} \caption{Electron density (left) and H$_2$ density (right) as a function of deprojected radius derived from the PV ratio diagram in Fig.\ \ref{fig:pvratios} using the NLTE analysis as displayed in Fig.\ \ref{fig:ratiotkncoll}, and assuming temperatures predicted by the hydrodynamical model of \citet{Kral2016a}. Line ratios higher than 3.8 were masked due to their strong dependence on kinetic temperature, which only adds noise to the diagram. For the remaining line ratios, our temperature choice does not influence the resulting electron densities strongly. Error bars in both directions were derived from uncertainties in the line ratio and deprojected radial location. } \vspace{-6 mm} \label{fig:neradial} \end{figure*} The electron density in the disk shows a power law radial dependence between 40 and 200 AU (i.e. where the CO is detected), with a slope of $\gamma \sim -1$; this is in line with the prediction by the \citet{Kral2016a} model, which we will discuss in more detail in Sect.\ \ref{sect:atomdom}. \subsection{Primordial origin: H$_2$ densities from line ratios} \label{sect:H2} In the previous section, we derived constraints on the density of electrons using the CO line ratios, where we assumed a gas disk of secondary origin, as already suggested by the CO morphology and short survival timescale \citep{Dent2014}. However, we note that the disk could still contain large amounts of unseen H$_2$, which may itself shield CO and allow it to survive since the protoplanetary phase of evolution. This would imply a primordial origin for the gas disk. In such scenario, H$_2$ dominates the disk gas mass and will act as the dominant collider species for CO excitation. Then, we can use the same line ratio analysis as in the previous subsection to estimate the H$_2$ density. Fig.\ \ref{fig:ratiotkncoll}, bottom shows the dependence of the 3-2/2-1 line ratios measured on $T_{\rm k}$ and $n_{H_2}$. Though once again for the highest line ratios the temperature dependence becomes stronger and we cannot make an accurate prediction, the large majority of the measured ratios have a weak temperature dependence. We can therefore use them to estimate the H$_2$ density, and use the PV diagram to once again obtain the radial dependence of $n_{H_2}$, shown in Fig.\ \ref{fig:neradial}, right. We find that if H$_2$ were to make up the bulk of the gas disk, its density would be between 10$^3$ and 10$^5$ cm$^{-3}$ at radii between 50 and 200 AU. Strictly speaking, these values should be considered upper limits, as the presence of other collider species, here unaccounted for, would lower the derived H$_2$ densities necessary to maintain the observed level of CO excitation. The H$_2$ density levels we derive are much below values observed and expected from theoretical models for protoplanetary disks \citep[e.g.][]{Boneberg2016}, proving that the gas content of the $\beta$ Pic debris disk is intrinsically different in molecular hydrogen content to a typical primordial disk, and is insufficient to allow CO survival over the system's lifetime (see discussion in Sect.\ \ref{sect:dichot}). \subsection{Optical thickness and total CO mass} \label{sect:optthick} Analysing the 3-2/2-1 line ratio also allows us to set improved constraints on the total CO mass in the system. \citet{Dent2014}, having only information on the J=3-2 integrated line flux, obtained a value within a factor 2 of 2.85$\times 10^{-5}$ M$_{\oplus}$, assuming optically thin emission and excitation temperatures $T_{\rm exc}$ between 20 and 85 K. We hereby test both these assumptions and their implications on the derived CO mass. For optically thin emission, the excitation temperature corresponds to the kinetic temperature only if LTE applies; in NLTE the discrepancy between the two can be significant, with $T_{\rm exc}<<T_{\rm k}$. In fact, our measured disk-integrated line ratio of $1.9\pm0.3$ corresponds to an excitation temperature $T_{\rm exc}=12\pm4$ K, which may appear low, but is entirely consistent with the expectation of NLTE. In order to calculate the CO mass from a given CO integrated line flux (we here choose the J=2-1), we need to know the fractional population of the upper level of the transition, where this can be obtained for each of the $\left(T_{\rm k},n_{\rm e^-}\right)$ pairs traced by the contour of our disk-integrated line ratio in Fig. \ref{fig:ratiotkncoll} (top). The intrinsic $\left(T_{\rm k},n_{\rm e^-}\right)$ degeneracy implies that a range of CO masses will be possible. We estimate the range of possible CO masses using Monte-Carlo methods. We assume both integrated line fluxes to follow a Gaussian probability distribution with standard deviation equal to the quoted uncertainty (which includes the absolute flux systematic added in quadrature to the noise level from the cube). For each integrated line flux, we sample this Gaussian 10$^4$ times and for each sample calculate the line ratio, which will itself be sampled 10$^8$ times. For each line ratio we calculate possible $\left(T_{\rm k},n_{\rm e^-}\right)$ pairs (i.e. draw a contour on Fig. \ref{fig:ratiotkncoll}, top) and randomly draw one of these pairs, assuming a uniform underlying $\left(T_{\rm k},n_{\rm e^-}\right)$ distribution. This pair will yield a value for the fractional population of the upper level of the transition in question ($x_2$), which then, combined with a sample of the integrated line flux ($F_{\rm 2-1}$), yields a sample for the CO mass \citep[through Eq. 2 in][]{Matra2015}. Repeating this procedure for the large number of samples drawn from the measured distributions of integrated line fluxes yields a probability distribution for the total CO mass in the disk. The CO mass range obtained is $3.4^{+0.5}_{-0.4} \times 10^{-5}$ M$_{\oplus}$, representing the $(50^{+34}_{-34})^{\rm th}$ percentiles of this distribution. Low line ratios and hence excitation temperatures, such as observed in $\beta$ Pic, can also be symptomatic of optical thickness of the CO line \citep[e.g.][]{Flaherty2016}. Optical thickness can be tested through observations of CO isotopologues such as $^{13}$CO and C$^{18}$O, assuming interstellar isotopic ratios \citep[e.g.][]{Kospal2013}; there is however no direct measurement of these at millimetre wavelengths in $\beta$ Pic. Another possibility is to estimate it directly through its definition, \begin{equation} \tau_{\nu}=\frac{h\nu}{4\pi \Delta\nu}(x_lB_{lu}-x_uB_{ul}) N, \label{eq:tauthree} \end{equation} where $h$ is Planck's constant, $\nu$ is the frequency of the transition in Hz, $\Delta \nu$ is the line width in Hz (a rectangular line profile is assumed), $x_u$ and $x_l$ are the fractional populations of the upper and lower energy level of the transition, respectively, $N$ is the CO column density along the line of sight in m$^{-2}$, and $B_{lu}$ and $B_{ul}$ are the Einstein B coefficients for the upward and downward transition. In our case, we measure $x_u$, $x_l$ and $N$ under the optically thin assumption, and use them to verify that the optical thickness is indeed $<1$. We follow this procedure in the PV spaxel where the CO flux is highest, and hence where we would expect the optical thickness to be highest. This corresponds to the location of the clump at a radial velocity of $-3.5$ km/s and midplane location of $75$ AU to the SW of the star. The line ratio measured here is $2.3\pm0.3$; from this, we can derive possible $\left(T_{\rm k},n_{\rm e^-}\right)$ combinations, and corresponding combinations of fractional populations $x_3$ and $x_2$. The column density in the spaxel can then be estimated through a modified version of Eq.\ 2 in \citet{Matra2015}, \begin{equation} N=\frac{4\pi d^2}{h\nu_{u,l}A_{u,l}\Delta A}\frac{F_{u,l}}{x_{u}}, \label{eq:coldens} \end{equation} where $d$ is the distance to the star, $A_{u,l}$ is the Einstein A coefficient of the transition, $F_{u,l}$ is the integrated line flux observed, and $\Delta A$ is the on-sky area of the line-of-sight column. Applying this column density to Eq.\ \ref{eq:tauthree}, we obtain an optical thickness $\tau_{3-2}=0.27\pm0.05$ for the 3-2 line at the clump location, where the error takes into account both the intrinsic $\left(T_{\rm k},n_{\rm e^-}\right)$ degeneracy and the observational uncertainties on the observed fluxes $F_{3-2}$ and $F_{2-1}$. This value of the optical depth $\tau_{3-2}$ derived at the clump location can be interpreted as an upper limit to the optical depth, which is likely lower in the rest of the disk, showing that our assumption of optically thin CO emission is a good approximation to the physical conditions in the $\beta$ Pic disk. This is also supported by the absence of the SW clump in the PV diagram of the CO line ratio, as opposed to the CO J=3-2 or J=2-1 PV diagrams; this indicates that CO excitation is independent of the CO column density and hence no optical depth effects are at play. It is valuable to note that increasing the clump CO density by an order of magnitude would have resulted in CO millimetre emission being optically thick along the line of sight to Earth. A similar argument applies for the vertical optical thickness of CO to UV light, which allows CO to self-shield against photodissociation and hence prolong his survival timescale in the disk \citep[see Sect. \ref{sect:codestr}, and][]{Visser2009}. Despite the low levels observed, if the total CO mass or the clump CO density were only an order of magnitude higher, the CO would have survived longer than an orbital timescale at 85 AU, significantly reducing the azimuthal asymmetry observed and casting significantly more uncertainty on its secondary nature. This suggests that significant optical thickness in a second generation gas disk can be easily attained for CO production rates slightly higher than observed in $\beta$ Pictoris; as such, observations of optically thick, azimuthally symmetric CO in debris disk systems \citep[e.g. HD141569A and HD21997, ][]{White2016, Kospal2013}, should not be treated as sufficient proof for a primordial disk origin. In such cases, multi-transition observations of optically thin isotopologues are necessary to probe the H$_2$ densities in the disk (Sect. \ref{sect:H2}), and discern between the primordial and secondary origin scenarios (Sect. \ref{sect:dichot}). | In this work, we presented new ALMA Band 6 observations of the CO J=2-1 line in the $\beta$ Pictoris debris disk, and combined them with archival Band 7 observations of the CO J=3-2 line to derive the 3D morphology, excitation conditions and total mass of the CO gas. We reach the following conclusions: \begin{itemize} \item We confirm the presence of the CO clump discovered by \citet{Dent2014}, peaking at radius of 85 AU and an azimuth of $\pm$32$^{\circ}$ in the orbital plane of the disk (SW on-sky). At the 0$\farcs$3 resolution of the new dataset, we conclude that the clump is radially extended, spanning $\sim$100 AU in orbital radius. Since CO should rapidly couple to the atomic gas disk already in place and quickly proceed in Keplerian rotation around the star, it does not have time to spread radially and must be produced at a broad range of radii. This rules out a giant impact between planetary bodies as a possible dynamical scenario to explain the clumpy morphology, leaving resonant trapping by outward planet migration as the only viable mechanism proposed so far. This scenario is also consistent with the observed azimuthal structure for an assumed disk inclination of $\sim$86$^{\circ}$, and can be tested by looking for the clump's predicted orbital motion. \item The CO disk is vertically tilted, i.e. its PA presents an extra anticlockwise rotation compared to the main disk observed in scattered light. The degree of misalignment is in line with that inferred for the warp observed in scattered light imaging of the disk, suggesting a common origin between the CO clump and the scattered light warp. \item Under the assumption of a vertically isothermal disk, the scale height measured is a function of orbital radius (increasing as $H \sim R^{0.75}$ with a value of 7 AU at the clump radial location). As observed for metallic atoms, this implies temperatures that are higher than predicted by thermodynamical models \citep{Kral2016a}. Aside from a geometrical effect due to our edge-on assumption, this discrepancy can be attributed to the fact that the disk is likely not vertically isothermal and/or to a potential higher electron abundance in the disk surface layers, where both effects are expected if the disk is vertically optically thick to C-photoionising UV photons. \item The CO J=3-2/J=2-1 line ratio shows a clear gradient with radial velocity in the PV diagrams, which is consistent with a power law decrease with orbital radius. Through NLTE modelling, we attribute this to a radial decrease in the electron density in the disk, in line with model predictions. No enhancement at the clump location nor a significant NE/SW asymmetry are observed, confirming that CO lies in an azimuthally symmetric, atom-dominated secondary disk. \item Repeating the NLTE analysis above under the assumption of an H$_2$-dominated primordial disk, we derive H$_2$ densities that are many orders of magnitude lower than expected for protoplanetary disks. These imply column densities that are too low to shield CO and allow it to survive over the age of the system, providing further proof that CO needs to be replenished and hence the gas disk must be of secondary origin. We propose such measurement of H$_2$ densities from subthermally excited, optically thin CO lines as a fundamental way to solve the primordial vs secondary dichotomy in other gas-bearing debris disks. \item Using both CO transitions, we refine the total CO mass measurement to $3.4^{+0.5}_{-0.4} \times 10^{-5}$ M$_{\oplus}$. We find that the vertical CO and \ion{C}{I} column densities are sufficient to partially shield CO from UV light, prolonging its survival timescale to $\sim$300 years, which is still much shorter than both the system age (hence requiring replenishment from cometary ices) and the orbital period (hence producing the observed clumpy morphology and NE/SW asymmetry). Assuming CO gas to be in steady state, being released from ices through the collisional cascade and then rapidly photodestroyed, we estimate the CO+CO$_2$ mass abundance in the comets to be at most 6\%. This is still consistent with cometary abundances measured in both our own Solar System and in coeval HD181327 system. \end{itemize} | 16 | 9 | 1609.06718 |
1609 | 1609.08705_arXiv.txt | We report absolutely calibrated measurements of diffuse radio emission between 90 and 190 MHz from the Experiment to Detect the Global EoR Signature (EDGES). EDGES employs a wide beam zenith-pointing dipole antenna centred on a declination of $-26.7^\circ$. We measure the sky brightness temperature as a function of frequency averaged over the EDGES beam from 211 nights of data acquired from July 2015 to March 2016. We derive the spectral index, $\beta$, as a function of local sidereal time (LST) and find $-2.60~\textgreater~\beta~\textgreater~-2.62~\pm$0.02 between 0 and 12~h LST. When the Galactic Centre is in the sky, the spectral index flattens, reaching $\beta = -2.50~\pm$0.02 at 17.7~h. The EDGES instrument is shown to be very stable throughout the observations with night-to-night reproducibility of $\sigma_{\beta}$~\textless~0.003. Including systematic uncertainty, the overall uncertainty of $\beta$ is 0.02 across all LST bins. These results improve on the earlier findings of \cite{rog01} by reducing the spectral index uncertainty from 0.10 to 0.02 while considering more extensive sources of errors. We compare our measurements with spectral index simulations derived from the Global Sky Model (GSM) of \cite{deo01} and with fits between the \cite{guz01} 45~MHz and \cite{has02}~408~MHz maps. We find good agreement at the transit of the Galactic Centre. Away from transit, the GSM \textcolor{black}{tends to} over-predict \textcolor{black}{(GSM less negative)} by 0.05~\textless~$\Delta_{\beta}\textcolor{black}{ = \beta_{\text{GSM}}-\beta_{\text{EDGES}}}$~\textless~0.12, while the 45-408~MHz fits \textcolor{black}{tend to} over-predict by $\Delta_{\beta}$~\textless~0.05. | The low-frequency radio sky spectrum between 50 and 200~MHz is a key area of interest because experiments seeking to detect redshifted 21~cm radiation from neutral hydrogen gas during the Epoch of Reionization (EoR) and earlier eras of First Light and X-ray heating must subtract astrophysical foregrounds in these frequencies to high-precision. At these frequencies, the sky is mostly dominated by Galactic synchrotron radiation but also contains contributions from supernova remnants and extragalactic radio sources. There are two approaches to detecting the redshifted 21~cm signal. The first approach is targeted by interferometeric arrays, such as the Murchison Widefield Array (MWA; \citealt{bow03, tin01}), the Precision Array to Probe the Epoch of Reionization (PAPER; \citealt{ali01}), the Hydrogen Epoch of Reionization Array (HERA; \citealt{pob01}), the Low-Frequency Array (LOFAR; \citealt{vha01}), and the Low-frequency Aperture Array component of the Square Kilometer Array (SKA; \citealt{mel01}). These arrays aim to measure spatial fluctuations in the sky brightness temperature on arcminute and degree scales resulting from variations in the density, ionisation, and temperature of the intergalactic medium (IGM) above redshift $z>6$ (below 200~MHz). The second approach, on the other hand, exploits the bulk properties of the high-redshift IGM that yield a global (monopole) contribution of redshifted 21~cm signal to the all-sky radio background. This approach is being pursued by the Experiment to Detect the Global EoR Signature (EDGES; \citealt{bow01,bow02}), Broadband Instrument for Global Hydrogen Reionisation Signal (BIGHORNS \citealt{sok01}), Sonda Cosmol\'{o}gica de las Islas para la Detecci\'{o}n de Hidr\'{o}geno Neutro (SCI-HI \citealt{voy01}), Large-aperture Experiment to detect the Dark Age (LEDA \citealt{ber01}), Shaped Antenna measurement of background Radio Spectrum (SARAS \citealt{pat01, sin01}), and the Dark Ages Radio Explorer (DARE; \citealt{bur01}). Both methods require careful and accurate subtraction of the sky foreground since the 21~cm signal is three to five orders of magnitude below the foreground. Although observations of the low-frequency radio sky were among the earliest in radio astronomy \citep{tur01, bri01}, detailed knowledge of the spectral properties of diffuse emission remains lacking. The \citet{has01, has02} all-sky map at 408~MHz, which was compiled from data taken in the 1960s and 1970s, is still the cornerstone for foreground templates extrapolated across many frequencies in cosmic microwave background (CMB) and redshifted 21~cm analyses. Improvements to the map have occurred throughout the years, including efforts by \citet{dav01, ben01, ben02, pla01}, and \citet{rem01} that focused on removing point sources and destriping the original data. \citet{deo01} combined the Haslam 408~MHz map and several other surveys between 10~MHz and 94~GHz to build a Global Sky Model (GSM), which provides spectral properties of the diffuse emission of the entire sky. In this model at 150 MHz, the spectral index outside the Galactic plane is $\sim-2.6$ and in the Galactic plane (in a narrow band) increases to $\sim-2.5$ with peaks as high as $\sim-2.3$. Both the Haslam map and the GSM have become widely used and cited in both simulations and data reduction pipelines for redshifted 21~cm observations \citep{bow04, pat01, sub01, thy01, ber02}. \citealt{guz01} created an all-sky temperature map at 45~MHz based upon the surveys of \citet{alv01} and \citet{mae01}. In addition, they produced an all-sky Galactic spectral index map based upon two frequency points by using their 45~MHz and the Haslam 408~MHz map after corrections for zero-level, extragalactic non-thermal emission, and CMB factors. At higher frequencies, observations of Galactic radio emission between 3 and 90 GHz have been made by the Absolute Radiometer for Cosmology, Astrophysics, and Diffuse Emission I and II (ARCADE I and II) sky surveys \citep{fix01,kog01,sei01}. This survey constrained models of extragalactic emission and suggested that models of electric dipole emission from spinning dust particles were a possible explanation for excess emission seen at 1 cm wavelengths. They find that, at most, three parameters (reference brightness temperature, spectral index, and curvature) are necessary to model their wide-band data combined with external radio measurements between 22 MHz and 1.4 GHz, and from WMAP at 23 GHz \citep{kog02}. Recently, the new redshifted 21~cm arrays have begun yielding the first large, multi-spectral maps sensitive to diffuse structures in the low-frequency sky, including recent surveys by MWA GLEAM \citep{way01} and LOFAR \citep{hea01}. GLEAM will scan the entire sky south of $\delta \sim+25^{\circ}$ between 72 and 231 MHz, and the LOFAR survey will scan 100 sq degrees in the northern sky centred on $(15^h, 69^{\circ})_{\text{J2000}}$ between 30 and 160 MHz. The LOFAR survey's primary purpose is to enable automated processing by providing an \textit{a priori} sky model, which also serves as an aid to foreground removal for EoR detection. Similarly, GLEAM's survey will serve a myriad of uses, one of which again will be foreground removal in EoR searches. The EDGES instrument is able to provide a unique measurement of the absolute sky brightness temperature averaged over large spatial scales on the sky due to its wide beam. \citet{rog01} found that the spectral index, $\beta_{100-200}$, of diffuse emission, defined as $T_\text{sky}\propto \nu^{\beta}$, was $-2.5\pm0.1$ at high-Galactic latitudes in the frequency range 100-200~MHz. Those measurements were taken using three days of data; two of which used a N-S orientation of the antenna's excitation axis and one with an E-W orientation. By combining their results with the Haslam sky map at 408~MHz, they were able to show that $\beta_{150-408} = -2.52\pm0.04$ at high Galactic latitudes. In this paper we present new observations taken over a span of 240 nights from July 2015 through March 2016 with the latest version of the EDGES instrument that deploys an improved antenna with better chromatic performance and a new high-precision receiver calibration approach. These advancements enable us to improve on our earlier measurements of the spectral index of the diffuse low-frequency radio emission and extend our coverage to all sidereal times at a constant declination of $-26.7^\circ$. The paper is organized in the following manner. In Section 2 we describe the instrument and calibration details. In Section 3 we present details of the data collected and chromatic beam corrections. Section 4 presents and discusses the spectral index results and comparisons to values predicted by relevant sky models. | \label{sec:conclusion} We measured the sky brightness temperature as a function of frequency and derived the spectral index $\beta$ as a function of sidereal time by fitting to a two parameter model over a span of 240 days using 211 days of nighttime data acquired from July 2015 to March 2016. Instrument calibration, including corrections for temperature gradients, ground loss, antenna losses, and beam chromaticity, has been applied to deliver instrument stability of over several months as demonstrated by spectral index standard deviation values $\sigma_{\beta}~\textless$~0.003. We have presented results of extensive measurements of the diffuse radio sky between the frequencies of 90-190~MHz. We find that the spectral index $\beta$ is in the range $-2.60~\textgreater~\beta~\textgreater~-2.62~\pm$~0.02 in the lower LST values, but increases to $-2.50$ with the Galaxy overhead. The GSM tends to over-predict the strength of the variation in the spectral index in the range 0.05~\textless~$\Delta_{\beta}$~\textless~0.12 for low LST. However, comparison with the spectral index as computed using the Guzm\'an sky map at 45 MHz and the Haslam Sky map at 408 MHz is a closer match and differs by 0.01~\textless~$\Delta_{\beta}$~\textless~0.05 away from the centre. At the Galactic Centre both models agree with our measurements of the spectral index to within one sigma. Future work is planned to investigate the criteria needed to fit to a three-parameter spectral equation. Updates to sky models will be used to simulate spectral index across LST using the EDGES blade antenna. We also plan to measure the spectral index in the $50 - 100$~MHz range with the low-band EDGES blade antenna. | 16 | 9 | 1609.08705 |
1609 | 1609.06142_arXiv.txt | We present preliminary results on on-sky test of sky subtraction methods for fiber-fed spectrograph. Using dedicated observation with FLAMES/VLT in I-band, we have tested the accuracy of the sky subtraction for 4 sky subtraction methods: mean sky, closest sky, dual stare and cross-beam switching. The cross beam-switching and dual stare method reach accuracy and precision of the sky subtraction under 1\%. In contrast to the commonly held view in the literature, this result points out that fiber-fed spectrographs are adapted for the observations of faint targets. | \label{sec:title} Historically, fiber-fed spectrographs had been deemed inadequate for the observation of faint targets, because of two main reasons: (1) the low throughput of fibers that implies a low global efficiency of the spectrograph; (2) the difficulty to achieve high accuracy on the sky subtraction. However, thanks to the important progress in fiber technology, modern fibers spectrographs now have global efficiencies close to multi-slit instruments. To date, the main drawback had been the quality of the sky subtraction, critical for the observation of faint targets. The impossibility to sample the sky in the immediate vicinity of the target in fiber instruments has led to a commonly held view that a multi-object fibre spectrograph cannot achieve an accurate sky subtraction under 1\% contrary to their slit counterpart. In the past years, severals studies have focused on the subject and several designs of sky subtraction strategies to properly subtract the sky have been proposed [\citenum{1992MNRAS.257....1W},\citenum{2005NewA...11...81L},\citenum{2008MNRAS.386...47E},\citenum{2010MNRAS.408.2495S},\citenum{2010SPIE.7735E.216R}]: \begin{itemize} \item \textbf{Simultaneous sky fibers} - Several fibers are dedicated to sampling the sky in the region of observations. The number of sky fibers depends on the wavelength domain observed, the dimension of the field of view and the required quality of sky-subtraction. Observations have to be previously corrected from the individual response of the fiber and scattered light. The mean sky among all sky fibers or the closest sky fiber is subtracted to the fiber object spectrum. \item \textbf{$\lambda-\lambda$ reconstruction}This method is a variant of the previous one [\citenum{2010SPIE.7735E.216R}]. Dedicated sky fibers are distributed in the field of view. The sky continuum is reconstructed at different wavelengths in all the FOV by interpolation and the sky emission lines are subtracted using the algorithm of Davies, 2009 [\citenum{2007MNRAS.375.1099D}]. \item \textbf{Dual fiber bottom in stare mode}. The sky is sampled simultaneously in the immediate vicinity of the object by a sky fiber associated to the object fiber. This setup is close to a pseudo slit. This configuration implies to dedicate half of the fibers to the sky measurement. \item \textbf{Beam Switching} - Each fiber is switched between an object and a sky position. This strategy has the advantage to observe the sky background with the same fibers used for the targets [e.g. \citenum{1992MNRAS.257....1W}]. The sky and the instrumental signal can be subtracted simultaneously. However, this procedure implies to dedicate half of the observation time to sky sampling. \item \textbf{Cross Beam Switching} - Each science target has two fibers associated, as in the dual fiber mode. The object is observed in the fibers following a sequence A B B A or A B A. Despite the drawback of decreased spectrograph multiplex capability, the dual fiber button design has the advantage to be similar to chopping into a slit and thus is 100\% of the time on the scientific targets and allows a very accurate sky and instrumental response subtraction. \end{itemize} We show hereafter the capabilities of four of these methods - mean sky, closest sky, dual stare and cross-beam switching - in the I-band using as a benchmark dedicated FLAMES/GIRAFFE/VLT observations. A similar assessment is ongoing in the near-IR regime using FMOS observations. | We present the preliminary results on on-sky test of different sky subtraction techniques for fiber-fed spectrograph. Using FLAMES/VLT observations, we have demonstrated that sky background can be subtracted within less that 1\% of residual, when using beam-switching or pairs fibers methods. This results point out that fiber-fed spectrographs are well suited for the observations of faint objects and that the issue of the sky subtraction is not a stopper for this technology. A similar study is currently in progress to test the accuracy of the different sky subtraction method for near-IR spectrograph. Other sky subtraction methods, such as the $\lambda-\lambda$ reconstruction method [\citenum{2010SPIE.7735E.216R}] and a details study of the accuracy of the method as a function of the number of dedicated sky fibers are also under investigation. This study have been carry out in the framework of the design of MOONS/VLT [\citenum{2011Msngr.145...11C}] and OPTIMOS-EVE/E-ELT [\citenum{2011Msngr.145...11C},\citenum{2010SPIE.7735E..88N}] - two projects of multi-object spectrographs in the optical-to-nearIR domain based on fiber technology. | 16 | 9 | 1609.06142 |
1609 | 1609.03883_arXiv.txt | {In this work I review the observational constraints imposed on the energetics and magnetisation of quasar jets, in the context of theoretical expectations. The discussion is focused on issues regarding the jet production efficiency, matter content, and particle acceleration. I show that if the ratio of electron-positron-pairs to protons is of order $15$, as is required to achieve agreement between jet powers computed using blazar spectral fits and those computed using radio-lobe calorimetry, the magnetization of blazar jets in flat-spectrum-radio-quasars (FSRQ) must be significant. This result favors the reconnection mechanism for particle acceleration and explains the large Compton-dominance of blazar spectra that is often observed, without the need to postulate very low jet magnetization.} \keyword{quasars; blazars; jets} \begin{document} | One of the biggest unresolved puzzles in the theory of active galactic nuclei (AGN) regards their ability to launch very powerful, relativistic jets. According to several studies, the most powerful jets reach or even exceed the associated accretion disk luminosities \cite{Rawlings,Fernandes,Punsly,SSKM,Ghisellini14}. Obviously, production of such jets cannot be treated as a marginal byproduct of the accretion flow and most likely is governed by the Blandford-Znajek mechanism \cite{BZ}, with the black holes possessing very large spins and magnetic fluxes. The magnetic flux required to explain the production of the most powerful jets has recently been found to agree with the maximum magnetic flux that can be confined on black holes by the ram pressure of `magnetically-arrested-disks' (MAD) \cite{Narayan}. In recent years, the MAD scenario has been thoroughly investigated, and is now considered to be the likely remedy for the production of very powerful \mbox{jets \cite{Tchek11,McKinney,Sikora-Begelman}}. However, as numerical simulations suggest, powers of jets launched in the MAD scenario depend not only on the spin and magnetic flux, but also on the disk's geometrical \mbox{thickness \cite{Avara}}, with the jet power scaling approximately quadratically with all these quantities. According to standard accretion disk models, accretion disks become geometrically thick only when they are advection dominated, i.e., for the Eddington-ratio $\lambda_{Edd} \equiv L_d/L_{Edd}$ larger than \mbox{$\sim$0.3 \cite{Jaroszynski,Belob,Abramowicz}} or smaller than $\sim$0.003, where $L_d$ is the disk luminosity and $L_{Edd}$ is the Eddington luminosity \cite{Ichimaru,Rees,Narayan-Yi,Stern-Laor}. Hence, one should not expect to observe powerful jets in AGN with \mbox{$0.003 < \lambda_{Edd} < 0.3$.} This theoretical expectation contradicts with the observational fact that there is no deficit of radio-loud AGN in this range of $\lambda_{Edd}$. On the contrary, some studies show a trend of increasing jet production efficiency with decreasing Eddington-ratio \cite{SSL,Rusinek} (see Figure~\ref{f1}). A possible reason for the aforementioned contradiction is modulation of the accretion disk luminosity and jet production. Noting that the power of a jet calculated using the energy content of the radio lobes is actually the time-averaged jet power, averaged over the source lifetime, and that according to the MAD scenario modulation of a jet power at the base is driven by modulation of the accretion rate, modulation of the jet production on time scales shorter than the lifetime of radio lobes will lead to modulation of the ``apparent'' jet production efficiency and modulation of the Eddington ratio. For~example, modulation of the accretion power by a factor 10 will cause the object to have 10~times lower Eddington ratio and 10~times larger apparent jet production efficiency during its accretion rate minimum relative to that at its maximum, and for a duty cycle ~1/2 its apparent jet production efficiency will be about 5~times larger than the real one. A natural driver of variability in the accretion rate and jet production is viscous instabilities in accretion disks \cite{Janiuk1,Janiuk2}. Observational support for this hypothesis seems to come from the spatial modulation of the radio brightness distributions seen in some large scale jets~\cite{Godfrey}. \begin{figure}[H] \centering \includegraphics[width=0.90\textwidth]{f1.pdf} \caption{\textls[-10]{$P_j/L_d$ ratio as a function of Eddington ratio $\lambda_{Edd} \equiv L_d/L_{Edd}$. Green diamonds---FRII Narrow-Line-Radio-Galaxies \cite{SSKM}; red squares---Broad-Line-Radio-Galaxies plus radio-loud quasars~\cite{SSL}; grey dots---FRII quasars~\cite{vanVelzen}; and the ellipse marks the approximate location of $\gamma$-ray selected FSRQs assumed to have jets with zero pair content \cite{Ghisellini14}. The vertical dashed lines mark the range of the Eddington ratio within which the standard accretion disks are predicted to be radiatively efficient and geometrically thin. (The figure is adopted from Rusinek et al. 2016, in preparation \cite{Rusinek}).}} \label{f1} \end{figure} However, the situation is complicated if we consider the jet power in $\gamma$-ray detected FSRQs (flat-spectrum-radio-quasars) calculated by fitting their broad-band spectra assuming the ERC (external-radiation-Compton) model for $\gamma$-ray production \cite{SBR}. The median of $P_j/L_d$ calculated by Ghisellini et al. (2014) for jets in FSRQs is $\sim$10, which is $50$ times larger than the median of $P_j/L_d$ calculated by van Velzen \& Falcke (2013) for radio-selected FRII quasars using the radio-lobe calorimetry ({Willott et al. 1999} \cite{Willott}) (see Figure~\ref{f1}). Studies of jet powers in blazars using calorimetry of their extended radio sources \cite{Kharb,Meyer} allowed to verify whether such a difference is associated with selection of two different populations of quasars. As it has been found, the $P_j/L_d$ median calculated using radio-lobe calorimetry is still much smaller than the $P_j/L_d$ median calculated using the blazar spectral fits, but now they differ by a factor $\sim$16 \cite{Pjanka}. Whilst the larger averaged values of $P_j/L_d$ for jets in FSRQs than in FR II quasars, in both cases calculated using the radio-lobe calorimetry, can be explained by selection procedures, the difference between medians of $P_j/L_d$ measured by the blazar spectral fits and using radio-lobe calorimetry for these same samples must have a different explanation. Following~possibilities have been considered: \begin{enumerate}[leftmargin=*,labelsep=5mm] \item[--] jet energy losses during propagation between the blazar zone and radio lobes (e.g., by the work done against the external medium by reconfinement shocks which may change their sizes following a jet power modulation by the central engine); \item[--] overestimation of jet power using the blazar models (e.g., by assuming zero pair content and/or a one zone model); \item[--] a significant fraction of blazars may be hosted by young or short lived compact double radio sources. In this case, the methods of spectral decomposition and core subtraction adopted to use radio-lobe calorimetry in blazars may lead to underestimation of the lobe radio luminosities, and therefore underestimation of the jet power. \end{enumerate} In this presentation I will assume that the main reason for the discrepancy between jet power estimates in blazars is overestimation of the jet power by the blazar models by assuming zero pair content. It will be shown that $\sim$$15$ pairs per proton is enough to reconcile the difference between the jet power calculated by the two methods and that with such a pair content the magnetic reconnection mechanism is strongly favored as the energy source of blazar activity. | The jet powers in FR II quasars calculated using radio-lobe calorimetry \cite{vanVelzen} are a factor \mbox{$\sim$50 smaller} than jet powers calculated using spectral fits of $\gamma$-ray detected FSRQs when assuming $n_p=n_e$ jet plasma \cite{Ghisellini14} (see Figure~\ref{f1}). Measurements of radio luminosities of extended radio-structures in some FSRQs \cite{Kharb,Meyer} has enabled a comparison of the results of the two jet power measurement techniques by applying both techniques to the same objects. As Pjanka et al. \cite{Pjanka} showed, the average difference for the cross-matched samples is smaller, but still significant, by a factor $\sim$$16$. Noting that the power calculated by Ghisellini et al. includes the blazar radiation, whilst the power calculated using the radio lobe energetics does not, the difference is reduced to a factor $\sim$$8$. Assuming that this remaining difference is due to overestimation the blazar power by Ghisellini et al. by ignoring pair plasma in a jet, we found that on average: \begin{itemize}[leftmargin=*,labelsep=5mm] \item the pair content: $n_{pairs}/n_p \sim 15$; \item the jet production efficiency: $\eta_j \simeq 0.14 \, (\epsilon_d/0.1)$; \item the magnetization at entrance and exit of blazar zone is $\sigma_0 \simeq 4.4$ and $\sigma \simeq 2$, respectively; \item the average energies of accelerated electrons/positrons correspond to typical observed locations of synchrotron and $\gamma$-ray luminosity peaks provided the acceleration is powered by magnetic reconnection operating in a jet at a distance corresponding to spatial extension of the BLR. \end{itemize} The pair content obtained above is larger by a factor $3/2$ than the maximal one, \scalebox{.95}[1.0]{$(n_{pairs}/n_p)_{max} \sim 10$}, above which the jet is expected to be efficiently decelerated due to the Compton-rocket effect \cite{GT-Rocket}. However this limit was obtained by assuming an isotropic distribution of the external diffuse radiation field and neglecting Klein-Nishina effects and therefore can be relaxed somewhat if some level of flattening of the BLR is considered, and taking into account Klein-Nishina recoil effects \cite{Moderski}. \noindent Noting that the MAD scenario predicts production of jets with powers \begin{equation} P_{j,0} \simeq a^2 \, (H/R)^2 \, \dot M_d c^2 \end{equation} and assuming that spins $a$ in $\gamma$-ray selected quasars are close to their maximum value, $\sim$1, the value of $\eta_j \sim 0.14$ obtained above may simply result from suppression of jet production efficiency due to having geometrically thin disks in quasars, i.e., with $H/R \ll 1$. This requires $H/R \sim 1/3$, which is much larger than predicted by standard accretion disk models \cite{Shakura,Novikov-Thorne}. However, as some studies indicate, real disks can be thicker than the standard disks \cite{BegPri,Rozanska,BAR}. Then the $\sim$$7$ times lower jet production efficiency in radio selected FRII quasars than in $\gamma$-ray detected FSRQs may result from on average \mbox{$\sim$$\sqrt{7}$ times} lower BH spins in the entire FRII quasar population than in the $\gamma$-ray selected one. And~this can be explained by noting, that in $\gamma$-ray loud quasars jets are more powerful and therefore are expected to be more relativistic. This interpretation is supported by the fact that only about $9$\% of the FSRQs are found to be $\gamma$-ray loud \cite{Linford}. \vspace{6pt} | 16 | 9 | 1609.03883 |
1609 | 1609.08643_arXiv.txt | {The radiation of stars heats dust grains in the diffuse interstellar medium and in star-forming regions in galaxies. Modelling this interaction provides information on dust in galaxies, a vital ingredient for their evolution. It is not straightforward to identify the stellar populations heating the dust, and to link attenuation to emission on a sub-galactic scale. Radiative transfer models are able to simulate this dust-starlight interaction in a realistic, three-dimensional setting. We investigate the dust heating mechanisms on a local and global galactic scale, using the Andromeda galaxy (M31) as our laboratory. We perform a series of panchromatic radiative transfer simulations of Andromeda with our code SKIRT. The high inclination angle of M31 complicates the 3D modelling and causes projection effects. However, the observed morphology and flux density are reproduced fairly well from UV to sub-millimeter wavelengths. Our model reveals a realistic attenuation curve, compatible with previous, observational estimates. We find that the dust in M31 is mainly ($91 \%$ of the absorbed luminosity) heated by the evolved stellar populations. The bright bulge produces a strong radiation field and induces non-local heating up to the main star-forming ring at 10 kpc. The relative contribution of unevolved stellar populations to the dust heating varies strongly with wavelength and with galactocentric distance. The dust heating fraction of unevolved stellar populations correlates strongly with $NUV-r$ colour and specific star formation rate. These two related parameters are promising probes for the dust heating sources at a local scale.} | Starlight in galaxies is processed by dust grains through absorption and scattering. On average, about one third of starlight in normal spiral galaxies is attenuated by dust \citep{Popescu2002,Skibba2011,Viaene2016}. Dust resides around new stars in their birth clouds as well as in the diffuse interstellar medium (ISM). A Milky Way-like dust mixture is highly efficient in scattering and absorbing UV radiation, but also significant fractions of optical and sometimes even near-IR (NIR) light. All the energy that is absorbed by the dust is reprocessed and emitted at longer wavelengths. In order to understand the processes governing the observed dust-starlight interplay, observations at all wavelengths are necessary. This allows the investigation of how the UV and optical energy from stars is converted into far-IR (FIR) and sub-millimeter (submm) emission. Such knowledge is important since FIR/submm emission is a useful tool to study galaxies both near and far; the amount of dust obscuration roughly follows the star formation rate density in cosmic time \citep[see e.g.][]{Daddi2005, Gruppioni2013, Madau2014}. A correct understanding of dust heating allows the separation of dust into multiple temperature components. This in turn results in better dust mass estimates. Accurate dust masses can then be used to estimate the total ISM content in distant objects for which H\textsc{i} content cannot be observed \citep[see e.g.][]{Corbelli2012, Eales2012, Scoville2014, Groves2015}. Nearby galaxies are good test laboratories for such dust heating studies. Their dust heating mechanisms have been studied through various techniques such as correlations with star formation rate (SFR) indicators and stellar mass tracers \citep{Galametz2010, Boquien2011, Bendo2012, Foyle2013, Hughes2014, Bendo2015} or through panchromatic energy balance SED fitting \citep{Groves2012, Aniano2012, Dale2012, MentuchCooper2012, Ciesla2014, RemyRuyer2015, Boquien2016}. While the situation differs from galaxy to galaxy, the current understanding is that the cold dust in most galaxies is heated by the evolved stellar populations which feed the general interstellar radiation field (ISRF). The warmer dust is then predominantly heated by the young and new stars, through strong UV radiation. In certain cases, even active galactic nuclei (AGN) can contribute to the dust heating \citep[see e.g.][]{Wu2007, Kirkpatrick2012, Schneider2015}. Usually, these investigations provide a qualitative view on the dominant heating source. In starbursts and galaxies with active star formation, dust is predominantly heated by young stellar populations. For early-type galaxies, little research has been conducted to estimate the dust heating sources. Based on their low star formation rates, one would expect that the evolved populations are dominant in these systems \citep[see e.g.][]{Smith2012b, Boquien2014}. But other heating sources are possible, for example X-rays from hot halo gas \citep{Natale2010}. Most galaxies, however, fall in the ambiguous intermediate regime, where both evolved and young stellar populations contribute to the dust heating \citep{Bendo2015}. It is dangerous to infer properties like dust mass and SFR from FIR/submm data alone in these systems. A powerful method to investigate dust heating processes is through dust continuum radiative transfer (RT) simulations, which mimic the transport of radiation through a dusty medium. For a review of this method, we refer the reader to \citet{Steinacker2013}. Such simulations treat the dust-starlight interaction in 3D, allowing realistic geometries, multiple viewing angles and non-local heating. But it also comes with a large computational cost and the need for ``simple'', well-behaved targets to model. Therefore, the most common application is in models of edge-on spiral galaxies \citep[see e.g.][]{Popescu2000, Misiriotis2001, Bianchi2008, Baes2010, Popescu2011, MacLachlan2011, DeLooze2012b,DeGeyter2015} or early-type galaxies \citep{DeLooze2012a, Viaene2015}. Through consistent treatment of primary emission, scattering, absorption and thermal re-emission, dust heating mechanisms can be investigated. A general result of these studies is that starlight absorption by diffuse dust usually fails to heat this dust to sufficient levels to match the observed FIR/submm emission. Often, obscured star formation is necessary to balance the energy between UV/optical (absorption) and FIR/submm (emission). In a recent attempt to quantify the dust heating mechanisms, \citet{DeLooze2014} performed a detailed radiative transfer simulation of M51. Based on observed images, they closely mimic the distribution of both stars and dust, and then perform an accurate treatment of the dust-starlight interaction. They find that the contribution of evolved stars to the thermal re-emission is significant and varies with location and observed IR wavelength. In the mid-IR (MIR), the evolved stellar populations contribute about $10\%$ to the total dust heating from primary stellar emission, while young stars consequently contribute $90 \%$. This changes at submm wavelengths, where the contribution of evolved stars is $\sim40\%$. There is also a significant enhancement of the contribution by young stars in the spiral arms (>$80\%$) with respect to the inter-arm regions (<$60\%$). In this paper, we apply this novel technique to the Andromeda galaxy (M31). It is the most massive object in our Local Group and close to our own Milky Way. In the optical, the galaxy is dominated by its bright bulge \citep{Tempel2010}. The smooth disk is intersected by several dark lanes where dust obscures the starlight. The dark dust patches coincide with bright emission in the FIR and submm \citep{Fritz2012, Groves2012}. On the other side of the spectrum, in the UV, a striking similarity with the FIR morphology is observed \citep{Thilker2005}. The morphological (anti-)correlations are a manifestation of intricate interactions between dust and starlight. It is also evident that the observed features point at a complex 3D structure. Looking at M31 as it is projected on the sky inevitably leads to parameters which are summed or averaged along the line of sight. A 3D model of the sources and sinks for radiation in M31 can help to understand our closest neighbour beyond the standard line-of-sight quantities. It grants us the opportunity to investigate the morphology from different viewing angles and its influence on the spectral energy distribution (SED), the attenuation law and the processes of scattering, absorption and re-emission by dust. This endeavour sets new challenges to the radiative transfer modelling as M31 is much larger and has a higher inclination angle than M51 (in this work, we will use $i = 77.5 \degree$, which is the average value for the disk of M31 as derived from H\textsc{i} data by \citealt{Corbelli2010}). On the other hand, M31 is an obvious choice for studying dust heating mechanisms in great detail. Even for the hardest accessible wavelengths, the spatial resolution is still <140 pc along the major axis. Dust heating mechanisms in M31 have been investigated previously using UV-FIR energy balance SED fitting \citep{Montalto2009, Groves2012, Viaene2014}, using FIR/submm SED fitting by \citet{Smith2012} and \citet{Draine2014}, and through FIR colours \citep{PlanckM31}. All of these methods show that the emission from evolved stellar populations are the main contributor to the dust heating, especially at wavelengths beyond 160~$\upmu$m. However, quantifying the contributions of the different heating sources and their wavelength dependency remains difficult. Our study approaches this problem from a new perspective (radiative transfer simulations), and will provide quantitative measures related to dust heating in this galaxy. In Sect.~\ref{sec:data} of this paper we describe the panchromatic dataset we use and core data products we derive from it. Our model and all its components are outlined in Sect.~\ref{sec:methods} and validated in Sect.~\ref{sec:validation}. We present a 3D view of Andromeda in Sect.~\ref{sec:3dview} and a dust heating analysis in Sect.~\ref{sec:heating}. We present our main conclusions in Sect.~\ref{sec:conclusions}. | \label{sec:conclusions} We have constructed a highly detailed model for the Andromeda galaxy to investigate the dust heating mechanisms in this galaxy. Our model is based on observed morphologies and uses 3D panchromatic radiative transfer to simulate the dust-starlight interactions in a realistic setting. The main points of this work are: \begin{itemize} \item The integrated SED of M31 is fitted well and the resulting attenuation curve is consistent with observations, but with a broader UV bump. We are able to constrain 2 of our 3 free parameters: the dust mass and the luminosity of the young stellar component. The intrinsic luminosity of the ionizing stellar population is more difficult to constrain. \item The model is able to reproduce the observed morphologies fairly well from far-UV to submm wavelengths. The median (absolute value) deviation between model and observations across all bands is $22 \%$. The flux in the rings is generally underestimated, and the flux in the inter-ring regions is overestimated. Lowering the vertical scale height of the galaxy somewhat mitigates this effect, but cannot resolve it. The discrepancies are a combination of deprojection effects, variations in the nature and size distribution of the dust grains, and the subgrid treatment of the star-forming regions. With an inclination of $77.5 \degree$, M31 is about the limiting case for these kind of deprojected radiative transfer models. \item The dust in Andromeda is mainly heated by the evolved stellar populations. From a 3D analysis of the radiation field, we find that $91 \%$ of absorbed stellar radiation originates in evolved stellar populations. This high value is mainly due to the bright bulge, which dominates the radiation field out to the main star-forming ring at 10 kpc. Inside and beyond the star-forming ring, the contribution of unevolved stellar populations (i.e. ionizing and non-ionizing young stellar populations) to the radiation field increases, but usually remains in the $10-30 \%$ range. \item The sSFR (and its observational counterpart, $NUV-r$ colour) is a promising tracer for the total dust heating fraction and thus for the relative contributions to the total IR emission. We find that regions in M31 match the best fit relation derived from M51 pixels. In fact, the two datasets make a rather smooth and continuous sequence. More research is required to assess whether sSFR (and $NUV-r$) is a general tracer of dust heating fractions in galaxies at a local scale. \end{itemize} Our study has shown that the heating of dust by stellar populations is a complex problem with a large influence of geometry in three dimensions. Effects like non-local heating make it difficult to draw conclusions from 2D `on-sky' analysis. The contribution of evolved stellar populations is dominant in M31, and can also be significant in other galaxies. One should therefore be careful to directly link dust emission to the properties of unevolved stellar populations. As a final remark, we want to underline that this is one of the first attempts to construct a detailed geometrical model of stars and dust of a resolved and moderately inclined galaxy, based purely on 3D radiative transfer simulations. Because 3D radiative transfer models are computationally demanding, we were forced to make a number of simplifying assumptions on the geometry, and limit the number of free parameters in the model. In the future, we will refine our method on several points and apply it to galaxies of different morphologies and inclination. | 16 | 9 | 1609.08643 |
1609 | 1609.04686_arXiv.txt | We investigate the intrinsic properties of a sample of bright (with isotropic equivalent energy $E_{iso}>10^{52}$ erg) gamma-ray bursts, comparing those with and without radio afterglow. We find that the sample of bursts with no radio afterglows has a significantly shorter mean intrinsic duration of the prompt gamma-ray radiation, and the distribution of this duration is significantly different from those bursts with a radio afterglow. Although the sample with no radio afterglow has on average lower isotropic energy, the lack of radio afterglow does not appear to be a result of simply energetics of the burst, but a reflection of a separate physical phenomenon likely related to the circumburst density profile. We also find a weak correlation between the isotropic $\gamma-$ray energy and intrinsic duration in the sample with no radio afterglow, but not in the sample which have observed radio afterglows. We give possible explanations for why there may exist a sample of GRBs with no radio afterglow depending on whether the radio emission comes from the forward or reverse shock, and why these bursts appear to have intrinsically shorter prompt emission durations. We discuss how our results may have implications for progenitor models of GRBs. | Over the last couple of decades, we have gained a general understanding of the nature of gamma-ray bursts (GRBs) thanks to satellites such as BATSE, BeppoSAX, Swift, Fermi, Integral, and many others, not to mention the many ground-based follow-up observations of GRB afterglows (for a summary of results, see reviews by van Paradijs et al. 2000; Piran 2004; Zhang \& Meszaros 2004; Meszaros 2006; Woosley \& Bloom 2006; Gehrels, Ramirez-Ruiz \& Fox 2009; Gombec 2012; Berger 2014). However, these data have also opened up many new questions, and in some ways increased the number of viable models for GRBs. Although it appears likely GRBs are associated with a massive stellar progenitor in the case of long bursts (see, e.g., Gehrels, Ramirez-Ruiz \& Fox 2009 and references therein for a summary of the observations; for an early theoretical perspective see Popham, Woosley, \& Fryer 1999), and a merger of compact objects in the case of short bursts \cite{Berg14}, uncertainties in the details of the progenitor remain. It is clear that in order to shed light on the nature of GRBs, we must continue to analyze their broad-band spectral data and light curves. In particular, features in the light curves such as plateaus, flares, and steep decays (Swenson et al. 2013; Swenson \& Roming 2014) all contain clues to the dissipation mechanism and, potentially, the progenitor. One of the most difficult aspects of GRBs, however, is the number of parameters that can play a role in the behaviors of the spectra and light curves. In addition to global burst parameters (such as the energy emitted, the duration of the inner engine, the density profile of the circumburst medium), the microphysical parameters (e.g. fraction of energy in the magnetic field, and the energy distribution of radiating particles) can significantly affect the resultant light curve. The degeneracy among all of the various physical parameters make it difficult to draw firm conclusions about the detailed physics of GRBs. In this paper, we examine the properties of GRBs with and without radio afterglows, in an attempt to gain insight into the inner engine and environment of a GRB. Because the radio afterglow generally peaks at later times and the emission mechanism is fairly solidly understood as synchrotron emission, we can circumvent some uncertainties that arise in the X-ray and optical afterglow emission (Frail et al. 1997; Galama et al. 2000). The long-lived radio afterglow may be a better probe (compared to optical and X-ray) of the far-out circumstellar environment of the GRB, and offer a better estimate of the energetics (see, e.g., Frail, Waxman, \& Kulkarni 2000) which can, in turn, help us learn something about the progenitor. Chandra \& Frail (2012) presented analysis of a sample of 304 GRBs that were followed up in the radio over a span of 14 years, from 1997-2011. They carried out a number of statistical analyses, and found a detection rate of radio afterglows around $31\%$. This is in sharp contrast to the detection rates of X-ray afterglows ($\sim 95 \%$) and optical afterglows ($\sim 70 \%$). The radio light curve at 8.4GHz peaks at around 3-6 days with a median peak luminosity of $10^{31}$erg s$^{-1}$ Hz$^{-1}$. Although they suggest there is a relationship between the detectability of a radio afterglow and the fluence or energy of the GRB, they find no significant correlations between the strength of the radio flux density and the GRB energy, fluence or X-ray flux (they do find a mild correlation between the strength of the optical flux density at 11hr and the peak radio flux density; see their Table 5). Ultimately, they conclude that radio afterglow samples are sensitivity-limited and therefore bursts without radio afterglow are not inherently radio quiet. However, Hancock, Gaensler, \& Murphy (2013) - hereafter HGM - present an alternative view. By using visibility stacking techniques (see the method described in Hancock, Gaensler \& Murphy 2011) of 737 radio observations consisting of 178 GRBs for which VLA data could be calibrated, they showed the stacked data of radio faint GRBs did not produce any detections. Instead, they suggest that there are two intrinsically different populations of GRBs - radio loud and radio quiet (interestingly, after decades of debate, it has emerged that there is a bimodal distribution of quasars in terms of the presence/absence of radio emission, and this appears to be a true, physical - i.e. not a selection - effect; see Kellerman et al. 2016 and references therein). They estimate that $\sim 30-40 \%$ of GRBs are truly intrinsically radio quiet. Although they find that the redshift distributions between radio loud and faint are statistically the same, they claim signficant differences between their radio loud and quiet samples in observed prompt duration, gamma-ray fluence, optical and x-ray flux, and isotropic equivalent energy (see their Table 3). They speculate that the inherent difference between radio loud and faint GRBs could be a reflection of either different emission mechanisms, or a magnetar-driven engine (radio quiet) vs. black-hole driven engine (radio loud). Indeed bimodality in GRB afterglow emission - particularly in the temporal decay indices and luminosities - has previously been suggested in X-rays (Boer \& Gendre 2000; Gendre \& Boer 2005; Gendre et al. 2008) and optical (Nardini et al. 2006; Liang \& Zhang 2006). Motivated by HGM, we investigate further the suggestion of an intrinsically radio quiet sub-population of GRBs. In particular, we examine a sample of the intrinsically brightest GRBs (in terms of isotropic emitted $\gamma-$ray energy $E_{iso}$). Selecting only those bursts with $E_{iso} > 10^{52} erg$, we investigate the differences of various GRB {\em intrinsic} properties, for those bursts with and without a radio afterglow. We find a significant difference in the mean isotropic $\gamma-$ ray energy between the radio loud and quiet samples (similar to Chandra \& Frail 2012 and HGM, who made no cut in $E_{iso}$). Interestingly, however, we also find a significant difference between the intrinsic duration distributions. We find the latter difference to be the most robust when comparing the radio loud and radio quiet samples. In addition, we find a weak correlation between isotropic energy and intrinsic duration in the radio quiet sample, but not the radio loud sample. We also compare radio loud and quiet samples for intrinsically faint GRBs (in terms of isotropic energy) and find no difference among the two samples. We explore the implications our findings have on progenitor models. This paper is organized as follows: In \S 2, we describe our data sample taken from the Chandra \& Frail (2012) catalog. In \S 3, we present our statistical analysis of the bright bursts ($E_{iso} > 10^{52}$ erg) with and without a radio afterglow. For comparison, we also present an analysis of radio loud and quiet bursts with energies below our energy cutoff. In \S 4, we review some of the physical parameters that play a role in determining the strength of the radio flux from the forward and reverse shock of the external blast wave. In \S 5, we discuss the implications of our results for progenitor models of GRBs. Conclusions are presented in \S 6. Throughout the paper we use the term ``radio loud'' and ``radio quiet'' to refer to GRBs with and without a detected radio afterglow, respectively. | We have examined a sample of bright gamma-ray bursts (defined by $E_{iso} > 10^{52} erg$) that have been followed up in the radio band (Chandra \& Frail 2012), and compared the intrinsic properties of bursts with and without radio afterglows. We find that there is a significant difference in the distributions of intrinsic durations between the two samples. In particular, the radio quiet sample shows significantly shorter prompt burst durations, with an average intrinsic duration more than a factor of two shorter than the radio loud sample. In addition, we found a mild positive correlation ($\sim 3 \sigma$) between intrinsic duration and isotropic energy for the radio quiet sample, but {\em not} the radio loud sample. We suggest these results may offer clues to the progenitors of long GRBs, potentially distinguishing between collapsars and various merger scenarios, although the many parameters that play a role in the determining the radio flux obscure an obvious interpretation. Nonetheless, our results suggest a connection between the prompt gamma-ray emission (often believed to reflect primarily the physics of the inner engine) and the later-time radio afterglow (a reflection of the circumburst environment), implying that both likely depend on the circumburst environment. If the radio afterglow emission comes from the forward shock of the external blast wave, a zeroth order interpretation is that a sufficiently dense circumburst medium produces both an observable radio afterglow and a longer duration burst (from more/extended shock events in the surrounding medium). If the radio afterglow is a result of emission from the reverse shock, the presence of a radio afterglow could suggest a more tenuous ISM-like medium (as opposed to a wind) that would give rise to longer-lived reverse shock emission; in this case, the prompt duration appears to be more directly connected to the amount of angular momentum of the inner engine. A potentially important extension of this is to examine in further detail the multi-wavelength properties of the radio loud and quiet samples. As mentioned in the \S 1, other studies have suggested bimodality of the afterglow emission properties of GRBs in the optical and X-ray, and Gendre et al. (2008) suggest that there could be in fact three populations of radio afterglows based on the properties of their X-ray and optical afterglow emission. Future work should tie the results in all bands to the properties of the progenitor and circumburst medium. We note that only a few GRBs of the short-duration class ($T_{90} < 2s$) have an observed radio afterglow. Their isotropic-equivalent energies are in general a couple of orders of magnitude lower than the long-duration class of GRBs so it is difficult to extend this analysis (i.e. selecting the brightest bursts to avoid contamination effects) to this class of bursts. However, it is worth considering the presence/absence of the trends we see in this paper in the context of short GRBs. We may be able to add significantly to the sample of both long and short GRBs with radio follow-up with the advent of more sensitive radio telescopes. In addition, continued broad band follow-up of GRBs will allow us to get a better handle on whether there truly exist two populations of GRBs and what we might learn about their progenitors from the presence - or lack - of their radio afterglows. | 16 | 9 | 1609.04686 |
1609 | 1609.04153_arXiv.txt | {{\it Gaia} is a cornerstone mission in the science programme of the European Space Agency (ESA). The spacecraft construction was approved in 2006, following a study in which the original interferometric concept was changed to a direct-imaging approach. Both the spacecraft and the payload were built by European industry. The involvement of the scientific community focusses on data processing for which the international {\it Gaia} Data Processing and Analysis Consortium (DPAC) was selected in 2007. {\it Gaia} was launched on 19 December 2013 and arrived at its operating point, the second Lagrange point of the Sun-Earth-Moon system, a few weeks later. The commissioning of the spacecraft and payload was completed on 19 July 2014. The nominal five-year mission started with four weeks of special, ecliptic-pole scanning and subsequently transferred into full-sky scanning mode. We recall the scientific goals of {\it Gaia} and give a description of the as-built spacecraft that is currently (mid-2016) being operated to achieve these goals. We pay special attention to the payload module, the performance of which is closely related to the scientific performance of the mission. We provide a summary of the commissioning activities and findings, followed by a description of the routine operational mode. We summarise scientific performance estimates on the basis of in-orbit operations. Several intermediate {\it Gaia} data releases are planned and the data can be retrieved from the {\it Gaia} Archive, which is available through the {\it Gaia} home page at \url{http://www.cosmos.esa.int/gaia}.} | \label{sect:introduction} Astrometry is the astronomical discipline concerned with the accurate measurement and study of the (changing) positions of celestial objects. Astrometry has a long history \citep{2012EPJH...37..745P} even before the invention of the telescope. Since then, advances in the instrumentation have steadily improved the achievable angular accuracy, leading to a number of important discoveries: stellar proper motion \citep{1717RSPT...30..736H}, stellar aberration \citep{1727RSPT...35..637B}, nutation \citep{1748RSPT...45....1B}, and trigonometric stellar parallax \citep{1838AN.....16...65B,1840MmRAS..11...61H,1840AN.....17..177V}. Obtaining accurate parallax measurements from the ground, however, remained extremely challenging owing to the difficulty to control systematic errors and overcome the disturbing effects of the Earth's atmosphere, and the need to correct the measured relative to absolute parallaxes. Until the mid-1990s, for instance, the number of stars for which ground-based parallaxes were available was limited to just over 8000 \citep[][but see \citealt{2016yCat.1333....0F}]{1995gcts.book.....V}. This situation changed dramatically in 1997 with the {\it Hipparcos} satellite of the European Space Agency (ESA), which measured the absolute parallax with milli-arcsecond accuracy of as many as $117\,955$ objects \citep{1997ESASP1200.....E}. The {\it Hipparcos} data have influenced many areas of astronomy \citep[see the review by][]{2009aaat.book.....P}, in particular the structure and evolution of stars and the kinematics of stars and stellar groups. Even with its limited sample size and observed volume, {\it Hipparcos} also made significant advances in our knowledge of the structure and dynamics of our Galaxy, the Milky Way. The ESA astrometric successor mission, {\it Gaia}, is expected to completely transform the field. The main aim of {\it Gaia} is to measure the three-dimensional spatial and the three-dimensional velocity distribution of stars and to determine their astrophysical properties, such as surface gravity and effective temperature, to map and understand the formation, structure, and past and future evolution of our Galaxy \citep[see the review by][]{2016arXiv160207702B}. The Milky Way contains a complex mix of stars (and planets), interstellar gas and dust, and dark matter. These components are widely distributed in age, reflecting their formation history, and in space, reflecting their birth places and subsequent motions. Objects in the Milky Way move in a variety of orbits that are determined by the gravitational force generated by the integrated mass of baryons and dark matter, and have complex distributions of chemical-element abundances, reflecting star formation and gas-accretion history. Understanding all these aspects in one coherent picture is the main aim of {\it Gaia}. Such an understanding is clearly also relevant for studies of the high-redshift Universe because a well-studied template galaxy underpins the analysis of unresolved galaxies. {\it Gaia} needs to sample a large, representative, part of the Galaxy, down to a magnitude limit of at least 20 in the {\it Gaia} $G$ band to meet its primary science goals and to reach various (kinematic) tracers in the thin and thick disks, bulge, and halo \citep[][Table~1]{2001A&A...369..339P}. For the 1000 million stars expected down to this limit, {\it Gaia} needs to determine their present-day, three-dimensional spatial structure and their three-dimensional space motions to determine their orbits and the underlying Galactic gravitational potential and mass distribution. The astrometry of {\it Gaia} delivers absolute parallaxes and transverse kinematics (see \citealt{2015PASP..127..994B} on how to derive distances from parallaxes). Complementary radial-velocity and photometric information complete the kinematic and astrophysical information for a subset of the target objects, including interstellar extinctions and stellar chemical abundances. Following the {\it R{\o}mer} mission proposal from the early 1990s \citep[see][]{2008IAUS..248..300H}, the {\it Gaia} mission was proposed by Lennart Lindegren and Michael Perryman in 1993 \citep[for historical details, see][]{2014arXiv1408.4668H}, after which a concept and technology study was conducted. The resulting science case and mission and spacecraft concept are described in \cite{2001A&A...369..339P}. In the early phases, {\it Gaia} was spelled as {\it GAIA,} for Global Astrometric Interferometer for Astrophysics, but the spelling was later changed because the final design was non-interferometric and based on monolithic mirrors and direct imaging and the final operating principle was actually closer to a large {\it R{\o}mer} mission than the original {\it GAIA} proposal. After the selection of {\it Gaia} in 2000 as an ESA-only mission, followed by further preparatory studies, the implementation phase started in 2006 with the selection of the prime contractor, EADS Astrium (later renamed Airbus Defence and Space), which was responsible for the development and implementation of the spacecraft and payload. Meanwhile, the complex processing and analysis of the mission data was entrusted to the Data Processing and Analysis Consortium (DPAC), a pan-European, nationally funded collaboration of several hundred astronomers and software specialists. {\it Gaia} was launched in December 2013 and the five-year nominal science operations phase started in the summer of 2014, after a half-year period of commissioning and performance verification. Unlike the {\it Hipparcos mission, the {\it Gaia} collaboration does not have data rights.} After processing, calibration, and validation inside DPAC, data are made available to the world without limitations; this also applies to the photometric and solar system object science alerts (Sect.~\ref{subsect:initial_data_treatment}). Several intermediate releases, with roughly a yearly cadence, have been defined and this paper accompanies the first of these, referred to as {\it Gaia Data Release~1} \citep[{\it Gaia DR1;}][]{DPACP-8}. The data, accompanied by several query, visualisation, exploration, and collaboration tools, are available from the {\it Gaia} Archive \citep{DPACP-19}, which is reachable from the {\it Gaia} home page at \url{http://www.cosmos.esa.int/gaia} and directly at \url{http://archives.esac.esa.int/gaia}. This paper is organised as follows: Section~\ref{sect:scientific_goals} summarises the science goals of the mission. The spacecraft and payload designs and characteristics are described in Sect.~\ref{sect:spacecraft_and_payload}. The launch and commissioning phase are detailed in Sect.~\ref{sect:launch_and_commissioning}. Section~\ref{sect:mission_and_spacecraft_operations} describes the mission and mission operations. The science operations are summarised in Sect.~\ref{sect:science_operations}. Section~\ref{sect:dpac} outlines the structure and flow of data in DPAC. The science performance of the mission is discussed in Sect.~\ref{sect:scientific_performance}. A summary can be found in Sect.~\ref{sect:conclusions}. All sections are largely stand-alone descriptions of certain mission aspects and can be read individually. The use of acronyms in this paper has been minimised; a list can be found in Annex~\ref{sect:acronyms}. | \label{sect:conclusions} {\it Gaia} is the space-astrometry mission of the European Space Agency which, after successful commissioning, started scientific operations in mid-2014. The primary science goal of {\it Gaia} is to examine the kinematical, dynamical, and chemical structure and evolution of our Milky Way. In addition, the data of {\it Gaia} will have a strong impact on many other areas of astrophysical research, including stellar evolution and physics, star formation, stellar variability, the distance scale, multiple stars, exoplanets, solar system bodies, unresolved galaxies and quasars, and fundamental physics. With a focal plane containing more than 100 CCD detectors, {\it Gaia} surveys the heavens and repeatedly observes all objects down to $G \approx 20.7$~mag during its five-year nominal lifetime. The science data of {\it Gaia} comprise absolute astrometry (positions, proper motions, and parallaxes), broadband photometry in the unfiltered $G$ band, low-resolution blue and red (spectro-)photometry (BP and RP), and integrated $G_{\rm BP}$ and $G_{\rm RP}$ photometry for all objects. Medium-resolution spectroscopic data are collected for the brightest few hundred million sources down to $G_{\rm RVS} \approx 16.2$~mag. The concept and design of the spacecraft and the mission ultimately allows, after five years, stellar parallaxes (distances) to be measured with standard errors less than 10~$\mu$as for stars brighter than $G \approx 13$~mag, around 30~$\mu$as for stars around $G \approx 15$~mag, and around 600~$\mu$as around $G \approx 20$~mag. End-of-life photometric standard errors are in the milli-magnitude regime. The spectroscopic data allow the measurement of (mission-averaged) radial velocities with standard errors at the level of 1~km~s$^{-1}$ at $G_{\rm RVS} \approx 11$--$12$~mag and 15~km~s$^{-1}$ at $G_{\rm RVS} \approx 15$--$16$~mag, depending on spectral type. The {\it Gaia} Data Processing and Analysis Consortium (DPAC) is responsible for the processing and calibration of the {\it Gaia} data. The first intermediate release of {\it Gaia} data \citep{DPACP-8} comprises astrometry \citep{DPACP-14}, photometry \citep{DPACP-12}, and variability \citep{DPACP-15}; later releases will include BP/RP and RVS data. The validation of the data is described in \cite{DPACP-16} and the {\it Gaia} Archive is described in \cite{DPACP-19}. | 16 | 9 | 1609.04153 |
1609 | 1609.08711_arXiv.txt | High-amplitude variability in Young Stellar Objects (YSOs) is usually associated with episodic accretion events. It has not been observed so far in massive YSOs. Here, the high-amplitude variable star sample of ContrerasPe\~{n}a et al.(2016) has been used to search for highly-variable($\Delta$K$\ge$1\,mag) sources coinciding with dense clumps mapped using the 850\mum continuum emission by the ATLASGAL survey. 18 variable sources are centred on the sub-mm clump peaks, and coincide ($<$1\arcsec) with a 24\mum point or compact ($<$10\arcsec) source. 13 of these 18 sources can be fit by YSO models. The 13 variable YSOs(VYSO) have luminosities of $\sim$10$^3$ \lsun, an average mass of 8~\msun and a range of ages up to 10$^6$\,yr. 11 of these 13 VYSOs are located in the midst of infrared dark clouds. 9 of the 13 sources have $\Delta$K$>$2\,mag, significantly higher compared to the mean variability of the entire VVV sample. The light curves of these objects sampled between 2010-2015 display rising, declining, or quasi-periodic behaviour but no clear periodicity. Light-curve analysis using Plavchan method show that the most prominent phased signals have periods of a few hundred days. The nature and time-scale of variations found in 6.7 Ghz methanol maser emission (MME) in massive stars are similar to that of the VYSO light curves. We argue that the origin of the observed variability is episodic accretion. We suggest that the timescale of a few hundred days may represent the frequency at which a spiralling disk feeds dense gas to the young massive star. | \label{sec:intro} Variability studies of young low mass stars, both in the line and continuum, have proven to be powerful tools to decipher the physics of star formation and pre-main-sequence evolution. Low mass Young Stellar Objects (YSOs) displaying optical/infrared flux variability trace a variety of phenomena \citep{carpenter01,1996AA...310...143F} such as accretion events in the disk, magnetospheric activity \citep{bouvier2007}, spots \citep{boubert89} and flares on the stellar surface. High-amplitude variability is often associated with episodic events of accretion, well-known through objects such as FUors (named after FU Orionis) and EXors (named after EX Lupi). Hence, they are excellent laboratories to understand the accretion phenomenon, especially at unresolved spatial scales representing the accretion disk and the young star. Higher mass young stars are elusive objects that spend their brief youth while deeply embedded in extremely dense molecular cores. Optical photometric variability studies of Herbig Ae/Be stars (intermediate mass YSOs) concluded that large amplitude variability is confined to stars with spectral types later than B8 \citep{b1}. This result should not be surprising, considering that stars more massive than 8~\msun\, would lack a pre-main-sequence phase appearing directly on the zero-age-main-sequence \citep{b5,b6}. In other words, optically visible intermediate and massive stars should have already arrived on the zero-age-main-sequence \citep{b7} with very little episodic accretion activity. Moreover, once a massive star becomes optically visible, the accretion rates are low \citep{hartman93} and the accretion luminosity itself is insignificant compared to the total luminosity. On the other hand, the infrared counterparts ({\em IRcs}) to high-mass protostellar objects ({\em HMPO}) \citep{b3,b4}, represent some sort of a pre-main-sequence phase for the massive stars because these objects are deeply embedded in their natal dense molecular cores, show high accretion rates, and they are detected only in the infrared bands. Hence, they are more likely to display variability associated with accretion episodes. However, a systematic search for variability in such objects is still lacking. {\em IRcs} to {\em HMPO}'s are often visible as point-sources in the near-infrared K-band in the midst of dark clouds. The following work is an attempt to find variability in such sources. The Vista Variables in the Via Lactea survey \citep[VVV,][]{2010Minniti} provides $ZYJHK_{s}$ photometry of $\approx 560$~deg$^{2}$ of the Galactic Bulge and the adjacent mid-plane. In addition, the survey has yielded $\approx$ 50 to 70 epochs of $K_{s}$ photometry over a period of 5 years. The VVV survey covers much of the Galactic fourth quadrant, which is known for its intense activity of high-mass star formation in the Milky-Way. This virtue of the fourth quadrant has caused it to be the focus for several other Galactic plane surveys such as ATLASGAL \citep{schuller09} and HiGal \citep{molinari2010}, aiming to uncover deeply embedded high-mass stars and cluster forming cores. The ATLASGAL survey has provided an unbiased data set of dense molecular clumps. These are massive clumps, often associated with high-mass star formation. Prior to the VVV study, no eruptive variable YSOs were known with luminosities higher than a few hundred solar luminosities \citep{audard14}. In this work we inspect the VVV sample of 816 high amplitude infrared variable stars discovered by \citet{carlos16a} and we isolate variables that coincide with ATLASGAL clumps in an effort to find variable young intermediate/high-mass stars. | This study has found hitherto unknown near-infrared variability in intermediate to high-mass young stars by using the VISTA VVV data from 2010-2015. Following a stringent selection criteria to select targets with $\Delta K \ge 1$mag, 13 VYSOs located at the peak of ATLASGAL clumps are identified. These sources are characterised by modelling their 1-850\mum SEDs and by analysing their light-curves with a phase-dispersion minimisation method. \begin{itemize} \item The SED modelling of the 13 VYSO show that their luminosities are of $\sim$10$^3$ \lsun, the stellar masses and ages in the range of 8-11~\msun and 10$^4$ - 10$^6$\,yrs respectively. \item The light-curves are not periodic in nature. They can be classified as rising, declining or quasi-periodic. Analysis using the Plavchan method reveal that the most prominent underlying periodic signal would have an average period of $\sim$500days. \item The high-amplitude variability in young massive stars is attributed to episodic accretion events. \end{itemize} \floattable \begin{deluxetable}{lccccccc} \tablecaption{Source Details \label{table:source}} \tablewidth{100pt} \tablenum{1} \tablecolumns{8} \tablehead{ \colhead{VYSO} & \colhead{RA} & \colhead{Dec} & \dcolhead{K_s\tablenotemark{a}} & \dcolhead{\Delta K_s \tablenotemark{b}} & \dcolhead{ \sigma K_s} \tablenotemark{c} & \colhead{Light curve} & \colhead{Association}\\ \colhead{} & \colhead{deg} & \colhead{deg} & \colhead{mag} & \colhead{mag} & \colhead{mag} & \colhead{type\tablenotemark{d}} & \colhead{} } \startdata VVVv244 & 245.00828 & -51.43392 & 14.4 & 2.08 & 0.59 & \footnotesize{LPV-YSO} & \footnotesize{IRDC}\\ VVVv263 & 245.43405 & -50.34484 & 13.9 & 2.24 & 0.64 & \footnotesize{Eruptive} & \footnotesize{IRDC}\\ VVVv336 & 252.77721 & -45.72340 & 14.9 & 2.27 & 0.51 & \footnotesize{Eruptive} & \footnotesize{IRDC}\\ VVVv367 & 255.12338 & -43.88343 & 14.5 & 2.35 & 0.67 & \footnotesize{Fader} & \footnotesize{IRDC}\\ VVVv374 & 254.64164 & -42.83201 & 11.7 & 2.41 & 0.73 & \footnotesize{Eruptive} &\footnotesize{IRDC, EGO, RMS\tablenotemark{e}}\\ VVVv389 & 255.82157 & -42.43052 & 14.3 & 1.56 & 0.41 & \footnotesize{Fader} & \footnotesize{IRDC}\\ VVVv405 & 257.41092 & -41.64772 & 14.5 & 2.35 & 0.44 & \footnotesize{Dipper} & \footnotesize{HII}\\ VVVv406 & 257.48944 & -41.59691 & 13.5 & 2.06 & 0.78 & \footnotesize{Dipper} & \footnotesize{HII}\\ VVVv665 & 242.49040 & -50.80262 & 13.4 & 1.63 & 0.43 & \footnotesize{Eruptive} & \footnotesize{IRDC}\\ VVVv717 & 249.02318 & -46.67795 & 12.5 & 2.47 & 0.64 & \footnotesize{LPV-YSO} &\footnotesize{IRDC}\\ VVVv736 & 252.73104 & -44.11650 & 15.5 & 1.52 & 0.25 & \footnotesize{Dipper} &\footnotesize{IRDC}\\ VVVv750 & 253.18580 & -43.08889 & 15.8 & 2.73 & 0.82 & \footnotesize{STV} &\footnotesize{IRDC}\\ VVVv802 & 258.54427 & -38.50329 & 13.2 & 1.42 & 0.40 & \footnotesize{LPV-Mira} &\footnotesize{IRDC}\\ \enddata \tablenotetext{a}{Average magnitudes} \tablenotetext{b}{The amplitudes for these sources are typically larger than the mean amplitudes for the 816 sample of \cite{carlos16a}, irrespective of the light curve classification.} \tablenotetext{c}{RMS variation of $\Delta K_s$ as a function of $K_s$ for the given VVV tile} \tablenotetext{d}{LPV= long periodic variable, STV= short time scale variable} \tablenotetext{e}{RMS=Red MSX source \citep{lumsden13}} \end{deluxetable} \floattable \begin{deluxetable}{lccccccccccccc} \tablecaption{Photometric data used for SED fitting \label{table:seddata1} } \tablewidth{50pt} \tablenum{2} \tablecolumns{15} \tablehead{ \colhead{VYSO} & \colhead{I1} & \colhead{I2} & \colhead{I3} & \colhead{I4} & \colhead{W3} & \colhead{W4} & \colhead{M1} & \colhead{PACS70} & \colhead{PACS160} & \colhead{SPIRE250} & \colhead{SPIRE350} & \colhead{SPIRE500} & \colhead{AGAL850} \\ \colhead{} & \colhead{mag} & \colhead{mag} & \colhead{mag} & \colhead{mag} & \colhead{mag} & \colhead{mag} & \colhead{mag} & \colhead{Jy} & \colhead{Jy} & \colhead{Jy} & \colhead{Jy} & \colhead{Jy} & \colhead{Jy} } \startdata VVVv244 & 11.2& 10.0& 8.8& 8.2& 6.0& 4.1& -& 2.4& 10.73& 20.23& 12.88& 7.42& 0.84 \\ VVVv263 & 9.6& 8.1& 6.8& 6.0& 5.40& 2.3\tablenotemark{a}& 1.9& 3.63& 17.23& -& -& -& 15.0 \\ VVVv336 & 11.2& 9.7& 8.4& 7.5& -& -& 4.5& -& 2.31& 13.47& 15.87& -& 3.84 \\ VVVv367 & 9.8& 8.3& 7.0& 5.8& 4.6& 1.9& -& 6.05& 5.75& 7.75& -& -& 4.00 \\ VVVv374 & 7.4& 6.5& 5.6& 4.8& 3.9& 1.7& -& 40.52& 35.98& 65.92& 40.79& 25.93& 3.00 \\ VVVv389 & 10.0& 8.7& 7.9& 7.3& 6.2& 3.6& -& 0.84& 5.10& 12.99& 15.49& 38.74& 13.42 \\ VVVv405 & 8.8& 7.4& 6.0& 5.1& 4.4& -& 2.0& 7.68& 40.31& 89.33& 31.86& 71.33& 7.27 \\ VVVv406 & 10.2& 9.3& 8.5& 7.6& 5.6& 2.5& -& 3.54& 26.77& 41.01& -& -& 10.78 \\ VVVv665 & 10.0 & 8.9& 7.8& 7.0& 6.3 & 3.8\tablenotemark{a}& 3.7 & 0.94& 18.46& -& -& -& 1.89 \\ VVVv717 & 10.1& 8.8& 7.6& 6.8& 6.5& 4.4\tablenotemark{a} & 4.0 & 0.57 & 2.08 & -& -& -& 2.45 \\ VVVv736 & 10.6& 9.4& 8.0& 7.3& 5.7& 2.9\tablenotemark{a}& 4.5& 67.71& 71.60& 71.79 & 47.11& 28.77& 1.21 \\ VVVv750 & 12.4& -& 9.6& 9.0& 6.3& 2.0& -& 20.69& 15.56& 21.45& 17.50& 9.80& 1.89 \\ VVVv802 & 8.2& 6.5& 5.4& 4.7& 4.2& 1.7& -& 31.11& 13.97& 20.31& 14.87& 14.10 & 3.71\\ \enddata \tablenotetext{a}{not used} \end{deluxetable} \floattable \rotate \begin{deluxetable*}{LCCCCCCCCCCC} \tablecaption{SED Fitting results} \tablecolumns{12} \tablenum{3} \tablehead{ \colhead{VYSO} & \colhead{$M_{\ast}$}& \colhead{$ A_{V,core}$ } & \colhead{$A_{V,int}$ } & \colhead{$\dot{M}_{env}$} & \colhead{$\dot{M}_{disc}$} & \colhead{$\log Age$ } & \colhead{distance}& \colhead{$\log L_{tot}$} & \colhead{$\chi^{2}_{best}/N_{data}$} & \colhead{$N_{fits}$} & \colhead{$N_{fits2}$\tablenotemark{a}} \\ \colhead{} & \colhead{$M_{\odot}$} & \colhead{mag} & \colhead{mag} & \colhead{$10^{-5} M_{\odot}$~yr$^{-1}$} & \colhead{$10^{-6} M_{\odot}$~yr$^{-1}$} & \colhead{yr} & \colhead{kpc} & \colhead{$L_{\odot}$} & \colhead{} & \colhead{} & \colhead{} } \startdata VVVv244 & 5.9$\pm$2.6 & 192$\pm$4009 & 32$\pm$13 & 7.6$\pm$26.2 & 1.1$\pm$6.0 & 6.2$\pm$0.8 & 5.5$\pm$3.5 & 2.8$\pm$0.7 & 0.05 & 10000 & 1392\\ VVVv263 & 8.5$\pm$2.8 & 97$\pm$595 & 48$\pm$7 & 3.3$\pm$3.5 & 3.8$\pm$27.0 & 6.2$\pm$0.7 & 4.2$\pm$2.6 & 3.5$\pm$0.5 & 0.65 & 684 & 49\\ VVVv336 & 7.3$\pm$2.9 & 206$\pm$2951 & 43$\pm$9 & 0.0$\pm$0.0 & 0.7$\pm$2.8 & 6.4$\pm$0.2 & 5.7$\pm$3.3 & 3.2$\pm$0.6 & 0.09 & 3333 & 8\\ VVVv367 & 8.3$\pm$3.7 & 641$\pm$3857 & 31$\pm$14 & 3.8$\pm$4.2 & 8.7$\pm$34.0 & 5.7$\pm$1.2 & 4.9$\pm$2.9 & 3.3$\pm$0.6 & 0.16 & 1035 & 363\\ VVVv374 & 8.8$\pm$2.7 & 121$\pm$1480 & 15$\pm$4 & 1.6$\pm$7.9 & 0.6$\pm$4.2 & 6.3$\pm$0.2 & 4.4$\pm$2.5 & 3.5$\pm$0.4 & 0.14 & 1659 & 113\\ VVVv389 & 7.3$\pm$2.5 & 67$\pm$1185 & 37$\pm$9 & 0.4$\pm$0.9 & 0.7$\pm$3.1 & 6.4$\pm$0.3 & 5.1$\pm$3.1 & 3.2$\pm$0.5 & 0.38 & 3200 & 75\\ VVVv405 &11.1$\pm$3.3 & 340$\pm$3631 & 45$\pm$6 & 0.0$\pm$0.0 & 1.8$\pm$6.3 & 6.3$\pm$0.2 & 4.4$\pm$2.3 & 3.8$\pm$0.4 & 0.64 & 806 & 0\\ VVVv406 & 5.3$\pm$2.5 & 83$\pm$3391 & 13$\pm$11 & 2.8$\pm$3.2 & 2.8$\pm$8.7 & 4.9$\pm$0.9 & 5.7$\pm$3.6 & 2.6$\pm$0.7 & 0.25 & 3172 & 2812\\ VVVv665 & 7.6$\pm$2.5 & 69$\pm$1056 & 37$\pm$8 & 0.0$\pm$0.2 & 0.7$\pm$2.7 & 6.4$\pm$0.2 & 5.5$\pm$3.2 & 3.3$\pm$0.5 & 0.03 & 3969 & 51\\ VVVv717 & 8.5$\pm$2.8 & 73$\pm$691 & 44$\pm$6 & 0.0$\pm$0.0 & 1.5$\pm$4.1 & 6.3$\pm$0.2 & 5.7$\pm$3.3 & 3.5$\pm$0.5 & 0.49 & 1459 & 0\\ VVVv736 & 7.5$\pm$2.9 & 224$\pm$3415 & 36$\pm$12 & 58.8$\pm$96.1& 0.5$\pm$3.5 & 6.4$\pm$0.3 & 5.9$\pm$3.3 & 3.2$\pm$0.6 & 0.0 & 5515 & 204\\ VVVv750 & 7.4$\pm$3.3 & 450716$\pm$5232901 & 11$\pm$8 & 15.8$\pm$17.0& 19.8$\pm$71.2 & 4.1$\pm$0.7 & 6.2$\pm$3.8 & 2.9$\pm$0.6 & 0.08 & 1807 & 1806\\ VVVv802 &11.5$\pm$3.2 & 160$\pm$2169 & 47$\pm$5 & 0.9$\pm$1.7 & 2.3$\pm$10.0 & 6.3$\pm$0.2 & 3.5$\pm$1.6 & 3.9$\pm$0.4 & 0.29 & 1635 & 5\\ \enddata \tablenotetext{a}{The number of models with a non-zero envelope accretion rate.} \end{deluxetable*} \begin{table} \tablenum{4} \caption{Light curve analysis results}\label{tab:sedfits} \begin{tabular}{@{}lllllll} \hline \hline VYSO & Per1\tablenotemark{a} & Pwr1\tablenotemark{b} & Per2 & Pwr2 & Per3 & Pwr3\\ \hline VVVv244 & 107.7 & 28.5 & 809.0 & 26.0 & 7.0 & 24.7 \\ VVVv263 & 314.0 & 122.7 & 560.0 & 54.3 & - & - \\ VVVv336 & 886.3 & 20.8 & 283.5 & 20.1 & 327.1 & 9.5 \\ VVVv367 & 289.7 & 14.8 & 146.9 & 10.7 & 114.0 & 8.5 \\ VVVv374 & 454.0 & 59.1 & 251.3 & 22.4 & 124.3 & 12.1 \\ VVVv389 & 188.5 & 12.2 & 233.1 & 12.2 & 438.7 & 11.5 \\ VVVv405 & 491.5 & 12.4 & 231.1 & 6.5 & 113.4 & 6.5 \\ VVVv406 & 491.9 & 227.1 & 939.0 & 66.6 & - & - \\ VVVv665 & 834.7 & 23.1 & 303.9 & 7.2 & - & - \\ VVVv717 & 851.0 & 177.8 & 277.4 & 68.8 & - & - \\ VVVv736 & 493.1 & 18.8 & 311.5 & 13.3 & 235.6 & 9.5 \\ VVVv750 & 66.2 & 183.9 & 44.4 & 169.2 & - & - \\ VVVv802 & 631.4 & 326.7 & 890.7 & 165.4 & - & - \\ \hline \end{tabular} \tablenotetext{a}{Period in days} \tablenotetext{b}{Power of Per1} \tablecomments{Sources with missing p3 display relatively clean power spectrum with two significant periods of probability statistics p-value=0} \end{table} \hskip 10mm | 16 | 9 | 1609.08711 |
1609 | 1609.04824_arXiv.txt | \par We observe Arp 220, the nearest Ultra-Luminous Infrared Galaxy (ULIRG), over 4 GHz in the K and Ka bands. We provide constraints for the kinematics, morphology, and identify molecular species on scales resolving both nuclei (0.6" or 230 pc). We detect multiple molecular species, including hydroxyl (OH $^{2}\Pi_{3/2} J=9/2 F=4-4; 5-5$) in both cores. We tentatively detect H$_{2}$O(6$_{15}$-5$_{23}$) at $\sim$21.84 GHz in both nuclei, indicating the likely presence of maser emission. The observed frequency range also contains metastable ammonia transitions from (J,K) = (1,1) to (5,5), as well as the (9,9) inversion line, which, together are a well-known thermometer of dense molecular gas. Furthermore, the non-metastable (4,2) and (10,9) and possibly the (3,1) lines are also detected. We apply a standard temperature analysis to Arp 220. However, the analysis is complicated in that standard LTE assumptions do not hold. There are indications that a substantial fraction of ammonia could be in the non-metastable transitions as opposed to only the metastable ones. Thus, the non-metastable transitions could be essential to constraining the temperature. We compare all of these data to ALMA observations of this source, confirming the outflow previously observed by other tracers in both nuclei. | \par Ultra-Luminous Infrared Galaxies (ULIRGs) exhibit abnormally high far infrared luminosities ($L_{IR}$ 8-1000 $\mu$m) of $>10^{12}L_{\odot}$ (\citealt{1987ApJ...320..238S}, \citealt{1996ARA&A..34..749S}). They are crucial to our understanding of how SF evolves (e.g.\ \citealt{2010MNRAS.405..219B}). At a distance of 78 Mpc, Arp 220 is the nearest ULIRG, providing a unique opportunity to study these systems at high (380 pc arcsec$^{-1}$) resolution. Given Arp 220's location, it should not be surprising that it has drawn substantial interest over the years. Numerous observations at a variety of wavelengths have been obtained, as well as extensive simulations and empirical modeling. Detections of molecular species include CO, originally detected by \citet{1986ApJ...311L..47S}, formaldehyde (H$_{2}$CO) detected by \citet{2004ApJS..154..541A} and multiple species by \citet{2008AJ....136..389S}, some of which were never before seen in an extragalactic source. \citet{2011ApJ...742...95O} also observed the Hydroxyl (OH) $^{2}\Pi_{3/2} J=9/2 F=4-4; 5-5$ doublet (rest frequencies at 23.818 GHz and 23.827 GHz) in addition to the previously detected $^{2}\Pi_{3/2} J=5/2 F=2-2$ \citep{2008AJ....136..389S}. The former detection was confirmed by \citet{2013ApJ...779...33M} using GBT observations (which also included NH$_{3}$ metastable and non-metastable transitions). \citet{2006ApJ...646L..49C} detect a potential H$_{2}$O(3$_{13}$-2$_{20}$) megamaser (rest frequency 183.310 GHz) with the IRAM 30-meter telescope, although no H$_{2}$O(6$_{15}$-5$_{23}$) maser was seen near 22.235 GHz (e.g.\ \citealt{1986A&A...155..193H}). We search for this maser in our data and report on it in $\S$~\ref{molecules}. More generally, \citet{2011A&A...527A..36M} present an extended spectral survey of Arp 220 at higher frequencies, finding many molecular species. \par Observations and interpretation of molecular lines are key to assessing the mechanisms driving SF in ULIRGs. For example, ammonia (NH$_{3}$) traces the rotational temperature (T$_{rot}$), which can be used to approximate the kinetic temperature ($T_{kin}$). Especially useful are the metastable (J=K) transitions. These metastable transitions have relative populations set by collisional processes, rendering them excellent indicators of $T_{kin}$. Given this collisional dependency, however, the rotational temperature ($T_{rot}$) underestimates $T_{kin}$, especially for higher values of $T_{kin}$ (e.g.\ \citealt{1983A&A...122..164W}). Thus, $T_{rot}$ should only be used as a lower limit. Particularly relevant to this work is how near in frequency the inversion transitions are, allowing for simultaneous observations and thus the removal of complications resulting from inconsistent observing conditions and calibration (\citealt{1983A&A...122..164W}, \citealt{1988MNRAS.235..229D}). \par The initial detection of NH$_{3}$ in Arp 220 presented in \citet{2005PASJ...57L..29T} using single-dish Nobeyama data included the J=K (1,1) -- (4,4) transitions. Using the Australia Telescope Compact Array (ATCA) and Robert C. Byrd Green Bank Telescope (GBT) observations, \citet{2011ApJ...742...95O} detect the (5,5) and (6,6) inversion transitions. \citet{2013ApJ...779...33M} present observations of (1,1)--(9,9) metastable transitions in Arp 220 with the GBT, and detect all but the (9,9) transition. \citet{2013ApJ...779...33M} also detect the (10,9) transition. The two nuclei were not resolved in any of these observations. Higher resolution observations should reveal differences between the two nuclei, and stronger detections in cases where emission was diluted due to larger beam sizes. % \par Radial motions associated with inflows or outflows, controlling both fueling and feedback, have substantial impact on SF on both local and global scales. Distinguishing regions (e.g.\ main disk, central regions, outskirts, shocked regions, or tidal features) in which certain molecules/transitions are found is necessary to discern when and where SF occurs. Additionally, understanding the kinematics and morphology aids in assessing optical depth effects, which could potentially affect line ratios. Arp 220 is already known to have an outflow (e.g.\ \citealt{2009ApJ...700L.104S}), which we explore further. \par We utilize the Karl G. Jansky Very Large Array (VLA), with its newly available frequencies and extended bandwidths, to observe Arp 220. With the VLA, it is possible to resolve the two nuclei and observe the higher $NH_{3}$ (9,9) transition ($\sim$850 K above ground) in addition to those observed in \citet{2011ApJ...742...95O}. Furthermore, the observations presented here provide additional constraints on current models of the continuum such as those presented in \citet{2007A&A...468L..57D} and \citet{2015ApJ...799...10B}. Complementary to VLA data are those taken of this source with ALMA (e.g.\ \citealt{2015ApJ...800...70S}, \citealt{2015ApJ...806...17R}). We use both sets of observations to provide a more complete picture of the central regions of Arp 220 -- in particular the outflowing material. | \label{results} \subsection{Molecular Species in Arp 220}\label{molecules} \par Several molecular species are listed in Table~\ref{tbl_3} and shown in Figure~\ref{continuum_lines}, with the exception of the NH$_{3}$ metastable transitions, which we present in $\S$~\ref{temperature}. Unless otherwise stated, identifications are based on the Splatalogue database \citep{2010AAS...21547905R}, and are the most likely candidates at those frequencies for this environment. % \par We spatially resolve the OH $^{2}\Pi_{3/2} J=9/2 F=4-4; 5-5$ doublet at $\sim$23.4 GHz (originally detected at lower resolution by \citet{2011ApJ...742...95O} and confirmed by \citet{2013ApJ...779...33M}). The doublet is detected in both nuclei. The two separate lines as observed are blended, forming a single, broad component. \begin{figure*} \begin{centering} \includegraphics[width=150mm]{continuum_lines.eps} \caption{\textit{Zoomed-in spectra from Figure~\ref{continuum_slope_compact_avg} for all lines except the ammonia metastable transitions. As is the case for Figure~\ref{continuum_slope_compact_avg}, the western nucleus is shown in black and the eastern nucleus is shown in gray. The spectra in the upper right corner are likely a superposition of H$_{2}$O(6$_{15}$-5$_{23}$), NH$_{3}$(3,1), and possibly $^{13}$CH$_{3}$OH (see $\S$~\ref{molecules}). Thus, all relevant transitions are displayed on top of the panel. This spectrum is also shown in velocity units as the green line in Figure~\ref{spectrum_grid_west}. The systemic velocity of the entire system is indicated by dashed lines for H$_{2}$O(6$_{15}$-5$_{23}$) in the upper-right panel, and OH $^{2}\Pi_{3/2} J=9/2 F=4-4$ (lower frequency) and OH $^{2}\Pi_{3/2} J=9/2 F=5-5$ (higher frequency) in the left-most panel in the central row. The gap in frequency coverage in the panel showing NH$_{3}$(10,9) is due to artefacts that have been removed. The frequencies given on the x-axis are the observed frequencies. Some lines are prominent in the western nucleus, yet faint or absent in the eastern nucleus (e.g.\ NH$_{3}$(4,2), NH$_{3}$(10,9), either HC$_{3}$N transition). \ The dip seen at $\sim$23.45 GHz is (left-most panel, center row) NH$_{3}$(3,3). } \label{continuum_lines}} \end{centering} \end{figure*} \subsubsection{A Potential Detection of H$_{2}$O(6$_{15}$-5$_{23}$) in Arp 220} \par Of particular interest is the detection at $\sim$21.84 GHz (top, right panel of Figure~\ref{continuum_lines}). This complex is spatially-unresolved in the individual nuclei and exhibits both emission and absorption in the western nucleus, and emission in the eastern nucleus (with the possibility of absorption superimposed on the eastern nucleus). The most likely candidates for this feature are NH$_{3}$(3,1) (rest frequency 22.234 GHz), H$_{2}$O(6$_{15}$-5$_{23}$) (rest frequency 22.235 GHz), and $^{13}$CH$_{3}$OH (rest frequency 22.239 GHz). It is probable that there are at least two species present in the complex. \citealt{2011A&A...527A..36M} detect multiple CH$_{3}$OH lines in Arp 220 between 210 GHz and 240 GHz. These detections, however, are rather weak. Thus, it is unlikely that $^{13}$CH$_{3}$OH could be responsible for a majority of the emission in the $\sim$21.84 GHz complex. Based on a previous detection by \citet{2006ApJ...646L..49C} H$_{2}$O(3$_{13}$-2$_{20}$) was thought to be a megamaser (rest frequency 183.310 GHz) centered at $\sim$5400 km s$^{-1}$ and having a velocity width of 350 km s$^{-1}$. We conclude that most of the emission is likely due to H$_{2}$O(6$_{15}$-5$_{23}$), with NH$_{3}$(3,1) seen in absorption. \par One could, in theory, estimate the NH$_{3}$(3,1) contribution based on the population of the other non-metastable states. Nonetheless, given the unconstrained behavior seen in the metastable transitions (see $\S$~\ref{temperature}), only a very rough estimate can be made. A RADEX \citep{2007A&A...468..627V} calculation assuming T$_{k}$$\sim$150 K and n=10$^{5-6}$ cm$^{-2}$ yields an intensity of the NH$_{3}$(3,1) transition approximately 2.5 times that of NH$_{3}$(4,2). This ratio decreases almost linearly with T$_{k}$ and is close to 2 at 300 K. The measured optical depth of the NH$_{3}$(4,2) transition in the western nucleus is comparable to the absorption in the H$_{2}$O(6$_{15}$-5$_{23}$)/NH$_{3}$(3,1) complex in that nucleus (although the latter shows some additional structure). One possibility is that T$_{k}$ is substantially higher than indicated by data presented in $\S$~\ref{temperature} and in the literature. Alternatively, it may be that the non-metastable transitions have departures from theory similar to those of the metastable transitions. \par However, it is important to keep the following in mind: Given that NH$_{3}$(4,2) and NH$_{3}$(10,9) transitions do not prominently appear in absorption in the eastern nucleus, it may be that NH$_{3}$(3,1) absorption is not the source of the dip in the emission spectrum of the eastern nucleus. There may be an additional molecular species present (e.g.\ $^{13}$CH$_{3}$OH), contributing to the absorption/emission in both nuclei. Alternatively, the dip may not be due to absorption at all, and may instead be a double-peaked kinematic structure related to disk rotation (consistent with \citealt{2016arXiv160509381S}). The final molecular decomposition of this feature remains uncertain. \citet{2015ApJ...799...10B} show that the star formation rate surface density (which should be correlated with the H$_{2}$O(6$_{15}$-5$_{23}$) maser luminosity) of the western nucleus is 2.5 times that of the eastern nucleus. We multiply the H$_{2}$O(6$_{15}$-5$_{23}$) maser flux in the eastern nucleus by this factor. We assume that the NH$_{3}$(3,1) is the dominant source of absorption in the western nucleus. Based on these two assumptions, we find that the strength of the NH$_{3}$(3,1) line should be approximately twice of what is observed in that nucleus. The resulting optical depth of the NH$_{3}$(3,1) transition is approximately $\tau$=0.06. However, the RADEX calculations indicate that the optical depth of the NH$_{3}$(3,1) should be approximately twice that of the NH$_{3}$(4,2). Given the observed $\tau$=0.07 for NH$_{3}$(4,2) in the western nucleus, the corresponding value for NH$_{3}$(3,1) should be $\tau$=0.14 or higher. This discrepancy indicates that contamination from H$_{2}$O(6$_{15}$-5$_{23}$) maser emission may negate even more of the NH$_{3}$(3,1) absorption in the western nucleus than what the spectra at 22 GHz alone would indicate. \par If we integrate the H$_{2}$O(6$_{15}$-5$_{23}$) emission over the eastern nucleus only, we obtain a luminosity of approximately 1.5$\times$10$^{8}$ K km s$^{-1}$ pc$^{2}$ over a velocity width of $\sim$180 km s$^{-1}$. The strength of this detection is comparable to the 183 GHz emission detected by \citet{2006ApJ...646L..49C} of 2.5$\times$10$^{8}$ K km s$^{-1}$ pc$^{2}$ over 350 km s$^{-1}$. (The 22 GHz emission only considers one nucleus -- the 22 GHz flux could increase by a factor of 2--2.5 when considering both nuclei.) \par L$_{H_{2}O}$/L$_{FIR}$ is typically on the order of 10$^{-9}$ \citep{2005A&A...436...75H}. Using methods presented in \citet{2005A&A...436...75H}, if we assume the factor of two higher luminosity derived for the observed H$_{2}$O(6$_{15}$-5$_{23}$) via the RADEX calculation, a factor of 3.5 increase when including both nuclei (based on the luminosity ratio of the two), and adopt L$_{FIR}$=1.4$\times$10$^{12}$ L$_{\odot}$ from \citet{2003AJ....126.1607S}, we find L$_{H_{2}O}$ $\sim$ 200 L$_{\odot}$ and L$_{H_{2}O}$/L$_{FIR}$$\sim$10$^{-10}$ for Arp 220. This value is approximately an order of magnitude lower than what is typically seen in other galaxies with H$_{2}$O(6$_{15}$-5$_{23}$) detections. However, it is possible that there could be contamination from NH$_{3}$ (3,1) absorption in the eastern nucleus as well. This potential contamination could result in a value up to four times higher for the H$_{2}$O(6$_{15}$-5$_{23}$) luminosity. Such a scenario would render L$_{H_{2}O}$/L$_{FIR}$=10$^{-9}$, which is consistent with the sample observed in \citet{2005A&A...436...75H}. \par A detection of a H$_{2}$O(6$_{15}$-5$_{23}$) megamaser in Arp 220 is interesting since it is one of the few in a ULIRG reported to date. Aside from this detection, \citet{2016ApJ...816...55W} detect a $\sim$1600 L$_{\odot}$ H$_{2}$O(6$_{15}$-5$_{23}$) megamaser in the ULIRG UGC 5101. \citet{1984A&A...141L...1H}, \citet{2015ApJ...815..124H}, and \citet{2002PASJ...54L..27N} present H$_{2}$O(6$_{15}$-5$_{23}$) detections in NGC 6240 (LIRG) on the order of a few L$_{\odot}$, which is substantially lower than what we detect in Arp 220. However, the L$_{FIR}$ of NGC 6240 is 10$^{11}$--10$^{12}$ L$_{\odot}$ -- up to an order of magnitude lower than that of Arp 220. \par It is important to emphasize that, in spite of the detection at 183 GHz, no emission has previously been seen near 22 GHz in Arp 220 - only an upper limit of 0.15 Jy set by \citet{1986A&A...155..193H} for both nuclei (unresolved). However, neither the \citet{1986A&A...155..193H} nor the 183 GHz observations by \citet{2006ApJ...646L..49C} resolved the two nuclei. After creating a zeroth-moment map including all the channels in which emission from this line is seen, we find approximately $-$60 Jy bm$^{-1}$ km s$^{-1}$ in the western nucleus and $+$60 Jy bm$^{-1}$ km s$^{-1}$ in the eastern nucleus (the two values are within 3 Jy bm$^{-1}$ km s$^{-1}$ of each other), thus canceling all but a negligible fraction of the total emission. Thus, when the nuclei are blended together such as they are when observed at lower resolution, the result is a non-detection. \begin{deluxetable*}{lcccccc} \tabletypesize{\scriptsize} \tablecaption{Molecular Species Excluding Metastable Ammona \label{tbl_3}} \tablewidth{0pt} \tablehead { \colhead{$\nu_{obs}$ (GHz)}& \colhead{Molecular Species\tablenotemark{a}} & \colhead{$\nu_{rest}$ (GHz)}& \colhead{$\tau_{peak}$}& \colhead{$v_{peak}$ (km s$^{-1}$)}& \colhead{${\Delta}v_{1/2}$ (km s$^{-1}$)}& \colhead{${\int}{\tau}dv$ (km s$^{-1}$)}\\ } \startdata \\ \phd Western nucleus&&&&&& \\ \\ \phd 21.22&c-C$_{3}$H$_{2}$(2$_{20}$-2$_{11}$)&21.58740& \tablenotemark{b} &&& \\ \phd 21.32&NH$_{3}$(4,2)& 21.70341 & 0.07$\pm$0.002 & $-$115$\pm$4 & 118$\pm$4 & 8.8$\pm$0.4\\ \phd 21.84&H$_{2}$O(6$_{15}$-5$_{23}$), NH$_{3}$(3,1)\tablenotemark{c} &22.23508, 22.23456 & &&&\\ \phd &$^{13}$CH$_{3}$OH &22.23992 & &&&\\ \phd 23.40&OH $^{2}\Pi_{3/2}$ J=9/2&23.8176153, 23.8266211 & 0.05$\pm$0.005 & $-$159$\pm$16 & 124$\pm$16 &6.6$\pm$1.1 \\ \phd 23.78&NH$_{3}$(10,9)\tablenotemark{d}& 24.20536 & 0.05$\pm$0.004 & $-$143$\pm$13 & 163$\pm$14 & 8.7$\pm$1.0\\ \phd 26.61&c-C$_{3}$H$_{2}$(3$_{30}$-3$_{21}$) & 27.08435 & 0.23$\pm$0.13 & $-$133$\pm$51 & 79$\pm$51 & 19.4$\pm$16.7\\ \phd 26.82&HC$_{3}$N(3-2)\tablenotemark{e}& 27.29290-27.29623 & 0.10$\pm$0.05 & $-$135$\pm$71 & 116$\pm$71 & 12.4$\pm$9.8\\ \phd 35.75&HC$_{3}$N(4-3)\tablenotemark{e}& 36.39-36.394 & 0.10$\pm$0.009&$-$126$\pm$10 & 100$\pm$10 & 10.7$\pm$1.4\\ \\ \phd Eastern nucleus&&&&&& \\ \phd 21.21&c-C$_{3}$H$_{2}$(2$_{20}$-2$_{11}$)& 21.58740 & & & &\\ \phd 21.31&NH$_{3}$(4,2)& 21.70341 & 0.03$\pm$0.006 & 5$\pm$9 & 38$\pm$9 & 1.2$\pm$0.4 \\ \phd 21.84&H$_{2}$O(6$_{15}$-5$_{23}$), $^{13}$CH$_{3}$OH\tablenotemark{c}& 22.23508, 22.23992 & & & &\\ \phd 23.39&OH $^{2}\Pi_{3/2}$ J=9/2&23.8176153, 23.8266211 & 0.03$\pm$0.005 & $-$30$\pm$27 & 150$\pm$27 & 4.8$\pm$1.2\\ \phd 26.60&c-C$_{3}$H$_{2}$(3$_{30}$-3$_{21}$) & 27.08435 & 0.11$\pm$0.10 & $-$20$\pm$107 & 99$\pm$107 & 11.6$\pm$15.1\\ \enddata \tablenotetext{a}{Molecular species are identified using the Splatalogue database unless previously identified in the Arp 220 related literature. Each line is among the brightest in its respective frequency band and is matched to the systemic velocity within the uncertainties.} \tablenotetext{b}{The optical depth and kinematic parameters are not given in cases where the line is not cleanly fit by a gaussian due to additional structures present that cannot be unambiguously distinguished between kinematic and morphological features, as well as additional molecular species.} \tablenotetext{c}{There are indications of multiple lines present. A tentative ID of H$_{2}$O(6$_{15}$-5$_{23}$) is based on presence of H$_{2}$O(3$_{13}$-2$_{20}$) detected by \citet{2006ApJ...646L..49C} and the most likely molecules at this frequency in the Splatalogue database. $^{13}$CH$_{3}$OH may also be present, although it would likely contribute less to the emission in this frequency range.} \tablenotetext{d}{With the GBT, \citet{2013ApJ...779...33M} detect NH$_{3}$(10,9) at velocities consistent with the \textit{eastern nucleus, but not the western}. Our data show indications of NH$_{3}$(10,9) absorption towards the eastern nucleus, but no unambiguous detection. In the western nucleus the NH$_{3}$(10,9) absorption is clearly present.} \tablenotetext{e}{Hyperfine structure lines are present, but unresolved.} \end{deluxetable*} \subsection{Temperature Analysis Using Metastable Ammonia}\label{temperature} \subsubsection{Method}\label{method} \par Here we detect the NH$_{3}$ (1,1) -- (5, 5) inversion lines in absorption (see Figure~\ref{spectra_west} and Table~\ref{tbl_2}). Additionally, we detect the (9, 9) inversion line, which, in theory, substantially increases our leverage in determining $T_{rot}$ and $T_{kin}$. \begin{figure}[!htb] \begin{centering} \includegraphics[width=100mm]{fits_all_ammonia_east.eps} \includegraphics[width=100mm]{fits_all_ammonia_west.eps} \caption{\textit{Spectral fits for the metastable ammonia inversion transitions in the eastern nucleus (A), and the western nucleus (B). The top two panels show both the (1,1) and (2,2) inversion transitions, each shifted accordingly to the systemic velocity for their respective fits. The (9,9) inversion transition was problematic during fitting due to the increased rms noise at higher frequencies and intrinsically shallow depth of the line. Finer structures may indeed be present in some transitions (e.g.\ the (4,4) and (5,5) transitions in the western nucleus), but we fit these as single gaussians for the purposes of our analysis. These fits are used to determine the optical depth and line-width, which are then used in the temperature analysis presented graphically in Figure~\ref{boltzmann_combined}.} \label{spectra_west}} \end{centering} \end{figure} We use methods involving Boltzmann statistics such as those presented in \citet{2005PASJ...57L..29T}, \citet{2011ApJ...742...95O}, and \citet{2013ApJ...772..105M} to gauge $T_{rot}$, which can then be used to estimate $T_{kin}$. We adopt the assumption that the relative populations of each rotational transition are related to $T_{rot}$ \citep{1983A&A...122..164W}. We first determine a ratio of the column densities in the upper state ($N_{u}$) to excitation temperature $T_{ex}$. \begin{equation} \frac{N_{u}}{T_{ex}}=7.28\times10^{13}\frac{J(J+1)}{K^{2}\nu}\times\tau\times\Delta{v}_{1/2} \end{equation} where $\tau$ is the central optical depth, $\nu$ is the central frequency in GHz and $\Delta{v}_{1/2}$ is the FWHM in km s$^{-1}$. This equation is derived from Equation 30 in \citet{2015PASP..127..266M} under the assumption of using the peak optical depths and FWHMs (otherwise the prefactor would be 7.74). Furthermore, this prefactor differs from the often used 1.61$\times$10$^{14}$ (e.g.\ \citealt{1995A&A...294..667H}, \citealt{2011ApJ...742...95O}, \citealt{2013ApJ...772..105M}) by approximately a factor of two as it only includes one inversion level as opposed to two. Taking into account the statistical weight of each transition and using a Boltzmann law we obtain: \begin{equation} \frac{N_{u'}/T'_{ex}}{N_{u}/T_{ex}}=\frac{g_{op}(J')}{g_{op}(J)}\frac{2J'+1}{2J+1}exp\bigg(\frac{-{\Delta}E}{T_{rot}}\bigg), \end{equation} where $g_{op}$ is the statistical weighting factor of the line ($g_{op}=1$ for para and $g_{op}=2$ for ortho). The log of the weighted column densities is plotted against the energy of the upper level above the ground state in Kelvin. A line (or in the case of clear departures from a gaussian, a multiplet) is fit to the data (Figure~\ref{boltzmann_combined}). In the end $T_{rot}=-log_{10}(e)/m$ where $m$ is the slope of the best fit line. $T_{rot}$ can then be used to approximate $T_{kin}$. \begin{deluxetable*}{lcccccc} \tabletypesize{\scriptsize} \tablecaption{Line Parameters - Metastable Ammonia \label{tbl_2}} \tablewidth{0pt} \tablehead { \colhead{Line} & \colhead{$\nu_{rest}$ (GHz)}& \colhead{$\nu_{obs}$ (GHz)}& \colhead{$\tau_{peak}$}& \colhead{$v_{peak}$ (km s$^{-1}$)}\tablenotemark{a}& \colhead{${\Delta}v_{1/2}$ (km s$^{-1}$)}& \colhead{${\int}{\tau}dv$ (km s$^{-1}$)}\\ } \startdata \\ \phd Western nucleus&&&&&& \\ \phd NH$_{3}$ (1,1)&23.69477&23.27&0.069$\pm$0.017\tablenotemark{b}&$-$63$\pm$26&210$\pm$62&15.4$\pm$6.0\\ \phd NH$_{3}$ (2,2)&23.72260&23.30&0.342$\pm$0.016&$-$150$\pm$6&264$\pm$15&95.9$\pm$7.2\\ \phd NH$_{3}$ (3,3)&23.87008&23.45&0.326$\pm$0.034&$-$163$\pm$11&286$\pm$25&99.2$\pm$11.6\\ \phd NH$_{3}$ (4,4)&24.13935&23.71&0.104$\pm$0.003&$-$182$\pm$3&269$\pm$8&29.7$\pm$1.1\\ \phd NH$_{3}$ (5,5)&24.53292&24.10&0.169$\pm$0.003&$-$165$\pm$3&322$\pm$6&58.1$\pm$1.5\\ \phd NH$_{3}$ (9,9)&27.47794&26.99&0.096$\pm$0.087&$-$100$\pm$120&271$\pm$282&27.8$\pm$38.5\tablenotemark{c}\\ \\ \phd Eastern nucleus&&&&&& \\ \phd NH$_{3}$ (1,1)&23.69477&23.27&0.067$\pm$0.024&$-$30$\pm$25&142$\pm$60&10.2$\pm$5.7\\ \phd NH$_{3}$ (2,2)&23.72260&23.30&0.115$\pm$0.019&$-$42$\pm$18&216$\pm$42&26.5$\pm$6.9\\ \phd NH$_{3}$ (3,3)&23.87008&23.45&0.115$\pm$0.032&$-$26$\pm$30&219$\pm$71&26.9$\pm$11.6\\ \phd NH$_{3}$ (4,4)&24.13935&23.71&0.045$\pm$0.003&$-$19$\pm$7&204$\pm$18&9.9$\pm$2.0\\ \phd NH$_{3}$ (5,5)&24.53292&24.10&0.071$\pm$0.004&$-$35$\pm$6&235$\pm$14&17.9$\pm$1.42\\ \phd NH$_{3}$ (9,9)&27.47794&26.99&0.026$\pm$0.08&5$\pm$396&216\tablenotemark{c}&5.9$\pm$17.7\\ \enddata \tablenotetext{a}{Velocity centers are given with respect to the systemic velocity (optical, heliocentric) of Arp 220, 5434 km s$^{-1}$.} \tablenotetext{b}{Due to the possibility of incomplete coverage of the continuum by molecular clouds or contamination by cooler gas, the true optical depths are likely somewhat higher than what we measure here.} \tablenotetext{c}{The uncertainties for the (9,9) inversion transition are quite high for both nuclei. Due to a low SNR, we are unable to fit the line-width of the (9,9) inversion transition in the eastern nucleus. Thus, we force a value of 216 km s$^{-1}$ (consistent with the other line widths for the eastern nucleus) for the purpose of determining the optical depth.} \end{deluxetable*} \par It is immediately clear that these data are not described by a straight line, consistent with a single T$_{rot}$, \textit{which limits what can be gleaned.} An assumption for this method is LTE, which the two nuclei do not fulfill. For illustrative purposes, to compare with existing work, and to gauge the extent of the impact of non-metastable transitions, we present the most basic analysis steps. \par The slope of Boltzmann diagrams (Figure~\ref{boltzmann_combined}) typically shallows for higher metastable transitions (e.g.\ \citealt{2013ApJ...772..105M}). Thus, the seemingly overpopulated (9,9) transition is unsurprising. Given that there are no additional higher-order ortho transitions observed that could aid in constraining a two-temperature model, we omit the (9,9) transition from the analysis. The (1,1) transition is underpopulated for both nuclei, which was also observed by \citet{2011ApJ...742...95O} and \citet{2013ApJ...779...33M}. \citet{2011ApJ...742...95O} suggested cooler surrounding gas as an explanation. \citet{2013ApJ...779...33M} suggest that the (2,2) transition is broadened and amplified by an additional velocity component, potentially associated with an outflow. However, the latter scenario does not account for the (5,5) transition being deeper in absorption than expected relative to the (4,4) transition, which is apparent in the lower-resolution data of \citet{2013ApJ...779...33M} and which we clearly see in both nuclei. % \par To illustrate how much the rotational temperature is affected by these departures from linearity, we make two estimates of the rotational temperature. In the first we include the (1,1) through (5,5) transitions. In the second, we omit the (1,1) and (4,4) transitions. Thus, the second estimate excludes all transitions for which we are \textit{certain} do not conform to the expectations set forth by this method (Figure~\ref{boltzmann_combined}). The differences between the two estimates gives an indication of the impact of anomalous behavior on determinations of the rotational temperature. \par Relevant to the break-down of this analysis in the case of Arp 220, two non-metastable lines are also detected at comparable levels (and possibly a third -- the (3,1) transition, although this line is likely blended). Thus, the non-metastable transitions may be substantially influencing the derived excitation. For example, the (2,1) and (3,1) states could be substantially populated which would affect the (1,1) population. If the populations of the metastable (1,1) and the higher excitation (2,1) and (3,1) transitions are combined, then the expected population of the (1,1) state could be recovered. Naturally, these principles would apply to the other metastable transitions. To assess the likelihood of this explanation, we examine the (3,1) and (4,2) transitions for the Western nucleus. Using the same method as for the metastable transitions, if the (3,1) transition is included with the (1,1) transition, there is indeed a substantial effect - in fact the (3,1) state is more populated than the (1,1) transition, and the value for the (1,1) transition on the y-axis of Figure~\ref{boltzmann_combined} would increase to approximately 14.3 when they are combined (the new value is not plotted). The same can be done for the (4,2) and (2,2), and a more modest increase is seen to approximately 14.1. Note that \textit{the (1,1) transition is now higher than the (2,2) transition -- consistent with the assumptions used to derive $T_{rot}$}. This is after adding only one nonmetastable transition to each metastable one, which is nowhere near a complete analysis. Although not all metastable transitions are included here, we can already see that they could potentially account for the break-down of the metastable temperature analysis in Arp 220. \par We forgo further Large Velocity Gradient (LVG) and other analyses of these data since it is abundantly clear that even a basic analysis already results in a relatively poor fit to derive the rotational temperature. Additional data on the non-metastable transitions are required to derive further constraints. \par Consistent with the findings of \citet{2011ApJ...742...95O}, there is no clear indication of an ortho-para ratio far from unity. Thus, we can assume an ortho-para ratio close to one in both nuclei, indicating warm conditions when the ammonia formed. \begin{figure*}[!htb] \begin{centering} \includegraphics[width=130mm]{boltzmann_combined.eps} \caption{\textit{Boltzmann plots of the metastable ammonia inversion transitions in the eastern nucleus (A), and the western nucleus (B). Note the relatively low population of the (1,1) transition. Also, the population of the (9,9) transition is relatively high in both nuclei, likely better fit by a two-temperature solution. The (4,4) and (5,5) lines are also inconsistent with expectations relative to each other, while it is not clear which transition is problematic. The red line fits the (1,1)--(5,5) transitions, while the blue line fits the (2,2), (3,3), and (5,5) transitions only in order to show how T$_{rot}$ changes when the obviously discrepant data points are discarded. For the western nucleus, there is a substantial difference in rotational temperatures determined with each.} \label{boltzmann_combined}} \end{centering} \end{figure*} \subsection{An outflow demonstrated by a comparison with emission lines seen by ALMA}\label{outflow} \begin{figure}[!htb] \begin{centering} \includegraphics[width=70mm]{spectrum_grid_east.eps} \end{centering} \end{figure} \begin{figure}[!htb] \begin{centering} \includegraphics[width=70mm]{spectrum_grid_west.eps} \caption{\textit{We present representative molecular species from the sample of those detected in Arp 220. The systemic velocity of the entire system (LSR (radio) 5434 km s$^{-1}$) is at zero. The systemic values of each nucleus taken from \citet{2009ApJ...700L.104S} are $-$84 km s$^{-1}$ for the western and $-$24 km s$^{-1}$ for the eastern nucleus (also LSR (radio)). The top panels show ALMA observations of HCN(4-3) (red) and CS (7-6) (orange) by \citet{2015ApJ...800...70S}. The bottom panels show the H$_{2}$O(6$_{15}$-5$_{23}$)/NH$_{3}$(3,1) complex (green), NH$_{3}$(2,2) (light blue), and what we identify here as c-C$_{3}$H$_{2}$(3$_{30}$-3$_{21}$) (dark blue). All lines belonging to the bottom panels are listed in Tables~\ref{tbl_3} or~\ref{tbl_2}. The NH$_{3}$(2,2) spectra also include the NH$_{3}$(1,1) inversion transition (the shallower line to the right side). The self-absorption in the emission detected by ALMA is closely duplicated by the absorption lines seen with the VLA. In particular, the absorption in the western nucleus matches the CS(7-6) profile almost exactly (vertical scaling factors aside). The absorption appears to be blue-shifted with respect to the systemic velocities of both nuclei (dotted lines), indicating outflow is likely (more so for the western nucleus).} \label{spectrum_grid_west}} \end{centering} \end{figure} \par We compare the absorption spectra we observe with the VLA with HCN (4-3) and CS (7-6) spectra observed with ALMA by \citet{2015ApJ...800...70S}. The HCN (4-3) and CS (7-6) spectra show a decrease or dip in the spectrum of each nucleus (Figure~\ref{spectrum_grid_west}). In the western nucleus, the decrease is clearly blue-shifted with respect to the systemic velocity of that nucleus. The dip in the eastern nucleus is also blue-shifted, but to a lesser degree. A double-peak is also seen in the eastern nucleus. Considering also the CO(1-0) observations shown in Figure 3 of \citet{2016arXiv160509381S}, which reveal no analogous feature in the single-peaked CO (1-0) spectrum, it is clear that the decrease in the western nucleus is unlikely to be a kinematic feature. Thus, this decrease in the western nucleus is almost certainly due to absorption. The cause of the dip in the eastern nucleus is less clear as it is consistent with the two-peaked spectrum seen in the CO (1-0) at the farthest extent, also presented in \citet{2016arXiv160509381S}. When the self-absorption in the ALMA data is compared to the absorption in the VLA data in the western nucleus, one can see that they are aligned with each other. Assuming the LSR (radio) value of 5350 km s$^{-1}$ for the systemic velocity of the western nucleus \citep{2009ApJ...700L.104S}, the absorption spectra in that nucleus are blue-shifted to $\sim$80 km s$^{-1}$ at the peak and $\sim$400 km s$^{-1}$ at the farthest extent (with the exception of the HCN (4-3)). Evidence for blue-shifted absorption is less clear in the eastern nucleus, but may be on the order of $\leq$30 km s$^{-1}$ (adopting a systemic velocity for that nucleus of 5410 km s$^{-1}$ based on \citealt{2009ApJ...700L.104S}). \par The blue-shifted absorption indicates outflowing material, consistent with the picture presented in \citet{2009ApJ...700L.104S} and \citet{2015ApJ...800...25T}. \citet{2001ApJ...560..168M} and \citet{2009ApJ...700L.104S} noted outflowing CO in absorption with a velocity on the order of $\sim$100 km s$^{-1}$. Additionally, \citet{2015ApJ...800...25T} observed a symmetric outflow seen in velocities up to $\pm$500 km s$^{-1}$ in the western nucleus, which included multiple molecular species (e.g.\ SiO(6,5), H$^{13}$CN(3,2)). That we only see a blue-shift of only 400 km s$^{-1}$ in the western nucleus and even less in the eastern nucleus indicates that the outflow seen in absorption in our observations, is either impeded, driven by a different mechanism, and/or from emission confined to different radii. \par CS(7-6) and the absorption features we observe with the VLA show greater similarities than with those of the HCN(4-3). This indicates that the CS(7-6) and VLA features likely both originate from material at similar radii and share similar kinematics. The comparatively blue-shifted (on the order of 100 km s$^{-1}$ or more) self-absorption in the HCN(4-3) line could indicate different kinematics, presence in different parts of the western nuclear region, or both. If the HCN(4-3) is indeed present at larger radii, then the entirety of its emission is likely less affected by absorption against the continuum core. Furthermore, the material most likely to be self-absorbed would be that directly between the continuum core and the observer -- having the largest line-of-sight velocities (consistent with the relative blue-shift). This picture is consistent with figures in \citet{2015ApJ...800...70S} which show the HCN(4-3) line having a larger spatial extent than CS(7-6). Furthermore, the kinematic axes of HCN(4-3) and CS(7-6) are offset by 45$^{\circ}$, indicating distinct morphologies, with the VLA absorption we present here conforming more to the latter. | 16 | 9 | 1609.04824 |
1609 | 1609.04015_arXiv.txt | We present new Jansky Very Large Array observations of five pre-Swift gamma-ray bursts for which an ultraluminous (SFR $>100$ $M_\odot$ yr$^{-1}$) dusty host galaxy had previously been inferred from radio or submillimetre observations taken within a few years after the burst. In four of the five cases we no longer detect any source at the host location to limits much fainter than the original observations, ruling out the existence of an ultraluminous galaxy hosting any of these GRBs. We continue to detect a source at the position of GRB\,980703, but it is much fainter than it was a decade ago and the inferred radio star-formation rate ($\sim80 M_\odot$) is relatively modest. The radio flattening at 200--1000 days observed in the light curve of this GRB may have been caused by a decelerating counterjet oriented 180 degrees away from the viewer, although an unjetted wind model can also explain the data. Our results eliminate all well-established pre-Swift ULIRG hosts, and all cases for which an unobscured GRB was found in a galaxy dominated by heavily-obscured star-formation. When GRBs do occur in ULIRGs the afterglow is almost always observed to be heavily obscured, consistent with the large dust opacities and high dust covering fractions characteristic of these systems. | \label{sec:intro} Long gamma-ray bursts are produced by the explosion of massive, short-lived stars at cosmological distances (\citealt{HjorthBloom2012}). Their host-galaxy population should therefore reflect and reveal the diversity of star-forming galaxies responsible for the Universe's star-formation across cosmic history. One type of galaxy we may expect to frequently observe GRBs originating from is the broad class of luminous, dusty star-forming galaxies (DSGs). These include submillimetre galaxies (SMGs; galaxies at cosmological redshift detected at 850$\mu$m with single-dish telescopes), ultra-luminous infrared galaxies (ULIRGs; galaxies with infrared luminosity exceeding $>10^{12} L_\odot$), and similar systems containing extensive dust-obscured star-formation. They are nearly absent in the low-redshift universe but are relatively common at $z>1$, where they play an important role in galaxy evolution and cosmic star formation (see \citealt{Casey+2014} for a review). Large columns of interstellar dust obscure nearly all of the optical and UV light from young stars in galaxies of this type, making them difficult both to find and to study. Observations at long wavelengths (mid-IR, submillimetre, and radio) where the dusty ISM becomes transparent are critical. \begin{table*} \begin{minipage}{130mm} \caption{Previously Claimed Detections of ULIRGs Hosting Pre-Swift GRBs$^{a}$} \begin{tabular}{lll|lll|lll|l} \hline {} & {} & {} & \multicolumn{3}{|c|}{\underline{Radio}} & \multicolumn{3}{|c|}{\underline{Submillimetre}} & {} \\ {GRB} & {$z$} & {OA?$^{b}$} & {Freq.} & {$F_\nu$ $^{c}$} & {Ref.$^{d}$} & {Freq.} & {$F_\nu$ $^{c}$} & {Ref.$^{d}$} & {SFR$^{e}$} \\ {} & {} & {} & {(GHz)} & {($\mu$Jy)} & {} & {(GHz)} & {($\mu$Jy)} & {} & {($M_\odot$ yr$^{-1}$)} \\ \hline 980703 & 0.967 &yes (red) & 1.43 & 68 $\pm$ 7 & B01 & 350 &{\it $<$2280 } & T04 & 180, 212 \\ & & & 4.86 & 42 $\pm$ 9 & B01 & & & & \\ & & & 8.46 & 39 $\pm$ 5 & B01 & & & & \\ \hline 000210 & 0.8452 &none (dark)& 8.46 &{\it 18 $\pm$ 9 }& B03 & 350 & 3050$\pm$760 & T04 & 560, 179 \\ \hline 000418 & 1.1185 &yes (red) & 1.43 & 59 $\pm$ 15 & B03 & 350 & 3150$\pm$900 & B03 & 690, 330, 288 \\ & & & 4.86 & 46 $\pm$ 13 & B03 & 670 & 4199$\pm$1900 & B03 & \\ & & & 8.46 & 51 $\pm$ 12 & B03 & & & & \\ \hline 000911 & 1.0585 & yes & 8.46 &{\it $<$40 }& B03 & 350 &{\it2310$\pm$910} & B03 & 495 \\ \hline 010222 & 1.478 & yes & 4.86 &{\it 23 $\pm$ 8 }& B03 & 250 & 1050$\pm$220 & F02 & 610, 300, 278 \\ & & & 8.46 &{\it 17 $\pm$ 6 }& B03 & 350 & 3740$\pm$530 & F02 & \\ \hline 021211 & 1.006 & yes & 1.4 & 330 $\pm$ 31 & M12 & & & & 825 \\ & & & 2.1 &{\it $<$34 }& H12 & & & & \\ \hline \end{tabular} $^{a}${\ We exclude GRBs 980329, 000301C, and 000926, which are listed as possible low-significance radio host detections by B03 but acknowledged to contain significant afterglow contribution. We include 000911, which is not explicitly claimed as a detection by B03 but for which a submillimetre detection at $>2.5\sigma$ is presented in their plots and tables.} \\ $^{b}${\ Whether or not an optical afterglow was detected for this GRB. Only GRB\,000210 was ``dark'', indicating that the GRB occurred in an optically-thick region. GRBs\,980703 and 000418 show evidence for moderate ($A_V \sim 1-2$ mag rest-frame) extinction \citep{Klose+2000,Kann+2006}. The remaining GRBs show no evidence for extinction within their host galaxies.} \\ $^{c}${\ Italicized for events for which the reported detection is less than 3$\sigma$ and for nondetections.} \\ $^{d}${\ References for reported flux. B01 = \cite{Berger+2001}; F02 = \cite{Frail+2002}; B03 = \cite{Berger+2003}; T04 = \cite{Tanvir+2004}; M12 = \cite{Michalowski+2012b}; H12 = \cite{Hatsukade+2012}.} \\ $^{e}${\ Inferred submillimetre or radio star-formation rates from the referenced works and/or from \cite{Michalowski+2008}} \end{minipage} \label{tab:prevfluxes} \end{table*} The first luminous DSG candidates hosting GRBs were found incidentally: late-time flattenings of the light curves of GRB\,970803 and GRB\,010222 at radio and/or submillimetre wavelengths were interpreted as being due to host-galaxy emission (\citealt{Berger+2001,Frail+2002}). A large amount of dedicated effort was also invested during the pre-Swift era in conducting late-time, long-wavelength observations specifically with the intent of looking for late-time host emission. Some of these efforts \citep{Barnard+2003,Tanvir+2004} produced only upper limits. However, the comprehensive survey of \cite{Berger+2003} produced radio detections of at least three (and possibly as many as seven, if marginal detections are considered) out of 17 GRB host galaxies observed with the Very Large Array (VLA) and Australian Telescope Compact Array (ATCA) in observations reaching flux limits of typically 30\,$\mu$Jy at 1.4--8 GHz (3$\sigma$), corresponding to star-formation rates (SFR) of few hundred $M_\odot$/yr at $z\sim1.5$. \cite{Berger+2003} report a similar detection fraction at 850 $\mu$m (to limits of 3 mJy, or $\sim$500 $M_\odot$ at $z\sim1.5$). These observations were taken to support a simple picture, as follows. First, in agreement with the consensus view, a significant minority of high-redshift star-formation occurred in very luminous DSGs. Second, GRBs trace the global star-formation rate with reasonable fidelity (the fraction of stars that explode as GRBs is similar in DSGs and in other, more ordinary galaxies). However, the reported properties of the DSGs hosting pre-Swift GRBs differ markedly from the properties of DSGs found by other means. Classically-selected DSGs usually show some evidence of very active star-formation and dust extinction in the form of red optical/IR colors or exceptionally strong emission lines, and they usually have high stellar masses \citep{Michalowski+2012a}, often exceeding $>$10$^{11} M_\odot$. Yet, despite truly tremendous submm/radio-inferred star-formation rates ($>$300--500 $M_\odot$\,yr$^{-1}$), many of the claimed pre-Swift submillimetre/radio hosts show blue colors, low apparent optical extinction, and low masses uncharacteristic of the SMGs found in submillimetre/radio surveys \citep{Michalowski+2008}. Also, several were observed at 24 $\mu$m \citep{LeFloch+2006} and none of these were detected, even though 24$\mu$m observations are also thought to probe dust-obscured star-formation. It is possible that the classical submillimetre field surveys were simply ``missing'' a large population of young submillimetre galaxies with blue colors, high temperatures, and strong silicate absorption at 24 $\mu$m \citep{Michalowski+2008}. This would be an important result, since it would imply that a significant fraction of the Universe's stars formed in a class of galaxies that eludes classical surveys. \begin{table*} \begin{minipage}{150mm} \caption{VLA Observations} \label{tab:observations} \begin{tabular}{llllllllll} \hline {GRB} & {RA$^{a}$} & {Dec$^{a}$} & {$z$$^{b}$} & {Band} & {Config.$^{c}$} & {Observation date} & {$t_{\rm int}$ $^{d}$} & {Beam size$^{e}$} & {RMS noise$^{f}$} \\ {} & {} & {} & {} & {} & {} & {(UT)} & {(hr)} & {($\arcsec$)} & {($\mu$Jy/beam)} \\ \hline 980703 & 23:59:06.67 & +08:35:07.09 & 0.967 &C& C & 2014-10-18 & 1.02 & 4.6$\times$3.6\arcsec & 2.9 \\ & & & &C& A & 2015-07-06 & 1.02 & 0.40$\times$0.33\arcsec & 3.1 \\ & & & &L& B & 2012-06-24 & 5.31 & 5.5$\times$5.5\arcsec & 7.9 \\ 000418 & 12:25:19.3 & +20:06:11.6 & 1.1185 &C& C & 2014-10-17 & 1.04 & 3.8$\times$3.5\arcsec & 3.3 \\ 000911 & 02:18:34.36 & +07:44:27.7 & 1.0585 &C& C & 2014-11-20 & 1.26 & 4.3$\times$3.6\arcsec & 2.9 \\ 010222 & 14:52:12.55 & +43:01:06.2 & 1.478 &C& A & 2015-08-28 & 1.64 & 0.39$\times$0.34\arcsec & 2.6 \\ 021211 & 08:08:59.883 & +06:43:37.88 & 1.006 &C& C & 2014-10-22 & 0.79 & 4.3$\times$3.4\arcsec & 3.5 \\ \hline \end{tabular} $^{a}${\ Observation pointing centre (J2000).} $^{b}${\ Redshift of host or afterglow.} $^{c}${\ VLA array configuration.} $^{d}${\ Total time on-source in hours, excluding overheads.} $^{e}${\ Major and minor axis FWHM of the synthesized beam.} $^{f}${\ Noise (1$\sigma$) estimated from the standard deviation of 1000 randomly chosen points in the final map.} \end{minipage} \end{table*} Curiously, however, few of the GRBs actually found within these DSGs were optically-obscured themselves (Table \ref{tab:prevfluxes}): the afterglows showed only modest or even no evidence for extinction, corresponding to $A_V \lesssim 1$ mag along the line of sight to the GRB in all but one case \citep{Kann+2006}. It is hard to explain why, in a galaxy population purportedly dominated by optically-thick star-formation, the GRBs would occur in the bolometrically insignificant optically-thin regions. While GRBs can destroy dust in their close vicinity ($\sim$10 pc; \citealt{Waxman+2000}, see \citealt{Morgan+2014} for a possible observed example), it is not likely that this is possible out to the more extended spatial scales relevant to DSGs. Even more problematically, attempts to replicate the pre-Swift studies on the much larger Swift sample have not led to comparable success. Large, deep radio and Herschel surveys have produced a few secure examples of DSGs with star-formation rates $>$100--300\,$M_\odot$ hosting GRBs \citep{Perley+2013b,Perley+2015,Hunt+2014,Schady+2014}. But none of these would have been detected to the shallower limits of pre-Swift observations---and the bursts hosting them were heavily obscured in almost all cases, even though both obscured and unobscured GRBs were searched. It seems worth considering, therefore, that the pre-Swift long-wavelength late-time detections may not have been as robust as claimed a decade ago, or that they originated from some other process unrelated to star-formation in the host galaxy---in particular, afterglow emission. In this paper we investigate this topic directly by testing whether the purported long-wavelength host galaxy emission reported in previous studies is still present a decade after the initial detections. In \S \ref{sec:observations} we present new ultra-late-time ($>10$ years post-GRB) VLA observations of five proposed ULIRG-like submillimetre/radio-detected pre-Swift GRB host galaxies. We detect none of the hosts at their previously-measured level. Having ruled out a host-galaxy origin, in \S \ref{sec:results} we attempt to explain the previous data, and suggest that while some of these host ``detections'' were simply due to source confusion or statistical fluctuations, at least one provides evidence for interesting physical behavior of the afterglow on timescales of 1--5 years post-GRB: in particular, the possible emergence of the counterjet. We conclude in \S \ref{sec:conclusions}. | \label{sec:conclusions} In this paper, we have presented VLA re-observations of five pre-Swift GRBs for which luminous host-galaxy counterparts had been reported from radio and/or submillimetre data. All five counterparts had either disappeared or (in one case) faded to a level far lower than previously claimed, ruling out the presence of an ultraluminous star-forming galaxy at these locations. A sixth source, GRB\,000210, was not observable to the VLA, but a recent limit from the literature suggests a similar story for this event. We conclude that most of the preceding radio detections were due to lingering radio afterglow emission or to noise fluctuations or reduction artefacts. Our results similarly cast doubt on the reported submillimetre detections, suggesting that they originated from source confusion with background SMGs elsewhere in the SCUBA beam. Our observations offer several lessons relevant to the ongoing Swift era. \begin{table*} \begin{minipage}{110mm} \caption{Swift GRBs localized to ultraluminous host galaxies$^{a}$} \label{tab:swiftulirgs} \begin{tabular}{lllllll} \hline {GRB} & {$z$} & OA?$^b$ & $A_V$ $^c$ & $M^*$ & {SFR} & {Detections$^{c}$} \\ {} & {} & & (mag) & ($M_\odot$) & ($M_\odot$ yr$^{-1}$) & \\ \hline 060814 & 1.920 & IR & $>2$ & 1.6$\times$10$^{10}$ & 250 & VLA, SED \\ 070306 & 1.496 & IR & $\sim4$ & 5.0$\times$10$^{10}$ & 140 & VLA, Herschel \\ 080207 & 2.086 & none & $>3$ & 1.2$\times$10$^{11}$ & 850 & VLA, Herschel, MIPS \\ \hline 061121 & 1.314 & yes & $\sim0$ & 1.5$\times$10$^{10}$ & 160 & VLA (3$\sigma$) \\ 070521 & 1.1185 & none & $>10$ & 3.1$\times$10$^{10}$ & 800 & VLA (3$\sigma$) \\ 090404 & $\sim$3?& none & $>1.6$ & 5.5$\times$10$^{10}$ & 1230 & VLA (4$\sigma$) \\ \hline \end{tabular} $^{a}${\ We define an ultraluminous host galaxy as a galaxy with SFR$>100$ $M_\odot$yr$^{-1}$ or $L_{\rm IR} > 10^{12} L_\odot$}. We regard the ultraluminous nature of the GRB hosts above the horizontal bar as secure on the basis of strong radio detections and confirmation at another frequency. In the case of GRB060814, SED fitting to the optical and IR photometry also indicates a star-formation rate of $\sim$200 $M_\odot$ yr$^{-1}$. Those below the bar are less secure due to lower-significance detections and a lack of multiwavelength confirmation. References: \cite{Svensson+2012,Perley+2013b,Perley+2013a,Perley+2015,Hunt+2014,Greiner+2016}\\ $^{b}${\ Whether or not an optical afterglow was detected for this GRB.} \\ $^{c}${\ Line-of-sight extinction towards the GRB as measured from the afterglow.} \\ \end{minipage} \end{table*} \begin{itemize} \item Radio afterglows are truly long-lived objects, peaking on timescales of weeks to months and fading slowly thereafter, potentially remaining detectable for years---a fundamentally different situation from X-ray and optical counterparts which inexoriably are fading after the first day. While a complication for host searches (next paragraph), this provides advantages for afterglow follow-up. In the Swift era, the large number of events with near-instant positional notifications has shifted observational emphasis to very early times, with the indirect effect of making long-term dedicated campaigns much less common. Even so, systematic and complete studies of radio afterglow properties should still be possible for patient observers acquiring data on timescales of months to years. Interesting physical signatures may be found in such campaigns: our data hints that counterjet emission may have been detected from GRB\,980703 completely accidentally using the pre-upgrade VLA. If such features are common, detailed study of this behavior in newer bursts should be easily possible with the modern VLA. Events with similar physical properties as GRB\,980703 (a reddened event with a high inferred circumburst density, leading to chromatic radio evolution and a rapidly fading afterglow due to an early jet break) will be of particular interest for extended radio follow-up campaigns. (See also the discussion of this point in \citealt{Chandra+2012} and \citealt{Ghirlanda+2013}.) \item Searches for host galaxies in the radio band require long delays ($>$10 years) to rule out the contribution of a bright and/or late-peaking radio afterglow to any detections. Radio studies of GRB hosts have enjoyed a resurgence in the past five years \citep{Hatsukade+2012,Perley+2013b,Perley+2015,Berger+2013,Stanway+2014,Nicuesa+2014,Greiner+2016} thanks to the VLA's improved capabilities and similar improvements to other arrays, and while upper limits remain the norm a number of new detections have been reported. Already, it has become apparent that a few host candidates reported after a delay of only $\sim$1 year were actually long-lived afterglow emission (e.g., GRB\,100621A; \citealt{Greiner+2016}). Our new results suggest that even delays of several years may not always be enough; re-observations on a timescale of a decade will likely be necessary to avoid the risk of afterglow contamination. Complementary observations at submillimetre and/or FIR wavelengths represent a crucial test to verify the nature of luminous hosts identified based solely from radio observations, especially in cases where the afterglow evolution is poorly-constrained and/or the radio host detection is of marginal significance. \item Among the long GRB hosts with radio host detections and ULIRG-scale luminosities that have (so far) survived the test of time (Table \ref{tab:swiftulirgs}), a clear picture is beginning to emerge: they are typically massive and optically-luminous, and the GRBs that occur within them are almost always heavily obscured. This is exactly what would be expected given our current understanding of the DSG population. Luminous DSGs are massive galaxies, and the dust covering fraction in front of the youngest stellar population is quite high, concealing the optical afterglow emission from any GRBs which explode within them. The blue, low-mass ``SMGs'' reported to host several unobscured pre-Swift bursts (by, e.g., \citealt{Berger+2003} and \citealt{Michalowski+2008}) always seemed peculiar from a physical standpoint. It now appears that galaxies of this type do not exist, or at least do not produce GRBs. Future radio searches for ultraluminous GRB host galaxies can focus on galaxies known from their optical properties to have stellar masses, optical colors, and/or optical SFRs consistent with known populations of luminous DSGs. \end{itemize} \vskip 0.02cm | 16 | 9 | 1609.04015 |
1609 | 1609.03403_arXiv.txt | I discuss on our new theory on baryogenesis `Type-II leptogenesis' \cite{CoviKim16} which is different from the well-known `Type-I leptogenesis' \cite{FY86}. First, I will briefly comment on the Jarlskog phases in the CKM and PMNS matrices, $\delq$ and $\dell$. Then, the PMNS phase is used in the `Type-II' leptogenesis for Sakharov's condition on the global quantum number generation in the Universe. For this to be effective, the SU(2)$\times$U(1) gauge symmetry must be broken during the leptogenesis epoch. | \label{sect:intro} In this talk, I discuss the mere 5\,\% of the energy pie (mainly of atoms composed of baryons) of the Universe shown in Fig. \ref{fig:Epie}. At the most fundamental level of the grand unification(GUT) scheme, it belongs to the problem on the chiral representation of quarks \cite{Georgi79,KimICHEP1,KimJHEP15}. In cosmology, it belongs to Sakharov's three conditions. The first one is the existence of baryon number ($B$) violating interaction, and the second is the existence of CP violation \cite{Sakharov67}. For example, at the red clover point of Fig. \ref{fig:Parity} let us calculate baryons moving forward/backward in time. The ratio is the number of baryons over the number of antibaryons. Therefore, to have a nonzero $\Delta B$, we need T or CP violation. We also need to break C. To see this, firstly assume T violation and calculate $\Delta B$ at the red clover point in Fig. \ref{fig:Parity}. Second, integrate over solid angles. At the black clover point, if C is not broken then % \begin{figure}[!b] \begin{center} \begin{tabular}{c} \includegraphics[width=0.45\textwidth]{figEpie.eps} \end{tabular} \end{center} \caption{The energy pie of the Universe. } \label{fig:Epie} \end{figure} $\Delta B$ is minus that of red clover point, because $P=-1$ is multiplied. Then, integration over the solid angle gives $\Delta B=0$. Therefore, the needed T violation in the $\Delta B\ne 0$ processes must accompany the C violation also. The CP violation in the standard model(SM) arises as the ``V-A'' form and hence also breaks C. Sakharov's third condition on ``out of thermal equilibrium'' is satisfied by the decay of some heavy particle(s), which is usually assumed in most baryo- and lepto-genesis mechanisms. \begin{figure}[!t] \begin{center} \begin{tabular}{c} \includegraphics[width=0.45\textwidth]{figCPop.eps} \end{tabular} \end{center} \caption{The ${B}$ number in the parity operated part in the Universe. } \label{fig:Parity} \end{figure} The CP violation seems to work also in some models of dark matter in the Universe. The asymmetric dark matter scenario for this case follows the paradigm of baryogenesis and hence CP violation is the key here also. The axion scenario for dark matter \cite{Baer15} uses an oscillating axion field whose amplitude at present is of order $|\bar{\theta}_{\rm max}|\simeq 10^{-20}$ \cite{KimJeju16}. For nonzero $\bar{\theta}$ though oscillating, CP is violated and hence CP violation is the key in the axionic dark matter scenario also. Only, the WIMP scenario for dark matter uses just the cosmological freezeout temperature, not employing any kind of CP violation \cite{Baer15}. In this talk I will briefly review the weak CP violation first and then present a new mechanism on the leptogenesis that we call `Type-II leptogenesis' with CP violation in the chiral theory \cite{CoviKim16}. | Here, my talk on Type-II leptogenesis is centered on: \begin{itemize} \item[(1)] A short discussion on weak CP, \item[(2)] Introduction of a new leptogenesis mechanism in theories with SU(2)$\times$U(1) breaking at high temperature, \item[(3)] Relation of $\dell$ to the leptogenesis phase in certain CP violation models, \item[(4)] Need of one light intermediate scale Majorana neutrino $N_0$ and another neutrino ${\cal N}$ toward the desired lepton number asymmetry $\epsilon_L$. \item[(5)] Inert Higgs and the SM Higgs mix to provide $\Delta L\ne 0$ vertex in the loop diagram. \end{itemize} | 16 | 9 | 1609.03403 |
1609 | 1609.00894_arXiv.txt | {Stellar populations contain the most important information about star cluster formation and evolution. Until several decades ago, star clusters were believed to be ideal laboratories for studies of simple stellar populations (SSPs). However, discoveries of multiple stellar populations in Galactic globular clusters have expanded our view on stellar populations in star clusters. They have simultaneously generated a number of controversies, particularly as to whether young star clusters may have the same origin as old globular clusters. In addition, extensive studies have revealed that the SSP scenario does not seem to hold for some intermediate-age and young star clusters either, thus making the origin of multiple stellar populations in star clusters even more complicated. Stellar population anomalies in numerous star clusters are well-documented, implying that the notion of star clusters as true SSPs faces serious challenges. In this review, we focus on stellar populations in massive clusters with different ages. We present the history and progress of research in this active field, as well as some of the most recent improvements, including observational results and scenarios that have been proposed to explain the observations. Although our current ability to determine the origin of multiple stellar populations in star clusters is unsatisfactory, we propose a number of promising projects that may contribute to a significantly improved understanding of this subject.} | % \label{S1} Star clusters are the basic units of star formation \citep{Lada03a}: almost all stars form in clustered environments. Current consensus on the formation of star clusters suggests that most stars form tracing the turbulent structure of the interstellar medium and in an initially supervirial state. Within an extremely short period (about one crossing time), the initially turbulent, `fractal' structures will collapse into bound clusters \citep{Bonn08a,Alli09a,Giri12a,Moec15a}. Subsequently, a large proportion will gradually dissipate into the galactic field \citep{grijs10a}. Understanding the stellar populations of star clusters is, therefore, of fundamental importance for understanding many astrophysical processes, including star cluster formation and evolution, the chemical evolution of Galactic stellar populations, as well as the stellar dynamics in star clusters. The `simple stellar population' (SSP) scenario is the assumption that stars in a star cluster all originate from a common progenitor giant molecular cloud (GMC), during the same era, and thus they would share similar metallicities. It has been confirmed that the initial star-forming process in star clusters approximately resembles a single burst \citep{Cabr14a}. The combination of gas expulsion owing to energetic photons ejected by the most massive first-generation stars and the strong stellar winds triggered by the first batch of Type II supernovae will quickly exhaust all of the gas in the GMC, thus quenching the star- and cluster-forming process \citep{Bast14a}. The nature of most open clusters (OCs) and young massive clusters (YMCs) has been confirmed as resembling SSPs. During the last few decades, observations have revealed the presence of multiple stellar populations in Galactic globular clusters (GCs). The observational evidence can be classified into photometric and spectroscopic evidence. The former refers to the fact that the photometric color--magnitude diagrams (CMDs) of some GCs display multiple distinct features in or along their main sequences \citep[MSs; e.g., NGC 2808:][]{Piot07a}, their subgiant branches \citep[SGBs; e.g., 47 Tuc:][]{Ande09a}, their red-giant branches \citep[RGBs; e.g., NGC 288:][]{Piot13a}, or even in their horizontal branches \citep[HBs; e.g., NGC 2808:][]{Bedi00a}. Sometimes, individual GCs even display a combination of such multiple features. In the photometric CMDs, these features can be explained as the result of a diversity of ages, helium abundances, and metallicities. Since SSP stars formed at approximately the same time from a common molecular cloud, variations in age, helium, and metal abundance hence unambiguously reflect the occurrence of more than a single star-forming episode during their host clusters' evolution. GCs have also been subject to intense scrutiny based on spectroscopic analyses, which have revealed star-to-star chemical dispersions of specific elements. \cite{Cohe78a} first noted that the Na abundance variations of RGB stars in the GCs M3 and M13 exceeded the observational errors. Her pioneering work has stood the test of time: subsequent measurements of Galactic GCs have uncovered the well-known Na--O anticorrelation, where oxygen-depleted stars have higher sodium abundance \citep{Carr04a,Grat04a,Carr09a}. Another well-studied Galactic GC relationship is the Mg--Al anticorrelation, which is most easily seen in intermediate-metallicity clusters \citep[e.g., M13;][]{Shet96a}. The large scatter in the abundances of some specific elements is not expected if these GCs were SSPs. A straightforward explanation of the scatter properties is that there has been secondary star formation, fueled by abundance-enhanced material. In this review we will not discuss the chemical evolution of stellar populations in depth, since this aspect was introduced in great detail in the review of \cite{Grat04a}. A key problem associated with the stellar populations in star clusters relates to an important open question: do GCs have the same origin as OCs and YMCs? It seems that the latter, very young objects may encounter significant difficulties to survive to the cosmic age ($\geq$ 10 Gyr) owing to a range of effects, including internal two-body relaxation, which causes most stars to `evaporate' from the cluster \citep{Spit87a}. Only those clusters that initially contained at least 10$^5$ stars can avoid disruption within 10 Gyr \citep{Port10a}. On the other hand, in terms of their initial masses, only young star clusters with masses between $10^5$ $M_{\odot}$ and $10^6$ $M_{\odot}$ have the capacity to capture their initial runaway gas. Because the subsequent Type II supernovae explosions would further accelerate the runway gas flows, the mass threshold for a YMC to capture its initial runaway gas would increase dramatically. If a star cluster can not marshall additional gas reserves, its star-forming process will cease rapidly. As regards the stellar populations in star clusters, almost all observed OCs and YMCs will fail to generate multiple stellar populations, which, however, is a common feature of most observed GCs \citep[see][his Chapter 4]{LiTh_15}. This review is organized as follows. In Section \ref{S2} we show that the SSP approximation is not a tentative assumption but based on convincing evidence. Readers will realize why the presence of multiple stellar populations in GCs (and also in some young and intermediate-age clusters) is a problem. In Section \ref{S3} we discuss observational results of stellar populations in star clusters with different ages. In Section \ref{S4} we compare and contrast currently popular scenarios that aim at explaining the origin of multiple stellar populations; their advantages and disadvantages are also discussed. We next discuss, in Section \ref{S5}, how one can go about examining some of these compelling and controversial scenarios. A brief summary is given in the concluding section (Section \ref{S6}). | \label{S6} In this review, we have introduced the community's up-to-date insights into the physics governing stellar populations in star clusters. We have shown that because of initial gas expulsion, most star clusters are not expected to exhibit multiple episodes of star formation. This renders the origin of the common observation of multiple stellar populations in star clusters an intriguing open question. The observational status of stellar populations in star clusters can be summarized as follows: \begin{itemize} \item For star clusters younger than $\sim$100 Myr, no conclusive evidence exists that they may harbor multiple stellar populations or ongoing star formation; no residual gas has been detected in extremely young clusters \citep{Bast14a}. \item The eMSTO morphologies of some YMCs with ages older than 100 Myr \citep[e.g., NGC 1850 and NGC 1856;][]{Milo15a,Bast16a} are inconsistent with the expectations from SSPs. It appears that such eMSTOs are a common feature of intermediate-age star clusters in the LMC and SMC. However, spectroscopic analyses have shown that their member stars do no exhibit abundance anomalies \citep{Mucc14a}. \item The presence of multiple stellar populations in old GCs is irrefutable: both the morphologies of their photometric features and star-to-star chemical abundance variations challenge the SSP scenario. \end{itemize} Various scenarios have been proposed to explain these observed deviations from genuine SSPs. For young and intermediate-age star clusters, age spreads (which favor eSFHs) and rapid stellar rotation (which suggests that clusters are SSPs) are in competition. For old GCs, all scenarios can be classified as either primordial or evolutionary. We have proposed a number of projects that seem feasible in the near future and which may shed light on our understanding of stellar population problems in star clusters. These include direct measurements of stellar rotation rates in compact star clusters, studies of the elemental abundances of BSSs, and the use of numerical simulations to study gas accretion. Since a number of possible candidate young GCs have been identified in nearby starburst galaxies, employing next-generation telescopes to study these objects will significantly contribute to an improved understanding of the origin of stellar populations in star clusters. | 16 | 9 | 1609.00894 |
1609 | 1609.07150_arXiv.txt | We show that non-magnetic models for the evolution of pre-main-sequence (PMS) stars {\it cannot} simultaneously describe the colour-magnitude diagram (CMD) and the pattern of lithium depletion seen in the cluster of young, low-mass stars surrounding $\gamma^2$ Velorum. The age of $7.5 \pm 1$\,Myr inferred from the CMD is much younger than that implied by the strong Li depletion seen in the cluster M-dwarfs and the Li depletion occurs at much redder colours than predicted. The epoch at which a star of a given mass depletes its Li and the surface temperature of that star are both dependent on its radius. We demonstrate that if the low-mass stars have radii $\sim 10$ per cent larger at a given mass and age, then both the CMD and Li depletion pattern of the Gamma Vel cluster are explained at a common age of $\simeq 18$--21\,Myr. This radius inflation could be produced by some combination of magnetic suppression of convection and extensive cool starspots. Models that incorporate radius inflation suggest that PMS stars similar to those in the Gamma Vel cluster, in the range $0.2<M/M_{\odot}<0.7$, are at least a factor of two older and $\sim 7$ per cent cooler than previously thought and that their masses are much larger (by $>30$ per cent) than inferred from conventional, non-magnetic models in the Hertzsprung-Russell diagram. Systematic changes of this size may be of great importance in understanding the evolution of young stars, disc lifetimes and the formation of planetary systems. | Precise measurements of main-sequence K- and M-dwarf radii in eclipsing binaries have revealed alarming discrepancies between theoretical models and observations. For a given mass, the absolute radii of stars with $0.2<M/M_{\odot}<0.8$ can be $\sim 10$ per cent larger than predicted and hence, for a given luminosity, the effective temperature is overestimated by $\sim 5$ per cent (e.g. Lopez-Morales \& Ribas 2005; Morales et al. 2009a,b; Torres 2013). Since interferometric radii for nearby, slowly-rotating low-mass stars are much closer to ``standard'', non-magnetic evolutionary models (e.g. Demory et al. 2009; Boyajian et al. 2012), it is possible that the radius inflation of fast-rotating binary components is explained by dynamo-generated magnetic activity (Morales, Ribas \& Jordi 2008). The exact mechanism is debated, but could be magnetic fields inhibiting convection throughout the star (Mullan \& MacDonald 2001; Feiden \& Chaboyer 2013, 2014) or cool, magnetic starspots that block outward flux at the stellar surface (MacDonald \& Mullan 2013; Jackson \& Jeffries 2014b). \nocite{lopez-morales05a} \nocite{morales09a} \nocite{morales09b} \nocite{torres13a} \nocite{demory09a} \nocite{boyajian12a} \nocite{morales08a} \nocite{mullan01a} \nocite{feiden13a} \nocite{feiden14a} \nocite{macdonald13a} \nocite{jackson14a} If magnetic activity is implicated in inflating radii, then the same effect should also be present in low-mass pre main sequence (PMS) and zero-age main sequence (ZAMS) stars, which are frequently found to be as fast-rotating and magnetically active as the tidally-locked components of older eclipsing binary systems. Besides revealing an interesting new facet of the astrophysics of low-mass stars, radius inflation in PMS stars would have important practical consequences. Models that include such inflation lead to substantial increases in both the ages and masses that would be inferred from colour-magnitude diagrams (CMDs) and Hertzsprung-Russell diagrams (HRDs; perhaps by factors of two or more -- see Somers \& Pinsonneault 2015b; Feiden 2016), systematically affecting studies of the star formation process and the early evolution of stars and their planetary systems by altering the inferred timescales of important phases (Bell et al. 2013; Soderblom et al. 2014). At present it is not possible to directly measure the masses, radii {\it and} ages of young low-mass stars in order to compare them with evolutionary models. However, it has been suggested that discrepancies between masses, radii, temperatures and luminosities in PMS binaries (Kraus et al. 2015. 2016), the lithium depletion dispersion in PMS stars (Somers \& Pinsonneault 2015a,b) and the anomalous colours of PMS and ZAMS stars with respect to model isochrones (Stauffer et al. 2003; Covey et al. 2016 and see Section 5), might be explained by radius inflation or magnetic activity. Indirect evidence for enlarged stellar radii in young clusters, based on the product of their rotation periods and projected equatorial velocities, supports this view (Jackson, Jeffries \& Maxted 2009; Jackson et al. 2016). \nocite{kraus15a} \nocite{david16a} \nocite{hillenbrand04a} \nocite{azulay15a} \nocite{rizzuto16a} \nocite{stauffer03a} \nocite{covey16a} \nocite{jackson16a} \nocite{jackson09a} \nocite{jackson14b} \nocite{somers14a} \nocite{somers15a} \nocite{somers15b} \nocite{feiden16a} \nocite{bell13a} \nocite{soderblom14a} The Gaia-ESO spectroscopic survey of representative stellar populations at the ESO Very Large Telescope (GES, Gilmore et al. 2012; Randich \& Gilmore 2013) includes observations of large, unbiased samples of PMS stars in young clusters, hence providing an important dataset to further investigate these issues. This paper presents the results of a test, first suggested by Yee \& Jensen (2010, see also Feiden 2016 and Messina et al. 2016), that exploits the sensitive mass and radius dependence of the onset of lithium depletion in fully convective PMS stars. Using GES observations of lithium, we find strong evidence for radius inflation in a large group of low-mass PMS stars belonging to the Gamma Vel cluster (Jeffries et al. 2009). We show that standard, non-magnetic models fail to simultaneously describe the CMD and the pattern of lithium depletion, but that a simple inflation of the radius at a given mass and age could solve this problem. \nocite{jeffries09a} \nocite{jeffries14a} \nocite{prisinzano16a} \nocite{yee10a} \nocite{messina16a} | In Section~2 we showed that the most commonly used evolutionary models cannot simultaneously describe the CMD and Li depletion pattern of the Gamma Vel cluster at a common age. Ages based on Li appear to be much older, though we note that these models do not describe Li depletion at {\it any} age, because they predict Li depletion occuring at much bluer colours than observed. Based on what is known about the radii of magnetically active stars in eclipsing low-mass binaries, it is natural to seek a resolution in terms of modifying the mass-radius relationship at low-masses. Figures~3 and A1 show that a resolution is possible if the radii of stars are inflated with respect to standard models by about 10 per cent at a given mass and age. The results of a simple polytropic model are in remarkably good agreement with the ``magnetic'' Dartmouth models of Feiden \& Chaboyer (2014) for $M\leq 0.6M_{\odot}$, which show similar levels of inflation and are also a reasonable match to the data. Starspots could also be responsible for radius inflation. Our modelling (see Table~1) suggests that if they were to be the {\it sole} cause of the discrepancy between HRD/CMD ages and Li-depletion ages, then this would require significantly more radius inflation and an unrealistically high level of spot coverage -- spot modulation and doppler imaging can give only lower limits to spot coverage, but modelling of TiO bands in the spectra of magnetically active stars suggets 50 per cent coverage may be possible (e.g. O'Neal et al. 2004 and extensive discussion in Jackson \& Jeffries 2014b). In reality, these active stellar photospheres are more likely to feature a distribution of temperatures rather than the simple uniform or bi-modal extremes assumed by our models and the radius inflation would be due to a combination of magnetically moderated effects. \nocite{oneal04a} Yee \& Jensen (2010, see also Malo et al. 2014) noted a quantitatively similar discrepancy between ages from the HRD and ages inferred from Li depletion for stars in the young Beta Pic moving group. They also suggested that radius inflation might be a way to resolve the difference, noting that inflation would increase ages from the HRD and would shift Li depletion to cooler $T_{\rm eff}$. However, they suggested that inferred ages from Li depletion would be {\it reduced} by radius inflation. In fact as we have shown here, and has also been demonstrated by Jackson \& Jeffries (2014a) and Somers \& Pinsonneault (2014, 2015a), radius inflation {\it delays} the onset of Li depletion leading to {\it older} inferred ages. As a result, the ages from the CMD/HRD and Li-depletion can only be reconciled at ages at least a factor of two older than inferred from the CMD/HRD using standard models. This assumes that the inflationary factors were already in place prior to commencement of Li burning. If magnetic activity is the culprit then this seems reasonable, since high levels of magnetic activity are ubiquitously seen in much younger PMS stars than those considered here. Almost identical conclusions were reached for the Beta Pic group by Messina et al. (2016). They showed that a version of the magnetic Dartmouth models was able to describe the CMD and Li-depletion patterns at a common age of $25\pm 3$ Myr. This is entirely consistent with our analysis and age of 18-21 Myr for the Gamma Vel cluster using similar models -- an empirical comparison of the Li depletion patterns in the two datasets (compare Fig.~A1 with fig.~1 from Messina et al.) shows that Gamma Vel is definitely younger than Beta Pic; the lithium-dip is much wider in Beta Pic (by about 0.5 mag in $V-K$), and extends to significantly bluer colours. However, given the extreme age sensitivity of Li depletion, an age difference of a few Myr is all that is required. \nocite{malo14a} Radius inflation due to magnetic activity has the capacity to explain a number of observational puzzles that have emerged in recent years concerning young stars. The increase in age that would follow from using models with radius inflation solves a long-standing discrepancy between the ages derived from the HRD/CMD of low-mass PMS stars using standard models and the considerably older ages determined using the ZAMS turn-on or nuclear turn-off ages from higher mass stars with little magnetic activity (e.g. Naylor 2009; Pecaut et al. 2012). Bell et al. (2013) found that by adopting empirical relationships between bolometric correction and colour derived using a fiducial sequence of (magnetically active) ZAMS stars in the Pleiades cluster, they could bring the ages derived from high- and low-mass stars in young clusters into agreement. The empirical modification to the bolometric corrections is equivalent to changing the radius of the low-mass stars at a given $T_{\rm eff}$. More recently, Feiden (2016) showed that the magnetic Dartmouth models (discussed in Section 3) inflated the radii and increased the derived ages of low-mass PMS stars in the Upper Sco association by a factor of two, bringing them into agreement with ages determined from higher mass stars. \nocite{naylor09a} \nocite{pecaut12a} The large age increases suggested here apply to young clusters for which the age has been previously determined using isochronal fits to their low-mass PMS stars. Ages derived from the ``lithium depletion boundary'' (LDB) -- the {\it luminosity} below which Li remains unburned in the low-mass stars of clusters with ages from 20--130\,Myr (e.g. Bildsten et al. 1997), will be considerably less affected. LDB ages have been proposed as the most model-independent of age determination methods in young clusters (Soderblom et al. 2014) and indeed Jackson \& Jeffries (2014a) showed that these ages are only increased by $\sim (1-\beta)^{-0.5}$ due to magnetically inflated radii. Thus a 10 per cent radius inflation requiring $\beta=0.25$ would increase the determined LDB age by just 15 per cent. For example Binks \& Jeffries (2016) showed that adopting the inflated Dartmouth magnetic models discussed here increased the LDB age of the Beta Pic moving group from 21\,Myr to 24\,Myr. \nocite{binks16a} There are also discrepancies between model predictions and the measured radii and masses for low-mass PMS and ZAMS eclipsing binary systems in clusters and associations (Kraus et al. 2015, 2016; David et al. 2016; Sandberg Lacy et al. 2016). On the basis of position in the HRD, evolutionary models predict masses that are too low and ages that are much younger than suggested by higher mass stars in the same clusters/systems. Similarly, the dynamical masses of astrometric PMS binaries are higher than implied by their measured luminosities and standard evolutionary models (Hillenbrand \& White 2004; Azulay et al. 2015; Rizzuto et al. 2016). Figure~2a demonstrates that these phenomena would be expected if stars were inflated by $\sim 10$ per cent with respect to the standard evolutionary models -- $T_{\rm eff}$ is reduced by 7 per cent, inferred ages are increased by a factor of $\geq 2$, whilst masses inferred from the HRD/CMD are almost doubled at the lowest masses considered here (from $0.2M_{\odot}$ to $\sim 0.35M_{\odot}$), with a smaller effect at higher masses (from $0.6M_{\odot}$ to $\sim 0.8M_{\odot}$). If masses were estimated from luminosities (or absolute magnitudes), the effect would be much smaller. \nocite{sandberg16a} Finally, an explanation of the well known issue of a rotation-dependent dispersion of Li abundance at a given $T_{\rm eff}$ in ZAMS stars (e.g. Soderblom et al. 1993; Barrado et al. 2016) has been proposed by Somers \& Pinsonneault (2014, 2015a,b), which assumes that stars have radii that are inflated by differing amounts depending on their level of rotation and magnetic activity. This leads to differing levels of Li depletion, as explained in Section 3, and a dispersion in Li abundances at the ZAMS that was imprinted during PMS evolution. This dispersion is important because it illustrates the need for a solution that can vary from star-to-star, rather than a global change to evolutionary models that would affect all stars of the same mass equally. For instance, similar radius inflation could be produced by artificially reducing the convective efficiency or altering the adopted relationship between temperature and optical depth in the atmosphere (Chen et al. 2014), but this could not explain any dispersion in stellar properties. \nocite{chen14a} \nocite{barrado16a} \nocite{bouvier16a} A considerable dispersion in EWLi at $V-I \sim 2.7\pm 0.2$ {\it is} present in the Gamma Vel data and cannot be explained by uncertainties in EWLi alone\footnote{The median uncertainty in EWLi is 15\,m\AA, see fig.~5 in Prisinzano et al. (2016)}. The presence of stars with undetectable levels of Li can also not be explained in terms of contamination by non-members; there are too many with a radial velocity close to the cluster centroid and all have some secondary indication of a youthful nature -- see Prisinzano et al. (2016) for details. If this dispersion were present {\it at a given $T_{\rm eff}$ or colour}, it would favour an explanation in terms of differences in $\beta$ caused by differing magnetic activity levels or rotation rates from star-to-star. Here, the simplified assumption has been made of a single value of $\beta$ across the mass range, which could perhaps be justified in terms of the consistent (saturated) levels of chromospheric activity exhibited by PMS stars in Gamma Vel despite a spread in rotation rates (see Frasca et al. 2015). On the other hand, it is uncertain how closely the levels of spot coverage or interior magnetic field strengths are correlated with chromospheric activity -- a Li-depletion-rotation connection has recently been identified in the similar PMS stars of NGC 2264 (age 5--10\,Myr) by Bouvier et al. (2016). Attempts to investigate this in Gamma Vel are hampered by a lack of rotation period data and by both intrinsic and measurement uncertainties. Photometric precision, variability, small reddening differences, differences in the spot coverage when the photometry was performed, the presence of unresolved binary companions and the possibility of a small age spread in the population (see Jeffries et al. 2014) can all contribute to a scatter in $V-I$ and EWLi that could obscure any relationship between Li depletion and rotation/activity over such a narrow Li-dip. The nature of the EWLi dispersion in Gamma Vel and in other young clusters observed by GES is deferred to another paper. A remaining puzzle is the status of the massive binary $\gamma^2$~Vel, which appears to be at the centre of the cluster. According to calculations by Eldridge (2009), the binary has an age of $5.5\pm 1$\,Myr. This age discrepancy between the $\gamma^2$~Vel and the PMS star surrounding it was already noted by Jeffries et al. (2009, 2014). The introduction of inflated models for the PMS stars makes the discrepancy larger. Data from the Gaia satellite should ultimately settle whether $\gamma^2$ Vel and the lower mass stars are physically related or are merely a line of sight coincidence. \nocite{kraus16a} \nocite{eldridge09a} | 16 | 9 | 1609.07150 |
1609 | 1609.00546_arXiv.txt | In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging, leading to an alternated minimization problem. In that work, only a positivity constraint was considered, and the problem was solved by an approximated Gauss-Seidel method. In this paper, we propose to improve the approach on three fundamental aspects. First, we define the estimated image as a solution of a regularized minimization problem, promoting sparsity in a fixed dictionary using either an $\ell_1$ or a (re)weighted-$\ell_1$ regularization term. Secondly, we solve the resultant non-convex minimization problem using a block-coordinate forward-backward algorithm. This algorithm is able to deal both with smooth and non-smooth functions, and benefits from convergence guarantees even in a non-convex context. Finally, we generalize our model and algorithm to the hyperspectral case, promoting a joint sparsity prior through an $\ell_{2,1}$ regularization term. We present simulation results, both for monochromatic and hyperspectral cases, to validate the proposed approach. | With the advent of astronomical interferometers, it has become possible to image the sky at very high angular resolution. An interferometer basically consists of an array of telescopes such that each pair of telescopes probes a spatial frequency in the Fourier plane (denoted by $u-v$ plane) of the image of interest. Given the limited number of telescopes, incomplete sampling of the $u-v$ plane is obtained. In particular, for radio interferometry, measurements consist of complex visibilities, related to Fourier coefficients of the intensity image of interest \citep{Thompson2001}. In this context, the incomplete Fourier sampling leads to a linear ill-posed inverse problem for image reconstruction, and iterative algorithms need to be designed to solve this problem. Classical reconstruction methods for radio interferometry are mainly based on iterative deconvolution (\textsc{clean}; \cite{Hogbom1974}), and on {maximum entropy methods} (MEM) to impose smoothness on the sought image by maximizing the entropy of the image \citep{Cornwell1985}. More recently, imaging techniques within the framework of compressive sensing have been proposed \citep{Wiaux2009}. These methods rely on finding an image that is sparse in a given dictionary, using convex optimization algorithms \citep{Boyd2004, Combettes2010}. As compared to the radio interferometers, optical interferometers involve a less number of telescopes, which in turn provides a sparser $u-v$ coverage. Moreover, atmospheric turbulence at optical wavelengths causes random phase fluctuations leading to cancellation of the visibility values. Indeed the measurements consist of phase insensitive observables: power spectrum and bispectrum, resulting into loss of partial phase information \citep{Thiebaut2010}. This induces non-linearity in the inverse problem for image reconstruction in optical interferometry. Thus, the image recovery methods used in radio interferometry cannot be directly applied, and new methods need to be developed. Research in this direction has led to the development of various algorithms, based on different approaches. In \citet{Thiebaut2008}, the so-called MIRA method has been developed, using a {maximum a posteriori} (MAP) approach to recover the image, where different types of quadratic regularization can be considered. The author proposed to solve the resulting minimization problem using a limited variable metric algorithm which accounts for parameter bounds (namely, the VMLMB algorithm \citep{Thiebaut2002}). Another technique, proposed by \citet{Meimon2005}, namely WISARD, makes use of a self-calibration approach to solve for missing phase information, using smooth regularizations. The so-called BSMEM method, proposed in \citet{Buscher1994}, consists of using MEM to impose smoothness on the estimated image. Recently, \citet{Hofmann2014} proposed the IRBis method (image reconstruction software using the bispectrum), which solves the minimization problem from a MAP approach, considering smooth regularization terms, and employing a non-linear optimization algorithm based on conjugate gradients \citep{Hager2005,Hager2006a}. However, due to the non-linearity of the considered inverse problem, the minimization problems solved by the above methods perform only local optimization. For global minimum search, different approaches have been proposed these last years. In particular, techniques based on a {Markov Chain Monte Carlo} (MCMC) method \citep{Gamerman1997} have been adopted in MACIM \citep{Ireland2006a} and SQUEEZE \citep{Baron2012}, while in \citet{Auria2013}, a tensor approach has been proposed. In the latter, following the idea of phase-lift methods for phase retrieval problems \citep{Cand2011, Waldspurger2013}, the data model is lifted from a vector to a super-symmetric rank-1 order-3 tensor formed by the tensor product of the vector representing the sought image with itself. This yields a linear inverse problem, and a convex minimization problem can be deduced from a MAP approach. In \citet{Auria2014}, the tensor approach has been extended to account for the signal sparsity and thereby improving the reconstruction quality. However, solving for order-3 tensor instead of an image (i.e. a vector) increases the dimensionality of the problem drastically and makes this approach computationally very expensive. Thus, \citet{Auria2013} proposed another method which involves solving linear and convex sub-problems alternately and iteratively for 3 images. Although the global minimization problem remains non-convex and dependent on the initial guess, in practice it has been shown that it provides much better reconstruction quality and accelerates the convergence speed as compared to the tensor approach. Moreover, contrary to the state-of-the-art-methods, it brings convexity to the sub-problems. However, \citet{Auria2013} proposed to solve the tri-linear problem using a Gauss-Seidel method {(\citet{Zangwill1969}, \citet[Chap~7]{Ortega1970}, \citet[Chap.2]{Bertsekas1999})}, which does not have any convergence guarantees in this context. Additionally, only positivity constraints have been considered, without imposing any other \emph{a priori} information on the underlying image. All of the above mentioned methods are designed to reconstruct monochromatic images. However, electromagnetic radiations at different wavelengths can be emitted from an astrophysical source, corresponding to its spectrum. In order to exploit the spectrum of the source, modern optical interferometers are paving the way for multi-wavelength imaging. Instruments such as AMBER \citep{Petrov2001}, GRAVITY \citep{Eisenhauer2008} and MATISSE \citep{Lopez2009}, can take measurements at multiple wavelength channels. This necessitates the progression of imaging techniques from monochromatic to hyperspectral case. Lately, initial work are done in the direction of hyperspectral imaging for optical interferometry. In particular, the method proposed by \citet{Kluska2014}, namely SPARCO, is a semi-parametric approach for image reconstruction of chromatic objects, whereas the method proposed by \citet{Thiebaut2013} deals with a sparsity regularized approach considering the observed scene to be a collection of point-like sources. Recently the use of differential phases for hyperspectral imaging has been proposed in PAINTER \citep{Schutz2014}. The methods proposed by \citet{Thiebaut2013} and \citet{Schutz2014} use the {alternating direction method of multipliers} (ADMM) algorithm \citep{Boyd2010} to solve the considered minimization problem. In this article, we propose an image reconstruction algorithm which can be applied both for monochromatic and hyperspectral cases in optical interferometry. More precisely, in the monochromatic case, we propose to improve the method based on the tri-linear data model proposed by \citet{Auria2013}. First, we propose to impose sparsity as a regularization term, by means of an $\ell_1$-norm, either in the image domain or in a given basis \citep{Wiaux2009, Carrillo2012}, leveraging the recent compressive sensing theory \citep{Donoho2006}. In addition, we have developed an algorithm, based on the block-coordinate forward-backward algorithm recently proposed, e.g., by \citet{Bolte2014,Frankel2015,Chouzenoux2016}, which allows to deal with non-necessarily smooth regularization terms such as the $\ell_1$ norm. Moreover, this algorithm benefits from the convergence guarantees even for the non-convex global minimization problems. Finally, we generalize the proposed method to the hyperspectral case. It translates to a new approach for hyperspectral imaging in optical interferometry. We exploit the joint sparsity of the image cube through an $\ell_{2,1}$ norm \citep{Thiebaut2013}. The rest of the article is organized as follows. Section~\ref{sec:optical_imaging} describes the observation model, whereas the corresponding regularized minimization problem is detailed in Section~\ref{sec:min_prob}. In Section~\ref{sec:proposed_algo}, the proposed algorithm to solve the resultant minimization problem is presented along with the implementation details, incorporating various regularization terms. The simulations performed and the results obtained thereby for monochromatic case are discussed in Section~\ref{sec:simulations}. Section~\ref{sec:hyperspectral} is devoted to the hyperspectral case. Starting with the problem statement, the optimization details and the simulations performed are then presented with the results obtained. Finally, the conclusion is provided in Section~\ref{sec:Conclusion}. | \label{sec:Conclusion} We have presented a new method for image reconstruction in optical interferometry, based on the tri-linear data model proposed in \citet{Auria2013}. While only monochromatic imaging was considered in the previous work, we have extended this model to hyperspectral imaging. Furthermore, to improve the reconstruction quality, since in \citet{Auria2013} only positivity constraints were considered, we have proposed additionally to promote sparsity using either an $\ell_1$ or a weighted-$\ell_1$ regularization term in the monochromatic case, and an $\ell_{2,1}$ regularization term in the hyperspectral case. Moreover, in order to solve the resultant minimization problem, we have developed an alternated minimization algorithm, based on a block-coordinate forward backward algorithm. This algorithm presents convergence guarantees, and benefits from the fact that it can be designed to work with smooth functions, using gradient steps, and with non-necessarily smooth functions thanks to proximity steps. We have assessed the performance of the proposed method on several simulations both for synthetic and realistic $u-v$ coverages, in monochromatic and hyperspectral cases. On the one hand, for monochromatic imaging, adding a sparsity prior gives promising results. On the other hand, for hyperspectral imaging, we have shown numerically that exploiting joint sparsity, using an $\ell_{2,1}$ norm, improves drastically the quality of reconstruction as compared to single-channel reconstruction. To summarise, we have proposed a method which presents a general framework, where the regularization term can be non-smooth and adapted either for the monochromatic case or for the hyperspectral case. Future work includes testing the proposed algorithm on realistic data sets and comparing our method with the state-of-the-art methods in optical interferometry. | 16 | 9 | 1609.00546 |
1609 | 1609.04773_arXiv.txt | Among young binary stars whose magnetospheres are expected to collide, only two systems have been observed near periastron in the X-ray band: the low-mass DQ Tau and the older and more massive HD 152404. Both exhibit elevated levels of X-ray emission at periastron. Our goal is to determine whether colliding magnetospheres in young high-eccentricity binaries commonly produce elevated average levels of X-ray activity. This work is based on {\it Chandra} snapshots of multiple periastron and non-periastron passages in four nearby young eccentric binaries (Parenago 523, RX J1622.7-2325 Nw, UZ Tau E, and HD 152404). We find that for the merged sample of all 4 binaries the current X-ray data show an increasing average X-ray flux near periastron (at a $\sim 2.5$-sigma level). Further comparison of these data with the X-ray properties of hundreds of young stars in the Orion Nebula Cluster, produced by the Chandra Orion Ultradeep Project (COUP), indicates that the X-ray emission from the merged sample of our binaries can not be explained within the framework of the COUP-like X-ray activity. However, due to the inhomogeneities of the merged binary sample and the relatively low statistical significance of the detected flux increase, these findings are regarded as tentative only. More data are needed to prove that the flux increase is real and is related to the processes of colliding magnetospheres. | \label{intro_section} High-amplitude X-ray variability and hard spectra associated with magnetic reconnection flaring are ubiquitous in young stars \citep[e.g.,][]{Feigelson99,Stelzer15}. These frequently ``observed'' X-ray flares exhibit a wide range of durations, from about an hour for faint flares to over a day for bright flares \citep[e.g.,][]{Caramazza07,Getman08a}. The energy distribution of these flares is a power-law with the spectral index similar to that of the Sun \citep{Caramazza07,AlbaceteColombo07,Stelzer07}. This suggests the presence of numerous nano-flares that could be responsible for coronal heating in young stars. Due to insufficient signal such flares remain undetected in the light-curves of young stars making up the ``quiescent'' (a.k.a., ``characteristic'') level of the observed X-ray emission. The 13-day continuous observation obtained for the {\it Chandra} Orion Ultradeep Project \citep[COUP;][]{Getman05} provided a unique opportunity to study the infrequent large X-ray flares ($<$1~flare/week/star) characteristic of pre-main sequence (PMS) stars \citep{Favata05}. The 200 largest COUP flares rank among the most powerful, longest, and hottest stellar flares known; their inferred coronal structures are the largest reported, comparable to several stellar radii in both disk-bearing (Class II) and diskless (Class III) systems \citep{Getman08a,Getman08b}. The ionization induced in circumstellar disks by these powerful and hard X-rays is expected to significantly influence their chemistry and turbulence (via magneto-rotational instability), perhaps with profound effects on accretion, dust settling, protoplanet migration and other physical processes \citep[e.g.,][]{Ilgner06,Ercolano13}. The origin of the large COUP flares is unclear. For instance, \citet{Favata05} suggest magnetic loops linking the stellar photosphere with the inner rim of the circumstellar disk. \citet{Getman08a,Getman08b} propose that the majority of the large COUP flares can be viewed as enhanced analogs of the rare solar long-decay events (LDEs) --- eruptive events that produce X-ray emitting arches and streamers with altitudes rising to $>10^5$~km. Both these scenarios involve only a single star. However, the eccentric short-period PMS binary DQ~Tau has recently been found to exhibit large mm-band and X-ray flares coincident with DQ~Tau's ${\sim}$10~R$_{\star}$ periastron passage \citep{Salter2008,Salter10,Getman11}. These have properties similar to those of large COUP flares, but have been attributed to collisions between the magnetospheres of the binary components. This interpretation is supported by the recurrence of mm flaring in 4 monitored periastron encounters and consistency with a synchrotron model, by the time relationship between the mm and X-ray flares (a Neupert-like effect), and by consistency between the inferred flare loop size and the binary separation. This discovery suggests that some of the large COUP flares could also be produced by colliding magnetospheres. Although star forming regions (SFRs) are expected to contain a large fraction of multiple systems \citep[e.g.,][]{Duchene07}, the frequency of close-separation short-period ($P<100$~days) binaries is not well known. At least 10--15\% of young stars in the nearby SFRs Taurus-Auriga, Scorpius-Ophiuchus, and Corona Australis have been found to be such binaries, via spectroscopy \citep{Prato07}. However, only $\sim 60$ PMS binaries with estimated orbital elements have been reported in total (Figure \ref{fig_e_vs_p}), largely because the precise radial velocity measurements of young stars are often difficult to obtain owing to the random and/or systematic contributions by chromospheric and/or accretion activity. Little is known about spectroscopic binaries (SBs) in the Orion Nebula Cluster (ONC). The three known SBs within the COUP field of view (Parenago~1540, 1771, 1925) have incomplete or highly uncertain orbital parameters. Among young binary stars whose magnetospheres are expected to collide, only the low-mass DQ~Tau system \citep{Getman11} and the older and more massive HD 152404 system \citep{GomezDeCastro13} have been observed near periastron in the X-ray band. The goal of the current work is to determine whether colliding magnetospheres in young high-eccentricity binaries commonly produce elevated levels of X-ray activity. This work is based on short (3 ks) {\it Chandra} observations of multiple periastron passages in four nearby young eccentric binaries, complemented by observations of the systems away from periastron. In some cases, we monitored the periastrons at optical or near-infrared wavelengths from the ground as well. Our binary sample includes three K-M-type systems (Parenago 523, RX J1622.7-2325, and UZ Tau E) and one older F-type system (HD 152404). It is important to stress here our realistic expectations about the outcome of this experiment. Within the 60~ks {\it Chandra} X-ray observation of the part of the DQ Tau's periastron, \citet{Getman11} detect one large flare event (with the duration typical to that of the COUP large flares, $\sim 50$~ks) and one much smaller event, superimposed on the large one. Getman et al. also speculate that the large DQ Tau event, in turn, may be a combination of multiple weaker events. Based on these observational results for DQ Tau, we therefore assume that a powerful magnetosphere collision process might release a significant amount of energy stored in large-scale magnetic structures that might result in a flaring activity comprising a wide range of flares. At the same time, as mentioned above, young stars are highly magnetically active objects exhibiting regular ``normal'' X-ray activity powered by magnetic reconnection events on single stars regardless the presence or absence of a binary component. {\it For a young eccentric binary with a strong magnetosphere collision, we thus expect to have a superposition of these two types of flaring activities at periastron.} Unlike in the \citet{Getman11} study, in the current project our individual 3~ks {\it Chandra} exposures are generally too short for a detection and characterisation of even faint X-ray flares; recall that the typical durations of faint short ``observed'' $Chandra$ X-ray flares are roughly an hour or so \citep[][]{Wolk05,AlbaceteColombo07}. Even if such a $Chandra$ exposure captures the part of the rise/decay phase of a large X-ray flare, it would be impossible to infer the main properties of the parental flare (such as morphology, duration, and energetics). {\it Here, we thus are not so much interested in detailed variability analyses of any ``observed'' flares but rather in comparison of the average levels of X-ray activities between periastron and non-periastron passages.} Further, it should be noted that for individual periastron passages, an elevated level of X-ray activity might not be detected at least for the following two reasons: (astrophysical) a significant flaring activity due to magnetosphere collisions might not take place for every periastron passage, for instance due to the lack of time for the stellar magnetospheres to restore the energies between the passages and/or due to the unfavorable orientation and topologies of the magnetospheres \citep{Salter10}; (observational) if the activity due to a magnetosphere collision is dominated by large flares, but our $3$~ks exposures "land" on inter-flare levels. For the above reasons, our project is set up to sample multiple periastron passages. If a strong flare activity due to magnetosphere collisions happens, we expect to find, on average, a higher X-ray flux near periastrons compared to that of non-periastrons. The target sample is reviewed in \S \ref{sec_sample} and the {\it Chandra} and the ground-based observations are described in \S \ref{observation_section}. The inferred X-ray photometric and spectral properties are given in \S\S \ref{sec_phot}, \ref{sec_spec}. Comparison of the X-ray binary data with the X-ray data of the ONC PMS stars are presented in \S \ref{sec_sim}. Optical and near-IR results are given in \S \ref{sec_onir_results}. We end with discussion of our new observational findings and directions of further research (\S \ref{sec_discussion}). | \label{sec_discussion} Two major mechanisms for optical/radio/X-ray activity in young high eccentric binaries have been discussed in the literature. The first mechanism, magnetic activity due to colliding magnetospheres, was considered to explain the optical/mm/X-ray activity in DQ Tau \citep{Salter10,Getman11}, optical/mm in UZ Tau E \citep{Kospal11}, and radio activity in V773 Tau A \citep{Massi08,Adams11}. As a manifestation of the magnetic activity due to colliding magnetospheres the X-ray flux near periastron of a young high eccentric binary is expected to be higher and generally harder than that away from periastron \citep{Getman11}. The second major mechanism, pulsed accretion from binary-disk interactions, was invoked to explain the optical/NIR activity in DQ Tau \citep{Mathieu97,Bary14} and optical in UZ Tau E \citep{Jensen07}. See for instance \citet{Bary14} and references therein, for details regarding different pulsed accretion scenarios. Our goal is to determine whether colliding magnetospheres in young high-eccentricity binaries commonly produce elevated average levels of X-ray activity. The current work is based on {\it Chandra} snapshots of multiple periastron and non-periastron passages in four nearby young eccentric binaries (Parenago 523, RX J1622.7-2325 Nw, UZ Tau E, and HD 152404). For three of these binaries, X-ray emission was observed (Parenago 523, RX J1622.7-2325 Nw) or resolved (UZ Tau E) here with a modern X-ray telescope for the first time; their average intrinsic X-ray properties are presented in \S \ref{sec_spec}. We believe that the current X-ray dataset is too sparse to clearly reveal the effects of colliding magnetospheres in our binaries, but two findings presented here certainly encourage additional observations. X-ray photometric analysis (\S \ref{sec_phot}) shows that for the merged binary sample X-ray flux near periastron is higher and the emission is harder (at the significance level of $\sim 2.5$-$\sigma$) than that away from periastron. The COUP simulations (\S \ref{sec_sim}) show that for the merged binary sample, as well as the individual system UZ Tau E, the X-ray flux variations between the ``periastron'' and ``non-periastron'' states can not be explained by the ``normal'' X-ray activity observed in numerous PMS members of ONC. However, the following opposing arguments may cast some doubts on the supporting ideas above. First, at this relatively low $\sim 2.5$-$\sigma$ level the result of the increased and hardened X-ray emission near periastron could still be spurious. Second, our sample of binaries was chosen to include systems with a certain orbital geometry, such as high eccentricity, relatively low orbital period, and periastron separations limited to $15$~R$_{\star}$ (\S \ref{sec_sample}). The latter was chosen to be comparable to the coronal loop sizes inferred for some large COUP flares \citep{Getman08a} to insure that interacting magnetospheres at such proximities would be capable of producing strong X-ray flares. Nevertheless, the range of the periastron separations among our binaries is wide, [$5-15$]~R$_{\star}$. Other parameters, such as stellar mass, accretion rate, and age are also known to affect the X-ray emission of PMS stars \citep[][and references therein]{Getman2014}. All these and other parameters, many of which drastically vary across our binary sample, might affect the production of X-rays (both ``normal'' X-rays and X-rays from colliding magnetospheres) in different ways. This reasoning might cast doubt on the validity of combining the 4 binaries in a single merged sample. Although, with regards to one of the most influential parameters on X-ray emission (stellar mass), our COUP simulations show that the results remain similar among different mass strata (Table \ref{tbl_simulation_predictions}). Future coordinated multi-wavelength observation campaigns of young eccentric binaries, spanning both a larger number of periastron passages and a larger range of orbital phase, are thus desirable to search for the excess X-ray emission and provide better understanding of the underlying mechanisms. With the assumption that the X-ray flux increase found in \S \ref{sec_phot} is real and is persistent at a similar level for each of the individual binaries, we suggest that as many as $>50$ ``periastron'' and $>50$ ``non-periastron'' short ($3$~ks) passages of individual binary systems to be observed in X-rays in order to derive meaningful information (at $5$-$\sigma$ significance level) on the presence/absence of the excess X-ray emission. The disk-free systems Parenago~523 and RX~J1622.7-2325 Nw could be considered as good observation candidates since these cases allow disentangling from the effects of accretion. Parenago~523 system is also advantageous for its extreme brightness in X-rays, allowing good statistics in each of the short X-ray observations (Table~\ref{tbl_xray_photometry}). Meanwhile, RX~J1622.7-2325 Nw is preferred for its relatively short orbital period ($3.23$~days) to allow a swift observation campaign. In addition, a potential unique feature of RX~J1622.7-2325 Nw is that due to the very small component separation, even at apastron ($\sim 10$~R$_{\odot}$), the system might experience strong magnetosphere interactions throughout the entire orbital phase. The disky system UZ Tau E could be considered as a valuable observation candidate as well since the results of our COUP simulations for this system indicate inconsistency of its X-ray emission with the model of ``normal'' X-ray activity. | 16 | 9 | 1609.04773 |
1609 | 1609.06540_arXiv.txt | {The \ion{H}{i} halo clouds of the Milky Way, and in particular the intermediate-velocity clouds (IVCs), are thought to be connected to Galactic fountain processes. Observations of fountain clouds are important for understanding the role of matter recycling and accretion onto the Galactic disk and subsequent star formation.} {Here, we quantify the amount of molecular gas in the Galactic halo. We focus on the rare class of molecular IVCs (MIVCs) and search for new objects.} {The \ion{H}{i}-FIR correlation was studied across the entire northern and southern Galactic hemispheres at Galactic latitudes $|b|>20^\circ$ to determine the amount and distribution of molecular gas in IVCs. We used the most recent large-scale \ion{H}{i} and FIR data, the Effelsberg Bonn-\ion{H}{i} Survey, the Parkes Galactic All-Sky Survey, and the \textit{Planck} FIR surveys.} {We present a catalogue of 239 MIVC candidates on the northern and southern Galactic hemispheres. Among these candidates, all previously known MIVCs are recovered except for one single source. The frequency of candidates differs significantly between the northern and southern Galactic hemispheres and between negative and positive LSR velocities as well.} {In our approach we analyse the local Galactic environment. Extrapolating our results to the entire Galaxy, the global inflow of atomic and molecular IVC gas onto the Milky Way may account for the major fraction of the gaseous mass that is required to sustain the current Galactic star formation rate.} | \label{sec:introduction} A star-forming galaxy such as the Milky Way requires the continuous accretion of matter to sustain its star formation activity over timescales of Gyr \citep[e.g.][]{Fraternali2012,Putman2012}. The accreted material needs to be of low metallicity to match the observed abundances in Galactic stellar populations, which is known as the G-dwarf problem \citep{Alibes2001}. Gaseous halos of galaxies are thought to be an important reservoir for such material \citep[e.g.][]{Wakker2001}. The intermediate- and high-velocity clouds (IVCs and HVCs) are prominent structures of extra-planar cold atomic gas in our Galaxy \citep[][for a recent review on gaseous halos]{Putman2012}. These classes of \ion{H}{i} halo clouds are defined by their anomalous radial velocity that is incompatible with simple rotation models. IVCs are typically defined with $40\,\mathrm{km}\,\mathrm{s}^{-1}\leq |v_\mathrm{LSR}| \leq 90\,\mathrm{km}\,\mathrm{s}^{-1}$, and HVCs with $90\,\mathrm{km}\,\mathrm{s}^{-1}\leq |v_\mathrm{LSR}|$ \citep[e.g.][]{Wakker2001}. The IVCs are located within a distance of $\sim$2\,kpc and consist of gas of near solar metallicity. The HVCs have distances of $5\lesssim D \lesssim 20\,$kpc and lower metallicities \citep[e.g.][]{Wakker2001}. A main exception is the Magellanic System, which is located at much larger distance \citep[e.g.][]{Nidever2010}. Commonly, FIR emission is detected towards IVCs \citep{Planckcollaboration2011XXIV}, however, no dust emission could be convincingly associated with HVCs so far \citep{Wakker1986,Planckcollaboration2011XXIV,Williams2012,Saul2014,Lenz2016}, and in other cases they are only tentatively detected \citep{MivilleDeschenes2005a,Peek2009}. These properties suggest that IVCs may be connected to a Galactic fountain process, while HVCs represent an extragalactic reservoir of gas \citep[e.g.][]{Putman2012}. According to this picture, IVCs are considered as an inflow of gas consisting predominantly of recycled disk material. During the fountain cycle, clouds may gain mass by the local cooling of the hot halo medium \citep{Marinacci2010,Marasco2012}. As fountain clouds, IVCs may therefore contribute to the global accretion. Star formation requires cold and dense gas as fuel \citep[e.g.][]{Putman2012}. Such gas may harbour molecules, whose presence can be used to identify cold and dense gas. Studies using absorption spectroscopy reveal a widespread distribution of low molecular hydrogen (H$_2$) column densities of $N_{\mathrm{H}_2}=10^{14}-10^{16}\,\mathrm{cm}^{-2}$ within IVCs \citep{Richter2003,Wakker2006}. There are a few molecular intermediate-velocity clouds (MIVCs) that contain significant amounts of molecular gas, such that carbon monoxide $^{12}$CO(1$\rightarrow$0) emission is detected \citep{Magnani2010}. These MIVCs are of prime interest for studies of inflowing cold, dense, and molecular material onto the Milky Way \citep[e.g.][]{MivilleDeschenes2016}. MIVCs are located at scale heights of a few hundred parsecs above the disk with in-falling radial velocities \citep{Magnani2010}. These rare objects are Draco, IVC\,135, IVC\,210, G\,283.8+54.9, G\,288.4+53.2, and G\,295.0+57.1. The latter three appear to be part of the same gaseous structure \citep{Magnani2010}. Because of their large amounts of molecular gas, Draco \citep{Mebold1985,Mebold1987,Rohlfs1989,Herbstmeier1993,Herbstmeier1996,Moritz1998,Heithausen2001b,MivilleDeschenes2016}, IVC\,135 \citep{Heiles1988,Weiss1999,Heithausen2001b,Hernandez2013,Lenz2015}, and IVC\,210 \citep{Desert1990a,Roehser2014,Roehser2016} have been extensively studied. Furthermore, there are confirmed distance limits for these three MIVCs \citep{Gladders1998,Benjamin1996,Roehser2014}. The low number of MIVCs suggests that either MIVCs are rare and require special conditions to form, or that only a small fraction of the MIVC population has been detected so far. The CO survey conducted by \citet{Dame2001} covers only latitudes of $|b|\lesssim20^\circ$ , except for a few known high-latitude molecular structures. The CO maps extracted from the \textit{Planck} surveys \citep{Planckcollaboration2014XIII} only have a limited sensitivity and do not provide spectral information. We have therefore to rely on the indirect inference of molecular hydrogen on Galactic scales. One method is the correlation of \ion{H}{i} and FIR dust emission and the analysis of its residuals. With respect to the linear \ion{H}{i}-FIR correlation, FIR excess is inferred, which is commonly attributed to the presence of molecular hydrogen \citep{Desert1988,Reach1994,Reach1998}. The most recent and comprehensive study of FIR-excess emission was conducted by \citet{Reach1998}. However, they only considered the total \ion{H}{i} column density within $-100\,\mathrm{km}\,\mathrm{s}^{-1}\leq v_\mathrm{LSR} \leq 100\,\mathrm{km}\,\mathrm{s}^{-1}$ and therefore did not make use of the velocity information of the \ion{H}{i} data. In addition, the angular resolution and quality of their data, especially in \ion{H}{i}, is significantly surpassed by the new all-sky surveys that are available today \citep{Winkel2016,Kalberla2015,Planckcollaboration2013I}. Here, we present an all-sky search for MIVCs focussing on high Galactic latitudes of $|b|>20^\circ$. At lower latitudes many different gas components are superimposed along the lines of sight, which does not allow reliably distinguishing different FIR emission components by their \ion{H}{i} counterparts. This paper is organised as follows. In Sect.~\ref{sec:data} we present the \ion{H}{i} and FIR data that we use in this all-sky analysis. In Sect.~\ref{sec:methods} we discuss the \ion{H}{i}-FIR correlation and how we estimate H$_2$ column densities on Galactic scales. In addition, MIVC candidates are defined by a set of observed quantities. In Sect.~\ref{sec:nor-gal-hem} we present the distribution of the inferred MIVC candidates on the northern Galactic hemisphere at $b>20^\circ$. In Sect.~\ref{sec:sou-gal-hem} the same analysis is shown for the southern Galactic hemisphere at $b<-20^\circ$. An additional analysis of the global MIVC samples is presented in Sect.~\ref{sec:results}. Our results are discussed in Sect.~\ref{sec:discussion} and we conclude in Sect.~\ref{sec:summary}. | \label{sec:discussion} We searched for potential MIVC candidates of the Milky Way towards high Galactic latitudes. All previously known MIVCs were recovered except for one single source. This positive result justifies the simplifying assumptions in the inference of MIVCs. For instance, we only considered a single gas-to-dust ratio for either northern or southern hemisphere. The fact that we still recover all the known MIVCs suggests that we captured their observational properties well. The local conditions also appear to remain substantially the same across the sky. The complete candidate list is given in Tables \ref{tab:mivc-candidates-large} and \ref{tab:mivc-candidates-small}. These objects are ranked by analysing their \textit{\textup{local}} \ion{H}{i}-$\tau$ correlation. Only Draco and IVC\,135 are clearly associated with nearby HVC \ion{H}{i} emission, wherefore this connection has been invoked explicitly as a possible formation channel \citep{Herbstmeier1993,Moritz1998,Weiss1999,Lenz2015}. In all other cases this association is not observed. This means that collisions between IVCs and HVCs appear not to be an important formation channel of MIVCs. The detection of $^{12}$CO(1$\rightarrow$0) emission that is associated with the MIVC candidates is thought to be clear proof of the molecular nature of the IVCs. However, the existence of CO-dark H$_2$ gas \citep{Grenier2005,Wolfire2010,Planckcollaboration2011XIX} indicates that a stage in the transition from atomic to molecular clouds is not yet traceable by detectable amounts of CO emission \citep[also][]{Meyerdierks1996,Reach2015,DuarteCabral2016}. For this molecular component the \ion{H}{i}-FIR correlation is one of the few methods for identifying and quantifying this material. \subsection{Selection parameters and completeness} \label{sec:selection-completeness} Motivated by the properties of known MIVCs, we devised selection criteria (Sect.~\ref{sec:def-mivc}) to identify the most prominent MIVCs from observations. We defined IVCs by $20\,\mathrm{km}\,\mathrm{s}^{-1}\leq|v_\mathrm{LSR}|\leq100\,\mathrm{km}\,\mathrm{s}^{-1}$ and $|b|>20^\circ$. In the following we discuss how these two criteria bias the identified population of Galactic IVCs. For this we consider a typical Galactic fountain as simulated by \citet{Melioli2008}. In their model the fountain ejects $\sim$$2.5\times10^5\,\mathrm{M}_\odot$ up to scale heights of $z\simeq2\,$kpc. The maximum downward motion (back onto the disk) is $v_\mathrm{z}\simeq-100\,\mathrm{km}\mathrm{s}^{-1}$. Matching these characteristics, we adopted a plane-parallel slab of fountain material with $|z|=2\,$kpc and $|v_\mathrm{z}|=100\,\mathrm{km}\mathrm{s}^{-1}$ down onto the disk all over the Milky Way. Because of the symmetry, both cases of $z=\pm2\,$kpc are identical. These considerations are similar to \citet{Schwarz2004}. We studied the dependency of the observable Galactic latitude coordinate $b$ and of the projected vertical velocity $v_\mathrm{z}^\mathrm{proj}$ on the heliocentric distance $x$ in one dimension (Fig.~\ref{fig:disc-selection}). Analytically, at a heliocentric distance of $x\simeq5.5\,$kpc the considered fountain ejecta would be observed at $b\simeq20^\circ$ with $v_\mathrm{z}^\mathrm{proj}\simeq-34\,\mathrm{km}\mathrm{s}^{-1}$. At $x\simeq9.8\,$kpc we obtain $b\simeq12^\circ$ and $v_\mathrm{z}^\mathrm{proj}\simeq-20\,\mathrm{km}\mathrm{s}^{-1}$. For our search the global population of IVCs of the Milky Way is therefore restricted most by the latitude limit of $|b|>20^\circ$. The situation is even more severe for the MIVCs Draco, IVC\,135, and IVC\,210, which are located at $z\lesssim0.5\,$kpc and are observable only within $x\simeq1.4\,$kpc. With our search parameters we trace approximately a cylindrical volume of the Milky Way with a radius of $\sim$5.5\,kpc and thickness of $2\times2\,$kpc, which is twice the height of the plane-parallel slab. We approximated the volume in our Galaxy in which star formation and fountain activity is expected to occur by the largest Galactocentric radius of high-mass star formation of $\sim$16\,kpc \citep{Reid2009}. Comparing these volumes, we find that our search may only target $\sim$12\% of the volume of interest in the Milky Way. When we extrapolate from the local MIVC population to the entire Galaxy, this yields a global H$_2$ inflow rate from MIVCs of $\dot{M}_{\mathrm{H}_2}\simeq0.05\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}-0.17\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}$. Similarly, the extrapolated upper total \ion{H}{i} and H$_2$ inflow rate from IVCs is $\dot{M}_{\mathrm{H}}\simeq1.3\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}-4.3\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}$. Despite the considerable uncertainties in these estimates, we can draw two main conclusions from this result. \begin{enumerate} \item The total in-fall of atomic and molecular material in the form of IVC gas onto the Milky Way Galaxy as a whole may account for the entire inflow that is required to sustain the current Galactic star formation rate. \item A vertical scale height of $h_z\lesssim0.5\,$kpc appears to be more plausible for the class of MIVCs. Larger heights lead to unrealistically high inflow rates, even more so since there are additional fuelling sources \citep{Putman2012}. This also supports the idea that MIVCs constitute a late stage in the Galactic fountain cycle. Thus, IVCs may turn molecular when they reach the disk-halo interface during their descent. Here, the environmental pressure is sufficiently high to form high density and high column density environments, allowing the rapid formation of molecules and the protection against dissociating radiation \citep[][their Fig.~14]{Roehser2014}. \end{enumerate} \begin{figure} \resizebox{\hsize}{!}{\includegraphics{VOBS_VZ_DIST}} \caption{Dependency of observable Galactic latitude $b$ (black) and projected vertical velocity $v_\mathrm{z}^\mathrm{proj}$ (blue) on heliocentric distance $x$ for a plane-parallel slab of fountain objects at vertical scale height $z=+2\,$kpc with a downward motion of $v_\mathrm{z}=-100\,\mathrm{km}\mathrm{s}^{-1}$. The 1D heliocentric distance $x$ is measured within the plane of the disk. The vertical and horizontal lines indicate the limits of our search for MIVCs of $20\,\mathrm{km}\mathrm{s}^{-1}\leq|v_\mathrm{LSR}|\leq100\,\mathrm{km}\mathrm{s}^{-1}$ and $|b|>20^\circ$. The coloured areas show the observable parameter spaces.} \label{fig:disc-selection} \end{figure} \subsection{Comparison with \texorpdfstring{\citet{Reach1998}}{Reach et al. (1998)}} \label{sec:disc-comp-reach1998} The last all-sky study of the FIR excess emission was performed by \citet{Reach1998}. Today, we analyse significantly improved data in \ion{H}{i} and the FIR. This is one of the main reasons why we identify many more FIR excess objects. The most important difference between our analysis and that of \citet{Reach1998} is that they fitted a single-component model integrated over $-100\,\mathrm{km}\,\mathrm{s}^{-1}\leq v_\mathrm{LSR} \leq +100\,\mathrm{km}\,\mathrm{s}^{-1}$. This means that they did not consider the radial velocity information. Furthermore, \citeauthor{Reach1998} fitted the \ion{H}{i}-FIR correlation in cells with radius of $10^\circ$ on a regular grid with $10^\circ$ spacing. Towards some fields this subdivision does not allow a robust estimation of their linear parameters, for example because of large molecular cloud complexes. It is therefore worthwhile to compare our results more closely to those of \citet{Reach1998}. In Sects.~\ref{sec:mivcs-north} and \ref{sec:mivcs-south} we quantified the statistical significance of the inferred FIR excess. Using these values on the northern Galactic hemisphere at $b>20^\circ$, we found 694 statistically significant FIR excess objects that have angular sizes larger than a GASS beam and 232 objects that are larger than an LAB beam of $36\,\arcmin$ \citep{Kalberla2005}. The LAB data comprise the Leiden-Dwingeloo \ion{H}{i} survey \citep{Hartmann1997}, which were used by \citet{Reach1998} as well. In comparison to the 232~objects that are reported here, \citet{Reach1998} identified 56 FIR excess objects on the northern Galactic hemisphere. For $b<-20^\circ$, we identified 389 statistically significant FIR excess objects that are larger than a GASS beam and 105 objects larger than a LAB beam, compared to 85 FIR excess objects reported by \citet{Reach1998}. \citeauthor{Reach1998} reported thresholds for their FIR excess derived at $100\,\mu\mathrm{m}$ of 1.0\,MJy\,$\mathrm{sr}^{-1}$ at $|b|>20^\circ$ and of 0.3\,MJy\,$\mathrm{sr}^{-1}$ at $|b|>45^\circ$ (compare with their Fig.~6). These thresholds measure the intrinsic scatter of their residual FIR emission. To quantify similar thresholds, we performed our fitting of the \ion{H}{i}-FIR correlation data as before, but with the IRIS $100\,\mu\mathrm{m}$ data \citep{MivilleDeschenes2005b}. We find that the positive FIR excess dominates above $\sim$0.3\,MJy\,$\mathrm{sr}^{-1}$ for $|b|>20^\circ$ and above $\sim$0.2\,MJy\,$\mathrm{sr}^{-1}$ for $|b|>45^\circ$. This shows that our methods and our data allow us to deduce more reliable results that appear to be less affected by intrinsic variations of the \ion{H}{i}-FIR correlation than those of \citet{Reach1998}. \subsection{Differences between Galactic hemispheres} \label{sec:disc-diff-hemis} There are some notable differences between the populations of MIVC candidates on the northern and southern Galactic hemispheres, both in terms of number and distribution. On the northern hemisphere there are 184 MIVC$^-$ and only three MIVC$^+$ candidates, on the southern there are 31 MIVC$^-$ and 21 MIVC$^+$ candidates. If the Galactic IVC population is connected to a Galactic fountain process \citep[e.g.][]{Putman2012}, then it is unlikely to find such a significant difference in candidate numbers between the two hemispheres. The lack of high-latitude southern IVC structures has been known for a long time now \citep[e.g.][]{Wakker2004}, but there is still no explanation. There is a clear lack of northern MIVC$^+$ candidates. To some degree this difference is related to the different amounts of northern IVC$^\pm$ gas: At $b>20^\circ$ there is about three times more total \ion{H}{i} column density in IVCs$^-$ than in IVCs$^+$. Furthermore, the median ratio $N_\mathrm{\ion{H}{i}}^{\mathrm{IVC}^-}/N_\mathrm{\ion{H}{i}}^\mathrm{LVC}$ is about four times higher than $N_\mathrm{\ion{H}{i}}^{\mathrm{IVC}^+}/N_\mathrm{\ion{H}{i}}^\mathrm{LVC}$ at $b>20^\circ$. Combined, this may account for a factor of $\sim$10 in candidate numbers. Still, this is not sufficient to explain the lack of northern MIVC$^+$ candidates since at least ten northern MIVC$^+$ candidates would be expected. We suggest that the lack of northern MIVC$^+$ candidates is not only related to observational biases due to the different amounts of IVC$^-$ and IVC$^+$ gas and their distribution relative to the LVC gas. Instead, there may be physical reasons for the formation and existence of MIVCs in general that are linked to the kinematics and direction of motion of the IVCs within the Galactic fountain cycle, as argued by \citet{Roehser2014,Roehser2016}. Only inflowing objects, for instance, objects~moving towards the Galactic disk, appear to form large amounts of molecular gas that are traceable by the \ion{H}{i}-FIR correlation. The distributions of the northern and southern MIVC candidates are also clearly distinct. In the north, the candidates are located preferentially at high Galactic latitudes well above the latitude limit of $b>20^\circ$. In the south, the candidates are found at $b>-30^\circ$. Some southern IVC structures coherently connect to structures that extend up to the Galactic disk. This suggests that at least some of the southern IVC structures are objects of the disk and not the halo. Furthermore, at lower absolute latitudes there is typically more LVC gas. This hinders the evaluation of the southern candidates. \subsection{Negative offset on the southern Galactic hemisphere} \label{sec:disc-neg-offset} The \ion{H}{i}-$\tau$ correlations on the northern and southern Galactic hemispheres were fitted in the exact same way. However, in the south, a negative offset in the FIR model is obtained (Table \ref{tab:hi-tau-coeff}). Such a negative offset is unphysical since there is no negative FIR emission. The only difference in method is the masking of the Magellanic System on the southern hemisphere. This masking, in fact, slightly alleviates the problem. This offset indicates that the modelled \ion{H}{i}-$\tau$ correlation is too steep, which suggests some bias that is introduced by the distribution of gas and dust on the southern Galactic hemisphere. This offset might be related to the spatial offset of the Sun above the Galactic plane of $20.5\pm3.5\,$pc \citep{Humphreys1995}. This height is a significant fraction of that of the molecular and cold atomic gas in our Galaxy \citep[e.g.][his Table 3]{Kalberla2003}, which means that there should be more cold and dense gas towards the southern than towards the northern Galactic hemisphere. This is consistent with our \ion{H}{i} data. The total \ion{H}{i} column density at $b<-20^\circ$ is $\sim$23\% higher than at $b>20^\circ$. Furthermore, the mid-plane pressure and the amount of molecular gas in the disk of galaxies are correlated \citep{Wong2002,MacLow2012}. This suggests that in the innermost plane, where the vertical pressure is highest, the atomic hydrogen is most efficiently converted into molecular hydrogen. There may therefore be more molecular gas at lower \ion{H}{i} column densities on the southern Galactic hemisphere, which causes the slight bias in the southern \ion{H}{i}-$\tau$ correlation. We studied the IVC population of the Milky Way and its FIR properties by correlating the \ion{H}{i} and FIR emission at Galactic latitudes $|b|>20^\circ$. The recent \ion{H}{i} single-dish surveys EBHIS and GASS were complemented by the dust model obtained from \textit{Planck} FIR data. This new data set allows an exceptional analysis of global ISM properties of the Milky Way. The \ion{H}{i} and FIR data are correlated at the angular resolution of GASS of $\theta\simeq16.1\arcmin$. By subtracting the FIR emission associated with the atomic gas, we derived H$_2$ column densities across the sky with the focus on the molecular content of IVCs and on the search for molecular IVCs (MIVCs). We defined MIVCs from observables obtained from the \ion{H}{i} and FIR data only. The all-sky H$_2$ maps (Figs.~\ref{fig:nh2-north} and \ref{fig:nh2-south}) reveal a multitude of small FIR excess objects that are not apparent in previous studies of the large-scale FIR emission and excess \citep[e.g.][]{Reach1998}. This stresses the wealth of information obtained by the new all-sky survey data. We retrieved all previously known MIVCs except for a single source, which is not identified because of our velocity selection between LVC and IVC gas. In total, we identified 239 MIVC candidates on the two Galactic hemispheres for both negative and positive radial velocities as compiled in Tables \ref{tab:mivc-candidates-large} and \ref{tab:mivc-candidates-small}. If these candidates are real MIVCs, then we should be able to detect associated $^{12}$CO(1$\rightarrow$0) emission, although during the initial stages of formation CO-dark gas may dominate the H$_2$ content of a molecular cloud \citep{Wolfire2010}. The existing CO large-scale surveys fail to detect these objects. The numbers and distributions of candidates differ strongly between the two hemispheres and between the two radial velocity regimes: There are many more candidates found on the northern hemisphere with negative radial velocities. Such a clear dichotomy between north and south is unexpected when we assume that the IVC gas is related to a Galactic fountain process. The lack of MIVC candidates with positive radial velocities appears not to be accounted for by a different amount and distribution of LVC and IVC gas. Instead, the formation of MIVCs may be related to physical mechanisms that are connected to the inflow of the clouds onto the Galactic disk. The association of HVCs with MIVC candidates is only valid for a few objects, most notably for Draco and IVC\,135, for which a possible interaction between the MIVCs and HVCs has been explicitly mentioned before \citep{Herbstmeier1993,Moritz1998,Weiss1999,Lenz2015}. The MIVC samples appear to be compatible with a model of Galactic rotation that contains radial, vertical, and lagging velocity components for different scale heights and latitudes. This may suggest that the sample is associated with Galactic rotation in the disk and that some fraction of these objects is very likely connected to Galactic fountain processes within the Galactic disk. The estimated maximum inflow rate derived from our analysis of IVCs in the local Galactic environment is $\sim$$0.52\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}$. We applied a latitude limit of $|b|>20^\circ$, which allowed us to probe only $\sim$10\% of the volume of the Milky Way, in which IVCs are expected to be located. Extrapolating from the local IVC population to the entire Milky Way, the in-falling atomic and molecular IVC gas may account for the main fraction of the matter inflow onto our Galaxy. We derived plausible IVC inflow rates for vertical distributions with scale heights of $h_z\lesssim0.5\,$kpc. Larger heights exceed the expected mass inflow by far, suggesting that the class of MIVCs constitutes a late stage during the descent in the Galactic fountain cycle. Future studies of the Galactic IVC population should focus on lower latitudes, for which, however, the \ion{H}{i}-FIR correlation becomes increasing uncertain because many emission components are mixed along the lines-of-sight. Sophisticated modelling approaches are required to extend the traceable volume so that a more complete picture of the Galactic fountain and halo material in the Milky Way can be obtained. | 16 | 9 | 1609.06540 |
1609 | 1609.04403_arXiv.txt | We present late-time optical spectroscopy taken with the Large Binocular Telescope's Multi-Object Double Spectrograph, late-time \SWIFT\ UVOT and XRT observations, as well as improved ASAS-SN pre-discovery limits on the nearby ($d=90.3$ Mpc, $z=0.0206$) tidal disruption event (TDE) \asli. The late-time optical spectra show \halpha\ emission well in excess of that seen in the SDSS host galaxy spectrum, indicating that the processes powering the luminous flares associated with TDEs can operate for several hundreds of days. The \SWIFT\ observations reveal the presence of lingering apparently thermal UV (T$_{\rm UV} \sim 3.5\times10^4$~K) and X-ray (T$_{\rm X} \sim 7\times10^5$~K) emission. The characteristic temperatures evolve by, at most, a factor of $\sim2$ over the 600 day follow-up campaign. The X-ray, UV, and \halpha\ luminosities evolve roughly in tandem and at a rate that is consistent with a power-law decay at late times. This behavior is in stark contrast with the majority of optically discovered TDEs, which are X-ray faint and evolve on shorter timescales. Finally we address how the unique properties of \asli\ can be used to probe the relationship between the TDE rate and host galaxy properties. | \label{sec:intro} Near the centers of galaxies, stars can make close approaches to supermassive black holes (SMBHs). Roughly speaking, if the pericenter of a star's orbit is outside the SMBH horizon but inside the Roche limit, the star will be disrupted. When a main sequence star is disrupted, approximately half of the stellar debris will remain on bound orbits and asymptotically return to pericenter at a rate proportional to $t^{-5/3}$ \citep{Rees88,Evans89,Phinney89}. The observational consequences of these tidal disruption events (TDEs) are varied and depend on the physical properties of the disrupted star \citep[e.g.][]{MacLeod12,Kochanek16_stellar}, the post-disruption evolution of the accretion stream \citep[e.g.][]{Kochanek94,Strubbe09,Guillochon13,Hayasaki13,Hayasaki16,Piran15,Shiokawa15}, and complex radiative transfer effects \citep[e.g.][]{Gaskell14,Strubbe15,Roth16}. A large sample of well studied TDEs is crucial for understanding the observational characteristics and physical processes governing these exotic objects. While the number of well studied TDE candidates is growing \citep[e.g.][]{vanVelzen11, Cenko12, Gezari12, Arcavi14, Chornock14, Holoien14, Gezari15, Vinko15, Holoien16_15oi, Holoien16_14li, Brown16b}, the diversity of the observational signatures is surprising given that observed TDEs should be heavily dominated by stars and SMHBs spanning a narrow parameter range \citep{Kochanek16_demo}. Perhaps most notably, the majority of optically discovered TDEs show little evidence of X-ray emission, while the energetics of other TDE candidates may be dominated by their X-ray emission \citep[e.g.][]{Grupe99,KomossaBade99,KomossaGreiner99}. ASASSN-14li \citep{Jose14,Holoien16_14li} was a nearby ($d\sim$~90 Mpc, $z=0.0206$) TDE discovered by the All-Sky Automated Survey for SuperNovae \citep[ASAS-SN;][]{Shappee14} on 2014-11-22.6 (MJD~=~56983.6). An immediate follow-up campaign \citep{Holoien16_14li} observed \asli\ for $\sim$~200 days. We gathered data from a wide variety of both ground and space based observatories and found that the spectral characteristics of \asli\ resembled the ``intermediate H$+$He'' TDEs from \citet{Arcavi14}, while the optical/NUV evolution was consistent with that of a blackbody and a roughly exponentially declining luminosity. We also found significant spectral evolution: at early times the \heii\ feature is dominant, while at later times it is merely comparable in strength to the Balmer lines. This is in contrast with ASASSN-14ae, in which the \heii\ line became stronger relative to the Balmer lines as the event progressed \citep{Brown16b}. Unlike the two other ASASSN TDEs, \asli\ showed strong X-ray emission, and, due to it's proximity, was the target of several ground-based \citep{Alexander16,vanVelzen16,RomeroCanizales16}, space-based \citep{Miller15,Cenko16,Peng16,Jiang16}, and theoretical efforts \citep{Krolik16,Kochanek16_stellar}. In this paper we follow the evolution of \asli\ to $\sim600$ days after discovery. We present improved ASAS-SN pre-discovery upper limits, late-time optical spectra taken with the Multi-Object Double Spectrograph 1 (MODS1) on the 8.4 m Large Binocular Telescope (LBT), and extensive UVOT and XRT observations from the \SWIFT\ space telescope, which provide unprecedented insight into this rare class of objects. In Section~\ref{sec:data} we describe our observations, in Section~\ref{sec:discussion} we present our measurements of the late-time evolution, and finally in Section~\ref{sec:conclusions} we provide a summary of our results and discuss the implications for future studies. | \label{sec:conclusions} \begin{figure*} \centering{\includegraphics[scale=1.,width=\textwidth,trim=0.pt 0.pt 0.pt 0.pt,clip]{fig7.eps}} \caption{Measurements and limits on late-time \halpha\ emission from optical TDE candidates. The late-time spectra of most of these objects are simply assumed to be host dominated and lack formal upper limit estimates. For these objects, we assume an upper limit of 2\AA\ for the \halpha\ equivalent width, and compute the luminosity based on the approximate continuum and distances to the hosts available for each TDE. The dotted lines show lines of constant emitted energy.} \label{fig:ensemble} \end{figure*} \begin{figure} \centering{\includegraphics[scale=1.,width=0.5\textwidth,trim=0.pt 0.pt 0.pt 0.pt,clip]{fig8.eps}} \caption{Histogram showing the difference between observed GALEX NUV magnitudes and the expected NUV magnitudes based on models of the optical SED for a sample of \ea\ galaxies from the SDSS. The vertical dashed line shows the difference between the \asli\ late-time NUV and the archival GALEX NUV magnitudes of the host. We estimate the late-time NUV magnitude based on the SWIFT UVW2 observations.} \label{fig:synthObsComp} \end{figure} We have presented late-time optical follow-up spectra taken with LBT/MODS1, extensive UVOT and XRT observations from \SWIFT, and improved ASAS-SN pre-discovery non-detections of the nearby TDE \asli. Our observations span from the epoch of detection to $\sim$~600 days after discovery. In contrast to the late time evolution of ASASSN-14ae \citep{Brown16b}, observations of \asli\ show that TDEs can remain luminous, particularly in the UV and X-ray, for many hundreds of days. We find that the energy radiated in the X-rays is comparable to that of the UV/optical. Integrating over the duration of our campaign, we find that the total radiated energy is $E \approx 7 \times 10^{50}$ ergs. The entire event can be powered by the accretion of a small faction of the overall mass budget ($\Delta M \sim 4 \times 10^{-3}\eta_{0.1}^{-1}$\msun), where $\eta_{0.1}$ is the radiative efficiency relative to 0.1. While the late-time emission is broadly consistent with the accretion of material onto an SMBH, \asli\ differs from typical AGN. For example, as we have observed in other TDEs (\citealt{Holoien14,Holoien16_14li,Holoien16_15oi} and \citealt{Brown16b}), the optical emission lines narrow as the luminosity decreases, which is the reverse of the behavior observed in AGN \citep{McGill08,Denney09}. In Figure~\ref{fig:ensemble} we show our late time measurements of the \halpha\ luminosity from \asli. Unlike ASASSN-14ae, the \halpha\ luminosity in \asli\ remains significant for at least 500 days after disruption. We emphasize that the late-time brightness of \asli\ is not simply due to its proximity; it is indeed more luminous at later times than other TDE candidates. Similarly, the evolution of the \halpha\ line width in \asli\ spans a much smaller dynamic range than that of ASASSN-14ae. While the evolution of the \halpha\ line width and luminosity likely encodes information about the evolution of the tidal debris, a larger sample of objects with follow-up spectra is required in order to draw any firm conclusions. The modest decrease in the X-ray temperature is one of the strongest observational constraints to come out of this work. Most TDE theory predicts that the observed spectrum will become harder at later times \citep[e.g.][]{Lodato11,Strubbe11,Metzger16}, but these claims are typically made in the context of a super-Eddington outflow that obscures the X-rays at early times. For the assumed black hole mass of $10^6\msun$, the X-ray (and optical/UV) luminosity remains below the Eddington limit even at early times, immediately bringing into question the applicability of these theoretical predictions to \asli. Given the variable nature of the X-ray spectra from one epoch to the next as well as the early-time results from \citet{Miller15}, it is likely that the column density and ionization state of the absorbing material along the line of sight are variable, further complicating the evolution of the observed spectrum. This is supported by the fact that X-ray emission comparable to the optical/UV emission is not ubiquitous among optically selected TDE candidates \citep[e.g.][]{Holoien14,Arcavi14,Holoien16_15oi,Brown16b}. Thus, it is not particularly surprising that theoretical predictions fail to match the observations in this instance. We remain agnostic with regard to the adoption of any specific model characterizing the luminosity evolution. While the rate of material returning to pericenter is frequently invoked to explain the luminosity evolution of TDEs, given the complexity of the physical processes involved \citep{Kochanek94,Guillochon13,Guillochon14,Metzger16,Krolik16}, it is likely that the rate of material returning to pericenter has limited bearing on the overall luminosity evolution. The extended lifetime of \asli\ has important implications for future TDE studies. Our results demonstrate that, even after 500 days, spectra of TDE host galaxies may be contaminated by residual emission from the flare, particularly near strong recombination lines. While this complicates the characterization of TDE host galaxies, it extends the baseline over which residual TDE emission can potentially be discovered in spectroscopic surveys like MaNGA \citep{Bundy15}. Unfortunately, even under the assumption that TDE rates are sharply peaked in E+A galaxies \citep{French16}, the chances of trivially discovering residual TDE emission in a MaNGA-like survey may be hampered by the rarity of these galaxies \citep[see the discussion in][]{Brown16b}. Alternatively, the \halpha\ emission in TDEs is driven by the ionizing UV continuum, and the strong residual UV emission results in unusually blue UV$-$optical colors. In order to assess the peculiarity of the late time colors, we examine the UV$-$optical colors of a sample of \ea\ galaxies selected from the SDSS. The original selection criteria is described in \citet{Goto04,Goto07}. In short, the selection criteria require that EW(H$\delta$) $> 5.0$\AA, EW([\ion{O}{ii}]) $> -2.5$\AA, EW(H$\alpha$)$ > -3.0$\AA, and S/N$(r) > 10$. We adopt an updated catalog\footnote{\url{http://www.phys.nthu.edu.tw/~tomo/cv/index.html}} based on the SDSS Data Release 7 \citep{Abazajian09}, yielding an initial sample of 837 \ea\ galaxies. We then select a subsample of \ea\ galaxies that also have a GALEX NUV detection within 5\farcs0 of the SDSS position, yielding 683 galaxies with both SDSS optical and GALEX NUV observations. In the absence of late-time GALEX observations of \asli, we estimate the late-time GALEX NUV magnitude based on the late-time SED and find that $NUV \approx W2-0.14$. We find that, relative to other \ea\ galaxies, the late-time NUV$-$optical colors of \asli\ are indeed substantially bluer than the majority of \ea\ galaxies. Given the peculiarity of the \asli\ late-time colors, we also attempt to identify galaxies with similarly peculiar NUV$-$optical colors. We model each E+A galaxy with the public SED fitting code FAST \citep{Kriek09} based on the SDSS $u,g,r,i,$ and $z$ photometry. We then estimate synthetic GALEX NUV magnitudes from the best fit SED for each galaxy, and compute the difference between the observed GALEX NUV magnitudes and the synthetic NUV magnitudes based on the optical SED. The distribution of the observed and synthetic magnitude difference is shown as the histogram in Figure~\ref{fig:synthObsComp}. The vertical red line shows the late-time NUV excess for \asli, which we know is due to residual TDE emission. We note that the early-time NUV excess for \asli\ (as well as ASASSN-14ae and ASASSN-15oi) is several magnitudes bluer, well outside the range shown here. We can estimate the upper limit of the TDE rate in \ea\ galaxies by examining the UV excess observed in our sample and making a few basic assumptions. The first assumption we make is that UV excesses larger than that of \asli\ are due to residual emission from a TDE. We also assume that the residual emission is strictly blueward of the optical bandpasses and does not affect the SED modeling of the host galaxy, which is justifiable given the short duration of excess optical TDE continuum emission seen in \asli\ and other TDEs \citep[e.g.][]{Holoien14,Holoien16_15oi}. Additionally, our modeling of the SED is clearly imperfect, as there are a number of galaxies that appear significantly \textit{dimmer} in the UV than the optical colors would suggest. Thus some of the apparent UV excesses are likely due to systematic errors in the modeling. We estimate the magnitude of this contamination by counting the number of galaxies with UV deficits that are greater in magnitude (relative to 0) than the UV excess of \asli, and subtract this number (9) from the population of galaxies with UV excesses greater than that of \asli\ (41). This leaves 32 out 683 \ea\ galaxies showing excess UV emission characteristic of residual TDE emission. If we make the additional assumption that the residual UV emission remains for, on average 2 years, this yields an upper limit on the rate of $\sim 2\times 10^{-2}$ yr$^{-1}$ per galaxy, which is approximately an order of magnitude larger than the rate estimate from \citet{French16}. Alternatively, if no instances of UV excess are associated with residual TDE emission, then the upper limit on the TDE rate in E+A galaxies becomes $\sim7\times10^{-4}$. We note that this is simply an illustrative exercise and is subject to many systematic effects, including the robustness of the SED modeling, potential source confusion in the NUV, and contamination by other sources of UV excess \citep{Oconnell99,Brown04}. A similar exercise with a large sample of early type galaxies yields an even broader distribution in NUV$_{\rm obs}-$NUV$_{\rm synth}$, suggesting that the E+A galaxies with blue excess may indeed be due to modeling systematics. Nonetheless, the substantial UV excess in some of the galaxies may be due to residual emission from a TDE. Identification of residual TDE emission in spectroscopic surveys like MaNGA is reliant upon archival spectra of the host, whereas the approach illustrated here has yielded a relatively small sample of galaxies well suited for targeted follow-up observations without the need for archival spectroscopy. Spectroscopic signatures that are sensitive to TDE emission on a longer temporal baseline \citep[e.g. coronal line emission][]{Komossa08,Wang11,Yang13} could prove useful in determining if the UV excess in these galaxies is due to residual TDE emission and, ultimately, improving our understanding of TDE host galaxies. | 16 | 9 | 1609.04403 |
1609 | 1609.06406_arXiv.txt | Currently only a small number of Milky Way (MW) stars are known to exist beyond 100 kpc from the Galactic center. Though the distribution of these stars in the outer halo is believed to be sparse, they can provide evidence of more recent accretion events than in the inner halo and help map out the MW's dark matter halo to its virial radius. We have re-examined the outermost regions of 11 existing stellar halo models with two synthetic surveys: one mimicking present-day searches for distant M giants and another mimicking RR Lyrae (RRLe) projections for LSST. Our models suggest that color and proper motion cuts currently used to select M giant candidates for follow-up successfully remove nearly all halo dwarf self-contamination and are useful for focusing observations on distant M giants, of which there are thousands to tens of thousands beyond 100 kpc in our models. We likewise expect that LSST will identify comparable numbers of RRLe at these distances. We demonstrate that several observable properties of both tracers, such as proximity of neighboring stars, proper motions, and distances (for RRLe) could help us separate different accreted structures from one another. We also discuss prospects for using ratios of M giants to RRLe as a proxy for accretion time, which in the future could provide new constraints on the recent accretion history of our Galaxy. | \label{sec:intro} Stellar halos of spiral galaxies typically contain of order a few percent of the total number of stars associated with their host dark matter halos, spread over spatial scales ten times larger than the disks that they surround. Hence they are insignificant in terms of understanding the bulk of baryonic material that has occurred throughout the history of the Universe, and their extremely low densities (and corresponding surface brightness) makes them in any case difficult to study. However, two properties of stellar halos make them uniquely interesting. First, it is here that it is most productive to search for stars that were {\it not} formed in the current host halo, but rather accreted from other objects. Hence, the properties of the stellar populations of the halo can tell us something both about the accretion histories of galaxies, as well as the properties of the (now-dead) dwarf galaxies that formed them. Secondly, the low total mass and vast spatial scales that halos stars explore makes them powerful probes of the mass and structure of dark matter halos that surround all galaxies. The production of vast catalogues of faint stars around our own \citep[see][for a review]{ivezic12} and other \citep{ferguson02} galaxies have for the first time allowed the global structure of several stellar halos to be convincingly mapped \citep{ibata14}. These studies have also revealed the presence of a significant contribution of substructure in space \citep{ferguson02,newberg02,belokurov06} and velocity \citep{schlaufman09,gilbert09} which can be attributed to the hierarchical nature of galaxy formation \citep{bullock01} —-- the substructures are the debris from the destruction of infalling dwarf galaxies. Comparisons with concurrent theoretical work suggests broad consistency of these observations with the expectations for the scales, structure, and frequency of substructure in stellar halos built within the $\Lambda$CDM paradigm \citep{bell08,bell10,xue11}. Some of these substructures have been exploited as probes of the underlying gravitational potential \citep{2004Helmi,2005Johnston,2005Law,2009Willett,2009Law,2010Koposov,2010Newberg,2010Law,2012MNRAS.424L..16L,2013ApJ...776...26S,2013Vera-Ciro,kuepper15,pearson15}. A remaining frontier in this field is the mapping and interpretation of the outermost regions of galactic halos all the way out to the virial radius ($\sim$300kpc for a Milky-Way-mass galaxy). M31 is the only galaxy in the Universe for which a global map has been made on these scales, reaching to $\sim150$kpc \citep{ibata14}. In contrast, for the Milky Way, the views of the stellar halo afforded by Main Sequence Turnoff Stars selected from SDSS extend to $\sim$40kpc and the M-giants extracted from 2MASS reach distances of less than 100kpc \citep{belokurov06,majewski03}. In the next few years, data releases from the Gaia satellite promise to fill in these maps with vast numbers of stars and additional dimensions of information, but Gaia's magnitude limit of roughly $V\sim 20$ again restricts sensitivity to within roughly 100 kpc of the Galactic center for bright giant tracers. The number of Milky Way stars known to lie beyond 100 kpc from the Galactic center is still very small, but steadily growing. Large areal surveys with deep, precise photometry have been critically important to identifying relatively rare, but luminous, halo stars. Two classes of stars are bright enough to be observed beyond 120 kpc with current surveys: blue horizontal branch (BHB) stars and M giants. \cite{2012MNRAS.425.2840D} selected a sample of seven spectroscopically confirmed BHB stars in SDSS with distances of 80 kpc $< d <$ 150 kpc. At distances greater than 150 kpc, only M giants are bright enough to be readily observed in modern day surveys. \cite{2014AJ....147...76B} assembled a sample of nearly 500 M giant candidate stars with optical and infrared photometry from SDSS and UKIDSS. The M giants in the \citeauthor{2014AJ....147...76B} sample can be seen from 30 to $\sim$ 300 kpc, making them the first to probe the stellar content of the Milky Way near the virial radius. Unfortunately, photometry and the lack of proper motions are not sufficient to identify M giants, making spectroscopy necessary. Despite an estimated contamination rate near 80\%, \cite{2014ApJ...790L...5B} have already spectroscopically confirmed two distant M giants, with estimated distances over 200 kpc. The most distant M giant known, ULAS J001535.72+015549.6 has a distance of 274 $\pm$ 74 kpc. This sample has yielded 10 confirmed M giants to date, most being part of the Sagittarius dwarf galaxy remnant. Further into the future, we can anticipate dramatic additions to these outer halo detections as the Large Synoptic Survey Telescope \citep{ivezic08} produces catalogs of stars as faint as $g=24.5$ in a single pointing, corresponding to a distance limit of $\sim$ 50 kpc for a main-sequence turnoff (MSTO) star and $\sim$ 600 kpc for an RR Lyrae (RRL) star. After 5 years the co-added data will reach $g=27$, out to $\sim$ 300 kpc for an MSTO and $\sim$ 3 Mpc for an RRL. It is as yet unclear what to expect in this regime. Model stellar halos show them becoming more dominated by substructure at larger galactocentric radii as the dynamical timescales become comparable to the age of the Universe and the debris from the few recent accretion events has little time to phase-mix away \citep{johnston08}. M31’s stellar halo extends at least to 150 kpc and is richly substructured \citep{ibata14}, but the stochastic nature of hierarchical structure formation ensures a vast variety in stellar halo structures, especially on these spatial scales, so the Milky Way's stellar halo could differ dramatically. Even if the populations of stars in the outermost halo prove to be very sparse, they will have some important implications: they will provide a view of accretion (or perhaps lack of accretion?) in a new and unique regime, likely more sensitive recent events; and they will provide dynamical tracers to map the dark matter halo all the way out to the virial radius. This paper is motivated by the steadily growing number of stars known to be beyond 100kpc from the Galactic Center, as well as the longer-term prospects for LSST, to re-examine the outermost reaches of 11 existing stellar halo models \citep{2005ApJ...635..931B} in order to explore our expectations for these populations in a little more detail. In particular, this study looks at two different types of stars that might be selected in current and future stellar catalogues: color-selected M giants and time-domain selected RR Lyrae. For each tracer, we examine the trends and diversity in numbers of stars and properties of objects from which they came in the models. We also discuss the likelihood of being able to make associations between stars from their observed properties - associations that will increase our ability to reconstruct both the full accretion history of our Galaxy as well as the structure of its dark matter halo. This paper is organized as follows: in Section 2 we describe the computational tools (the mock halos and {\sc Galaxia}) used to generate synthetic stellar populations in the outer halo; in Section 3 we use these synthetic surveys to discuss expectations for present-day searches for distant M giants and in Section 4 we discuss future prospects for RR Lyrae. In Section 5 we discuss the possibility of using ratios of these two tracers to reconstruct the Milky Way's accretion history. In Section 6 we summarize our findings, draw some conclusions, and indicate some directions for future work. | \label{sec:concl} In this paper we discuss prospects for observing and untangling the distant stellar halo in two tracers: M giants and RR Lyrae. We focused on the very distant stellar halo, beyond 100 kpc, where very few stars are presently detected. Using synthetic surveys of the eleven Bullock and Johnston mock stellar halos, we found that the total number of tracers at distances beyond 100 kpc varies by about an order of magnitude from halo to halo, with most of that variation due to the number of still-bound satellites. With these removed the halo-to-halo variation is more like 0.5 dex. Excluding bound structures, our models predict roughly a few tens of thousands of M giants and a few thousand RR Lyrae beyond 100 kpc, though these absolute numbers should be taken with caution since they depend strongly on our model's assumptions about the luminosities and stellar populations assigned to the building blocks. Although the different mock halos display wide variety, in general there are a few to half dozen large structures (besides the still-bound satellites) that are most prominent in a given halo and provide the best chance of identification. In quite a few cases debris from the same accreted satellite is found on opposite sides of the sky with the radial velocity signatures of shells (material piled up at apocenter), which is a result of the fairly radial orbits assigned to satellites by the model. In studying the M giant tracers, we presumed photometric errors based on current data from the UKIDSS survey, which had the effect of scattering stars into and out of the color-color boxes used to filter out foreground dwarfs and background quasars. We found that these color cuts, combined with a very loose proper motion selection, were effective in removing self-contamination by halo dwarfs (\citet{2014AJ....147...76B} expect roughly 80 percent contamination from foreground disk dwarfs). In the future, both infrared and visible photometry should improve substantially: the WFIRST HLS will cover roughly the same sky area as UKIDSS and have significantly better IR photometric quality. While UKIDSS has sub-0.1-mag photo errors to about 18th magnitude in the J band, the WFIRST HLS will detect point sources to 5$\sigma$ down to 26.9 mag in the J band \citep{2013arXiv1305.5425S}, although it will not cover the K band. In the visible bands, LSST will see even deeper (down to 27.5 mag in the r band for 10-year coadds). Thus the technique of photometric selection should be promising for the next generation of surveys. The main challenge with so much data will be to improve the contamination by foreground disk stars, which may be possible with the improved proper motions that such surveys will also provide. We next considered a survey with a similar footprint size to UKIDSS, and found that a typical such footprint included stars from about $14\pm 4$ different satellites. A typical survey of this size in our mock halos is dominated by 3--5 of these satellites, each sampled by 100s--1000s of M giants. These structures could be bound or unbound, but generally appear coherent on the sky. Doubling the survey size increases the number of component satellites by less than a factor of 2, to a median of around 18, and mainly has the effect of filling in the few most dominant structures. We examined which components of position and velocity might offer the best chance of disentangling different accreted structures. At these distances we found that proper motions were more diagnostic than radial velocities, which reflects the fact that most unbound structures at these distances are shells (and hence have a relatively wide range of RVs within each structure). Interestingly, the differences in proper motions between accreted structures are on the order of $\sim 50-100 \mu$as/yr, comparable to the forecasted PM uncertainties for LSST in the optical \citep{2009arXiv0912.0201L} and WFIRST in the infrared \citep{2015arXiv150303757S}. For M giants we expect distance uncertainties to be too large (about 20 percent) to be useful for disentangling tracers, but for RR Lyrae this coordinate should prove useful as well. Finally, we considered the prospect of untangling accretion using ratios of M giants to RR Lyrae. We found that this ratio does indeed vary substantially from one building block to another, with less luminous, older, more metal-poor satellites tending to have higher numbers of RR Lyrae relative to M giants. Given a way to confidently assign stars to structures, one could in principle use this dependence to map the accretion history of the outer halo, since the older/more metal-poor structures containing more RR Lyrae also tend to have accreted earlier. However, our preliminary attempts to separate different structures by defining one- or two-dimensional ranges in proper motion space and searching the remaining coordinates for structure were not successful, indicating that a more sophisticated strategy that takes advantage of the full multidimensionality of the available data \citep{2009ApJ...703.1061S}, and/or attempts to reduce the dimensionality to a few useful hybrid dimensions, will be needed to untangle the different accreted structures in the outer halo. Once this is done, it may be possible to then connect stars in structures on opposite sides of the sky using population ratios, which would provide valuable constraints on the Milky Way dark matter distribution at large distances. | 16 | 9 | 1609.06406 |
1609 | 1609.02822_arXiv.txt | The Galactic Archaeology with HERMES (GALAH) Survey is a massive observational project to trace the Milky Way's history of star formation, chemical enrichment, stellar migration and minor mergers. Using high-resolution (R$\simeq$28,000) spectra taken with the High Efficiency and Resolution Multi-Element Spectrograph (HERMES) instrument at the Anglo-Australian Telescope (AAT), GALAH will determine stellar parameters and abundances of up to $29$ elements for up to one million stars. Selecting targets from a colour-unbiased catalogue built from 2MASS, APASS and UCAC4 data, we expect to observe dwarfs at 0.3 to 3~kpc and giants at 1 to 10~kpc. This enables a thorough local chemical inventory of the Galactic thin and thick disks, and also captures smaller samples of the bulge and halo. In this paper we present the plan, process and progress as of early 2016 for GALAH survey observations. In our first two years of survey observing we have accumulated the largest high-quality spectroscopic data set at this resolution, over 200,000 stars. We also present the first public GALAH data catalogue: stellar parameters (T$_{\rm eff}$, log(g), [Fe/H], [$\alpha$/Fe]), radial velocity, distance modulus and reddening for 10680 observations of 9860 {\it Tycho-2} stars that may be included in the first {\it Gaia} data release. | Massive observational surveys are an increasingly important force in astronomy. In particular, spectroscopic stellar surveys are revolutionising our understanding of Galactic structure and evolution (e.g., \citealt{H08}; \citealt{RB13}; \citealt{HHB14}; \citealt{HBH15}; \citealt{MFR16}). As in many areas of astronomical research, this development is driven by technology. Efficient methods for accurately positioning many optical fibres at telescope focal planes are enabling an increasing number of observatories to add highly multiplexed high-resolution spectrographs to their instrument suites (e.g., \citealt{CZC12}; \citealt{STK15}). The Galactic Archaeology with HERMES (GALAH) Survey\footnote{http://galah-survey.org} is a high-resolution spectroscopic survey that is exploring the chemical and dynamical history of the Milky Way, with particular focus on the disk. GALAH aims to collect a comprehensive data set, in terms of both sample size and detail, with abundances for as many as 29 elements (Li, C, O, Na, Mg, Al, Si, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Rb, Sr, Y, Zr, Ru, Ba, La, Ce, Nd, Eu) for each target. Our overall science goal is to carry out chemical tagging (e.g., \citealt{FBH02}; \citealt{DSS06}; \citealt{BHK10}) within this data set, identifying stars that formed at the same time and place by matching their abundance patterns. A thorough explanation of the GALAH survey science goals is given in \citet{DSF15}. The project of chemical tagging in the Galactic disk demands a very large data set. Given the observational selection for GALAH targets (discussed in Section 3 below), we anticipate that roughly $75\%$ of stars observed by GALAH will belong to the thin disk and $24\%$ to the thick disk, with smaller numbers of nearby halo stars and bright red giants in the bulge making up the rest of the sample. From theoretical explorations of clustered star formation (e.g., \citealt{BHKF10}; \citealt{FK14}), we expect there to be stars from a large number of unique star-forming events (``initial star-forming groups") mixed throughout both the thin and thick disks. The number of these groups in the disk, and the number of stars per group, will depend on the initial mass function and maximum mass of each group. \citet{TCG15} predicted that a survey of 10$^5$ stars can expect to observe 10 stars per group down to an initial mass limit of $\sim 10^6 M_{\odot}$, while a survey of 10$^6$ stars would capture 10 stars per group down to a group mass of $\sim 10^5 M_{\odot}$. \citet{TCR16} took data for 13,000 stars from the Apache Point Observatory Galaxy Evolution Experiment (APOGEE; \citealt{MSF15}; \citealt{HSJ15}) Survey from the twelfth data release of the Sloan Digital Sky Survey (DR12, \citealt{Alam15}). By analysing the ``clumpiness" of the chemical abundance data rather than carrying out strict chemical tagging, they were able to rule out the presence of an initial star-forming group in the thick disk with a mass greater than 10$^7 M_{\odot}$. Our observational program must therefore collect enough stars from each initial star-forming group, and derive precise enough stellar parameters and elemental abundances, to confidently apply chemical tags to them. Since the observing time for GALAH is allocated through the competitive time allocation process of the 3.9m Anglo-Australian Telescope (AAT), our observing strategy must provide this large, high-quality sample in a reasonable amount of observing time. This paper describes the balance between sample size, signal-to-noise ratio (SNR) and observing time that has been designed into our observational program. Section 2 outlines the capabilities of the HERMES spectrograph and Two Degree Field (2dF) fibre positioner, Section 3 discusses our target selection for the main survey, Section 4 describes the observing procedure, Section 5 discusses the Pilot Survey, Section 6 describes the K2-HERMES program, Section 7 presents observing progress through January 2016 (the end of AAT observing semester 15B), Section 8 discusses our potential synergies with other large Galactic survey programs, and Section 9 presents the GALAH-TGAS catalogue. The overlap between GALAH and {\it Gaia} is an extremely important data set. GALAH stars are all in the magnitude range (12$\le V \le$ 14) for which {\it Gaia} parallaxes and proper motions will be at their best and most complete. Ultimately GALAH will be able to contribute elemental abundances for a large number of stars with high-precision {\it Gaia} data, forming a very powerful resource for studying Galactic chemodynamics. | The GALAH Survey has made significant progress toward its goal of observing one million stars in the Milky Way over its first two years of survey observing. Up to 30 January 2016 we have observed 209,345 stars in the main survey, 845 targeted stars in globular and open clusters, 2,218 stars in the CoRoT anticentre fields, and 9,847 stars for the thin-thick disk program during the Pilot Survey, and an additional 31,365 stars have been observed by the K2-HERMES program. \begin{figure*} \resizebox{0.8\textwidth}{!}{\includegraphics{ra-dec-rv.png}} \caption{Map of the GALAH-TGAS catalogue in right ascension and declination, colour-coded by radial velocity. The Solar motion relative to the Local Standard of Rest can be clearly seen.} \label{lbrv} \end{figure*} We have also intentionally observed 4448 Tycho-2 stars in 26 fields to correspond with the first {\it Gaia} data release, with another 6586 stars observed serendipitously in the regular GALAH Survey fields. Of these, we are making available analysis results for 10680 observations of 9860 stars (3801 observations of 3675 targeted stars and 6879 observations of 6185 serendipitous stars) that have successfully been processed through our parameter and abundance determination pipeline. A catalogue of stellar parameters, radial velocities, distance moduli and reddening for these successfully analysed stars is presented in this publication, to support broad scientific exploitation of the first {\it Gaia} data release. As demonstrated above, these parameters look quite robust. We anticipate that they will improve further when we adapt our spectroscopic analysis pipeline to include the stellar distances derived by the Tycho-Gaia Astrometric Solution \citep{MLH15} and future {\it Gaia} data releases. Combining spectroscopic datasets with {\it Gaia} data serves many important purposes beyond improving spectroscopic analysis. Future GALAH data releases will add elemental abundance information for the stars with the best {\it Gaia} parallaxes and proper motions, enabling chemodynamic studies in the Solar neighbourhood and throughout the Galaxy, and adding kinematic information into chemical tagging. The target selection and field tiling for GALAH are fixed, and we will continue to follow the same observing rules for the duration of the survey, maintaining our straightforward selection function. Based on Galactic models and our target selection strategy we anticipate a final data set that is dominated by the thin and thick disks, but despite the small fraction of halo and bulge stars expected ($<1\%$), these data sets will also have significant scientific value. Further details on the data set as observed will be available in Sharma et al. (in prep). | 16 | 9 | 1609.02822 |
1609 | 1609.00016_arXiv.txt | An important aspect of searching for exoplanets is understanding the binarity of the host stars. It is particularly important because nearly half of the solar-like stars within our own Milky Way are part of binary or multiple systems. Moreover, the presence of two or more stars within a system can place further constraints on planetary formation, evolution, and orbital dynamics. As part of our survey of almost a hundred host stars, we obtained images at 692~nm and 880~nm bands using the Differential Speckle Survey Instrument (DSSI) at the Gemini-North Observatory. From our survey, we detect stellar companions to HD~2638 and HD~164509. The stellar companion to HD~2638 has been previously detected, but the companion to HD~164509 is a newly discovered companion. The angular separation for HD~2638 is $0.512 \pm 0.002\arcsec$ and for HD~164509 is $0.697 \pm 0.002\arcsec$. This corresponds to a projected separation of $25.6 \pm 1.9$ AU and $36.5 \pm 1.9$ AU, respectively. By employing stellar isochrone models, we estimate the mass of the stellar companions of HD~2638 and HD~164509 to be $0.483 \pm 0.007$ $M_\sun$ and $0.416 \pm 0.007$ $M_\sun$, respectively, and their effective temperatures to be $3570 \pm 8$~K and $3450 \pm 7$~K, respectively. These results are consistent with the detected companions being late-type M dwarfs. | Much of the focus in the exoplanetary field still lies in the detection of planets using a variety of techniques, such as radial velocity (RV) signatures, transits, direct imaging, microlensing, among others. A significant factor that can affect the detection of exoplanets is the binarity of the host stars. In fact, it is believed that nearly half of all sun-like stars are part of a multiple-star system \citep{raghavan10}. This high-rate of multiplicity has also been found in exoplanet host stars through follow-up of {\it Kepler} candidates \citep{eve15,kra16} and Robo-AO observations of RV exoplanet host stars \citep{riddle15}. The mere presence of a binary companion can substantially affect astrometric and RV measurements of the host star, and cause severe blended contamination for transit experiments \citep{car15,cia15,gil15}. It is therefore imperative to verify the multiplicity of exoplanet host stars to ensure correct interpretation of exoplanet signals. Moreover, the binarity of the stars can place further constraints on planetary formation. \citet{holman99} explored the orbital stability of the planets in the presence of a binary star system. Additionally, correlations between planets' mass and their period \citep{zucker02} and eccentricities \citep{eggenberger04} were examined. Several binary systems have been studied, such as $\alpha$ Centauri \citep{benest88}, Sirius \citep{benest89}, $\eta$ Coronae Borealis \citep{benest96}, and 30 Arietis B \citep{kane15,roberts15}, which provide us rich information on orbital dynamics in a N-body system. This paper presents new results on stellar companions to the exoplanet host stars HD~2638 and HD~164509. The stellar companion to HD~2638 has been previously detected and characterized \citep{riddle15,roberts15}. However, this is an independent detection, and this paper shall present independent analysis of that system. In the meanwhile, the companion to HD~164509 has not been previously reported. In Section~\ref{properties} we briefly describe the properties of HD~2638 and HD~164509, along with their known exoplanets. Section~\ref{obs} discusses the method of detection, the range of targets that were selected for analysis, and the details of the data reduction. Section \ref{res} presents the results from the data analysis and stellar isochrone fitting. Section \ref{impl} explains the potential implication of those findings for the planetary systems, including limits to the eccentricities of the binary companion that allow orbital stability. Section \ref{con} provides discussion of further work and concluding remarks. \begin{deluxetable*}{lCC} \tablecolumns{3} \tablewidth{0pt} \tablecaption{\label{prop} Stellar \& Planetary Properties} \tablehead{ Properties & \colhead{HD~2638\tablenotemark{a, b}} & \colhead{HD~164509\tablenotemark{c}}} \startdata \sidehead{Stellar} ~~~~Spectral Type\tablenotemark{d} & G5V & G5V \\ ~~~~$M_{\star}$ ($M_{\sun}$)\tablenotemark{e} & 0.87 \pm 0.03 & 1.10 \pm 0.01 \\ ~~~~$R_{\star}$ ($R_{\sun}$)\tablenotemark{e} & 0.81 \pm 0.02 & 1.11 \pm 0.02 \\ ~~~~$L_{\star}$ ($L_{\sun}$)\tablenotemark{e} & 0.42 \pm 0.01 & 1.31 \pm 0.02 \\ ~~~~$T_e$ (K)\tablenotemark{e} & 5173 \pm 26 & 5860 \pm 31 \\ ~~~~$\log$ $g$ ($cm/s^2$)\tablenotemark{e} & 4.55 \pm 0.03 & 4.38 \pm 0.02 \\ ~~~~Age (Gyr)\tablenotemark{e} & 5.1 \pm 4.1 & 3.2 \pm 0.8 \\ ~~~~$[$Fe/H$]$ & 0.16 \pm 0.05 & 0.21 \pm 0.03 \\ ~~~~Apparent Magnitude m$_V$\tablenotemark{f} & 9.58 & 8.24 \\ ~~~~Proper Motion ($\alpha$, $\delta$) (mas/yr)\tablenotemark{f} & -105.63, -223.46 & -7.40, -20.98 \\ ~~~~Parallax (mas)\tablenotemark{f} & 20.03 \pm 1.49 & 19.07 \pm 0.97 \\ ~~~~Distance (pc)\tablenotemark{f} & 49.93 \pm 3.71 & 52.44 \pm 2.67 \\ \sidehead{Planetary} ~~~~$M_p \sin i$ ($M_J$) & 0.48 & 0.48 \pm 0.09 \\ ~~~~P (Days) & 3.43752 \pm 0.00823876 & 282.4 \pm 3.8 \\ ~~~~a (AU) & 0.044 & 0.875 \pm 0.008 \\ \enddata \tablenotetext{a}{\citet{wang11}} \tablenotetext{b}{\citet{moutou05}} \tablenotetext{c}{\citet{giguere12}} \tablenotetext{d}{\citet{esa97}} \tablenotetext{e}{\citet{bonfanti16}} \tablenotetext{f}{\citet{leeuwen07}} \end{deluxetable*} | \label{con} Determining the stellar architecture of planetary systems is an on-going process, improving as the capability to detect faint stellar companions increases. Stellar binarity can have a profound effect on exoplanetary systems, both in terms of formation processes and long-term orbital stability. Thus determining the binarity of known exoplanet host stars is a critical step in the characterization of those systems. Here we have presented detections of stellar companions to two known exoplanet host stars: HD~2638 and HD~164509. Though the stellar companion to HD~2638 was previously detected by \citet{roberts15}, the new data from DSSI will provide additional information of the astrometry of the companion and the stellar properties, given that the passbands used are particular to the DSSI camera. We have shown that the detected companions have properties consistent with them both being M dwarfs, and the isochrone analysis shows that they are both likely to be gravitationally bound to the host stars. Fortunately, the presence of the stellar companions do not pose serious orbital stability problems for the known exoplanets, making the overall architecture of the systems self-consistent. These planetary systems represent additional interesting examples of planet formation and evolution in the presence of multiple stars. | 16 | 9 | 1609.00016 |
1609 | 1609.05633_arXiv.txt | It is believed that type II radio bursts are generated by shock waves. In order to understand the generation conditions of type II radio bursts, in this paper, we analyze the physical parameters of a shock front. The type II radio burst we selected was observed by Siberian Solar Radio Telescope (SSRT) and Learmonth radio station and was associated with a limb CME occurring on 2014 January 8 observed by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). The evolution of the CME in the inner corona presents a double-layered structure that propagates outward. We fit the outer layer of the structure with a partial circle and divide it into 7 directions from -45$^\circ$ to 45$^\circ$ with an angular separation of 15$^\circ$. We measure the outer layer speed along the 7 directions, and find that the speed in the direction of -15$^\circ$ with respect to the central direction is the fastest. We use the differential emission measure (DEM) method to calculate the physical parameters at the outer layer at the moment when the type II radio burst was initiated, including the temperature ($T$), emission measure ($EM$), temperature ratio ($T_{d}/T_{u}$), compression ratio ($X$), and Alfv\'{e}n Mach number ($M_{A}$). We compare the quantities $X$ and $M_{A}$ to that obtained from band-splitting in the radio spectrum, and find that this type II radio burst is generated at a small region of the outer layer that is located at the sector in 45$^\circ$ direction. The results suggest that the generation of type II radio bursts (shock) requires larger values of $X$ and $M_{A}$ rather than simply a higher speed of the disturbance. | MHD shocks are an important phenomenon in the solar atmosphere, which can accelerate and heat charged particles effectively \citep{Schwartz1988,Mann1995}. They can be generated by coronal mass ejections \citep[CMEs,][]{Vrsnak2008}, reconnection jets \citep{Magara2000}, fast expanding loops \citep{Su2015}, or the ``CME-streamer" interaction in the lower corona \citep{Eselevich2015}. A coronal shock from the Sun can produce a significant impact on the space weather and human beings. Type II radio bursts represent a typical feature of coronal shocks in radio wavelengths \citep{Wild1950,Zheleznyakov1970}. Generally, type II radio bursts are believed to originate from the shock front, but it is difficult to determine the exact position along the shock front. \citet{Kouloumvakos2014} calculated the compression ratio of the shock, and found that the type II radio burst can originate from the whole sheath region between the CME leading edge (LE) and the shock front. However, most authors considered that the source region of the type II radio burst is at a small region of the shock front \citep{Bain2012,Zimovets2012,Carley2013,Zucca2014b,Zimovets2015}. Previous works suggested that the type II radio burst is most likely generated at the nose of the shock fronts \citep{Bemporad2011}, because the shock speed at the nose is usually higher than that at the flank. However, \citet{Reiner2003} found that type II radio bursts can be generated in the high density coronal streamer when the shock flank travels through it. Similar type II radio bursts with such a generation mechanism have been reported successively \citep{Cho2007a,Feng2012,Kong2015}. The key question on where the source region of the type II radio burst in the shock front is, or what physical conditions are needed for the generation of the type II radio, is still open. There are some studies on this question. As is well known, Alfv\'{e}n Mach number is a key parameter to describe the strength of a shock, and the type II radio bursts can be generated more easily when the Alfv\'{e}n Mach number is larger \citep{Shen2007}. \citet{Gopalswamy2009} analyzed the data from Solar Terrestrial Relations Observatory \citep[{\it STEREO};][]{Kaiser2008} and found that the type II radio bursts are generated at the height where the Alfv\'{e}n speed is the minimum. \citet{Cho2013} found a type II burst that originates in the low corona (0.08 R$_{\odot}$) when the shock passes through high density coronal loops. They attributed it to the low Alfv\'{e}n speed because of the high density. \citet{Kozarev2011} used the Differential Emission Measure (DEM) method to get the compression ratio ($X$) and the temperature ratio of the shock. It was found that the temperature does not change obviously before and after the shock passes through the region, and a lower limit of $X$ was obtained for the shock. \citet{Zucca2014a} made a density map using extreme ultraviolet (EUV) data from the Atmospheric Imaging Assembly \citep[AIA;][]{Lemen2012} on board the Solar Dynamics Observatory \citep[{\it SDO};][]{Pesnell2012} and polarized brightness data from Large Angle and Spectrometric Coronagraph \citep[{\it LASCO};][]{Brueckner1995} on board the Solar and Heliospheric Observatory ({\it SOHO}). Combining with the potential-field source-surface (PFSS) model, they also calculated the Alfv\'{e}n speed map. \citet{Bemporad2014} obtained the vector magnetic field at the pre- and post-shock regions by measuring the profile and speed of the shock and assuming a radial direction of the magnetic field in the field of view of LASCO/C2. \citet{Susino2015} derived 2-dimensional (2D) maps of the electron density, the compression ratio, and the Alfv\'{e}n Mach number in the region where the shock swept based on the LASCO/C2 observation. The purpose of this work is to study the physical properties of the coronal shock responsible for a type II burst based on combined observations including multi-wavelength EUV data and the radio dynamic spectrum. Besides, we try to get the properties of the coronal shocks from the radio dynamic spectrum. More than ten years ago, \citet{Vrsnak2002} proposed a method to get the compression ratio of a shock from the band-splitting of type II radio bursts. \citet{Ma2011} calculated the compression ratio and the temperature of the 2010 June 13 event from band-splitting. However, the obtained values of these parameters are larger than those yielded by the DEM method. The reason may be the over-simplified assumption that the emission measure (EM) per unit length along the line of sight (LOS) is uniform, which actually is not, especially in the situation where different structures exist along the LOS. To obtain a more consistent result, it is thus necessary to combine two different methods, like the DEM analysis of the multi-wavelength data and the band-splitting in radio dynamic spectrum, as mentioned above, to investigate the properties of the coronal shock. To this end, we select a typical event of type II radio burst on 2014 January 8 and study its generation conditions (the properties of the coronal shock). This paper is organized as follows. Observations are presented in Section \ref{sect:Observations}, and data analysis and results are described in Section \ref{sect:Data Analysis}. We then have some discussions in Section \ref{sect:Discussion}, followed by the conclusion in Section \ref{sect:Conclusions}. | \label{sect:Conclusions} In this paper, we studied a typical type II radio burst associated with a CME-driven shock that occurred on the west limb of the Sun. There is a pileup region ahead of an erupting flux rope, the pileup region is a double-layered structure and propagates outward as seen in 193 {\AA} and 211 {\AA} passbands. The OL is well fitted by a standard circle arc, and we divided the circle into 7 directions from -45$^\circ$ to 45$^\circ$ with a separation of 15$^\circ$ between each. We measure the OL speed in each direction and found that the OL is the fastest in the direction of -15$^\circ$. We used the DEM method to derive the temperature, emission measure, temperature radio, compression ratio, and Alfven Mach number for each direction and each time. The main results are summarized as follows: 1. We proposed a new method to estimate the effective LOS depth by considering that the EM per unit length in the disturbed region along the LOS path is different from that in the undisturbed region, and this method can also be used for other structures in the corona, such as coronal loops, coronal streams, and so on. A more reasonable compression ratio is then derived using this method. 2. Through comparing the compression ratio derived by the DEM method with that derived by the band-splitting in the radio dynamic spectrum of the type II radio burst, we concluded that the source region of the type II radio burst is in the part of the OL at the direction of 45$^\circ$. It indicates that the OL front sharpens to become a shock wave at the direction of 45$^\circ$. 3. The type II radio burst is probably generated at the part of the disturbance where $M_{A}$ is the largest but not the part where the disturbance speed is the fastest. Thus, the disturbance speed alone cannot serve as a sufficient factor in the generation of a shock. Instead, a more appropriate factor is the Alfv\'{e}n Mach number, i.e., the generation of a shock requires a larger $M_{A}$ of the disturbance. | 16 | 9 | 1609.05633 |
1609 | 1609.09071_arXiv.txt | } The imprints of the history of our Galaxy are kept in the stellar atmospheres \cite{2015A&A...577A..47B}, their chemical composition can help us to unravel past events that took place in the stellar aggregate where they belonged (or still belong) and in its surroundings. Abundances can also help to explain the nucleosynthesis since the abundance of certain elements can be altered by stellar evolution processes. This wide variety of topics has motivated an increase in the number of spectroscopic surveys in the last years, such as APOGEE \cite{2011AJ....142...72E} or the Gaia-ESO Public Spectroscopic Survey (GES) \cite{2012Msngr.147...25G} \cite{2013Msngr.154...47R}. The increase in high-resolution spectra has lead to the development of tools for their automatic analysis \cite{2016arXiv160908092B}, each one with its peculiarities and its ingredients (e.g. model atmospheres, radiative transfer codes, normalization procedures). Therefore, the published abundances are not homogeneously derived and the scatter can be significant \cite{2014A&A...561A..93H}. On the other hand, it is common to compile chemical abundances from different studies to create bigger samples to increase the statistics \cite{2014AJ....148...54H}. But, given the mentioned inhomogeneities, this may affect the accuracy of the scientific conclusions based on combined results. One of the ingredients in the spectroscopic pipelines that may lead to different results is the radiative transfer code. In \cite{2016arXiv160908092B} we presented an experiment to evaluate the impact on the determination of atmospheric parameters when different codes are used. In this study we evaluated the impact on the determination of chemical abundances using iSpec\footnote{\href{http://www.blancocuaresma.com/s/}{http://www.blancocuaresma.com/s/}} \cite{2014A&A...569A.111B}. | Even if we have used the same atomic line list and model atmosphere for all the codes, not all of them use the same information. For instance, all the codes except MOOG recompute the electron number density internally, by solving the equation of state (i.e. the ionization fractions of different elements) consistently given the particular chemical composition. Additionally, MOOG is also the only radiative transfer code that does not accept any input parameter for the Stark broadening (it does an internal approximation). Other differences between synthesis codes may include continuous opacities and the treatment of scattering, the implementation of van der Waals broadening, sphericity effects, etc. Thus, every radiative transfer code has its peculiarities that leads to the differences presented in this study. Even executing an homogeneous analysis with the same ingredients and the exactly same atmospheric parameters, we found differences in the determination of abundances that cannot be ignored. In \cite{2016arXiv160908092B}, we demonstrated how different codes also lead to differences in the determination of atmospheric parameters, we can expect that this will propagate to the determination of abundances and worsen the differences presented in this study. This results shows the importance of being extremely careful when combining chemical abundances derived by different surveys/studies with different pipelines and setups. If the option of re-analyzing all the spectra in an homogeneous way is not feasible, it is strongly recommended to assess the dispersion introduced and prove that its impact is not relevant for our scientific goal. \small % | 16 | 9 | 1609.09071 |
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1609 | 1609.05069_arXiv.txt | We examine the classical dynamics of multifield inflation models with quadratic potentials. Such models are shown to have inflationary attractors in phase space, consistent with the stretching of phase space trajectories along the volume factor of the universe during inflation. Using the symplectic structure associated with Hamiltonian systems we form a measure on the phase space, as initially proposed by Gibbons, Hawking and Stewart. This is used to calculate lower bounds on the probabilities of observational agreement (i.e. the probability the model gives a value for the spectral index within the region $n_{s}=0.968\pm{0.006}$) for equal mass two and three field models with quadratic potentials, giving values of 0.982 and 0.997 respectively. We derive the measure for a general $N$-field model and argue that as the number of fields approaches infinity, the probability of observational agreement approaches one. | \subsection{Inflation} Since it was originally developed by Guth, Linde, Albrecht and Steinhardt, inflationary theory has become a pillar of modern cosmology. The theory was initially motivated by the horizon, flatness and magnetic monopole problems~\cite{GuthInflation,Linde,Albrecht}. Soon after it was proposed it was realised that inflation could also produce the perturbations that would act as the seeds of structure formation~\cite{Starobinsky,Pi,Hawkpert,Bardeen,Kahn,Pi2,Dodelson}. We will work throughout in Planck units ($G=c=\hbar=1$). Let us first consider how we can implement inflation in the early universe. We begin by asking what generic properties the field driving inflation will have. From the Friedmann equation: \begin{equation} H^2\equiv\left(\frac{\dot{a}}{a}\right)^2=\frac{8\pi}{3}\rho-\frac{k}{a^{2}} \end{equation} where $H$ is the Hubble parameter, $a$ is the scale factor, $\rho$ is the energy density of the universe and $k$ is the curvature parameter. Differentiating this equation and using the equation for energy conservation in an FRW universe ($\dot{\rho}+3\frac{\dot{a}}{a}(\rho+P)=0$, where $P$ is the pressure), we obtain the Raychaudhuri equation: \begin{equation} \frac{\ddot{a}}{a}=-\frac{4\pi}{3}(\rho+3P) \end{equation} For inflation we require that $\ddot{a}>0$ so that the expansion rate is accelerating. This is satisfied if our matter has an equation of state that satisfies $P<-\rho/3$. This cannot be achieved with normal matter or radiation however we can obtain a natural implementation with some generic scalar field/s. Consider the equation of state parameter for a single, spatially constant scalar field $\phi$~\cite{Peacock}: \begin{equation} w\equiv\frac{P}{\rho}=\frac{\frac{1}{2}\dot{\phi}^2-V(\phi)}{\frac{1}{2}\dot{\phi}^2+V(\phi)} \end{equation} where $V(\phi)$ is the potential of our scalar field. We can see here that if $\frac{1}{2}\dot{\phi}^{2}\ll V(\phi)$ our equation of state parameter $w\approx-1$, satisfying the condition for an accelerating expansion rate. This slow roll inflation where the kinetic energy of the field is negligible is precisely the implementation most commonly used and will be the focus of our attention. This can be visualised as the inflaton (the particle associated with the scalar field) slowly rolling down the field potential. We can characterise the slow roll for a set of $N$ scalar fields $\phi_{i}$ by defining slow roll parameters as in~\cite{Bassett}: \begin{equation} \epsilon\equiv\frac{1}{16\pi}\frac{\sum_{i}\left(\partial V/\partial\phi_{i}\right)^{2}}{V^{2}} \end{equation} \begin{equation} \eta_{\sigma\sigma}\equiv\frac{1}{8\pi}\frac{V_{\sigma\sigma}}{V} \end{equation} where for a general multifield model, $V_{\sigma\sigma}$ is the second derivative of the potential along the field direction in the field space defined by: \begin{equation} \sigma=\int\sum_{i}\hat{\sigma}_{i}\dot{\phi}_{i}\dif t \end{equation} where $\hat{\sigma}_{i}$ is the unit vector along the field direction: \begin{equation} \hat{\sigma}_{i}=\frac{\dot{\phi}_{i}}{\sqrt{\sum_{k}\dot{\phi}_{k}\dot{\phi}_{k}}} \end{equation} Other slow roll parameters can be defined but these are the only parameters that will be relevant. During the slow roll phase $w\approx-1$. It is important to note here that there is currently no verified particle physics mechanism for inflation~\cite{Dodelson}. Given this our aim will not be to ground the discussion of inflationary mechanisms in any known physics, but rather to examine the possibilities presented by multiple scalar fields. \subsection{The measure problem} The measure problem in classical inflationary cosmology may be framed as follows; given some model for inflation and the set of all possible model universes, how do we go about counting fractions of these universes i.e. which measure should be used when counting over the universes? Moreover, given a suitable measure, what is the probability that some inflationary model yields a universe observationally similar to our own? The precise meaning of observationally similar in this context will be made clear in section 3. Inflation was developed to provide an explanation for why the universe did not need to exist in a very peculiar, finely tuned initial state. However if we were to find that inflation was incredibly unlikely to produce a universe like our own, we would be hard pressed to claim it as a complete solution to such tuning problems. We would effectively be replacing a special initial state with another special initial state. Moreover, whilst the work discussed here focuses on inflationary models and their measures, the study of measures has potential applications for more general dynamical problems, allowing us to calculate the probabilities of systems exhibiting certain properties \cite{SloanMin}. Significant work has been carried out in trying to answer the above questions. Gibbons, Hawking and Stewart proposed the Liouville measure as a natural measure on the set of model universes. This is formed from the symplectic structure associated with the Hamiltonian phase space of an FRW universe coupled to matter. A Hamiltonian system possesses the canonical coordinates $(q_{i},p_{i})$, where $q_{i}$ are the generalised positions for our system and $p_{i}$ the associated generalised momenta. For a system with $n$ degrees of freedom we therefore have a $2n$ dimensional phase space equipped with a symplectic structure given by: \begin{equation} \omega=\sum_{i=1}^n \dif q_{i}\wedge\dif p_{i} \end{equation} where the $\wedge$ is the antisymmetric wedge product. The symplectic structure is a differential two-form that is a property of the Hamiltonian phase space. In general a $p$-form is a completely antisymmetric, rank $(0,p)$ tensor i.e. it acts as a map from a collection of $p$ vectors to $\mathbb{R}$ (the set of real numbers). In the language of index notation, a $p$-form is a completely antisymmetric tensor with $p$ covariant indices. Given the antisymmetry of the wedge product we can see immediately that $\dif f\wedge\dif z=-\dif z \wedge\dif f$ and hence $\dif f\wedge\dif f=0$ for some $f$ and $z$~\cite{Carroll}. The important point here is that we can form a volume element $\Omega_{L}$ with the symplectic structure by raising it to the power $n$~\cite{Turok}: \begin{equation} \Omega_{L}=\frac{(-1)^{n(n-1)/2}}{n!}\omega^{n} \end{equation} This is the Liouville volume element of our phase space which is unique up to a functional freedom i.e. this is the only $2n$-form on our phase space up to a choice of multiplicative function. If we differentiate the symplectic structure with respect to time and apply Hamilton's equations of motion to the result we find that $\dot{\omega}=0$ under Hamiltionian flow. An immediate consequence of this is that the Liouville volume element is conserved, and that phase space volume elements are conserved for a Hamiltonian system. This is simply a statement of Liouville's theorem. Let us consider what we mean when we claim that the measure formed from the symplectic structure is the natural measure to use when counting universes. To a certain extent the phase space measure we choose is ad hoc~\cite{Schiffrin, Sloan}. If we wished we could take any function of our phase space variables to construct a new measure. However we can argue that the symplectic measure should be viewed as a natural or privileged measure on phase space. Here we appeal to Laplace's principle of indifference which tells us that we should adopt the distribution with the least amount of information content. The Hamiltonian phase space is naturally equipped with a symplectic structure and so we should use a uniform distribution on the symplectic measure to minimize the information content~\cite{Sloan}. One of the apparent contradictions that arose from the study of the measure problem in inflation was the existence of inflationary attractors, as noted in~\cite{Turok,Remmen,AshProbLQC,Corichi,Sloan}. Scalar field trajectories in phase space display a focusing on a very narrow range of field values as they evolve. This seems to sit in contradiction with Liouville's theorem that tells us phase space volumes should remain constant under Hamiltonian flow. The resolution to this problem was discussed in detail in~\cite{Corichi,Sloan}. The trajectories do indeed display the focusing on a narrow range of field values, however the key observation is that as these solutions inflate the trajectories are stretched dramatically along the volume factor axis. The total phase space volume remains conserved under evolution, it is simply stretched out along the volume factor of the universe as it expands. Other issues do exist in forming this measure. The most notable is the fact that, because the volume direction is non-compact, the integral over the volume factor is infinite. This must be regularised in order to yield meaningful probabilities. These issues will be discussed in detail when we consider measures and probabilities in multifield inflation. \subsection{Measures in single field inflation} The measure problem has received significant attention in the context of single field inflation~\cite{Hawking,Turok,Remmen,Remmen2,AshProbLQC,Corichi}. In the case of a single quadratic field the symplectic structure can be used to obtain an expression for the probability that the universe evolves to have a value for the spectral index, $n_{s}$, consistent with the Planck results \cite{Sloan}. The process of obtaining a probability from the symplectic structure will be discussed in detail when we consider multifield models. Starting the evolution from a surface of constant Hubble rate $H=1$ (reinserting units this is $H=5.72\times10^{62} $kms$^{-1}$Mpc$^{-1}$) they were able to obtain a probability of observational agreement of $P(X)=(1-10^{-5})$~\cite{Sloan}. Similarly high results were obtained earlier in the context of loop quantum cosmology in~\cite{AshProbLQC,Corichi,AshLQC}. These results are in stark contrast with an earlier result by Gibbons and Turok, who obtained a probability of there being more than 60 $e$-folds\footnote{The questions of whether we obtain more than 60 e-folds or an observationally consistent value for $n_{s}$ are similar. To have a universe with properties similar to our own we want a sufficient amount of inflation, however universes which underwent a large number of e-folds are not necessarily consistent with our own. The latter question can therefore be viewed as a refinement of the former~\cite{Sloan}.} of inflation of $~e^{-180}$~\cite{Turok}. The reason for the incredibly low value calculated by Gibbons and Turok was explained in~\cite{Corichi,Sloan}. Gibbons and Turok had evaluated their measure on a very late constant energy density surface (or equivalently constant $H$ surface from the Friedmann equation), assuming a uniform probability distribution of initial conditions at this time. This late in the evolution, most of the trajectories will have been focused in on a very narrow range of field values consistent with observation by the attractor. By assuming the uniform distribution at this late surface they gave an equal weighting to the trajectories focused in on the attractor to those that had not funnelled in, resulting in a low probability being calculated. Had they assumed a uniform distribution on an earlier constant $H$ surface they would have obtained a high probability for inflation. This was extended by asking what would be required for the probabilities calculated on the two separate surfaces to be the same. It was realised that if we assume a uniform probability distribution on an early constant $H$ surface, a probability distribution is induced on later Hubble surfaces that is heavily weighted towards field values consistent with observation. This is a consequence of the attractor behaviour. Solutions are funnelled in towards a very narrow range of field values during their evolution, giving us a much higher density at these attractor regions. \subsection{Multifield Inflation} Most of the existing literature has focused on single field inflation. In the context of the measure problem, no major efforts have been made so far to form measures and calculate probabilities for multifield models. Indeed, the authors of~\cite{Hawking,Carroll,Turok,Remmen,Remmen2,AshProbLQC,Corichi,Sloan,AshLQC} all consider single field models when discussing measures and probabilities in inflation. Of course, single field models are simpler to study and do yield interesting behaviour but we do have good reason to study multifield inflation models. The Planck collaboration recently presented a comprehensive set of constraints on inflation driven by single field models. The results from this survey mean that single field $V(\phi)\propto\phi^2$ and natural inflation are currently disfavoured compared to models that predict a lower value of the tensor to scalar ratio $r$ (this is the ratio of amplitudes of tensor and scalar perturbations)~\cite{Planck}. It is therefore prudent to consider whether, despite these simple models being disfavoured in the single field case, they can still be viable models when driven by multiple fields of this type. The interest in multifield inflation also extends beyond the fact that simple single field models are disfavoured by Planck data. Many current theories of beyond the standard model particle physics predict the existence of multiple scalar fields. For example, string compactifications often predict the existence of hundreds of scalar fields~\cite{Easther,Grana,Douglas,DenefDoug,Denef}. It would be surprising if only one of these fields was driving inflation. Whilst we have no experimental confirmation of any of these beyond the standard model theories, if we wish to ground inflation in them we must seriously consider the possibility of multifield inflation. If we are to study multifield inflation models in general, we should also wish to extend our analysis of the measure problem to these models. It was noted by Easter et al. that multifield models give a wider range of possible predictions for perturbation power spectra etc. It is therefore important to ask what sort of predictions can be considered generic~\cite{Easther}. The observational consequences of multifield models through cosmological perturbations and non-gaussianities have been studied extensively in ~\cite{Easther,Giblin, Vernizzi, Battefeld,Lyth}. Multifield models can predict large non-gaussianities in the CMB, meaning searching for non-gaussianities provides one of the main observational tests of multifield models. No significant evidence for this primordial non-gaussianity was found in the Planck 2015 results~\cite{Gauss}. Important work on making generic predictions from multifield inflation has been carried out in~\cite{Easther}, which presented a set of generic predictions for multifield models. They found that their probability distribution functions for cosmological observables become more sharply peaked as they increase the number of fields. The same research group also presented a powerful and efficient numerical solver for multifield models, \texttt{MULTIMODECODE}, in Price et al.~\cite{Price} In~\cite{Easther}, Easther et al. use a simple measure, $\dif\phi_{1}\wedge\dif\dot{\phi}_{1}\wedge...\wedge\dif\phi_{N}\wedge\dif\dot{\phi}_{N}$, to count solutions in phase space. Although it is a simple measure to employ, and will give a reasonable idea of the probability distributions, it is not a well motivated measure. Following the arguments of Gibbons, Hawking and Stewart, the most natural phase space measure to use is that formed by the symplectic structure associated with the phase space. We will derive the equations of motion for the multiple scalar fields and implement them numerically to study their dynamics. We present derivations of the measures and expressions for the probabilities of observational agreement for simple two and three field quadratic models, along with a discussion of the issues in forming these measures. Lower bounds on the probabilities of observational agreement for these models in the case of equal mass fields are also found, with the probability increasing with the number of fields. We then derive a general $N$-field measure that can be implemented in future work and argue that the probability of observational agreement will approach 1 as the number of fields approaches infinity. | Let us now summarise what has been found. We have derived expressions for the two and three field measures and used these to obtain explicit expressions for the probabilities of observational agreement in the equal mass scenario. Starting from the initial Hubble surface $H_{i}=9.15\times10^{-5}$ and assuming the region of observational disagreement extended out to the radius $r_{0}$, we calculated lower bounds on the probabilities of observational agreement. For the equal mass two and three field models these were found to be $0.982$ and $0.997$ respectively, both of which were greater than the single field probability of $0.9653$. It should be noted here that there is an important ambiguity in these probability calculations, that is the choice of initial Hubble surface. In principle, we could have chosen to form the measure on an earlier or later Hubble surface and would have obtained a different value for the probability of observational agreement. This issue remains unresolved, the key controversy being over whether to choose a uniform distribution of initial conditions early or late in the inflation. We presented a derivation of the symplectic measure for a general $N$-field inflation model. This can be implemented in any future work by following the standard procedure of imposing a finite volume cut-off and integrating over the appropriate regions of phase space. This measure can be used in a detailed numerical study with \texttt{MULTIMODECODE} to precisely determine the regions of observational disagreement. Finally the increase in probability with the number of fields was found to be a result of the scaling of surface areas as we increase the number of fields and hence the dimension of our phase space. Further it was argued that as the number of fields approaches infinity the probability of observational agreement approaches one. This result was robust under a different choice of initial Hubble surface meaning that, provided we have a sufficient number of fields, we can obtain a high probability of observational agreement irrespective of our choice of initial Hubble surface. Further extensions of this work include studying models with a range of field masses, introducing field interactions into the potential, and going beyond the FRW case to consider anisotropic Bianchi cosmologies. Here we have presented analytic results obtained in the case of symmetries, which indicate that increasing the number of fields increases the likelihood of agreement with observations (given appropriate inflaton masses). Further we have provided the theoretical framework from which a more rigorous exploration of the likelihoods can be analysed in the more complex multifield approach. When different field masses are used we expect the lightest fields to dominate the slow roll phase, with the heavier fields reaching the oscillatory phase very quickly in comparison. This behaviour should be apparent in any numerical exploration of different mass models. Moreover, we expect the argument presented in section VI can be extended here to include different masses. Provided the heaviest field starts above a certain point on the potential surface we expect there will be enough inflation for observational agreement. Extending the same scaling arguments we should see the probability of observational agreement approach one as the number of fields approaches infinity in the different mass case as well. | 16 | 9 | 1609.05069 |
1609 | 1609.02155_arXiv.txt | The nature of warm, ionized gas outside of galaxies may illuminate several key galaxy evolutionary processes. A serendipitous observation by the MaNGA survey has revealed a large, asymmetric $\Ha$ complex with no optical counterpart that extends $\approx8\arcsec$ ($\approx6.3$ kpc) beyond the effective radius of a dusty, starbursting galaxy. This $\Ha$ extension is approximately three times the effective radius of the host galaxy and displays a tail-like morphology. We analyze its gas-phase metallicities, gaseous kinematics, and emission-line ratios, and discuss whether this $\Ha$ extension could be diffuse ionized gas, a gas accretion event, or something else. We find that this warm, ionized gas structure is most consistent with gas accretion through recycled wind material, which could be an important process that regulates the low-mass end of the galaxy stellar mass function. | \label{sec:introduction} \setcounter{footnote}{26} Understanding the warm, ionized gas outside of galaxies is a critical aspect of galaxy evolution. To study this gas, there have been two main probes: (1) observations of extraplanar ionized gas in edge-on galaxies \citep[e.g.,][]{rand90, tullmann00, otte01, miller03, rossa03} and (2) low ionization metal-line absorption studies using quasar sightlines \citep[e.g.,][]{tumlinson11, werk13, werk14}. These studies have led to the discovery of diffuse ionized gas (DIG; \citealt{hoyle63, reynolds85}), which is a layer of warm, low-density ionized gas that extends out to several kpc into the haloes of galaxies, and the confirmation of the circumgalactic medium (CGM; \citealt{bergeron86, lanzetta95}), which is a gas reservoir containing warm, ionized gas that is of even lower density than the DIG and extends hundreds of kpc into the haloes of galaxies. But how this gas relates to the evolution of their host galaxies is an open question. In this work, we further our understanding of warm, ionized gas in the haloes of galaxies by studying a rare and unusual gas complex in the SDSS-IV MaNGA survey \citep{bundy15}. Designed to observe galaxies out to a maximum radius of 2.5 effective radius ($R_{\rm e}$), the MaNGA survey has observed a dusty, starbursting\footnote{We define starbursts as galaxies with $\log~\Sigma_{\rm SFR} > -1 ~\rm M_{\odot}~yr^{-1}~kpc^{-2}$ \citep{kennicutt12}} galaxy that is on the upper end of the mass-metallicity relationship \citep{tremonti04} out to 6.3$R_{\rm e}$ through a fortuitous overestimation of $R_{\rm e}$\footnote{MaNGA uses $R_{\rm e}$ measurements from the NASA-Sloan Atlas, which estimated $R_{\rm e}=7.4\arcsec$ for this galaxy. After masking out the bright, nearby stars, we used GALFIT \citep{peng02} to fit a single S\'ersic model to this galaxy, yielding $R_{\rm e}=2.6\arcsec$; see \S2}. This galaxy shows no signs of interaction and displays a large $\Ha$ extension with no optical counterpart in the Sloan Digital Sky Survey Data Release 7 (SDSS DR7; \citealt{york00, abazajian09}). Throughout this work, we assume a flat cosmological model with $H_{0} = 70$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_{m} = 0.30$, and $\Omega_{\Lambda} =0.70$. \begin{deluxetable*}{cccccccccccc} \tabletypesize{\scriptsize} \tablewidth{0pt} \tablecaption{{\bf Galaxy properties}} \tablehead{ \colhead{MaNGA-ID} & \colhead{Plate-IFU} & \colhead{RA} & \colhead{DEC} & \colhead{$z$\tablenotemark{a}} & \colhead{$\log~M_*$\tablenotemark{b}} & \colhead{$u-r$\tablenotemark{c}} & \colhead{$\log~SFR$\tablenotemark{d}} & \colhead{$\log~\Sigma_{\rm SFR}$\tablenotemark{e}} & \colhead{$R_{\rm e}$\tablenotemark{f}} & \colhead{$R_{\rm e}$} & \colhead{$n$\tablenotemark{g}} \\ \colhead{} & \colhead{} & \colhead{(J2000.0 deg)} & \colhead{(J2000.0 deg)} & \colhead{} & \colhead{(M$_{\odot}$)} & \colhead{} & \colhead{(M$_{\odot}~\rm yr^{-1}$)} & \colhead{(M$_{\odot}~\rm yr^{-1} kpc^{-2}$) } & \colhead{($\arcsec$)} & \colhead{(kpc)} & \colhead{} } \startdata 1-113700 & 8618-12703 & 319.45182 & 11.66059 & 0.038 & 9.77 & 2.05 & 0.22 & $-0.37$ & 2.6 & 2.0 & 3.7 \enddata \tablenotetext{a}{Spectroscopic redshift from NSA catalog.} \tablenotetext{b}{Galaxy stellar mass from MPA-JHU DR7 data release.} \tablenotetext{c}{Rest-frame $u-r$ color from NSA catalog.} \tablenotetext{d}{Fiber star-formation rate from MPA-JHU DR7 data release.} \tablenotetext{e}{Fiber star-formation rate surface density using the MPA-JHU DR7 data release.} \tablenotetext{f}{Effective radius from GALFIT \citep{peng02}.} \tablenotetext{g}{Galaxy S\'ersic index from GALFIT \citep{peng02}.} \label{tab:properties} \end{deluxetable*} \begin{figure*}[t!] \centering \includegraphics[scale=.7]{fig1.eps} \caption{ {\it a:} SDSS $gri$ color image of the object, with the MaNGA field of view in magenta. {\it b:} $\Ha$ flux map with contours of $\log~{\Ha}~\rm Flux =-1,~ -0.5, ~ 0, ~ 0.5, ~ \rm and ~ 1$; the flux units are $10^{-17} ~ \rm ergs ~ s^{-1} cm^{-2}$. There is an asymmetric extension in the $\Ha$ flux distribution to the left (East) of the host galaxy. The green circle, which has a radius of $3\arcsec$, is an approximation of this $\Ha$ extension---we refer to this as the ``$\Ha$ circle'' throughout the text. The lower left hatched circle represents the effective spatial resolution of MaNGA, FWHM $= 2.5\arcsec$. {\it c:} SDSS $r$ band image with the $\Ha$ flux contours superimposed; the blue circle marks the $R_{\rm e}$ of the host galaxy. There is no optical source in the region of the $\Ha$ extension. {\it d-e:} Spectra (before stellar continuum subtraction) from the indicated spaxels in the $\Ha$ extension {\it (d)} and in the center of the galaxy {\it (e)}. The vertical, dashed lines indicate the expected wavelengths of the $\NII$ doublet, $\Ha$, and $\SII$ doublet emission lines at the systemic velocity of the host galaxy. \label{fig:spectra}} \end{figure*} | In this paper, we present the serendipitous observation of an ionized gas structure that protrudes out of a dusty, starbursting galaxy. Our analysis indicates that this ionized gas complex is most consistent with gas accretion through recycled wind material. To better understand the nature of this phenomenon, and to constrain the importance of gas accretion through recycled wind material, we need to find more of these extended gas complexes. However, the current MaNGA sample has not observed any other isolated galaxy with an adequately-sized integral field unit ($\gs6.3R_{\rm e}$) to allow such a search. We hope to address this issue with future MaNGA releases. | 16 | 9 | 1609.02155 |
1609 | 1609.02045_arXiv.txt | Quintessential dark energy with pressure $p$ and density $\rho$ is related by equation of state $p=\omega\rho$ with the state parameter $-1<\omega<-1/3$. The cosmological dark energy influence on black hole spacetime are interesting and important. In this paper, we study the Kerr-Newman-AdS solutions of the Einstein-Maxwell equation in quintessence field around a black hole by Newman-Janis algorithm and complex computations. From the horizon structure equation, we obtain the expression between quintessence parameter $\alpha$ and cosmological constant $\Lambda$ if the black hole exists two cosmological horizon $r_{q}$ and $r_{c}$ when $\omega=-2/3$, the result is different from rotational black hole in quintessence matter situation. Through analysis we find that the black hole charge cannot change the value of $\alpha$. But the black hole spin and cosmological constant are opposite. The black hole spin and cosmological constant make the maximum value of $\alpha$ to become small. The existence of four horizon leads seven types of extremal black holes to constraint the parameter $\alpha$. With the state parameter $\omega$ ranging from $-1$ to $-1/3$, the maximum value of $\alpha$ changes from $\Lambda$ to $1$. When $\omega\rightarrow -1$, the quintessential dark energy likes cosmological constant. The singularity of the black holes is the same with that of Kerr black hole. We also discuss the rotation velocity of the black holes on the equatorial plane for $\omega=-2/3,-1/2$ and $-1/3$. For small value of $\alpha$, the rotation velocity on the equatorial plane is asymptotically flat and it can explain the rotation curves in spiral galaxies. | In recent years, cosmological observations found that the universe is accelerating expansion, demanding the existence of dark energy (\cite{2004ApJ...607..665R,2003RvMP...75..559P,2006IJMPD..15.1753C}). The recent measurements of CMB anisotropy by PLANCK also confirmed this results (\cite{2011ApJS..192...18K}). Cosmological tests indicate that the dark energy accounts for 70$\%$ of energy content in the universe. The state equation of the dark energy is very close to the cosmological constant or vacuum energy. Besides the cosmological constant, an important dark energy model is called quintessence (\cite{2006IJMPD..15.1753C}). The dark energy content such as the cosmological constant or quintessence changes the spacetime structure of black hole. For the case of the cosmological constant, the asymptotic structure of black hole becomes the asymptotical de Sitter spacetime (\cite{1918AnP...361..401K,1999PhRvD..60d4006S}), in which a cosmological horizon exists. For the black hole in quintessence field, the cosmological horizon also exists (\cite{2003CQGra..20.1187K}). The importance of cosmological constant in high energy astrophysical objects, such as active galactic nuclei and supermassive black holes, has been discussed (\cite{2005MPLA...20..561S}). The spherically symmetric spacetime influenced by $\Lambda$ term is described by the vacuum Schwarzschild-de Sitter spacetime (SdS) (\cite{1918AnP...361..401K}). When the spacetime metric satisfies the axially symmetric case, the vacuum spacetime is described by Kerr-de Sitter spacetime (KdS) (\cite{1973blho.conf...57C}). In these spacetimes, the motion of test particles or photons have been discussed by many authors (\cite{2010PhRvD..81d4020H,2005CQGra..22.4391K,2004CQGra..21.4743K,2002PhRvD..65h7301L,2011MPLA...26.2923O,2008PhRvD..77d3004S,2000CQGra..17.4541S,2004PhRvD..69f4001S,1983BAICz..34..129S,1991GReGr..23..507S}). For the spherically symmetric black hole in quintessence field, its spacetime solution has been discussed by \citep{2003CQGra..20.1187K}. The universe accelerating expansion demands the state parameter to be in range $-1<\omega<-1/3$. The recent works generalized this result to Kerr black hole by Janis-Newman algorithm (\cite{2016EPJC...76..222G,2015arXiv151201498T}), and the spacetime metric were studied (\cite{2016EPJP..131..275H,2016Ap&SS.361..269O,2016arXiv160609037S}). Following these works, we generalize Kerr black hole solutions to Kerr-Newman black hole solutions in quintessential dark energy. Following we extend the Kerr-Newman solution to the cosmological constant presented case of quintessential dark energy. In this paper, we want to seek for Kerr-Newman-AdS solution in the quintessence by Janis-Newman algorithm and complex computations, we also discuss the properties of black hole solution. The outline of the paper is as follows. In section II, we introduce the Reissner-Nordstrom black hole in quintessence matter and derive the Kerr-Newman solution through Janis-Newman algorithm. Later we extend quintessence Kerr-Newman black hole to the case of existing cosmological constant. In section III, we study the horizon structure, stationary limit surfaces and singularity of the black hole in Boyer-Lindquist coordinates. In section IV, we calculate the circular geodesics on the equatorial plane. Summary are drawn in Section V. | Using Newman-Janis algorithm, we obtain Kerr-Newman solutions in quintessential dark energy. Because Newman-Janis algorithm do not include the cosmological constant, we cannot use this method to derive Kerr-Newman-AdS solution around by quintessential dark energy. Through direct complex computation, we extend the Kerr-Newman solution to Kerr-Newman-AdS in quintessential dark energy. By analysing the horizon equation, we obtain the value of $\alpha$ for $\omega=-2/3, -1/2$. When $\Lambda=0$, we find that $\alpha\leq\sqrt{2}/5$ for $\omega=-1/2$ and $\alpha<1/6$ for $\omega=-2/3$ which is the same with one given by \citep{2015arXiv151201498T} in quintessential dark energy, showing that the black hole charge cannot change the value of $\alpha$. When $\Lambda\neq 0$ and four horizons especially $r_{q}$ exist, we obtain the constraint equation on $\alpha$, implying that the black hole spin and cosmological constant make the maximum value of $\alpha$ to become more small. With the state parameter $\omega$ ranging from $-1$ to $-1/3$, the maximum value of $\alpha$ change $\Lambda$ to $1$. If $\omega\rightarrow -1$, $r_{q}$ arrives at $r_{c}$ and $\alpha$ is close to the cosmological constant. For all Kerr-Newman-AdS solution in quintessential dark energy, the naked singularity appears when $\Sigma^{2}=0$. Finally, we calculate the geodetic motion on equatorial plane for three situations of $\omega=-2/3, -1/2$ and $-1/3$. We find that the parameters $Q, a, \Lambda$ have small influence on rotation velocity, while the parameters $\alpha$ and $\omega$ have large influence on rotation velocity. For small value of $\alpha$, the rotation velocity on the equatorial plane is asymptotically flat and it can explain the rotation curves in spiral galaxies. The Kerr-Newman-AdS solution around by quintessential dark energy maybe useful in astrophysics. In the future we want to study the effects of rotation and charge in a more thorough manner, and the influence of quintessential dark energy on Blandford-Znajek mechanism and black hole accretion disk. | 16 | 9 | 1609.02045 |
1609 | 1609.08860.txt | The aim of this paper is to present an analytical relationship between the power spectral density of GRACE-like mission measurements and the accuracies of the gravity field coefficients mainly from the point of view of theory of signal and system, which indicates the one-to-one correspondence between spherical harmonic error degree variances and frequencies of the measurement noise. In order to establish this relationship, the average power of the errors due to gravitational acceleration difference and the relationship between perturbing forces and range-rate perturbations are derived, based on the orthogonality property of associated Legendre functions and the linear orbit perturbation theory, respectively. This method provides a physical insight into the relation between mission parameters and scientific requirements. By taking GRACE-FO as the object of research, the effects of sensor noises and time variable gravity signals are analyzed. If LRI measurements are applied, a mission goal with a geoid accuracy of 7.4 cm at a spatial resolution of 101 km is reachable, whereas if the KBR measurement error model is applied, a mission goal with a geoid accuracy of 10.2 cm at a spatial resolution of 125 km is reachable. Based on the discussion of the spectral matching of instrument accuracies, an improvement in accuracy of accelerometers is necessary for the match between the range errors and accelerometer noises in the future mission. Temporal aliasing caused by the time variable gravity signals is also discussed by this method. | \label{intro} The last dedicated gravity satellite missions like CHAMP, GRACE, GOCE and GRAIL have mapped the Earth's and Moon's gravity field with unprecedented high accuracy and resolution in the past decades \citep{Reigber 2002,Tapley 2004,Rummel 2011,Zuber 2013}. CHAMP and GOCE are mainly based on satellite-to-satellite tracking in the high-low mode (HL-SST) and satellite gravity gradiometry (SGG) respectively, while both GRACE and GRAIL satellite-to-satellite tracking use the low-low mode (LL-SST). Compared to HL-SST and SGG configurations, the LL-SST observations can derive the long wavelength components of the Earth's gravity field with higher accuracy and map their variability in time in an efficient way. LL-SST missions based on intersatellite ranging may achieve significant improvements in spatial resolution and accuracy of gravity field model by using interferometric laser ranging instead of microwave ranging. Due to these advantages, the proposed future missions, like the GRACE Follow-On (GRACE-FO) \citep{Flechtner 2015}, Next-Generation Gravity Mission (NGGM) \citep{Cesare and Sechi 2013} concept and Earth System Mass Transport Mission (e.motion) proposal \citep{Gruber 2014}, are all based on LL-SST configuration. Until now there exist four basic types of LL-SST satellites formations for the missions to choose from, i.e. collinear tandem (GRACE-like), pendulum, Cartwheel and LISA-type formation \citep[c.f.][]{Elsaka 2014}. Several studies were published to investigate the performance of these satellite formations, e.g. by \citet{Sharifi 2007}, \citet{Sneeuw 2008}, \citet{Wiese 2009}, \citet{Massotti 2013}, \citet{Elsaka 2014} and \citet{Elsaka 2015}. The upcoming GRACE-FO mission based on the collinear tandem configuration is about to be launched in 2017 and will have a nominal life-time of 7 years \citep{Flechtner 2014}. By taking advantages of GRACE and GRAIL heritage, the GRACE-FO mission will continue to obtain the global models of the Earth's time-variable gravity field, while on the other hand it will try to improve the LL-SST measurement performances. For this purpose, a 50-100 nm precise laser ranging interferometer (LRI) is included into the GRACE-FO payload as a science demonstrator instrument, which supplements the $\mu $m-level accuracy K-band ranging system (KBR). The GRACE-FO mission is expected to provide meaningful guidance to the future gravity satellite missions of LL-SST type after GRACE-FO. The pre-mission error analysis is a key issue for the future mission design, which concerns the field where geodesy is in contact with physics and technical sciences. It allows one to determine the science requirements and parameters of missions before launch. The conventional error analysis and recovery methods of LL-SST are based on orbit perturbation theory or the principle of energy conservation in establishing the observation equations, which are generally solved by using least-squares (LS) theory \citep{Colombo 1984,Touboul 1999,Tapley 2004}. However, there was no one-to-one correspondence between spherical harmonics and frequencies in the measurements \citep{Inacio 2015}, i.e. accelerometer data, range-rate data. That means the conventional methods estimate the individual effects of parameters and noise are too complicated to be described analytically since these methods address the effect of measurement errors mainly from a numerical point of view \citep{Migliaccio 2004,Cai 2012}. By applying the theory of signal and system, this paper provides an analytical relationship between the power spectral density (PSD) of LL-SST measurements and the accuracies of gravity field coefficients, which indicates the one-to-one correspondence between spherical harmonic error degree variances and frequencies of the measurement noise. This error analysis method allows us to efficiently evaluate the science requirements and parameters of the missions. It is a helpful tool for identifying the frequency characteristics of signals in future gravity missions. \citet{Sneeuw 2000} and \citet{Kim 2000} developed their respective semi-analytical theory on error analysis with different principles. The semi-analytical approach established by \citet{Sneeuw 2000} obtains the 2-D Fourier spectrum first by Fourier analysis and then transforms the Fourier coefficients into the spherical harmonic coefficients. In the latter step, the relationship between spherical harmonics and 2-D Fourier spectrum cannot be analytically given and must be preceded with applying least-squares. The semi-analytical method for degree error prediction established by \citet{Kim 2000} can obtain degree error variance of the gravity by a expression when that of range-rate is available. But before this step, the range-rate measurement noises due to various error sources need to be covered the entire sphere with the same latitude and longitude lengths and then mapped from the space domain into the spectral domain to obtain the degree variance of range-rate. These works made a significant contribution to the progress of efficient computation of error analysis of gravity field, however, these methods cannot lead to directly evaluate the frequency characteristics of measurement noise which affects spherical harmonic coefficient recovery due to the lack of analytical expression. This paper, with GRACE-FO as the object of the research, discusses an analytical error analysis method of LL-SST (a collinear tandem configuration), and is organized as follows. In Sect. 2, the forces variation relationship between two satellites produced by the gravitational and non-gravitational accelerations is derived based on dynamic analysis of the satellite. The information of the range-rate is put in relation with the differential effect of the resultant forces acting on the twin satellites, which consist of gravitational terms, due to the gravity field of the Earth and third bodies, and non-gravitational terms, due to the surface forces like atmospheric drag and solar radiation. A direct analytical expression for the error analysis of LL-SST is then concluded based on the dynamic analysis and spectral analysis in Sect. 3. The transfer function between satellite perturbing forces and the range-rate are deduced in detail in Sects. 4. In Sect. 5, the effects of sensor noise and their matching together with temporal aliasing from both non-tidal and tidal sources on gravity field recovery are explicitly and quantitatively discussed by taking the advantage of this method. | Based on the spectral analysis and orbit perturbation theory, an analytical relationship between the PSD of LL-SST measurements and the accuracies of gravity field coefficients is presented mainly from the point of view of theory of signal and system, which indicates the one-to-one correspondence between spherical harmonic error degree variances and frequencies of the measurement noise. This relationship provides a physical insight into how the measurement noises affect the accuracy of the gravity field recovery. The method is an efficient and convenient tool for the design of future mission, especially for high accuracy and resolution gravity field models. By taking GRACE-FO as the object of research, the effects of sensor noises and time variable gravity signals are analyzed. If LRI measurements are applied, a mission goal with a geoid accuracy of 7.4 cm at a spatial resolution of 101 km is reachable, whereas if the KBR measurement error model is applied, a mission goal with a geoid accuracy of 10.2 cm at a spatial resolution of 125 km is reachable. The spectral matching of instrument accuracies is also investigated by taking the advantage of the analytical relationship. It is necessary to improve the accuracy of accelerometers for the match between the range errors and accelerometer noises in the future mission, especially for removing or suppressing the 1/f noise. Temporal aliasing caused by the time variable gravity signals is also discussed by this method. The one-to-one correspondence in the spectral domain may provide a way for reducing the aliasing effects, but this still needs further study based on the actual data. This study is based on the hypothesis that the satellite orbit is a polar circular orbit, while the realistic orbit with an inhomogeneous data distribution should cause a lower accuracy and resolution model. It should be noted that the gravity signal can not exactly recovered according to the Nyquist theorem if polar gaps occurs with a non-polar inclination. In this case the results of error propagation computed by least-square methods are fitted values, unless the gaps are filled with other data. Furthermore, the linear orbit perturbation theory is adopted, which means that we have ignored the higher-order effect terms. Notwithstanding its limits, the essential relationship is clearly indicated. Further improvements in all these problems need to be further analyzed. | 16 | 9 | 1609.08860 |
1609 | 1609.02759_arXiv.txt | {Due to the failure of the second reaction wheel, a new mission was conceived for the otherwise healthy \textit{Kepler} space telescope. In the course of the K2 Mission, the telescope is staring at the plane of the Ecliptic, hence thousands of Solar System bodies cross the K2 fields, usually causing extra noise in the highly accurate photometric data. } {In this paper we follow the {\it someone's noise is another one's signal} principle and investigate the possibility of deriving continuous asteroid light curves, that has been unprecedented to date. In general, we are interested in the photometric precision that the K2 Mission can deliver on moving Solar System bodies. In particular, we investigate space photometric optical light curves of main-belt asteroids.} {We study the K2 superstamps covering the M35 and Neptune/Nereid fields observed in the long cadence (29.4-min sampling) mode. Asteroid light curves are generated by applying elongated apertures. We use the Lomb-Scargle method to find periodicities due to rotation.} {We derived K2 light curves of 924 main-belt asteroids in the M35 field, and 96 in the path of Neptune and Nereid. The light curves are quasi-continuous and several days long. K2 observations are sensitive to longer rotational periods than usual ground-based surveys. Rotational periods are derived for 26 main-belt asteroids for the first time. The asteroid sample is dominated by faint (>20~mag) objects. Due to the faintness of the asteroids and the high density of stars in the M35 field, only 4.0\% of the asteroids with at least 12 data points show clear periodicities or trend signalling a long rotational period, as opposed to 15.9\% in the less crowded Neptune field. We found that the duty cycle of the observations had to reach $\sim$ 60\% in order to successfully recover rotational periods.} {} | \begin{figure*} \centering \includegraphics[width=18.4cm]{ds9.eps} \caption{Mosaic of the M35 open cluster (as well as NGC~2158) as seen by K2. The area is covered by 154 sub-apertures amounting to 800$\times$550 pixels ($53^\prime\times36^\prime$).} \label{FigM35} \end{figure*} The \textit{Kepler} space telescope revolutionized time-domain astronomy, and its unique capabilities were demonstrated by the detection of short \citep{sanchis2014} and long period transiting exoplanets \citep{kipping2016}, the application of stellar seismology \citep{chaplin2011}, and the renewed interest in studying classical variable stars \citep{gilliland2010}. In the latter case \eg a new dynamical phenomenon was discovered in RR\,Lyrae stars \citep{szabo2010}, whose detection had been previously hampered by the diurnal variations affecting ground-based observations. In 1901 von Oppolzer first noticed the brightness variation of an asteroid, (433) Eros \citep{oppolzer1901}, and its first correct period was published in \citet{bailey1913} with several other minor planets. During the more than hundred years since then the light variation of over 10000 main-belt asteroids were measured, but the length of the continuous observations has been always limited by the maximal duration of a winter night. The re-purposed \textit{Kepler} mission (K2) \citep{howell2014} made it possible for the first time to measure the brightness of a large number of main-belt asteroids quasi-continuously. In this paper we show the results obtained from the photometry of close to 1000 main-belt asteroids, most of them followed continuously for up to 3--4 days or longer, a small fraction of them up to 6 days in two large super-stamps of the K2 Mission. In a series of works we have been investigating the possibilities of high-precision space photometric observations of Solar System objects with the rejuvenated \textit{Kepler} space telescope \citep{howell2014}. In \citet{szabo2015} the effects of main-belt asteroid encounters on K2 photometry of stellar targets were investigated. In \cite{pal2015} we analyzed two faint Trans-Neptunian Objects, namely \gv and \jjs, measuring their rotation periods. These are among the faintest objects \textit{Kepler} has measured so far. We also outlined the methodology to deal with these moving targets that \textit{Kepler} had not been designed for. Special masks were allocated to these targets making their continuous observations possible. By complementing recent K2 observations with archival \textit{Herschel} data, we analyzed the thermophysical parameters of \ortiz\ in \cite{pal2016}. In this work we turn our attention to two special fields that K2 has observed, both of which have been covered by multiple sub-apertures, creating large enough fields to search for asteroids. In Campaign 0 a well-known, bright open cluster, M35 (NGC\,2168) was observed with Kepler. It was covered with a mosaic of 154 50$\times$50 pixel small stamps amounting to 800$\times$550 pixels ($53^\prime\times36^\prime$ on the sky), EPIC IDs ranging from 2000000811 to 200000964. The observed field includes the open cluster NGC~2158 as well. By quickly investigating the images it was immediately obvious that hundreds of asteroids crossed this field of view. We choose these observations because of the large, contiguous field and the large number of asteroids available. Campaign 0 covers the period Mar 8 to May 30, 2014, it was implemented as a full-length engineering test to prove that K2 was a viable mission. The \textit{Kepler} spacecraft was not in fine point for the first 16 days of C0, causing large photometric scatter. Eventually, the \textit{Kepler} spacecraft went into safe mode that lasted for about 24 days. After that stopping, high-quality, fine-point measurements began, which span 35 days. The data quality improved in the second half of the campaign. We used data from only this part of the campaign. Jupiter was crossing the field, but fell on the dead Module\,3, and caused only increased background flux. \begin{figure*} \centering \includegraphics[width=18.4cm]{nereid-field-median.eps} \caption{Mosaic covering the paths of Neptune and Nereid observed by the K2 Mission. The length of the mosaic is approximately 20$^\prime$.} \label{FigNereid} \end{figure*} Campaign 3 started on 15 November, 2014, and ended on 23 January, 2015. In this campaign Neptune and its satellite, Nereid was observed (GO IDs: 3057, 3060, 3115), their path was also tiled with 305 narrow strips of pixel masks (EPIC IDs 200004468--200004762). We refer to this field as Nereid field henceforth. While Campaign 0, and especially the vicinity of M35 contains a crowded field, this small stripe of the sky gave an opportunity to analyze light curves of asteroids usually free of too large number of stellar sources. However, due to the proximity of Neptune we had to deal with other problems (high background, saturation, etc). The change in bandwidth for pointing control (from 50 to 20 seconds) for C3 resulted in an increase in SNR for short cadence by a factor of roughly 4--9, with the larger improvement seen at the higher frequency end. Campaign 3 had a nominal duration of 80 days, but an actual duration of only 69.2 days. The campaign ended earlier than expected because the on-board storage filled up faster than anticipated due to unusually poor data compression\footnote{http://keplerscience.arc.nasa.gov/k2-data-release-notes.html}. A similar study about Jovian Trojan asteroids observed by the K2 Mission will be published in a related paper (Szab\'o et al., 2016). | We utilized the \textit{Kepler} space telescope for the first time to derive quasi-continuous light curves of a large number of main-belt asteroids in long cadence mode (29.4~min sampling). The main conclusions of this work are the following: \begin{itemize} \item{Out of 924 (96) asteroids in the M35 (Nereid) field in Campaign~0 (3), 867 (88) had twelve or more useful photometric data points and only 23 (14) exhibited clear periodicities which is attributed to rotation. In addition, 12 (0) objects showed a slow trend or were observed through an incomplete rotational cycle implying a long rotational period.} \item{By comparing the M35 and Nereid samples we found a remarkable difference regarding the number of main-belt asteroids with detected rotational periods in the two fields. While in the dense M35 field only 4.0\% of the asteroids showed clear periodicities or trend, in the Nereid field we recovered periodicities in 15.9\% of the observed asteroids. The difference is significant given the large number of observed asteroids in both fields. To explain this difference we propose two arguments: } \item{First, we conclude that the dense stellar field precluded the derivation of meaningful photometry in the case of many asteroids, because too many points had to be discarded, due to the disturbing effects of stellar residuals along the paths of the asteroids (see Fig.~\ref{duty}). This is partly explained by the undersampled PSFs delivered by the {\it Kepler} spacecraft.} \item{Second, in Fig.~\ref{magdist} we plot the magnitude distribution of our full M35 asteroid sample (in blue) as seen from Kepler, and also those that showed periodicities or long-term trends in their light variations (red). The plot convincingly shows that our sample is heavily dominated by faint targets (>20~mag). Together with Fig.~\ref{magerr} this clearly demonstrates that there is a rather low chance to pull out rotational signal of asteroids below the ${\rm 20^{th}}$ magnitude brightness limit. This reasoning helps to explain the relatively low rate of recovered rotational periods in our fields, especially in the M35 superstamp.} \item{More sophisticated photometric methods may improve our results and provide more reliable and robust space photometric data of moving objects. Testing of such methods is currently is under way.} \end{itemize} \begin{figure} \centering \includegraphics[width=6.1cm, angle=270]{maghist.eps} \caption{Magnitude distribution of the asteroids in the M35 field seen by \textit{Kepler} (924, blue columns), and the selected sample where significant rotational signal (period or trend) could be derived (35, red columns). Two brighter objects were omitted from the figure for the sake of clarity.} \label{magdist} \end{figure} \begin{table} \centering \caption{Rotational signal detected in asteroids observed in the K2 M35 superstamp.} \begin{tabular}{ccccc} \hline\hline ID & period & ampl. & ref. \\ & [h] & [mag] & \\ \hline 228 & 6.437 $\pm$ 0.047 & 0.158 & this paper \\ & 6.47 & 0.27 & \citet{ivarsen2004} \\ & 6.484 & 0.27 & \citet{cooney2005} \\ 767 & >60. & > 0.1 & this paper\\ 2785 & 5.479 $\pm$ 0.031 & 0.310 & this paper \\ & 5.49 & 0.45 & \citet{polishook2009} \\ & 5.478 & & \citet{hanus2016} \\ 3345 & >34. & >0.7 & this paper \\ & 187. & 0.59 & \citet{benishek2014} \\ 3512 & 6.67 $\pm$ 0.25 & 0.212 & this paper \\ & 6.782 & 0.35 & \citet{ditteon2004} \\ & 6.784 & 0.25 & \citet{skiff2011} \\ 3903 & 28.09 $\pm$ 0.97 & 0.190 & this paper \\ 4282 & >34. & >0.6 & this paper \\ 7122 & >96. & >0.6 & this paper \\ 7241 & 59.6 $\pm$ 5.7 & 0.606 & this paper \\ 10269 & 10.81 $\pm$ 0.33 & 0.090 & this paper \\ 10683 & 75.3 $\pm$ 3.1 & 1.0 & this paper \\ 12379 & 50.6 $\pm$ 3.1 & 0.378 & this paper \\ 13243 & 88.4 $\pm$ 9.8 & 0.784 & this paper \\ 14439 & 9.94 $\pm$ 0.38 & 0.322 & this paper \\ 17771 & 15.97 $\pm$ 0.26 & 0.456 & this paper \\ 21207 & >120. & >0.5 & this paper \\ 24192 & 19.9 $\pm$ 1.0 & 0.464 & this paper \\ 25468 & 5.573 $\pm$ 0.078 & 0.482 & this paper \\ 29296 & >48. & >0.9 & this paper \\ 30329 & 28.4 $\pm$ 2.1 & 0.708 & this paper \\ 37750 & 5.15 $\pm$ 0.21 & 0.204 & this paper \\ 42573 & 3.888 $\pm$ 0.083 & 0.164 & this paper \\ & 3.887 & 0.55 & \citet{waszczak2015} \\ 49039 & >72. & >0.8 & this paper \\ 49193 & 5.66 $\pm$ 0.55 & 0.400 & this paper \\ 52786 & >144. & >0.5 & this paper \\ 55949 & 11.16 $\pm$ 0.15 & 0.324 & this paper \\ & 11.135 & 0.43 & \citet{waszczak2015} \\ 57648 & 8.359 $\pm$ 0.079 & 0.266 & this paper \\ 66340 & >62. & >1.0 & this paper \\ 67087 & 17.7 $\pm$ 1.5 & 0.316 & this paper \\ 69759 & >41. & >0.6 & this paper \\ 69853 & 8.17 $\pm$ 0.83 & 0.454 & this paper \\ 109978 & >144. & >0.3 & this paper \\ 115554 & 8.11 $\pm$ 0.91 & 0.402 & this paper \\ 149686 & >72. & >1.0 & this paper \\ 218609 & 9.72 $\pm$ 0.22 & 0.690 & this paper \\ \hline \end{tabular} \label{tab5} \end{table} \begin{table} \centering \caption{Observed periods and amplitudes of the asteroids in the K2 Nereid field.} \begin{tabular}{cccc} \hline\hline ID & period & ampl. & ref. \\ & [h] & [mag] & \\ \hline 2954 & 4.691 $\pm$ 0.010 & 0.174 & this paper \\ & 4.690 & 0.21 & \citet{wisniewski1997} \\ & 4.68 & 0.25 & \citet{ferrero2010} \\ 3785 & 3.782 $\pm$ 0.007 & 0.256 & this paper \\ & 3.7992 & 0.30 & \citet{behrend2009} \\ 9105 & 4.769 $\pm$ 0.032 & 0.770 & this paper \\ 31907 & 3.786 $\pm$ 0.081 & 0.076 & this paper \\ 57575 & 4.641 $\pm$ 0.077 & 0.436 & this paper \\ 87632 & 14.6 $\pm$ 2.7 & 0.128 & this paper \\ 211339 & 5.14 $\pm$ 0.20 & 0.734 & this paper \\ 242602 & 8.600 $\pm$ 0.094 & 0.706 & this paper \\ 249866 & 3.71 $\pm$ 0.20 & 0.172 & this paper \\ & 3.7982 & 0.18 & \citet{waszczak2015} \\ 250648 & 5.95 $\pm$ 0.17 & 0.564 & this paper \\ 311247 & 11.94 $\pm$ 0.48 & 0.584 & this paper \\ 314616 & 7.81 $\pm$ 0.24 & 0.270 & this paper \\ \hline \end{tabular} \label{tab6} \end{table} | 16 | 9 | 1609.02759 |
1609 | 1609.07510_arXiv.txt | Transitional protostellar disks have inner cavities heavily depleted in dust and gas, yet most show signs of ongoing accretion, often at rates comparable to full disks. We show that recent constraints on the gas surface density in a few well-studied disk cavities imply that the accretion speed is at least transsonic. We propose that this is the natural result of accretion driven by magnetized winds. Typical physical conditions of the gas inside such cavities are estimated for plausible X-ray and FUV radiation fields. The gas is molecular and predominantly neutral, with a dimensionless ambipolar parameter in the right general range for wind solutions of the type developed by K\"onigl, Wardle, and others. That is to say, the density of ions and electrons is sufficient for moderately good coupling to the magnetic field, but not so good that the magnetic flux need be dragged inward by the accreting neutrals. | \label{sec:intro} Transitional protostellar disks (hereafter TDs) are deficient in mid-infrared emission ($\lambda\lesssim 10\micron$), implying a dearth of small dust grains interior to a few to several tens of $\au$ \citep[and references therein] {Skrutskie+etal1990, Espaillat+etal2014}. TDs are often supposed to represent an evolutionary stage intermediate between classical T Tauri systems, which have full disks, and weak-lined T Tauri systems, which have little or none. In this view, disks disperse from the inside out through some combination of photoevaporation, viscous evolution, and planet formation \citep[and references therein] {Marsh+Mahoney1992, Hollenbach+etal1994, Clarke+etal2001, Alexander+etalPPVI}. TDs tend to accrete less than full disks of comparable mass by factors $\sim3$-$10$ \citep{Najita+etal2015}. The abundance of small dust in the disk cavity is suppressed by much larger factors \citep{vanderMarel+etal2015}. Some TDs, however, have accretion rates entirely comparable to those of full disks despite inner gaps of tens of $\au$ \citep{Manara+etal2014}. Evidently gas somehow crosses the gap between the outer disk and the star. Indeed, gas is detected within dust cavities of accreting TDs via $\mathrm{H}_2$ fluorescence \citep{Ingleby+etal2009,Gorti+etal2011} and rovibrational CO emission \citep{Pontoppidan+etal2008,Salyk+etal2009}. In both cases the emission appears to correlate with $\dot M$. \citet{Owen2016} suggests that there are two types of TDs: (i) those that are faint at submillimeter wavelengths, have cavities $\lesssim 10\au$, and accrete at $\dot M\lesssim 10^{-9}\msunperyr$; (ii) those that are bright in the submillimeter, have cavities $\gtrsim 20\au$, and accrete at $\sim 10^{-8}\msunperyr$. The first type is consistent with expectations for photoevaporating disks, he suggests, whereas the latter is not. The present paper pertains mainly to class (i)---TDs that accrete rapidly despite large cavities. The persistence of accretion suggests that within TD dust cavities either the ratio of small dust to gas is reduced, or the velocity of accretion is increased (implying a lower surface density for a given $\dot M$). Since quantitative measures of the gaseous surface density within TD cavities are sparse, many theoretical explanations for TDs have focussed on the former possibility, i.e. on mechanisms for altering the abundance of small grains per unit gas mass, such as photophoresis \citep{Krauss+Wurm2005}, radiation pressure \citep{Chiang+Murray-Clay2007}, pressure-induced dust filtering \citep{Paardekooper+Mellema2006, Rice+etal2006, Zhu+etal2012}, or grain coagulation \citep{Tanaka+etal2005}. Alternatively or in combination with modified dust, mechanisms for increasing the radial speed of accretion ($v_{\rm acc}$) within TD cavities have been proposed. These include enhanced MRI turbulence \citep{Chiang+Murray-Clay2007,Suzuki+etal2010} and planetary torques \citep{Varniere+etal2006,Zhu+etal2011, Rosenfeld+etal2014}. At $\dot M\sim 10^{-8}\msunperyr$, MRI alone cannot reduce the surface density below a few $\unit{g\,cm^{-2}}$ at relevant radii, which does not render the disk optically thin with standard ISM dust and would appear also to violate direct constraints on the gas column in some systems (\S\ref{subsec:vr}). Planetary-torque models, even with multiple planets, have difficulty opening wide and clean gaps while still maintaining high accretion rates. In this paper, we focus on a well-recognized mechanism that naturally produces rapid accretion: magnetized disk winds. Despite much work on disk winds since the seminal papers of \citet{Blandford+Payne1982} and \citet{Pudritz1985}, applications to transitional disks have rarely been remarked upon. Notably however, \citet{Combet+Ferreira2008} envisage a disk with relatively high surface density driven by turbulent viscosity at large radius, but with a lower wind-driven surface density within some transition radius $r_J$. Even in that paper, the term ``transitional disk'' appears only once in passing. The authors' motivation appears to have been mainly theoretical, having to do with inward concentration of large-scale poloidal magnetic flux brought about by competition between radial advection and turbulent diffusion. The radial redistribution of magnetic flux is a difficult problem (\S\ref{subsec:flux}), and we are agnostic as to whether CF08's transition radius $r_J$ can be predicted from first principles. Our motivation for considering this type of model arose from other considerations. First, MRI-driven turbulence in active layers of disks with total surface densities comparable to the minimum-mass solar nebula seems only marginally viable at radii $\sim\mbox{1-10}\au$: such turbulence requires field strengths approaching equipartition with the local gas pressure in order to reproduce observed accretion rates \citep{Bai+Goodman2009,Bai2011}. Secondly, recent numerical simulations of MRI turbulence with ambipolar diffusion often laminarize and produce spontaneous outflows \citep{Bai+Stone2013,Gressel+etal2015}. Thirdly, recent constraints derived from ALMA data on the gas content within the cavities of a few robustly accreting TDs demand accretion speeds at least as high as the gas sound speed (\S\ref{subsec:vr}). The outline of the paper is as follows. \S\ref{sec:background} summarizes the observational evidence for rapid inflow and the theoretical reasons for expecting wind-driven accretion to be transsonic. We also review the importance of ambipolar diffusion, at least under laminar conditions, for allowing the gas to accrete without overly concentrating the magnetic flux. This leads to a calculation in \S\ref{sec:environment} of the expected degree of ionization and ambipolar coupling of the gas to the field in the cavity regions. It is found that ambipolar diffusion is plausibly in the Goldilocks range: neither so rapid as to undercut the magnetic wind torque on the neutrals, nor so slow as to cause the field to be accreted with the gas. We write ``plausibly'' because this is a complex calculation subject to many uncertainties in the chemical network, dust effects, and radiation field. \S\ref{sec:discussion-summary} summarizes our findings and directions for future research. | \label{sec:discussion-summary} We have seen that magnetized winds can rather naturally explain the combination of low gas and dust surface density and relatively robust accretion in transition-disk cavities. From a theoretical point of view, the suggestion is all the more natural because of previous work demonstrating the likelihood of \emph{photoevaporative} winds on the one hand \citep{Hollenbach+etal1994, Clarke+etal2001, Alexander+Clarke+Pringle2006, Owen+etal2010}, and the need for net poloidal magnetic flux to sustain magnetorotational turbulence in the minimally ionized parts of protostellar disks, on the other \citep{Fleming+etal2000, Oishi+MacLow2011, Flock+etal2012, Bai+Stone2011, Simon+etal2013a, Simon+etal2013b}. A thermally-driven outflow threaded by magnetic lines is bound to exert a torque on the gas remaining in the disk and drive some accretion, though just how much will require detailed modeling of a sort not attempted in the present work. If the whole vertical column of the disk were to accrete at $v_{\rm acc}\sim\cs$, then the surface density corresponding to observed accretion rates would be much less than what is inferred observationally, e.g. from submillimeter observations \citep{Beckwith+Sargent1993,Andrews+etal2013}. Thus in the parts of TDs exterior to their cavities, as well as in full (non-transitional) T~Tauri disks, either accretion is driven turbulently (and hence relatively slowly), or else it is again driven by a magnetized wind, but one that couples to only a small fraction of the vertical column where FUV and X-ray photons sufficiently ionize and heat the gas \citep{Bai2016}. Not addressed here is the \emph{cause} of the transition between slow/layered accretion at large radii and fast, wind-driven, full-column accretion within the cavity. Perhaps, as proposed by \citet{Combet+Ferreira2008}, this has to do with a critical value of magnetization brought about by advection of poloidal flux. But as discussed in \S\ref{subsec:flux}, the advection and diffusion of magnetic flux in a turbulent disk is an unsolved problem. Also, if this is the explanation, why aren't all T~Tauri disks transitional? Perhaps indeed giant planets are implicated, but rather than producing the entire cavity by gravitational torques alone, such planets trigger a local change in the mass-to-flux ratio by stemming the inflow of gas near the midplane (which feels little magnetic torque) but not the inflow of the more ionized surface layers (which are more strongly magnetically driven, whether by winds or MRI). In any case, one should entertain the possibility that transitional disks---or at least those that have accretion rates comparable to those of full disks---may not be an evolutionary phase that all disks pass through immediately before complete dispersal. \vspace*{10pt} This work was supported by NASA Origins of Solar Systems grant NNX10AH37G. | 16 | 9 | 1609.07510 |
1609 | 1609.05209_arXiv.txt | \noindent We study particle production at the preheating era in inflation models with nonminimal coupling $\xi \phi^2R$ and quartic potential $\lambda \phi^4/4$ for several cases: real scalar inflaton, complex scalar inflaton and Abelian Higgs inflaton. We point out that the preheating proceeds much more violently than previously thought. If the inflaton is a complex scalar, the phase degree of freedom is violently produced at the first stage of preheating. If the inflaton is a Higgs field, the longitudinal gauge boson production is similarly violent. This is caused by a spike-like feature in the time dependence of the inflaton field, which may be understood as a consequence of the short time scale during which the effective potential or kinetic term changes suddenly. The produced particles typically have very high momenta $k \lesssim \sqrt{\lambda}M_\text{P}$. The production might be so strong that almost all the energy of the inflaton is carried away within one oscillation for $\xi^2\lambda \gtrsim {\mathcal O}(100)$. This may partly change the conventional understandings of the (p)reheating after inflation with the nonminimal coupling to gravity such as Higgs inflation. We also discuss the possibility of unitarity violation at the preheating stage. | \label{sec_introduction} \setcounter{equation}{0} After the results from the Planck satellite, a simple chaotic inflation model with a power-law potential~\cite{Linde:1983gd} is excluded or disfavored~\cite{Ade:2015xua}. Hence large field inflation models need to be modified so that the prediction of the scalar spectral index and tensor-to-scalar ratio falls into the observationally favored region. One of the simple ideas is to add a nonminimal gravitational coupling of the inflaton to the Ricci scalar: \begin{align} S &= \int \dd^4x \sqrt{-g_J} \left[ \left( \frac{M_\text{P}^2}{2} + \frac{\xi}{2}\phi_J^2 \right)R_J - \frac{1}{2}g_J^{\mu \nu}\partial_\mu \phi_J \partial_\nu \phi_J - V_J(\phi_J) \right], \label{eq:B_SJ} \end{align} where the potential is given by \begin{align} V_J(\phi_J) &= \frac{\lambda}{4}\phi_J^4. \label{eq:B_V} \end{align} Here $M_\text{P}$ is the reduced Planck mass, $g_{J \mu\nu}$ is the metric, $\phi_J$ is the inflaton, $R_J$ is the Ricci scalar, and $\xi$ and $\lambda$ are model parameters.\footnote{ We attach the subscript $J$ to quantities in the Jordan frame to distinguish them from those in the Einstein frame in this paper. } An interesting feature of this model is that the potential becomes effectively flat in the large field value region, providing a good candidate for the inflaton potential~\cite{Futamase:1987ua,Fakir:1990eg}. Throughout this paper, we focus on this class of models. A specific example is the so-called Higgs inflation~\cite{CervantesCota:1995tz,Bezrukov:2007ep,Bezrukov:2009db}, where the standard model (SM) Higgs boson plays the role of the inflaton.\footnote{ The applicability of Higgs inflation after the discovery of Higgs boson at LHC is found in Refs.~\cite{Degrassi:2012ry,Bednyakov:2015sca,George:2015nza}. } This model is consistent with the observations when the parameter satisfies $\xi \sim 5\times 10^{4}\sqrt{\lambda}$~\cite{Ade:2015xua}, and we assume $\xi \gg 1$ throughout this paper. The quartic coupling for the Higgs inflation case, $\lambda \sim 0.01$, satisfies this condition,\footnote{ It has been pointed out that in Higgs inflation $\xi \gg 1$ generically generates large $R^2$ term in the action without some fine-tuning~\cite{Salvio:2015kka}. } though we do not limit ourselves to the SM Higgs field as the inflaton but consider more general scalar fields in this paper. For example, a gauge-singlet scalar dark matter~\cite{Lerner:2009xg,Lebedev:2011aq}, or U(1)$_{\rm B-L}$ Higgs~\cite{Okada:2011en} as an inflaton has been considered. After inflation ends, the universe enters the (p)reheating phase in which the inflaton field is rapidly oscillating around its potential minimum. It is known that the first stage of the reheating after inflation is often accompanied with explosive particle production, if either the inflaton strongly couples to other fields and/or the inflaton oscillation amplitude is large enough, and this is called preheating~\cite{Traschen:1990sw,Shtanov:1994ce,Kofman:1994rk,Kofman:1997yn}. Actually there may be several possible large couplings in the present model: the nonminimal coupling, inflaton self-coupling, gauge coupling etc. The (p)reheating of the Higgs inflation was studied in Refs.~\cite{Bezrukov:2008ut,GarciaBellido:2008ab,Bezrukov:2014ipa,Repond:2016sol}, where it was pointed out that gauge bosons are efficiently produced at the preheating stage. In this paper we revisit the preheating after inflation with the nonminimal coupling. We first analyze the background dynamics of the inflaton carefully, and find that there are two mass scales (or inverse time scales) in the inflaton oscillation for $M_\text{P}/\xi \ll \Phi \ll M_\text{P}$, where $\Phi$ is the inflaton oscillation amplitude in the Einstein frame (see Sec.~\ref{sec:Weyl} for the definition of the Einstein frame). One is the usual inflaton oscillation scale, \begin{align} m_\mathrm{osc} = \Delta t_\mathrm{osc}^{-1} \sim \frac{\sqrt{\lambda}M_\text{P}}{\xi}, \end{align} and the other is a much shorter time scale which we call the ``spike'' scale, \begin{align} m_\mathrm{sp} = \Delta t_\mathrm{sp}^{-1} \sim \sqrt{\lambda}\Phi. \end{align} This time scale $\Delta t_\mathrm{sp}$ corresponds to the time interval at which the inflaton passes through the region with $\lvert \phi_J \rvert \sim \lvert \phi \rvert \lesssim M_\text{P}/\xi$, where $\phi$ is the inflaton in the Einstein frame. The spike time scale appears in the dynamics of $\phi_J$ and $\phi$. The dynamics of $\phi_J$ imprints this fast time scale in the following reason. $\phi_J$ and the scalar component of the metric have kinetic mixing due to the nonminimal coupling. For $\lvert \phi_J \rvert \gtrsim M_\text{P}/\xi$, this mixing term dominates over the original inflaton kinetic term $-g^{\mu\nu}_J \partial_\mu \phi_J\partial_\nu \phi_J/2$, and the kinetic term of the inflaton effectively changes at around $\lvert \phi_J \rvert \sim M_\text{P}/\xi$. Thus, the time scale $\Delta t_\mathrm{sp}$ is induced in the dynamics of $\phi_J$ as a change of the kinetic term. The dynamics of $\phi$ also imprints this fast time scale because the shape of the inflaton potential changes at around $\lvert \phi \rvert \sim M_\text{P}/\xi$. It appears as a peculiar behavior in, \textit{e.g.} the effective inflaton mass in the Jordan frame and the conformal factor when the inflaton passes through near the origin, which we call ``spike''-like feature. This peculiar feature has long been overlooked in the literature except for a few studies~\cite{Tsujikawa:1999me,DeCross:2015uza},\footnote{ We will clarify differences of our study from them in Secs.~\ref{sec:real} and~\ref{sec:global_U1}, respectively. } and has recently been investigated in detail by one of the present authors~\cite{J:kurorekishi}. In this paper, we point out that this feature causes much more violent particle production than previously thought. In particular, if the inflaton is gauge-charged, the production of the longitudinal gauge boson is significantly enhanced compared with that of the transverse gauge boson. The difference in the behavior of the longitudinal and transverse modes has already been pointed out in Ref.~\cite{Lozanov:2016pac} in the context of preheating without the nonminimal coupling, and we see that this difference becomes a significant one if the inflaton has a large nonminimal coupling to gravity. The energy transfer to the longitudinal mode is so violent that almost all the energy density of the inflaton can be transferred to the longitudinal gauge bosons within one oscillation after the end of inflation. The organization of this paper is as follows. In Sec.~\ref{sec_background}, we analyze the background dynamics in the Einstein frame. In Sec.~\ref{sec_pp}, we discuss particle production by this oscillating background, taking real, global U(1) charged, and gauge U(1) charged inflaton as examples. Sec.~\ref{sec_conc} is devoted to conclusions and discussion. | \label{sec_conc} \setcounter{equation}{0} In the present paper, we have analyzed the inflaton oscillating regime, or the preheating regime, of the inflation model with nonminimal coupling $\xi \phi^2 R$ between the inflaton $\phi$ and the Ricci scalar $R$, and with quartic potential $\lambda \phi^4/4$. We have pointed out that there are two typical mass scales (or inverse time scales) in the dynamics of the inflaton for $M_\text{P}/\xi \ll \Phi \ll M_\text{P}$ where $\Phi$ is the inflaton oscillation amplitude in the Einstein frame. One is the inflaton oscillation scale, \begin{align} m_\mathrm{osc} = \Delta t_\mathrm{osc}^{-1} \sim \frac{\sqrt{\lambda}M_\text{P}}{\xi}, \end{align} and the other is a much shorter time scale which we call the ``spike'' scale, \begin{align} m_\mathrm{sp} = \Delta t_\mathrm{sp}^{-1} \sim \sqrt{\lambda}\Phi, \end{align} which can be as high as $m_\mathrm{sp} \sim \sqrt{\lambda} M_\text{P}$ at the beginning of the inflaton oscillation. This time scale $\Delta t_\mathrm{sp}$ corresponds to the time interval at which the inflaton passes through the region with $\lvert \phi_J \rvert \sim \lvert \phi \rvert \lesssim M_\text{P}/\xi$ where $\phi$ ($\phi_J$) is the inflaton in the Einstein frame (Jordan frame). The spike scale appears in the dynamics of $\phi_J$ as a change of the kinetic term, while it appears in the dynamics of $\phi$ as a sudden change of the shape of the potential. We have found that several quantities such as the inflaton mass scale in the Jordan frame $m_{J\mathrm{eff}}^2$ or the conformal factor blow up during this time interval $\Delta t_\mathrm{sp}$ (see Figs.~\ref{fig:phi_mJ2} and~\ref{fig:ddOmega}). The mass scale of this blow-up $m_\mathrm{sp}$ is extremely high, $m_\mathrm{sp} \sim \sqrt{\lambda} M_\text{P}$ at the beginning of the inflaton oscillation, and this is why we call this feature as a ``spike'' in this paper. Some light particles inevitably couple to this spike-like feature, and hence we have studied particle production caused by it. What we have found is the following: \begin{itemize} \item In the case where the inflaton is a real scalar, the inflaton particle itself couples to the spike-like feature. Inflaton particles with momentum $\sim m_{\rm sp}$ are produced, though their energy density is far below that of the inflaton oscillation. If one introduce an additional light scalar field, it may be sizably produced by the spike-like feature of the conformal factor. \item In the case where the inflaton has a global U(1) charge, the production of the U(1) partner $\theta$ of the inflaton is so efficient that almost all the initial inflaton energy density is converted to $\theta$ within one oscillation for $\xi \gtrsim 9\times10^{2}$ or $\lambda \gtrsim 3\times10^{-4}$. \item In the case where the inflaton has a gauged U(1) charge, the longitudinal component of the gauge field plays the same role as $\theta$ in the global U(1) case. \end{itemize} Thus, the preheating dynamics of the inflation model with the nonminimal coupling to the gravity can be much more violent than previously thought. In this paper, we investigated only the very first stage of the preheating just after inflation. In order to fully understand the reheating phenomena, we must first take into account the back-reaction effects, which is expected to be important when Eqs.~(\ref{eq:cond_back}) or (\ref{eq:cond_back_gauge}) are satisfied. On top of that, we must take account of resonant amplification of the coupled fields and thermalization processes after that. A typical situation is that produced particles decay into lighter particles leading to efficient production of thermal plasma~\cite{Felder:1998vq} and then particles in thermal bath scatter off the inflaton~\cite{Mukaida:2012qn,Mukaida:2012bz}. The reheating is completed through these processes, which, however, is significantly model dependent, and hence it is beyond the scope of this paper to study the reheating dynamics till the end. Most of the discussion on the particle production in the gauged U(1) case holds true even for gauged SU(2) case. Hence our study is also relevant for the Higgs inflation: the production of gauge bosons with extremely high momenta are unavoidable. At this point, one may encounter a unitarity problem. Since the momentum scale of particles produced by the spike is extremely high ($\sim \sqrt{\lambda} M_\text{P}$), we must be careful on the cutoff scale of the theory~\cite{Lerner:2009na,Ferrara:2010in,Bezrukov:2010jz}. As noted in Refs.~\cite{Ferrara:2010in,Bezrukov:2010jz}, the cutoff scale depends on the inflaton field value and actually we can safely treat fluctuations during inflation. During the preheating stage, however, particles with momentum higher than the cutoff scale may be excited due to the spike, which may imply a difficulty to describe the reheating without some UV completion~\cite{Giudice:2010ka,Lerner:2010mq,Lerner:2011it}. It might be non-trivial to correctly estimate the cutoff of the energy scale under the rapidly oscillating background, but readers should keep in mind that the extremely high mass scale of the spike can invalidate the analysis of (p)reheating within the original framework, though a phenomenological consequence that the Higgs field is thermalized at very high temperature~\cite{Bezrukov:2008ut} might not be affected much. We will come back to this issue in a separate publication. Our results heavily rely on the fact that we have started from a simple action in the Jordan frame, \textit{i.e.}~the kinetic term and potential of the inflaton have minimal forms except for the nonminimal coupling $\xi |\phi|^2 R$. Instead, we could start with a \textit{minimal} kinetic term of the inflaton in the Einstein frame with a special form of the potential $V(|\phi|)$ suitable for inflation, as discussed in Ref.~\cite{Lerner:2010mq}. In such a case, the preheating is not as violent as the Jordan-frame-originated case. Interestingly, even if we start from the Einstein frame action, we can have a violent particle production due to a spike-like feature, once \textit{nonminimal} kinetic terms are introduced. As an example, let us consider the following action as assumed in the running kinetic inflation model~\cite{Takahashi:2010ky,Nakayama:2010kt}: \begin{align} S = \int \dd^4x \sqrt{-g}\left[\frac{M_\text{P}^2}{2}R -g^{\mu\nu}\partial_\mu\phi^\dagger \partial_\nu \phi -\frac{1}{M^2}g^{\mu\nu}\left(\partial_\mu |\phi|^2 \right)\left(\partial_\nu |\phi|^2 \right) - V(|\phi|)\right]. \end{align} In this model, the potential becomes effectively flatter for $\lvert \phi \rvert \gg M$, providing a good candidate for the inflaton potential. Inflation ends at around when $\lvert \phi \rvert \sim \sqrt{M_\text{P} M}$, and the inflaton oscillates at around the origin of the potential after that. During the inflaton oscillation regime, the kinetic term changes for $\lvert \phi \rvert \gg M$ and $\lvert \phi \rvert \ll M$, and hence there must be again a spike scale in this model. Thus, we expect that the situation is similar to the case of the inflaton dynamics in the Jordan frame. In particular, the U(1) partner of the inflaton is expected to feel the strong spike and violently produced. It may be interesting to study further on how the spike scale affects the preheating dynamics in this class of models. Finally we comment on the Starobinsky inflation model~\cite{Starobinsky:1980te}, \begin{align} S = \int \dd^4x \sqrt{-g_J}\frac{M_\text{P}^2}{2}\left[ R_J + \frac{R_J^2}{2M^2}\right]. \end{align} In this case, by introducing an auxiliary field $\phi_J$, we can rewrite the action as \begin{align} S = \int \dd^4x \sqrt{-g_J}\frac{M_\text{P}^2}{2}\left[f(\phi_J) + f'(\phi_J)\left(R_J - \phi_J\right)\right], ~~ f(\phi_J) = \phi_J + \frac{\phi_J^2}{2M^2}, \end{align} where the prime denotes the derivative with respect to $\phi_J$. It is clear from the above action that the inflaton (or scalaron) $\phi_J$ has only kinetic mixing with the scalar component of the metric through the nonminimal coupling, and hence there does not appear any spike scale in this model. Thus, although the prediction for the scalar and tensor fluctuations is similar for the Starobinsky and Higgs inflation models, the reheating dynamics can be much different between them. | 16 | 9 | 1609.05209 |
1609 | 1609.05723_arXiv.txt | The spectral line polarization encodes a wealth of information about the thermal and magnetic properties of the solar atmosphere. Modeling the Stokes profiles of strong resonance lines is, however, a complex problem both from the theoretical and computational point of view, especially when partial frequency redistribution (PRD) effects need to be taken into account. In this work, we consider a two-level atom in the presence of magnetic fields of arbitrary intensity (Hanle-Zeeman regime) and orientation, both deterministic and micro-structured. Working within the framework of a rigorous PRD theoretical approach, we have developed a numerical code which solves the full non-LTE radiative transfer problem for polarized radiation, in one-dimensional models of the solar atmosphere, accounting for the combined action of the Hanle and Zeeman effects, as well as for PRD phenomena. After briefly discussing the relevant equations, we describe the iterative method of solution of the problem and the numerical tools that we have developed and implemented. We finally present some illustrative applications to two resonance lines that form at different heights in the solar atmosphere, and provide a detailed physical interpretation of the calculated Stokes profiles. We find that in strong resonance lines sensitive to PRD effects the magneto-optical $\rho_V$ terms of the Stokes-vector transfer equation produce conspicuous $U/I$ wing signals along with a very interesting magnetic sensitivity in the wings of the linear polarization profiles. We also show that the weak-field approximation has to be used with caution when PRD effects are considered. | \label{sec_intro} The most important physical observable for probing the thermal, dynamic, and magnetic properties of stellar atmospheres is the emerging radiation. Aside from its intensity, the radiation is characterized by a given polarization state, which contains crucial information about the magnetic fields present in the atmosphere. Although the magnetic field is known to play a key role in the atmosphere of the Sun and other stars, our empirical knowledge of its intensity and orientation is still largely unsatisfactory, and basically limited to the deepest layers (the photosphere). This explains the importance of developing new techniques for magnetic field diagnostics, based on the accurate measurement and interpretation of the polarization properties of the radiation field. Each line of the solar spectrum gives information on the physical properties of the solar atmosphere at a certain height range, depending on the opacity of the atmosphere at the frequency of the line in question. As examples, the Sr~{\sc i} line at 4607~{\AA} can be used to obtain information on the Sun's photosphere \citep[e.g.,][]{Trujillo+04}, while the lower chromosphere can be studied via the Sr~{\sc ii} line at 4078~{\AA} \citep[e.g.,][]{Bianda+98}. Interpreting these Stokes profiles requires solving a radiative transfer problem out of local thermodynamic equilibrium (non-LTE), which becomes more complex if, besides the well-known Zeeman effect, we wish to model the impact of scattering polarization and its modification due to the presence of a magnetic field (Hanle effect). \newline A solid theory for the generation and transfer of polarized radiation, based on a first-order perturbative expansion of the atom-radiation interaction within the framework of quantum electrodynamics, is today available \citep[e.g.,][hereafter LL04]{BLandiLandolfi2004}. Within this theory, the scattering of a photon, which is intrinsically a second-order process, is described as a temporal succession of independent absorption and re-emission processes (Markov approximation). This case, generally referred to as the limit of complete frequency redistribution (CRD) is strictly correct either when collisions are extremely efficient in relaxing any possible correlation between the frequencies of the incoming and outgoing photons, or when the pumping field is spectrally flat \citep[e.g.,][]{CasiniLandi07}. Nonetheless, it can be shown that even when the above-mentioned conditions are not strictly verified, the limit of CRD represents in any case a suitable approximation for modeling the center of the spectral lines, where the Hanle effect takes place. This theory, on the other hand, turns out to be unsuitable to model the wings of strong spectral lines, where coherent scattering and partial frequency redistribution (PRD) effects play a fundamental role. Different theoretical approaches suitable to describe coherent scattering processes have been proposed during the last years.\footnote{ By ``coherent scattering'' we mean here a scattering process in which the frequencies of the absorbed and emitted photons are either identical (if the initial and final states coincide), or satisfy the Raman scattering rule (if the initial and final states differ). In this sense, coherent scattering is strictly valid in the atomic reference frame, when the atom does not interact with any other particle (collisionless regime), and when the lower level can be assumed to be infinitely sharp (which is generally a good approximation when this is either the ground or a metastable level).} One is based on the Kramers-Heisenberg scattering formula. This approach was initially proposed by \cite{Stenflo94}, and it has been recently extended to increasingly complex atomic models in the presence of arbitrary magnetic fields \citep[e.g.,][]{Sowmya14,Sowmya15}. Another approach, also suitable to describe complex atomic models in the presence of arbitrary magnetic fields, is based on the heuristic idea of metalevels \citep[see][]{Landi+97}. A new quantum mechanical approach, capable of considering higher-order processes through a diagrammatic treatment of the atom-radiation interaction, has been recently proposed by \cite{Casini+14}.\newline The coherency of scattering can be relaxed through two different physical mechanisms: the Doppler effect and collisional processes. Doppler redistribution must always be considered when going from the atomic frame to the observer's one. Its inclusion in the above-mentioned approaches does not present particular difficulties from the theoretical point of view, although it leads to rather complex mathematical expressions. On the contrary, the generalization of these approaches so to include collisional processes is not trivial, and it is still under investigation. A theoretical approach based on a perturbative expansion of the atom-radiation interaction, which includes collisional redistribution, has been proposed by \cite{Bommier97a,Bommier97b} for the case of a two-level atom. This approach, which is based on the redistribution matrix formalism, is the starting point of our work. We consider a two-level model atom with an unpolarized and infinitely sharp lower level. This atomic model is not only of academic interest, but is suitable to model various strong resonance lines of diagnost relevance, such as the Sr~{\sc i} line at 4607~{\AA}, or the Ca~{\sc i} line at 4227~{\AA}. Indeed, we observe that the lower levels of these lines, having total angular momenta $J=1/2$ and $J=0$, respectively, cannot be polarized (in particular, they cannot carry atomic alignment) by definition\footnote{Note that levels with $J=1/2$ can be polarized (they can carry atomic orientation) if the incident radiation is circularly polarized. In this work, we asume that collisional depolarization is always sufficiently strong so to destroy any atomic orientation that might be induced in the (long-lived) lower level of these resonance lines}. Moreover, these levels are the ground levels of the corresponding atomic species, so that the assumption that they are infinitely sharp is a very good approximation. In this work the solar atmosphere is modeled as one-dimensional, static, and plane-parallel. Though considering the atmosphere as dynamic and three-dimensional is a much more realistic treatment for the generation and transfer of polarized radiation, the approach presented here is a suitable first step, in which much faster calculations can be performed, yielding many insights into the physical mechanisms involved. In Sect.~\ref{sec_form}, we present the starting equations, written in the atomic reference frame, with the quantization axis directed along the magnetic field, and we discuss their transformation into an arbitrary reference frame. Obtaining the emergent intensity and polarization requires finding the self-consistent solution of the statistical equilibrium (SE) equations for the atomic state, and of the radiative transfer (RT) equations.\footnote{ This investigation is carried out within the framework of the redistribution matrix formalism. We recall that the redistribution matrix is based on an analytical solution of the SE equations, which therefore do not explicitly appear in the problem, when this formalism is applied.} This is done through an iterative method that is described in Sect.~\ref{sec_iter}, together with the numerical tools that have been developed and implemented, considering the particular characteristics of the problem under investigation. When PRD phenomena are taken into account, the emitted radiation at a given frequency does not depend only on the incoming radiation at that specific frequency (as would happen for coherent scattering), nor does it depend on a frequency-averaged radiation field (as in CRD). In consequence, the iterative scheme has to consider that all frequencies are coupled to one another in the scattering process. The possiblity of having a magnetic field which is micro-structured, and its effect in this radiative transfer problem is discussed in Sect.~\ref{sec_micro}. In Sect.~\ref{sec_res} we present some illustrative applications to some lines of diagnostic interest, based on the theory and numerical methods discussed in this paper. | In order to correctly model the scattering polarization signals of strong resonance lines in an optically thick plasma, in the presence of magnetic fields of arbitrary intensity and orientation, it is necessary to solve a complex non-LTE radiative transfer problem, taking into account the joint action of the Hanle and Zeeman effects, as well as the impact of PRD phenomena. In this work, we have considered the theoretical approach of \cite{Bommier97a,Bommier97b}, which is capable of accounting for all these physical ingredients, and we have developed and applied a series of numerical methods required for the efficient and accurate solution of the equations involved. The resulting radiative transfer code provides a new tool for solar and stellar spectropolarimetry. It considers a two-level atomic model with an unpolarized and infinitely sharp lower level, which is suitable for investigating the magnetic sensitivity of several resonance lines of diagnostic interest such as Sr~{\sc ii} $4078$~{\AA}, Sr~{\sc i} $4607$~{\AA}, or Ca~{\sc i} $4227$~{\AA}. The above-mentioned theoretical approach is based on the redistribution matrix formalism. The total redistribution matrix is given by a linear combination of two terms: one describing coherent scattering processes (${\mathcal R}_{\mbox{\sc \footnotesize II}}$) and another describing scattering processes in the limit of complete frequency redistribution (${\mathcal R}_{\mbox{\sc \footnotesize III}}$). We have started from the expressions provided in \cite{Bommier97b}, valid in the atomic frame, taking the quantization axis directed along the magnetic field. We have shown how to rotate them in a reference system with the quantization axis directed along an arbitrary direction, and how to transform them from the atomic rest frame into the frame of the observer. The expressions corresponding to the case in which a magnetic field that changes its direction over scales smaller than the line photon's mean free path have also been studied. We have presented illustrative results for the Sr~{\sc i} photospheric line at 4607~{\AA} and for the Sr~{\sc ii} chromospheric line at 4078~{\AA}, and in forthcoming publications we will describe in detail other interesting applications to the $k$ line of Mg~{\sc ii} at 2795 \AA\ and to the Ca~{\sc i} line at 4227 \AA. The main results are the following: \begin{itemize} \item{{\it The impact of PRD phenomena}. Calculations accounting for the effects of PRD have been compared to those in the CRD limit, in order to quantitatively evaluate the suitability of this approximation. In photospheric lines without significant wings such as Sr~{\sc i} 4607 \AA , we can confirm that the CRD limit is a very good approximation for modeling the intensity and scattering polarization. Nevertheless for strong chromospheric lines, with extended wings outside the Doppler core, such as Sr~{\sc ii} 4078 \AA\, the impact of PRD phenomena is very significant, especially in the near wings. The resulting scattering polarization profiles show extended wings and complex multi-peak structures. Such profiles cannot be found in the limit of CRD, which however keeps representing a quite good approximation for modeling the line-center amplitude of both intensity and scattering polarization signals. While in the atomic reference frame coherent scattering effects play an important role also in the line center, in the observer's frame the effects of Doppler redistribution cause the CRD approximation to be suitable to estimate the polarization at the line center. But in the near wings the effects of PRD need to be taken into account, for both the intensity and the emergent scattering polarization.} \item{{\it The weak-field approximation in the general PRD case}. In another application to the Sr {\sc ii} 4078 \AA\ line we compared the results obtained when applying the weak field approximation with the results of our Hanle-Zeeman calculation. While in the line core the resulting scattering polarization signals agree, in the wings we find that the results for the weak-field approximation become inaccurate, since artificial signals are found when neglecting the Zeeman splitting in the absorption and emission profiles.} \item{{\it Magneto-optical effects in the general PRD case}. Furthermore, we have found that in strong resonance lines for which PRD effects produce sizable $Q/I$ wing signals, such as that of Sr {\sc ii} at 4078 \AA, a novel physical mechanism operates that creates $U/I$ wing signals and introduces a very interesting magnetic sensitivity in the wings of the $Q/I$ and $U/I$ profiles. This magnetic sensitivity has nothing to do with the Hanle effect, nor with the Zeeman effect in emission. Instead, we conclude that it is caused by magneto-optical effects; in particular, by the coupling between Stokes $Q$ and $U$ due to the $\rho_V$ term of the propagation matrix as the radiation propagates through the magnetized solar atmosphere.} \end{itemize} | 16 | 9 | 1609.05723 |
1609 | 1609.08351_arXiv.txt | Energy levels, radiative rates (A-values) and lifetimes, calculated with the {\sc grasp} code, are reported for an astrophysically important O-like ion Mg~V. Results are presented for transitions among the lowest 86 levels belonging to the 2s$^2$2p$^4$, 2s2p$^5$, 2p$^6$, and 2s$^2$2p$^3$3$\ell$ configurations. There is satisfactory agreement with earlier data for most levels/transitions, but scope remains for improvement. Collision strengths are also calculated, with the {\sc darc} code, and the results obtained are comparable for most transitions (at energies above thresholds) with earlier work using the DW code. In thresholds region, resonances have been resolved in a fine energy mesh to determine values of effective collision strengths ($\Upsilon$) as accurately as possible. Results are reported for all transitions at temperatures up to 10$^6$~K, which should be sufficient for most astrophysical applications. However, a comparison with earlier data reveals discrepancies of up to two orders of magnitude for over 60\% of transitions, at all temperatures. The reasons for these discrepancies are discussed in detail. | Spectral lines of Mg~V are frequently observed from a wide range of astrophysical plasmas, including the Sun (see for example, \cite{fd}, \cite{sand}, \cite{tom}, \cite{dhb}), other stars \cite{pens}, and planetary nebulae \cite{rus}. Similarly, Mg~V lines have also been detected from laboratory plasmas (\cite{hg}, \cite{kart}). Since many emission line pairs of Mg~V are density or temperature sensitive \cite{pry}, they provide excellent diagnostics for astrophysical plasmas. However, the analysis of observations requires information on atomic data, such as energy levels, radiative rates (A-values), and excitation rates which are obtained from the collision strengths ($\Omega$). Measurements of energy levels for Mg~V have been compiled and assessed by \cite{mz} and their recommended values are available on the NIST (National Institute of Standards and Technology) website {\tt http://www.nist.gov/pml/data/asd.cfm}. However, to our knowledge there are no measurements for the A-values and $\Omega$, and therefore theoretical results for these are required. Early calculations for $\Omega$ (and effective collision strengths $\Upsilon$) for Mg~V were performed by \cite{cmz} and \cite{bz}, but only for transitions among levels of the $n$=2 configurations. Their results are not sufficient for the analysis of observed lines in the x-ray region, because these arise from levels of the $n$=3 configurations \cite{ble}. Therefore, \cite{hud} extended the work to include 37 levels of the 2s$^2$2p$^4$, 2s2p$^5$, 2p$^6$, 2s$^2$2p$^3$3s, and 2s$^2$2p$^3$3p configurations. They adopted the Breit-Pauli $R$-matrix method of \cite{scot}, although their calculations were primarily in $LS$ coupling (Russell-Saunders or spin-orbit coupling). However, for a lowly ionised ion, such as Mg~V, this method should not affect the accuracy of the calculated data, because relativistic effects are not too important. Furthermore, \cite{hud} resolved resonances in a narrow energy mesh and presented values of $\Upsilon$ over a wide temperature range, up to 10$^7$~K. However, a much larger calculation involving 86 levels of the 2s$^2$2p$^4$, 2s2p$^5$, 2p$^6$, and 2s$^2$2p$^3$3$\ell$ configurations, has already been reported by \cite{ble}. For the calculation of energy levels they adopted the {\em SuperStructure} (SS) code and considered up to 24 configurations ($n \le$ 4). However, for the scattering calculations, their wavefunctions were rather basic (among the above listed six configurations) and hence the discrepancies between the calculated energies and the NIST compilation are significant for several levels, in both magnitude and orderings -- see table 1 of \cite{ble}, and note particularly the position of the 2p$^6$~$^1$S$_0$ level. More importantly, they calculated their data for $\Omega$ at only five energies, in the 10--50~Ryd range, with the {\em distorted wave} (DW) method, and did not consider resonances in the thresholds region. Since resonances for transitions in Mg~V are very important (see section 5), the results obtained for $\Upsilon$ from their calculated values of $\Omega$ are likely to be highly underestimated for many transitions, particularly non-dipole allowed ones. Therefore, recently \cite{sst} have performed yet another calculation for Mg~V. They have considered the same 86 levels of the six configurations as by \cite{ble}, but have made several improvements over their work. For the determination of atomic structure (i.e. to calculate energy levels and A-values) they adopted the multi-configuration Hartree-Fock (MCHF) code of \cite{mchf}, used non-orthogonal orbitals up to $n$=5 ($\ell \le$ 4), and included very large {\em configuration interaction} (CI), up to 5179. As a result, the accuracy of their calculated energy levels is much better -- see their table 1. Advantages of this methodology (over the use of orthogonal orbitals) include the determination of accurate energy levels, but avoidance of pseudo resonances in the subsequent scattering calculations, as faced by \cite{hud}. However, the inclusion of such a large CI is not feasible in the scattering calculations, due to computational limitations. Therefore, \cite{sst} had to make a compromise by reducing the CI to 427 configurations, and the energies obtained with this reduced model are not too different from the larger one -- see their table~1. For the calculation of $\Omega$, \cite{sst} adopted the B-spline $R$-matrix (BSR) code developed by \cite{zat}. They included a moderately large range of partial waves with angular momentum $J$ up to 29.5, but calculated $\Omega$ over a wide energy range up to 50~Ryd. To resolve resonances in the thresholds region they considered up to as narrow an energy mesh as 0.000~05~Ryd, and reported values of $\Upsilon$ up to T$_e$ = 10$^6$~K. Therefore, their calculated results not only cover a larger range of transitions, but would be expected to be the most accurate. Hence, there should be no strong reason to perform yet another calculation for Mg~V. However, they conclude that they observed a good agreement for most transitions between their results of $\Upsilon$ and those of \cite{hud}. We do not find this to be true (as discussed below), and hence have undertaken a further calculation. In Fig. 1 (a, b and c) we show comparisons of $\Upsilon$ calculated by \cite{hud} and \cite{sst}, referred to as RM1 and RM2 for convenience, at three temperatures of 10$^4$, 10$^5$, and 10$^6$~K. These are shown as the ratio (R) of $\Upsilon_{RM2}$/$\Upsilon_{RM1}$, with negative values indicating $\Upsilon_{RM1}$/$\Upsilon_{RM2}$. Two conclusions can be easily drawn from this figure. First, the discrepancies are large (up to two orders of magnitude) for a significant number of transitions ($\sim$80\%), and second the agreement worsens with increasing T$_e$. It is interesting to note that at T$_e$ = 10$^6$~K, the $\Upsilon_{RM1}$ of \cite{hud} are much larger than those of \cite{sst}, whereas the opposite would be expected, because the RM2 calculations included more levels, and hence significantly more resonances. We discuss these comparisons in more detail below to try to understand the reasons for the discrepancies. At T$_e$=10$^4$~K, the $\Upsilon_{RM2}$ are larger than $\Upsilon_{RM1}$ for many transitions, by up to two orders of magnitude. Differences between the two sets of $\Upsilon$ are greater than 20\% for 83\% of transitions. For only a few, $\Upsilon_{RM1}$ are larger than $\Upsilon_{RM2}$, by a maximum of a factor of 40. Although 10$^4$~K is a comparatively low temperature at which the positions and magnitudes of resonances are very important, the differences between the two sets of $\Upsilon$ are still very large, considering that both calculations resolved resonances in a fine energy mesh, i.e. 0.0008~Ryd in RM1 and 0.000~05~Ryd in RM2. The most noticeable discrepancies seen in Fig. 1a are for the transitions: 5--10 (2s$^2$2p$^4$~$^1$S$_0$ -- 2s$^2$2p$^3$3s~$^5$S$^o_2$ : R = 430, out of scale), 5--31 (2s$^2$2p$^4$~$^1$S$_0$ -- 2s$^2$2p$^3$3p~$^3$F$_2$ : R = 60), 5--32 (2s$^2$2p$^4$~$^1$S$_0$ -- 2s$^2$2p$^3$3p~$^3$F$_3$ : R = 92), 5--33 (2s$^2$2p$^4$~$^1$S$_0$ -- 2s$^2$2p$^3$3p~$^3$F$_4$ : R = 126), and 5--34 (2s$^2$2p$^4$~$^1$S$_0$ -- 2s$^2$2p$^3$3p~$^1$F$_3$ : R = 60). All these are forbidden transitions and therefore the number and magnitude of resonances may considerably affect the determination of $\Upsilon$. We also note that the ordering (labelling) of these levels is that given in Table~1 (but slightly different from RM1 and RM2, which position the 2s$^2$2p$^3$3s~$^5$S$^o_2$ level at number 11), but there is no ambiguity in comparing results. Since the discrepancy is greatest for the 5--10 transition, we focus our attention on this alone. The background value of $\Omega$ ($\Omega_B$) for this transition in the thresholds region is $\sim$10$^{-3}$ in our calculations (see section 4) and is $\sim$10$^{-8}$ at energies well above the thresholds, comparable to the DW results of \cite{ble}, and resonances are neither too numerous nor too large in magnitude. Subsequently, our values of $\Upsilon$ for this transition are $\sim$10$^{-3}$ (see Table~5 in section 5). However, the corresponding $\Upsilon$ of RM1 and RM2 are lower and higher, respectively, than our result by about an order of magnitude, and hence the discrepancies. If \cite{sst} have some very large resonances close to the threshold, then their $\Upsilon$ may be considerably higher towards the lower end of T$_e$. Indeed this is the case as may be noted from Fig. 1 (b and c), because the discrepancies have decreased with increasing temperature. At T$_e$=10$^5$~K, the RM1 and RM2 values of $\Upsilon$ differ for 79\% of transitions by over 20\%, and in most cases the results of \cite{sst} are larger, as seen in Fig. 1b. However, at T$_e$=10$^6$~K the trend has reversed, as for most transitions the $\Upsilon$ of \cite{hud} are larger by up to three orders of magnitude (note that a few transitions are out of scale in Fig.~1c). This is not expected (as noted already) and the greatest discrepancies are for the transitions: 16--24 (2s$^2$2p$^3$3p~$^5$P$_1$ -- 2s$^2$2p$^3$3s~$^3$P$^o_1$ : R = 980), 16--25 (2s$^2$2p$^3$3p~$^5$P$_1$ -- 2s$^2$2p$^3$3s~$^3$P$^o_2$ : R = 980), and 18--34 (2s$^2$2p$^3$3p~$^5$P$_3$ -- 2s$^2$2p$^3$3p~$^1$F$_3$ : R = 820). The first two are inter-combination transitions (but very weak as their f-values are 3.6$\times$10$^{-8}$ and 1.6$\times$10$^{-7}$, respectively) whereas the third is forbidden. A temperature of 10$^6$~K corresponds to $\sim$6.3~Ryd and the above transitions are close to the highest level (37) considered by \cite{hud}. Hence, the contribution of resonances (if any) should not be too significant. Clearly, the $\Upsilon$ of \cite{hud} are overestimated at high values of T$_e$, because they calculated data for $\Omega$ only up to 28~Ryd, but determined $\Upsilon$ up to T$_e$ = 10$^7$~K, i.e. $\sim$63~Ryd. There is no mention in their paper if they extrapolated values of $\Omega$ to high energies, but one of the authors (Cathy Ramsbottom) confirms that they did not. An inspection of the $\Upsilon$ values of \cite{hud} over a wide temperature range also indicates they are overestimated at high T$_e$, because for many transitions (such as: 16--24, 16--25, 17--34, 18--32, and 18--34) their results increase by (almost) up to three orders of magnitude between the lowest (10$^3$~K) and the greatest (10$^7$~K) temperature. Values of $\Upsilon$ are not (generally) known to vary so largely. Additionally, these transitions are either weak inter-combination or forbidden, and therefore their values of $\Omega$ and subsequently $\Upsilon$ should decrease considerably with increasing energy/temperature. This is indeed the case with the results of \cite{ble} and \cite{sst}, or in our calculations -- see Table~5 in section 5. In conclusion, we may confidently state that the results of \cite{hud} are overestimated, at least at high T$_e$. We therefore do not discuss their results further. The temperature range below 10$^6$~K is most important for the analysis of astrophysical observations of Mg~V lines \cite{ble}, and unfortunately there are large discrepancies between the values of $\Upsilon$ calculated by \cite{hud} and \cite{sst}, as shown in Fig. 1 and discussed above. Additionally, we have reason to suspect the accuracy of the results for $\Upsilon$ reported by \cite{sst}, but will discuss these in detail more appropriately in section 5. Therefore, we have performed one more calculation for this important ion, and for consistency as well as for practical (computational) reasons include the same 86 levels as by \cite{sst}. However, our approach is different (but similar) from their work because for the generation of wavefunctions we have adopted the fully relativistic {\sc grasp} (General-purpose Relativistic Atomic Structure Package) code, originally developed by \cite{grasp0}, but significantly revised by Dr. P. H. Norrington. It is a fully relativistic code, based on the $jj$ coupling scheme. Further higher order relativistic terms arising from the Breit interaction and QED (quantum electrodynamics) effects (vacuum polarisation and Lamb shift) have also been included in the same way as described in the original version. Additionally, we have used the option of {\em extended average level} (EAL), in which a weighted (proportional to 2$j$+1) trace of the Hamiltonian matrix is minimised. This produces a compromise set of orbitals describing closely lying states with moderate accuracy, and generally yields results comparable to other options, such as {\em average level} (AL). Finally, energy levels and radiative data determined with {\sc grasp} are generally comparable with those obtained with other codes, such as CIV3, FAC, MCHF, and SS, provided similar CI is included. A particularly useful feature of the adopted version is that it also has provisions for listing the $LSJ$ designations of the levels/configurations, apart from the usual $jj$ nomenclature of the relativistic codes. This feature helps in correctly identifying the states/levels and facilitates direct comparisons with other calculations. Another useful advantage of this version is that its output can be directly linked to the collisional code (i.e. the {\em Dirac atomic R-matrix code}, DARC), adopted here for the scattering calculations. This code also includes the relativistic effects in a systematic way, in both the target description and the scattering model, because it is based on the $jj$ coupling scheme, and uses the Dirac-Coulomb Hamiltonian in the $R$-matrix approach. However, the code does not include the Breit and QED corrections, and hence the target energies obtained are slightly different (and comparatively less accurate) than from {\sc grasp}. A disadvantage of this code is that the calculations are more time consuming because the size of the Hamiltonian matrix is large, due to the inclusion of fine-structure in the definition of channel coupling. On the other hand, an advantage of the code is that resonances arising in between the fine-structure levels of a state can be included, and hence improving the further calculations of effective collision strengths -- note particularly the ground state levels (2s$^2$2p$^4$~$^3$P$_{0,1,2}$) in Table~1. Both the atomic structure and scattering codes, i.e. {\sc grasp} and {\sc darc}, are hosted at the website: \\{\tt http://amdpp.phys.strath.ac.uk/UK\_APAP/codes.html}. Finally, we stress that although we have adopted fully relativistic codes for calculations of both atomic structure and collisional parameters, the relativistic effects are not too important for a comparatively light ion such as Mg~V. | In this paper we have reported energies and lifetimes for the lowest 86 levels of the 2s$^2$2p$^4$, 2s2p$^5$, 2p$^6$, and 2s$^2$2p$^3$3$\ell$ configurations of Mg~V. Differences with the compiled experimental energies of NIST are within 0.1~Ryd for most levels, except 2p$^6$~$^1$S$_0$ for which our result is higher by 0.4~Ryd. In addition, the ordering of levels also slightly differs in a few instances. Similarly, there is a good agreement (within 20\%) between our calculated values of $\tau$ and those of \cite{tff} (available on the web) for most levels, and differences for a few are within a factor of two, due to the corresponding differences in the A-values. Radiative rates for E1. E2, M1, and M2 transitions are also provided and there is a good agreement with other available theoretical results for E1 transitions. Although scope remains for improvement in the accuracy of the reported data, due to computational restraints it is not possible in the present work, bearing in mind our further calculations for the more important collisional parameters. Collision strengths have been calculated with the fully relativistic {\sc darc} code and are listed for all transitions, from ground to higher excited levels, at energies up to 30~Ryd. Furthermore, resonances in the thresholds region have been resolved in a fine energy mesh (0.0001~Ryd) to determine $\Upsilon$ values at temperatures up to 10$^6$~K, sufficient for applications to the modelling of a variety of plasmas. Similar results for the same number of transitions and with the $R$-matrix code (BSR) are available \cite{sst}, but discrepancies between the two sets of data are significant (up to two orders of magnitude) for over 60\% of the transitions, and at all temperatures. In some cases the earlier $\Upsilon$ are larger, but for a majority of transitions our results are higher. These discrepancies have been discussed in detail and the likely reasons for them include: pseudo resonances, overestimation in the values of $\Omega$ at higher energies, and incorrect trends in the behaviour of transitions. Based on a number of comparisons, the earlier values of $\Upsilon$ by \cite{sst} are assessed to be inaccurate. Some discrepancies between the present and \cite{sst} sets of $\Upsilon$ are expected because the atomic structures are different. However, the scale of the discrepancies cannot be explained by differences in the atomic structure alone. For example, discrepancies in $\Upsilon$ for the allowed transitions are not proportionate to the corresponding differences in the f-values. Similarly, for many forbidden transitions (including the weak(er) ones), the $\Upsilon$ trends of \cite{sst} cannot be correct, because their results significantly increase with increasing temperature whereas the reverse is expected. Our presented results for $\Upsilon$ are probably the best available todate and therefore, we believe, should be adopted for the modelling and diagnostics of plasmas. However, scope remains for improvement. Apart from improving the accuracy of the wavefunctions, the main scope is in expanding the collisional calculations to all 226 levels of Mg~V. This will definitely improve the accuracy of transitions, particularly among the higher levels, because all remaining 140 levels lie just above the lowest 86 and at energies below 13.7 ~Ryd. Resonances arising from these levels will significantly contribute to the calculations of $\Upsilon$. Unfortunately our present computational resources are inadequate to undertake such a large calculation, but that may be possible sometime in the future. | 16 | 9 | 1609.08351 |
1609 | 1609.01793_arXiv.txt | { We present a brief qualitative overview of the current state of the problem of Hubble expansion at the sufficiently small scales (e.g.,~in planetary systems or local intergalactic volume). The crucial drawbacks of the available theoretical treatments are emphasized, and the possible ways to avoid them are outlined. Attention is drawn to a number of observable astronomical phenomena that could be naturally explained by the local Hubble expansion. } | \label{sec:Introduction} The problem of small-scale cosmological effects has a long history: the question if planetary systems are affected by the universal Hubble expansion was posed by McVittie as early as 1933~\cite{mvi33}, i.e., approximately at the same time when the concept of Hubble expansion became the dominant paradigm in cosmology. Although this question never was a hot topic, the corresponding papers occasionally appeared in the astronomical literature in the subsequent eight decades~\cite{and95,coo98,dav03,dic64,dom01,ein45,far07,kli05,lin05,% noe71,ser07}. Using quite different physical models and mathematical approaches, most of these authors arrived at the negative conclusions. As a result, it is commonly believed now% \footnote{ One of a few exceptions is a~short review by Bonnor~\cite{bon00}, which appealed for a~critical reconsideration of the available studies. } that Hubble expansion should be strongly suppressed or absent at all at the sufficiently small scales, for example, in planetary systems or inside galaxies. However, a surprising thing is that the commonly-used arguments not only prohibit the local Hubble expansion but also strongly contradict each other. For example, the most popular criterion for the suppression of Hubble expansion (especially, among the observational astronomers) is just a gravitational binding of the system, e.g., determined by the virial theorem of classical mechanics~\cite{lan76}. Namely, if mass of the particles concentrated in the system becomes so large that the corresponding energy of gravitational interaction approaches by absolute value the double kinetic energy, then orbits of the particles should be bounded, i.e., no overall expansion of\, the\, system\, is\, possible.\, In\, other\, words,\, just\, the\, classical\, forces\, of gravitational attraction\, break\, the\, global\, Hubble\, flow\, in\, the\, regions\, of\, local\, mass\, enhancement. \begin{figure}[t] \begin{center} \includegraphics[width=7cm]{E-S_Th_2} \medskip \caption{\label{fig:E-S_th_2} Schematic illustration of Einstein--Straus theorem.} \end{center} \end{figure} On the other hand, yet another well-known theoretical argument against the local Hubble expansion, based on the self-consistent theoretical analysis in the framework of General Relativity~(GR), is the so-called Einstein--Straus theorem~\cite{ein45}, illustrated in Figure~\ref{fig:E-S_th_2}: Let us consider a uniform distribution of the background matter with density~$ \rho $ and then assume that substance in a spherical volume with radius~$ R $ is cut off and concentrated in its center, thereby forming the point-like mass~\hbox{$ M \! = ( 4 \pi / 3 ) R^3 \rho $}. Then, according to the this theorem, there will be no Hubble expansion inside the empty cavity, but the Hubble flow is restored again beyond its boundary with the background matter distribution (and this boundary itself moves exactly with Hubble velocity). It is important to emphasize that, as distinct from the first criterion, there is no any excessive mass in the above-mentioned sphere and, moreover, the Hubble expansion is absent just in the empty space rather than in the region of mass enhancement. In\, principle,\, this\, fact\, is\, quite\, natural:\, according\, to\, the\, standard\, GR\, formula, Hubble constant~$ H $ is related to the local energy density~$ \rho $ in the spatially-flat Universe as% \footnote{ We use everywhere the system of units where the speed of light is equal to unity ($ c \equiv 1 $) and, therefore, there is no difference between the mass- and energy-density. } \begin{equation} \label{eq:Hubble_const} H = \, \sqrt{\frac{8 \pi G}{3} \, \rho } \: , \end{equation} where $ G $~is the gravitational constant. So, from the relativistic point of view, it is not surprising that Hubble constant tends to zero when the energy density disappears% \footnote{ Of course, strictly speaking, formula~(\ref{eq:Hubble_const}) is applicable only to the totally uniform Universe. }. Therefore, the above discussion demonstrates that the attempts to treat the problem of local Hubble expansion in terms of the classical gravitational forces can be very misleading. Indeed, the global Hubble expansion exists even in the perfectly-uniform Universe, where there are no any ``classical'' gravitational forces at all (since such forces can be produced only by nonhomogeneity of mass distribution). In other words, it should be kept in mind that Hubble expansion corresponds to another ``degree of freedom'' of the relativistic gravitational field as compared to the degrees of freedom reduced to the classical gravitational forces. Unfortunately, a lot of textbooks tried to estimate the local Hubble expansion in terms of the ``classical'' gravity or just \textit{postulated} its absence in the small-scale systems. A typical example is the famous textbook~\cite{mis73}, where the behavior of small-scale systems (galaxies) in the globally-expanding Universe was pictorially described as a set of coins pinned to the surface of an inflating ball (see Figure~27.2 in the above-cited book), but no justification for such a picture was given. | \label{sec:Conclusion} \begin{enumerate} \item Despite a lot of theoretical works rejecting the possibility of local Hubble expansion, we believe that this problem is still unresolved: Firstly, the available arguments often contradict each other. Secondly, the most of them become inapplicable to the case when the Universe is dominated by the perfectly-uniform dark energy (or~$ \Lambda $-term). Moreover, a~self-consistent theoretical treatment of the simplest models (such as the restricted two-body problem against the $ \Lambda $-background) demonstrates a~principal possibility of the local cosmological influences: the Hubble expansion is not suppressed completely in the vicinity of a~massive body. \item A few long-standing problems in planetology, geophysics, and celestial mechanics can be well resolved by the assumption of local Hubble expansion whose rate is comparable to that at the global scales. It is quite surprising that many theorists believe that the possibility of local cosmological influences is strictly prohibited just by the available observational data, while a~lot of observers believe that there are irrefutable theoretical proofs that Hubble expansion is absent at small scales. \item However, the important conceptual question still persists: What is the spatial scale from which the cosmological expansion no longer takes place? This is of crucial importance since otherwise, as pictorially explained by Misner et al.~\cite[p.\,719]{mis73}, the ``meter stick'' will also expand and, therefore, it will be meaningless to speak about any expansion at all... We cannot give a definitive numerical answer to this question. However, we believe that the systems dominated by non-gravitational interactions should not experience the cosmological expansion (e.g.,~the meter stick, the solid Earth, etc. do not expand). \end{enumerate} \pagebreak | 16 | 9 | 1609.01793 |
1609 | 1609.03569_arXiv.txt | { The standard paradigm of collisionless cold dark matter is in tension with measurements on large scales. In particular, the best fit values of the Hubble rate $H_0$ and the matter density perturbation $\sigma_8$ inferred from the cosmic microwave background seem inconsistent with the results from direct measurements. We show that both problems can be solved in a framework in which dark matter consists of two distinct components, a dominant component and a subdominant component. The primary component is cold and collisionless. The secondary component is also cold, but interacts strongly with dark radiation, which itself forms a tightly coupled fluid. The growth of density perturbations in the subdominant component is inhibited by dark acoustic oscillations due to its coupling to the dark radiation, solving the $\sigma_8$ problem, while the presence of tightly coupled dark radiation ameliorates the $H_0$ problem. The subdominant component of dark matter and dark radiation continue to remain in thermal equilibrium until late times, inhibiting the formation of a dark disk. We present an example of a simple model that naturally realizes this scenario in which both constituents of dark matter are thermal WIMPs. Our scenario can be tested by future stage-IV experiments designed to probe the CMB and large scale structure. } | \label{sec:intro} For nearly two decades, the $\Lambda$CDM paradigm in which dark matter (DM) is composed of cold, collisionless particles has provided an excellent fit to cosmological data. Although on galactic scales or smaller there have been long-standing issues such as the core-vs-cusp~\cite{Moore:1994yx, Flores:1994gz} and too-big-to-fail~\cite{2011MNRAS.415L..40B} problems that are difficult to explain within this framework, it has been very successful on larger scales. However, in recent years, as the data has become more precise, the $\Lambda$CDM framework has also come into tension with measurements on large scales. In particular, the value of today's Hubble rate $H_0$ obtained from a fit to the cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) data \cite{Ade:2015xua} is smaller than the results from local measurements~\cite{Riess:2011yx, 2013ApJ...766...70S, Riess:2016jrr,DiValentino:2016hlg, Bernal:2016gxb}, with a $\sim 3\sigma$ discrepancy. Similarly, the inferred value of $\sigma_8$ (the amplitude of matter density fluctuations at the scale of $8h^{-1}\Mpc$) is larger by $3$--$4\sigma$~\cite{Heymans:2013fya, Ade:2013lmv, MacCrann:2014wfa} than the values from direct measurements such as weak lensing survey~\cite{Fu:2014loa}, CMB lensing~\cite{Ade:2015zua}, and Sunyaev-Zeldovich cluster counts~\cite{2012ApJ...755...70R, Hasselfield:2013wf, Ade:2015fva}. These large-scale anomalies are particularly intriguing because the theoretical understanding of dynamics at large scales is rather simple and robust, essentially requiring only the application of linear perturbation theory to density fluctuations. This is in contrast to the studies of small scale structure, which not only require an understanding of the nonlinear evolution of a many-body system but also crucially depend on the detailed dynamics of baryons, which is quite challenging to simulate. Therefore, while it is possible that these large scale discrepancies are due to systematic errors in the associated experiments~\cite{Joudaki:2016mvz,Kitching:2016hvn}, it is important to consider the possibilty that they are in fact robust problems that require a fundamental shift away from the $\Lambda$CDM framework. Several proposals have been put forward to explain one or the other of these anomalies by going beyond the $\Lambda$CDM paradigm. For example, DM that decays at late times, well after the CMB epoch, can reduce the size of $\sigma_8$~\cite{Enqvist:2015ara,Poulin:2016nat}. Alternatively, neutrinos with masses near the top of the allowed range or sterile neutrinos with an eV mass can fit the CMB and BAO data with a smaller $\sigma_8$~\cite{Battye:2014qga}, but have the effect of making the $H_0$ problem worse~\cite{Ade:2015xua}. If there is dark radiation (DR) that behaves like a tightly coupled fluid (as opposed to free streaming like neutrinos), this can ameliorate the tension in $H_0$ measurements~\cite{Baumann:2015rya}. If DM further scatters with such DR, it may be possible to solve both the $H_0$ and $\sigma_8$ problems~\cite{Buen-Abad:2015ova, Lesgourgues:2015wza, Ko:2016uft, Ko:2016fcd}. These proposals, however, require a rather tiny DM-DR interaction constrained in a very narrow range to solve both problems. In this article we propose a new simple framework, ``Partially Acoustic Dark Matter'' (PAcDM), that can robustly solve both problems. We assume that DM consists of two components, $\chi_1$ and $\chi_2$, and that there is also DR that behaves as a tightly coupled relativistic fluid.\footnote{Earlier work on multi-component DM may be found in, for example,~\cite{Goldberg:1986nk, Khlopov:1989fj, Berezhiani:1995am, Kaplan:2009de, Kaplan:2011yj, CyrRacine:2012fz, Dienes:2011ja}.} The primary component $\chi_1$ is cold and collisionless, and dominates the DM mass density. The subdominant component, $\chi_2$, is also cold, but is tightly coupled to the DR\@. The interactions within the DR, and between the DR and $\chi_2$, are both strong enough that the tight coupling treatment is valid not only during radiation domination before the CMB epoch but also well into the era of structure formation. Then, since our DR is a tightly coupled relativistic fluid as considered in \Ref{Baumann:2015rya}, we can solve the $H_0$ problem by choosing the amount of DR appropriately. We will then demonstrate that the persistent $\chi_2$-DR interaction inhibits the growth of density perturbations in $\chi_2$, which in turn reduces the growth of density fluctuations in the dominant DM component, $\chi_1$, provided that the modes in question enter the horizon before matter-radiation equality. The modes at the $8h^{-1}\Mpc$ scale do indeed come inside the horizon before equality, so we can also solve the $\sigma_8$ problem just by choosing an appropriate amount of $\chi_2$ to match the observed discrepancy in $\sigma_8$. This class of theories fits very naturally into a ``hidden WIMP" scenario~\cite{Finkbeiner:2007kk, Pospelov:2007mp, Feng:2008ya, Feng:2008mu}, in which the relic abundance of both DM components $\chi_1$ and $\chi_2$ is set by annihilation into a hidden sector, rather than into the SM. Massless states in this hidden sector could then constitute interacting DR~\cite{Chacko:2015noa}, ameliorating the $H_0$ problem, while scattering of $\chi_2$ off DR solves the $\sigma_8$ problem. In the next section, we construct an explicit model along these lines. However, we stress that the qualitative features of our scenario---an enhancement in $H_0$ and a reduction in $\sigma_8$---are robust and only require the coupling constants in the DR-$\chi_2$ sector to be sufficiently large that DR is a tightly coupled fluid and $\chi_2$ remains in equilibrium with DR\@. The mechanism is therefore quite general, and is not restricted to a specific DM framework. The PAcDM paradigm shares some features of the ``double-disk dark matter'' scenario explored in~\cite{Fan:2013yva, Fan:2013tia}, but there are several crucial differences. In particular, since our ``dark electrons'' are massless, they never form bound states and, consequently, the $\chi_2$-DR system never undergoes recombination. Therefore, after matter-radiation equality, it continues to undergo \emph{dark acoustic oscillations}~\cite{Cyr-Racine:2013fsa} without being disrupted by ``dark recombination.'' This has the effect of holding back the growth of density perturbations in $\chi_2$ until the energy density in DR falls too much for the oscillations to be maintained. Furthermore, by assumption, the $\chi_2$-DR system remains tightly coupled throughout the evolution of the universe, even into the era of structure formation. At later times it continues to remain a \emph{thermal system}, and hence does not virialize. Therefore, we expect that it does not collapse into a disk but instead forms a spherical halo around the galactic center. The rest of this paper is organized as follows. In \Sec{model}, we describe a concrete, complete model that realizes our solution to the $H_0$ and $\sigma_8$ problems within the hidden WIMP framework. In \Sec{evolution}, we develop an analytical understanding of how the $\sigma_8$ problem is solved in the PAcDM scenario by studying the linear evolution equations for the density and metric perturbations. This is done without assuming any particular particle physics model of the DM and DR\@. In \Sec{numerical}, we present the results of our more detailed numerical simulations of the matter power spectrum to determine the precise fraction of $\chi_2$ to match the observed discrepancy in $\sigma_8$. We then show that the corrections to the CMB spectrum and the CMB lensing measurement are small and within the present uncertainties. We conclude in \Sec{conc}. | \label{sec:conc} We have presented a new framework in which DM is composed of two distinct components that can provide a solution to both the $H_0$ and $\sigma_8$ problems. While the dominant component of DM is cold and collisionless, the subdominant component is also cold but interacts strongly with DR, which itself constitutes a tightly coupled fluid. Our framework is very general and can be adopted in a wide variety of DM models. In particular, it can easily be accommodated in the hidden WIMP framework, with both constituents of DM arising as thermal relics. Our scenario predicts distinctive modifications to the matter and CMB power spectra, allowing it to be tested by future experiments. By solving a set of linear evolution equations, we have shown that the observed $10\%$ discrepancy in $\sigma_8$ requires the mass density in the subdominant, interacting DM species to constitute $\simeq 2.0\%$ of the total DM density, while the amount of DR can be separately chosen to fix the $H_0$ problem. This apparently small ratio of the two DM components could easily arise in, for example, the WIMP framework without introducing hierarchically small parameters into the Lagrangian. The required tight couplings between the interacting DM and DR and within DR itself can be obtained in a wide range of perturbative coupling constants, as we showed in a concrete model. We found that, with an interacting DM component of about $2\%$ to solve the $\sigma_8$ problem and the appropriate amount of DR to address the $H_0$ problem, the deviations in the CMB spectrum and the CMB lensing measurements are well within the current uncertainties. It is interesting to compare and contrast our proposal with the scenario put forward in~\cite{Buen-Abad:2015ova, Lesgourgues:2015wza, Ko:2016uft}. In the PAcDM framework, only a subcomponent of DM experiences acoustic oscillations, while the primary component of DM is responsible for building up structure. As seen in Eq.~(\ref{eq:powerlaw}), this suppresses the rate of growth of power during the era of matter domination, with the result that most of the corrections to the DM density perturbations, and hence corrections to the gravitational potential, arise well after matter-radiation equality. However, in the proposal of~\cite{Buen-Abad:2015ova, Lesgourgues:2015wza, Ko:2016uft}, the entirety of DM undergoes oscillations prior to matter-radiation equality that continue through to the CMB epoch. In this case, the corrections to the DM density perturbations are already significant at the time of matter-radiation equality, and the resulting corrections to the CMB are expected to be significantly larger. Hence future precision studies of the CMB may be able to distinguish these two classes of models. It is important to note that our mechanism to reduce $\sigma_8$ is not especially sensitive to the precise value of $\Neff^{\text{scatt}}$. Hence, if future measurements were to settle on a smaller $\Neff^{\text{scatt}}$, our mechanism would still constitute a solution to the $\sigma_8$ problem. Note that lowering $\Neff^{\text{scatt}}$ would also imply even smaller corrections to the CMB, since most of the modes that are observed in the CMB would now enter the horizon at a time when the contribution of DR to the energy density is small. While the primary focus of this article is on large scale structure, our framework may also have potentially observable effects on smaller scales. It follows from Eq.~\Eq{Gamma>>H0} that at each locale in the universe the $\chi_2$ particles continue to experience a sufficient number of collisions with surrounding DR particles to maintain thermal equilibrium, at least locally, at all times. This remains true during the era of structure formation. The same condition also ensures that the DR itself remains a tightly coupled relativistic fluid at all times. Being strictly massless, the dark charged particles in DR never undergo recombination. Being tightly coupled, DR is non-dissipative and hence behaves as a perfect thermal fluid. Because of these properties, which are qualitatively different from those of the baryon-photon system, we expect that the $\chi_2$-DR system does not collapse into a disk but instead forms a smooth, spherical halo around the galactic center. This is qualitatively distinct from the dynamics of the recently proposed ``double-disk DM'' or partially dissipative DM~\cite{Fan:2013yva}. The existence of this halo would impact galactic dynamics, with the exact nature of its effects depending on the details of its density profile. We defer a careful study of these effects on the small scale structure of DM halos for future work. The current discordance between direct and indirect measurements of $H_0$ and $\sigma_8$ may be the first hint for new cosmology beyond the $\Lambda$CDM paradigm. These discrepancies can be naturally addressed within the non-minimal dark sector structure we have proposed. In the coming years, the experimental precision in the indirect measurement of $N_{\rm eff}$ and $\sigma_8$ from the CMB~\cite{Abazajian:2013oma, Errard:2015cxa, Wu:2014hta, Dodelson:2016wal} (e.g. CMB stage-IV), and in direct measurements of the Hubble constant~\cite{Macri:2006wm, Greenhill:2009yi}, and $\sigma_8$~\cite{Hannestad:2007fb, Dodelson:2016wal} (LSST, DESI) are all expected to improve significantly. If the current discrepancies in the $H_0$ and $\sigma_8$ measurements are indeed due to new physics, these future experiments have great potential for distinguishing between different candidate theories such as the framework presented in this paper. | 16 | 9 | 1609.03569 |
1609 | 1609.08167_arXiv.txt | We present a measurement of galaxy-galaxy lensing around a magnitude-limited ($i_{AB} < 22.5$) sample of galaxies from the Dark Energy Survey Science Verification (DES-SV) data. We split these lenses into three photometric-redshift bins from 0.2 to 0.8, and determine the product of the galaxy bias $b$ and cross-correlation coefficient between the galaxy and dark matter overdensity fields $r$ in each bin, using scales above 4 Mpc/$h$ comoving, where we find the linear bias model to be valid given our current uncertainties. We compare our galaxy bias results from galaxy-galaxy lensing with those obtained from galaxy clustering \citep{Crocce2015} and CMB lensing \citep{Giannantonio2015} for the same sample of galaxies, and find our measurements to be in good agreement with those in \citet{Crocce2015}, while, in the lowest redshift bin ($z\sim0.3$), they show some tension with the findings in \citet{Giannantonio2015}. We measure $b\cdot r$ to be $0.87\pm 0.11$, $1.12 \pm 0.16$ and $1.24\pm 0.23$, respectively for the three redshift bins of width $\Delta z = 0.2$ in the range $0.2<z <0.8$, defined with the photometric-redshift algorithm BPZ. Using a different code to split the lens sample, TPZ, leads to changes in the measured biases at the 10-20\% level, but it does not alter the main conclusion of this work: when comparing with \citet{Crocce2015} we do not find strong evidence for a cross-correlation parameter significantly below one in this galaxy sample, except possibly at the lowest redshift bin ($z\sim 0.3$), where we find $r = 0.71 \pm 0.11$ when using TPZ, and $0.83 \pm 0.12$ with BPZ. | 16 | 9 | 1609.08167 |
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1609 | 1609.06450_arXiv.txt | We report on observations obtained at IRAM on two semi-regular variable Asymptotic Giant Branch (AGB) stars, RS Cnc and EP Aqr, undergoing mass loss at an intermediate rate of $\sim 10^{-7}$ \Msold. Interferometric data obtained with the Plateau-de-Bure interferometer (NOEMA) have been combined with On-The-Fly maps obtained with the 30-m telescope in the CO(1-0) and (2-1) rotational lines. The spectral maps of spatially resolved sources reveal an axisymmetric morphology in which matter is flowing out at a low velocity ($\sim$ 2\,\kms) in the equatorial planes, and at a larger velocity ($\sim$ 8\,\kms) along the polar axes. There are indications that this kind of morpho-kinematics is relatively frequent among stars at the beginning of their evolution on the Thermally-Pulsing AGB, in particular among those that show composite CO line profiles, and that it might be caused by the presence of a companion. We discuss the progress that could be expected for our understanding of the mass loss mechanisms in this kind of sources by increasing the spatial resolution of the observations with ALMA or NOEMA. | Stars on the Asymtotic Giant Branch (AGB) are in a short phase of their life (from 1 to a few 10$^6$ years). They evolve rapidly owing to their large luminosity (few 10$^3$ \Lsol), and to the ejection of their stellar envelopes. The mechanism by which stars expel their envelopes is essential to the understanding of the terminal phases of stellar evolution, and to a proper description of their contribution to the replenishment of the interstellar medium. Carbon monoxide (CO) is one of the best tracers of the winds from AGB stars. It originates in the stellar atmospheres and survives up to a few 10$^{16-17}$\,cm where it is distroyed by UV photons from the interstellar radiation field \citep{mamon1988}. It thus can be used to probe the region where the winds are shaped and accelerated. The first rotational lines of CO (1-0 and 2-1) are easily accessible from the Plateau-de-Bure (NOEMA), and higher degree lines can be observed from the Atacama desert (ALMA). Modelling of the CO line profiles has provided the best mass loss rate estimates \citep[e.g. ][]{schoier2001,teyssier2006}. In the process of an investigation on the mass loss mechanisms \citep{winters2000,winters2003}, we became interested in sources that exhibit composite CO line profiles, with a narrow component (FWHM $\sim$ 2-3 \kms) overimposed on a broader (FWHM $\sim$ 8-10 \kms) one. These sources were first pointed out by \citet{knapp1998} who suggested that the peculiar line profiles reveal two different successive winds. We report on our recent work on two such cases, EP Aqr and RS Cnc. We selected these two stars for which a wealth of ancillary data is available, and allows us to characterize their stages of evolution. Although our first investigation on EP Aqr \citep{winters2007} tended to support the Knapp et al. interpretation, our study of RS Cnc \citep{libert2010} showed that a composite CO line profile might also result from an axi-symmetrical structure, with a slow equatorial wind, and a rapid bipolar outflow. This encouraged us to revisit both sources with a new modelling approach based on the fitting of CO(1-0) and (2-1) spectral maps \citep{hoai2015}. | Axisymmetry seems to be a common feature in stellar winds, even in the early phases of the TP-AGB. For instance, for EP Aqr the likely absence of Tc in the atmosphere suggests that dredge-up events are still not operating. It shows that non-spherical shapes observed often in planetary nebulae may arise from phenomena that are already active during the AGB phase, although with effects which are less dramatic. In sources like RS Cnc or EP Aqr, the axi-symmetry becomes apparent only if the kinematical information is available. The two important conclusions for these objects are that (i) the flux of matter is larger along the polar axis than in the equatorial plane, (ii) the stellar winds might still be accelerated at a few hundred AU. We stress the importance of the high spectral resolution for studying the relatively slow winds from AGB stars. Indeed, we need to resolve spectrally the emission for detecting the axi-symmetry of the source, but also this axi-symmetry may appear only as a kinematic effect (i.e. not as a density effect). The origin of bipolarity still needs to be identified. The fact that we find sources with a flux of matter larger along the polar axis than in the equatorial plane does not favor magnetic fields. The presence of a companion should produce sub-structures, such as spirals that can be detected in CO lines. It may affect the rate of mass loss, and may play an important role in the ultimate phases of evolution of its primary. The presence of a rotating disk may have a considerable meaning for the mass loss mechanism, that up to now has not been well explored in the models. High spatial resolution imaging at high spectral resolution of the central parts of these sources where the winds are launched and accelerated with ALMA and NOEMA is clearly essential. | 16 | 9 | 1609.06450 |
1609 | 1609.09094_arXiv.txt | The spectral anisotropy of turbulent structures has been measured in the solar wind since 1990, relying on the assumption of axisymmetry about the mean magnetic field, $B_0$. However, several works indicate that this hypothesis might be partially wrong, thus raising two questions: (i) is it correct to interpret measurements at 1 AU (the so-called Maltese cross) in term of a sum of slab and 2D turbulence? (ii) what information is really contained in the Maltese cross? We solve direct numerical simulations of the MHD equations including the transverse stretching exerted by the solar wind flow and study the genuine 3D anisotropy of turbulence as well as that one resulting from the assumption of axisymmetry about $B_0$. \chb{We show that the evolution of the turbulent spectrum from 0.2 to 1 AU depends strongly on its initial anisotropy. An axisymmetric spectrum with respect to $B_0$ keeps its axisymmetry, i.e., resists stretching perpendicular to radial, while an isotropic spectrum becomes essentially axisymmetric with respect to the radial direction.} We conclude that close to the Sun, slow-wind turbulence has a spectrum that is axisymmetric around $B_0$ and the measured 2D component at 1 AU describes the real shape of turbulent structures. On the contrary, fast-wind turbulence has a more isotropic spectrum at the source and becomes radially symmetric at 1 AU. Such structure is hidden by the symmetrization applied to the data that instead returns a slab geometry. | In a pioneering paper, \citet{1990JGR....9520673M} obtained for the first time an average picture of the turbulent structures in the solar wind by computing the autocorrelation of the interplanetary magnetic field fluctuations in different directions with respect to the mean field ($B_0$). and assuming axisymmetry about $B_0$. Considering that single spacecraft measurements allow only to explore the radial structure of the fluctuations, obtaining the Maltese cross was a big progress, as it revealed the multidimensional structure of turbulence. The two-dimensional (2D) autocorrelation was made up of two lobes, one elongated along increments parallel to mean field, and the other elongated along increments perpendicular to it (hence the term ``Maltese cross''). This particular shape was interpreted in terms of a mixture of 2D fluctuations with wavevectors and fluctuations perpendicular to the mean field (2D component), and of waves with wavevectors parallel to it (slab component), respectively. The hypothesis of axisymmetry about $B_0$ underlying the Maltese cross picture is fully justified for homogeneous turbulence by theoretical, experimental and numerical results \citep{1981PhFl...24..825M,1983JPlPh..29..525S,1986PhFl...29.2433G} which all indicate that the nonlinear cascade leading to a turbulent spectrum proceeds mainly in directions perpendicular to the mean magnetic field. However, in the solar wind, the mean field direction is not the only symmetry axis for turbulent structures. Theoretical and numerical evidence \citep{1973Ap&SS..20..267V,1993PhRvL..70.2190G,Grappin:1996ey,Dong:2014fi} indicate that the flow direction, i.e. the radial axis, also plays a role in shaping the symmetry of the turbulent spectrum in the Fourier space. Also, for fluctuations with frequencies between 3 and 10 hours \cite{Saur:1999gy} found that the best theoretical model fitting solar wind data is a mixture of 2D turbulence with wavevectors lying in a plane perpendicular to the mean field and a spectrum of wavevectors aligned with the radial, not aligned with the mean field. The argument that explains why the radial axis also plays a role is simple: as a plasma volume is advected by the solar wind, the large scale flow cannot be eliminated by a Galilean transformation, because it is \textit{radial, not uniform}. Indeed, after such a transformation, there remains an expanding flow transverse to the radial that leads to a transverse stretching of the plasma volume: this stretching has several consequences, an important one being that it slows down nonlinear coupling, at least in directions perpendicular to the radial. In principle, at small enough scales the axisymmetry about $B_0$ should be valid, since nonlinear couplings should overcome the transverse stretching: in fact their time scale becomes smaller while the expansion time scale is scale-independent. However, we will see in this paper that the situation is less simple and that the radial symmetry can prevail even at small scales. More specifically, this paper aims at understanding when the hypothesis of axisymmetry about $B_0$ and the associated Maltese cross picture are valid or not, and, at the same time, at guessing the true initial properties of turbulence close to the Sun that could lead to the structures observed at 1 AU. We shall use for that the expanding box model (EBM \citep{1993PhRvL..70.2190G}), which consists in magnetohydrodynamic (MHD) equations modified to include the effect of the large scale radial flow of the wind. \chb{The EBM equations describe the evolution of a plasma parcel advected by a radial, uniform radial wind. Its conditions of validity are the following: (i) the angular width of the plasma volume must be small in order to allow neglecting curvature terms (but see however \cite{Grappin:1996ey}); (ii) the radial extent of the domain must be small enough to allow assuming homogeneity within the domain; (iii) heliocentric distance must be larger than, say, 0.1 AU to be able to neglect systematic large-scale variations of the solar wind speed with heliocentric distance.} The EBM equations have been used recently with success \citep{Verdini:2015bx} to reproduce and fully explain the local anisotropy of turbulent structures measured in the solar wind by \cite{2012ApJ...758..120C}. The term \textit{local} means that the anisotropy is measured in a frame attached to the \textit{local} mean magnetic field that varies both with scale and location. Note, however, that \textit{local} anisotropy is not easily related to the standard anisotropy studied in the present paper that is defined in a fixed frame, independent of scale (see \cite{2012ApJ...750..103M}). In a previous work, \cite{1998JGR...10323705G} attempted to reproduce the Maltese cross via direct numerical simulations of MHD equations, thus without taking into account the large scale radial flow of the wind. Using the hypothesis of axisymmetry about $B_0$, they were able to find separately the two lobes by varying the initial conditions of their runs. They obtained the 2D component for initial conditions corresponding to 2D turbulence or to pressure balance structures \citep{1995JGR...100.1763C}, and the slab component for initial conditions corresponding to unidirectional Alfv\'en waves with wavevectors quasi-parallel to the magnetic field. However a mixture of these initial conditions led to isotropic autocorrelation, so they concluded that the two lobes of the Maltese cross result from a mixture of different solar wind states. This is indeed the case, as was shown by \cite{2005ApJ...635L.181D} and subsequent works \citep{2008JGRA..11301106H,2009JGRA..114.7213W,Weygand:2011p3064}, which successfully isolated the slab component and the 2D component by partitioning the fluctuations in fast and slow streams, respectively. Our purpose here is twofold: (i) to propose a description of the possible properties of turbulence close to the Sun compatible with these observations at 1 AU; (ii) explain how the hypothesis of axisymmetry about $B_0$ transforms this turbulence into the classical (2D, slab) model. An extreme example of such a transformation is provided in fig.~\ref{fig1} which represents the effect of symmetrization around $B_0$ on a turbulent spectrum with radial symmetry, that is, an anisotropy completely ruled by expansion\footnote{We consider the 3D spectrum instead of the 3D autocorrelation because rotating and averaging are more easily visualized in the Fourier space}. The projection in the ecliptic plane of the 3D spectrum with radial symmetry is shown in panel (a). By averaging around the mean field direction, we obtain successively the panels (b) and (c). This is equivalent to applying the hypothesis of axisymmetry about $B_0$ to measurements that belong to several samples with different angles of the mean field with respect to the radial. Panel (d) represents the last step, i.e. the spectrum rotated in the frame associated with the mean field. The final spectrum has two properties: (i) by construction, it is axisymmetric with respect to the mean field, while the true spectrum is axisymmetric with respect to the radial; (ii) it has a complicated structure with main excitation along the mean field (i.e. the observed slab component), which masks the true (physical) structure of the spectrum. To reveal the possible initial structure and evolution of the (2D, radial slab) two-component turbulence of \cite{Saur:1999gy}, we follow in this paper the evolution of a plasma volume advected by the wind from $0.2$~AU to $1$~AU (fig.~\ref{f2}), using the EBM equations. The EBM equations have been used in \citet{Dong:2014fi} to explain basic properties of solar wind turbulence, namely the anisotropy of the different components of fluctuations, both kinetic and magnetic (also termed variance anisotropy). The present work extends this study by varying (i) the initial conditions at 0.2 AU; (ii) the ratio between the nonlinear turnover time based on the largest eddies and the linear stretching time. The plan of the paper is as follows. Simulations and parameters are described in Section 2. Results on the anisotropy of solar wind turbulence and its appearance in data under the assumption of axisymmetry about the mean field are given in Section 3. In section 4 we present a discussion on the results and the impact of initial spectra and expansion parameter on anisotropy. The last section contains the conclusions. \begin{figure}[t] \begin{center} \includegraphics [width=\linewidth]{maltaise.eps} \caption{Symmetrization around $B_0$ of a spectrum axisymmetric with respect to the radial direction, with the mean field $B_0$ at an angle $\pi/4$ with the radial. (a) projection on the ($B_0,~e_R$) plane of an isocontour of the 3D spectrum that is axisymmetric around the radial direction; (b) applying to the isocontour the assumption of axisymmetry about $B_0$; (c) filling the interior of the contour to give an idea of the new symmetrized spectrum; (d) rotating the cartesian frame, with the $x$ axis aligned with the mean field $B_0$ as done when presenting the Maltese cross. } \label{fig1} \end{center} \end{figure} | We studied the anisotropy of turbulence in the solar wind carrying out numerical simulations of the expanding box model for MHD (EBM). We varied both the initial conditions and the expansion rate of our simulations, thus extending recent works on the evolution of turbulence in the solar wind \citep{Dong:2014fi}. To compare with solar wind data we computed how the anisotropy shows up in 2D autocorrelation functions. We found that if the initial spectrum is already axisymmetric with respect to the mean field, then the spectrum at 1~AU conserves this symmetry and shows up as a 2D-turbulence component, consistent with the above assumption. However, if the initial spectrum is isotropic, then the spectrum at 1~AU is not axisymmetric and the anisotropy is determined by two symmetry axes, the radial axis and the mean-field axis. This is true for a large range of expansion rates and of wavenumbers, suggesting that the mean-field anisotropy is a weak attractor, or in other words that the recovery of homogenous-turbulence properties at small scales is not a universal feature of solar wind turbulence. We also showed that the assumption of axisymmetry about the mean field, which is often conjectured to hold at small enough scales, may mask the true anisotropy of the magnetic field spectrum. In fact, when the spectrum displays a slab component along the radial, as for isotropic initial conditions, the assumption of axisymmetry about the mean field transforms the anisotropy into an apparent slab component along the mean field. Thus, on the one hand we confirm earlier results of homogenous turbulence simulations for the origin of the 2D component \citep{1990JGR....9520673M,1998JGR...10323705G}, on the other hand we provide an explanation for the slab component observed in fast streams. What controls the anisotropy at 1~AU? The \gyrotropic{} initial conditions we have used do not only possess the ``right'' symmetry properties, but also an aspect ratio that is characteristic of strong turbulence (compare the values of $\chi$ in table~\ref{table1}). For reasonable expansion rates, $\epsilon_{end}\in[0.4,~2]$ \citep{1991AnGeo...9..416G}, turbulence remains strong and its properties are similar to homogenous turbulence. On the contrary, in isotropic initial conditions we excited a large range of field-parallel wavevectors, which makes the cascade weaker. On top of this, expansion slows down the nonlinear interaction due to the kinematic stretching of the plasma. Thus, we have two weakening factors that counteract the natural tendency of MHD turbulence to develop small scales perpendicular to the mean field. In this case, the development of turbulence is more sensitive to the expansion rate and the final anisotropy depends on the expansion symmetry axis, the radial, and on the initial anisotropy. This leads us to conjecture that slow-wind turbulence is already strongly anisotropic with symmetry axis given by the mean field, and that fast-wind turbulence is more isotropic. Recall that in fast-wind turbulence a strong correlation between velocity and magnetic fluctuations is observed (high cross-helicity), which results into an additional weakening of the cascade \citep{2012ApJ...750L..33V,Perez:2013fb}. Such weakening could also be responsible for the formation of the 1/f spectrum inside the Alfv\'enic critical point \citep{2012ApJ...750L..33V}, which is a characteristic of the fast solar wind \citep[e.g.][]{Bruno:2013p434}. Preliminary EBM simulations with initial strong cross helicity and isotropic spectra compare well with turbulence observed in the fast streams \citep{1990JGR....95.8197G}. Indeed, at 1~AU they have flatter spectra and a higher cross helicity compared to runs with \gyrotropic{} initial spectra, suggesting that one needs to account for all the three factors (expansion rate, initial anisotropy, and initial cross helicity) in order to understand the different evolution of turbulence in fast and slow streams. \chb{The so-called Bieber test \citep{1996JGR...101.2511B,Saur:1999gy,Smith:2011ep} that relates spectral and component anisotropy could be used to further test our conjecture after a proper generalization, i.e., by including the radially-symmetric models of turbulence proposed here.} We conclude by noting that the NASA Solar Probe Plus and ESA Solar Orbiter missions will sample plasma in between 0.1~AU and 0.8~AU. This makes extremely interesting and timely to understand which mechanisms can lead to different initial anisotropies close to the Sun for fast and slow streams. Shell-Reduced-MHD simulations \citep{2009ApJ...700L..39V,2012A&A...538A..70V,2012ApJ...750L..33V,2012PhRvL.109b5004V} are particularly promising, since allow to span 5 decades in wavenumbers and the large parameter space that characterizes slow and fast wind, as well as true Reduced MHD simulations \citep{Perez:2013fb}, since they provide more detailed informations on turbulence. Another promising tool is the Accelerating Box Model \citep{2013JGRA..118.7507T}, which not only incorporates the acceleration of the solar wind into the EBM but also allows to treat compressible effects, such as parametric instability \citep[e.g][]{2015JPlPh..81a3202D}, that are neglected in the above models and may contribute to the acceleration of the solar wind and shape the turbulent spectrum close to the Sun \citep{Suzuki:2005kf,Matsumoto:2012ck}.\\ \textit | 16 | 9 | 1609.09094 |
1609 | 1609.05045_arXiv.txt | The detection of complex organic molecules (COMs) toward cold sources such as pre-stellar cores (with T$<$10 K), has challenged our understanding of the formation processes of COMs in the interstellar medium. Recent modelling on COM chemistry at low temperatures has provided new insight into these processes predicting that COM formation depends strongly on parameters such as visual extinction and the level of CO freeze out. We report deep observations of COMs toward two positions in the L1544 pre-stellar core: the dense, highly-extinguished continuum peak with A$_V$$\geq$30$\,$mag within the inner 2700$\,$au; and a low-density shell with average A$_V$$\sim$7.5-8$\,$mag located at 4000$\,$au from the core's center and bright in CH$_3$OH. Our observations show that CH$_3$O, CH$_3$OCH$_3$ and CH$_3$CHO are more abundant (by factors $\sim$2-10) toward the low-density shell than toward the continuum peak. Other COMs such as CH$_3$OCHO, c-C$_3$H$_2$O, HCCCHO, CH$_2$CHCN and HCCNC show slight enhancements (by factors $\leq$3) but the associated uncertainties are large. This suggests that COMs are actively formed and already present in the low-density shells of pre-stellar cores. The modelling of the chemistry of O-bearing COMs in L1544 indicates that these species are enhanced in this shell because i) CO starts freezing out onto dust grains driving an active surface chemistry; ii) the visual extinction is sufficiently high to prevent the UV photo-dissociation of COMs by the external interstellar radiation field; and iii) the density is still moderate to prevent severe depletion of COMs onto grains. | Complex Organic Molecules (COMs) are carbon-based species with $\geq$6 atoms in their molecular structure \citep[][]{her09}. The most prolific regions in the detection of COMs in the interstellar medium (ISM) have been massive hot cores and Giant Molecular Clouds in the Galactic Center \citep[SgrB2 (N) and (M);][]{holl00,holl06,req08,bell08,bell14} and low-mass hot corinos \citep[IRAS16293-2422;][]{cec00,bott04,jor12}. Until recently, it was believed that COMs form on dust grains via hydrogenation \citep[][]{char95} or radical-radical reactions favoured by the heating from the central protostar \citep[at T$\geq$30$\,$K; see][]{garr08}. However, the detection of COMs such as propylene (CH$_2$CHCH$_3$), acetaldehyde (CH$_3$CHO), dimethyl ether (CH$_3$OCH$_3$) or methyl formate (CH$_3$OCHO) in dark cloud cores and pre-stellar cores with T$\leq$10$\,$K (B1-b, TMC-1, L1689B or L1544) has recently challenged our understanding of COM formation \citep[][]{mar07,oberg10,bac12,cer12,vas14,loi16}. Several mechanisms have been proposed to explain the presence of COMs in cold cores: gas-phase formation, non-canonical chemical explosions, cosmic-ray induced radical diffusion, impulsive spot heating of grains, or radical-radical recombination after H-atom addition/abstraction reactions on grain surfaces \citep[][]{vasy13,raw13,bal15,reb14,ivlev15,chu16}. However, information about the spatial distribution of COMs in cold cores is lacking (as well as of their radial abundance profile probing different density and extinction regimes), which prevents us from testing these COM formation scenarios. The detection of a low-density, CH$_3$OH-rich shell around the continuum peak of the L1544 pre-stellar core \citep[][]{biz14} offers a unique opportunity to test COM formation scenarios in cold sources. Species such as C$_3$O, ketene (H$_2$CCO), formic acid (HCOOH) and acetaldehyde may be spatially co-located to CH$_3$OH in L1544 and may form at this low-density shell \citep{vas14}. We report high-sensitivity observations of COMs toward two positions in the L1544 pre-stellar core: the continuum peak and a position within the low-density, CH$_3$OH-rich shell reported by \citet[][hereafter the {\it CH$_3$OH peak}]{biz14}. Our results suggest that COMs are actively formed in the low-density shells of pre-stellar cores\footnote{Part of these observations belong to the ASAI (Astrochemical Surveys at IRAM) program.}. | 16 | 9 | 1609.05045 |
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1609 | 1609.02386_arXiv.txt | The Nobel prize in physics 2015 has been awarded ``... for the discovery of neutrino oscillations which show that neutrinos have mass". While SuperKamiokande (SK), indeed, has discovered oscillations, SNO observed effect of the adiabatic (almost non-oscillatory) flavor conversion of neutrinos in the matter of the Sun. Oscillations are irrelevant for solar neutrinos apart from small $\nu_e$ regeneration inside the Earth. Both oscillations and adiabatic conversion do not imply masses uniquely and further studies were required to show that non-zero neutrino masses are behind the SNO results. Phenomena of oscillations (phase effect) and adiabatic conversion (the MSW effect driven by the change of mixing in matter) are described in pedagogical way. | The Nobel prize in physics 2015 has been awarded to T. Kajita, Super-Kamiokande, and A. B. McDonald, Sudbury Neutrino Observatory (SNO). Super-Kamiokande (SK, among other things) studied properties of the atmospheric neutrinos. The oscillatory dependence of the number of $\mu$-like events on $L/E$ (distance over energy) has been observed which is the key signature of oscillations \cite{atm}. The SNO collaboration studied the solar neutrinos: the flux of the $\nu_e$ neutrinos and the total flux of all neutrino flavors ($\nu_e$, $\nu_\mu$, $\nu_\tau$) have been measured via the charged current interactions and the neutral current interactions correspondingly. Comparing the two fluxes, SNO has established transformation of $\nu_e$ into $\nu_\mu$ and $\nu_\tau$ \cite{sol}. The prize has been awarded ``... for the discovery of neutrino oscillations, which shows that neutrinos have mass". Two remarks concerning this citation are in order \begin{itemize} \item While SK has, indeed, discovered neutrino oscillations, the SNO has established, as we understood later, almost {\it non-oscillatory} adiabatic flavor conversion (the MSW effect). Oscillations are irrelevant for interpretation of the SNO results apart from small regeneration effect inside the Earth. \item Oscillations do not necessarily imply the mass. \end{itemize} In what follows I will explain these two points and give simple description of the phenomena of oscillations and adiabatic conversion. Comments on physics and terminology will be given in conclusion \footnote{This paper is based on several colloquia delivered by the author during the last year.}. \\ Neutrino oscillations and adiabatic conversion are consequences of mixing \cite{pont}, \cite{mns}. Graphic representation of the vacuum mixing is shown in Fig.~\ref{fig:gr-mix}. There are three types of neutrinos: $\nu_e$, $\nu_\mu$, $\nu_\tau$ which we refer to as neutrinos with definite flavors. Mixing means that the flavor neutrino states do not coincide with the mass states $\nu_1$, $\nu_2$, $\nu_3$. The flavor states are combinations (mixture) of mass states, and inversely, the mass states are combinations of the flavor states (see Fig. \ref{fig:gr-mix}, left). According to this Figure, e.g. $\nu_2$ is composed of nearly equal amount of $\nu_e$, $\nu_\mu$, $\nu_\tau$. In $\nu_3$ the flavor states $\nu_\mu$ and $\nu_\tau$ are presented almost equally with very small admixture of $\nu_e$. Therefore, $\nu_3$ would show up (interact) with probability $\sim 0.48$ as $\nu_\mu$, with probability $\sim 0.5$ as $\nu_\tau$ and with probability 0.02 as $\nu_e$. If the beam of high energy $\nu_3$ is created, it will produce (in the CC interactions) numbers of $e$, $\mu$ and $\tau$ leptons with fractions $2:48:50$. Second aspect of mixing is that the flavor states are combinations of the mass states (Fig.~\ref{fig:gr-mix}, right). E.g. $\nu_e$ is composed of about 2/3 of $\nu_1$, 1/6 of $\nu_2$ and 1/6 of $\nu_3$. A mass spectrometer studying $\nu_\mu$ (in a ``gedadken'' experiment) would find three peaks: at values of mass $m_1$, $m_2$ and $m_3$ with intensities $2/3~:~1/6~:~1/6$ correspondingly. \begin{figure}[t] \includegraphics[width=5.0in]{nob0.png} \caption{Graphic representation of neutrino mixing. {\it Left panel:} neutrino mass spectrum and flavor composition of the mass eigenstates. The mass states are shown by boxes. Each box contains mixture of different flavors (color parts). Areas of colored parts give probabilities to find the corresponding flavor neutrino in a given mass state, if the area of the box is 1. {\it Right panel:} Mass composition of the flavor states. The gray-black boxes correspond to the mass states in a given flavor state. Relative areas of the boxes give probabilities to find the corresponding mass state in a given flavor state.} \label{fig:gr-mix} \end{figure} The key point which can not be seen in this figure is that flavor states are coherent combinations of the mass states. The mass states $\nu_i$, in a given flavor state $\nu_\alpha$ ($\alpha~ =~ e, \mu, \tau$) have definite relative phases. In terms of Fig. \ref{fig:gr-mix} left, SK has measured value of large (2-3) mass splitting and distribution of the $\nu_\mu$ and $\nu_\tau$ flavors (green and blue) in the third mass state $\nu_3$. SNO has constrained the small (1-2) mass splitting and established the distribution of the $\nu_e$ flavor (red) in $\nu_1$ and $\nu_2$. | In some cases (for historical or other reasons) terminology does not correspond to real physics. In most of the cases we understand difference and what is behind. Still bad terminology can be misleading producing wrong physics interpretations. Calling the two different effects (oscillations and adiabatic conversion) just oscillations is simpler and shorter. In fact, both the oscillations and adiabatic conversion can be consequences of neutrino mass and mixing. Also neutrino decay is a consequence of mass and mixing, but we do not call it oscillations. Partly it was our fault with Mikheyev: In our early publications we described two different matter effects under the same name: \begin{itemize} \item Resonance enhancement of oscillations which takes place in matter with constant (quasi constant) density, like mantle of the Earth. Here the phase is crucial. Graphic representation of this effect is given in Fig. \ref{fig:os-ad}c. The effect hopefully will be observed by PINGU, ORCA experiments, and will allow us to determine the neutrino mass hierarchy. \item Adiabatic conversion of neutrinos which (as we have discussed) takes place in matter with slowly changing density (the Sun, supernovae). Resonance is important also here determining strength of transitions: strong transitions occur in the resonance channel when e.g. neutrinos are produced at densities much above the resonance one, cross the resonance layer and then exit matter at densities much below the resonance density. \end{itemize} In January 1986 at the Moriond workshop A. Messiah (he gave the talk \cite{messiah}) asked me: `` why do you call effect that happens in the Sun the resonance oscillations? It has nothing to do with oscillations, I will call it the MSW effect". My reply was ``yes, I agree, we simply did know how to call it. I will explain and correct this in my future talks and publications''. Messiah's answer was surprising: ``No way..., now this confusion will stay forever". That time I could not believe him. I have published series of papers, delivered review talks, lectures in which I was trying to explain, fix terminology, {\it etc.}. All this has been described in details in the talk at Nobel symposium \cite{s-nob}, and for recent review see \cite{maltoni}. Ideally terminology should reflect and follow our understanding of the subject. Deeper understanding may require a change or modification of terminology. At the same time changing terminology is very delicate thing and can be done with great care. \\ In conclusion, the answer to the question in the title of the paper is \\ \begin{center} ``Solar neutrinos: Almost No-oscillations''. \\ \end{center} The SNO experiment has discovered effect of {\it the adiabatic flavor conversion} (the MSW effect). Oscillations (effect of the phase) are irrelevant. Evolution of the solar neutrinos can be considered as independent (incoherent) propagation of the produced eigenstates in matter (Fig.~\ref{fig:incoh}). Flavors of these eigenstates (described by mixing angle) change according to density change. At high energies (SNO) the adiabatic conversion is close to the non-oscillatory transition which corresponds to production of single eigenstate. Oscillations with small depth occur in the matter of the Earth. \begin{figure}[h] \includegraphics[width=5in]{non-osc7.png} \caption{Scheme of flavor transformations of solar neutrinos. The plot represents complete theory of the conversion. The shadowed triangles illustrate loss of coherence between the eigenstates. For the SNO energy range $\nu_e \approx \nu_{2m}$.} \label{fig:incoh} \end{figure} | 16 | 9 | 1609.02386 |
1609 | 1609.07937_arXiv.txt | {% In weak gravitational lensing, weighted quadrupole moments of the brightness profile in galaxy images are a common way to estimate gravitational shear. We employ general adaptive moments (\glam\!) to study causes of shear bias on a fundamental level and for a practical definition of an image ellipticity. The \glam ellipticity has useful properties for any chosen weight profile: the weighted ellipticity is identical to that of isophotes of elliptical images, and in absence of noise and pixellation it is always an unbiased estimator of reduced shear. We show that moment-based techniques, adaptive or unweighted, are similar to a model-based approach in the sense that they can be seen as imperfect fit of an elliptical profile to the image. Due to residuals in the fit, moment-based estimates of ellipticities are prone to underfitting bias when inferred from observed images. The estimation is fundamentally limited mainly by pixellation which destroys information on the original, pre-seeing image. We give an optimized estimator for the pre-seeing \glam ellipticity and quantify its bias for noise-free images. To deal with images where pixel noise is prominent, we consider a Bayesian approach to infer \glam ellipticity where, similar to the noise-free case, the ellipticity posterior can be inconsistent with the true ellipticity if we do not properly account for our ignorance about fit residuals. This underfitting bias, quantified in the paper, does not vary with the overall noise level but changes with the pre-seeing brightness profile and the correlation or heterogeneity of pixel noise over the image. Furthermore, when inferring a constant ellipticity or, more relevantly, constant shear from a source sample with a distribution of intrinsic properties (sizes, centroid positions, intrinsic shapes), an additional, now noise-dependent bias arises towards low signal-to-noise if incorrect prior densities for the intrinsic properties are used. We discuss the origin of this prior bias. With regard to a fully-Bayesian lensing analysis, we point out that passing tests with source samples subject to constant shear may not be sufficient for an analysis of sources with varying shear.} | Over the past decade measurements of distortions of galaxy images by the gravitational lensing effect have developed into an important, independent tool for cosmologists to study the large-scale distribution of matter in the Universe and its expansion history \citep[recent reviews:][]{2006glsw.conf..269S,2008PhR...462...67M,2008ARNPS..58...99H,2010RPPh...73h6901M,2014arXiv1411.0115K}. These studies exploit the magnification and shear of galaxy light bundles by the tidal gravitational field of intervening matter. The shear gives rise to a detectable coherent distortion pattern in the observed galaxy shapes. The distortions are usually weak, only of order of a few per cent of the unlensed shape of a typical galaxy image. Therefore, the key to successfully devising gravitational shear as cosmological tool are accurate measurements of the shapes of many, mostly faint and hardly resolved galaxy images. There has been a boost of interest in methods of shape measurements in anticipation of the gravitational lensing analysis of the upcoming next generation of wide-field imaging surveys \citep[e.g., Euclid;][]{2011arXiv1110.3193L}. Despite being sufficient for contemporary surveys, current methodologies are not quite at the required level of accuracy to fully do justice to the amount of cosmological information in future lensing surveys \citep{2006MNRAS.368.1323H,2007MNRAS.376...13M}. The challenge all methodologies face is that observable, noisy (post-seeing) galaxy images are modifications of the actual (pre-seeing) image owing to instrumental and possible atmospheric effects. Post-seeing galaxy images are subject to pixellation as well as instrumental noise, sky noise, photon noise, and random overlapping with very faint objects \citep{2012MNRAS.423.3163K,2015MNRAS.449..685H}. In addition, galaxies are not intrinsically circular such that their ellipticities are noisy estimators of the cosmic distortion. Current theoretical work consequently focuses on sources of bias in shape measurements, such as pixel-noise bias, shape-noise bias, underfitting bias, colour gradients, or several selection biases \citep{2003MNRAS.343..459H,2004MNRAS.353..529H,2005MNRAS.361.1287M,2010A&A...510A..75M,2011MNRAS.410.2156V,2012MNRAS.424.2757M,2012MNRAS.427.2711K,2013MNRAS.429..661M,2013MNRAS.432.2385S}. One major source of bias is the pixel-noise bias or simply noise bias hereafter. This bias can at least partly be blamed on the usage of point estimates of galaxy shapes in a statistical analysis, i.e., single-value estimators of galaxy ellipticities \citep{2012MNRAS.425.1951R}. This begs the question whether it is feasible to eradicate noise bias by means of a more careful treatment of the statistical uncertainties in the measurement of galaxy ellipticities within a fully Bayesian framework. Indeed recent advances in image processing for weak gravitational lensing strongly support this idea, at least for the inference of constant shear (\citealt{2014MNRAS.444L..25S}; \citealt{2014MNRAS.438.1880B}, BA14 hereafter; \citealt{2015arXiv150805655B}, BAKM16 hereafter). In contrast, the contemporary philosophy with point estimates is to perform elaborate, time-consuming calibrations of biased estimators by means of simulated images; the calibration accuracy is, additionally, only as good as the realism of simulated images \citep[e.g.,][]{2015MNRAS.449..685H}. To be fair, code implementations of non-Bayesian techniques are typically an order of magnitude or more faster than Bayesian codes which could be a decisive factor for upcoming surveys. We take here a new look into possible causes of bias in shear measurements on a fundamental level. To this end, we examine, step-by-step with increasing complexity, a fully-Bayesian lensing analysis based on weighted brightness moments of galaxy images \citep{gelman2003bayesian,2003Book...MACKAY}. While the method in BA14 and BAKM16 is set in Fourier space, we work with moments in angular space which has benefits in the case of correlated noise or missing pixels in realistic images. Moment-based methods as ours are non-parametric; this means they are free from assumptions about the galaxy brightness profile. They hence appear to be advantageous for reducing bias, but nonetheless the specific choice of the adaptive weight for the moments is known to produce bias \citep{2014MNRAS.439.1909V,2010MNRAS.404..458V}. The origin of this problem, which principally also affects unweighted moments, becomes obvious in our formalism. We define as practical measure of galaxy shape a generalization of the impractical ellipticity $\epsilon$ expressed in terms of unweighted moments \citep[][SS97 hereafter]{1995ApJ...449..460K,1997A&A...318..687S}. Being Bayesian, our measurement of ellipticity results in a Monte-Carlo sample of the probability distribution function (PDF) of $\epsilon$ which should be propagated in a fully Bayesian analysis. That is: we do not devise point estimators in order to ideally stay clear of noise bias. This overall approach of general adaptive moments, \glam hereafter, is inspired by and comparable to \citet{2002AJ....123..583B} apart from the Bayesian framework and some technical differences: (i) for any adaptive weight, the perfectly measured \glam ellipticity is an unbiased estimator of gravitational shear unaffected by shape-noise bias; (ii) the adaptive weight may have a non-Gaussian radial profile; (iii) our inference of the pre-seeing ellipticity is realised as forward-fitting of elliptical profiles (so-called templates), that is we do not determine the brightness moments of the post-seeing image and correct them to estimate the pre-seeing moments \citep[cf.][]{2003MNRAS.343..459H,2005MNRAS.361.1287M}. As a disclaimer, the \glam methodology outlined here is prone to bias, even where a fully Bayesian analysis can be realised, and, at this stage, its performance is behind that of other techniques. The aim of this paper is to elucidate causes of bias, instead of proposing a new technique that is competitive to existing techniques. However, these findings are also relevant for other methodologies because model-based or moment-based approaches are linked to \glam\!\!. For this paper, we exclude bias from practically relevant factors: the insufficient knowledge of the PSF or noise properties, blending of images, and the selection of source galaxies \citep[see e.g.,][]{2006MNRAS.368.1323H,2011A&A...528A..51H,2014arXiv1406.1506D}. We focus on the core of the problem of shape measurements which is the inference of pre-seeing ellipticities from images whose full information on the brightness profile have been lost by instrumental limitations. The paper is laid out as follows. In Sect. 2, we introduce the formalism of \glam for a practical definition of ellipticity with convenient transformation properties under the action of gravitational shear. We also analytically investigate the limits of measuring the pre-seeing ellipticity from a noise-free but both PSF-convolved and pixellated image. In Sect. 3, we construct a statistical model for the \glam ellipticity of noisy post-seeing images. We then study the impact of inconsistencies in the posterior model of ellipticity in three, increasingly complex scenarios. First, we analyse with independent exposures of the same pre-seeing image the ellipticity bias due to a misspecified likelihood in the posterior (underfitting bias). Second, we consider samples of noisy images with the same ellipticity but distributions of intrinsic properties such as sizes or centroid positions. Here a new contribution to the ellipticity bias emerges if the prior densities of intrinsic properties are incorrectly specified (prior bias). Third in Sect. 4, we perform numerical experiments with samples of noisy galaxy images of random intrinsic shapes that are subject to constant shear. With these samples we study the impact of inconsistent ellipticity posteriors on shear constraints (shear bias). We also outline details on our technique to Monte-Carlo sample ellipticity or shear posteriors. We discuss our results and possible improvements of the \glam approach in Sect. 5. | \label{sect:discussion} Unlike galaxy ellipticities defined in terms of unweighted moments, \glam provide a practical definition of ellipticity with useful properties for any chosen adaptive weight $f^\prime(\rho)$: they (i) are identical with the ellipticity of isophotes of elliptical galaxy images; (ii) under the influence of shear they behave exactly like $\epsilon$ defined with unweighted moments; (iii) they are unbiased estimators of reduced shear. (i)-(iii) assume ideal conditions without pixellation, PSF convolution, or pixel noise. These effects fundamentally limit our ability to determine the \glam ellipticity (see below). Under ideal conditions, see SS97, it is known that $\epsilon$ for unweighted moments already obeys (iii). However, unweighted moments are formally infinite for realistic galaxy images because of pixel noise so that weighting is a necessity which is done adaptively for \glam\!\!. For adaptive weights, we have shown (i) and (ii) in Sect. \ref{sect:interpretation} and Sect. \ref{sect:shear}. Their relevance as unbiased estimators for reduced shear, statement (iii), follows thereafter from (ii) and the conclusions in SS97 for unweighted moments. We emphasise that \glam do not require ``deweighting'' in a lensing analysis \citep{2011MNRAS.412.1552M}: the ellipticity in term of the weighted moments is actually unbiased. In particular, we do not have to devise the same weight function for all galaxies as any weight function equally obeys (ii). If the minimum of the functional \Ref{eq:functional} uniquely exists, the moments $(\vec{x}_0,\alpha\,\mat{M}_{\rm I})$ of the best-fitting template $f(\rho)$ will, for a constant scalar $\alpha$, be the adaptively weighted moments $(\vec{x}_0,\mat{M}_{\rm I})$ of the galaxy light profile $I(\vec{x})$ for the weight $f^\prime(\rho)$ (Appendix \ref{sect:gam}). This means that the radial profile of the weight at separation $r$ from the centroid is \mbox{$w(r)\propto r^{-1}\d f_r(r)/\d r$} for a template profile \mbox{$f_r(r):=f(r^2)$}. We exploited this relation between adaptive moments and moments of a best-fitting elliptical profile to analyse limits to adaptive moment-based methods under the loss of image information. Namely, for realistic images subject to pixellation and PSF effects, underfitting bias can be present for \glam$\!$ if estimated from the post-seeing image. It potentially arises because of a loss of information on the pre-seeing galaxy image, fundamentally due to pixellation. To explore the limitations, we assume noise-free images and express in Sect. \ref{sect:psfpixel} the mapping between a pre-seeing and post-seeing image by the linear operation $\mat{L}$. The pre-seeing adaptive moments are equivalent to a least-square fit with residual $\vec{R}_{\rm pre}$ of an elliptical profile $f(\rho)$ to the pre-seeing image $I(\vec{x})$. If estimated from the post-seeing image whilst ignoring residuals, the inferred ellipticity is biased for \mbox{$\mat{L}\vec{R}_{\rm pre}\ne0$} \emph{and} a singular $\mat{L}$. The latter indicates a loss of information on the pre-seeing image. For noise-free images and the estimator \Ref{eq:functional2} the bias is, to linear order, given by Eq. \Ref{eq:bias}. In \Ref{eq:functional2} the bias is optimally reduced through the metric \mbox{$\mat{U}=(\mat{L}\mat{L}^{\rm T})^+$}. With this metric the estimator is unbiased for regular $\mat{L}$, hence in principle also for an invertible convolution with an anisotropic PSF; invertible convolutions have kernels $K(\vec{x})$ with \mbox{$\tilde{K}(\vec{\ell})\ne0$} in the Fourier domain. Practically, however, a singular mapping is always present due to pixellation so that the quadratic estimator \Ref{eq:functional2} could never fully remove underfitting bias. The inference of \glam ellipticity from noisy images with a likelihood that ignores fitting residuals produces underfitting bias; the underfitting bias depends on the correlation of pixel noise and its homogeneity over the image. To deal with pixel noise in images, we have put \glam in a Bayesian setting in Sect. \ref{sect:shearanalysis} by employing an approximate model \Ref{eq:likee1} for the likelihood that ignores fit residuals and thus equals an imperfect model fit with an elliptical profile. We use this to explore the impact of a misspecified likelihood that, as a result, can be shown to be subject to underfitting bias. The bias is revealed in the limit of combining the likelihoods of \mbox{$n\to\infty$} independent exposures of the \emph{same} image (see Sect. \ref{sect:glamnoise}). To lowest order in $\vec{R}_{\rm pre}$, we find the bias to vanish if \mbox{$\mat{L}^{\rm T}\mat{N}^{-1}\mat{L}$} is proportional to the unit matrix. The underfitting bias is unchanged for a rescaled noise covariance: there hence is no noise bias from a misspecified likelihood. Additionally, the magnitude of bias depends on the details of $\mat{N}$ and can also emerge for \mbox{$\mat{L}=\mat{1}$} if $\mat{N}$ is not proportional to the unit matrix, which is the case for heterogeneous or correlated noise. Due to the close relation of \glam ellipticity to other definitions of ellipticity we expect similar dependencies of bias on the noise covariance there, which may impact future calibration strategies in lensing applications because they apparently should not ignore cases of correlated or heterogeneous noise. Note that several steps in the reduction of lensing data can produce correlated pixel noise. The underfitting bias from the likelihood can presumably be addressed at the expense of an increased statistical error, such as by means of a follow-up high-resolution survey that gathers statistical information on the residuals $\vec{R}_{\rm pre}$. First of all, one obvious way to reduce underfitting bias is to choose a template that provides a good fit to galaxy images to reduce the residuals. The optimal template has the profile \mbox{$f_r(r)\propto S_r(r)$} for a pre-seeing galaxy profile $S_r(r)$; this also optimises the signal-to-noise ratio of the ellipticity \citep{2002AJ....123..583B}. Even so, realistic galaxies can never be perfectly fit by an elliptical model; there are always fitting residuals $\vec{R}_{\rm pre}$. To deal with these residuals, we can imagine a more elaborate Bayesian scheme where $\vec{R}_{\rm pre}$ are additional nuisance parameters that we marginalize over by using an empirical distribution $P(\vec{R}_{\rm pre}|\vec{p})$ of $\vec{R}_{\rm pre}$ given $\vec{p}$ (prior), i.e., \begin{equation} {\cal L}(\vec{I}|\vec{p})= \int\d\vec{R}_{\rm pre}\;{\cal L}(\vec{I}|\vec{p},\vec{R}_{\rm pre})\,P(\vec{R}_{\rm pre}|\vec{p})\;, \end{equation} where ${\cal L}(\vec{I}|\vec{p},\vec{R}_{\rm pre})$ is the likelihood of a post-seeing image, correctly specified by the post-seeing model \mbox{$\vec{m}(\vec{p})=\mat{L}(A\,\vec{f}_\rho+\vec{R}_{\rm pre})$} and the noise distribution. The marginalization would then increase the statistical uncertainty in the posterior $P_\epsilon(\epsilon|\vec{I})$ in Eq. \Ref{eq:posterior}. It is conceivable to measure the prior in a dedicated survey by assessing the distribution of residuals in template fits to high resolution, high S/N images. This approach would be similar to that of BA14 where a (correct) prior on galaxy-specific descriptors is needed. In comparison to BA14, it is noteworthy here that the residuals $\vec{R}_{\rm pre}$ in the pre-seeing frame are those of sheared images for which we infer $\epsilon$; no assumptions on the unsheared, source-plane images have to be made for this prior. All this, however, still has to be tested, and it is not clear how this can be properly implemented and if this marginalization is not the source of another bias. A consistent likelihood of single images is not sufficient for a lensing analysis as new inconsistencies for $\epsilon$ or $g$ can arise in samples of intrinsically different sources through incorrect priors for intrinsic source parameters, such as sizes or centroid positions (prior bias). Take for example our TMP galaxies in Sect. \ref{sec:testsandresults} which have a correctly specified likelihood by definition; they are free of underfitting bias. For the two experiments presented in Fig. \ref{fig:biasbymarg} and Fig. \ref{fig:glamtest2}, the source sample consists of pre-seeing images with an unknown distribution of intrinsic parameters. The first experiment considers samples with constant ellipticity, the second samples with constant reduced shear. Despite the absent underfitting, noise bias now emerges in both cases if we apply our uniform prior for the nuisance parameters in the marginal posterior of either ellipticity or reduced shear; see TMP data points at $\nu\lesssim20$. We argue in Sect. \ref{sect:glammarginal} that the emerging noise bias is related to the specific choice of priors and can only be avoided by a special family of correct priors related to the maximum of the posterior of noise-free images. According to previous work, correct priors are the distributions of nuisance parameters of the sources in the sample which have to be defined externally (e.g., BA14, \citealt{2013MNRAS.429.2858M}, \citealt{2008MNRAS.390..149K}). A conceivable alternative to external priors, potentially worthwhile investigating in future studies, might be to specify the priors down to a family of distributions, so-called hyperpriors, with a finite, preferably small number of hyperparameters \citep{gelman2003bayesian}. A hierarchical approach would then jointly determine the posterior density of $\epsilon$ or $g$ and the hyperparameters from all $\vec{I}_i$ alone in a fully Bayesian way. Marginalizing over the hyperparameters accounts for the uncertainty in the priors. Note that the incorrect uniform prior for $\epsilon_{\rm s}$ in Fig. \ref{fig:glamtest2} has no significant impact on the shear bias (compare open to filled data points). Clearly, the importance of a correct prior depends on the type of nuisance parameter. That prior bias in Fig. \ref{fig:glamtest2} or Table \ref{tab:euclidlike} becomes relevant only at low S/N can be understood qualitatively. For a sufficiently high S/N, the mass of an (identifiable) likelihood ${\cal L}(\vec{I}_{\rm post}|\vec{p})$ concentrates around $\vec{p}_{\rm post}$ such that the prior $P_{\rm p}(\vec{p})$ details have no strong impact on the marginal posterior of one source. We also expect for high S/N the likelihood to be well approximated by a normal Gaussian with maximum $\vec{p}_{\rm post}$ such that the marginalization over $\vec{q}=(A,t,\vec{x}_0)$ approximately yields a Gaussian posterior $P_\epsilon(\epsilon|\vec{I}_{\rm post})$ with maximum near $\epsilon_{\rm post}$, which is the true pre-seeing ellipticity for a correctly specified likelihood. Note that the marginalization over $\vec{q}$ of a multivariate Gaussian with maximum at \mbox{$\vec{p}_0=(\epsilon_0,\vec{q}_0)$} produces another Gaussian density with maximum at $\epsilon_0$. In addition, should the likelihood be misspecified, $\epsilon_{\rm post}$ will be prone to underfitting bias which is clearly visible by the offsets in $m$ for EXP and DEV in Fig. \ref{fig:glamtest2}. Finally, we point out that while marginal posteriors $P_\epsilon(\epsilon|\vec{I}_i)$, obtained on an image-by-image basis, are sufficient to infer a constant ellipticity (or shear) it is not obvious how to incoorporate them into a fully Bayesian analysis of sources with varying shear. For example, in a fully Bayesian inference of ellipticity correlations $\xi_\vartheta=\ave{\epsilon_i^{}\epsilon_j^\ast}$ for images $ij$ at separation $\vartheta$, we would compute the likelihood ${\cal L}(\hat{\vec{I}}|\xi_\vartheta)$ for given values of \mbox{$\xi_\vartheta$} and a range of $\vartheta$, which principally requires the repeated shape measurements for the entire sample of images $\hat{\vec{I}}$ for every new $\xi_\vartheta$. This poses a practical, computational problem. Proposed solutions to this problem leave the path of a fully Bayesian analysis and commonly use unbiased point estimators of $\epsilon_i$ on a image-by-image basis as input for a statistical analysis \citep[e.g.,][]{2013MNRAS.429.2858M}. This technique has essentially been applied to all lensing analyses so far, but requires a calibration of the ellipticity estimates, especially for the noise bias. The recently proposed hierarchical Bayesian technique by \citet{2016MNRAS.455.4452A}, applied to data in \citet{2017MNRAS.466.3272A}, is closest to a fully Bayesian analysis in the above sense but also uses as input unbiased estimators of source ellipticities with a multivariate Gaussian probability density for the statistical errors of the estimates. Yet, it is surely conceivable to extend this technique by directly modelling the likelihood of source images $\vec{I}_i$. To reverse-propagate our $P_\epsilon(\epsilon|\vec{I}_i)$ to a posterior of $\xi_\vartheta$, we might be tempted here to Monte-Carlo a posterior PDF of $\xi_\vartheta$ by independently drawing ellipticities \mbox{$\epsilon_{im}\sim P_\epsilon(\epsilon|\vec{I}_i)$} from the marginal posteriors to produce realisations of a joint vector $\vec{\epsilon}_m=(\epsilon_{1m},\ldots,\epsilon_{nm})$, which could be used with an estimator of $\xi_\vartheta$. Unfortunately, this falsely assumes a separable joint posterior \mbox{$P_\epsilon(\vec{\epsilon}|\hat{\vec{I}})= P_\epsilon(\epsilon_1|\vec{I}_1)\times \ldots\times P_\epsilon(\epsilon_n|\vec{I}_n)$} with statistically independent ellipticities, potentially biasing (low) constraints on $\xi_\vartheta$. As alternative we speculate about the following hierarchical Bayesian scheme. We assume a parametric model $P_\epsilon(\vec{\epsilon}|\hat{\vec{I}},\vec{\theta})$ for the joint posterior density of ellipticities that is determined by (i) the measured marginal ellipticities $P_\epsilon(\epsilon|\vec{I}_i)$ and (ii) a set of unknown hyperparameters $\vec{\theta}=(\theta_1,\theta_2,\ldots)$ that quantify the correlations between the source ellipticities. A convenient choice in this respect seem to be copula models that are specified exactly that way \citep[e.g., Sect. 2 in][]{2010MNRAS.406.1830T}. We further express our ignorance about $\theta_i$ by a (sufficiently uninformative) hyperprior $P_\theta(\vec{\theta})$. We then produce realisations $\vec{\epsilon}_m$ by first randomly drawing $\vec{\theta}_m\sim P_\theta(\vec{\theta})$ followed by $\vec{\epsilon}_{\rm m}\sim P_\epsilon(\vec{\epsilon}|\hat{\vec{I}},\vec{\theta}_m)$. A sample $\{\vec{\epsilon}_1,\vec{\epsilon}_2,\ldots\}$ of joint ellipticities is then utilized to propagate uncertainties on source ellipticities and their mutual correlations through the lensing analysis, based on an estimator for $\xi_\vartheta$ given a joint sample $\vec{\epsilon}$. Note that in the limit $\nu\to\infty$ the hyperprior for $\vec{\theta}$ becomes irrelevant because all marginal posteriors $P_\epsilon(\epsilon|\vec{I}_i)$ will be sharply peaked at the true ellipticity (if correctly specified). | 16 | 9 | 1609.07937 |
1609 | 1609.07106_arXiv.txt | I model the effect of rapid stellar rotation on a planet's insolation. Fast-rotating stars have induced pole-to-equator temperature gradients (known as gravity-darkening) of up to several thousand Kelvin that affect the star's luminosity and peak emission wavelength as a function of latitude. When orbiting such a star, a planet's annual insolation can strongly vary depending on its orbit inclination. Specifically, inclined orbits result in temporary exposure to the star's hotter poles. I find that gravity-darkening can drive changes in a planet's equilibrium temperature of up to $\sim15\%$ due to increased irradiance near the stellar poles. This effect can also vary a planet's exposure to UV radiation by up to $\sim80\%$ throughout its orbit as it is exposed to an irradiance spectrum corresponding to different stellar effective temperatures over time. \\ | A planet's climate is heavily influenced by the type of star it orbits. For example, stellar type determines a planet's exposure to cosmic rays and UV radiation \citep{bruzual1993spectral,griessmeier2009protection}, as well as the system's ice line and habitable zone \citep{traub2011terrestrial}. Planetary atmospheric and climatic behaviors are driven by insolation patterns, which in the right circumstances can result in seasons unlike any in our solar system. This work models insolation around fast-rotating early-type stars and demonstrates potential effects rapid rotation can have on a planet's climate. Early-type stars with effective temperatures $\geq6200$ K possess radiative exteriors and almost no magnetic field. As a result, their primordial rotation rates are not magnetically damped \citep{2012ApJ...757...18A}. Early-type stars therefore often rotate rapidly, which induces pole-to-equator temperature gradients of up to several thousand Kelvin \citep{harrington1968intrinsic,fremat2005effects}. This gradient affects both the star's luminosity and peak emission wavelength as a function of stellar latitude \citep{von1924radiative}. When orbiting such a star, a planet's seasonal insolation pattern can strongly vary depending on orbit geometry. Specifically, an inclined orbit results in more exposure to the host star's hotter poles, affecting temperature variations over the course of the planet's year. The pole-to-equator stellar flux gradient, called gravity-darkening, can also affect chemical processes in a planet's atmosphere as it is exposed to irradiance corresponding to different stellar effective temperatures over time. This effect could play a major role in the thermal structure, photochemistry, and photoionization of planetary atmospheres \citep{lammer2003atmospheric,ribas2005evolution,yung2005photochemistry}. Exoplanets orbiting early-type stars frequently misalign from their host star's rotation plane \citep{winn2010hot,2009ApJ...705..683B,ahlers2014spin,2015ApJ...814...67A}. Therefore, gravity-darkened seasons likely occur on a significant number of exoplanets orbiting early-type stars. Understanding this phenomenon is an important step in revealing exoplanet atmospheric and surficial properties in the regime of early-type systems. in this paper, I demonstrate how spin-orbit misalignment and gravity-darkening can combine to produce unusual seasonal patterns. In \S2 I derive the insolation model, in \S3 I calculate the insolation of a spin-orbit misaligned planet orbiting a gravity-darkened star and demonstrates its effects on planet equilibrium temperature and received UV flux, and in \S4 I discuss implications for climate and atmospheric behavior. | \label{sec:discussion} \subsection{Climate Effects} The equilibrium temperature of an inclined planet around a gravity-darkened star can vary by as much as $\sim 15\%$ throughout its year due to changing total solar irradiance. This effect is additive with traditional seasons -- hemispherical temperature changes brought about by a planet's obliquity. Traditional seasons occur once per orbit, but gravity-darkened seasons occur twice per orbit -- how these two effects coincide plays a large role in determining the planet's seasonal behaviors. Ultimately, the nature of gravity-darkened seasons is driven by the phase difference between the planet's precession angle and longitude of ascending node. If traditional summer/winter occurs near the stellar poles, the planet experiences hot summers and mild winters. If traditional summer/winter instead occur near the stellar equator, mild summers and extreme winters occur, with unusually warm spring/autumn seasons. In fact, Figure \ref{fig:spinup} shows that the gravity darkening effect can overpower seasonal temperature changes caused by obliquity such that traditional spring and autumn are hotter than a hemisphere's summer, producing two distinct peak heating seasons. This temporal heterogeneity in total solar irradiance would likely drive radiative forcing on an Earth-like planet, directly impacting its sea surface temperature and hydrological cycle. For example, as the climate warms, its atmosphere would hold more water vapor, increasing greenhouse gases and further increasing the planet's temperature \citep{held2000water,forster2007changes}. The reverse would hold true when the climate cooled. Changes in total irradiance could also affect giant planet deflation/inflation rates \citep{podsiadlowski1993planet,fortney2011discovery}. This starkly constrasts with insolation in our solar system, where total solar irradiance varies by only $\sim0.2\%$ over 11-year cycles \citep{haigh2007sun}. The equilibrium temperature changes due to gravity darkening shown in Figure \ref{fig:spinup} are maximum values -- in reality, this effect would be mitigated by the planet's albedo, thermal inertia, and atmosphere. The planet would likely not be able to circulate heat globally as quickly as its total irradiance changed, especially for close-in planets. For example, 55 Cancri e is an exoplanet with observed poor global heat transport \citep{demory2016map}. However, the general trends in Figure \ref{fig:spinup} would still be driven by the planet's changing exposure to sunlight intensity. Figures \ref{fig:latitude} and \ref{fig:obliquity} demonstrate how a planet's precession angles and obliquities can affect seasonal insolation patterns when orbiting a gravity-darkened star. These values can change throughout a planet's lifetime. For example, Earth's rotation axis precesses every 26,000 years and oscillates in magnitude every 41,000 years \citep{lissauer2012obliquity,barnes2016obliquity}. A spin-orbit misaligned planet undergoing these changes in axial tilt would be driven through the different insolation scenarios in Figure \ref{fig:latitude} on its precession timescale. Obliquity variations could drive Milankovich cycles whose nature depends on orbit geometry. Future studies of these phenomena could help reveal planetary processes driven by gravity-darkened seasons for the first time. Recent works on habitable planet Proxima Centauri b \citep{2016Natur.536..437A} offer a path for characterizing exoplanets in detail. By constraining the planet's formation and migration history, high-energy irradiance, incoming stellar particle winds, and tidal interactions, along with the host star's evolution history, one can estimate the planet's atmospheric loss rate, its water budget, and its overall climate regime \citep{ribas2016habitability,turbet2016habitability}. \citet{barnes2016habitability} and \citet{meadows2016habitability} demonstrate that a planet's geologic behavior can be constrained by modeling its orbit evolution and tidal history, as well as heavy element abundances in the planets core. Such works provide possible next steps toward characterizing the nature of exoplanets in early-type systems. \subsection{Atmospheric Effects} Figure \ref{fig:irradiance} shows how the irradiance by wavelength on a spin-orbit misaligned exoplanet orbiting a gravity-darkened star can vary throughout its orbit. These changes occur at all wavelengths, with the strongest variations occuring at wavelengths lower than the peak emission wavelength (near UV-violet for early-type stars). The total UV irradiance can vary by as much as 80\% throughout an exoplanet's year, with the changes occuring near-sinusouidally at twice the orbit frequency. Variations in a planet's UV irradiance play a significant role in its photochemistry \citep{forster2007changes}. UV light drives the production of ozone in the Earth's stratosphere \citep{caldwell1994stratospheric}. UV irradiation also plays a significant role in the atmosphere of Saturn's moon Titan, driving much of the organic chemistry in its atmosphere and producing large amounts of aerosols \citep{szopa2006pampre}. Extreme UV irradiation can drive loss processes in an exoplanet's atmosphere. Hydrogen-rich exoplanets under extreme ultraviolet radiation may evaporate down to their cores \citep{lammer2003atmospheric}. \citet{forster2007changes} shows how even very small changes in UV irradiation on the Earth can have significant impacts on the structure of its atmosphere. Gravity-darkening can cause massive changes in UV irradiance throughout an inclined planet's orbit; future photochemical and radiative tranfer models could reveal the full impact of gravity-darkening on a planet's atmopshere. \subsection{Conclusion} With rapid stellar rotation and planet spin-orbit misalignment common in early-type systems \citep{winn2010hot,2012ApJ...757...18A}, gravity-darkened seasons likely occur in a significant number of exoplanets. I quantify how this phenomenon scales with stellar rotation rate, planet inclination, and semi-major axis and shows that a planet's equilibrium temperature can nominally vary by as much as 15\%. Such a planet's total solar influx varies at twice its orbit frequency. This work shows how traditional seasons caused by planet obliquity can combine with its changing irradiance, and demonstrates how planet obliquity and gravity-darkening can combine to produce unusual seasonal patterns. In early-type systems, these effects are strongest in UV irradiance, which can have profound impacts on a planet's atmosphere. The insolation patterns modeled in this work represent a preliminary investigation into the nature of planets orbiting fast-rotating stars. As planet detection and characterization techniques improve, more and more planets undergoing gravity-darkened seasons will likely be revealed. Future atmospheric models could reveal how gravity-darkened seasons can affect a planet's climate and photochemistry, shedding new light on planets orbiting stars dissimilar to our own. | 16 | 9 | 1609.07106 |
1609 | 1609.05335_arXiv.txt | \vskip12pt The study of magnetic activity of the Sun and the stars which is called by the complex of electromagnetic and hydrodynamic processes in their atmospheres is of fundamental importance for astrophysics. The relative sunspot number SSN is a very popular, widely used solar activity index: the series of relative sunspot numbers direct observations continue almost two hundred years. The SSN index has an advantage over other indices of activity because data on annual variation available from the 1700's: for 1700--1849 on the basis of undirect data, later then 1850 -- according to the direct observations. The SSN (also known as the International sunspot number, relative sunspot number, or Wolf number) is a quantity that measures the number of sunspots and groups of sunspots present on the surface of the sun. Sunspots are temporary phenomena on the photosphere of the Sun that appear visibly as dark spots compared to surrounding regions. They are caused by intense magnetic activity, which inhibits convection by an effect comparable to the eddy current brake, forming areas of reduced surface temperature. Although they are at temperatures of roughly 3000-4500K), the contrast with the surrounding material at about 5.780 K leaves them clearly visible as dark spots. Manifesting intense magnetic activity, sunspots host secondary phenomena such as coronal loops(prominences) and reconnection events. Most of solar flares and coronal mass ejections originate in magnetically active regions around visible sunspot groupings. Similar phenomena indirectly observed on stars are commonly called stars pots and both light and dark spots have been measured. Thus the cyclic variations of the SSN and the evolution of these cycles in time is an important task for the study of all complex phenomena on the Sun associated with different indices of solar activity. The historical sunspot record was first put by Wolf in 1850s and has been continued later in the 20th century until today. Wolf's original definition of the relative sunspot number for a given day as $R = 10 \cdot$ Number of Groups + Number of Spots visible on the solar disk has stood the test of time. The factor of 10 has also turned out to be a good choice as historically a group contained on average ten spots. Almost all solar indices and solar wind quantities show a close relationship with the SSN, see [1],[2]. We have to point out that close interconnection between radiation fluxes characterized the energy release from different atmosphere's layers is the widespread phenomenon among the stars of late-type spectral classes, see [3]. It was confirmed that there exists the close interconnection between photospheric and coronal fluxes variations for Sun-like stars of F, G, K and M spectral classes with widely varying activity of their atmospheres, see [4],[5]. It was also shown that the summary areas of spots and values of X-ray fluxes increase gradually from the sun and Sun-like Mount Wilson HK project stars [6] with the low spotted discs to the highly spotted K and M-stars. The main characteristic describing the photospheric radiation is the spottiness of the stars. Thus, the study of the relative sunspot numbers is very important to explain the observations of sun-like stars. The level of chromospheric activity of the Sun is consistent with that of HK-project stars, which have well-defined cycles of activity, but the level of coronal activity of the Sun is significantly below that of the coronal activity of Sun-like G-stars from the different observational Programs which are studied Sun-like stars: (1) HK-project -- the Mount Wilson program, see [6]; (2) The California \& Carnegie Planet Search Program which includes observations of approximately 1000 stars at Keck \& Lick observatories in chromospheric CaII H\&K emission cores, see [7]; (3) The Magellan Planet Search Program which includes Las Campanas Observatory CA measurements of 670 F, G, K and M main sequence stars of the Southern Hemisphere. $S_{HK}$-indexes of these stars are also converted to the Mount Wilson system, see [8]. A comparative analysis of chromospheric, coronal and cyclic activity of the Sun and Sun-like stars of F, G and K spectral classes from these different observational Programs shows the similar characteristics of magnetic cycles on the Sun and on the Sun-like stars, see [9],[10]. We have studied: (1) -- yearly averaged values of SSN during solar activity cycles 1 -- 23, the tree-hundred yrs data set; (2) -- yearly averaged values of sunspot areas A, the 400 yrs data set, see [11]; (3) -- monthly averaged values of SSN during activity cycles 18 -- 24 and (4)-- daily averaged values of SSN during activity cycle 22. All SSN data are available at NGDC web site, see observational data from National Geophysical Data Center. Solar Data Service [12]. For the HK-project stars study we have applied the wavelet analysis for partially available data from the records of relative CaII emission fluxes - the variation of $S_{HK}$-indexes for 1965--1992 observation sets from Baliunas et al. (1995) and for 1985-- 2002 observations from [13]. We used the detailed plots of $S_{HK}$-indexes time dependencies: each point of the record of observations, which we processed in this paper using wavelet analysis technique, corresponds to three months averaged values of $S_{HK}$. \vskip12pt | \vskip12pt The study of the evolution of solar cyclicity by observations of the Relative Sunspot Number and Sunspot Areas variation using the wavelet analysis allows us to make more accurate predictions of indices of solar activity (and consequently the predictions of the parameters of the earth's atmosphere), and also to take a step towards a greater understanding of the nature of cyclicity of solar activity. The close interconnection between activity indices make possible new capabilities in the solar activity indices forecasts. For a long time the scientists were interested in the simulation of processes in the earth's ionosphere and upper atmosphere. For these purposes it is necessary the successful forecasts of maximum values and other parameters of future activity cycles and also it has been required to take into account the century component. The study of the evolution of Sun-like stars cyclicity by example of Mount Wilson observations of $S_{HK}$ - index using the wavelet analysis reveals the similar features in solar and stellar cyclic activity: the existence of multiple cycles and their evolution in time. Wavelet analysis of these data reveals the following features: the period and phase of these relatively low frequency variations of the solar or stellar fluxes, previous to the studied time point, influence to the amplitudes and to the phase of studied time point. Solar or stellar fluxes show the gradually changing of their values in time: as a result, the periods of variations are getting longer. | 16 | 9 | 1609.05335 |
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1609 | 1609.01720_arXiv.txt | Dalessandro et al. observed a similar distribution for blue straggler stars and main-sequence turn-off stars in the Galactic globular cluster NGC 6101, and interpreted this feature as an indication that this cluster is not mass-segregated. Using direct $N$-body simulations, we find that a significant amount of mass segregation is expected for a cluster with the mass, radius and age of NGC 6101. Therefore, the absence of mass segregation cannot be explained by the argument that the cluster is not yet dynamically evolved. By varying the retention fraction of stellar-mass black holes, we show that segregation is not observable in clusters with a high black hole retention fraction (>50\% after supernova kicks and >50\% after dynamical evolution). Yet all model clusters have the same amount of mass segregation in terms of the decline of the mean mass of stars and remnants with distance to the centre. We also discuss how kinematics can be used to further constrain the presence of a stellar-mass black hole population and distinguish it from the effect of an intermediate-mass black hole. Our results imply that the kick velocities of black holes are lower than those of neutron stars. The large retention fraction during its dynamical evolution can be explained if NGC 6101 formed with a large initial radius in a Milky Way satellite. | \label{Intro} Globular clusters (GCs) are old stellar systems ($\sim 10 - 13 \gyr$) with masses ($\sim$ few $10^5 \msun$) and densities ($\sim$ few $1000 \msun \pcd$) resulting in two-body relaxation time-scales shorter than their age. In two-body encounters, the lighter stars generally gain velocity while the heavier stars lose velocity. After many subsequent encounters, the low-mass stars gain velocity with respect to the high-mass stars, which in turn means that in GCs, light stars are found further away from the centre than high-mass stars \citep{1995ApJ...452L..33K}. This effect is generally referred to as mass segregation. Because GCs are older than their respective half-mass relaxation time ($\trh$) \citep{1961AnAp...24..369H,2011MNRAS.413.2509G}, we expect the stars and remnants of different masses to have different distributions in phase space. This effect has been confirmed observationally \citep{1995ApJ...452L..33K,2014MNRAS.437.1918S}. There are different ways to study mass segregation in GCs. The one we will mostly refer to in this study is the use of cumulative radial distributions of stars with different masses: in a mass-segregated cluster, we expect the stars with high mass, such as blue straggler stars (BSSs) to be more centrally concentrated than main-sequence turn-off stars (MSTO). If the cluster is not mass-segregated, then the cumulative radial distributions are the same. \cite{2008ApJ...686..303G} showed that the presence of an intermediate-mass black hole (IMBH) reduces the amount of mass segregation among observable stars, and they suggest that this could be used as an observable indication of the presence of an IMBH. \cite{Dalessandro2015} (hereafter D15) recently studied different properties of the GC NGC 6101, such as the radial distribution of the BSSs, the radial variation of the binary fraction and the radial variation of the luminosity and mass function (MF). From their analyses, they conclude that this cluster is not mass-segregated. They also found a large core radius relative to the half-light radius (effective radius) for the GC ($R_{\rm c} / R_{\rm eff} \approx 0.4$). NGC 6101 is a metal-poor cluster with $\feh = -1.98$ \citep{2009A&A...508..695C} located at a distance of $14.6$ kpc (D15) from the Sun and $11.2$ kpc \citep{1996AJ....112.1487H} from the Galactic Centre. When fitting a \cite{1966AJ.....71...64K} model to the observed number density profile, D15 obtained a concentration $c = \log(r_{\rm t}/r_{\rm c}) = 1.3$ and a projected effective radius of $R_{\rm eff} = 128.2$ arcsec. These values are larger than the values listed in the \cite{1996AJ....112.1487H} catalogue and those given by \cite{2005ApJS..161..304M}. D15 attribute the larger radii to their improved method of background subtraction. D15 estimate that NGC 6101 has an half-mass relaxation time-scale of $\trh \sim 5.4 - 6.3$ Gyr. The value of the initial half-mass relaxation time ($\trhz$) for NGC 6101 should be smaller than the one we measure today for this cluster, because in roughly the first half of the evolution of tidally limited GCs, the half-mass relaxation time increases due to stellar mass-loss and two-body relaxation-driven expansion \citep{2010MNRAS.408L..16G}. In Section~\ref{sec:Nbody}, we estimate $\trhz$ to be $\sim 2.8 \gyr$. \cite{2008ApJ...686..303G} found that a cluster needs to be $\sim 5 \trhz$ old to appear fully mass-segregated. Given the estimated age of $13 \gyr$ \citep{2010ApJ...708..698D}, we expect NGC 6101 to show signs of mass segregation. The objective of this study is to understand this contradiction: on one hand, the cluster appears to be not mass-segregated, on the other hand mass segregation is expected based on the age and estimated $\trhz$. It has been shown \citep{2004MNRAS.355..504M,2004ApJ...608L..25M,2013A&A...558A.117L} that a population of heavy remnants can result in a large core radius ($\rc$) over half-mass radius ($\rh$), as observed for NGC 6101. Because black hole (BH) candidates have recently been observed in several GCs \citep{2012Natur.490...71S,2013ApJ...777...69C}, we investigate the effect of a population of remnants on the apparent mass segregation for the case of NGC 6101. To do this, we use a set of $N$-body simulations with different retention fractions of BHs, and we compare them to the observations. We also use dynamical equilibrium models to formulate predictions on other observable quantities. This paper is organized as follows: in Section \ref{sec:Nbody}, we present the $N$-body models used in this analysis. In Section \ref{sec:Results}, we discuss the results of the analysis of our $N$-body models and we show the effects produced by a population of stellar-mass BHs on the observations. In Section \ref{sec:discussion}, we propose a method to observationally distinguish the scenario we introduce here from other possible explanations, by looking at the kinematics of the cluster. In Section \ref{sec:Conclusion}, we discuss our results in the context of other scenarios and present our conclusions. \begin{table*} \caption{Initial and final properties of the three $N$-body models, as indicated in the first column. We list the values of the number of bound stars $N$, the total mass of bound stars $M$ in $\msun$, the half-mass radius $\rh$ in pc, the number of black holes contained in the cluster $N_{\rm BH}$ and their total mass $M_{\rm BH}$ in $\msun$: the values provided for these quantities in the first part of the table refer to the initial properties of the clusters, the ones in the second part to the properties they have at an age of 13 Gyr. Moreover, we also provide the total number of black holes contained in the clusters before taking into account the effect of the kick velocity, $N_{\rm BH,created}$.} \label{tab:NBody} \begin{tabular}{ccccccccccccc} \hline $N$-body & \multicolumn{6}{c}{Initial properties} & & \multicolumn{5}{c}{Final properties} \\ model & $N$ & $M$ & $\rh$ & $N_{\rm BH}$ & $M_{\rm BH}$ & $N_{\rm BH,created}$ & & $N$ & $M$ & $\rh$ & $N_{\rm BH}$ & $M_{\rm BH}$ \\ \hline N0 & $10^{5}$ & $5.4 \times 10^{4}$ & $7.6$ & $0$ & $0$ & $176$ & & $8.8 \times 10^{4}$ & $3.2 \times 10^{4}$ & $13.6$ & $0$ & $0$ \\ N0.5 & $10^{5}$ & $6.3 \times 10^{4}$ & $7.6$ & $105$ & $1442$ & $177$ & & $8.5 \times 10^{4}$ & $3.1 \times 10^{4}$ & $14.1$ & $64$ & $486.6$ \\ N1 & $10^{5}$ & $6.3 \times 10^{4}$ & $7.6$ & $176$ & $2024$ & $176$ & & $8.3 \times 10^{4}$ & $3.1 \times 10^{4}$ & $20.0$ &$120$ & $840.3$ \\ \hline \end{tabular} \end{table*} | \label{sec:Conclusion} Recently, D15 observed that BSS and MSTO stars have the same radial distribution in the GC NGC 6101, and they argue that the cluster is not mass-segregated and not dynamically evolved. \cite{1991AJ....102..628S} and \cite{2001A&A...380..478M}, who also studied the radial distribution of the BSSs in this cluster, found indications for mass segregation. The reason for this discrepancy is that each of these papers analyse a different sample of BSS stars. \cite{1991AJ....102..628S} were the first ones to study BSSs in this cluster and they found 28 BSSs. \cite{2001A&A...380..478M} found and studied 73 BSSs in NGC 6101. D15, however, reduced the sample of BSSs in NGC 6101 to 52 objects, after identifying and removing sources which are contaminated and/or blended by other MS stars or evolved stars. Given these and other improvements by D15, we adopt their interpretation that NGC 6101 does not show any observable signs of mass segregation. By carrying out three numerical $N$-body simulations containing a different amount of BHs, we showed that the same behaviour is found in a mass-segregated cluster containing a population of stellar-mass BHs. Indeed, even if they are not directly observable, BHs have an effect on the overall distribution of stars in the mass range available for observations ($0.7-1.6 \msun$) that appear to have the same distribution, as shown in Fig.~\ref{fig:CPlot-All-1}. We also see from our simulation without BHs (N0) that the age and present-day mass and half-mass radius suggest that NGC 6101 is dynamically evolved, and is expected to be mass-segregated. Model N0 shows clear evidence for observable mass segregation. The scenario of a non-mass-segregated cluster could then only be explained if some of our assumptions, such as the age of the cluster, its stellar evolution or its IMF, were significantly different from what we assumed here, which we consider unlikely. We therefore favour the explanation that NGC 6101 contains a stellar-mass BH population. Stellar-mass BH candidates were recently found in M22 and M63 by \cite{2012Natur.490...71S} and \cite{2013ApJ...777...69C}, respectively. Several studies have shown that, if the initial supernova kicks are not large enough to eject the BHs from the cluster at creation, then a significant fraction of BHs can be retained for more than $12 \gyr$ \citep{2013MNRAS.432.2779B,2013MNRAS.436..584B,2013MNRAS.430L..30S,2015ApJ...800....9M}; in particular, this happens when clusters have large initial radii \citep{2015ApJ...800....9M, 2016arXiv160104227R}. Moreover, \cite{2008MNRAS.386...65M} showed that the large cores of GCs in the Magellanic Clouds can be explained by the presence of a population of stellar-mass BHs in the systems. The fact that NGC 6101 is on a retrograde orbit is seen as an indication for an extragalactic origin \citep{1995AJ....109..605G}. More recently, it has been suggested that NGC 6101 was accreted into the Milky Way \citep{2004MNRAS.355..504M} and could originally come from the Canis Major dwarf galaxy \citep{2004MNRAS.348...12M}. One of the arguments used by \cite{2004MNRAS.355..504M} to support the claim that NGC 6101 is accreted is the observation that the large core radius of the cluster is more comparable to the core radii of GCs in dwarf galaxies than to those of clusters in the Milky Way. This raises the question why GCs that form in dwarf galaxies contain more BHs than GCs that form \textit{in situ}. There are no reasons to expect that the initial stellar MF is significantly different in dwarf galaxies (although, see \citealt{2013ApJ...771...29G}), nor that the supernova kicks are different in dwarf galaxies. One idea is that all GCs retain a large fraction of their BHs after supernova kicks (i.e. BH kicks are low), and that GCs in dwarf galaxies form with lower densities (e.g. \citealt{2008ApJ...672.1006E}). A low-density implies a long $\trh$ (for a given mass), such that fewer BHs are dynamically ejected. An alternative explanation for the observed properties of NGC 6101 could be the presence of an IMBH. This central object would cause, in many respects, effects similar to those of a population of stellar-mass BHs, such as the formation of a large core and a large ratio of core radius to half-mass radius \citep{2007MNRAS.374..344T,2013A&A...558A.117L}. In addition, an IMBH can quench mass segregation among the visible stars: \cite{2008ApJ...686..303G} show that this effect is due to close encounters between stars and the IMBH, resulting in slingshot ejections to large distances, thereby reversing mass segregation. Moreover, the IMBH is likely to acquire a companion, either a star or a remnant, which makes stellar ejections particularly common. \cite{2008ApJ...686..303G} also measured mass segregation by looking at the variation with radius of the average mean mass of MS stars with mass in the range $0.2-0.8 \msun$. They showed that an IMBH with mass equal to $1\%$ of the cluster mass generates a small variation of this quantity between the centre and the half-mass radius, and they conclude that if such variation is smaller than $\sim 0.07 \msun$, the cluster is likely to be hosting an IMBH. As a comparison, in both our $N$-body simulations containing a population of BHs, the variation of the average mass between the centre and the half-mass radius is also smaller than $0.07 \msun$ (for N0.5, we find a variation of $0.03 \msun$, for N1 of $0.04 \msun$), when considering MS stars. \cite{2008ApJ...686..303G} also discuss the possibility that a BH population could create the same observable effect, but they assume that BHs will leave the GC rather quickly and their impact on the observed mass segregation should therefore be rather small. Another possible alternative explanation could be the presence of binaries alone: it is known that binaries inflate the core \citep{1994ApJ...431..231V,2011MNRAS.410.2698G} and could therefore also explain the large core of NGC 6101. With our current results, we cannot quantify the degree of expected mass segregation due to binaries. A qualitative result can be drawn if one assumes that the binaries have a mass distribution comparable to the one of the NSs: the first panel of Fig.~\ref{fig:model_cum_profile}, relative to model M1, shows that the NSs alone have a negligible effect on the apparent observational mass segregation and therefore the expected effect due to binaries alone should also be rather low. Due to recent confirmation of the existence of gravitational waves by a binary BH merger \citep{2016PhRvL.116f1102A}, it is worth mentioning that GCs with a sizeable BH population, such as NGC 6101, could be a cradle of gravitational wave sources \citep{2000ApJ...528L..17P,2012MNRAS.422..841A}: not only do recent studies show that a significant fraction of BHs can be retained for more than $12 \gyr$ but they also predict a high binary fraction among the BHs in the core \citep{2015ApJ...800....9M}. Finally, we propose an observational test to distinguish the various possible scenarios for the cluster. From a comparison of distribution function-based models to the number density profile of NGC 6101, we show that a mass-segregated cluster with stellar-mass BHs is expected to have a central line-of-sight velocity dispersion $\sim 0.5 \, \rm {km \, s^{-1}}$ larger than a non-segregated cluster without BHs. When considering the presence of an IMBH in the centre of the cluster, the predicted central line-of-sight velocity dispersion should be even larger, assuming a value up to $\sim 5.1 \, \rm {km \, s^{-1}}$. Looking at the star counts by D15 for NGC 6101, one can see that approximately 100 RGB stars (or $20\%$ of D15 sample), with a $V$-band magnitude between $13.5$ and $18.7$, are located within the core radius, with around $7$ of them located within the inner $10$ arcsec. By obtaining an accurate measure of the velocity dispersion of NGC 6101 within the core radius, it should be possible to discriminate between the proposed scenarios, and to determine the dynamical state of this cluster. | 16 | 9 | 1609.01720 |
1609 | 1609.08092_arXiv.txt | In the last years we have experienced a significant increase in the number of high-resolution stellar spectra available to the scientific community. This has been possible thanks to different surveys such as APOGEE \citep{2011AJ....142...72E} or the Gaia-ESO Public Spectroscopic Survey \citep[GES; ][]{2012Msngr.147...25G, 2013Msngr.154...47R}. The analysis of all these data can be carried out by different approaches like the synthetic spectral fitting technique or the classical equivalent width method. But such a huge quantity of data requires to automatize the analysis, and different authors have developed codes and pipelines to derive stellar atmospheric parameters \citep{2006MNRAS.370..141R, 2009A&A...501.1269K, 2012A&A...547A..13T, 2013A&A...558A..38M, 2013ApJ...766...78M, 2014MNRAS.443..698S, 2015ApJ...808...16N, 2015ApJ...812..128C, 2016ascl.soft05004M, 2016ApJS..223....8C, 2016arXiv160705792B}. The result of all this recent development in the field of stellar spectroscopy is an increase in the number of available atmospheric parameters and chemical abundances, provided by independent studies and surveys using different setups (e.g., radiative transfer codes, stellar model atmospheres, continuum normalization). However, when combining all these results into a single data set in order to increase the statistical value, a challenge arises: The inhomogeneities of the original studies might end up affecting our scientific conclusions. Thus, it is important to evaluate the impact of these differences. Previous studies, such as \cite{2016arXiv160703130H}, already evaluated the global impact of different spectroscopic methods with different setups. In this study, we decided to tackle the problem by focusing on one single element. We fixed all the components of the spectroscopic analysis except one: the radiative transfer code. With this approach, we can better isolate the impact on the atmospheric parameter determination and compare the results between the synthetic spectral fitting technique and the equivalent width method. To address this complex experiment, we used iSpec\footnote{\url{http://www.blancocuaresma.com/s/}} \citep{2014A&A...569A.111B} and its flexibility to build a spectroscopic pipeline with different radiative transfer codes. | We showed how different radiative transfer codes impact the determination of atmospheric parameters, and we quantified this impact for a wide range of stars. The level of agreement varies between different codes and it is noteworthy that the disagreement is higher when different methods are used (i.e. synthesis and equivalent width). More importantly, this experiment was designed to keep all the variables fixed except the radiative transfer code and the method. The selection of lines was careful done to chose only the ones that reproduce better the Sun for all the codes. The condition were very favorable for a good converge toward similar values. Nevertheless, the disagreement cannot be completely ignored. This should discourage us from blindly mixing results coming from different sources where complete different setups and ingredients (and not only the radiative transfer codes) were used to derive their atmospheric parameters. Additionally, the discrepancies in atmospheric parameters are going to propagate to the determination of chemical abundances. Thus, if we want accurate scientific conclusions when using abundances to study stellar aggregates and the Galaxy, it is necessary to make sure they were obtained homogeneously or, at least, perform an exhaustive assessment of the consequences of combining results obtain with different setups. | 16 | 9 | 1609.08092 |
|
1609 | 1609.06787_arXiv.txt | Magnetic null has long been recognized as a special structure serving as a preferential site for magnetic reconnection (MR). However, the direct observational study of MR at null-points is largely lacking. Here, we show the observations of MR around a magnetic null associated with an eruption that resulted in an M1.7 flare and a coronal mass ejection. The GOES X-ray profile of the flare exhibited two peaks at $\sim$02:23 UT and $\sim$02:40 UT on 2012 November 8, respectively. Based on the imaging observations, we find that the first and also primary X-ray peak was originated from MR in the current sheet underneath the erupting magnetic flux rope (MFR). On the other hand, the second and also weaker X-ray peak was caused by MR around a null-point located above the pre-eruption MFR. The interaction of the null-point and the erupting MFR can be described as a two-step process. During the first step, the erupting and fast expanding MFR passed through the null-point, resulting in a significant displacement of the magnetic field surrounding the null. During the second step, the displaced magnetic field started to move back, resulting in a converging inflow and subsequently the MR around the null. The null-point reconnection is a different process from the current sheet reconnection in this flare; the latter is the cause of the main peak of the flare, while the former is the cause of the secondary peak of the flare and the conspicuous high-lying cusp structure. | Magnetic reconnection (MR) has long been recognized as the principal physical mechanism responsible for solar flares. Where and how it takes place remains so essential in understanding the triggering and evolution of flares and associated coronal mass ejections (CMEs). The dual phenomena of flares and CMEs can be collectively called a solar eruption, because of close time coincidence between the impulsive phase of flares and strong acceleration phase of CMEs, both of which are likely driven by MR \citep{Zhang2001a}. Over the past several decades, the flare-producing MR has been intensively studied and succinctly described with a standard `CSHKP' flare model \citep{Svestka1992a} (CSHKP refers to the studies of \citealt{Carmichael1964a, Sturrock1966a, Hirayama1974a, Kopp1976a}). This model, consisting of a magnetic flux rope (MFR) and an underneath current sheet (CS) \citep{Lin2000a}, has been largely validated by many observational studies that showed consistent features, such as plasma inflows \citep{Yokoyama2001a, Sun2013a, Sun2015a, Zhu2016a} , outflows or down flows \citep{McKenzie1999a, Liu2013a}, loop-top hard X-ray sources\citep{Masuda1994a}, coronal X-ray sources \citep{Sui2003a}, the termination shock \citep{Chen2015a}, and so on. The CSHKP model has been successful in explaining a large array of observational features associated with eruptive flares. Nevertheless, it is largely a two-dimensional (2D) model and has a simple bipolar magnetic configuration. It has an intrinsic shortage in describing certain realistic solar flare events, which may explicitly involve the three-dimensional (3D) structure in the modeling in order to understand certain observational features.\par One of the important subjects in 3D MR theories concerns the peculiar structure of null-points. Previous theoretical studies suggest that 3D null-point may be a preferential site for the generation of MR \citep{Priest1996a, Priest2009a}. Based on the theoretical models, a series of numerical experiments are conducted through applying perturbations, like rotational and shearing motions, to the spine and fan structures extended from the null. As a result, strong current is found to develop around the null-point \citep{Pontin2007a, Galsgaard2011a, Wyper2012a}. \cite{Pontin2013a} demonstrated that the connectivity of the magnetic field line would change when it transfers across the CS forming around the null-point and treat that as a feature of spine-fan reconnection. In addition, the role of 3D reconnecting null-point in accelerating particles is also confirmed by several simulations \citep{Browning2010a, Stanier2012a, Baumann2013a, Baumann2013b}. However, in observations, the reconnection around null-point has only been reported in a handful of studies in the Sun \citep{Filippov1999a, Fletcher2001a, Sun2012a, Wang2012a, Sun2014a} and in the Earth's magnetosphere \citep{Xiao2006a}. The detailed evolution of the magnetic field and plasma surrounding the null-point during the reconnection, i.e. the observational features of the null-point reconnection, has been seldom obtained. Such lack of observational studies restrict the improvement of theoretical models. Consequently, how the null-point reconnection is triggered and conversely how it affects the evolution of flares are still open questions that need more observations to answer \citep{Torok2011a}.\par Here, we show the direct observations that reveal the processes of how MR is triggered and how it proceeds at a null-point. The observations are based on an array of instruments, including the Solar Dynamics Observatory (SDO; \citealt{Pesnell2012a}), Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI; \citealt{Lin2002a}), Nobeyama Radioheliograph (NoRH; \citealt{Nakajima1994a}), and Geostationary Operational Environmental Satellites (GOES). The overall observations are presented in $\S$2.1. $\S$2.2 focuses on the process of MR, followed by the analysis of the 3D magnetic topology in $\S$2.3. We conclude the results and discuss their significance in $\S$3.\par | In this work, we analyze the MR around a null-point in an M1.7 flare. The main results can be summarized as follows: \begin{enumerate} \item{There existed two separate peaks in SXR and HXR time profiles resulted from MR in two different locations: one from the vertical CS created by the erupting MFR, and the other probably from the null-point roughly stationed above the pre-eruption MFR.} \item{The magnetic field associated with the null-point went through two distinct steps: (1) separation distortion due to the throughput motion of the eruption/expanding MFR, and (2) inflow or recovery motion of the displaced field lines following the eruption.} \end{enumerate}\par Based on the above results, the two-step MR during the flare is schematically shown in Figure 5. During the flare impulsive phase, the MR (red star) takes place in the CS underneath the erupting MFR (red field lines) and produces the flare arcade 1(blue loops). As the MFR erupts through the MN, the magnetic field surrounding the null (green and yellow field lines) are pushed aside. When the MFR moves away, these distorted field lines begin to move back and produce the MR around the MN, produce the cusp (orange region) and flare arcade 2 (red loop).\par In classical flare models that involve the current sheet, the reconnection site always keeps rising with time, due to the upward erupting MFR leading to the further stretching of the overlying magnetic field to a higher altitude. However, during the null-point reconnection, both the evolution of the above-the-loop-top hot region and the outflows indicated that the reconnection site (i.e. the magnetic null) almost keeps at the same altitude. However, the null-point reconnection also shows many similarities to the traditional flare reconnection, including the plasma inflow toward and outflow from the reconnection site, the flare cusp, the above-the-loop-top hot region, the HXR coronal source, and the post-flare loop arcade etc. Moreover, from the emission feature of the cusp, the most intensive emission region also lies somewhere outside the MR site \citep{Krucker2010a, Liu2013a, Sun2014b}. Since magnetic nulls are rather common in the corona, they have the potential to trigger the reconnection there when encountered by an erupting MFR \citep{Torok2011a}, like what we observed in this event. This kind of MR may not be uncommon in solar flares, but is largely ignored in previous studies, mainly limited by observations. \par Due to uncertainties in the magnetic field measurements, which are used as the bottom boundary, and the NLFFF modeling, we cannot completely rule out other MR regimes at flare second peak. However, based on the above observations, we believe the null-point reconnection is a reasonable explanation. More features need to be explored theoretically and observationally to uncover the mechanism of the null-point reconnection in the future. | 16 | 9 | 1609.06787 |
1609 | 1609.04920_arXiv.txt | We analyze photometry from deep B-band images of 59 void galaxies in the Void Galaxy Survey (VGS), together with their near-infrared 3.6$\mu$m and 4.5$\mu$m Spitzer photometry. The VGS galaxies constitute a sample of void galaxies that were selected by a geometric-topological procedure from the SDSS DR7 data release, and which populate the deep interior of voids. Our void galaxies span a range of absolute B-magnitude from $\rm{M_B=-15.5}$ to $\rm{M_B=-20}$, while at the 3.6$\mu$m band their magnitudes range from $\rm{M_{3.6}=-18}$ to $\rm{M_{3.6}=-24}$. Their B-[3.6] colour and structural parameters indicate these are star forming galaxies. A good reflection of the old stellar population, the near-infrared band photometry also provide a robust estimate of the stellar mass, which for the VGS galaxies we confirm to be smaller than $3 \times 10^{10}$ M$_\odot$. In terms of the structural parameters and morphology, our findings align with other studies in that our VGS galaxy sample consists mostly of small late-type galaxies. Most of them are similar to Sd-Sm galaxies, although a few are irregularly shaped galaxies. The sample even includes two early-type galaxies, one of which is an AGN. Their S\'{e}rsic indices are nearly all smaller than $n=2$ in both bands and they also have small half-light radii. In all, we conclude that the principal impact of the void environment on the galaxies populating them mostly concerns their low stellar mass and small size. | \label{sec:intro} Voids are prominent features of the cosmic web \citep{weyplaten2011}. Formed from primordial underdensities they now occupy a major fraction of the volume of the universe, surrounded by denser filaments, walls and sheets. They are the most underdense regions where galaxy evolution will have progressed slowly, without the dominant and complex influence of the environment. Voids therefore are extremely well suited for assessing the role of the environment in galaxy evolution, as here the galaxies are expected not to be affected by the complex processes that modify galaxies in high density environments. The void environment covers the lowest density environments found in the universe, though some voids do approach similar (and still low) densities as found in tenuous filaments and walls \citep{marius2014}. In order to get a good picture of galaxies in voids the Void Galaxy Survey (VGS) was designed, a multiwavelength study of 59 galaxies in geometrically defined voids \citep{stanonik2009,wey2011,kreckel2011,kreckel2012,beygu2016}. Previous papers based on the Void Galaxy Survey have focused on the $\rm{H\textsc{i}}$ properties of galaxies in voids \citep{kreckel2011,kreckel2012,beygu2013} and on the star formation properties of void galaxies \citep{beygu2016}. They found that voids contain a population of galaxies that are relatively HI rich of which many present evidence for ongoing gas accretion, interactions with small companions and filamentary alignments . Even though based on a wide variety of selection methods, previous studies have lead to the general contention that void galaxies appear to be blue and low-luminosity galaxies with stellar masses lower than the average galaxy - typically in the order $3 \times 10^{10} M_\odot$ - and of a late morphological type, residing in a more youthful state of star formation and possessing larger and less distorted supplies of gas \citep{szomoru1996,kuhn1997,popescu1997,karachentsev1999,grogin1999,grogin2000,rojas2004,rojas2005,croton2005,goldberg2005,hoyle2005,tikhonov2006,patiri2006a,patiri2006b,ceccar2006,wegner2008, kreckel2012,beygu2016}. \cite{penny2015} recently reported to have found some galaxies with stellar masses $\rm{10^{10}M_{\odot}}$ $<$ $M_{*}$ $<$ $\rm{5 \times 10^{11}M_{\odot}}$ that are located in voids, although the identification with underdense regions similar to those of our study is not clear. The pristine environment of voids represents an ideal and pure setting for the study of environmental influences on galaxy formation and evolution. The clearest indication for the significance of environmental influences on galaxy properties is the tight relation between morphology and density \citep{oem1974,dressler1980,dressler1985}. The fraction of elliptical and lenticular galaxies rises steeply with increasing environmental density. This goes along with the opposite trend for late-type and irregular galaxies, down towards the lowest density regions. This can be understood by observing that the evolution of galaxies in high-density regions is strongly influenced by the complex interplay of a range of physical processes, mostly induced by the interaction of galaxies amongst themselves and the intergalactic medium. Processes such as quenching, ram pressure, strangulation and tidal stripping render galaxies gas poor, yielding reddish galaxies \citep{gunn1972,larson1980,moore1996,koop2004,gabor2010,peng2010,wetzel2012}. In more moderate and low density regions these processes cease to be effective, explaining the increasing fraction of late-type and gas-rich galaxies. An additional and related environmental influence that manifests itself in voids and that still needs to be understood is the finding that void galaxies appear bluer, a trend that continues down into the most rarefied void regions. For the purpose of better understanding environmental influences on the evolution of galaxies, recent years saw a considerable increase of interest in the nature of void galaxies \citep{kreckel2011,kreckel2012,hoyle2012,beygu2013,alp2014,moorman2014,kreckel2015,tava2015,penny2015,moorman2015,beygu2016}. Amongst the issues relevant for our understanding of galaxy and structure formation, void galaxies have posed several interesting riddles and questions. Arguably the most prominent issue is that of the near absence of low-luminosity galaxies in voids, while standard LCDM cosmology expects voids to be teeming with dwarfs and low-surface-brightness galaxies \citep{peebles2001}. An interesting point of focus for void galaxy studies has therefore been the study of dwarf galaxies in nearby voids, such as in the Bo\"otes, Lynx-Cancer, Hercules and Eridanus void \citep{grogin2000, cruzen2002, pet2005, pustilnik2011a,pustilnik2013}. \cite{kreckel2011b} made a detailed HI study of the dwarf KK246 in the Local Supercluster, one of the darkest galaxies known with an M/L = 89. Another recent example concerns the study by \cite{kara2013}, who looked for faint void galaxies, not brighter than the Magellanic Clouds, in the Local Supercluster and immediate vicinity out to a distance of 40 Mpc. They found no less than 89 voids which do not appear to contain any galaxies brighter than $M_K<-18.4$. One of these voids is the Local Void. Another issue of interest is whether we can observe the intricate filigree of substructure in voids, expected as the remaining debris of the merging of voids and filaments in the hierarchical formation process \citep{weykamp1993,sheth2004,weyplaten2011,aragon2012}. Evidence for such substructure, three interacting galaxies embedded in a common HI envelope, has been reported by \cite{beygu2013}, who hypothesised it to be an assembly of a filament in a void. Of key importance towards deciphering the nature and evolutionary history of void galaxies are their structural properties. Most of the previous observational studies of void galaxies were based on an analysis of photometric data from existing all sky surveys, such as the Sloan Digital Sky Survey and the Center for Astrophysics Redshift Survey \citep{hoyle2002a,rojas2004,rojas2005,patiri2006b,hoyle2012,tava2015,alp2015,penny2015}. Lately, also within the context of the Galaxy Mass and Assembly Survey (GAMA, \cite{driver2011}) considerable attention has been devoted to voids and void galaxies \citep{alp2014,alp2015,penny2015}. Using catalogues of large-scale structure including voids, group and pair membership from the GAMA survey, \cite{alp2015} examined the galaxy properties and found that the stellar mass is the dominant factor in shaping the galaxy properties. Such studies are limited in depth or resolution because of the magnitude limits of the surveys. The present study of the galaxies in the Void Galaxy Survey focusses on the analysis of deeper photometric data that we obtained for the VGS galaxies, to assess their colour, stellar mass, galaxy concentration, morphology and specific star formation. We use deep B-band and 3.6$\mu$m near-infrared imaging to investigate the structural characteristics and morphologies of galaxies in the Void Galaxy Survey (VGS, see section 2). The analysis involves the determination of the total luminosity, characteristic scale $\rm{r_{e}}$ and the surface brightness $\rm{\mu_{e}}$ of the galaxies, along with the concentration of the stellar population, quantified by the Sersic index $n$. The inferred measurements are compared to literature values of structural parameters for a wide range of different galaxies. Amongst these are late-type disk galaxies, dEs as well as giant early-type galaxies. By using photometry in three bands, two near-infrared and one optical, our photometric study yields important insights into the morphology and stellar populations of the VGS galaxies. The deep B-band images trace both the younger and older population. A unique aspect of our study is the inclusion of the Spitzer 3.6$\mu$m and 4.5$\mu$m imaging data. In particular the 3.6$\mu$m band data represents a major asset for our understanding of the stellar population of these galaxies, given the insensitivity of the 3.6$\mu$m band images to dust extinction and the fact that they provide a good reflection of the old stellar population in these galaxies (see e.g. \cite{peletier2012} and \cite{meidt2014} for a discussion). This also means that the 3.6$\mu$m flux, together with the [3.6]- [4.5] colour provide us with a robust estimate of the stellar mass of a galaxy, since the old stellar population constitutes its major share. In addition, by combining information on the young and older stellar populations, the B-[3.6] colour provides us with a good indicator of the composition of the stellar population. In addition, we seek to extract information on the star formation and evolution of void galaxies. From the colour comparison of B-band photometry with the Spitzer 3.6$\mu$m band photometry of the void galaxies, we assess their star formation histories. This information is combined with the results obtained from near-UV imaging to infer colours and the specific star formation rates $SFR_{NUV}/M_{*}$ (see \cite{beygu2016}). The paper is organized as follows: In section~\ref{sec:vgssample} we describe the VGS sample and the results found so far. Section~\ref{sec:observ} contains a description of the observations and the data analysis. In section~\ref{sec:morphology_structure} we subsequently present the morphology of the void galaxies, and attempt to relate this to their underdense void environment. In the same section, we present and briefly discuss the structural parameters of these galaxies. The star formation properties and evolution of the stellar population form the subject of section~\ref{sec:stel_pop}. Finally, in section~\ref{sec:discussion} and section~\ref{sec:conclusion} we shortly discuss and summarize our findings. | \label{sec:conclusion} We analysed Spitzer 3.6 and 4.5$\rm{\mu m}$ and B-band imaging of 59 void galaxies as part of the Void Galaxy Survey (VGS) to study their colour, stellar mass, galaxy concentration, morphology and star formation properties. The main conclusions are: \begin{itemize} \item We find that our void galaxy sample mostly consists of late-type galaxies. Most of them are similar to (Sd-Sm) galaxies, although a few are earlier type spirals and some are irregularly shaped galaxies. \item The VGS galaxies have small half-light radii and scale lengths, rather similar to those of late-type dwarfs and small spirals. In terms of size, morphology and colour properties they clearly resemble late-type galaxies. \item Interestingly, the light distributions of VGS galaxies bear some resemblance to that of dE galaxies. Like the latter, in both wavelength regimes their S\'{e}rsic indices are smaller than 2, $n$ $<$ 2. \item They span a wide colour range in $B-[3.6]$ and most of them are blue, gas rich and star forming galaxies. An occasional VGS galaxy is gas poor, small and blue. However, they cover a considerable range of morphological types and different star formation properties \citep{beygu2016}. The same is true for their hydrogen gas content \citep{kreckel2012}. \item The voids in our sample do not appear to be populated by a particular type of void galaxy and despite the very low-surface-brightness limit of our B-band images, we have not found any dwarfs or small galaxies with $\rm{M_{*}}$ $<$ $10^{7}$ $\rm{M_{\odot}}$. After deriving the stellar masses using near-infrared images, we confirmed the upper limit of $10^{10.5}$ $\rm{M_{\odot}}$ inferred by \cite{kreckel2012}. We can conclude that the most prominent effect of the void environments is that it prohibits the formation of large and massive galaxies. \end{itemize} | 16 | 9 | 1609.04920 |
1609 | 1609.06322_arXiv.txt | \noindent Self-regulated feedback by active galactic nuclei (AGNs) appears to be critical in balancing radiative cooling of the low-entropy gas at the centres of galaxy clusters and in regulating star formation in central galaxies. In a companion paper, we \C{found steady-state solutions} of the hydrodynamic equations that are coupled to the cosmic ray (CR) energy equation for a large cluster sample. In those solutions, radiative cooling in the central region is balanced by streaming CRs through the generation and dissipation of resonantly generated Alfv{\'e}n waves and by thermal conduction at large radii. Here, we demonstrate that the predicted non-thermal emission resulting from hadronic CR interactions in the intra cluster medium exceeds observational radio (and gamma-ray) data in a subsample of clusters that host radio mini halos (RMHs). In contrast, the predicted non-thermal emission is well below observational data in cooling galaxy clusters without RMHs. These are characterized by exceptionally large AGN radio fluxes, indicating high CR yields and associated CR heating rates. We suggest a self-regulation cycle of AGN feedback in which non-RMH clusters are heated by streaming CRs homogeneously throughout the central cooling region. We predict {\em radio micro halos} surrounding the AGNs of these CR-heated clusters in which the primary emission may predominate the hadronically generated emission. Once the CR population has streamed sufficiently far and lost enough energy, the cooling rate increases, which explains the increased star formation rates in clusters hosting RMHs. Those could be powered hadronically by CRs that have previously heated the cluster core. | The central cooling time of the intracluster medium (ICM) of approximately half of all galaxy clusters is less than 1~Gyr, establishing a population of cool core (CC) clusters \citep{Cavagnolo2009, Hudson2010}. Since this cooling time falls below the cluster formation time by up to an order of magnitude, a copious amount of cold gas is expected to precipitate from the hot gaseous atmospheres and to form stars at rates up to several hundred $\rmn{M}_\odot~\rmn{yr}^{-1}$ \cite[see][for a review]{Peterson2006}. The absence of radiative cooling and star formation at the predicted high rates calls for a heating mechanism that stabilizes the system. A promising framework is provided by energy feedback from an active galactic nucleus (AGN) at the cluster centre that accretes cooling gas and launches relativistic jets, which inflate radio lobes that are co-localized with the cavities seen in the X-ray maps. As the energy is transferred to the surrounding gas, this offsets radiative cooling until the heating reservoir is exhausted and the cooling gas can fuel the central AGN again, thus establishing a tightly self-regulated feedback loop. However, there has been little direct evidence supporting the existence of this hypothetical feedback cycle. In this paper, we will provide empirical evidence for such a self-regulating heating/cooling cycle and present a theoretical model to explain the underlying physics. \C{Because the energetics of AGN feedback is more than sufficient to balance radiative cooling, it has been suggested that AGN feedback can transform CC into non-CC clusters \citep{Guo2009, Guo2010b}. However, correlating the cavity enthalpy with the central gas entropy demonstrates that CC clusters cannot be transformed into non-CC clusters on the buoyancy time-scale due to the weak coupling of the mechanical to internal energy of the cluster gas \citep{2012ApJ...752...24P}.} This calls for a {\em process that operates on a slower time-scale than the sound crossing time}. Several physical processes associated with the rising radio lobes have been proposed to be responsible for the heating, including \C{mixing \citep{Kim2003Turb, Yang2016b}}, redistribution of heat by buoyancy-induced turbulent convection \citep{2007ApJ...671.1413C, 2009ApJ...699..348S} and dissipation of mechanical heating by outflows, lobes or sound waves from the central AGN \citep[e.g.,][]{2001ApJ...554..261C, Brueggen2002, 2002ApJ...581..223R, 2012MNRAS.424..190G}. \C{Also the role of thermal conduction in combination with AGN feedback has been explored \citep{Kannan2016, Yang2016a}.} As those jet-inflated lobes rise in the cluster potential, they excite gravity modes \citep{Reynolds2015}, which successively decay and generate turbulence that dissipates and heats the cluster gas \citep[e.g.,][]{Zhuravleva2014}. Recent micro-calorimetric X-ray observations of the core of the Perseus cluster find a low ratio of the turbulent-to-thermal pressure of 4\% \citep{Hitomi2016}. Such low-velocity turbulence cannot propagate far from the excitation site without being replenished, requiring turbulence to be generated in situ throughout the core or to be transported (non-thermally) from the radio lobes. There is an alternative that explains the slow dissipation rate (acting on the Alfv{\'e}n crossing time) and operates homogeneously throughout the cluster core. Relativistic particles (called cosmic rays, CRs) that are accelerated in the relativistic jet are likely mixed into the ambient thermal plasma during the buoyant rise of radio lobes \C{\citep{Sijacki2008, Guo2011, Pfrommer2013}}. As they propagate from the injection site, they are following the ubiquitous magnetic fields \citep{Kuchar2011} that redistribute their momenta to homogeneously fill the central core before they propagate towards larger radii. Fast-streaming CRs along the magnetic field excite Alfv{\'e}n waves through the ``streaming instability'' \citep{Kulsrud1969}. Scattering on this wave field limits the macroscopic speed of GeV CRs to velocities of order the Alfv{\'e}n speed. Non-linear Landau damping of these Alfv{\'e}n waves provides a means of transferring CR energy to the cooling gas. This may provide an efficient mechanism of suppressing the cooling catastrophe of cooling cores \citep{Loewenstein1991, Guo2008, Ensslin2011, Fujita2011,Pfrommer2013, Wiener2013}. To scrutinize this model, we compiled a large sample of 39 CC clusters in our first companion paper \citep[][hereafter JP17]{Jacob2016a} and \C{found steady-state solutions} that match all observed density and temperature profiles well. In those models radiative cooling is balanced by CR heating in the cluster centres and by thermal conduction on larger scales. Most importantly we found a continuous sequence of cooling properties in our sample: clusters hosting radio mini halos (RMHs) are characterized by the largest cooling radii, star formation and mass deposition rates and thus signal the presence of a higher cooling activity. Correspondingly, more CRs are needed to balance cooling in those clusters. RMHs are radio-emitting diffuse sources with typical radial extensions of 100 to 200~kpc that are centred on some CC clusters \citep{Giacintucci2014}. The detection of unpolarized radio synchrotron emission from RMHs proves the existence of volume-filling magnetic fields and CR electrons in the cooling regions of those clusters. In contrast, Mpc-sized giant radio halos occur in a fraction of X-ray luminous non-CC clusters that are currently merging with another cluster \citep[see e.g.][for a review]{Feretti2012}. In this second paper about CR heating in CC clusters, we assess the viability of our steady-state solutions by comparing the resulting non-thermal radio and gamma-ray emission to observational data \C{ \citep[similarly to][]{Pfrommer2004,Colafrancesco2008,Fujita2012,Fujita2013}}. As CR protons interact inelastically with the ambient gas protons, they produce primarily pions (provided their energy exceeds the kinematic threshold of the reaction). Neutral pions decay into gamma-rays and charged pions produce secondary positrons and electrons that emit radio-synchrotron radiation\footnote{\C{Throughout the paper, the term secondary electrons also includes secondary positrons.}}. Confronting our model predictions with data enables us to put forward an observationally supported model for self-regulated feedback heating, in which an individual cluster is either stably heated, predominantly cooling, or is transitioning from one state to the other. Our paper is structured as follows. In Section~\ref{sec:properties}, we briefly discuss the cluster sample and the density and CR pressure profiles that we base our analysis on. In Sections~\ref{sec:radio} and \ref{sec:gamma}, we compare the non-thermal emission of our steady-state solutions to observational radio and gamma-ray data, respectively. In Section~\ref{sec:picture}, we present the emerging picture of the self-regulation cycle of CC clusters and conclude in Section~\ref{sec:conclusions}. Throughout this paper, we use a standard cosmology with a present-day Hubble factor $H_0=70~\rmn{km~s}^{-1}\rmn{Mpc}^{-1}$, and density parameters of matter, $\Omega_{\rmn{m}} = 0.3$, and due to a cosmological constant, $\Omega_{\Lambda} = 0.7$. | \label{sec:conclusions} CR heating has recently re-emerged as an attractive scenario for mediating energetic feedback by AGNs at the centres of galaxy clusters \citep{Guo2008, Ensslin2011, Fujita2011, Wiener2013, Pfrommer2013}. However, all theoretical studies to date have concentrated on individual objects or a very small sample size, precluding statistically sound conclusions on any heating model. In this sequence of two papers, we have selected a rich sample of 39 CC clusters and \C{found steady-state solutions} of the hydrodynamic equations coupled to the CR energy equation. In those, radiative cooling is balanced by thermal conduction at large scales and by CR heating in the central regions. We find that those solutions are ruled out in a subsample of clusters that host RMHs because the predicted hadronically induced non-thermal emission exceeds observational radio and (some) gamma-ray data. On the contrary, the predicted non-thermal emission respects observational radio data in CC clusters without RMHs (with the exception of A~383 and A~85, in which the CR-heating solution is barely ruled out). Those non-RMH clusters show exceptionally large AGN radio fluxes, which should be accompanied by an abundant injection of CRs and -- by extension -- should give rise to a large CR heating rate. This enables us for the first time to put forward a statistically rooted, self-regulated model of AGN feedback. We propose that non-RMH clusters are heated by streaming CRs homogeneously throughout the cooling region through the generation and dissipation of Alfv{\'e}n waves. On the contrary, CR heating appears to be insufficient to \C{fully} balance the enhanced cooling in RMH clusters. These clusters are also characterized by large SFRs, questioning the presence of a stable heating mechanism that balances the cooling rate. In those systems, thermal conduction should still regulate radiative cooling on large scales, which however is unable to adjust to local thermal fluctuations in the cooling rate because of the strong temperature dependence of the conductivity and may give rise to local thermal instability. \C{However, there will still be some residual level of CR heating in those cooling systems that quenches radiative cooling but is not able to completely offset it}. We emphasize that our self-regulation scenario of CR-induced heating not only predicts stably heated clusters and cooling clusters with abundant star formation, but also systems transitioning from one state to the other, a prominent example of which appears to be the Perseus cluster. We predict {\em radio micro halos} of scales up to a few kpcs surrounding the AGNs of these CR-heated clusters, resembling the diffuse radio emission around Virgo's central galaxy, M87. Once the CR population has streamed sufficiently far from the centre, it has lost enough energy so that its heating rate is unable to balance radiative cooling any more. As a result star formation increases in clusters that we empirically identify to host an RMH. We suggest that the CR population that has heated the cluster core in the past is now injecting secondary electrons that power the RMH. Our new picture makes a number of novel predictions that allow scrutinizing it. \begin{enumerate} \item We predict the presence of {\em radio micro halos} associated with {\em all} CC clusters that host no classic RMH and have small SFRs \citep[or alternatively H$\alpha$ luminosities,][]{Voit2008}. While this secondary emission component is expected to have a harder spectrum in comparison to the convexly curved, primary radio emission, we find that the negative flux decrement owing to the thermal Sunyaev--Zel'dovich effect typically cuts these emission components off at high frequencies ($\nu\gtrsim10-50$~GHz). In Virgo, the primary emission component predominates the hadronically induced secondary emission at all observable radio emission frequencies. Hence, we envision the harder secondary emission to predominate the primary component only in those cases where the latter has already cooled sufficiently down, i.e., at late times after the release of the CR electrons from the bubbles or at larger cluster-centric radii. \item We predict an observable steady-state gamma-ray signal resulting from hadronic CR interactions with the ICM. The spectral index that is expected to be correlated to the injection (electron and proton) index that can be probed at small radii with low-frequency radio observations \citep{Pfrommer2013}. \end{enumerate} Future magneto-hydrodynamic, three-dimensional cosmological simulations that follow CR physics are necessary to study possible time-dependent effects of the suggested scenario such as the impact of CR duty cycles on the heating rates and to address non-spherical geometries associated with the rising AGN bubbles. | 16 | 9 | 1609.06322 |
1609 | 1609.08615_arXiv.txt | { Using data from the \wse\ all-sky survey we discovered that the non-thermal infrared (IR) emission of blazars, the largest known population of extragalactic $\gamma$-ray sources, has peculiar spectral properties. In this work, we confirm and strengthen our previous analyses using the latest available releases of both the \wse\ and the \fer\ source catalogs. We also show that there is a tight correlation between the mid-IR colors and the $\gamma$-ray spectral index of \fer\ blazars. We name this correlation {\it the infrared--$\gamma$-ray connection}. We discuss how this connection links both the emitted powers and the spectral shapes of particles accelerated in jets arising from blazars over ten decades in energy. Based on this evidence, we argue that {\it the infrared--$\gamma$-ray connection} is stronger than the well known {\it radio--$\gamma$-ray connection}.} | \label{sec:intro} Blazars are one of the most extreme class of radio-loud active galaxies whose emission extends from radio to TeV energies. They generally show extreme variability at all wavelengths and with timescales spanning from weeks to minutes, evidence of superluminal motions, high and variable polarization, flat radio spectra \citep[see e.g.][]{urry95}, recently observed even below $\sim$1GHz \citep[i.e. ,][]{ugs3,massaro13d} and a characteristic double bumped spectral energy distribution \citep[SED; see also][for a recent review]{massaro09}. Since the launch of the \fer\ satellite \citep{atwood09}, blazars { have been identified} as the dominant class of $\gamma$-ray sources, not only extragalactic. { Blazars account for} about 1/3 of the \fer\ detected objects \citep{acero15} and { likely for} a significant fraction { of} the unidentified/unassociated $\gamma$-ray sources \citep[UGSs;][]{massaro12a,ugs2}. Together with star forming { regions} \citep[e.g.][]{ackermann12a} and radio galaxies \citep[e.g.][]{dimauro14,lobes}, blazars produce a significant contribution to the extragalactic $\gamma$-ray background \citep[][and references therein]{ajello12,ajello14,review}. At optical frequencies blazars are historically { split} in two subclasses: BL Lac objects and flat spectrum radio quasars. The former, { that will be indicated in this paper} as BZBs { following} the nomenclature { introduced by} the \bzcat\ \citep{massaro15b}, show featureless spectra and/or with weak absorption lines of equivalent width lower than 5$\AA$, while the latter, { usually indicated} as BZQs, have quasar-like optical spectra \citep{stickel91,falomo14}. { Since} 2010, { the NASA} Wide-field Infrared Survey Explorer \citep[\wse;][]{wright10} { has} mapped the sky in the infrared (IR) at 3.4, 4.6, 12, and 22 $\mu$m, { making possible the investigation} of the mid-IR properties of a large, statistically significant, sample of confirmed blazars. We discovered that \fer\ blazars inhabit a region of the mid-IR color-color diagram, built with the \wse\ magnitudes, well separated from the location of other extragalactic sources \citep{paper1,paper2}. This 2-dimensional region in the mid-IR color-color diagram [3.4]-[4.6]-[12] $\mu$m was originally indicated as the {\it \wse\ Gamma-ray Strip}, and it is the projection of a 3-dimensional volume in the [3.4]-[4.6]-[12]-[22] $\mu$m mid-IR color space known as the \wse\ {\it locus} of $\gamma$-ray blazars \citep{ugs1,wibrals}. { These findings} led to the development of different procedures to search for $\gamma$-ray blazar candidates within the positional uncertainty regions of the \fer\ UGSs { that selected hundreds of IR sources as candidate blazars}. Thanks to an extensive optical spectroscopic follow-up campaign \citep{paggi14,massaro14,refined} we confirmed the { nature of} hundreds of new $\gamma$-ray blazars \citep[see also][]{massaro15c,landoni15,ricci15} { and assessed the reliability of our association methods}. Optical { spectroscopy was also used} to determine the nature of \fer\ sources classified as active galaxies of uncertain type \citep[AGUs;][]{nolan12,ackermann11} and/or blazar candidates of uncertain type \citep[BCUs;][]{acero15,ackermann15a}. Here we present an update of the {\it \wse\ Gamma-ray Strip} obtained { by} combining the latest releases of both the \wse\ All-Sky catalog\footnote{http://wise2.ipac.caltech.edu/docs/release/allsky/} and the Fermi Large Area Telescope Third Source Catalog \citep[3FGL;][]{acero15}. Additionally, for the first time, we discuss the link found between the \wse\ mid-IR colors and the $\gamma$-ray photon index, comparing it with the radio--$\gamma$-ray connection \citep[e.g.][]{ackermann11b}. For our numerical results, we use cgs units unless stated otherwise. Gamma-ray photon index, $\Gamma$ is defined by the usual convention on the flux density, $N(E)\propto\,E^{-\Gamma}$, being $N(E)$ the number of $\gamma$-ray photons detected per unit of time, area and energy. \wse\ magnitudes are in the Vega system and are not corrected for the Galactic extinction since, as shown in our previous analyses, such correction affects significantly only the magnitude at 3.4$\mu$ for sources lying at low Galactic latitudes~\citep[see e.g.][]{wibrals}. { \wse\ bands are indicated as $w1$, $w2$, $w3$ and $w4$ and corresponds to the following nominal wavelengths: 3.4$\mu$m, 4.6$\mu$m, 12$\mu$m and 22$\mu$m, respectively}. | \label{sec:summary} Five years after the discovery that the non-thermal emission of $\gamma$-ray blazars can be traced using mid-IR colors obtained { from the photometry of} the \wse\ all-sky survey, we present an updated analysis based on the latest releases of both the \wse\ and the \fer\ catalogs. Then, for the first time, we discuss on the existence of a {\it IR--$\gamma$-ray connection} for the \fer\ blazars that appears to be at least as strong as the well-known radio--$\gamma$-ray one. Our results can be summarized as follows. \begin{enumerate} \item Using the largest sample of \fer\ blazars available to date, we confirmed that this extreme class of active galaxies { occupied a narrow and well defined region} in the mid-IR color-color { plane, the so called} {\it \wse\ Gamma-ray Strip}. \item Comparing mid-IR \wse\ and near-IR 2MASS diagnostic diagrams, we { confirmed} that in the latter \fer\ blazar are distinct from generic 2MASS sources, { even though} no clear color-color trend appears as in the former. \fer\ blazars { have} a low detection rate in the 2MASS catalog, mainly due the { 2MASS} higher flux limit { compared to \wse\ survey}. These reasons { advice against the use of} near-IR colors to search for potential blazar-like counterparts of the UGSs. \item We describe the { statistically significant} correlations between the $\gamma$-ray photon index and the mid-IR colors { for both the whole sample of \fer\ blazars and the BZBs and BZQs spectral classes separately}, the basis of the {\it IR--$\gamma$-ray connection}. { This correlation} appears ``stronger'' than the well known radio--$\gamma$-ray connection because { it} involves the spectral shapes of the \fer\ blazars over $\sim$10 orders of magnitude and not only their flux densities. \item { We argue that the peculiar mid-IR colors of \fer\ blazars do not depend on} their $\gamma$-ray photon index. { In turn,} the {\it IR--$\gamma$-ray connection is} unexpected. { We have also highlighted} its potential use to implement the search for blazar-like counterparts of the \fer\ UGSs. \item We show that a large fraction of the BCUs listed in the 3FGL whose \wse\ counterpart have mid-IR colors consistent with the {\it \wse\ Gamma-ray Strip}, { have \fer\ spectral index values consistent} with the {\it IR--$\gamma$-ray connection}. \end{enumerate} { Taking advantage of the overwhelming fraction of \fer\ blazars detected in the \wse\ all-sky survey (i.e., $\sim$99\%) in the first two mid-IR filters, we suggest that a comprehensive investigation of their IR properties at the light of the {\it IR--$\gamma$-ray connection} described in this paper, can represent a powerful tool to reveal the real fraction of \fer\ blazars hidden within the sample of UGSs.} | 16 | 9 | 1609.08615 |
1609 | 1609.01734_arXiv.txt | Mounting discoveries of debris discs orbiting newly-formed stars and white dwarfs (WDs) showcase the importance of modeling the long-term evolution of small bodies in exosystems. WD debris discs are in particular thought to form from very long-term (0.1-5.0 Gyr) instability between planets and asteroids. However, the time-consuming nature of $N$-body integrators which accurately simulate motion over Gyrs necessitates a judicious choice of initial conditions. The analytical tools known as \textit{periodic orbits} can circumvent the guesswork. Here, we begin a comprehensive analysis directly linking periodic orbits with $N$-body integration outcomes with an extensive exploration of the planar circular restricted three-body problem (CRTBP) with an outer planet and inner asteroid near or inside of the $2$:$1$ mean motion resonance. We run nearly 1000 focused simulations for the entire age of the Universe (14 Gyr) with initial conditions mapped to the phase space locations surrounding the unstable and stable periodic orbits for that commensurability. In none of our simulations did the planar CRTBP architecture yield a long-timescale ($\gtrsim 0.25$\% of the age of the Universe) asteroid-star collision. The pericentre distance of asteroids which survived beyond this timescale ($\approx 35$~Myr) varied by at most about 60\%. These results help affirm that collisions occur too quickly to explain WD pollution in the planar CRTBP $2$:$1$ regime, and highlight the need for further periodic orbit studies with the eccentric and inclined TBP architectures and other significant orbital period commensurabilities. | Unprecedented images of the rings and dust surrounding HL Tau \citep{almetal2015} provide a glimpse into the complexity of planet formation. At the other end of the life cycle of exosystems, the labile remnant planetary discs orbiting white dwarfs (WDs) are strikingly variable in both brightness and morphology \citep{wiletal2014,xujur2014,manetal2015,wiletal2015,farihi2016}. Connecting the future development of systems like HL Tau and the past history of WD debris discs represents an important step towards establishing a unified evolution theory. This evolution is not limited to planets. Both protoplanetary and WD discs contain dust and potentially asteroids or other small bodies. In fact, asteroids represent the favoured progenitors of WD discs for at least three reasons: \begin{itemize} \item At least one asteroid has now been observed to be disintegrating in real time around WD 1145+017 \citep{vanetal2015,aloetal2016,ganetal2016,rapetal2016,xuetal2016,zhoetal2016} \item Planets collide with WDs too infrequently \citep{veretal2013b,musetal2014,vergae2015,veretal2016} as do exo-Oort cloud comets \citep{alcetal1986,veretal2014c,stoetal2015} \item Measured bulk compositions in WD atmospheres are incompatible with those from Solar system comets \citep{zucetal2007,kleetal2010,kleetal2011,gaeetal2012,juretal2012, xuetal2013,xuetal2014,wiletal2016} \end{itemize} Therefore, understanding the interaction between planets and asteroids is paramount for WD planet studies. Further, the wide range of WD cooling ages (the time since the star became a WD) at which metal pollution is observed (up to 5 Gyr; see \citealt{faretal2011} and \citealt{koeetal2011}) necessitate understanding the long-term evolution of planets and asteroids. For a recent review summarizing our current knowledge of the long-term behaviour of planetary systems, see \citep{davetal2014}, and for post-main-sequence systems in particular, see \citep{veras2016}. For the more specific case of an asteroid and planet interacting under the guises of the restricted three-body problem (RTBP), a vast body of literature has covered specific examples and techniques. For example, \citet{holmur1996} and \citet{murhol1997} analytically and numerically determined the long-timescale stability of asteroids in or near mean motion resonance (MMR) under the guise of the planar elliptic RTBP, and focused on computing Lyapunov times. Other measures of chaos, such as MEGNO \citep{hinetal2010}, have also been applied to the elliptic RTBP. $N$-body numerical integrations provide a crucial means of determining orbital evolution, but can be computationally demanding. Alternatively, predictive analytic formulations may yield the desired result more quickly, but their correctness is subject to validation from $N$-body integrations. One example is classic Laplace-Lagrange theory \citep[see Chapter 7 of][]{murder1999}, which can fail to reproduce quantitative behaviour in exosystems when compared to $N$-body integrations, even when the theory is extended to fourth-order in eccentricity \citep{verarm2007}; other types of extensions yield better results \citep{libsan2013}. Another example is Lidov-Kozai theory, where differences in its quadrupole-order versus octupole-order accuracy are dramatically highlighted through comparison to $N$-body integrations \citep[e.g.][]{naoetal2013,naoz2016}. Our purpose in this paper is to begin a series of investigations comparing long-term $N$-body integrations to \textit{periodic orbits}, which are defined in Section 2. \cite{tsietal2002} also relate numerical integrations to periodic orbits, but carry out integrations for just 5 Myr and perform a broad sweep of different period commensurabilities, rather than focusing on one, as we do here. Periodic orbits can be treated as analytical tools which can gather information regarding a system's dynamics, such as in TBPs. We herein implement the high predictive power of periodic orbits to explore the phase space of a system consisting of a WD, planet and massless asteroid where the planet and asteroid are evolving in or near a particular MMR. Using periodic orbits to remove the guesswork involved in choosing initial conditions can reduce the phase space which needs to be explored and increase the relevance of the simulation suites that are run. We provide definitions and context in Section 2, the results of our numerical simulations in Section 3, a discussion in Section 4 and our conclusion in Section 5. | We have evaluated the predictive power of periodic orbits and their phase space surroundings to determine the long-term (1-14 Gyr) stability of systems containing one star, one planet and one asteroid in the planar CRTBP. We utilized the three families of periodic orbits which are associated with the $2$:$1$ MMR, such that the asteroid is interior to the planet. Our resource-consuming 14~Gyr simulations revealed good agreement between the final dynamical outcome and the structure of phase space about the periodic orbits. Consequently, researchers can use these orbits as broadly reliable guides to choose sets of initial conditions ($a_{\rm A}^{(\rm N)}, e_{\rm A}, \omega_{\rm A}, M_{\rm A}$) for $N$-body simulations to predict whether a given system will remain stable over the age of the Universe. Of particular interest for Gyr-old WDs which host circumstellar debris discs and atmospheric metal pollution are \textit{unstable} planetary systems that feature very late collisions between the asteroid and star. Therefore, in this paper we have focused on unstable cases. Despite this emphasis, in none of our simulations did a collision occur after 36 Myr, thereby providing analytical backing to the findings of \citet{frehan2014} that a circular planet fails to pollute WDs with a sufficient number of asteroids at sufficiently late ages. | 16 | 9 | 1609.01734 |
1609 | 1609.00504_arXiv.txt | Parameter inference with an estimated covariance matrix systematically loses information due to the remaining uncertainty of the covariance matrix. Here, we quantify this loss of precision and develop a framework to hypothetically restore it, which allows to judge how far away a given analysis is from the ideal case of a known covariance matrix. We point out that it is insufficient to estimate this loss by debiasing a Fisher matrix as previously done, due to a fundamental inequality that describes how biases arise in non-linear functions. We therefore develop direct estimators for parameter credibility contours and the figure of merit, finding that significantly fewer simulations than previously thought are sufficient to reach satisfactory precisions. We apply our results to DES Science Verification weak lensing data, detecting a 10\% loss of information that increases their credibility contours. No significant loss of information is found for KiDS. For a Euclid-like survey, with about 10 nuisance parameters we find that 2900 simulations are sufficient to limit the systematically lost information to 1\%, with an additional uncertainty of about 2\%. Without any nuisance parameters 1900 simulations are sufficient to only lose 1\% of information. We further derive estimators for all quantities needed for forecasting with estimated covariance matrices. Our formalism allows to determine the sweetspot between running sophisticated simulations to reduce the number of nuisance parameters, and running as many fast simulations as possible. | 16 | 9 | 1609.00504 |
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1609 | 1609.08942_arXiv.txt | We present new measurements of the power spectra of the cosmic infrared background (CIB) anisotropies using the \Planck\ 2015 full-mission HFI data at 353, 545, and 857\,GHz over 20\,000 square degrees. We use techniques similar to those applied for the cosmological analysis of \Planck, subtracting dust emission at the power spectrum level. Our analysis gives stable solutions for the CIB power spectra with increasing sky coverage up to about 50\% of the sky. These spectra agree well with \ion{H}{i} cleaned spectra from \Planck\ measured on much smaller areas of sky with low Galactic dust emission. At 545 and 857\,GHz our CIB spectra agree well with those measured from \textit{Herschel} data. We find that the CIB spectra at $\ell \simgt 500$ are well fitted by a power-law model for the clustered CIB, with a shallow index $\gamma^{\rm cib} =0.53 \pm 0.02$. This is consistent with the CIB results at 217\,GHz from the cosmological parameter analysis of \Planck. We show that a linear combination of the 545 and 857\,GHz \Planck\ maps is dominated by CIB fluctuations at multipoles $\ell \simgt 300$. | 16 | 9 | 1609.08942 |
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1609 | 1609.03782_arXiv.txt | Soon to be operational H\,{\small I} survey instruments such as APERTIF and ASKAP will produce large datasets. These surveys will provide information about the H\,{\small I} in and around hundreds of galaxies with a typical signal-to-noise ratio of $\sim$ 10 in the inner regions and $\sim$ 1 in the outer regions. In addition, such surveys will make it possible to probe faint H\,{\small I} structures, typically located in the vicinity of galaxies, such as extra-planar-gas, tails and filaments. These structures are crucial for understanding galaxy evolution, particularly when they are studied in relation to the local environment. Our aim is to find optimized kernels for the discovery of faint and morphologically complex H\,{\small I} structures. Therefore, using H\,{\small I} data from a variety of galaxies, we explore state-of-the-art filtering algorithms. We show that the intensity-driven gradient filter, due to its adaptive characteristics, is the optimal choice. In fact, this filter requires only minimal tuning of the input parameters to enhance the signal-to-noise ratio of faint components. In addition, it does not degrade the resolution of the high signal-to-noise component of a source. The filtering process must be fast and be embedded in an interactive visualization tool in order to support fast inspection of a large number of sources. To achieve such interactive exploration, we implemented a multi-core CPU (OpenMP) and a GPU (OpenGL) version of this filter in a 3D visualization environment ($\tt{SlicerAstro}$). | Radio data are intrinsically noisy and most sources are faint and often extended (see for example the WHISP catalog, \cite{Whisp}). Very faint coherent H\,{\small I} signals, below a 3 sigma \textit{rms} noise level, are difficult to find \citep{Popping}. Depending on the source structure, spatial and/or spectral smoothing can increase the signal-to-noise ratio. Smoothing is usually applied to multiple spatial and spectral scales to ensure that sources of different size are extracted at their maximum integrated signal-to-noise ratio. In upcoming blind H\,{\small I} surveys such as WALLABY, using the ASKAP telescope \citep{askap, duffy}, and the shallow and medium-deep APERTIF surveys, using the WSRT telescope \citep{Apertif3}, source finding will be a major concern. Source finders \citep[e.g.,][]{Whiting, sofia} are designed to automatically detect all the sources in the field and to achieve this goal they must employ an efficient mechanism to discriminate between interesting candidate sources and noise. Due to the complex 3-D nature of the sources \citep{Sancisi} and the noisy character of the data, constructing a fully automated and reliable pipeline is not trivial. \citet{Popping} reviewed the current state of the art and described the issues connected with the noisy nature of the data, and the various methods and their efficiency. In the source-finding process, \textit{masks} are generated enclosing the sources. The determination of the final masks involves a variety of filtering operations in order to pick up faint and extended emissions. However, users are ultimately provided with the mask and data products determined from the original data within the masks. In order to examine the original data within and around the mask, to check the performance of the source finding process and to investigate whether all faint structures have been included, it is necessary to have a visualization tool that not only shows the original data and the mask, but also has the ability to interactively filter the data to bring out the very faint structures in the data. Our goal therefore is the development of a suitable filtering method in a 3D visualization environment that maximizes the local signal-to-noise ratio of the very faint structures (signal-to-noise ratio $\sim 1$) while preserving its specific 3-D structure (e.g. tidal tails, filaments and extra-planar gas). Ideally, the method should be adaptive (in such a way that the user does not have to explore a large parameter space to get the best result), interactive, and fast, i.e. applicable in real-time. In this paper, we explore a number of existing filtering methods in combination with a 3D visualization tool \citep{Punzo} in order to find a method fulfilling such requirements. In Section \ref{cases} we describe the datasets used for our investigation and in Section \ref{filter} we give an overview of state-of-the-art filtering packages and algorithms, with a focus on radio astronomy. We also describe the filtering techniques chosen for the analysis performed in this paper. In Section \ref{results} we report an analysis of the best parameters for each of the filtering methods. In Sections \ref{noise} and \ref{performance} we test the quality and the performance of the filtering algorithms implemented. In Section \ref{conclusion} we discuss the overall results and conclude that the adaptive method is the best solution for our problem. | Future blind surveys of H\,{\small I} will deliver a large variety of data in terms both of the number of galaxies and additional complex features such as tails, extra-planar gas and filaments. These faint structures can be found in nearby medium/high resolved galaxies (e.g. Model and WEIN069 data cube) and groups of non-resolved galaxies (e.g. NGC-3379 and NGC4111). They have a very low signal-to-noise ratio of $\sim 1$, but are extended over many pixels. Efficiently separating such signals from the noise is not straightforward (visual examples are shown in sections \ref{cases} and \ref{filter}). Moreover, in the case of APERTIF and ASKAP, it is estimated that tens of such sub-cubes will be collected weekly \citep{duffy}. This is a large volume of data, and a coupling between the filtering algorithms shown in this paper and 3-D visualization can enhance the inspection process of large numbers of galaxies and masks provided by source finder algorithms. In Section \ref{filter}, we reviewed state-of-the-art filtering algorithms. We qualitatively illustrated the filtering results using several methods. We then performed a visual inspection of the filtering results, followed by a systematic quantitative analysis of the algorithms in Section \ref{results}. First, we extensively investigated the parameter space of the input parameters (i.e.\ the extension and shape of the kernels) of the box and Gaussian filters by applying them to several test data cubes. In Table \ref{resulttable}, we indicated the best filtering runs and their input parameters. As criterion for selecting the best runs we used the $F$-value, our smoothing quality control parameter defined in Sections \ref{results} and \ref{noise}, requiring $F$ to be large. Thereafter, we confirmed the selection by visually inspecting the filtered output data cube. Table \ref{resulttable} highlights, for our sample, that finding the input parameters of the best runs is not straightforward. In fact, the box and Gaussian kernels are highly dependent on the spatial and velocity extents, and the signal-to-noise ratio of the unknown faint signal. Note that the Gaussian smoothing gives better results than the box smoothing, because a gentler smoothing preserves better the shape of the data (the differences are clearly visible in the second and third panels in Fig.~\ref{WEIN069Screeshot}). Two examples which suffer from these limitations are: \begin{enumerate}[1)] \item ModelB: very faint signal (signal-to-noise ratio $\sim$ 1) with limited extent; \item NGC~4111: very extended, relatively faint, signal. \end{enumerate} In the first case large kernels are necessary to considerably enhance the very low level signal. Large kernels (e.g.\ for the box filter $N_i > 5 $ and for the Gaussian filter $FWHM_i > 3$) will, however, wash out the signal because it is not coherent at such large scales. In the second case, very large kernels ($N_i = 9$ for the box filters and $FWHM_i = 7$ for the Gaussian filter) provide the best smoothing and the maximum $F$-values. Such kernels drastically reduce, however, the spatial and velocity resolution of the data. The optimal dimensions of the box and Gaussian kernels strongly depend on the extent of the signal and the signal-to-noise ratio. The quite different, best input parameters of ModelA, ModelB and ModelC, with their different signal-to-noise ratios, illustrate this clearly. For example, the best runs for modelB use larger kernels in the $y$ direction compared to the other models. The optimal kernels for smoothing ModelA and ModelC have, on the other hand, a very narrow $z$ component. This is expected as a higher noise level hides the signal and modifies the overall shape of the signal itself (i.e. the faintest parts will disappear into the noise). Second, we analyzed wavelet filters in detail. Our investigation focused on thresholding the data in the wavelet domain. We performed the filtering operation exploiting a wavelet lifting algorithm. Two main wavelets have been used: the Haar and the Le Gall wavelet. Wavelet lifting is a powerful technique, but unfortunately it generates artifacts undesirable for our visualization purposes (see Fig.~\ref{ScreenshotThreshold}). The filtering results give very high values of the $F$-parameter as shown in Table \ref{resulttable}. The wavelet thresholding filter, however, requires a thorough investigation of the main parameters (choice of the basic wavelet, maximum number of levels for wavelet decomposition, thresholding values for each decomposition level) for obtaining an optimal denoising of the data. We consider this a drawback for user-friendly visualization purposes. The optimal input parameters reported in Table \ref{resulttable} vary for each data cube of our sample. The thresholds parameters, $t_{l, wavelet}$, have strong dependencies on the choice of the wavelet and the signal-to-noise ratio of the faint signal. Moreover, the choice of the optimal wavelet and decomposition level, $l$, depends on the extent of the faint structure. For example, the arc-shape structure in the ModelB is very thin along the velocity direction (few channels). Therefore, a the Haar wavelet and $l = 2$ are the optimal choice, while the Le Gall wavelet and a higher decomposition level, $l = 3$, provide the optimal filtering results for WEIN069, NGC3379 and NGC4111, because these data shows a more extended component. Filtering with a higher order wavelet than Le Gall may give optimal results without requiring a pre-smoothing step. However, we showed that the choice of the wavelet is constrained by the unknown extent of the faint signal. For example, very high-order wavelets are not optimal for filtering the models. Using different decomposition levels in each spatial and velocity dimension \citep[or a tree structure, e.g. $\tt{Octree}$;][]{octree} may also improve the filtering quality. However, in the case of morphological complex resolved galaxies this approach is rather difficult. For example, it is necessary to determine the optimal levels of decomposition for each dimension and these depend on the signal extent and signal-to-noise ratio as well. This is analogous to the issue of finding the optimal kernel for the box and Gaussian filters. Applying wavelet decomposition and thresholding the approximation bands, as shown in Section \ref{wavelet}, is effectively a segmentation of the data. Though efficient, the disadvantage is that it also eliminates very low signal-to-noise emission if the thresholding parameters are not properly tuned to the data. Since our aim is to couple filtering techniques to visualization, thresholding techniques are not favored as they limit the interactive visual data exploration. Third, we implemented a modification of the diffusion filter: the intensity-driven gradient filter (see \ref{gradientFilter}). This smoothing algorithm has adaptive characteristics which helps in preserving the smaller scale structure of the signal, thus avoiding the limitations of the box and Gaussian filters. The parameters of intensity-driven gradient filter mainly depend on the signal-to-noise ratio of the emission, which we found to be quite similar for the objects studied here. In fact, the intensities of the majority of the voxels of the faint signal are between 1 and 2 $rms$. For example, in Section \ref{cases}, we illustrated 3-D visualizations of the output of the intensity-driven gradient filter with default parameters ($K = 1.5$, $\tau = 0.0325$, $n = 20$ and $C_{x,y,z} = 5$) for two very different objects (WEIN069 and NGC3379). In both cases, the smoothing is successful in bringing out the low signal-to-noise structures. In fact, in the case of the gradient filter, the $F$-values of the best runs, reported in Table \ref{resulttable}, do not differ more than $15\%$ from the runs with default parameters. The main input parameters ($K$, $\tau$ and $n$) of the best filtering results for the three models in Table \ref{resulttable} do not vary. The peak signal-to-noise ratio of ModelC is $\sim 3$ times higher than that of ModelA. Therefore, the dependencies of the input parameters of the intensity-driven gradient respect to the signal-to-noise ratio are not stiff functions. We conclude that the intensity-driven gradient is the most promising filter because it preserves the detailed structure of the signal with high signal-to-noise ratio ($> 3$) at the highest resolution, while smoothing only the faint part of the signal (S/N $< 3$). Moreover, the input parameters need only minimal tuning to the signal itself. \noindent On the other hand, this filter applies a diffusion process which has the following drawbacks: \begin{enumerate}[a)] \item the flux scale is not conserved and depends on the signal-to-noise ratio and hence degree of \enquote*{smoothing} or resulting resolution; \item setting too high values of the parameters $n$ and $\tau$ can create unrealistic web structures (negative and positive) between the peaks of the negative and positive parts of the noise. \end{enumerate} The first issue is not a problem for visualization. In fact, the main purpose of the filtering operation, in this context, is to find and enhance low-level signals. Quantitative analysis, such as calculating column densities, intensity weighted mean velocities, velocity dispersions etc., can always be performed on the original data cube once the volume that contains all the signal has been identified. Regarding the second issue: in Fig.~\ref{Ffinal} we show as a guideline the dependencies of the $F$-parameter on the input parameters $K$, $\tau$ and $n$. \begin{figure}[!ht] \centering \includegraphics[width=0.48\textwidth]{F_final} \caption{The $F$-values applying to WEIN069 an intensity-driven gradient filter with parameters $K$, $\tau$, $n$ and $C_{x,y,z} = 5$. In this 3-D scatter plot, the $F$-values are displayed as a 4-th dimension using a color scale. The red dots represents filtering with an high value of the parameter $F$ ($F$-values $> 1.75$). The $F$-parameter shows low values ($< 1$) for high values of $n$ and $\tau$ ($n > 15$ and $\tau > 0.0475$). For more information regarding the $F$-parameter refer to sections \ref{results} and \ref{noise}. } \label{Ffinal} \end{figure} Finally, the previous results suggest that intensity-driven gradient smoothing can be employed for finding H\,{\small I} sources as well. This technique could be an alternative for the smooth-and-clip method and has the advantage that the user does not have to specify the smoothing kernels. The robustness of such a method should be tested on a larger number of different cases than we have used here. This is beyond the scope of the present investigation. In Section \ref{performance}, we reported the benchmark of our CPU and GPU implementations of the filtering algorithms investigated in this paper. The codes are publicly available\footnote{\url{https://github.com/Punzo/SlicerAstro/AstroSmoothing}} and we integrated them in a module of $\tt{SlicerAstro}$\footnote{\url{http://wiki.slicer.org/slicerWiki/index.php/Documentation/Nightly/Extensions/SlicerAstro}}, a first design of an astronomical extension of $\tt{3DSlicer}$\footnote{ $\tt{3DSlicer}$ (\url{https://www.slicer.org/}) is a medical visualization package with advanced 3-D visualization capabilities.} \citep{Slicer}. We showed that for data cubes with a number of voxels up to $5 \times 10^6$, GPU implementations of the smoothing filters can reach interactive performance (maximum execution time, $T_p < 0.3\;s$) exploiting a GTX860M, i.e.\ a GPU suitable for gaming, found on laptops with mid-level performance. For data cubes up to $10^8$ voxels, the filters can still reach relatively fast performance (maximum execution time with a GTX860M, $T_p < 3.5\;s$). In conclusion, the GPU implementation of the intensity-driven gradient filter satisfies our filtering and visualization requirements best. The filter provides interactive performance, requires minimal tuning of the input parameters, and efficiently enhances faint structures in our data sample without degrading the resolution of the high signal-to-noise data. | 16 | 9 | 1609.03782 |
1609 | 1609.04677_arXiv.txt | In this work we report the detection of seven Neptune Trojans (NTs) in the Pan-STARRS 1 (PS1) survey. Five of these are new discoveries, consisting of four L4 Trojans and one L5 Trojan. Our orbital simulations show that the L5 Trojan stably librates for only several million years. This suggests that the L5 Trojan must be of recent capture origin. On the other hand, all four new L4 Trojans stably occupy the 1:1 resonance with Neptune for more than 1\,Gyr. They can, therefore, be of primordial origin. Our survey simulation results show that the inclination width of the Neptune Trojan population should be between $7^{\circ}$ and $27^{\circ}$ at $>$ 95\% confidence, and most likely $\sim 11^{\circ}$. In this paper, we describe the PS1 survey, the Outer Solar System pipeline, the confirming observations, and the orbital/physical properties of the new Neptune Trojans. | The best known Trojans are the asteroids in a co-orbital 1:1 mean motion resonance with Jupiter. Those in stable libration around the Lagrange point $60^\circ$ ahead of Jupiter are called L4 Trojans, and those around the Lagrange point $60^\circ$ behind are called L5 Trojans. There are more than 6000 known Jovian Trojans with sizes $\gtrsim$ 10\,km. \citet{yos05} estimated that the total number of 1\,km sized Jovian Trojan could be as many as 600,000. After Jupiter, Neptune has the second largest population of Trojans. Prior to this study, nine L4 Neptune Trojans (or NTs) and three L5 NTs had been discovered \citep{ale14, ger16, par13, she06, she10a, ell05}. \citet{nes02} examined the orbital evolution and long-term stability of Trojans of Saturn, Uranus, and Neptune, under the current planetary configuration. They found that unlike the cases of Saturn and Uranus, where their Trojans could be removed on relatively short time scales, the primordial population of NTs can survive to the present time after their formation. Subsequently, the first Neptune Trojan, 2001 QR$_{322}$ at L4, was found in the Deep Ecliptic Survey \citep{ell05}. Based on the low inclination ($\sim 1.3^\circ$) of 2001 QR$_{322}$ with a size of $\sim$100 km, \citet{chi05} proposed that large ($\sim$100 km sized) NTs might be primordial objects formed in-situ by accretion in a thin disk. This means that NTs should generally have {\it i} $\lesssim 10^\circ$. Following the discovery of three more NTs, one of which has a high inclination (see Table~\ref{tab1} with a list of the known NTs and those detected in this study), \citet{she06} suggested that a thick cloud of high-inclination NTs which could be of capture origin, should exist with a 4:1 ratio over the low-inclination population. In the context of the Nice model \citep{gom05, tsi05}, \citet{mor05} investigated the chaotic capture of small bodies at the two Lagrangian points of Jupiter during the planetary migration phase. Following a similar approach, \citet{nes09} produced a model calculation of the capture process of NTs. Although the inclinations of the objects captured from the thin solar nebula disc could be later increased by dynamical processes, the numerical results could not account for the 4:1 high-{\it i} to low-{\it i} NTs ratio indicated by the observations of \citet{she06}. This discrepancy might be worsened if the orbits of the planetesimals before chaotic capture were excited by the gravitational scattering effect of a population of Pluto-sized objects according to these authors. \citet{par15} applied a statistical method to debias the observed distributions of orbital inclinations, eccentricities and libration amplitudes of NTs. His treatment confirmed the existence of the thick cloud population with $\sigma _i > 11^\circ$. Here, $\sigma _i$ is the inclination width of the Brown's distribution \citet{bro01}: \begin{equation} p(i) = \sin(i)\exp(-\frac{1}{2}(i/\sigma_{i})^2)di \end{equation} From a numerical study of the resonant capture effect via planetary orbital migration, \citet{par15} showed that low-inclination objects can be captured into high-inclination NTs, but the conversion efficiency is too low to account for the presence of the high-inclination population. On the other hand, if the original planetesimals were characterized by high-inclination orbits, their NT-counterparts captured into 1:1 resonance with Neptune could preserve their high inclinations, and hence cause the formation of a thick NT cloud. \citet{che16} provided an alternative mechanism to effectively form the high-inclination NTs. They investigated how planetary migration affects the orbital elements distribution of NTs, and found that if orbital eccentricities and inclinations of Neptune and Uranus were damping during planetary migration, the secular resonances with Neptune will increase the probability of trapping the test particles into high inclination NT orbits. Moreover, most of primordial NTs, especially the high inclination ones, were unstable and lost in the damping case. From these results, their concluded that the current existent NTs can be explained by the capture origin, particular the trapping scenario with orbital damping of Neptune and Uranus during planet migration. The first Neptune Trojan at L5, 2008 LC$_{18}$, was discovered by \citet{she10a}. One more was found by \citet{par13}. According to \citet{she06} and \citet{par15}, the difference in the numbers of known NTs in the L4 and L5 points, respectively, could be an observational bias caused by the fact that the L5 point of the NTs is currently in the vicinity of the Galactic center, making it difficult to clearly identify slowly moving foreground objects. Due to the small number of known NTs, it has been difficult to reconstruct their size distribution and to estimate their total number. \citet{chi05} and \citet{she06} suggested that the number of large (size $>$ 65 km) NTs should exceed that of the Jovian Trojans by more than a factor of ten. \citet{ale14} discovered one temporary and one stable NTs and derived the populations of $210^{+900}_{-200}$ and $150^{+600}_{-140}$, respectively, with $H \lesssim 10.0$. From an ultra-deep, pencil-beam survey with a detection efficiency of 50$\%$ for objects with R $\sim 25.7$ mag, \citet{she10b} derived that the cumulative luminosity function of $m_R < 23.5$ mag follows a steep power law of index $\alpha \sim 0.8 \pm 0.2$: \begin{equation} \Sigma(m_R) = 10^{0.8(m_R-m_0)}. \end{equation} In other words the size frequency distribution of the bright NTs at size a $>$ 100 km have a power-law index $\sim 5 \pm 1$: \begin{equation} dN/da \propto a^{-5}. \end{equation} For reference, Jovian Trojan population, cold population and hot population of TNOs have $\alpha \sim$ 1.0, 1.5 and 0.87, respectively \citep{fra14}. It clearly shows that the luminosity function of NT population has power law index, $\alpha$, similar to the Jovian Trojans and hot population of TNOs. This result is obvious interpretation from the fact that they all have the same size frequency distribution. The long-term orbital stability of NTs has been studied by \citet{nes02}, \citet{dvo07} and \citet{zho09, zho11} who showed that NTs can be stable for over 4 Gyr even with orbital inclinations $\sim 30^\circ$. However, the stable region is restricted in eccentricity ($e\lesssim 0.1$). The orbital stability of individual known NTs has been investigated by \citet{bra04}, \citet{gua12}, \citet{mar03}, \citet{hor10a}, \citet{hor12a}, \citet{hor12b} and \citet{lyk09}. In general, they can be classified into three different dynamical regimes: \begin{enumerate} \item Objects temporarily captured into unstable orbits: these kind of NTs are located completely outside the stable region and have a dynamical lifetime as short as 1 Myr \citep{hor12b, gua12}. \item Objects in marginally stable orbits: these NTs are found near the edge of the stable region or in the proximity of the secular resonances with a dynamical life time of about 100 Myr \citep{hor10a, lyk11, zho11}. \item Stable objects: they are located deep inside the stable region with a dynamical life time as long as the age of the Solar System and could be of primordial origin. \end{enumerate} Our current knowledge of the NTs is based on the discoveries by several different surveys \citep{ale14, ell05, ger16, par13, she10a, she06}. Without a comprehensive full-sky survey to cover most of the Trojan clouds, it is difficult to estimate the total number, the size distribution, the orbital distribution and the L4/L5 asymmetry of Neptune Trojans. In comparison, the PS1 project covering the whole Northern Hemisphere to a limiting magnitude of $r_{\rm P1}\sim 22$ presents an ideal opportunity to search for NTs with significant reduction in the latitudinal and longitudinal biases. In this paper, we report the detections of seven NTs by PS1, five of which are new discoveries. This paper is organized as follows. Section 2 will introduce the PS1 survey and the Outer Solar System pipeline for searching of distant moving objects. In Section 3, we describe how to select, confirm the Trojan candidates and report the discoveries. In Section 4, we calculate the orbital and physical properties of the NTs. In Section 5, we describe how to perform the inclination debiasing of PS1 survey and investigate the intrinsic inclination distribution of stable L4 NTs. In Section 6, we roughly estimate the luminosity function of stable L4 NTs. In Section 7, we discuss the ratio of high- and low-inclination populations of NTs, and the possible asymmetry of L4 and L5 distributions. A summary is given in Section 8. | \citet{par15} suggested that if the stable NT cloud follows an inclination distribution similar to that of the Jovian Trojan population, the corresponding inclination width must be greater than $11^{\circ}$. Our result, which is based on six stable L4 NTs, is roughly consistent with his finding. Note that our most likely value of $\sigma_{i} \sim 11^{\circ}$ is the minimal acceptable value in \citet{par15}. Therefore, our present result might be indicative of a lower inclination distribution. It is worth noting that a high and wide NT inclination distribution with $\sigma_{i} \sim 20^{\circ}$ is unlikely to result from capture from a dynamically cold disk without orbital damping during planet migration. However, the scenario is possible if the actual NT inclination distribution has $\sigma_{i}$ only around $10^{\circ}$ \citep{nes09, par15, che16}. One other fact that should be taken into consideration is that the PS1 survey can only detect larger NTs ($H \lesssim 8$) compared to the other surveys with fainter limiting magnitudes. It may be the case that large and small NTs have different high/low-{\it i} ratios: If the NT cloud actually has cold and hot populations like the classical Kuiper Belt and the two populations have different size distributions, it might also explain the inconsistent measurements of the high/low inclination ratio. \citet{par15} and \citet{che16} simulated the captured NTs after planet migration and found that there is no difference between the numbers of captured L4 and L5 Trojans. The PS1 survey should not have any bias to detect high eccentricity objects in L4 the region. However, we did not detect any unstable L4 NTs with high eccentricity. In the near future, as the L5 region moves away from the Galactic center, we will be able to test the possible asymmetry between the L4 and L5 populations. The ongoing PS1 + PS2 survey would be able to cover more than $\pm 20^{\circ}$ above and below the ecliptic plane, and will be very useful in deriving a less-biased inclination distribution of NTs. In addition, the future LSST survey will detect many more NTs, allowing a more nuanced understanding of their distribution to be gained. | 16 | 9 | 1609.04677 |
1609 | 1609.04394_arXiv.txt | Correlations between stellar chemistry and kinematics have long been used to gain insight into the evolution of the Milky Way Galaxy. Orbital angular momentum is a key physical parameter and it is often estimated from three-dimensional space motions. We here demonstrate the lower uncertainties that can be achieved in the estimation of one component of velocity through selection of stars in key directions and use of line-of-sight velocity alone (i.e. without incorporation of proper motion data). In this first paper we apply our technique to stars observed in the direction of Galactic rotation in the APOGEE survey. We first derive the distribution of azimuthal velocities, $\vphib$, then from these and observed radial coordinates, estimate the stellar guiding centre radii, $R_g$, within $6.9\leq R \leq 10\kpc$ with uncertainties smaller than (or of the order of) $1\kpc$. We show that there is no simple way to select a clean stellar sample based on low errors on proper motions and distances to obtain high-quality 3D velocities and hence one should pay particular attention when trying to identify kinematically peculiar stars based on velocities derived using the proper motions. Using our $\vphib$ estimations, we investigate the joint distribution of elemental abundances and rotational kinematics free from the blurring effects of epicyclic motions, and we derive the $\partial \vphib / \partial \afe$ \& $\partial \vphib / \partial \feh$ trends for the thin and thick discs as a function of radius. Our analysis provides further evidence for radial migration within the thin disc and hints against radial migration playing a significant role in the evolution of the thick disc. | Correlations between stellar chemistry and kinematics, as well as the way these quantities change across the Galaxy, provide valuable insight into how the Milky Way formed and evolved \citep[e.g.][]{Eggen62,Freeman02}. Full six-dimensional (6D) kinematic-position phase space information is obviously preferred for such analyses; this requires proper motions and distances, in addition to line-of-sight velocities. In the pre-Gaia era, for stars beyond the immediate solar neighbourhood distances must in general be obtained through isochrone fitting \citep[e.g.][]{Pont04, Jorgensen05, Binney14a} and only ground-based measures of proper motions are available. The uncertainties in the estimated values of each of these quantities are relatively high. Indeed ground-based proper motion catalogues such as PPMXL or UCAC4 \citep{Roeser10,Zacharias13} have random errors of the order of $4-10 \mas\yr^{-1}$, resulting in transverse velocity errors of $60-150\kms$ for a star with a perfectly known distance of $3\kpc$ from the Sun\footnote{Gaia will provide at least an order-of-magnitude improvement in proper-motion errors.}. Typical uncertainties in distances obtained through isochrone-fitting are 15-30~percent, further increasing the error in transverse velocity. In comparison, line-of-sight velocities can routinely be obtained with uncertainties of below $1\kms$, so that the transverse velocity dominates the error budget in the derived 3D space motion. The higher precision and accuracy of line-of-sight velocities motivate spectroscopic studies of stars in selected key directions where the line-of-sight velocities are particularly sensitive to one component of space motion. These include lines-of-sight at low-to-moderate Galactic latitudes towards the Galactic centre and anti-centre (Galactic longitudes $\ell \sim 0^\circ, \, 180^\circ$ respectively) which probe velocities along the radial coordinate; towards the Galactic Poles (latitudes $|b| \sim 90^\circ$), which probe velocities perpendicular to the plane; and low-to-moderate Galactic latitudes towards and against Galactic rotation (Galactic longitudes $\ell \sim 90^\circ; \; 270^\circ$ respectively) which probe azimuthal velocities. In this paper, the first of a series, we analyse the joint distributions of azimuthal velocity and elemental abundances of stars in the \lq rotation' fields of the Apache Point Observatory Galactic Evolution Experiment \citep[APOGEE,][]{Majewski15}. In subsequent papers of this series we will apply the techniques developed below to other large spectroscopic surveys, namely RAVE \citep{Steinmetz06} and Gaia-ESO \citep{Gilmore12}, and extend the analysis to the other cardinal directions. The azimuthal velocity is of course the component with the largest expected mean value, measuring the orbital angular momentum. Angular momentum about the $Z-$axis is an integral of motion in an axisymmetric system and is often still a meaningful quantity in more realistic potentials. The surface elemental abundances are conserved through most of the lifetime of most low-mass stars (excepting those in close binary systems with mass transfer) and reflect the abundances in the gas from which the star formed, and hence constrain its birthplace. The combination of azimuthal velocity and elemental abundances provides insight into dynamical processes such as the creation of moving groups - whether as tidal debris from a disrupted satellite/star cluster or created through resonant interactions with gravitational perturbations - and radial migration of stars through the disc \citep[e.g.][]{Dehnen98,Helmi99,Sellwood02,Antoja08,Minchev10b}. \bigskip The paper is structured as follows: in Sect.~\ref{sec:method} we present the method that we will use to derive reliable measures of the azimuthal velocities without the use of proper motions and we test it by means of a mock catalogue derived from the Besan\c con model \citep{Robin03}. In Sect.~\ref{sec:application_to_data} we apply this method to the APOGEE-Data Release 12 catalogue \citep{Alam15,Holtzman15}. Section~\ref{sect:chemodynamics} presents our investigation of the relationships between the derived kinematics and chemical abundances for this sample and in Sect.~\ref{sect:thick} and Sect.~\ref{sect:constraints_churning} we interpret these results for the thick disc and thin disc, respectively. Our conclusions are given in Sect.~\ref{sect:conclusions}. | \label{sect:conclusions} We have investigated the increased precision with which one component of space motion can be measured by restricting a sample of stars to only those in lines-of-sight close to a Cardinal direction. We demonstrated that a restriction to stars lying towards the direction of Galactic rotation allow us to probe the azimuthal velocities with a precision better than $\sim 20\kms$. We have also demonstrated that caution needs to be taken when analysing extreme velocities derived using proper motions. Application of this los technique to the APOGEE survey defines, with unprecedented precision, the correlations between $\vphib$, $\meta$ and $\aM$ for the $\alpha$-high and $\alpha$-low stars, usually identified as the chemical thick and thin discs, respectively. The trends that we measured confirmed that these two populations are not only chemically different, but also exhibit different kinematics, likely resulting from the different dynamical processes that were important during their evolution. Combination of the azimuthal velocities with distances allow the orbital angular momenta to be derived, and from these the guiding centre radii, with a precision of $\sim1\kpc$. Use of the guiding radii as opposed to the observed radii eliminates the blurring effects of epicyclic motions in the spatial and chemical distributions of the stars. Our results confirm that $\alpha$-high stars are more radially concentrated than the $\alpha$-low disc stars. Furthermore, we identified for the thin disc clear signatures of radial migration as well as a flattening of the $\partial \vphib / \partial \afe$ and $\partial \vphib / \partial \feh$ with Galactocentric radius. We excluded radial migration from being important in the formation of the chemically defined thick disc, on the basis of a very strong correlation between the azimuthal velocity and the $\aM$ abundances (in agreement with previous analyses). Future papers of this series will analyse samples selected from the APOGEE survey in the other cardinal directions, probing the vertical and radial motions of the stars, and for the Gaia-ESO and RAVE surveys. We expect to gain valuable insight into the chemo-dynamic evolution of the Milky Way Galaxy. | 16 | 9 | 1609.04394 |
1609 | 1609.01925_arXiv.txt | 23 giant flares from 13 active stars (eight RS CVn systems, one Algol system, three dMe stars and one YSO) were detected during the first two years of our all-sky X-ray monitoring with the gas propotional counters (GSC) of the Monitor of All-sky X-ray Image (MAXI). The observed parameters of all of these MAXI/GSC flares are found to be at the upper ends for stellar flares with the luminosity of $10^{31-34}$ ergs s$^{-1}$ in the 2--20 keV band, the emission measure of 10$^{54-57}$ cm$^{-3}$, the $e$-folding time of 1 hour to 1.5 days, and the total radiative energy released during the flare of 10$^{34-39}$ ergs. Notably, the peak X-ray luminosity of 5$^{+4}_{-2} \times10^{33}$ ergs s$^{-1}$ in the 2--20 keV band was detected in one of the flares on II Peg, which is one of the, or potentially the, largest ever observed in stellar flares. X-ray flares were detected from GT Mus, V841 Cen, SZ Psc, and TWA-7 for the first time in this survey. Whereas most of our detected sources are multiple-star systems, two of them are single stars (YZ CMi and TWA-7). Among the stellar sources within 100 pc distance, the MAXI/GSC sources have larger rotation velocities than the other sources. This suggests that the rapid rotation velocity may play a key role in generating large flares. Combining the X-ray flare data of nearby stars and the sun, taken from literature and ou\ r own data, we discovered a universal correlation of $\tau \propto L_{\rm X}^{0.2}$ for the flare duration $\tau$ and the intrinsic X-ray luminosity $L_{\rm X}$ in the 0.1--100 keV band, which holds for 5 and 12 orders of magnitude in $\tau$ and $L_{\rm X}$, respectively. The MAXI/GSC sample is located at the highest ends on the correlation. | Cool stars, which have spectral types of F, G, K, and M, are known to show X-ray flares. The flares are characterized with the fast-rise and slow-decay light curve. The flares generally accompany the rise and decay in the plasma temperature. The general understanding, based on the numerous studies of solar flares, is that such features arise as a consequence of a sudden energy release and relaxation process in the reconnection of magnetic fields on/around stellar surfaces. In solar flares, the reconnection, which occurred in somewhere at large coronal heights, accelerates primarily electrons (and possibly ions) up to MeV energies, and the electrons precipitate along the magnetic fields into the chromosphere, suddenly heating the plasma at the bottom of the magnetic loop to very high temperatures. A large amount of plasma streams from the bottom to the top of the magnetic loop, while cooling has already started by that time. The flare temperature thus peaks before the Emission Measure ({\it EM}) does, or analogously, harder emission peaks before softer emission. Numerous studies on flare stars have been made with pointing observations. For the reviews, see \citet{Pettersen89}, \citet{Haisch+91}, \citet{Favata+03}, \citet{Gudel04}, and references therein. However, we cannot yet answer some fundamental questions, such as how large a flare a star can have, and how very large flares are generated. The poor understanding is rooted in the fact that the larger flares occur less frequently. Hence, all-sky monitoring is crucial to detect such large flares. X-ray all-sky monitors like Ariel-V/SSI, GRANAT/WATCH, and Swift/BAT have detected some large stellar flares. Using the data of Ariel-V/SSI spanning for 5.5 years, \citet{Pye+83} and \citet{Rao+87} detected in total twenty flares from seventeen stellar sources, including ten RS CVn systems and seven dMe stars. \citet{Rao+87} showed that there is a positive correlation between the bolometric luminosity and the X-ray peak luminosity. GRANAT/WATCH detected two X-ray transients, which have a counterpart of a flare star in their respective positional error boxes \citep{Castro+99}. Swift with BAT prompted the follow-up observations with XRT after detecting large flares from an RS CVn system II Peg \citep{Osten+07} and that from a dMe star EV Lac \citep{Osten+10}. Flares from two other RS CVn stars (CF Tuc and UX Ari) have been detected with Swift/BAT \citep{Krimm+13}. Following successful detections of large flares with all-sky X-ray surveys, we executed a survey of stellar flares with the Monitor of All-sky X-ray Image (MAXI; \cite{Matsuoka+09}). MAXI is a mission of an all-sky X-ray monitor operated in the Japanese Experiment Module (JEM; Kibo) on the International Space Station (ISS) since 2009 August. It observes an area in the sky once per 92 min orbital cycle, and enables us to search for stellar flares effectively. In this paper, we report the results with the gas proportional counters (GSC) of MAXI obtained by the first two-years operation from 2009 August to 2011 August. The results with the CCD camera of MAXI (SSC) will be given elsewhere. We describe the MAXI observation in $\S$2, our flare-search method and the results in $\S$3, then discuss the properties of the detected flares and the flare sources in $\S$4. | \subsection{Detected Flares and the Source Categories} We detected twenty-three flares, whose X-ray luminosities are $10^{31-34}$ ergs s$^{-1}$ in the 2--20 keV band and the emission measures are 10$^{54-57}$ cm$^{-3}$. The flares released the energy of 10$^{34-39}$ ergs radiatively with the $e$-folding times of 1 hour to 1.5 days (see figure~\ref{Histogram}). All the detected flares are from active stars; eight RS CVn systems, one Algol system, three dMe stars and one YSO, totaling thirteen stars. This confirms that RS CVn systems and dMe stars are intense flare sources, as reported in \citet{Pye+83} and \citet{Rao+87}. The X-ray flares from GT Mus, V841 Cen, SZ Psc, and TWA-7 were detected for the first time in this survey. Notably, II Peg showed the $L_{\rm X}$ of 5$^{+4}_{-2} \times~10^{33}$ ergs s$^{-1}$ in the 2--20 keV band at the peak of the flare, which is one of the largest ever observed in the stellar flares. Most of the flare sources that we detected with MAXI/GSC are multiple-star system (see table~\ref{prop}). However, two of them were single stars: TWA-7 \citep{Uzawa+11} and YZ CMi. In addition, another two (AT Mic and EQ Peg) have, though a binary system, a very wide binary-separation of roughly 6000 \RO, and so are the same as single stars practically. All of these four stars are known to have no accretion disk. These results reinforce the scenario that neither binarity (e.g. \cite{Getman+11}) nor accretion (e.g. \cite{Kastner+02}, \cite{Argiroffi+11}), nor star-disk interaction (e.g. \cite{Hayashi+96}, \cite{Shu+97}, \cite{Montmerle+00}) is essential to generate large flares, as has been already discussed in \citet{Uzawa+11}. According to the catalog of active binary stars \citep{Eker+08}, 256 active binaries (e.g. RS CVn binaries, dMe binaries etc.) are known within the distance of 100 pc from the solar system. However, we detected flares from only ten of them. Four of them (UX Ari, HR1099, AR Lac and II Peg) exhibited flares more than twice. \subsection{X-ray Activity on Solar-type Stars} As for the solar-type stars, fifteen G-type main-sequence stars are known within the 10-pc distance (from {\it AFGK ``bright'' stars within 10 parsecs}\footnote{http://www.solstation.com/stars/pc10afgk.htm\#yellow-orange}). The MAXI/GSC has not detected any X-ray flares from these stars. The nearest G-type star is $\alpha$ Cen A (G2 V) at the distance of 1.3 pc \citep{Soderhjelm99}. The upper limit on the $L_{\rm X}$ of $\alpha$ Cen A is estimated to be 2$~\times~10^{28}$ ergs s$^{-1}$, based on the detection limit of 10 mCrab with MAXI/GSC. This is consistent with the X-ray luminosities observed in solar flares; $L_{\rm X}$ is mostly lower than $10^{27}$--$10^{28}$ ergs s$^{-1}$ \citep{Feldman+95}. However, large X-ray flares with the respective $L_{\rm X}$ of $10^{29}$ ergs s$^{-1}$ and $2~\times~10^{31}$ ergs s$^{-1}$ have been observed from ordinary solar-type stars $\pi^1$ UMa \citep{Landini+86} and BD$+$10$^{\circ}$2783 \citep{Schaefer+00}. \citet{Schaefer+00} called such flares ``superflares''. So far, very few extensive studies have been made in the X-ray band and reported to give any good constraints on the frequency of the occurrence of ``superflares'' in the band. Our MAXI/GSC two-year survey is the best X-ray study of this kind. From our result, we can claim that the flares with $L_{\rm X}$ of larger than $1~\times~10^{30}$ ergs s$^{-1}$ must be very rare for solar-type stars. \subsection{$EM$ vs. $kT$ and the Derived Loop Parameters} Figure \ref{kT_EM} shows a plot of $EM$ vs. plasma temperature $(kT)$ for the flares in our study of the MAXI/GSC sources, together with solar flares \citep{Feldman+95}, solar microflares \citep{Shimizu95}, and flares from the stars in literature (see table~\ref{ref_fig} for the complete set of references). All of the plotted samples are roughly on the universal correlation over orders of magnitude (\cite{Feldman+95}, \cite{Shibata+99}). Our sample is located at the high ends in the correlation for both the temperatures and emission measures. Now, we consider the two important physical parameters of flares, that is, the size and magnetic field. \citet{Shibata+99}\ formulated the theoretical $EM$-$kT$ relations for a given set of a loop-length and magnetic field as equations (5) and (6) in their paper\footnote{ Their calculation of the $EM$-$kT$ relations is based on the magnetohydrodynamic numerical simulations of the reconnection by \citet{Yokoyama+98}. The simulation takes account of heat conduction and chromospheric evaporation on the following four assumptions: (1) the plasma volume is equal to the cube of the loop length, (2) the gas pressure of the confined plasma in the loop is equal to the magnetic pressure of the reconnected loop, (3) the observed temperature at the flare peak is one-third of the maximum temperature at the flare onset, (4) the pre-flare proton ($=$ electron) number density outside the flare loop is $10^{9}$ cm$^{-3}$.} (see figure~\ref{kT_EM} for a few representative cases). We calculated the loop-length and magnetic-field strength for each of the observed flares with MAXI-GSC, based on the relations \citep{Shibata+99}, as listed in table~\ref{para}. The magnetic field of our sample is comparable with those of flares on the Sun ($\sim$15--150~G). On the other hand, our sample has orders of magnitude larger sizes of flare loops than those on the Sun ($<$0.1~\RO). Especially noteworthy ones among our sample are the two largest flares relative to their binary separations, FN4 from UX Ari and FN16 from II Peg. Their loop lengths are 10 and 20 times larger than their respective binary separations, which are unprecedentedly large among stellar flares. The extraordinary large loop lengths could possibly be an artifact due to the systematic error in the model by \citet{Shibata+99}. In fact, their derived loop lengths are 10 times larger than those obtained by \citet{Favata+01}, who used a hydrodynamic model by \citet{Reale+98}. In \citet{Shibata+02}, which is the follow-up paper of \citet{Shibata+99}, it is argued that their derived loop length could be reduced to roughly 1/10 if the two assumptions (the points 3 and 4 mentioned in the footnote below) are altered. In our MAXI sample, even if the true loop sizes are 1/10 of the above-estimated values as a conservative case, the largest ones are 0.2--5 times larger than their binary separation and so are still large. \subsection{Duration vs. X-ray Luminosity} We search for potential correlations in various plots to study what are the deciding factors to generate large stellar flares and to which extent. Figure~\ref{Decay_Lx} plots the duration of flares ($\tau_{\rm lc}$) vs. the intrinsic X-ray luminosity ($L_{\rm X\_bol}$) in the 0.1--100 keV band for the stars detected with MAXI/GSC and with other missions (see table~\ref{ref_fig} for the complete set of references). Here, we have introduced $L_{\rm X\_bol}$ in order to take all the radiative energy into our calculation \footnote{See Appendix for the detailed process to derive $L_{\rm X\_bol}$ for each data-set.}. Solar flares (\cite{Pallavicini+77}, \cite{Shimizu95}, \cite{Veronig+02}) too are superposed \footnote{As the duration, we used $e$-folding time for each flare in our work and the works introduced in table~\ref{ref_fig}. For the data of \citet{Pallavicini+77} and that of \citet{Veronig+02}, we used ``decay time'', of which the definitions are up to the corresponding authors. For the data of \citet{Shimizu95}, we used the duration itself in FWHM reported in the paper. Generally, flares in any magnitude have fast-rise and slow-decay light curves, and the rise times at longest are comparable to the corresponding decay times (e.g. \cite{Pallavicini+77}, \cite{Imanishi+03}). Therefore the samples are consistent with one another within a factor of 2, or 0.3 in the logarithmic scale as in the vertical axis of figure~\ref{Decay_Lx}.}. The data points of the MAXI/GSC flares are found to be located at the highest ends in both the $L_{\rm X\_bol}$ and duration axes among all the stellar flares. The plot indicates that there is a universal correlation between $L_{\rm X\_bol}$ of a flare and its duration, such that a longer duration means a higher $L_{\rm X\_bol}$. Remarkably, the correlation holds for wide ranges of parameter values for $10^{22}$$\lesssim L_{\rm X\_bol} \lesssim 10^{34}$~ergs~s$^{-1}$ and $10^{1}$ $\lesssim \tau_{\rm lc} \lesssim 10^{6}$~s. Using the datasets of the stellar flares detected with MAXI (this work) and other missions (table~\ref{ref_fig}), and the solar flares reported by \citet{Pallavicini+77}, we fitted the data with a linear function in the log-log plot \footnote{ \citet{Shimizu95} and \citet{Veronig+02} presented the plots which indicate the X-ray luminosity and duration of each flare, but not tables for them to give the exact values. Then we excluded both datasets from the fitting.} and obtained the best-fit function of \begin{eqnarray} \tau_{\rm lc} = (1.1^{+4.7}_{-0.9}) \times 10^{4}~\left(\frac{L_{\rm X\_bol}}{10^{33}~{\rm ergs~s^{-1}}}\right)^{0.20\pm0.03} {\rm sec}, \label{eq0} \end{eqnarray} where the errors of both the coefficient and the power are in 1-$\sigma$ confidence level. The best-fit model is shown with a solid line in figure~\ref{Decay_Lx} top panel. We found that the best-fit model agrees also with the range of the data for solar microflares reported by \citet{Shimizu95}, even though the luminosities $L_{\rm X\_bol}$ of their data are smaller than $\sim10^{25}$ ergs~s$^{-1}$, whereas those used for our fitting are larger than that. For comparison, \citet{Veronig+02} and \citet{Christe+08} have derived similar power-law slope as ours, $\sim$0.33 for the GOES data and $\sim$0.2 for the RESSI data, respectively, though with the limited energy bands. The ranges of their luminosities are $L_{\rm X} = 10^{23.5-25.5}$~ergs~s$^{-1}$ in the 3.1--24.8 keV band and $L_{\rm X} = 10^{22.5-25.5}$~ergs~s$^{-1}$ in the 6--12 keV band, respectively. \medskip \smallskip \indent In the following subsections, we discuss the plausible models to explain this positive correlation, examining three potentially viable scenarios: the radiative-cooling dominant, conductive-cooling dominant, and propagating-flare models. Note that we have chosen the former two models for simplicity and examine them separately, although it is expected, as most star-flare models assume, that both radiation and conduction are present in a flare and that the latter is active early in the decay and the former is, later (e.g. \cite{Shibata+02}, \cite{Cargill04}, \cite{Reale07}). We assume that the duration of a flare $\tau_{\rm lc}$ represents the cooling time of the heated plasma when we examine the radiative- and conductive-cooling dominant models. \subsubsection{Radiative Cooling Model} First, we consider the condition where the radiative cooling is dominant. Since the thermal energy is lost via radiation, $\tau_{\rm lc}$ and the radiative cooling time $\tau_{\rm rad}$ are given by, \begin{eqnarray} \tau_{\rm lc} \simeq \tau_{\rm rad} & = &\frac{3 n_{\rm e} kT}{n_{\rm e}^{2}~F(T)} = \frac{3 kT}{n_{\rm e}~F(T)}, \label{eq1-1} \end{eqnarray} where $n_{\rm e}$ and $F(T)$ are the electron density and radiative loss rate, respectively. We obtained the radiative loss rate, using the {\it CHIANTI} atomic database (version 8.0) and the {\it ChiantiPy} package (version 0.6.4) \footnote{http://www.chiantidatabase.org/chianti.html}. On the other hand, based on the plot of $EM$ vs. $kT$ (figure~\ref{kT_EM}), we confirm that most of the observed data of stellar and solar flares are confined in the region of 15~G $< B <$ 150~G, where $B$ is magnetic field strength. The region is mathematically described as \begin{eqnarray} EM \simeq 10^{48}~ \alpha^{-5} \left(\frac{T}{10^{7}~{\rm K}}\right)^{17/2} ~{\rm cm^{-3}}~, \label{eq1-2} \end{eqnarray} where $\alpha$ is a non-dimensional parameter ranging between 0.3 and 3. Since the derived $EM$ and $F(T)$ compose $L_{\rm X\_bol}$ as \begin{eqnarray} L_{\rm X\_bol} = EM~F(T)~, \label{eq1-3} \end{eqnarray} we obtain, combining it with equation (\ref{eq1-2}), \begin{eqnarray} L_{\rm X\_bol} \simeq 10^{48}~ \alpha^{-5} \left(\frac{T}{10^{7}~{\rm K}}\right)^{17/2}~F(T)~. \label{eq1-4} \end{eqnarray} Now that both $\tau_{\rm lc}$ and $L_{\rm X\_bol}$ have been parameterized with the temperature $T$, we insert solid lines in figure \ref{Decay_Lx} as their relation for radiative-cooling dominant model. Observationally, the electron density $n_{\rm e}$ was measured to be $10^{11}~{\rm cm^{-3}}$ in flares of Proxima Centauri with a high-resolution spectroscopy in the X-ray band \citep{Gudel+02}. In the solar flares, $n_{\rm e}$ of $10^{10-11}~{\rm cm^{-3}}$ has been calculated from the $EM$ and the volume of the loop \citep{Pallavicini+77}. Some other spectroscopic observations of solar flares have indicated a wide range of $n_{\rm e}$; $10^{11-13}~{\rm cm^{-3}}$ (see references in \cite{Gudel04}). Therefore, we derived the permitted ranges for radiative cooling plasma in the following two cases: (1) $n_{\rm e}~=~10^{11}~{\rm cm^{-3}}$ and $\alpha$=~0.3--3 (figure~\ref{Decay_Lx} middle panel), (2) $n_{\rm e}~=~10^{10-13}~{\rm cm^{-3}}$ and $\alpha$~=~1 (figure~\ref{Decay_Lx} bottom panel). With the wide permitted range, the figures indicate that radiative cooling explains all the flares in our dataset. \subsubsection{Conductive Cooling Model} Second, we consider the condition where the conductive cooling is dominant, assuming a semicircular loop of the flare with the cross-section of $\pi\left(\frac{l}{10}\right)^{2}$ for the half-length $l$, which is often observed in solar flares. In this case, $\tau_{\rm lc}$ and the conductive cooling time $\tau_{\rm con}$ are given by \begin{eqnarray} \tau_{\rm lc} \simeq \tau_{\rm con} & = & \frac{3 n_{\rm e} kT}{10^{-6}~T^{7/2}~l^{-2}} \nonumber \\ & = &1.3\times10^{2}~ \left(\frac{n_{\rm e}}{10^{11}~{\rm cm^{-3}}}\right)\nonumber\\ &\times&\left(\frac{T}{10^{7}~{\rm K}}\right)^{-5/2} \left(\frac{l}{10^{9}~{\rm cm}}\right)^{2} {\rm sec}. \label{eq2-1} \end{eqnarray} On the other hand, a fraction of the thermal energy is observed as radiation. The luminosity $L_{\rm X\_bol}$ and $EM$ for the temperature $T$ are written as equations (\ref{eq1-3}) and (\ref{eq1-2}), respectively. With the plasma volume of $\frac{\pi}{50}l^{3}$, $EM$ is also written as, \begin{eqnarray} EM = \frac{\pi}{50}~n_{\rm e}^{2}~l^{3}~. \label{eq2-1-2} \end{eqnarray} Combining equations (\ref{eq1-2}), (\ref{eq2-1}) and (\ref{eq2-1-2}) gives \begin{eqnarray} \tau_{\rm lc} \simeq 1.3\times10^{5}\left(\frac{50}{\pi}\right)^{2/3}~\alpha^{-10/3}~n_{\rm e}^{-1/3}~ \left(\frac{T}{10^{7}~{\rm K}}\right)^{19/6} ~. \label{eq2-2} \end{eqnarray} Now that both $\tau_{\rm lc}$ and $L_{\rm X\_bol}$ have been parameterized with the temperature $T$, we insert dotted lines in figure \ref{Decay_Lx} as their relation for conductive-cooling dominant model. The values of $n_{\rm e}$ and $\alpha$ are varied independently within the ranges of $10^{10}$ $\lesssim n_{\rm e} \lesssim$ $10^{13}~{\rm cm^{-3}}$ and 0.3 $\lesssim \alpha \lesssim$ 3, respectively. The figure indicates that the model and the data overlap with each other in the given parameter space. \subsubsection{Propagating Flare Model} Third, we examine spatially propagating flare, like two-ribbon flares seen on the Sun. The total energy released during a flare via radiation, $E_{\rm rad}$, is described as \begin{eqnarray} E_{\rm rad} \simeq \tau_{\rm lc} L_{\rm X\_bol}~. \label{eq3-1} \end{eqnarray} On the other hand, $E_{\rm rad}$ originates from thermal energy confined in the plasma, and the thermal energy comes from stored magnetic energy, $E_{\rm mag}$. Then, it can be also written as \begin{eqnarray} E_{\rm rad} = f~E_{\rm mag} = \frac{f~B^2~D^3}{8\pi}~, \label{eq3-2} \end{eqnarray} where $f$ is the energy conversion efficiency from magnetic energy to that released as radiation, and $D$ is the scale length of the flaring region. When we assume that the magnetic reconnection propagates with the speed $v$, $\tau_{\rm lc}$ satisfies the following formula \begin{eqnarray} \tau_{\rm lc} = D/v~. \label{eq3-3} \end{eqnarray} Eliminating $E_{\rm rad}$ and $D$ with the equations (\ref{eq3-1}), (\ref{eq3-2}) and (\ref{eq3-3}), we obtain \begin{eqnarray} \tau_{\rm lc} & \simeq & 1.2 \times 10^4 \left(\frac{f}{0.1}\right)^{1/2} \left(\frac{B}{50~{\rm G}}\right)^{-1}\nonumber\\ & \times &\left(\frac{v}{3\times10^7~{\rm cm~s^{-1}}}\right)^{-3/2} \left(\frac{L_{\rm X\_bol}}{10^{33}~{\rm ergs~s^{-1}}}\right)^{1/2} {\rm sec}. \label{eq3-4} \end{eqnarray} If the values of $f$, $B$ and $v$ are common among stars, \begin{eqnarray} \tau_{\rm lc} \propto L_{\rm X\_bol}^{1/2}~. \label{eq3-5} \end{eqnarray} The power of $L_{\rm X\_bol}$ is slightly larger than what we obtained. \subsection{Origin of Large Flares} \subsubsection{Rotation Velocity} The positive correlation between quiescent X-ray luminosity and rotation velocity has been reported by \citet{Pallavicini89} and in subsequent studies. However, no studies have been published about this type of correlation for the flare luminosity. Compiling our data sample and those in literature, we search for the potential correlation of this kind. \newline \indent We plot the total energy released during a flare (i.e., $E_{\rm rad}$) vs. the square of rotation velocity ($v_{\rm rot}^{2}$) in figure \ref{V_Etot}, where $E_{\rm rad}$ is derived by multiplying $L_{\rm X}$ in the 2--20 keV band by the $e$-folding time of the flare decaying phase\footnote{ If flares have been detected from a source multiple times with MAXI and/or other missions, only the largest total energy is used. If the flare source is a multiple-star system, we use the rotation velocity of the star with the largest stellar radius in the system. In our sample, the source with the largest radius has a higher velocity than the other stars in the same system for all the multiple-star systems except EQ Peg.}. From figure \ref{V_Etot}, we find that the MAXI sample is concentrated at the region of the high rotation velocity and the large total energy. This is the first indication with an unbiased survey that stellar sources with higher rotation velocities can have a very high $E_{\rm rad}$. In order to validate this tendency further, we made two histograms of the number of sources as a function of the star-rotation velocity for flare sources. One is for our MAXI/GSC sample, and the other is for cataloged nearby stars from the literature (active binaries; \cite{Eker+08}, X-ray-detected stellar sources; \cite{Wright+11}). Both the samples are within 100~pc distance, and from the latter sample, MAXI/GSC sources are excluded. Figure~\ref{Histogram_V} shows the two histograms. The MAXI/GSC sources have the median logarithmic rotation velocity of 1.52 in units of log (km s$^{-1}$) with the standard deviation of 0.37 dex. On the other hand, the undetected sources with MAXI/GSC have the median logarithmic value of 0.80 in the same units with the standard deviation of 0.52 dex. Therefore, the rotation velocities of the MAXI sources, which have shown huge flares as reported in this paper, are significantly higher than those of the other active stars that are comparatively quiet. This supports that the sources with faster velocities generate larger flares. \subsubsection{Stellar Radius} We investigate whether the MAXI sources and/or the size of the flare-emitting region have any common characteristics or correlations in their stellar radii. \newline \indent Figure~\ref{R_EM} plots $EM$ vs. the square of the stellar radius ($R_*^{2}$) for the stars detected with MAXI/GSC and those detected with other missions (see table~\ref{ref_fig} for the complete set of references)\footnote{The largest $EM$ is used for each source if flares have been detected multiple times, and the radius of the larger star is used if the source is a multiple-star system.}. Though the sample is limited, a hint of the positive correlation between $EM$ and $R_*^{2}$ is seen at least in the MAXI/GSC sources\footnote{ A similar plot has been made by \citet{Rao+87}, for the flares detected with Ariel-V/SSI, which shows a similar correlation to ours, although their plot was the bolometric luminosity vs. X-ray peak luminosity.}. We also made a number-distribution histogram as a function of the radius in figure~\ref{Histogram_R}, similar to figure~\ref{Histogram_V}. From figure~\ref{Histogram_R}, we find MAXI/GSC sources are concentrated at the radii of about 3 and 0.3 \RO, which correspond to RS CVn-type and dMe stars, respectively. On the other hand, the undetected sources with MAXI/GSC are widely distributed in figure~\ref{Histogram_R}, which implies that the magnitude of flares is not as sensitive to the stellar radius as to the rotation velocity. | 16 | 9 | 1609.01925 |
1609 | 1609.06734_arXiv.txt | Abell 2146 ($z$\,=\,0.232) consists of two galaxy clusters undergoing a major merger. The system was discovered in previous work, where two large shock fronts were detected using the {\it Chandra} X-ray Observatory, consistent with a merger close to the plane of the sky, caught soon after first core passage. A weak gravitational lensing analysis of the total gravitating mass in the system, using the distorted shapes of distant galaxies seen with ACS-WFC on {\it Hubble Space Telescope}, is presented. The highest peak in the reconstruction of the projected mass is centred on the Brightest Cluster Galaxy (BCG) in Abell 2146-A. The mass associated with Abell 2146-B is more extended. Bootstrapped noise mass reconstructions show the mass peak in Abell 2146-A to be consistently centred on the BCG. Previous work showed that BCG-A appears to lag behind an X-ray cool core; although the peak of the mass reconstruction is centred on the BCG, it is also consistent with the X-ray peak given the resolution of the weak lensing mass map. The best-fit mass model with two components centred on the BCGs yields $M_{200}$ = 1.1$^{+0.3}_{-0.4}$$\times$10$^{15}$\,M$_{\odot}$ and 3$^{+1}_{-2}$$\times$10$^{14}$\,M$_{\odot}$ for Abell 2146-A and Abell 2146-B respectively, assuming a mass concentration parameter of $c=3.5$ for each cluster. From the weak lensing analysis, Abell 2146-A is the primary halo component, and the origin of the apparent discrepancy with the X-ray analysis where Abell 2146-B is the primary halo is being assessed using simulations of the merger. | Galaxy clusters are the most massive bound structures in the universe, forming at the intersections of filaments in the cosmic web and providing a sensitive test of the cosmological model and structure formation paradigm (e.g. Spergel \& Steinhardt 2000; Bahcall et al. 2003; Allen et al. 2011). Most of the mass in galaxy clusters is dark matter and the bulk of the baryonic mass is in the form of hot X-ray emitting plasma, comprising about 15\% of the total mass. Stars bound in cluster galaxies account for at most a few percent of the total cluster mass (e.g. Allen et al. 2011). Massive galaxy clusters form from the hierarchical merger of groups and smaller clusters which collide at speeds of up to several thousand km\,s$^{-1}$. During a cluster merger, cluster galaxies behave like collisionless particles and are slowed only by tidal interactions. The hot plasma clouds behave in a different manner and slow down as they pass through each other, since they are affected by ram pressure. Shortly after each collision in the merger process, the plasma clouds are expected to lag behind the major concentrations of cluster galaxies, for example as seen in 1E0657-56, the ``Bullet Cluster" (Markevitch et al. 2004; Clowe et al. 2004; Brada\v{c} et al. 2006; Clowe et al. 2006). Dark matter is expected to be located near to the cluster galaxies, since it does not have a large self-interaction cross-section (e.g. Randall et al. 2008). Thus the dominant baryonic component can be offset from the bulk of the total mass. Clusters that have recently undergone a major merger close to the plane of the sky are very rare systems, but they are extremely important events: as well as investigating the properties of dark matter, these systems are very promising laboratories for the study of the hot plasma in clusters and the physical transport processes in the intracluster medium (ICM) (e.g. Russell et al. 2012). They can also be used to test the $\Lambda$CDM paradigm, and alternative theories of gravity and models for dark energy, through for example their pair-wise velocity distribution (e.g. see the review in Clifton et al. 2012). Major mergers between two massive clusters are the most energetic events since the Big Bang. The kinetic energy of the systems can reach $\sim$10$^{57}$\,J, and a significant fraction is dissipated by such large-scale shocks driven into the ICM and by subsequent turbulence in the post-shock regions and ICM (e.g. Sarazin 2001; Markevitch \& Vikhlinin 2007). In addition to the Bullet Cluster, several other merging cluster systems have been studied in detail, for example MACS J0025.4-1222 \citep{BR08.1}, Abell 1758 \citep{OK08.1,RA12.1}, Abell 754, Abell1750, Abell 1914, Abell 2034, Abell 2142 \citep{OK08.1}, Abell 2744 \citep{ME11.1}, Abell 2163 (Okabe et al. 2011; Soucail 2012), and Abell 520 (e.g. Clowe et al. 2012). Some of these systems are complex however, involving several primary clusters undergoing mergers, or with merger axes with a large angle to the plane of the sky, making analysis and interpretation more challenging. \begin{figure*} \begin{center} \includegraphics[width=18cm]{fig1} \caption{Colour composite of Abell 2146 from {\it HST} F435W, F606W and F814W observations. Labels for Cluster Abell 2146-A and cluster Abell 2146-B are placed to the east of their Brightest Cluster Galaxies. The label C to the east of the BCG in Abell 2146-B is discussed in Section 4. Contours show the X-ray intensity from {\it Chandra} X-ray Observatory as described in Russell et al. (2012). Note that in this figure East is to the top-right and North is to the bottom-right as indicated, and the X-ray contours from Russell et al. (2012) are rotated accordingly for comparison with the {\it HST} composite.} \label{hst} \end{center} \end{figure*} The nature of Abell 2146 (Struble \& Rood 1999) as a merger system was first realised by Russell et al. (2010) who mapped the hot gas structure using the {\it Chandra} X-ray Observatory. These observations revealed an X-ray morphology similar to that of the Bullet Cluster, consistent with two massive galaxy clusters having undergone a recent merger with first core passage $\approx 0.1-0.3$\,Gyr ago, and still moving away from each other. The existence of 2 large shock fronts (Mach number $M\sim 2$) is unique among these merger systems, and is indicative of clusters which are closer in mass than those in the Bullet Cluster system (e.g. Markevitch et al. 2004; Mastropietro \& Burkert 2008; Lage \& Farrar 2014). Deeper {\it Chandra} observations of the system are presented in Russell et al. (2012). We refer to what appears to be the ``bullet" cluster component on X-ray maps of Abell 2146 as Abell 2146-A, and to the other cluster component as Abell 2146-B. It has been established that the location of the X-ray cool core of Abell 2146-A is offset from the location of the BCG by 36\,kpc. However, remarkably, the cool core {\it leads} rather than {\it lags} the BCG. In Abell 2146-B, the centroid of the galaxies is leading the bulk of the plasma, as expected, with the shock front being almost coincident with the BCG. The origin of the direction of the offset in Abell 2146-A is unclear, possibly being due to perturbation by another galaxy, or to a merger that is somewhat off axis (Canning et al. 2012; White et al. 2015). BCGs are very rarely seen to lag behind the ICM in merger systems. In Abell 168, Hallman \& Markevitch (2004) suggested that the BCG lagging the ICM is due to a ``ram pressure slingshot", resulting from a drop in ram pressure on the plasma when the sub-cluster is approaching the apocentre of its orbit, at a late stage in the merger. In the complex merger system Abell 2744, the ICM also leads the galaxies and dark matter in one of the four clusters undergoing a merger; Owers et al. (2011) and Merten et al. (2011), however, suggest that a ram pressure slingshot is responsible. The direction of the offset of the eastern mass and X-ray peaks in Abell 754 are also indicative of the eastern mass component reaching the apocentre of the merger orbit, and falling back towards the centre for the second core passage (Okabe \& Umetsu 2008). This effect would not be expected in Abell 2146, since it is observed at an earlier stage in the merger; Russell et al. (2010) estimated that the time scale for a ram pressure slingshot to occur would be $\approx$\,1\,Gyr after first core passage, several times longer than the age estimated from observations. Canning et al. (2012) estimated that in Abell 2146 the merger axis is inclined at only $\sim17^{\circ}$ to the plane of the sky, using the line of sight velocity difference between the brightest cluster galaxies in each of the clusters along with the X-ray shock velocities. A dynamical analysis of cluster galaxies presented in White et al. (2015) is also consistent with a recent merger that is relatively close to the plane of the sky, with a merger axis inclined at $13^{\circ}-19^{\circ}$ and a time scale since first core passage of $\approx 0.12-0.14$\,Gyr. In addition, the detection of the shock fronts with {\it Chandra} in itself requires a relatively recent merger with a small angle to the line of sight; a larger angle would result in smearing of the sharp surface brightness edges when seen in projection, and in a system observed later in the merger process the shock fronts would have travelled further into the low density region and would go undetected. Mass estimates for the system have been obtained using several different techniques. Using a mass - X-ray temperature scaling relation (e.g. from Finoguenov et al. 2001) yields a mass estimate of $M_{\rm 500} \sim7 \times 10^{14} M_{\odot}$ \footnote{Throughout we use $M_{n}$ to denote the mass inside the radius $r_{n}$ where the mean mass density is $n$ times the critical density at the redshift of halo formation.}, with X-ray observations indicating that Abell 2146-A is the lower mass cluster (Russell et al. 2010). The system has also been detected in Sunyaev-Zel'dovich (SZ) observations; clusters distort the intensity of the Cosmic Microwave Background (CMB) when about 1\% of CMB photons undergo inverse-Compton scattering and gain energy from the electrons in the intracluster gas (Sunyaev \& Zel'dovich 1970). The SZ signal was measured using the Arcminute MicroKelvin Imager (AMI), with a peak signal-to-noise ratio of 13$\sigma$ in the radio source subtracted map (AMI Consortium: Rodr\'iguez-Gonz\'alvez et al. 2011). The total mass inside $r_{200}$ estimated by the AMI Consortium from the SZ signal is $4.1\pm 0.5 \times 10^{14} h^{-1}M_{\odot}$. The total dynamical mass estimated by applying the virial theorem to spectroscopic observations of cluster members in the system is $M_{\rm vir}= 8.5^{+4.3}_{-4.7}\times 10^{14} M_{\odot}$ (White et al. 2015), not corrected downwards for a surface pressure term of $\approx 20\%$ (The \& White 1986), with Abell 2146-A being the higher mass cluster. Deep radio observations of Abell 2146 by Russell et al. (2011) using the Giant Metrewave Radio Telescope (GMRT) at 325\,MHz do not detect an extended radio halo or radio relics associated with the shock fronts, at odds with all other merging galaxy clusters with X-ray detected shock fronts, including the Bullet Cluster, Abell 520 and Abell 754, and with candidate shock fronts. The radio power expected from the P$_{\rm{radio}}$-L$_{\rm X-ray}$ correlation for merging systems of Cassano et al. (2013) is significantly higher than the measured upper limit, which remains a puzzle. However, see the discussion in White et al. (2015) of the absence of a detected radio halo in Abell 2146 in the context of the P$_{\rm{radio}}$-$M_{500}$ correlation of Cassano et al. (2013). Gravitational lensing is sensitive to the total gravitating mass of the system, probing both dark and luminous matter. In this paper we present a weak gravitational lensing analysis of Abell 2146, using the distorted shapes of distant galaxies on ACS-WFC {\it Hubble Space Telescope} images (PI: King, proposal 12871). In Section 2 we describe the {\it HST} observations. In Section 3 we outline the relevant aspects of weak lensing and describe how the catalogues of galaxies used in the weak lensing analysis were obtained. We present weak lensing mass maps and parameterized mass models of the system in Section 4. The results are discussed in Section 5, and we conclude in Section 6. Throughout this paper, for comparison with previous work, we assume a $\Lambda$CDM cosmology with present day Hubble parameter $H_{0}$\,=\,$70\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$, and present day matter density and dark energy density parameters $\Omega_{\rm M}$\,=\,0.3 and $\Omega_{\Lambda}$\,=\,0.7 respectively. We assume dark energy to be a cosmological constant, equation of state parameter $w=-1$. At the redshift of Abell 2146 ($z=0.2323$), the physical scale is 3.702 kpc per arcsecond, and the Hubble parameter $H$\,=\,$78.7\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$. | We have carried out a weak lensing analysis of the cluster merger system Abell 2146 using data from ACS/WFC on {\it HST}. This is a unique system in that it presents two large shocks on {\it Chandra} X-ray maps (Russell et al. 2010; Russell et al. 2012) and along with dynamical analysis (Canning et al. 2012; White et al. 2015) these limit the time since first core passage to about 0.15 Gyr ago, with a merger axis inclined at about $15^{\circ}$ to the plane of the sky. Thus, we are observing this system at a relatively early stage in the merger, with the clusters still moving apart. Our weak lensing mass map and parametric models simultaneously fitting two NFW mass components are consistent with Abell 2146-A being the more massive cluster. The mass ratio between the components centred on the BCG in Abell 2146-A and on the BCG in Abell 2146-B is $\approx 3-4:1$ and the total mass is $\approx$1.2$\times$10$^{15}$M$_{\odot}$, assuming NFW mass profiles for each cluster and a mass concentration parameter of $c=4$ for each. Abell 2146-B has a more extended mass distribution, perhaps due to it being a less concentrated cluster that was more disrupted during the merger, and the distribution of mass is likely better described by the mass map rather than by a parametric model. The similarity in the masses of the clusters is in accord with the presence of two large shocks on X-ray maps, in contrast to for example the Bullet Cluster (Markevitch et al. 2004; Clowe et al. 2004; Brada\v{c} et al. 2006; Clowe et al. 2006). Weak lensing reveals the larger-scale mass distribution, and the peak of the total mass in Abell 2146 is coincident with the BCG in Abell 2146-A. Both the BCG and total mass peak appear to lag the X-ray cool core, though as noted in the Discussion any offset is within the error bar on the mass peak position on the weak lensing map. This error bar was estimated by bootstrap resampling the galaxy catalogues used for the weak lensing analysis, and determining the statistics of the peak locations on 30,000 resampled mass maps. The resolution of weak lensing mass maps is primarily limited by having to average over a sufficient number of galaxies, which have an intrinsic distribution of shapes and orientations, in order to measure a weak lensing signal. A strong lensing analysis of the system, using newly discovered multiple image systems as constraints and revealing the mass in the centre of Abell 2146-A at higher resolution, will shortly be presented in Coleman et al. (in prep.). Simulations are now underway to understand the merger dynamics and the time-evolution of the luminous and dark matter in the system, constrained by gravitational lensing, X-ray, galaxy kinematics and SZ observables. These simulations will allow us to explore the factors that lead to Abell 2146-A being the more massive cluster from weak lensing, yet the less massive cluster from the analysis of the X-ray data. | 16 | 9 | 1609.06734 |
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