subfolder
stringclasses 367
values | filename
stringlengths 13
25
| abstract
stringlengths 1
39.9k
| introduction
stringlengths 0
316k
| conclusions
stringlengths 0
229k
| year
int64 0
99
| month
int64 1
12
| arxiv_id
stringlengths 8
25
|
|---|---|---|---|---|---|---|---|
1609 | 1609.05208_arXiv.txt | In this second of a series of radiation-hydrodynamical studies of protostellar outflows and radiative force feedback from massive protostars we perform 2D axially symmetric simulations to assess the impact of varying 1) when the protostellar outflow starts, 2) the ratio of ejection to accretion rates, and 3) the strength of the wide angle disk wind component. The star formation efficiency, defined here as the ratio of final stellar mass to initial core mass, is dominantly controlled by radiative forces and the assumed ratio of ejection to accretion rates of the outflow. Increasing this ratio has three effects: First, the protostar grows more slowly and thus has lower luminosity at \vONE{any} given time, lowering the radiative feedback. Second, the low density bipolar cavity cleared by the outflow is larger, which further diminishes the radiative feedback on disk and core scales. Third, the higher momentum outflow sweeps up more material from the collapsing envelope, and the potential mass reservoir of the forming star is decreased via entrainment. The star formation efficiency varies with the ratio of ejection to accretion rates from 50\% in the case of very weak outflows to as low as 20\% for very strong outflows. At latitudes between the low density bipolar cavity and the high density accretion disk, wide angle disk winds remove some of the gas, which otherwise would be part of the accretion flow onto the disk; varying the strength of these wide angle disk winds, however, alters the final star formation efficiency by only $\pm6\%$. For all cases, the opening angle of the bipolar outflow cavity remains below $20\degr$ during early protostellar accretion phases, increasing rapidly up to $65\degr$ at the onset of radiation pressure feedback. We perform two-dimensional axially symmetric radiation-hydrodynamic simulations to assess the impact of outflows and radiative force feedback from massive protostars by varying when the protostellar outflow starts, the ratio of ejection to accretion rates, and the strength of the wide angle disk wind component. The star formation efficiency, i.e.~the ratio of final stellar mass to initial core mass, is dominated by radiative forces and the ratio of outflow to accretion rates. Increasing this ratio has three effects: First, the protostar grows slower with a lower luminosity at any given time, lowering radiative feedback. Second, bipolar cavities cleared by the outflow are larger, further diminishing radiative feedback on disk and core scales. Third, the higher momentum outflow sweeps up more material from the collapsing envelope, decreasing the protostar's potential mass reservoir via entrainment. The star formation efficiency varies with the ratio of ejection to accretion rates from 50\% in the case of very weak outflows to as low as 20\% for very strong outflows. At latitudes between the low density bipolar cavity and the high density accretion disk, wide angle disk winds remove some of the gas, which otherwise would be part of the accretion flow onto the disk; varying the strength of these wide angle disk winds, however, alters the final star formation efficiency by only $\pm 6\%$. For all cases, the opening angle of the bipolar outflow cavity remains below $20\degr$ during early protostellar accretion phases, increasing rapidly up to $65\degr$ at the onset of radiation pressure feedback. | \label{sect:introduction} Massive stars impact their natal environment via a variety of feedback effects. To begin with they inject momentum, mechanical and thermal energy into their surroundings via protostellar jets and outflows and radiation pressure. The irradiation and heating also modify the gas' chemical state, an effect not considered further here. Later, additional mechanical/thermal input comes from heating due to photo-ejection of electrons from dust, molecular dissociation and ionization, stellar winds, and supernovae. In this investigation, we address the feedback effects of the protostellar phases only, namely protostellar outflows and radiation pressure. The impact of protostellar outflows can be subdivided into three components: First, the redirection of a fraction of the accretion flow into an outflow implies a decrease of the actual stellar accretion rate. Second, outflows inject outward directed momentum into the infalling gas and hence counteract the stellar gravitational attraction, resulting in a slow-down or even reversal of the infall from the pre-stellar core ({\sl entrainment}). Third, outflows produce low density bipolar cavities, which in turn alter the effects of radiation pressure during later phases. In the first article of this series \citep[][hereafter Paper I]{Kuiper:2015p28986}, we labeled these components as ``mass loss feedback'', ``kinematic feedback'', and ``radiative feedback'', respectively. In Paper I we focussed on the latter of the three protostellar outflow feedback effects. These previous simulations used a nominal value of the ratio of ejection to accretion rates of only 1\%, minimizing the effects of mass loss feedback and kinematic feedback, but allowing us to investigate how protostellar outflows change the morphology of the stellar environment and how this affects the efficiency of the later radiative feedback phase. We found that the low density outflow cavities initiate a large scale anisotropy of the thermal radiation field, which extends the so-called flashlight effect from the disk out into the core. The disk's flashlight effect denotes the anisotropy of the thermal radiation field around a forming star due to the high optical depth of its accretion disk \citep{Nakano:1989p497, Yorke:1999p156, Yorke:2002p735, Kuiper:2010p541, Kuiper:2011p21204}. The core's flashlight effect enables sustained accretion from the core to the disk in an analogous fashion as the disk's flashlight effect enables sustained accretion from the disk to the star. Further details on the impact of radiation pressure feedback is given in Sect.~\ref{sect:intro_previous}, where we discuss the current investigation in the context of our former simulation studies. Here, we consider the effects of higher mass loss and vary the ratio of ejection to accretion rates from 1\% up to a maximum value of 50\%. Additionally, we explore the broad parameter space of outflow configurations by varying its launching time and the strength of a large angle disk wind component. Such a numerical study necessarily involves considering a broad range of parameter space, see Sect.~\ref{sect:parameterspace} for details. In general, jets and outflows vary strongly with respect to the ratio of ejection to accretion rates and degree of collimation. First trends of these variations have been detected, e.g.~collimation seems to weaken with increasing age and stellar mass \citep{Beuther:2005p142}. The current theoretical and observational understanding of jets and outflows does not allow one to fully trace these parameters back to stellar and/or environmental properties. Naturally, the launching physics on the smallest scale is the most difficult to obtain from observations, and the launching picture lacks of a detailed theoretical description as well. A review of observational outflow studies with a focus on the launching physics is given by e.g. \citet{Ray:2007p10756}. The recent review by \citet{Frank:2014p29566} is structured along spatial scales of jets and outflows and also includes a chapter on the launching scales. Other observational reviews in this context were presented by \citet{Arce:2007p10514} and \citet{Bally:2008p20721}. For a description of the theoretical context of jets and outflows from young stars, we refer the reader to the reviews by \citet{Konigl:2000p9442} and \citet{Pudritz:2007p549}. \subsection{Feedback effects of protostellar outflows} Outflows are considered an important feedback mechanism which reduces the overall star formation efficiency, especially on spatial scales from pre-stellar cores to accretion disks \citep[see e.g.~review by][and references therein]{Frank:2014p29566}. \citet{Banerjee:2007p691} and \citet{Hennebelle:2011p5748} followed the collapse of a magnetized pre-stellar core collapse to study the self-consistent launching of a bipolar outflow from a forming high mass star, but both studies neglected the radiative feedback of the protostar. More recent studies \citep{Wang:2010p2487, Cunningham:2011p953, Peters:2014p27736, Federrath:2014p28884, Kuiper:2015p28986} make use of subgrid modules for protostellar outflow feedback. \citet{Wang:2010p2487} studied the interaction of outflows and the ambient large scale magnetic field in a cluster-formation simulation, which leads to a kind of self-regulation of the overall collapse in the sense that higher accretion rates are coupled to higher feedback efficiencies. In the context of cluster formation, \citet{Peters:2014p27736} presented a study of the combined feedback of multiple low mass outflows as an alternative explanation for high mass loss rates and momentum feedback, if the associated protostars are forming with nearly the same direction of their angular momentum vectors, e.g.~as a consequence of a global common rotation of the cluster-forming gas. The overall reduction of the star formation efficiency due to the outflows' kinematic feedback during cluster formation was presented in \citet{Federrath:2014p28884}, focussing on low mass stars as well. Simulations of higher mass protostars, including protostellar outflows and radiative feedback were presented in \citet{Cunningham:2011p953}. They report a reduction of radiative flux in the equatorial plane perpendicular to the outflow due to the low density outflow cavities, a finding, which we extended in Paper I to the super-Eddington regime, including strong radiative forces by massive protostars. Studies of the combined effects of protostellar outflows and radiative forces remain limited. Here, we expand on our earlier work by covering the parameter space of outflow injection, including different strengths of the total outflow and of a disk wind. One of the key aspects of our numerical studies is the long evolutionary timescales covered by the simulations. Our simulations are stopped after the total depletion of the mass reservoir due to feedback; this process takes up to 10 free-fall times of the original pre-stellar core. The modeling of the full stellar accretion and feedback phase allows a quantitative determination of the overall feedback efficiencies in terms of total mass loss. By contrast, the numerical simulations cited above cover timescales of about one free-fall time or less \citep{Banerjee:2007p691, Cunningham:2011p953, Peters:2014p27736}, up to 2 free-fall times only in simulations without radiation transport \citep{Hennebelle:2011p5748, Federrath:2014p28884}, and up to a maximum of 5 free-fall times only in the simulation by \citet{Wang:2010p2487}. From an observational perspective of large cluster-scales, magnetic-field-regulated accretion \citep[e.g.][]{Vlemmings:2010p10559} and outflow regulated feedback \citep[e.g.][]{Nakamura:2014p28897} seem to be likely. Molecular outflows from protostars may even contribute to the final mass depletion of the stellar surroundings \citep[see e.g.][]{Shepherd:2004p31878}. On these scales, outflows may also contribute to the replenishment of turbulence within the star-forming region \citep[see review by][and references therein]{MacLow:2004p350}. \vONE{ However the importance of this contribution is being questioned and observations seem to produce contradictory results \citep{Arce:2011p32946, DrabekMaunder:2016p32992}. } \subsection{Outline of our preceding studies} \label{sect:intro_previous} In this section, we embed the simulation series into (our) preceding simulation studies regarding massive stars in the super-Eddington regime. Massive stars can become so luminous that their stellar radiative force on the directly illuminated surrounding gas and dust exceeds their gravitational attraction. For spherically symmetric accretion flows, this feedback causes the so-called radiation pressure problem in the formation of massive stars \citep{Kahn:1974p799, Yorke:1977p376}, which sets a stellar upper mass limit of about $40 \mbox{ M}_\odot$. Based on the studies by \citet{Nakano:1989p497} and \citet{Yorke:1999p156}, it is expected that this radiation pressure problem is reduced in the presence of anisotropic thermal radiation fields, which are naturally generated by a massive accretion disk forming around the protostar, also known as the ``disk's flashlight effect''. In subsequent numerical studies of the anisotropic radiation pressure in the formation of massive stars \citep{Yorke:2002p735, Krumholz:2009p687} the highest mass of the forming protostars was still limited to $M_* \lesssim 43 \mbox{ M}_\odot$, only marginally above the 1D limit. The formation of massive stars up to $M_* \lesssim 140 \mbox{ M}_\odot$ was demonstrated in \citet{Kuiper:2010p541}, utilizing a more accurate treatment of the radiation transport and higher resolution of the forming accretion disk. The force analysis of the simulation data shows that the radiation pressure problem is indeed circumvented by the flashlight effect. Later on, these numerical models were enhanced from axially symmetric configurations to three-dimen\-sional simulations, investigating the non-axially symmetric morphology of the accretion disk and the radiation-pressure-dominated outflow region \citep{Kuiper:2011p21204}. Self-gravity in the massive accretion disk generates spiral arms, which transport angular momentum outward, while gas is transported inward. A comparison of the resulting accretion with the results of axially symmetric simulations with different strengths of the so-called $\alpha$-shear viscosity, reveals the self-gravity as a very efficient driver of the disk's accretion towards the protostar. The disk accretion rates driven by the self-gravity were found to be high enough to overcome the diminished radiation pressure in the disk. Although direct observations of massive accretion disks at these early stages are extremely difficult, very recent ALMA observations were able to reveal Keplerian-like rotation profiles around a high mass O7 star \citep{Johnston:2015p32366}. The inner gaseous disk surrounding a massive protostar inside the dust sublimation zone further contributes to the disk's flashlight effect and at the same time shields the large scale collapsing environment from the direct stellar irradiation, allowing for sustained envelope-to-disk accretion \citep{Kuiper:2013p17358}. These results were obtained by including the gas opacities from \citet{Helling:2000p1117}, also used in the protoplanetary disk models by \citet{Semenov:2003p79}. We studied the impact that stellar evolution has on the environment and vice versa in \citet{Kuiper:2013p19987}. Whereas on long timescales, this interplay seems to have only limited consequence on the final mass, on timescales $< 5$~kyr, the interplay of stellar evolution and accretion results in variable accretion and accretion bursts. More interestingly, different initial conditions of the cloud collapse yield a broad range of the protostellar bloating epoch. In the different runs, the protostar reaches the zero-age main-sequence between $20 \mbox{ M}_\odot$ and $40 \mbox{ M}_\odot$. This point in evolution is of special interest, because it denotes the beginning of strong ionization feedback of the forming massive star, creating an expanding HII region around it. The reduction of the radiative impact on the disk accretion flow due to low density outflow cavities has been studied in both purely static \citep{Krumholz:2005p406} and hydrodynamic models \citep[][Paper I]{Cunningham:2011p953% }. In Paper I we demonstrate that protostellar outflows can enlarge the anisotropy out to core scales. This is the basis for what we call the ``core's flashlight'' effect, i.e.~the core-scale anisotropy, which shields large portions of the core from intense thermal radiation, allowing mass to accrete from the collapsing envelope onto the accretion disk in an analogous manner to the disk's flashlight effect, which allows mass to accrete from the disk onto the (proto)star. With the present investigation we further elaborate on these previous studies. Methodologically, the outcome of radiation hydro\-dynamics simulations in the super-Eddington regime depends crucially on the accuracy of the method used to compute the stellar radiative feedback \citep{Kuiper:2012p1151}. In the past, most large scale star formation simulations were limited to the gray flux-limited diffusion approximation, which generally provides an accurate estimate of the dust temperature but which yields a very poor estimate of the radiative force. Recently, \citet{Klassen:2014p27924} introduced an implementation of the hybrid radiation transport scheme of \citet{Kuiper:2010p586} into the adaptive grid code FLASH \citep{Fryxell:2000p768, Dubey:2009p32315}, \citet{Harries:2015p32122} added a hydrodynamics module for the Monte Carlo radiative transfer code TORUS, and \citet{Buntemeyer:2016p32167} independently implemented a radiation transport module for FLASH using characteristics on the adaptive grid. First simulations carried out with these tools \citep{Harries:2014p28908, Klassen:2016p32943} address the accuracy of radiative forces in the formation of a massive protostar as discussed in \citet{Kuiper:2012p1151} and confirm these earlier results. Furthermore, the simulations by \citet{Klassen:2016p32943} and \citet{Kuiper:2011p21204} agree in identifying the self-gravity of the massive accretion disks as a sufficiently strong driver of angular momentum transport, and hence mass accretion against the diminished radiative force. | \label{sect:summary} Following our study of protostellar outflow and radiative force feedback from massive (proto)stars in Paper I, we performed three series of parameter studies to investigate the impact of the time when the outflow is launched, the ratio of ejection to accretion rates, and the strength of the large angle disk wind component on the evolution of the star, its accretion disk, and large scale environment. We focussed on the feedback efficiency, the stellar accretion rate, and the final stellar mass. We find that in the high mass star formation regime, where the accretion is super-Eddington, the total feedback efficiency in terms of mass loss from the immediate stellar vicinity is dominated by radiative forces. Varying e.g.~the launching time of the protostellar outflow over reasonable values does not affect the final mass of the forming star. Even simulation runs with protostellar outflows injected well before and well after the formation of a circumstellar disk show deviations of the final stellar mass below $1\%$. The final stellar mass is affected by the ratio of ejection to accretion rates, which impacts the evolution of the accretion-outflow system in three ways. First, a greater re-direction of the accretion flow into an outflow directly implies a lower stellar accretion rate. Second, a stronger protostellar outflow is able to entrain more mass from the protostellar environment. Third, the formation of a low density cavity alters the radiative feedback on both disk and core scales (c.f. Paper I). A quantitative comparison of the efficiencies of the individual feedback components and the resulting final stellar masses in simulations with different ratios of ejection to accretion rates reveals a fairly constant impact of the sum of radiative forces and entrainment independent of the ejection to accretion ratio in the regime of $f_\mathrm{ejec-acc} \ge 20 \%$. The ejected outflow mass increases roughly linearly toward higher ratios of ejection to accretion rates. The latter outcome implies that the efficiency of the large scale accretion flow from core to disk is only marginally influenced by the outflow. The fact that the sum of radiative feedback and entrainment remains fairly constant for the higher values of the ratio of ejection to accretion rates implies that the decrease of radiative feedback (due to the formation of lower mass stars) is compensated by the increased entrainment of the core material. Increasing the strength of the large angle disk wind component adds to the entrainment as it impacts the intermediate density gas at mid-latitudes between the low density outflow cavity and the high density accretion disk. Quantitatively, with changing the relative mass flow of the large angle disk wind by $+30\%$ / $-17\%$ results in a $\pm6\%$ change of the final stellar mass. The high mass protostars considered in this work fall in the final stellar mass range of $M_* = 20 \ldots 50 \mbox{ M}_\odot$. For these protostars, radiative forces are the dominant feedback mechanism. Bipolar cavities carved by protostellar outflows diminish the radiative feedback efficiency due to the ``core's flashlight effect'' (c.f.~Paper I). Varying the outflows as we do here does not change this general conclusion. The new results summarized above show that the total feedback efficiency also depends on the strength of the protostellar jet and outflow, both in terms of the ratio of ejection to accretion rates and the strength of the large angle disk wind component. While the reduction of the large scale radiative acceleration by the core's flashlight effect is quantitatively about 5\% (see Paper I), the increased mechanical feedback due to re-direction of the disk-to-star accretion flow and the entrainment of the larger-scale environment can be much stronger in the regime of reasonably strong outflows (ratios of ejection to accretion rates of more than 10\%). Comparing the observed stellar initial mass function (IMF) and the core initial mass function suggests a core-to-star efficiency of about 30\%, especially in the case of low mass star formation. In our study -- focussing on the high mass end of the IMF -- we find core-to-star efficiencies of 30\% for values of the ratio of ejection to accretion rates of 20-30\%. For a much higher ratio of ejection to accretion rates of 50\%, the core-to-star efficiency is as low as 20\%. The opening angle of the bipolar outflow cavity remains below $15\degr-20\degr$ during the early protostellar phase and then quickly opens up to $65\degr$ at the onset of radiation pressure feedback. In the case of reasonably high ratios of ejection to accretion rates greater than 20\% and large angle disk winds that are not too weak, the outflow opening angle increases further with time. After two free-fall times of the initial core, the outflow opening has expanded up to $85\degr$, limiting the large scale accretion flow to the shadowed regions of the circumstellar disk. | 16 | 9 | 1609.05208 |
1609 | 1609.03568_arXiv.txt | We present an improved photometric redshift estimator code, CuBAN$z$, that is publicly available at \href{https://goo.gl/fpk90V}{https://goo.gl/fpk90V}. It uses the back propagation neural network along with clustering of the training set, which makes it more efficient than existing neural network codes. In CuBAN$z$, the training set is divided into several self learning clusters with galaxies having similar photometric properties and spectroscopic redshifts within a given span. The clustering algorithm uses the color information (i.e. $u-g$, $g-r$ etc.) rather than the apparent magnitudes at various photometric bands as the photometric redshift is more sensitive to the flux differences between different bands rather than the actual values. Separate neural networks are trained for each cluster using all possible colors, magnitudes and uncertainties in the measurements. For a galaxy with unknown redshift, we identify the closest possible clusters having similar photometric properties and use those clusters to get the photometric redshifts using the particular networks that were trained using those cluster members. For galaxies that do not match with any training cluster, the photometric redshifts are obtained from a separate network that uses entire training set. This clustering method enables us to determine the redshifts more accurately. SDSS Stripe 82 catalog has been used here for the demonstration of the code. For the clustered sources with redshift range $z_{\rm spec}<0.7$, the residual error ($\langle (z_{{\rm spec}}-z_{{\rm phot}})^2\rangle^{1/2} $) in the training/testing phase is as low as 0.03 compared to the existing ANNz code that provides residual error on the same test data set of 0.05. Further, we provide a much better estimate of the uncertainty of the derived photometric redshift. | Even though there is a huge advancement in the telescope technology, spectroscopy of a large number of galaxies is still very time expensive especially for high redshift large scale galaxy surveys. Thus photometry is still the best bet for such surveys whether they are the existing ones, i.e. Solan Digital Sky Surveys (SDSS), 2dF Galaxy redshift Survey, Blanco Cosmological Survey, Dark Energy Survey \citep{2014ApJS..211...17A,1999RSPTA.357..105C,2015ApJS..216...20B} or the future planed ones like Large Synoptic Survey Telescope \citep{2008arXiv0805.2366I}, etc. Hence we need to infer redshift of the sources from the photometric measurements only. Two types of photometric redshift (photo-$z$) determination processes are vastly used. One is the template base analysis such as HyperZ, ImpZ, BPZ, ZEBRA \citep{2000A&A...363..476B,2004MNRAS.353..654B,2000ApJ...536..571B,2006MNRAS.372..565F}. The other uses the neural networks to get empirical relation between redshift and available colors, such as ANNz, ArborZ \citep{2004PASP..116..345C,2010ApJ...715..823G}. Recently, some other techniques have also been proposed to get the photo-$z$ such as genetic algorithm, gaussian processes etc., \citep{2015MNRAS.449.2040H, 2010MNRAS.405..987B}. Both template fitting and neural network approaches possess their merits and demerits \citep{2011MNRAS.417.1891A}. The template base redshift determinations are always biased from the available templates and need to know the filter response, detector response etc., very well. On the other hand, the neural network methods provide better results than the template analysis method if there are large number of galaxies available for the training set. Given the present day increase in the number of spectroscopic sample of galaxies, this method would be the best possible choice and thus it's timely to make some improvement on it. Here, we propose an improved technique that uses existing neural network algorithm combined with clustering of the training set galaxies in order to get more accurate photometric redshifts for sources with known photometric properties. Our method is better in the following ways. We use a back propagation of error to train the neural networks compare to the existing ANNz code that uses quasi-Newton method \citep{2004PASP..116..345C}. Secondly and most importantly, we build self-learning clusters from the training set with galaxies having similar photometric properties and spectroscopic redshifts. Our modified clustering algorithm takes into account of the uncertainty in the measurements where as the traditional clustering algorithms just ignore these uncertainties. Separate neural networks are trained using the members of each clusters. The training of neural networks are done considering all possible differences in photometric magnitudes between different bands (i.e. the color) along with the apparent magnitudes in each bands and the errors associated with them. It allows us to map the redshift from the photometric measurements more accurately as colors are more sensitive to redshift. In order to obtain photometric redshift of unknown sources, we first seek for clusters that have similar photometric properties. If there is any, the neural networks that are trained using those clusters are used to find the photometric redshift of that galaxy. Otherwise, a separate network which is trained using all available galaxies for the training is used to get the photometric redshift. This ensures a much more accurate estimate of the redshift for the sources that match with clusters having similar properties in the training set. Finally, we provide more realistic treatment to estimate the uncertainty in the derived photometric redshift by considering the possible uncertainty in the training process, so that it can be used more confidently for further analysis of the galaxy properties such as number distribution, finding groups/clusters of galaxies etc. The paper is organised as follows. In section~\ref{sec_data} the data set that has been used in this paper is described in details. Our clustering models are discussed in section~\ref{sec_cluster}. The back propagation neural network is described in section~\ref{sec_bnn}. We show the performance of our code in section~\ref{sec_result}. In section~\ref{sec_code} we describe our code and its usages. Finally we discuss and conclude in section~\ref{sec_cd}. | \label{sec_cd} We have introduced a new photometric redshift estimator, CuBAN$z$, that provides a much better photo-$z$ compared to the existing ones. The code is publicly available and very simple to use. It can be run in any machine having standard C compiler. It uses back propagation neural networks clubbed with clustering of training sources with known photometric broad band fluxes and spectroscopic redshifts. The clustering technique enables us to get a better estimate of photometric redshifts particularly for galaxies that fall under clusters. In particular the rms residue in the testing set is as low as 0.03 for a wide redshift range of $z \le 0.7$ compare to existing ANNz code that gives 0.055 on the same data set. Moreover, we provide much better estimate on the uncertainty in the redshift estimator considering the uncertainty in the weight factors of the trained neural networks. We hope that it will be very useful to the astronomy community given the existing large photometric data as well as large upcoming photometric surveys. The present version of the code is very simple and we are in the process of making it more flexible as well as user friendly. | 16 | 9 | 1609.03568 |
1609 | 1609.08485_arXiv.txt | {% J1407 (\object{1SWASP J140747.93-394542.6} in full) is a young star in the Scorpius-Centaurus OB association that underwent a series of complex eclipses over 56 days in 2007. To explain these, it was hypothesised that a secondary substellar companion, J1407b, has a giant ring system filling a large fraction of the Hill sphere, causing the eclipses. Observations have not successfully detected J1407b, but do rule out circular orbits for the companion around the primary star. } { We test to what degree the ring model of J1407b could survive in an eccentric orbit required to fit the observations. } { We run $N$-body simulations under the AMUSE framework to test the stability of Hill radius-filling systems where the companion is on an eccentric orbit. } { We strongly rule out prograde ring systems and find that a secondary of $60$ to $100 \MJup$~with an 11 year orbital period and retrograde orbiting material can survive for at least $10^4$ orbits and produce eclipses with similar durations as the observed one. } % | \label{sec:intro} Giant planet formation consists of the transfer of material from the circumstellar environment to the circumplanetary environment. The change in angular momentum of the circumstellar material results in the formation of a disk of gas and dust surrounding the protoplanet \citep{Ward10,Alibert05}. In our Solar system, the primordial gas is no longer present, but evidence of the circumplanetary disk exists in the form of coplanar moons and rings \citep[e.g. see review by][]{Tiscareno13}. All Solar system gas giant ring systems show structure. This structure consists of gaps in the rings themselves and sudden changes of particle density as a function of radius from the planet. The K5 pre-MS 16 Myr-old star J1407 showed a complex series of eclipses in 2007, lasting a total of 56 days, and a series of papers investigating the J1407 system \citep{Mamajek12, vanWerkhoven14, Kenworthy15, Kenworthy15b} conclude that there is a secondary substellar companion (called J1407b) with a giant multi-ring system in orbit around the primary star. The ring system shows detailed structure down to the temporal resolution set by the diameter of the primary star and their mutual relative projected velocity. A study of the stability of a Hill sphere-filling system on a circular orbit has been explored in \citet{2016arXiv160502365Z}. The derived diameter of the ring system combined with the observational limits set on the companion J1407b \citep[as described in][]{vanWerkhoven14,Kenworthy15} imply that J1407b is on an eccentric orbit about J1407. In this paper we investigate the effects of an elliptical orbit on the stability of the ring system surrounding J1407b. Our goal is to determine whether there are any bound orbital solutions for the secondary companion that can explain both the derived relative velocity and the duration of the eclipse seen towards J1407. To this end, we construct a model containing J1407, its companion J1407b and a co-planar disc around J1407b; based on the model in \citet{Kenworthy15b}. In Section~\ref{sec:model}, we describe this model and the parameters we investigate in this article. We run simulations of this model using {\tt AMUSE}\footnote{\url{http://amusecode.org}} \citep{Pelupessy13, PortegiesZwart13} with the {\tt Rebound/WHFast}\footnote{\url{http://rebound.readthedocs.io}} \citep{Rebound, WHFast} $N$-body integrator. We give the resulting disc sizes and eclipse durations in Section~\ref{sec:size} and discuss our results and the consequences in Section~\ref{sec:results}. | \label{sec:conclusions} We have performed simulations that consist of a companion on an eccentric orbit consistent with the most probable orbital parameters as detailed in \citet{Kenworthy15}. A disk composed of particles initially orbiting the secondary in circular orbits out to the Hill radius are added and the simulation is run for $10^{5}$ years. The particles are run in both a prograde orbital sense and a retrograde sense. As expected, the prograde ring system loses a significant portion of its mass in a few orbits, and we do not find a stable prograde ring system consistent with the observed orbital parameters and eclipse duration. For the retrograde ring system, we find it retains a larger fraction of its mass out to larger radii, and for the proposed orbital parameters of J1407b, a disk size and orbital velocity consistent with observations is seen. Circumplanetary disks are expected to be prograde with respect to the circumstellar disks they formed in. With a retrograde ring system, the question is raised as to how it came into existence. Uranus has a tilt of 98 degrees, with an associated ring system, but no consensus of how it ended up with this obliquity. Early theories suggested a single giant impactor caused the planet to tilt over \citep{Safronov66}, and possibly disrupt an initially circular orbit into the elliptical one we hypothesise. More recently, \citet{Morbidelli12} show that a single impactor leads to retrograde motions in the rings and moons, and that a series of smaller impacts can preserve the orbital motion of the rings. There is precedence for planets with retrograde orbits beyond our Solar system. Extrasolar planets have been detected with their orbital axes inclined by more than 90 degrees with respect to their star's rotation axis \citep[e.g. WASP-17b;][]{Anderson10}. An interaction with a third companion in the system through the Kozai mechanism \citep{Kozai62} is thought to provide the mechanism in these cases. The hypothesized third companion may still be within the J1407 system, but a deep direct imaging search with Keck reveals no candidates within 400 AU greater than $6~\MJup$~\citep{Kenworthy15}. An alternative explanation is that the third companion was ejected out of the system and is a free floating object. Evidence of strong gravitational scattering may be present in the distribution of dust within the J1407 system, and observations at sub-mm wavelengths with telescopes such as ALMA may provide additional information. One way to discriminate between these two hypotheses is to measure the planet's obliquity and determine if it is greater than 90 degrees, but this is not possible to test with current instruments. Spectroscopic measurements during the next eclipse, however, can reveal the orbital direction of the rings with respect to the rotation axis of the star and confirm the retrograde ring hypothesis. | 16 | 9 | 1609.08485 |
1609 | 1609.06721_arXiv.txt | Searching for active galactic nuclei (AGN) in dwarf galaxies is important for our understanding of the seed black holes that formed in the early Universe. Here, we test infrared selection methods for AGN activity at low galaxy masses. Our parent sample consists of ~18,000 nearby dwarf galaxies ($\mathrm{M}_{*} < 3\times10^9 \;\mathrm{M}_{\sun}$, $z<0.055$) in the Sloan Digital Sky Survey with significant detections in the first three bands of the AllWISE data release from the Wide-field Infrared Survey Explorer (\textit{WISE}). First, we demonstrate that the majority of optically-selected AGNs in dwarf galaxies are not selected as AGNs using \textit{WISE} infrared color diagnostics and that the infrared emission is dominated by the host galaxies. We then investigate the infrared properties of optically-selected star-forming dwarf galaxies, finding that the galaxies with the reddest infrared colors are the most compact, with blue optical colors, young stellar ages and large specific star formation rates. These results indicate that great care must be taken when selecting AGNs in dwarf galaxies using infrared colors, as star-forming dwarf galaxies are capable of heating dust in such a way that mimics the infrared colors of more luminous AGNs. In particular, a simple $\mathrm{W1}-\mathrm{W2}$ color cut alone should not be used to select AGNs in dwarf galaxies. With these complications in mind, we present a sample of 41 dwarf galaxies worthy of follow-up observations that fall in \textit{WISE} infrared color space typically occupied by more luminous AGNs. | \label{sec:intro} There is now an overwhelming body of evidence suggesting that all massive galaxies host a central supermassive black hole which grows alongside the stellar population \citep{kormendy1995,kormendy2013}. In addition, a relationship has been observed between the central black hole mass and the galaxy bulge stellar velocity dispersion that spans many orders of magnitude \citep{gebhardt2000, ferrarese2000}. The origin of this relationship is still not well understood, but current theories imply that galaxy mergers and interactions play a role, both in increasing the stellar mass of a galaxy and in driving gas towards the centers of galaxies, feeding black holes \citep{hopkins2008, koss2010, ellison2011, bessiere2012, sabater2013}. However, this view of galaxy growth implies the existence of low mass ``seed'' black holes that must have existed at high redshift. To understand these difficult-to-observe objects, researchers have turned to observations of nearby dwarf galaxies which may host analogous lower-mass black holes (for a review, see Reines \& Comastri 2016, submitted). By assembling large samples of low-mass black holes, it may be possible to distinguish between the different proposed theoretical scenarios for their creation: these objects may be remnants of massive Population III stars \citep{bromm2011}, a result of direct collapse of primordial dense gas \citep{haehnelt1993, lodato2006, begelman2006, vanwassenhove2010}, or perhaps they are the end product of very massive stars formed through stellar mergers in dense star clusters \citep{gurkan2004, freitag2006,goswami2012, giersz2015, lutzgendorf2016}. Assembling these large samples of low-mass black holes is made difficult by the fact that resolving their gravitational sphere of influence is currently not feasible at distances larger than a few Mpc. However, active galactic nuclei (AGN) emission across the electromagnetic spectrum can be used to infer the existence of a black hole. Observations at optical wavelengths have been used to uncover AGNs in NGC 4395 \citep{filippenko1989, filippenko2003} and POX 52 \citep{barth2004}, while data at X-ray and radio wavelengths have been used to find AGNs in both Henize 2-10 \citep{reines2011, reines2012} and the dwarf galaxy pair Mrk 709 \citep{reines2014}. Larger samples of low-mass AGNs have been uncovered at optical \citep{greene2004, greene2007, dong2012, reines2013, moran2014} and X-ray \citep{lemons2015, mezcua2015, pardo2016} wavelengths, which have been targeted with successful follow-up observations \citep{baldassare2016}, including the discovery of a $5 \times 10^4 \; \mathrm{M}_\sun$ BH in RGG 118 \citep{baldassare2015}. One important and often-used method for selecting luminous AGNs relies on observations made in the mid-IR, where dust, heated by the central accreting black hole, reprocesses the light and emits with a characteristic red IR power-law spectrum. Infrared emission only minimally suffers from nuclear and galaxy-scale obscuration, and so mid-IR observations have successfully uncovered large numbers of unobscured and obscured luminous AGNs and quasars \citep{lacy2004, lacy2013, stern2005, hickox2007, donley2008, ashby2009, assef2010, stern2012, mendez2013, hainline2014b}. The all-sky mid-IR coverage of the \textit{Wide-field Infrared Survey Explorer} \citep[\textit{WISE},][]{wright2010} has allowed for observations of large samples of objects, and multiple authors have proposed \textit{WISE} color schemes which select for the red AGN power law emission in the infrared \citep{jarrett2011, stern2012, mateos2012}. These selection methods rely on the fact that AGNs are capable of heating dust to temperatures well above what is observed from stellar processes in moderate to high-mass galaxies, and have demonstrated high levels of reliability when applied to these objects. Recently, \citet{satyapal2014} and \cite{sartori2015} used mid-IR selection methods to assemble large samples of low-mass galaxy AGN candidates from \textit{WISE} data. Under the assumption that \textit{WISE} selection targets optically obscured, ``hidden'' AGNs in these objects, these authors draw broad conclusions about the population of low-mass black holes. The \citet{satyapal2014} study targets ``bulgeless'' galaxies without optical evidence for an AGN, and the authors conclude that star formation is not the primary source of the IR emission in their sample. In addition, they propose that the fraction of galaxies hosting IR-selected AGN activity \textit{increases} at low masses. This puzzling trend was also seen (with lower significance) using a larger sample of dwarf galaxies by \cite{sartori2015}, who compared multiple AGN selection methods and concluded that dwarf galaxies with \textit{WISE} colors indicative of AGN activity are bluer and potentially may have more ongoing star formation and lower metallicities than those selected using optical emission lines. These results are intriguing in light of the fact that no other tracer of AGN activity has thus far uncovered such large samples of AGNs in dwarf galaxies. In most AGN selection regimes, more luminous AGNs are easier to find both because massive BHs have a higher Eddington limit and because of increasing confusion due to star formation at low mass. Thus, the observed increase in AGN fraction at the lowest dwarf galaxy masses is puzzling. Low-mass SMBHs that exist in dwarf galaxies power AGNs that have such low luminosities that star formation in their hosts becomes a significant source of contamination. In particular, it has been shown that low-metallicity dwarf starburst galaxies are capable of heating dust to very high temperatures \citep{hirashita2004, reines2008, izotov2011, izotov2014, griffith2011, remyruyer2015}, producing red mid-IR colors. This was recently explored in \citet{oconnor2016}, who found that galaxies with low stellar masses have predominantly red \textit{WISE} colors, which the authors associate with higher specific star formation rates (sSFR) in these galaxies. Thus, it may be that using common mid-IR AGN selection methods on dwarf galaxies results in the selection of a large number of star-forming galaxies that contaminate the samples, leading to erroneous conclusions about AGN fractions at these masses. In this paper, we use \textit{WISE} data to empirically examine the infrared colors of dwarf galaxies as a function of their properties as probed by Sloan Digital Sky Survey (SDSS) data. Our results suggest that star formation, and not AGN activity, is responsible for the red \textit{WISE} colors for the majority of the dwarf galaxy population \citep[also see][]{izotov2014}. We propose a small sample of dwarf galaxy AGN candidates that require follow-up observations to confirm black hole activity. In Section \ref{sec:sample}, we discuss our sample selection, and describe how these objects were matched to \textit{WISE} photometry. We start by exploring the infrared properties of dwarf galaxies which have optical spectroscopic evidence for an AGN in Section \ref{sec:IRpropertiesBPT}. We then investigate optically-selected star-forming galaxies and propose a sample of IR-selected AGN candidates in Section \ref{sec:IRproperties}. We expand our sample to include IR-selected AGN candidates without optical emission line flux measurements Section \ref{sec:noopticalemission}, after which we compare these objects to samples of IR-selected AGN candidates presented in the literature in Section \ref{sec:comparison}. Finally, we explore our \textit{WISE} detection limits in Section \ref{sec:detection} and we discuss our results and draw conclusions in Section \ref{sec:conclusions}. | \label{sec:conclusions} To better understand the birth and growth of supermassive black holes, it is fundamentally important to find evidence for AGN activity in low mass dwarf galaxies. Here, we looked at the mid-IR properties of a sample of dwarf galaxies at $z < 0.055$ to explore the use of \textit{WISE} colors to select for AGN activity. We used the most up-to-date AllWISE photometry and individually inspected each candidate AGN to select a sample that is significantly smaller than previous samples of IR-selected AGNs in dwarf galaxies. Our main conclusions are: \begin{itemize} \item The majority of optically-selected AGNs in dwarf galaxies have IR colors that are dominated by their host galaxies. \item Dwarf galaxies with the reddest \textit{WISE} colors are compact, blue galaxies with young stellar ages and high sSFRs. Dwarf galaxies with extreme star-formation are capable of heating dust to temperatures producing $\mathrm{W1}-\mathrm{W2} > 0.8$, \citep[e.g.][]{stern2012}, and this single color cut alone should not be used to select AGNs in dwarf galaxies. \item We provide a sample of 41 dwarf galaxies in the NSA which have \textit{WISE} colors in the \citet{jarrett2011} AGN selection box, 6 of which have optical spectroscopic evidence for an AGN \citep{reines2013}. While the majority of the objects in our sample have been included in previous samples of \textit{WISE}-selected dwarf galaxy AGN candidates, our sample is much smaller due to the updated \textit{WISE} photometry, more conservative selection criteria and SNR thresholds, and the removal of spurious candidates. We caution that follow-up observations are necessary to confirm the presence of active massive black holes in the other 35 objects. \end{itemize} From our analysis, optically blue, high sSFR dwarfs with young starbursts and associated high ionizing fluxes can have red mid-IR colors that could be mistaken for AGN activity, particularly if using a simple $\mathrm{W1}-\mathrm{W2}$ color cut. While these objects have a population of young stars that can heat dust to temperatures which result in red $\mathrm{W1}-\mathrm{W2}$ colors ($\mathrm{W1}-\mathrm{W2} > 0.5-0.6$), they primarily have \textit{very} red $\mathrm{W2}-\mathrm{W3}$ colors ($\mathrm{W2}-\mathrm{W3} > 4.2$), which is less extreme, but similar to the $\mathrm{W2}-\mathrm{W3}$ colors seen for the dwarf star-forming galaxies from \citet{izotov2011}. AGNs, which can heat dust to even higher temperatures, are predominantly found in a different region of \textit{WISE} color-color space, and we only find 10 optically-selected star-forming dwarf galaxies that would be classified as an AGN by the \citet{jarrett2011} selection criteria. Of those objects, only 5 have strong W3 and W4 fluxes as would be expected for an AGN. In addition, these objects are consistent with the overall trend of star-forming galaxies in \textit{WISE} color space, and these objects could represent an extreme star-forming population that has scattered into the \citet{jarrett2011} selection box. We also found 25 additional dwarf galaxies that fell into the \citet{jarrett2011} box that do not have optical spectroscopy, or their SDSS emission lines were not strong enough to classify them on the BPT diagram. We include them as candidates, but we caution against using the mid-IR colors of these objects alone to classify them as AGNs; follow-up observations at optical or X-ray wavelengths would be helpful to understand the nature of their IR emission. Overall, it is important to use both $\mathrm{W1}-\mathrm{W2}$ and $\mathrm{W2}-\mathrm{W3}$ colors when selecting candidate AGNs in dwarf galaxies, as any selection of AGNs in dwarf galaxies that only uses $\mathrm{W1}-\mathrm{W2}$ color \citep[for instance, the selection method of][which has been demonstrated to be reliable at higher masses]{stern2012} will include a large amount of contamination from dwarf star-forming galaxies. Starting with the BPT star-forming galaxies discussed in Section \ref{sec:IRproperties}, we find that 42 dwarf galaxies have $\mathrm{W1}-\mathrm{W2} > 0.8$ (compared to only 10 in the \citet{jarrett2011} selection box), while 183 objects have $\mathrm{W1}-\mathrm{W2} > 0.5$. This contamination from star-forming dwarf galaxies is likely the cause of the observed rise in the fraction of AGN candidates at lower galaxy masses in \citet{satyapal2014} and \citet{sartori2015}. While we certainly cannot rule out the presence of AGNs in the optically-selected star-forming dwarf galaxies with red \textit{WISE} colors, the systematic correlations between star formation properties and infrared colors leads us to conclude that the infrared emission is unlikely to be powered by AGNs. Furthermore, the majority of known optically-selected AGNs in dwarf galaxies do not dominate the \textit{WISE} colors. Our results are consistent with evidence in the literature that the ionizing UV radiation from young stars is one of the primary sources of dust heating in low-metallicity dwarf galaxies \citep{izotov2014}. Both \textit{IRAS} and \textit{Spitzer} observations demonstrated that dwarf galaxies have evidence for large quantities of hot dust \citep{helou1986, hunter1989, melisseisrael1994, rosenberg2006, cannon2006}. In addition, it has been shown that the IR SED peak of dwarf galaxies is broader, which is often explained as resulting from dust at higher temperatures than what is observed in more massive galaxies \citep{boselli2012,smith2012,remyruyer2013,remyruyer2015, ciesla2014}. The temperatures from the tracks in Figure \ref{fig:wisecolorcolorwithtracks} for the hot dust that would be necessary to produce the observed \textit{WISE} colors has been observed in local low-metallicity galaxies from \textit{Spitzer} 8$\mu$m observations \citep{engelbracht2005,jackson2006}, and even hotter dust has been invoked to explain the near-IR excesses observed in the dwarf galaxies SBS 0335-052 \citep{reines2008} and Haro 3 \citep{johnson2004}. Recently, in an analysis of the infrared properties of a large sample of low-metallicity dwarf galaxies, \citet{remyruyer2015} demonstrated that the dust SED for these galaxies peaks at shorter wavelengths as compared to higher-metallicity systems, which they attribute to a clumpy interstellar medium that allows for a wider range of dust temperatures. In addition, the lower-metallicity dust will attenuate the light from young stars less, and the dust can then be heated deeper within individual molecular clouds. \citet{cormier2015} used \textit{Herschel} PACS spectroscopy of low-metallicity dwarf galaxies to provide evidence that the interstellar medium in these galaxies is more porous than in metal-rich galaxies, leading to a larger fraction of the stellar UV radiation heating dust. These results are supported by modeling by \citet{hirashita2004}, which found that dust temperature and dust luminosity is higher in dense, compact, low-metallicity star-forming regions. | 16 | 9 | 1609.06721 |
1609 | 1609.04724_arXiv.txt | The classical equations of motion for an axion with potential $V(\phi)=m_a^2f_a^2 [1-\cos (\phi/f_a)]$ possess quasi-stable, localized, oscillating solutions, which we refer to as ``axion stars''. We study, for the first time, collapse of axion stars numerically using the full non-linear Einstein equations of general relativity and the full non-perturbative cosine potential. We map regions on an ``axion star stability diagram", parameterized by the initial ADM mass, $M_{\rm ADM}$, and axion decay constant, $f_a$. We identify three regions of the parameter space: {\it i)} long-lived oscillating axion star solutions, with a base frequency, $m_a$, modulated by self-interactions, {\it ii)} collapse to a BH and {\it iii)} complete dispersal due to gravitational cooling and interactions. We locate the boundaries of these three regions and an approximate ``triple point" $(M_{\rm TP},f_{\rm TP})\sim (2.4 M_{pl}^2/m_a,0.3 M_{pl})$. For $f_a$ below the triple point BH formation proceeds during winding (in the complex $U(1)$ picture) of the axion field near the dispersal phase. This could prevent astrophysical BH formation from axion stars with $f_a\ll M_{pl}$. For larger $f_a\gtrsim f_{\rm TP}$, BH formation occurs through the stable branch and we estimate the mass ratio of the BH to the stable state at the phase boundary to be $\mathcal{O}(1)$ within numerical uncertainty. We discuss the observational relevance of our findings for axion stars as BH seeds, which are supermassive in the case of ultralight axions. For the QCD axion, the typical BH mass formed from axion star collapse is $M_{\rm BH}\sim 3.4 (f_a/0.6 M_{pl})^{1.2} M_\odot$. | \label{sec:intro} The influence of dark matter (DM) can be seen over a vast range of astrophysical scales ~\cite{2012ApJ...749...90H}, from super clusters of galaxies with $M\sim 10^{15}M_\odot$ (e.g. Ref.~ \cite{2012ApJ...748....7M}), down to the disruption of tidal streams, and contribution to reionization, by substructures with $M\sim 10^6 M_\odot$ (e.g. Ref.~\cite{2016arXiv160603470B,2015MNRAS.450..209B}), yet the particle nature of DM remains unknown. Theories of DM span an even vaster range of scales, from primordial black holes (BHs), with mass as large as $M_{\rm BH}\sim 10^2 M_\odot\sim 10^{32}\text{ kg}$ (e.g. Ref.~\cite{2016arXiv160300464B}), down to ultra-light axions, with $m_a\sim 10^{-22}\text{ eV}\sim 10^{-60}\text{ kg}$ (e.g. Ref.~\cite{2016PhR...643....1M}). In the absence of direct detection of DM in the laboratory, the frontiers of our knowledge are pushed back by the gravitational interactions of DM, and its influence on astrophysics. \begin{figure*}[tb] \begin{center} \includegraphics[width=1.51\columnwidth]{money_plot_labelled.pdf} \vspace{-1.5em} \caption{{\bf The axion star stability diagram}. The stability diagram is parameterized by the axion decay constant, $f_a$, and the initial condition $M_{\rm ADM}$ (which we set using the initial field velocity, $\Pi$, at the centre). Solid lines mark the approximate boundaries between three regions of the axion star parameter space: quasi-stability (R1), collapse to a BH (R2), and dispersal (R3). We postulate the existence of a ``triple point" between these regions. The dashed line marks the region below which axion mass is effectively negligible. Simulated axion stars are marked as circles; other symbols mark points explored in more detail in Section~\ref{sec:simulations}. Below the triple point, for $f_a\ll M_{pl}$, under an increase in mass, dispersal of the star via winding of the axion field occurs before collapse to a BH. Above the triple point, stable axion stars can collapse to BHs by acquiring mass e.g. by accretion. \label{fig:money_plot}} \end{center} \end{figure*} DM composed of axions (or other scalar fields) can be created non-thermally in the early Universe via the vacuum realignment mechanism. The DM consists of a classical field undergoing coherent oscillations about a quadratic potential minimum~\cite{1983PhLB..120..127P,1983PhLB..120..133A,1983PhLB..120..137D,1983PhRvD..28.1243T}. Such a model differs from standard cold DM below the scalar field Jeans scale~\cite{khlopov_scalar}. Below the Jeans scale, DM perturbations are pressure supported by the field gradient energy. In the non-linear regime, the gradient energy supports quasi-stable localised solutions~\cite{1969PhRv..187.1767R,1994PhRvL..72.2516S,2006ApJ...645..814G}. We will refer to these solutions generally as ``axion stars''. \footnote{In the case of a pure $m^2\phi^2$ scalar potential these solutions are known as ``oscillotons''. In the case of axion DM, they go under various names depending on the mechanism of formation: axion miniclusters, axion drops, solitons etc.} Axion stars are closely related to the well-known boson star soliton solutions for a complex field with a conserved global $U(1)$ symmetry~\cite{Liddle:1993ha}. In the present work, we study the gravitational collapse of axion stars to BHs. In models of axion DM, axion stars are expected to be the smallest possible DM structures. Axion stars can form astrophysically either from hierarchical structure formation inside dark matter haloes~\cite{2014NatPh..10..496S}, or are seeded at early times from the large field fluctuations induced by the symmetry breaking leading to axion production~\cite{1988PhLB..205..228H}. Axion stars can range in mass from $\mathcal{O}(10^{-12}M_\odot)$ for the QCD axion~(e.g. Refs.~\cite{1994PhRvD..49.5040K,2007PhRvD..75d3511Z,2016PhRvD..93l3509D}), up to $\mathcal{O}(10^6M_\odot)$ in the cores of DM haloes formed of ultra-light axion-like particles~(e.g. Refs.~\cite{2014NatPh..10..496S,2014PhRvL.113z1302S,2015MNRAS.451.2479M,2016arXiv160605151S, 1990PhRvL..64.1084P,1995PhRvL..75.2077F,Matos:1999et,2000PhRvD..62j3517S,2000PhRvL..85.1158H, 2001PhRvD..63f3506M,2003PhRvD..68b3511A,2012MNRAS.422..135R,2014ASSP...38..107S}). The strength of the axion self interactions is governed by the ``axion decay constant", $f_a$. It is known that in the $m^2\phi^2$ approximation, which represents the limit $\phi/f_a\ll 1$, axion stars possess a critical mass~\cite{1969PhRv..187.1767R} beyond which they are unstable: they migrate to the stable branch under perturbations that decrease the total mass, or collapse to BHs under perturbations that increase the total mass~\cite{2003CQGra..20.2883A}. Criticality occurs when $\phi (r=0)\approx 0.48 M_{pl}$, where $M_{pl}=1/\sqrt{8\pi G_N}\approx 2.4\times 10^{18}\text{GeV}$ is the reduced Planck mass. The expectation from high-energy physics is that generically $f_a<M_{pl}$.\footnote{See e.g. Refs.~\cite{2003JCAP...06..001B,2006JHEP...06..051S,2007JHEP...06..060A,2008PhRvD..78j6003S,Bachlechner:2014hsa,2015JHEP...12..108H,2016JHEP...01..091B}. This subject and the related ``weak gravity conjecture'' are hotly debated at present with relation to axion inflation.} Therefore, axion stars may exist far from the $m^2\phi^2$ region of the potential, and their stability may be affected by the periodicity and anharmonicity of the axion potential. As we will discuss, the initial central field velocity of the axion star, $\Pi (r=0)$, specifies its ADM mass, $M_{\rm ADM}$, and thus collapse is ultimately determined by the star's mass. In this work we investigate the axion star solution space parameterized by $(M_{\rm ADM},f_a)$. For each value of $f_a$, we scan a range of initial values of ADM mass to identify regions on an ``axion star stability diagram". We explore this stability diagram numerically, solving the full non-linear Einstein equations of general relativity (GR) using the numerical GR code \textsc{GRChombo}~\cite{Clough:2015sqa}, see Appendix \ref{appendix:GRChombo}. Numerical GR permits us to evolve regimes in which strong gravity effects play a role without linear approximations. The development of stable numerical formulations (such as BSSN \cite{Baumgarte:1998te,Shibata:1995we}, which we use here) and of ``moving puncture" gauge conditions (see \cite{Campanelli:2005dd,Baker:2005vv}), have been critical for recent advances in the field. The use of these techniques allows us to stably evolve spacetimes up to and beyond collapse to a BH. The resulting axion star stability diagram is shown in Fig.~\ref{fig:money_plot}. We discuss our simulations and main results in Section~\ref{sec:simulations}. Possible astrophysical consequences of our results are discussed in Section~\ref{sec:observations}, and we conclude in Section~\ref{sec:conclusions}. The appendices contain some technical details of the code and simulations, and a brief introduction to axion cosmology and the more familiar non-relativistic axion stars. Some movies of simulations from this work can be accessed via the \textsc{GRChombo} website http://www.grchombo.org/. | \label{sec:conclusions} In this paper we have studied, for the first time, axion stars in full numerical relativity using \textsc{GRChombo} with the non-perturbative instanton potential, $V(\phi)=m_a^2f_a^2[1-\cos (\phi/f_a)]$. We studied the solution space, Fig.~\ref{fig:money_plot}, parameterized by the axion decay constant, $f_a$, and the initial ADM mass, $M_{\rm ADM}$, of a one parameter family of initial conditions. Our initial conditions are based on the quasi-stable $m^2\phi^2$ solutions known as oscillotons, and are specified in terms of a radial profile for the field velocity, $\Pi(r)$, with $\phi=0$ everywhere such that the Hamiltonian constraint is satisfied in the interacting cosine potential. We identified three distinct regions of the solution space: a (quasi-)stable region of true axion stars; an unstable region where the initial axion star collapses to a BH; an unstable region where the initial axion star disperses via scalar radiation. The stable axion stars are new solutions, and differ from oscillotons by the presence of a second modulating frequency in the solution. The existence of the second frequency can be understood from a perturbative analysis, as can the qualitative feature that the solution space is separated into stable and unstable regions depending on the value of $f_a$. BH formation via increase of $M_{\rm ADM}$ from the stable branch can only be achieved above the ``triple point" separating the three phases, $f_a>f_{\rm TP}\approx 0.3 M_{pl}$. This could have astrophysical consequences for axion stars as seeds for supermassive BHs. The existence of the dispersing region separating the stable region from BH formation when $f_a<f_{\rm TP}$ would appear to prohibit BH formation via slow accretion of mass onto axion miniclusters. For each value of $f_a$, as we scan the initial values of ADM mass, we expect within some range to see behaviour akin to that observed in critical collapse (\cite{Choptuik:1992jv}, for a review see \cite{Gundlach:2007gc}). That is, just above some critical value of $M_{\rm ADM}$, the star will collapse and form a BH, with a universal scaling relation between the masses. In the present work we do not seek to investigate the criticality of the solutions -- that is, we do not seek to demonstrate a universal scaling relation in the final masses of black holes which occur near the critical point -- since we are for the moment interested in the overall solution space. However, based on previous studies of massive scalar field collapse in Ref.~\cite{Brady:1997fj}, we would expect type II behaviour similar to that found in the massless case (e.g. in \cite{Choptuik:1992jv}) where the mass of the axion is negligible in comparison to the initial ADM mass of the star (that is, in the bottom right of our phase space, below the dashed line). In this case the mass of the critical BH formed would be zero. We may also expect to observe type I behaviour for larger values of $f_a$, in which case the black hole formed at the transition point has a finite mass. This appears consistent with our findings, although we have not investigated sufficiently close to the critical point to confirm it. Various authors have studied collisions of oscillotons in the $m^2\phi^2$ potential and boson stars, see Ref.~\cite{2016PhRvD..93d4045B} in the relativistic case, and Refs.~\cite{Gonzalez:2011yg,PhysRevD.74.103002,2014PhRvL.113z1302S,2016arXiv160605151S,2016PDU....12...50P,PhysRevD.94.043513} in the non-relativistic case. Studying collisions of axion stars, and in particular whether colliding stable axion stars can cause BH formation, is left to future work. The full 3+1 dimensional solutions possible with \textsc{GRChombo} will allow us to study non-spherically symmetric axion stars with angular momenta, and axion star binaries, with possible applications to experimental searches for gravitational waves with LIGO~\cite{2016PhRvL.116f1102A,2016arXiv160403958A}. | 16 | 9 | 1609.04724 |
1609 | 1609.07107_arXiv.txt | High levels of deuterium fraction in N$_2$H$^+$ are observed in some pre-stellar cores. Single-zone chemical models find that the timescale required to reach observed values ($D_{\rm frac}^{{\rm N}_2{\rm H}^+} \equiv {\rm N}_2{\rm D}^+/{\rm N}_2{\rm H}^+ \gtrsim 0.1$) is longer than the free-fall time, possibly ten times longer. Here, we explore the deuteration of turbulent, magnetized cores with 3D magnetohydrodynamics simulations. We use an approximate chemical model to follow the growth in abundances of N$_2$H$^+$ and N$_2$D$^+$. We then examine the dynamics of the core using each tracer for comparison to observations. We find that the velocity dispersion of the core as traced by N$_2$D$^+$ appears slightly sub-virial compared to predictions of the Turbulent Core Model of McKee \& Tan, except at late times just before the onset of protostar formation. By varying the initial mass surface density, the magnetic energy, the chemical age, and the ortho-to-para ratio of H$_2$, we also determine the physical and temporal properties required for high deuteration. We find that low initial ortho-to-para ratios ($\lesssim 0.01$) and/or multiple free-fall times ($\gtrsim 3$) of prior chemical evolution are necessary to reach the observed values of deuterium fraction in pre-stellar cores. | \label{s:intro} \subsection{Massive Star Formation}\label{ss:massivestars} Massive stars play a central role in galactic evolution through feedback and metal enrichment, yet the physical processes and conditions involved in massive star formation remain uncertain \citep{2014prpl.conf..149T}. The relative rarity of massive stars and thus their typical large distances from us, along with their deeply embedded formation environments, make it difficult to observe details of the massive star formation process. There are two main theories for massive star formation: 1) Core Accretion models, e.g., the Turbulent Core Accretion model \citep[][hereafter MT03]{2003ApJ...585..850M}, which assumes near-virialized starting conditions for relatively ordered collapse; and 2) the Competitive Accretion model \citep{2001MNRAS.323..785B}, which posits fragmentation and subsequent accretion by multiple stars from a turbulent, globally collapsing medium. Distinguishing these two scenarios relies on disentangling the numerous physical processes involved, such as turbulent motions, magnetic fields, and feedback. Numerical modeling is one means to extricate the various processes. Previous simulations of massive star formation have focused on the role of turbulence, magnetic fields, and radiation in clump fragmentation. \citet{2011MNRAS.413.2741G} investigated the fragmentation of hydrodynamic clumps, examining the effect of the initial density profile and turbulent driving. The authors found that single massive stars are more likely to form from centrally-concentrated initial conditions, while the details of the turbulence are relatively unimportant. Numerous authors \citep{2007ApJ...656..959K,2010ApJ...713.1120K,2011ApJ...729...72P,2011ApJ...740..107C,2011ApJ...742L...9C,2013ApJ...766...97M} have demonstrated that radiative feedback from protostars inhibits fragmentation of the clump. Magnetohydrodynamics (MHD) simulations both neglecting radiation \citep{2011A&A...528A..72H,2011MNRAS.417.1054S,2012MNRAS.422..347S} and with radiation \citep{2011ApJ...729...72P,2011ApJ...742L...9C,2013ApJ...766...97M} indicate that even a weak magnetic field suppresses clump fragmentation, and increasing the field strength further reduces the fragmentation. In all of the aforementioned MHD numerical studies, the magnetic field strength is initially super-critical, i.e., the field cannot prevent gravitational collapse. The central pre-stellar core contracts rapidly, forming a protostar within one to two free-fall times. Yet the timescale of core collapse remains an open question. In the Competitive Accretion model, cores form and rapidly collapse on the order of the free-fall time. In the Turbulent Core model, the cores persist longer -- at least one dynamical time -- possibly supported by magnetic fields and turbulence near virial balance. Indeed, some observed cores exhibit supersonic linewidths consistent with virial balance \citep{2013ApJ...779...96T,2016arXiv160906008K}. Yet, velocity dispersions due to virial equilibrium or energy equipartition (consistent with free-fall) differ only by a factor of $\sqrt{2}$ \citep{2007ApJ...657..870V}. Therefore, even a clear distinction between virial equilibrium and free-fall collapse based on velocity dispersion seems difficult. However, we note that where they have been measured, observed infall speeds generally generally seem to be small, i.e., $\sim 1/3$ of the free-fall velocity \citep{2016A&A...585A.149W}. \subsection{Deuteration as a Chemical Clock}\label{ss:dclock} An alternative means to probe the age and state of starless cores is using chemical tracers, in particular deuterated molecules. In sufficiently dense ($n_{\rm H} > 10^5$~cm$^{-3}$), cold ($T < 20$~K) environments, CO freeze-out opens a pathway for ion-neutral reactions that increase the deuterium fraction, i.e., the ratio of deuterated to non-deuterated species, $D_{\rm frac}$. For a full review of deuteration processes, see \citet{2014prpl.conf..859C}. Observationally, deuterated molecules are excellent probes of pre-stellar gas. \citet{2002ApJ...565..344C} traced low-mass star forming regions with N$_2$D$^+$ and DCO$^+$, finding deuterium fractions $D_{\rm frac} \gtrsim 0.1$, several orders of magnitude above the cosmic deuterium ratio (D/H $\sim 10^{-5}$). Similarly, \citet[][hereafter T13]{2013ApJ...779...96T} identified high-mass star-forming regions in infrared dark clouds (IRDCs) with the same deuterated molecules. \citet[][hereafter K16]{2016ApJ...821...94K} has subsequently estimated the deuterium fraction of N$_2$H$^+$ in these regions to be of comparable values to those in low-mass pre-stellar cores (\Dfracdef$\gtrsim 0.1$) \citep[see also][]{2011A&A...529L...7F}. As deuteration is expected to begin only when pre-stellar core conditions are satisfied, the deuterium fraction may be a useful estimator of core age. \citet[][hereafter K15]{2015ApJ...804...98K} developed a time-dependent astrochemical network to model the evolution of deuterium-bearing molecules. The authors followed the chemistry in a single zone with fixed physical conditions or with simple density evolution. Under typical core conditions, the K15 models suggest that the deuteration process is slow, with up to ten free-fall times required to reach the observed values of \Dfrac. Moving beyond single-zone chemical models is a difficult task, as the complex reaction network requires extensive computational resources. \citet{2013A&A...551A..38P} coupled the deuterium network of \citet{2009A&A...494..623P} with a 1D spherically-symmetric hydrodynamic calculation. The simulations followed deuteration in 200 radial zones during collapse of a low-mass pre-stellar core from a uniform, static state. In disagreement with K15, \citet{2013A&A...551A..38P} determined that fast collapse is preferred, as steady-state abundances determined from the model were typically much higher than observed. However, the models of \citet{2009A&A...494..623P} and \citet{2013A&A...551A..38P} begin with very high initial depletion factors, which greatly shortens the deuteration timescale. A full discussion and comparison is presented in K15, but it is worth noting that, given similar initial conditions, the models of K15 agree with \citet{2009A&A...494..623P} to within a factor of 3. If large-scale magnetic fields are present, the assumption of radial symmetry during collapse will not hold, as flux-freezing prevents significant collapse in directions perpendicular to the field. Further, the turbulent motions within the core are not fully captured in 1D simulations. Indeed, the chemical evolution may be altered by non-linear effects such as density fluctuations and turbulent diffusion. Implementing a full chemical network in high-resolution 3D simulations is currently not feasible given computational limits. One option may be to reduce the number of reactions and reactants; however, this would negatively affect the accuracy of the chemistry. Here, we develop an alternative approach. We construct an approximate deuterium chemistry model built on the full astrochemical network results of K15. By parameterizing the results across a wide range of densities, we formulate a robust and efficient method to follow the growth and deuteration of \nthp{} in 3D MHD simulations of massive core collapse. We generate a turbulent, magnetized pre-stellar core according to the paradigm of MT03, and we model the collapse of the core until the first protostar forms. We simultaneously follow the chemical evolution of \nthp{} and \ntdp{} and compare to observed massive pre-stellar cores. By varying the initial conditions, such as the mass surface density, magnetic energy, chemical age, and initial ortho-to-para ratio of H$_2$, we can estimate the core properties necessary to match observed deuterium abundances. We observe in our simulations that the collapse occurs on roughly the free-fall time, regardless of the initial mass surface density or magnetic field strength. We conclude that reaching the observed deuterium fractions requires significant prior chemical evolution, low initial ortho-to-para ratio, and/or slower collapse, possibly by stronger magnetic fields or sustained turbulence. We outline our numerical methods, including initial conditions and chemical model in (\S\ref{s:methods}). The results of our simulations are presented and discussed in \S\ref{s:results}. We discuss the implications for massive star formation in \S\ref{s:discussion} before concluding in \S\ref{s:conclusions}. | \label{s:conclusions} We have constructed an approximate chemical model for the deuteration of \nthp{} in cold, dense pre-stellar gas. Our model is based on the results of the astrochemical network presented in K15. The full network is prohibitively expensive in multi-dimensional hydrodynamics simulations. Rather than reducing the number of reactions, we parameterize the results across a range of densities into look-up tables. This approximate formulation is demonstrated to perform reasonably well in comparison to full network calculations with both constant and evolving density. We implement our approximate chemical model in the \textsc{Athena} MHD code. In 3D simulations, we follow deuteration during the collapse of a turbulent, magnetized pre-stellar core. The core is initialized in accordance with the Turbulent Core Accretion model of MT03. For our adopted initial conditions, the core collapses to the point of forming a protostar within roughly one free-fall time, regardless of the initial mass surface density or magnetic field strength. During most of this collapse phase the velocity dispersion of the core as traced by \ntdp(3--2) appears moderately sub-virial compared to predictions of the MT03 Turbulent Core Model, consistent with observations of T13 and \citet{2016arXiv160906008K}. Only near the end, just before protostar formation, does the velocity dispersion rise to appear super-virial. As the core collapses, the increase in density accelerates the deuteration of \nthp. However, we find that \Dfrac{} does not reach observed values ($\gtrsim 0.1$) in $\sim 1~t_{\rm ff}$, unless the initial ortho-to-para ratio of H$_2$ (\OPR) is $\lesssim 0.01$ or the core begins from an advanced chemical state ($t_{\rm chem} \gtrsim 3~t_{\rm ff}$). This is in agreement with K15 and suggests that the collapse rate in highly-deuterated cores may be significantly slower than the free-fall time, or the deuteration process begins earlier than assumed. | 16 | 9 | 1609.07107 |
1609 | 1609.05933_arXiv.txt | We present a time domain waveform model that describes the inspiral, merger and ringdown of compact binary systems whose components are non-spinning, and which evolve on orbits with low to moderate eccentricity. The inspiral evolution is described using third order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to non-linear memory. This framework reduces to the post-Newtonian approximant \texttt{TaylorT4} at third post-Newtonian order in the zero eccentricity limit. To improve phase accuracy, we also incorporate higher-order post-Newtonian corrections for the energy flux of quasi-circular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced prescription for the inspiral evolution is combined with a fully analytical prescription for the merger-ringdown evolution constructed using a catalog of numerical relativity simulations. We show that this inspiral-merger-ringdown waveform model reproduces the effective-one-body model of Ref.~[Y. Pan \textit{et al.}, Phys. Rev. D 89, 061501 (2014)] for quasi-circular black hole binaries with mass-ratios between 1 to 15 in the zero eccentricity limit over a wide range of the parameter space under consideration. Using a set of eccentric numerical relativity simulations, not used during calibration, we show that our new eccentric model reproduces the true features of eccentric compact binary coalescence throughout merger. We use this model to show that the gravitational wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasi-circular, spin-aligned waveforms if the eccentricity \(e_0\) of these systems when they enter the aLIGO band at a gravitational wave frequency of 14 Hz satisfies \(e_0^{\rm GW150914}\leq0.15\) and \(e_0^{\rm GW151226}\leq0.1\). We also find that varying the spin combinations of the quasi-circular, spin-aligned template waveforms does not improve the recovery of non-spinning, eccentric signals when \(e_0\geq0.1\). This suggests that these two signal manifolds are predominantly orthogonal. | \label{intro} The field of gravitational wave (GW) astronomy has been firmly inaugurated with the first direct detections of gravitational radiation from binary black hole (BBH) systems with the Advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) detectors~\cite{DI:2016,secondBBH:2016,bbhswithligo:2016}. The growing sample of GW observations that is expected in aLIGO's next observing runs~\cite{D5:2016,bbhswithligo:2016} will enable an accurate census of the mass and angular momentum distribution of BHs and neutron stars (NSs), gaining insights into formation and evolution scenarios of compact object binaries, and the environments in which they reside~\cite{SathyaLRR:2009,bel:2010ApJ,Anto:2015arXiv,D9:2016,scenarioligo:2016LRR,Carl:2016arXiv,bel:2016Na,marchant:2016,deMink:2016MNRAS}. For instance, the detection of GWs from eccentric compact binaries can provide important information of compact object populations in globular clusters and galactic nuclei~\cite{Anto:2015arXiv}. Any such analysis must start with the development of waveforms for eccentric compact binaries, which is the topic of this article. GWs encode information about the properties of the astrophysical sources that generate them, and can be used to map the structure of spacetime in the vicinity of compact binary systems~\cite{ryan}. aLIGO is expected to detect a wide variety of GW sources, including: (i) compact binary systems that form in the galactic field and evolve through massive stellar evolution. These are expected to enter aLIGO's frequency band on nearly quasi-circular orbits because GWs are very effective at circularizing the orbits of compact binaries~\cite{Peters:1964,peters}; (ii) compact binaries formed in dense stellar environments, e.g., core-collapsed globular clusters and galactic nuclei. In these environments, compact systems can undergo a variety of N-body interactions that lead to the formation of compact binaries that retain eccentricity during their lifetime (see~\cite{Maccarone:2007,Strader:2012,cho:2013ApJ,Anto:2015arXiv,CR:2015PRL,Carl:2016arXiv} and references therein). The detection of stellar mass BHs in the galactic cluster M22~\cite{Strader:2012} led to the development of more accurate N-body algorithms to explore the formation and detectability of BBHs formed in globular clusters with aLIGO. These improved analyses indicate that about \(20\%\) of BBH mergers in globular clusters will have eccentricities \(e_0\gtrsim0.1\) when they first enter aLIGO band at 10Hz, and that \(\sim 10\%\) may have eccentricities \(e\sim1\)~\cite{Anto:2015arXiv}. Furthermore, a fraction of galactic field binaries may retain significant eccentricity prior to the merger event~\cite{Samsing:2014}. BBHs formed in the vicinity of supermassive BHs may also merge with significant residual eccentricities~\cite{Van:2016}. Given the proven detecting capabilities of aLIGO, these results imply that we are now in a unique position to enhance the science reach of GW astronomy by targeting eccentric compact binary systems. The detection of these events requires the development of new waveform models and data analysis techniques because the imprint of eccentricity on GWs is multifold: it introduces modulations in the amplitude and frequency evolution of the waveforms, and it shortens their duration~\cite{pierro2001,Gopakumar:2002,Gopa:2004,Gopa:2004b,Gopakumar:2005b,GopakumarandK:2006,Blanchet:2006,Arun:2008,Arun:2009PRD,Brown:2010,Huerta:2013a,Huerta:2014}. GWs emitted by compact binaries that enter aLIGO band with moderate eccentricities, \(e_0\lesssim0.4\), can be modeled as continuous waves and searched for using matched-filtering algorithms. In contrast, systems that enter aLIGO band with \(e_0\sim 1\) emit individual GW bursts at each periastron passage, most suitable searched by excess power algorithms utilizing time-frequency tiling~\cite{Tai:2014}. In order to detect and characterize eccentric binary systems with aLIGO, we introduce an inspiral-merger-ringdown (IMR) waveform model that reproduces the dynamics of state-of-the-art non-spinning, quasi-circular waveform models~\cite{Tara:2014}. Using a set of non-spinning, eccentric numerical relativity (NR) simulations, we show that this new model can reproduce the dynamics of comparable mass-ratio, moderately eccentric binary systems throughout the merger. This model can be immediately used in the context of aLIGO to: (i) quantify the sensitivity of quasi-circular searches and burst searches to eccentric signals; (ii) study template bank construction for non-spinning, eccentric BBHs; (iii) estimate the eccentricity of detected BBH signals, under the assumption that the binary components are not spinning; (iv) explore the sensitivity of burst-like searches that have been tuned to detect highly eccentric systems (\(e_0\sim 1)\) to recover signals with moderate values of eccentricity~\cite{SKlimenko:2004CQGra,Klimenko:2004CQG,Sergey:2005K,Sergey:2008CQG,Sergey:2011PhRvD,Sergey:2016,Tiwari:2016}. Previous work related to this particular subject includes the following: (i) frequency domain inspiral-only waveforms that include leading order post-Newtonian (PN~\footnote{When we state the accuracy of PN expansions below, a term of Nth PN order implies that the term of highest order in the weak-field expansion is proportional to \((v/c)^{2N}\), where \(v\) represents the orbital velocity~\cite{Blanchet:2006}.}) corrections in a post-circular or small eccentricity approximation~\cite{yunes-eccentric-2009,Mico:2015}; (ii) frequency and time domain waveforms that reduce to the PN-based approximants \texttt{TaylorF2} and \texttt{TaylorT4} at 2PN in the quasi-circular limit~\cite{Tanay:2016}; (iii) inspiral-only waveforms that include 2PN and 3PN corrections to the radiative and conservative pieces of the dynamics, respectively~\cite{Hinder:2010}; (iv) inspiral-only waveforms that include 3PN corrections to the radiative and conservative pieces of the dynamics~\cite{Arun:2009PRD,Mishra:2015,Moore:2016,lou:2016arXiv}; (v) inspiral-only frequency domain waveforms that reduce to the PN-based approximant \texttt{TaylorF2} 3.5PN at zero eccentricity, and to the post-circular approximation of Ref.~\cite{yunes-eccentric-2009} at small eccentricity~\cite{Huerta:2014}; (vi) hybrid waveforms that describe highly eccentric systems. These waveforms describe the inspiral evolution using geodesic equations of motion. The merger phase is modeled using a semi-analytical prescription that captures the features of NR simulations~\cite{East:2013}; (vii) self-force calculations for non-spinning BHs along eccentric orbits~\cite{Letiec:2014IJ,ackay:2015prd,hopper:2016PhRv,forseth:2016PhRvD,binida:2016PhRvD,akcavan:2016PhRvD,binidam:2016,Osburn:2016}; (viii) NR simulations that explore the dynamics of eccentric binary systems~\cite{ihh:2008PhRvD,Hinder:2010,east:2012a,east:2012,Gold:2012PG,Gold:2013,East:2015PRDa,East:2016PhRvD,Radice:2016MNRAS,2016arXiv161107531T,2016arXiv161103418L}. Some of the aforementioned waveform models have been used in source detection~\cite{Huerta:2013a,Huerta:2014,MC:2014PhRvD,MC:2015PhRvD} and parameter estimation studies~\cite{Favata:2014,Sun:2015PRD} in the context of aLIGO. These studies have shown that detecting and characterizing eccentric binary systems will not be feasible using existing algorithms for quasi-circular binaries~\cite{Huerta:2013a,Favata:2014}. Furthermore, as discussed in~\cite{Huerta:2014}, to accurately model inspiral-dominated systems, i.e., binary systems with total mass \(M\lesssim 10\Msun\)~\cite{Prayush:2013a}, eccentric waveform models should reduce to high PN order approximants such as \texttt{TaylorT4} 3.5PN or \texttt{TaylorF2} 3.5PN~\cite{Huerta:2013a,Huerta:2014} in the zero eccentricity limit. On the other hand, for NSBH and BBH systems that require the inclusion of the merger and ringdown phase, eccentric waveforms models should reproduce the evolution rendered by IMR models such as~\cite{Pan:2013,khan:2016PhRvD,husacv:2016PhRvD} in the zero eccentricity limit. In this paper we start addressing these important issues by developing an IMR waveform model valid for compact binaries with moderate eccentricities. The key features of our model are: \begin{itemize} \item It includes third order PN accurate expansions for eccentric orbits both for the equations of motion of the binary and its far-zone radiation field. The radiative evolution includes instantaneous, tails and tails-of-tails contributions, and a contribution due to non-linear memory. \item The accuracy of the inspiral evolution is improved by including 3.5PN corrections for quasi-circular orbits (at all powers of symmetric mass-ratio), improving on~\cite{Huerta:2014}. \item To further improve phase accuracy especially for unequal mass systems, the 3PN accurate inspiral evolution for eccentric systems is corrected by including up to 6PN terms both for the energy flux of quasi-circular binaries and gravitational self-force corrections to the binding energy of compact binaries at first order in symmetric mass-ratio \(\eta\). \item We combine the aforementioned enhanced inspiral evolution with a merger and ringdown treatment using the \emph{implicit rotating source} (IRS) formalism~\cite{Kelly:2011PRD}, fitted against NR simulations up to mass-ratio 10. \end{itemize} The eccentric model we develop in this article is the first model in the literature that combines all these features, and makes it a powerful tool to explore the detection of eccentric signals with aLIGO. To exhibit the reliability of our eccentric model, we show that it agrees well with the IMR effective-one-body model SEOBNRv2~\cite{Tara:2012,Tara:2014} in the non-spinning limit over a wide range of the BBH parameter space accessible to aLIGO. Furthermore, using non-spinning, eccentric NR simulations, we show that our model can reproduce the true accurate dynamics of moderately eccentric BBH mergers with mass-ratios \(q\in\{1,\,2\}\) throughout the merger. Having established the validity of our new eccentric model, we use it to shed light for the first time on the importance of including eccentricity in the detection of IMR systems, such as NSBH and BBH systems with asymmetric mass-ratios. We also show that our waveform model has a favorable computational cost, suitable for large scale data analysis studies. Throughout this article we use units \(G=c=1\). We denote the components masses by \(m_1\) and \(m_2\), where \(m_1\geq m_2\). Mass combinations used throughout the article include: total mass \(M=m_1+m_2\), reduced mass \(\mu = m_1\,m_2/M\), mass-ratio \(q=m_1/m_2\), and symmetric mass-ratio \(\eta = \mu/M\). This paper is organized as follows: In Section~\ref{build} we describe the construction of our eccentric waveform model. In Section~\ref{catch_me} we apply our eccentric waveform model to explore the detectability of eccentric compact binary systems with aLIGO. We summarize our results and discuss future directions of work in Section~\ref{disc}. | \label{disc} We have developed a waveform model for eccentric compact binaries that represents the inspiral, merger and ringdown, and that reproduces zero eccentricity binary waveforms much more accurately than previous eccentric waveform models. We have also demonstrated that our new model can accurately describe comparable mass-ratio, moderately eccentricity BBH NR simulations. With this model we studied the importance of including eccentricity in detecting eccentric NSBH and BBH systems with aLIGO. We showed that using the design sensitivity of aLIGO and a lower frequency cut--off of 15Hz, the IMR \(ax\)--model can reproduce the SEOBNRv2 model in the zero eccentricity limit with overlap values \({\cal{O}}\gtrsim 0.95\) over a wide range of the stellar mass BBH and NSBH parameter space that is accessible to aLIGO. Using our IMR \(ax\) model we explore the detectability of eccentric compact binaries. Our results indicate that template banks of quasi-circular, spin-aligned SEOBNRv2 waveforms can recover GW150914 with \({\cal{FF}}\geq0.95\) if \(e_0\leq0.15\), and GW151226 with \({\cal{FF}}\geq0.94\) if \(e_0\leq0.1\). We have also found that template banks of quasi-circular, spin-aligned waveforms can improve the recovery of low total mass moderately eccentric signals. Our results also indicate that low mass BBH and NSBH systems with astrophysically motivated values of eccentricity \((e_0\sim0.1)\) will be poorly recovered with available quasi-circular matched-filtering algorithms (\({\cal{FF}}\leq0.85\)). In order to detect these events, it is necessary to develop new data analysis algorithms that specifically target eccentric GW sources. A key assumption in the construction of our \(ax\)--model is that compact binaries circularize prior to merger. We explore the validity of this assumption and find that we can cover a large portion of the parameter space of compact binaries that aLIGO will be able to detect. In order to minimize the effect of inherent waveform inaccuracies in the \(ax\)--model, particularly in the context of parameter estimation studies, we are exploring two ways to enhance its accuracy in the \(e\rightarrow 0\) limit. The first improvement deals with the hybridization between inspiral-PN model and gIRS merger--ringdown model: in its current version the \(ax\)--model consists of a simple hybridization between the PN--inspiral evolution and the gIRS model we have described in Section~\ref{liv}. The key for this procedure to work requires that both frameworks meet at an optimal frequency where they render the correct dynamical evolution. The results we have obtained in this work suggests that using up-to-date results from the self-force formalism and PN theory provides a robust framework to capture the inspiral dynamics of compact binaries with asymmetric mass-ratios. The enhanced inspiral evolution we have constructed is good to \textit{explore} the late time dynamics of BBHs, but it can only go so far. At the other end of the spectrum, the gIRS model is reliable in the vicinity of the light-ring. We can see in Figure~\ref{mer_fig} that this approach starts to deteriorate when we push the model several cycles prior to the merger event. Therefore, a critical correction to further improve the IMR \(ax\)--model is the development of a new merger-ringdown prescription that captures the true dynamical evolution \textit{several} cycles before merger, and which can provide a wider window of frequencies to hybridize the inspiral evolution with the merger phase. Our second planned improvement concerns the inspiral dynamics itself. Presently, 4-6PN terms in the binding energy of compact binaries \(E(x,\,\eta)^{\rm 6PN}\), cf. Eq.~\eqref{pre_hyb}, only include first order in symmetric mass-ratio corrections. We will further improve the inspiral dynamics by including terms at \emph{second order} in symmetric-mass ratio. Furthermore, building up on~\cite{Huerta:2014a,Kapadia:2016}, we will amend the energy flux prescription, \(\dot{E}(x,\,\eta)^{\rm 6PN}\), by constraining missing \(\eta^2\) corrections in the energy flux expression used in Eq.~\ref{pre_hyb}. We expect that combining the aforementioned improvements will provide an enhanced performance of the \(ax\)--model in the \(e_0\rightarrow0\) limit so that the overlap with SEOBNRv2 templates satisfies \({\cal{O}}\gtrsim0.99\) over the stellar mass BBH and NSBH parameter space accessible to aLIGO. The results we present in this article indicate that a consistent combination of higher-order PN calculations, self-force corrections and NR can enable the construction of accurate, computationally inexpensive waveform models that encode the dynamics of compact binary systems across the parameter space accessible to aLIGO--type detectors. These results further support the importance of deriving second order self-force effects~\cite{rosen:2006PhRvD,pound:2012PhRvL,gralla:2012PhRvD,pm:2014PhRvD,pojere:2014PhRvD,adampound:2015prd,binidamo:2016arXiv}. Previous studies have strongly relied on self-force calculations for waveform modeling, source detection and parameter estimation studies, and have exhibited their applicability for extreme and comparable mass-ratio systems~\cite{Amaro:2013GW,Huerta:2011vna,Huerta:2012,Huerta:2010,higherspin,Huerta:2009,Huerta:2011a,Huerta:2011b,wargar,Huerta:2014a,smallbody,Osburn:2016}. Moving forward, it is necessary to develop new waveform models that enable the description of compact binaries whose components have non-zero spin and which evolve on eccentric orbits. Using eccentric NR simulations both for calibration and validation purposes will enable the construction of robust waveform models that are adequate for detailed parameter estimation studies. This work should be pursued in the near future. | 16 | 9 | 1609.05933 |
1609 | 1609.00727_arXiv.txt | The $z = 6.6$ Lyman-$\alpha$ emitter `CR7' has been claimed to have a Population III-like stellar population, or alternatively, be a candidate Direct Collapse Black Hole (DCBH). In this paper we investigate the evidence for these exotic scenarios using recently available, deeper, optical, near-infrared and mid-infrared imaging. We find strong~\emph{Spitzer}/IRAC detections for the main component of CR7 at $3.6\mu {\rm m}$ and $4.5\mu {\rm m}$, and show that it has a blue colour (\IRACcolour $= -1.2\pm 0.3$). This colour cannot be reproduced by current Pop. III or pristine DCBH models. Instead, the results suggest that the \chone~band is contaminated by the {\sc [OIII]}$\lambda\,4959,5007$ emission line with an implied rest-frame equivalent width of $EW_{0}$\hboiii$ \gtrsim 2000$\AA. Furthermore, we find that new near-infrared data from the UltraVISTA survey supports a weaker He{\sc II}$\,\lambda 1640$ emission line than previously measured, with $EW_{0} = 40 \pm 30$\AA. For the fainter components of CR7 visible in~\emph{Hubble Space Telescope} imaging, we find no evidence that they are particularly red as previously claimed, and show that the derived masses and ages are considerably uncertain. In light of the likely detection of strong {\sc [OIII]} emission in CR7 we discuss other more standard interpretations of the system that are consistent with the data. We find that a low-mass, narrow-line AGN can reproduce the observed features of CR7, including the lack of radio and X-ray detections. Alternatively, a young, low-metallicity ($\sim 1/200\,{\rm Z}_{\sun}$) star-burst, modelled including binary stellar pathways, can reproduce the inferred strength of the \he line and simultaneously the strength of the observed {\sc [OIII]} emission, but only if the gas shows super-solar $\alpha$-element abundances (O/Fe $\simeq 5\,$(O/Fe)$_{\sun}$). | The Lyman-$\alpha$ emission line at $\lambda_{0} = 1216\,$\AA~provides a unique probe of the progress and topology of reionization at $z~>~6$~\citep[e.g.][]{Dijkstra2014}. Using narrow-band surveys it is possible to select large samples of Lyman-$\alpha$ emitting galaxies (LAEs) up to $z \simeq 7$~\citep[e.g.][]{Ouchi2008, Ouchi2010, Matthee2015} and potentially to higher redshifts~\citep[e.g.][]{Tilvi2010, Krug2012}. Several of these narrow-band selected galaxies at $z = 6.6$ have generated considerable interest due to their particularly strong (${\rm log}_{10}[L_{Ly\alpha}/{\rm ergs}/{\rm s}] > 43$) and extended ($> 10\,{\rm kpc}$) Lyman-$\alpha$ emission. The low-metallicity, triple-merger system `Himiko' has been extensively studied~\citep{Ouchi2009, Ouchi2013, Zabl2015}, and recently~\citet{Sobral2015} (hereafter S15) reported an even brighter LAE, `CR7', which was found within the degree-scale Cosmic Origins Survey (COSMOS) field. CR7 was initially discovered during a search for Lyman-break galaxies in~\citet{Bowler2012}, and was independently selected by S15 in Subaru/Suprime-Cam narrow-band imaging (using the $NB921$ filter centred at $9210$\AA). Follow-up spectroscopy confirmed the presence of a strong Lyman-$\alpha$ emission line with a rest-frame equivalent width in excess of ${EW}_{0} > 200$\AA. Near-infrared spectroscopy of CR7 also revealed a $\sim 6\sigma$ emission-line attributed to He{\sc II} $\lambda 1640$. The \he line was observed to be sufficiently strong to boost the available $J$-band photometry by $0.4$ magnitudes (S15), with an inferred equivalent width of ${EW}_{0} = 80\pm 20$\AA. The strong and narrow He{\sc II} line, coupled with the non-detection of metal lines in the near-infrared spectrum, has led to the interpretation that this galaxy has a Population III-like stellar population (S15,~\citealp{Pallottini2015},~\citealp{Visbal2016},~\citealp{Xu2016}~\citealp{Yajima2016}) or alternatively harbours an accreting Direct Collapse Black Hole (DCBH;~\citealp{Dijkstra2016, Smith2016, Agarwal2016, Hartwig2016, Smidt2016}). With high resolution imaging from archival~\emph{HST} data, CR7 appears as three distinct clumps, with the Lyman-$\alpha$ and \he emission peaking at the location of the brightest component (A). The two fainter objects (B and C) are separated from the A component by $\gtrsim 5\,{\rm kpc}$ (assuming that they are also at $z = 6.6$) and appear redder, leading to the interpretation that they are older (S15). In recent theoretical models of CR7, components B and C potentially provide the required ionizing photons to suppress star-formation in component A at earlier times, leading to the formation of a pristine Pop. III star-burst (S15) or DCBH~\citep{Agarwal2016}. In both scenarios, the presence of older companions is required to reproduce the observed rest-frame optical detections (in the~\emph{Spitzer} \chone~and \chtwo~bands), which are not predicted by the extremely blue Pop. III or DCBH spectral energy distributions (SED). In simulations of potential sites of Pop. III star-formation, it has appeared challenging to recreate the properties of CR7 due primarily to the large mass ($\ge 10^{7}\,{\rm M}_{\sun}$; S15;~\citealp{Visbal2016}) of Pop. III stars required to reproduce the Lyman-$\alpha$ and \he luminosities~\citep{Hartwig2016, Pallottini2015, Xu2016}. Another possible issue with the Pop. III scenario is the short ($\lesssim 5\,{\rm Myr}$) visibility timescale of such a burst if it occurred~\citep{Hartwig2016}. While the DCBH interpretation alleviates these concerns somewhat, with visibility timescales of tens of ${\rm Myr}$~\citep{Pallottini2015}, the line luminosities require a system with a mass greater than the maximum mass thought to be created by direct collapse, requiring the pristine DCBH to have accreted substantially~\citep{Dijkstra2016, Smidt2016}. Given the intense interest in CR7 and the exciting implications of the potential discovery of a Pop. III star-burst or a DCBH, it is important to scrutinise the observational evidence. While future observations with~\emph{HST} and the Atacama Large Millimeter/Sub-millimeter Array (ALMA) will provide further insights into the properties of CR7, it is possible to discern salient details about the system from currently available broad-band photometric data. In this work we present an analysis of the most recently available imaging data for CR7, which extends up to $1$ mag deeper than that presented in S15. Crucially this includes deeper near-infrared data from the third data release of the UltraVISTA survey and deeper~\emph{Spitzer} data at $3.6\mu {\rm m}$ and $4.5\mu {\rm m}$. The datasets are described in detail in Section~\ref{sect:data}. Our analysis of the updated photometric data is presented in Section~\ref{sect:results}. In Section~\ref{sect:discussion} we compare the observed~\emph{Spitzer}/IRAC colours to those predicted by Pop. III and DCBH models, where we find that neither model can reproduce the data. In light of our findings, we discuss alternative interpretations for the nature of CR7 in Section~\ref{sect:alternative}, which includes a comparison of the properties of CR7 to the Binary Population and Spectral Synthesis (BPASS) stellar population models~\citep{Eldridge2008, Eldridge2009}. We end with our conclusions in Section~\ref{sect:conc}. All magnitudes are quoted in the AB system~\citep{Oke1974, Oke1983}. At $z = 6.6$, a measured separation of $1\,$arcsec corresponds to a proper distance of $ 5.4\,{\rm kpc}$ assuming a cosmology with $\Omega_{m} = 0.3$, $\Omega_{\Lambda} = 0.7$ and $H_0 = 70\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$. | \label{sect:conc} We provide improved constraints on the broad-band photometry for CR7 using deeper near-infrared imaging from the DR3 of the UltraVISTA survey, and deeper~\emph{Spitzer}/IRAC photometry from the SPLASH dataset. The data show that the Pop. III/DCBH candidate in the CR7 system shows a strong, blue, rest-frame optical colour as measured by the~\emph{Spitzer}/IRAC \chone~and \chtwo~bands. The magnitude and colour of these detections cannot be reproduced by the current Pop. III and DCBH models, and instead imply that the \chone~band is contaminated by the \oiii $\lambda \lambda 4959, 5007$ doublet with an inferred rest-frame equivalent width of $EW_{0}$\hboiii$ \gtrsim 2000$\AA. Furthermore, the improved UltraVISTA DR3 near-infrared data show a lower $J$-band excess than previous studies, suggesting that the spectroscopically detected \he emission line has a lower inferred rest-frame equivalent width of $EW_{0} = 40 \pm 30$\AA. The observational constraints on the \he and {\sc [OIII]} emission line strengths are consistent with the properties of a narrow-line low-mass AGN or, alternately, a young low-metallicity $\sim 1/200\,{\rm Z}_{\sun}$ star-burst when modelled including binary stars and an enhanced O/Fe abundance ratio. However, we find that this star-burst model (from the BPASS code) cannot reproduce the current upper limits on the lack of metals in the near-infrared (rest-frame UV) spectrum. In contrast, such ratios of {\sc CIII]}/\he and {\sc OIII]}/\he are to be expected for an AGN source~\citep{Feltre2016}. Future observations of CR7 (and other high-redshift galaxies with likely strong rest-frame optical emission) with~\emph{JWST} will be able to directly detect the inferred \oiii~emission line at $\lambda_{\rm obs} \simeq 3.8\,\mu {\rm m}$, and through the measured line ratios and widths, will be able to distinguish between an AGN or a low-metallicity star-forming galaxy. | 16 | 9 | 1609.00727 |
1609 | 1609.09095_arXiv.txt | We present new spatially resolved astrometry and photometry from the Gemini Planet Imager of the inner binary of the young multiple star system V343 Normae, which is a member of the $\beta$ Pictoris moving group. V343 Normae comprises a K0 and mid-M star in a $\sim$4.5 year orbit (AaAb) and a wide $10\arcsec$ M5 companion (B). By combining these data with archival astrometry and radial velocities we fit the orbit and measure individual masses for both components of $M_{\rm Aa} = 1.10 \pm 0.10\ M_\odot$ and $M_{\rm Ab} = 0.290 \pm 0.018\ M_\odot$. Comparing to theoretical isochrones, we find good agreement for the measured masses and {\it JHK} band magnitudes of the two components consistent with the age of the $\beta$~Pic moving group. We derive a model-dependent age for the $\beta$~Pic moving group of $26 \pm 3$~Myr by combining our results for V343 Normae with literature measurements for GJ~3305, which is another group member with resolved binary components and dynamical masses. | Binaries remain the primary opportunity to directly measure the masses of stars. Resolved binaries provide the opportunity to simultaneously measure masses and individual fluxes of the components, and can be used to constrain atmospheric and evolutionary models (e.g., \citealt{muterspaugh:2008}, \citealt{schlieder:2016}, \citealt{dupuy:2014}, \citealt{crepp:2016}). For binaries in young moving groups, where the age can be determined by considering all the stars in the group at once, the constraints placed on the models can be especially strong. The $\beta$ Pic moving group was first identified by \citet{barrado1999}, and initially assigned an age of $20 \pm 10$~Myr, which was then revised to $12^{+8}_{-4}$~Myr by \citet{zucerkman:2001}. More recent analyses of the group favor an older age: $21 \pm 4$~Myr \citep{binks:2014}, $20 \pm 6$~Myr \citep{Macintosh:2015ew}, and $24 \pm 3$~Myr \citep{bell:2015}. Stars in the moving group host the imaged planets $\beta$~Pic~b \citep{Lagrange:2012} and 51~Eri~b \citep{Macintosh:2015ew}, and brown dwarfs HR~7329~B \citep{lowrance:2000} and PZ~Tel~B \citep{biller:2010,mugrauer:2010}; the group is also home to the free-floating substellar object PSO J318.5338-22.8603 \citep{liu:2013}. Since the inferred masses of these objects depend sensitively on their age, an accurate measurement of the age of the $\beta$ Pic moving group is of prime importance. In addition to a number of wide binaries (e.g., \citealt{alonso:2015}), and close spectroscopic binaries such as HD 155555 AB \citep{bennett:1967} and V4046 Sgr \citep{byrne:1986} in the $\beta$ Pic moving group, there are two systems with resolved spectroscopic binaries---GJ~3305 and V343~Nor, which is resolved for the first time in this study. GJ 3305 is part of a triple system with the planet-host 51~Eri \citep{delorme:2012}, and an orbit with dynamical masses has recently been presented by \citet{montet:2015}, who find a model-dependent age for the system (and so the moving group) of $37 \pm 9$~Myr, consistent with previous estimates. V343~Nor (HD~139084, HIP~76629, at a distance of $38.5^{+1.8}_{-1.6}$~pc \citep{vanLeeuwen:2007dc}), is a triple system consisting of a K0 primary and a mid-M secondary in a close binary orbit (V343 Nor Aa and Ab) and an outer $10\arcsec$ M5 companion (V343 Nor B; \citealp{song:2003}). An initial orbit fit to radial velocity (RV) measurements of V343 Nor A by \citet{thalmann:2014} found a 4.5-year orbit, eccentricity between 0.5 and 0.6, and a 0.11~$M_\odot$ minimum mass for the secondary. The Gemini Planet Imager (GPI; \citealp{Macintosh:2014js}) is a near-infrared (NIR) integral field spectrograph and polarimeter at the Gemini South telescope. As part of the ongoing GPI Exoplanet Survey (GPIES) we imaged V343~Nor A and resolved the Aa/Ab binary in 2015, and continued to monitor the system in 2016. By combining these new astrometric epochs with archival imaging and RV data, we fit the orbit of the system and derive dynamical masses for both components. We derive a new estimate for the age of the $\beta$ Pic moving group based on stellar evolution models by combining our dynamical mass measurements with previous results for components of the GJ~3305 system. | We have presented new imaging observations of V343 Nor A, as well as archival imaging of the pair and RVs of the primary, which taken together allow for a precise determination of the orbit. Our orbit fit shows well-defined orbital parameters, including dynamical masses of $1.10 \pm 0.10$~$M_\odot$ and $0.292 \pm 0.018$~$M_\odot$ for the two components. The V343 Nor A system thus joins GJ 3305 as only the second resolved spectroscopic binary with dynamical masses in the $\beta$ Pic moving group that can serve as a benchmark for testing models of pre-main sequence evolution. Future astrometric monitoring of this system will further improve the mass precision and thus the precision of the model-dependent age of the $\beta$ Pic moving group. At present there is no astrometric measurement of the system when the projected separation drops below 60 mas. Observations in 2017, when the projected separation should be between 20 and 40 mas, will be especially helpful in improving the precision of the mass measurements. Such close separations should be reachable with Non Redundant Masking (NRM) observations, and is an ideal target for GPI NRM \citep{greenbaum:2014}. 2017 will also see the rapid decrease in RV from 6 to -2~km~s$^{-1}$, a poorly sampled part of the RV phase curve. This system also makes an excellent target for NIR spectroscopic observations to detect the spectral lines of the secondary, making the system a double-lined spectroscopic binary. Such measurements would further constrain the orbital parameters, specifically the mass ratio of the system (e.g., \citealp{Mazeh:2003eo}). Overall there is excellent agreement between the age of the $\beta$ Pic moving group, as derived from isochrone fitting to all the stars \citep{bell:2015}, the theoretical models, and the dynamical masses and NIR photometry of these objects spanning a factor of $\sim$4 in stellar mass. Identification and monitoring of new resolved $\beta$ Pic moving group binaries with short enough orbital periods to provide dynamical masses on reasonable timescales can further test the reliability of the models' relations between mass, age, and photometry. | 16 | 9 | 1609.09095 |
1609 | 1609.07041_arXiv.txt | We present a new method to reconstruct the primordial (linear) density field using the estimated nonlinear displacement field. The divergence of the displacement field gives the reconstructed density field. We solve the nonlinear displacement field in the 1D cosmology and show the reconstruction results. The new reconstruction algorithm recovers a lot of linear modes and reduces the nonlinear damping scale significantly. The successful 1D reconstruction results imply the new algorithm should also be a promising technique in the 3D case. | The observed large-scale structure of the Universe, which contains a wealth of information such as the nature of dark energy, neutrino masses, and primordial power spectrum etc, is a powerful probe of cosmology. The matter power spectrum has been measured to significant accuracy in the current galaxy surveys and the precision will continue to improve with future surveys. However, the nonlinear gravitational evolution is a complicated process and makes it difficult to model the small-scale inhomogenities. This has led to many theoretical challenges in developing perturbation theories (see e.g. \cite{2016matt} for a brief review). On the other hand, various reconstruction techniques have been proposed to reduce nonlinearities in the density field, in order to obtain better statistics \cite{2007bao,2015PhRvD..92l3522S}. The standard BAO reconstruction uses the negative Zel'dovich (linear) displacement to reverse the large-scale bulk flows \cite{2007bao}. The nonlinear density field is usually smoothed on the linear scale ($\sim10\ \mr{Mpc}/h$) to make the Zel'dovich approximation valid. Actually, the fully nonlinear displacement which describes the motion beyond the linear order (the Zel'dovich approximation) can be solved from the nonlinear density field. While the algorithm is complicated in the three spatial dimensions, it is quite simple in the 1D case, which is basically the ordering of mass elements (sheets). The 1D cosmological dynamics corresponds to the interaction of infinite sheets of matter where the force is independent of distance \cite{2016matt}. The simplified 1D dynamics provides an excellent means of understanding the structure formation and testing perturbation theories \cite{2016matt}. In this paper we solve the fully nonlinear displacement in 1D and present a new method to reconstruct the primordial density field and hence the linear BAO information. This paper is organized as follows. In Section \ref{rec}, we present the reconstruction algorithm in the 1D case. In Section \ref{sim}, we briefly describe the 1D $N$-body simulation. In Section \ref{res}, we show the results of reconstruction. In Section \ref{dis}, we discuss the 3D case and future improvements. | \label{dis} The new reconstruction method successfully recovers the lost linear information on the mildly nonlinear scales (till $k\lesssim0.24\ \mr{Mpc}^{-1}$). The result in 1D provides an intuitive view of the algorithm and motivates us to develop the reconstruction method in 3D. The nonlinear displacement beyond the Zel'dovich approximation in 3D can be solved using the multigrid iteration scheme \cite{1995ApJS..100..269P}. The algorithm for solving the 3D nonlinear displacement is originally introduced for the adaptive particle-mesh $N$-body code \cite{1995ApJS..100..269P} and the moving mesh hydrodynamic code \cite{1998ApJS..115...19P}. The 3D case is also more complicated since the 3D displacement field involves a curl part (vorticity) which is generated after shell crossing, while this does not happen after particles cross over in 1D. This requires us to quantify the effect of vorticity, which can be accomplished using $N$-body simulations. By decomposing the simulated displacement field into a irrotational part and a curl part, we can study the statistical properties of different components \cite{2013PhRvD..87f3526Z,2013PhRvD..88j3510Z}. These will be presented in future. The reconstructed nonlinear displacement field is also important for the current BAO reconstruction \cite{2007bao}, where the linear continuity equation is adopted to solve the displacement under the Zel'dovich approximation. However, the nonlinear displacement retains much more information, describing the motion of dark matter fluid elements beyond the linear order. The reconstructed displacement field $s(q)$ is given on the Lagrangian coordinate instead of the final Eulerian coordinate. This helps to correct the effect due to the use of $s(x)$ instead of $s(q)$ in the BAO reconstruction \cite{2015MNRAS.450.3822W,2015PhRvD..92l3522S}. As more nonlinear effects will be removed using the nonlinear displacement, we expect the modeling of the reconstructed density field will be simplified. The Wiener filter is optimal for the case both the signal and the noise are Gaussian random fields. In Fig. \ref{fig:pdf}, the PDFs of the reconstructed density field and the noise are apparently nonGaussian. The reconstruction can be further improved using the nonlinear filter rather than the Wiener filter \cite{1999RSPTA.357.2561P}. We plan to study this in future. | 16 | 9 | 1609.07041 |
1609 | 1609.02178_arXiv.txt | {This work studies the correlation among environmental density and radio AGN presence up to $z = 2$. Using data from the photometric COSMOS survey and its radio 1.4 GHz follow-up (VLA-COSMOS), a sample of radio AGNs has been defined. The environment was studied using the richness distributions inside a parallelepiped with base side of 1 Mpc and height proportional to the photometric redshift precision. Radio AGNs are found to be always located in environments significantly richer than those around galaxies with no radio emission. Moreover, a distinction based on radio AGN power shows that the significance of the environmental effect is only maintained for low-power radio sources. The results of this work show that denser environments play a significant role in enhancing the probability that a galaxy hosts a radio AGN and, in particular, low-power ones.} | \label{intro} The problem of the transformation of the galaxy population from star-forming to quiescent is still an open one in modern astrophysics. General agreement has been reached on the fact that galaxy mass, galaxy environment and AGN feedback play a major role in star formation quenching. It has been suggested (see \cite{hickox09}) that the central AGN co-evolves with the host-galaxy: while the host-galaxy transforms from a star-forming to a quiescent one, the AGN passes from a quasar, X-ray emitter phase to a radio-galaxy one. These transformations happen at earlier epochs for haloes of higher mass, that were found to reside primarily in high-density environments, where early-type galaxies dominate at low redshifts (\cite{quadri12,chuter11}). Moreover, it was already known that many radio AGNs reside in early-type galaxies (\cite{ledlow96}), that the probability that a galaxy hosts a radio AGN is increasing with stellar mass (\cite{bardelli09}), and that the fraction of radio active early-type galaxies is an increasing function of local density (\cite{bardelli10}). In this work (see \cite{malavasi15}) the environment of radio sources of the VLA-COSMOS survey (\cite{schinnerer07}), cross-identified with the COSMOS photometric redshift sample (\cite{ilbert09}), is explored. | 16 | 9 | 1609.02178 |
|
1609 | 1609.00382_arXiv.txt | We present $H$-band near-infrared polarimetric imaging observations of the F5V star HD~157587 obtained with the Gemini Planet Imager (GPI) that reveal the debris disk as a bright ring structure at a separation of $\sim$80$-$100~AU. The new GPI data complement recent HST/STIS observations that show the disk extending out to over 500~AU. The GPI image displays a strong asymmetry along the projected minor axis as well as a fainter asymmetry along the projected major axis. We associate the minor and major axis asymmetries with polarized forward scattering and a possible stellocentric offset, respectively. To constrain the disk geometry we fit two separate disk models to the polarized image, each using a different scattering phase function. Both models favor a disk inclination of $\sim 70\degr$ and a $1.5\pm0.6$ AU stellar offset in the plane of the sky along the projected major axis of the disk. We find that the stellar offset in the disk plane, perpendicular to the projected major axis is degenerate with the form of the scattering phase function and remains poorly constrained. The disk is not recovered in total intensity due in part to strong adaptive optics residuals, but we recover three point sources. Considering the system's proximity to the galactic plane and the point sources' positions relative to the disk, we consider it likely that they are background objects and unrelated to the disk's offset from the star. | Circumstellar debris disks, composed of planetesimals and dust, are remnants of the planet formation process. Therefore, their study can provide insights into the planet formation and evolution history of the systems in which they reside. The dust grain composition of a disk traces grain growth and erosion, and, if spatially resolved, disk morphology can provide evidence of dynamical interactions with nearby planets. Such an interaction can manifest as a warp \citep[e.g. Beta Pic;][]{Burrows1995, Mouillet1997}, a stellocentric offset \citep[e.g. HR 4796A;][]{Wyatt1999, Telesco2000} or a sharp radial profile at the inner edge of a dust ring \citep[e.g. Fomalhaut;][]{Kalas2005,Quillen2006}. \begin{figure*}[Ht] \includegraphics[width=\linewidth]{figure1_phot_crop.pdf} \caption{\emph{Left}: GPI $H$-band radial polarized intensity image ($Q_r$) of the HD~157587 debris disk. The image has been smoothed with a Gaussian kernel ($\sigma$ = 1~pixel). The blue circle indicates the size of the central focal plane mask ($0\farcs12$ radius). The red circles denote the point sources seen in total intensity in Figure~\ref{fig:stokesi} (Section~\ref{sec:pyklip}). \emph{Right}: The $U_r$ image of HD~157587. For single scattering from circumstellar material we expect no contributions to the $U_r$ image. Thus, this image can be used as a noise map for the $Q_r$ image. The image appears to be largely free of correlated structure, except at small inner working angles. Both images have been cropped from the full GPI field of view to display only the inner $2\farcs6 \times 2\farcs6$ region. No polarized emission was seen outside the cropped region. \label{fig:diskimg}} \end{figure*} Debris disks are imaged via their thermal emission in infrared or millimeter wavebands, which typically traces the location of millimeter sized bodies, or via scattered light in the visible and near-infrared (NIR), which is more sensitive to micron-sized dust. Observations of debris disks in scattered light are typically able to resolve finer spatial scales than longer wavelength observations (though ALMA's spatial resolution is now competitive), but are challenging due to the extreme contrast ratios between the faint dust-scattered light and the bright host stars. Instrumental point-spread functions (PSFs) extend the stellar emission out to angular separations where debris disks are found, obscuring the scattered light from the dust. For ground-based observations this problem is compounded by the atmosphere, which scatters light from the PSF out to farther separations. The Gemini Planet Imager \citep[GPI;][]{Macintosh2014} is an instrument on the Gemini South 8-m telescope that has been designed specifically to mitigate these challenges. It employs a high-order adaptive optics (AO) system, combined with an apodized-pupil Lyot coronagraph and an integral-field spectrograph, to image exoplanets and debris disks at angular separations down to $\sim0\farcs1$. The GPI Exoplanet Survey (GPIES) is a long-term Gemini South program targeting 600 nearby stars with the goal of discovering and characterizing young Jovian exoplanets. A secondary goal of the survey is to image and characterize debris disks. Stars with previously resolved debris disks and survey stars that exhibit infrared excesses are observed using GPI's polarimetry mode. The polarimetry mode is implemented as a rotatable half-wave plate (HWP) modulator and a Wollaston prism analyser. This mode has been designed to take advantage of the inherent polarization of light scattered off circumstellar dust grains, to further suppress the unpolarized starlight and reveal the disk beneath \citep{Perrin2015}. Here we present GPIES observations of the debris disk around HD~157587, an F5V star with an infrared excess $L_{IR}/L_{star}$= 7.9$\times10^{-4}$, \citep{mcdonald12a} at a distance of 107.4~pc \citep{vanLeeuwen2007}. HST/STIS coronagraphic imaging (GO-12998; PI Padgett) first revealed the dust scattered light extending to $>$7$''$ radius, with a morphology resembling a fan \citep[such as for HD~15745;][]{kalas07a}, where the straight edge of the fan lies along the southwestern side of the nebulosity \citep{Padgett2015}. The inner working angle of these data corresponds to a projected separation of $\sim$100 AU. Our new scattered light images, obtained as part of the GPIES campaign, detect the structure of the circumstellar dust in the projected 30 - 130 AU radial region. | Using GPI we have imaged the dust ring around HD~157587 in $H$-band polarized intensity. The image reveals an inclined disk that appears to be cleared of material inside of a projected major axis of $\sim 80$ AU. The FOV of our observations overlaps with the inner regions of previous STIS images of the disk, and our analysis returns a similar disk inclination to that derived with the STIS data. The disk has a strong polarized brightness asymmetry in the NE-SW direction, where we interpreted the bright side of the disk to be tilted towards the observer. A similar brightness asymmetry has been seen in polarized observations of a number of other recently imaged disks, suggestive of similar grain compositions, size distributions and/or dust grain morphologies. Future detailed studies of these disks' dust composition that include multicolour observations or polarization fraction measurements will be able to further explore the similarities and differences of their dust grain populations. A second, weaker, brightness asymmetry is seen between the two ansae that could be due to a stellocentric offset in the plane of the sky. To test this hypothesis we used Bayesian MCMC methods to fit the polarized disk image to two disk models, one that used a HG polarized scattering phase function and one that combined a HG function with Rayleigh scattering phase function. Both models reveal an offset dust disk with an inner radius of 80 AU and an inclination of about $70\degr$. The center of the disk is found to be offset approximately 1.5 AU from the star's location in the plane of the sky and both models reproduce the brightness asymmetry between the two ansae. This offset could be confirmed with longer wavelength imaging using ALMA, which would trace thermal emission and therefore have less of a dependence on the scattering properties of the grains. In general the two model fits return similar disk properties, with the exception of $\Delta X_2$, the offset in the disk plane. We find that the form of the polarized scattered phase function is degenerate with the magnitude and direction of this offset and without further information on the form of the scattering phase function this value will remain poorly constrained. The total intensity observations are dominated by stellar residuals at the location of the disk in the polarized intensity image and no disk was recovered. However, three point sources were recovered. Considering HD~157587's proximity to the galactic plane and the positions of the point sources relative to the disk, we consider these point sources to be background objects. Nonetheless, follow up observations are required to confirm this proposition. The currently published ages of the system that rely on stellar evolutionary tracts indicate an age well over 1 Gyr old. However, such an evolved age is at odds with the stellar kinematics. The stellocentric offset, suggest that this system has a complicated dynamical history and may harbour one or more unseen planets. This notion is reinforced by the similarities between HD~157587's stellar properties and disk morphology, and those of the RV planet host HD~10647. If the stellocentric offset is due to perturbations by one or more planets, further detailed study of the system's debris disk will be required to thoroughly characterize the system; the system's advanced age would make it ill-suited for direct imaging planet searches and radial velocity measurements would require prohibitively long time baselines. On the other hand, if the disk is younger than 1 Gyr, as implied by the stellar kinematics, then it presents itself as a prime target for deeper direct imaging observations which may be able to image the disk's perturber. | 16 | 9 | 1609.00382 |
1609 | 1609.08093_arXiv.txt | Third generation ground-based interferometers as well as the planned space-based interferometer LISA are expected to detect a plethora of gravitational wave signals from coalescing binaries at cosmological distance. The emitted gravitational waves propagate in the expanding universe through the inhomogeneous distribution of matter. Here we show that the acceleration of the universe and the peculiar acceleration of the binary with respect to the observer distort the gravitational chirp signal from the simplest General Relativity prediction beyond a mere time independent rescaling of the chirp mass, affecting intrinsic parameter estimations for the binaries visible by LISA. We find that the effect due to the peculiar acceleration can be much larger than the one due to the universe acceleration. Moreover, peculiar accelerations can introduce a bias in the estimation of parameters such as the time of coalescence and the individual masses of the binary. An error in the estimation of the time of coalescence made by LISA will have an impact on the prediction of the time at which the signal will be visible by ground based interferometers, for signals spanning both frequency bands. | \label{sec:intro} Gravitational Wave (GW) astronomy has recently started \cite{TheLIGOScientific:2016pea,Abbott:2016blz}, showing that signals from coalescing binaries at cosmological distance (with redshift $z\sim 0.1$) are already a reality and in the near future ($\sim$ few years) dozens of similar signals are expected. The observational quest for GWs is now lead by earth-based interferometers \cite{TheLIGOScientific:2014jea,TheLIGOScientific:2016agk}, but in the future the space-based interferometric detector LISA is expected to widen the range of detectable sources up to redshift $z\sim 15$ \cite{elisaweb,Klein:2015hvg}. GWs from coalescing binaries provide a direct measurement of the luminosity distance of the source to the observer. However, to first approximation (as long as the variation of the cosmological expansion can be neglected during the duration of the signal as we will see), GW observations do not provide information about the redshift of the source. This happens because the redshift does change the waveform, but in a way that can be exactly compensated by a shift of the masses from their source to detector values and by replacing the comoving distance with the luminosity distance. It is therefore usually assumed that the redshift of the host galaxy is needed to infer the redshift of the GW event. Ref.~\cite{Schutz:1986gp} was the first to show that cosmological parameters like the Hubble constant can be measured with few percent precision with $O(10)$ GW detections, by combining the measurements of the luminosity distances and sky localisations of various GW events with the redshift information taken from galaxy catalogs. Since then, the problem has been widely studied both for advanced earth-based interferometers, e.g.~\cite{Sathyaprakash:2009xt,DelPozzo:2011yh,Taylor:2011fs,Taylor:2012db} and for LISA, e.g.~\cite{VanDenBroeck:2010fp,Arun:2007hu,Arun:2008xf,Tamanini:2016zlh}. On the other hand, Ref.~\cite{Seto:2001qf, Nishizawa} showed that the GW observation alone does in principle allow to measure the real masses \emph{and} the redshift. The expansion of the universe during the time of observation of the GW event can actually imprint into the waveform phase, to which the interferometer output is particularly sensitive, an effect with frequency dependence $f^{-8/3}$ with respect to the leading behavior. The investigation of the detectability of such effect, hence the possibility of measuring both the luminosity distance and the redshift from gravitational wave observations alone has been considered in \cite{Seto:2001qf, Nishizawa}. Here we re-analyse the issue, taking into account also the redshift perturbations due to the inhomogeneous matter distribution along the propagation of the GWs from the source to the detector. We show that the peculiar acceleration of the binary (i.e.~the time variation of the peculiar velocity) with respect to the cosmological flow can drown the effect of the expansion of the universe: therefore, the imprint of the background expansion on the phase of the GW signal cannot be used in general to infer the redshift of the GW source. Moreover, the peculiar acceleration pollutes the phasing signal introducing a bias in the measured parameters, like the binary constituent masses and the time of coalescence. This can be particularly important for those binaries that are visible first by LISA and afterwards by terrestrial interferometers \cite{Sesana:2016ljz,Barausse:2016eii,Vitale:2016rfr}, for which a precise determination of the arrival time of the signal in the LIGO/Virgo band is needed. The main result of this paper is Eq.~\eqref{Psi+}, showing the frequency-dependent modification of the phase of the GW signal due to the {\it time variation} of the redshift perturbations. The paper is structured as follows. In sec.~\ref{se:cosmoredshift} we review the chirp gravitational waveform when the redshift is kept constant and unperturbed. In sec.~\ref{se:astroredshift} we account for time variations of the redshift: first we concentrate on the background effect, due to the variation of the cosmological expansion during the observation time of the binary, and then we present the consequences of the time variation of the redshift perturbations due to the inhomogeneities in the matter distribution at linear order~\footnote{Note that constant perturbations to the redshift do not generate a shift in the phase since they can be reabsorbed in the redshifted chirp mass (see discussion in section~\ref{se:astroredshift}).}. In sec.~\ref{se:waveform} we study the modification of the waveform phasing due to both these effects. In sec.~\ref{se:mismatch} we proceed to a quantitative analysis: first we demonstrate that the most relevant contribution to the waveform comes from the peculiar acceleration of the binary; we then show qualitatively that this is only important for space-based detectors, which are capable to follow the chirp signal for a long enough time at low frequency; at last, we quantify the effect in the output of match-filtering commonly used in GW data analysis, focusing on the case of LISA. We show that the amount of lost detections due to the use of a waveform template without the peculiar acceleration of the binary is negligible. However, the peculiar acceleration introduces a {\it bias} in the determination of the binary parameters such as the time of coalescence and the masses. In sec.~\ref{se:conclusion} we conclude. Throughout the paper we only consider non-spinning binaries at the lowest Post Newtonian (PN) order (except in the last section, as specified). We adopt units such that the speed of light $c=1$. The cosmological metric is $ds^2=-dt^2+a^2\delta_{ij}dx^idx^j$ where $t$ denotes cosmic time, $a(t)$ is the scale factor and $H\equiv\dot a/a$ is the Hubble factor with $H_0\equiv 100 \, h \,{\rm km/sec/Mpc}$ denoting the Hubble factor today. | \label{se:conclusion} We have analysed the effect of redshift perturbations on the GW form. GWs emitted by inspiral binaries propagate through the inhomogeneous universe before reaching the detector. These inhomogeneities influence the observed frequency of the GW: in addition to the background redshift due to the expansion of the universe, the inhomogeneous distribution of matter generates a Doppler shift (due to the peculiar velocity of the binary with respect to the observer), a gravitational shift and an integrated Sachs-Wolfe effect. We have found that if the redshift perturbations are constant during the time of observation of the GW, the waveform does not change: the redshift perturbations can simply be reabsorbed into the redshifted chirp mass $\mathcal{M}_c(z)$. On the other hand if the redshift perturbations evolve during the time of observation, they generate a contribution to the waveform with frequency dependence $f^{-13/3}$ (formally a -4PN term). We have compared the amplitude of this novel effect with the correction generated by the background acceleration of the universe, derived previously in~\cite{Seto:2001qf, Nishizawa}. The dominant correction from redshift perturbations comes from the peculiar acceleration of the binary (i.e.~the variation of the peculiar velocity during the time of observation). We found that this contribution from the peculiar acceleration dominates, for realistic situations, over the background expansion one over a large range of redshift. As we do not know in practice what is the amplitude of the peculiar acceleration for individual binaries, this strongly challenges the possibility of using the background effect to determine the redshift of the binary. We have then performed a preliminary analysis of the impact of the binary peculiar acceleration on the recovery of the binary parameters for the LISA detector, using inspiral-only, spin-less waveforms as a test case. The effect is most relevant for low-mass binaries with source chirp mass $M_c<100\,M_\odot$ at low redshift and entering the detector at frequency around few mHz. For these kind of sources, the total phase shift due to the acceleration effect is comparable to the one induced by high PN terms: 2PN order at best. We have found that using a template without the acceleration effect to analyse GW signals does not cause significant loss of detections since the mismatch is at most of $10^{-3}$. However, our results show that the recovered parameters are biased by the acceleration effect. Although this does not happen for the redshifted chirp mass $\mathcal{M}_c$, we have found that for a large fraction of events at small masses, $\eta$ is not recovered within 1\% and the time of coalescence $t_c$ is wrong by more than 1 minute (we compare with the estimated errors with which LISA is expected to measure these quantities, according to \cite{Sesana:2016ljz}). Our analysis provides us with indications that the bias on $\eta$ can be of few percent, and the one on $t_c$ can be of several days: however, a more precise investigation is in progress to determine these biases more accurately at low masses (source chirp masses less than $50 M_\odot$). The estimate of $t_c$ is of particular significance for the binaries that can be detected first by LISA and then by ground based interferometers for which one needs a precise determination of the coalescing time. In order to remove this bias one should add to the GW templates a dependence on the acceleration effect and introduce a new search parameter $\epsilon$ (see Eq.~\eqref{epsilon}). This procedure might reduce the precision with which the parameters of the binary are recovered but it could possibly allow a measurement of the peculiar acceleration of the binary, which may convey valuable information about the environment in which the binary is living. | 16 | 9 | 1609.08093 |
1609 | 1609.04042_arXiv.txt | In the $\Lambda$CDM model of structure formation, a stellar spheroid grows by the assembly of smaller galaxies, the so-called building blocks. Combining the Munich-Groningen semi-analytical model of galaxy formation with the high resolution Aquarius simulations of dark matter haloes, we study the assembly history of the stellar spheroids of six Milky Way-mass galaxies, focussing on building block properties such as mass, age and metallicity. These properties are compared to those of the surviving satellites in the same models. We find that the building blocks have higher star formation rates on average, and this is especially the case for the more massive objects. At high redshift these dominate in star formation over the satellites, whose star formation timescales are longer on average. These differences ought to result in a larger $\alpha$-element enhancement from Type II supernovae in the building blocks (compared to the satellites) by the time Type Ia supernovae would start to enrich them in iron, explaining the observational trends. Interestingly, there are some variations in the star formation timescales of the building blocks amongst the simulated haloes, indicating that [$\alpha$/Fe] abundances in spheroids of other galaxies might differ from those in our own Milky Way. | The formation and evolution of the Galactic spheroid, consisting of the central bulge and the stellar halo, has been studied for more than fifty years since the classical paper of \citet{Eggen:1962} on the origin of the Milky Way. Although it is still unclear to which extent accretion plays a role besides instabilities of the disc in the formation of the Galactic bulge \citep[e.g.,][]{Combes:2000,Gerhard:2015,Di-Matteo:2016}, there is growing consensus on the formation of the Galactic halo. Since the proposed scenario of \citet{Searle:1978} in which the stellar halo formed via the merging of several protogalactic clouds, there have been many pieces of evidence suggesting indeed a hierarchical build-up of the Milky Way's stellar halo \citep[e.g.,][]{Ibata:1994,Helmi:1999a,Belokurov:2006,Bell:2008,Starkenburg:2009,Janesh:2015}. Presently, we have a firm theoretical framework provided by the $\Lambda$CDM paradigm predicting a hierarchical formation scenario that can be simulated in much detail \citep[e.g.,][]{Johnston:1998,Bullock:2001,Bullock:2005,Moore:2006,Abadi:2006}. On the other hand, the accretion history of our Galaxy in particular is not completely unravelled yet, although much progress is expected thanks to the Gaia mission \citep{Perryman:2001}. One particularly intriguing question is how the building blocks that formed our Milky Way's accreted spheroid compare to the satellite galaxies that we see around us today. In a pioneering paper, \citet{Unavane:1996} attempted to constrain the accretion history of the stellar halo from comparisons of the age distribution and chemical abundances of halo stars with those of the stars in present-day dwarf spheroidal (dSph) galaxies. Numerous observational studies \citep{Shetrone:1998,Shetrone:2001,Shetrone:2003,Tolstoy:2003,Venn:2004,Koch:2008,Tolstoy:2009,Kirby:2010} reported discrepancies between chemical abundances of satellite galaxies of the Milky Way and field halo stars. These studies show that the present-day satellites are, at least partly, unlike the building blocks of the Milky Way's stellar spheroid. The dSphs that we see around the Milky Way in our Local Group are survivors and thus had naturally more time to form stars than the building block galaxies that already dissolved into the halo \citep[e.g.,][]{Mateo:1996}. Even when comparing equal age populations in both environments \citep[as done by][using RR Lyrae stars]{Fiorentino:2015} discrepancies are found between the typical dSphs that survived and those that contributed majorly to the build-up of the spheroid. In this work we specifically focus on the properties (in terms of mass, age and metallicity) of the building blocks of our Milky Way's accreted spheroid modelled within a fully cosmological framework. We investigate when they merged and how they relate to the surviving satellite population. In the past decade several efforts have already focussed on the build-up of Milky Way stellar haloes and/or their chemical evolution, either using hydrodynamical simulations or with semi-analytic techniques \citep[e.g.,][]{Bullock:2005,Salvadori:2007,Tumlinson:2006,Tumlinson:2010,Zolotov:2009, Cooper:2010, Font:2011,Tissera:2013, Tissera:2014, Cooper:2015, Pillepich:2014, Lowing:2015,Pillepich:2015}. A specific focus on chemical evolution has been provided by \citet{Robertson:2005,Font:2006,Font:2006a}, using the hybrid semi-analytic plus N-body approach of \citet{Bullock:2005}. \citet[][C10 hereafter]{Cooper:2010} used the \textsc{galform} semi-analytic galaxy formation model to study the disruption of satellite galaxies within the cosmological N-body simulations of the six galactic haloes of the Aquarius project \citep{Springel:2008}, which have masses comparable to values typically inferred for the Milky Way halo. We use here a different semi-analytic model to study the formation of our Galaxy and its spheroids' building blocks than C10 \citep[][hereafter S13, and references therein]{Starkenburg:2013}, but using also the Aquarius simulations as a backbone. In Section~\ref{sec:2} we briefly describe our model, followed by a detailed description of the resulting stellar spheroids in Section~\ref{sec:3}. We will focus on their accreted components, but in this section we will also show how they relate to the full spheroids in terms of stellar mass. In Section~\ref{sec:4} we investigate the stellar mass $-$ metallicity relation for the building blocks of the accreted spheroids and compare this to the observed stellar mass $-$ metallicity relation for the surviving satellite galaxies of the Milky Way, and the simulated one by S13. In this section, we also show that the early star formation (i.e. over 12 Gyrs ago) in the accreted spheroid was dominated by its building blocks and was much lower in the satellite galaxies that survive until the present day. We apply our analysis to infer observable [$\alpha$/Fe] trends in galaxies with various accretion histories in Section~\ref{sec:5} and we conclude in Section~\ref{sec:6}. Throughout this paper we name all accreted stellar material together the ``accreted spheroid'' of a galaxy. This definition is preferred over the term ``halo'' to clarify that this component is present at all radii. Only in Section~\ref{sec:3}, we furthermore use the term ``accreted bulge'' for the innermost 3~kpc of the accreted spheroid. | \label{sec:6} In this paper we have investigated the accreted stellar spheroids of Milky Way like galaxies with the Munich-Groningen semi-analytical model of galaxy formation, combined with the high-resolution Aquarius dark matter simulations. Typically, each of the accreted spheroids was built by only a few main progenitor galaxies and the majority of stars that end up in our Milky Way like stellar spheroids is 10$-$13 Gyr old. In three of our six galaxies (C, D and F) a large fraction of the spheroid stars is stripped from satellites that are surviving to the present day. For spheroids C\&D these may be resembling the Sagittarius dwarf's contribution to the Milky Way halo. Spheroid F is atypical as a Milky Way analog because it accreted $\sim 10^{10} M_\odot$ in stars over the last $\sim 3$~Gyr. We compared the properties of the building blocks of the Milky Ways stellar spheroid to those of the surviving satellites and found that in terms of the stellar mass $-$ metallicity relation, the difference between the two populations is small, but that the former have significantly higher star formation rates on average - they form comparable amounts of stars in a shorter time (see Figures \ref{fig:6} and \ref{fig:10}). In particular, the more massive surviving satellites show a larger variety in stellar mass build-up over time than the massive building blocks (Figure~\ref{fig:8}). On the other hand, the faintest surviving satellites build up mass in a similar fashion to building blocks with similar mass (right panel of Figure~\ref{fig:10}). From these results, we expect the stellar spheroid to be more enriched in $\alpha$-elements compared to Fe than the surviving satellites, as we observe in the Milky Way system. However, a quantitative analysis of the detailed chemical evolution will require a more sophisticated model and accurate descriptions of the delay time for SNe type Ia. Furthermore, we are dealing with a stochastic process since we are comparing the spheroids of only six Milky Way-like galaxies, that have accreted components which are dominated by a few objects. This results in some of the Aquarius haloes having a better match with the Milky Way galaxy in terms of overall stellar mass and spheroid metallicity, while others have an accretion history that more closely matches that of the Milky Way. Also, we observe some scatter from system to system in our models of the timescale of star formation in satellite galaxies and the timescale of star formation in the main halo. A prediction of these models is therefore that not all Milky Way-mass systems will show [$\alpha$/Fe] ratios similar to those in the Milky Way. | 16 | 9 | 1609.04042 |
1609 | 1609.06337_arXiv.txt | % We report observations of resolved C$_2$H emission rings within the gas-rich protoplanetary disks of TW~Hya and DM~Tau using the Atacama Large Millimeter Array (ALMA). In each case the emission ring is found to arise at the edge of the observable disk of mm-sized grains (pebbles) traced by (sub)mm-wave continuum emission. In addition, we detect a C$_3$H$_2$ emission ring with an identical spatial distribution to C$_2$H in the TW~Hya disk. This suggests that these are hydrocarbon rings (i.e. not limited to C$_2$H). Using a detailed thermo-chemical model we show that reproducing the emission from C$_2$H requires a strong UV field and C/O $> 1$ in the upper disk atmosphere and outer disk, beyond the edge of the pebble disk. This naturally arises in a disk where the ice-coated dust mass is spatially stratified due to the combined effects of coagulation, gravitational settling and drift. This stratification causes the disk surface and outer disk to have a greater permeability to UV photons. Furthermore the concentration of ices that transport key volatile carriers of oxygen and carbon in the midplane, along with photochemical erosion of CO, leads to an elemental C/O ratio that exceeds unity in the UV-dominated disk. Thus the motions of the grains, and not the gas, lead to a rich hydrocarbon chemistry in disk surface layers and in the outer disk midplane. | The birth of planetary systems begins with the gravitational collapse of a centrally concentrated core in molecule-dominated gas that forms a star and disk system. Over time the energy released by the forming star, both dynamical and radiative, ablates the surrounding envelope, exposing the dense (n$_{\rm H_2}$ $\gg$ 10$^{5}$ cm$^{-3}$) disk to interstellar space. The gas and dust rich protoplanetary disk then continues to evolve both physically and chemically until the gaseous disk dissipates and the system transitions to one dominated by large bodies and their surrounding debris (so-called debris disk systems). A key facet of the disk evolution is the growth of the initially micron-sized dust particles to larger sizes, in which two aspects stand out. First, the gravitational settling of coagulating grains to the midplane removes dust from the surface layers of the disk \citep{wc_ppiii, dd04}. This process is constrained via observations of the dust spectral energy distribution because dust settling decreases continuum emission in the mid- to far-infrared \citep{dalessio99,Chiang01}. Surveys using the Spitzer Space Telescope infer dust depletion factors in the surface layers to be of the order of 100-1000 (relative to what is expected assuming interstellar grain abundances) in both Taurus and Ophiuchus \citep{furlan06, McClure10}. Second, dust becomes radially stratified by size-dependent gas drag, a process known as radial drift \citep{whipple1972,wc_ppiii, Youdin13}. % Small grains are coupled to gas motions while large km-sized planetesimals have significant inertia to resist the overall drag force. In between, mm to tens of cm-sized grains \citep{Youdin13} radially drift inwards unless subject to a local pressure maximum generated by a variety of mechanisms \citep{Johansen07, Chiang10}. There is now growing observational evidence for the pervasive presence of radial drift; one example is that the part of a disk composed of mm-sized grains seen in sub-mm emission is smaller in size than the part composed of smaller grains traced by scattered light or $^{12}$CO emission \citep{pdg07, isella07, panic09,andrews12}. \begin{turnpage} \begin{figure*}[h!] \begin{centering} \includegraphics[width=1.3\textwidth]{f1.pdf} \caption{Individual C$_2$H line detections for TW Hya (top row, $\rm N=4-3$) and DM~Tau (bottom row, $\rm N=3-2$). For both disks, the middle two columns are the sum of the emission of two partially blended hyperfine components as labeled. The weaker satellite components are not detected in the DM~Tau observations, consistent with the relative line strengths in the optically thin case. All molecular line emission maps presented in this figure and others are continuum subtracted. \label{fig:indiv}} \end{centering} \end{figure*} \end{turnpage} What is less clear is how the evolution of dust affects the gas, and in particular the gas chemical composition. The settling and growth of dust grains increases the transparency of the surface layers to UV radiation, while also increasing the local timescales for the freeze-out of the gas species \citep{aikawa99, an06,bb11a, Fogel11,Semenov11,Akimkin13}. However, the effects are difficult to disentangle, and, while many chemical dependencies have been found in the models, strong correlations are yet to be discovered. More recently, there is observational evidence that the abundances of key volatile species are depleted in the surface layers where the molecular emission originates --- the so-called ``warm molecular layer'' \citep{aikawa_vanz02}. The generic expectation is that CO would be present as vapor with ISM abundance ($\sim 10^{-4}$ relative to H$_2$) in layers where the dust temperature exceeds $\sim$20~K. In gas below 20~K, low gas-phase CO abundances relative to the ISM are a hallmark of volatile freeze-out, and are seen clearly in observations of the cold regions of protoplanetary disks \citep{dgg97}. However, \citet{Dutrey03} and \citet{Chapillon08} find that the gas-phase abundance of CO may also be reduced in layers above the sublimation temperature. A similar result is found for water vapor emitting from cold ($\sim 20-40$~K) layers well below the sublimation temperature \citep{bergin10b, hoger11a}. Still, molecular depletion is not the only explanation for the observed low volatile abundance in warm gas; the disk could also simply be less massive than the existing mass tracers predict. The degeneracy between abundance and gas mass can be minimized by using a gas tracer, such as HD, to infer the H$_2$ mass \citep{bergin_hd}. \citet{favre13a} use C$^{18}$O and HD emission to show that the CO abundance was significantly reduced in emissive layers in the TW Hya disk, while \citet{Du15} find that both CO and water appear to be depleted from the surface beyond their respective snow lines. They hypothesize, in concert with earlier and contemporary work\citep{Chapillon08, hoger11a, Kama16b, Kama16a}, that the ice-aided growth \citep{Gundlach15} and motions of grains deplete the upper layers of volatile species. Taking into account this effect, \citet{Du15} are able to match the observed emission from \ion{C}{2}, \ion{C}{1}, CO, \ion{O}{1}, OH, and H$_2$O; they also predict that regions of the disk surface and outer radii will be preferentially depleted in oxygen and will become subsequently hydrocarbon-rich. This composition arises because C- and N-bearing molecules exist in a sea of H$_2$ rich gas that is exposed to ionizing photons initiating hydrocarbon formation. Contemporaneously \citet{Kastner15}, using the SMA, detected the presence of a bright C$_2$H emission ring in TW Hya. Here we present the spatially resolved distribution of C$_2$H and C$_3$H$_2$ emission in TW Hya and C$_2$H in DM Tau obtained with the Atacama Large Millimeter/submillimeter Array (ALMA). Using the thermo-chemical model of \citet{Du14}, we demonstrate that hydrocarbon rings are a natural feature induced by the settling and drift of millimeter or larger sized grains, which removes UV opacity from the upper layers and outer disk, creating a UV-dominated disk (essentially a photon dominated region). The chemical outcome of this drift is to deplete the upper layers of oxygen and raise the C/O ratio there. This is also required to boost hydrocarbon emission in the ring to the detected levels. In \S\ref{secObs} we describe the observational setup and in \S\ref{secHydrRing} we present images of the two sources. In \S\ref{modeldesc} we use the thermo-chemical model of \citet{Du14} and \citet{Du15} to outline the ingredients required to produce hydrocarbon rings. In \S\ref{discussion}, we present source-specific models that reproduce the observed emission, compare these predictions with an excitation analysis of TW Hya, and discuss potentials sources for the active carbon chemistry. Finally, \S\ref{summary} summarizes these results and discusses the implications. | C$_2$H appears to be emitting from gas with densities greater than 10$^6$~cm$^{-3}$ consistent with our predictions. From \reffig{fig:dmt} we would predict that the outer C$_2$H ring in DM Tau is emitting from gas that has lower density ($3 \times 10^4$~cm$^{-3} < {\rm n_{H_2}} < 10^6$~cm$^{-3}$) and is colder (T$_{gas} \sim 10-20$~K). \begin{figure}[b] \begin{centering} \includegraphics[width=0.5\textwidth]{Density-nodust.pdf} \caption{Excitation calculations for the flux density ratio of the N = 4 -- 3, J = $\frac{9}{2} - \frac{7}{2}$, F = 4-3 to N = 3 -- 2, J = $\frac{9}{2} - \frac{7}{2}$, F = 4-3 transitions. The observed ratio (2.16) with 1$\sigma$ error bars is shown as contours \label{fig:xcit}} \end{centering} \end{figure} \subsection{Photodissociation of Carbonaceous Grains as the Origin of Simple Hydrocarbons} \label{sec:pah} In this paper we have outlined a consistent picture of coupled dust + gas physical chemical evolution that leads to the creation of hydrocarbon rings. We have implicitly assumed that C$_2$H is produced from carbon that was extracted from CO, aided by the depletion of oxygen in water ice. On the other hand, as discussed by \citet{Kastner15} the photo-ablation of aliphatic or aromatic hydrocarbon grains would be a ready source of carbon as carbon-rich grains contain nearly half of the cosmic abundance of carbon \citep{Jones13, Chiar13}. Moreover, if carbon grains are being destroyed in gas where water remains frozen, then the C/O ratio can be $>$ 1. \begin{figure*}[htbp] \centering \includegraphics[width=1.0\linewidth]{f12.pdf} \caption{The \ce{C2H} $J{=}7/2{-}5/2$, $F{=}4{-}3$ \& $3{-}2$ emission at $10^3$, $10^4$, and $10^5$ years, starting with a uniformly high \ce{C2H} abundance of $10^{-5}$. The underlying disk structure is the one specified in \reftab{tab:model} for TW~Hya.} \label{fig:pah} \end{figure*} To explore this issue we use a calculation of the equilibrium abundance of C$_2$H if produced via photodissociation of hydrogenated amorphous carbon grains, one of the potential carriers of refractory carbon, and destroyed by atomic oxygen. There are no calculations of photodissociation channels of hydrogenated amorphous carbon grains (a-C:H) that directly lead to C$_2$H. However, laboratory work and models of hydrogenated amorphous carbon photoablation and carbon chemistry by \citet{Alata15} show that creation of other hydrocarbons (CH$_4$, C$_2$H$_2$ as examples) leads to an increase in the abundance of C$_2$H. For this purpose we adopt their total photodissociation rate regardless of the product. This is $k_{ph} = 2 \times 10^{-12} G_0 \exp(-2.0A_V) F_i$~s$^{-1}$. For TW Hya, $G_0 is \sim 320$ at 100 AU \citep{bergin_lyalp}, including the contribution from Ly $\alpha$ this would increase to $\sim 2000$ \citep{herczeg_twhya1, bergin_h2}. $F_i$ is a factor that accounts for the fact that the parent a-C:H grain being ablated each time a photon is capable of breaking off a fragment. For simplicity we adopt $F_i = 0.5$. The unshielded photorate is consistent with the calculation of polycyclic aromatic hydrocarbon (PAH) photodissociation producing C$_2$, C$_2$H, or C$_2$H$_2$ fragments for a PAH consisting of $<$ 20 atoms \citep{Visser07}. Thus, this calculation is roughly appropriate for PAHs, which are another potential solid state carbon carrier. To obtain the maximum amount of C$_2$H that might be created with this rate as the source term we further assume that C$_2$H is the ultimate product of all dissociations. Under this case the equilibrium abundance will be as follows: \begin{equation} \frac{dn_{\rm C_2H}}{dt} = n_{\rm a-C:H}k_{ph} - n_{\rm C_2H} n_{\rm O} k_{\rm O, C_2H} \end{equation} \noindent Here $k_{\rm O, C_2H} = 10^{-10}$ cm$^3$/s is the destruction rate of C$_2$H with oxygen atoms (assuming this is the main destruction channel). In steady state both right hand terms are equivalent and we can solve for the C$_2$H abundance: \begin{equation} x_{\rm C_2H} = \frac{x_{\rm a-C:H} k_{ph}}{x_{\rm O}n_{\rm H_2} k_{\rm O, C_2H} } \end{equation} \noindent We assume that the abundance of carbon grains is $\sim 3 \times 10^{-7}$ relative to H and each grain carries $\sim 50$ carbon atoms as determined for PAHs \citep{tielens_book}. Strictly PAHs are not the same chemical form as a-C:H, but it provides a good baseline for the amount of carbon that might be present in the the solid state. We also assume that the distance is 60 AU, $A_V = 0.5^m$ (or $\tau_{UV} = 1$), and a gas density of 10$^8$~cm$^{-3}$ which is the density and UV optical depth seen in the C$_2$H layers in our models. Using these expressions if the abundance of oxygen atoms is near cosmic ($10^{-4}$) then the equilibrium abundance of C$_2$H would be $\sim 5 \times 10^{-10}$. Based on our simulations, this would be well below the value of $\sim 10^{-7}$ needed for detection. To be consistent with our results (with the H$_2$ gas mass constrained by HD), the oxygen abundance would need to be reduced by 2-3 orders of magnitude. Furthermore, species such as PAHs are difficult to detect in T Tauri systems with the suggestion their abundances are reduced by 10-100 orders of magnitude \citep{geers07, Akimkin13}; this would require even lower abundances of atomic oxygen. Thus, if carbonaceous grains are the source term for C$_2$H emission, it also requires reduced abundances of oxygen in the disk atmosphere. The timescale to reduce the grain by one small fragment is short and is only $\sim 100$ years. Depending on the size, small grains could be destroyed on timescales below 10$^5$ yrs \citep{Alata15}, but large grains or smaller grains in deeper layers would survive. However, the photorates of large ($>$ 25 atoms) grains are significantly reduced by many orders of magnitude \citep{Visser07} as there are more internal models to share the energy, as opposed to breaking a bond. Thus very large grains may not be the most viable source terms for C$_2$H production. If a-C:H or PAHs were the source term another question would be how long would C$_2$H last in the gaseous state. Since our chemical network does not explicitly include PAH chemistry, we mimic the effect of PAH/a-C:H photodissociation by artificially setting the initial abundance of \ce{C2H} to $10^{-5}$ (relative to hydrogen nuclei). This is consistent with the carbon grain abundance adopted above, assuming 50 carbon atoms which then uniformly produce C$_2$H. Otherwise this model assumes a normal C/O ratio. We then evolve the system for 1~Myr to see how the resulting emission in \ce{C2H} changes with time. \reffig{fig:pah} shows the \ce{C2H} emission map at $t=10^3$, $10^4$, and $10^5$ years. Here the \ce{C2H} emission decreases with time monotonically and only approaches observed values at early stages ($\sim 10^{3}$~yrs). As in the discussion above longer timescales would be found for lower oxygen abundances. However, without a continuous supply of small PAH/a-C:H grains as a source of hydrocarbons and without depletion of oxygen, the carbon budget contained in the initial hydrocarbons (such as \ce{C2H}) will quickly be converted into other species (such as CO through oxygen production via H$_2$O ice photodesorption). As noted in \citet{Kastner15}, the estimated PAH abundance is barely enough to account for the observed \ce{C2H} emission, especially if we consider that the PAH abundance is usually argued to be already depleted in the disk environment \citep{Akimkin13}. Thus, while destruction of carbon grains may be a source of carbon for C$_2$H, it is likely that the production of C$_2$H is fueled by the extraction of carbon from CO and depletion of oxygen from CO and other major oxygen-bearing species (such as water and \ce{CO2}). This is consistent with the measured depletion of CO in TW Hya at the very least \citep[][]{favre13a, Nomura16, Schwarz16}; we therefore predict that the outer disk of DM Tau should also exhibit a reduction in the abundance of volatile CO, while the inner disk must have high carbon content to remain consistent with C$^{18}$O measurements \citep{jWilliams14} \subsection{A physical or a chemical effect?} In our model we have associated dust evolution to two effects. One is physical, that is a redistribution of the UV opacity that increases the penetration of UV photons in the disk system. The other is the relative trapping of volatiles as icy mantles coating grains that settle, grow, and drift which induces an increase in the C/O ratio. This brings up the question as to whether one can reproduce these observations with an increased C/O ratio alone. The work by \citet{Kama16a} provides some insight to this issue as they explored the emission of several carbon-bearing species, including an unresolved observation of C$_2$H, in TW Hya. Similar to our result they find that reproducing the emission requires C/O $> 1$. Their model does include a vertically stratified dust model that accounts for the settling of larger grains, but does not include the effects of grain drift. At face value \citet{Kama16a} show that the total C$_2$H flux can be reproduced by increasing the C/O ratio. In our models for TW Hya alone we require central carbon depletion to reproduce the emission distribution. Thus it would be hard to directly point out the effects of the UV field in this case. However, we have the two rings seen in DM Tau. The outer ring in particular requires both UV to power the chemistry and C/O $> 1$. In addition, our models, for both sources, and \citet{Kama16a} have a stronger UV field on the disk surface due to dust settling; in our case we find $G_0 \ge 1$ in layers where C$_2$H is forming. This, and the known association of C$_2$H (and other hydrocarbons) with photodissociation regions \citep{Pilleri13, Nagy15}, argues that the UV field is also an important factor in hydrocarbon production. | 16 | 9 | 1609.06337 |
1609 | 1609.07530_arXiv.txt | We present a detailed spectral analysis of \xmm and \nustar observations of the accreting transient black hole \grs during a very faint low hard state at $\sim$0.02\% of the Eddington luminosity (for a distance of 8.5\,kpc and a mass of 10\,\msun). The broad-band X-ray spectrum between 0.5--60\,keV can be well-described by a power law continuum with an exponential cutoff. The continuum is unusually hard for such a low luminosity, with a photon index of $\Gamma=1.39\pm0.04$. We find evidence for an additional reflection component from an optically thick accretion disk at the 98\% likelihood level. The reflection fraction is low with $\rrefl=0.043^{+0.033}_{-0.023}$. In combination with measurements of the spin and inclination parameters made with \nustar during a brighter hard state by Miller and co-workers, we seek to constrain the accretion disk geometry. Depending on the assumed emissivity profile of the accretion disk, we find a truncation radius of 15--35\,$\rg$ (5--12\,$\risco$) at the 90\% confidence limit. These values depend strongly on the assumptions and we discuss possible systematic uncertainties. | \label{sec:intro} Galactic black hole (BH) transients typically undergo a very characteristic pattern during an outburst: during the first part of the rise, up to luminosities around 10\% of the Eddington luminosity (\ledd), they are in a so-called low/hard state. In this state the X-ray spectrum is dominated by a power law with a photon index $\Gamma$ between $\approx$1.4--1.8 with almost no contribution from the thermal accretion disk spectrum. At higher Eddington rates the source switches to the high/soft state, where a steeper power law is observed and the thermal accretion disk dominates the soft X-ray spectrum \citep[see, e.g.,][for a description of BH states]{remillard06a}. Compelling evidence exists that in the soft state the accretion disk extends to the innermost stable circular orbit (ISCO), enabling spin measurements through relativistically smeared reflection features and thermal continuum measurements \citep[e.g.,][]{nowak02a, miller02a, steiner10a, mcclintock14a, petrucci14a, kolehmainen14a, miller15a, parker16a}. At the end of an outburst the source transitions back to the low/hard state, albeit typically at much lower luminosities ($\approx$1--4\%\,\ledd) in a hysteretic behavior \citep[see, e.g.,][]{maccarone03a,kalemci13a}. It has been postulated that the accretion disk recedes, i.e., the inner accretion disk radius \rin is no longer at the ISCO. Instead the inner regions are replaced by an advection dominated accretion flow (ADAF) in the inner few gravitational radii \citep[e.g.,][]{narayan95a, esin97a}. Many observational results in a sample of different sources are at least qualitatively consistent with such a truncated disk as measured by, e.g., the frequency and width of quasi-periodic oscillations or multi-wavelength spectroscopy \citep[see, e.g.,][]{zdziarski99a, esin01a,kalemci04a,tomsick04a}. It is still not clear, however, at what luminosity the truncation occurs and how it is triggered. There have been several reports of broad iron lines (implying a non-truncated disk) in the brighter part of the low/hard state ($>1$\%\,\ledd) for \gx \citep{miller06a,reis11a,allured13a} as well as for other systems \citep{reis10a,reynolds10a}, including \grs \citep[hereafter M15]{miller15a}. Studies conducted recently mostly claim evidence for moderate (tens of gravitational radii $\rg$) truncation at intermediate luminosities ($\approx$0.5--10\%\,\ledd) in the low/hard state \citep{shidatsu11a,allured13a,petrucci14a,plant14a}. At a luminosity of $L=0.14\%\,\ledd$ in \gx, \citet{tomsick09a} measured a narrow \feka line, indicating a significant truncation. While this suggests that gradual truncation may occur, it is not clear that $\rin$ is only set by the luminosity \citep{petrucci14a, kolehmainen14a, garcia15a}. A more complex situation than a simple correlation with luminosity is also supported by recent measurements of the disk truncation at $\sim10\,\rg$ in \gx during intermediate states, i.e., during state transitions, at luminosities of 5--10\%\,\ledd \citep{tamura12a, gx339IHS}. Besides the truncation radius, the geometry of the hot electron gas, or corona, is still unclear. It is very likely compact, and it has been postulated that it might be connected to the base of the jet, though a commonly accepted model has not yet emerged \citep[see, e.g.][]{markoff05a, reis13a}. \nustar and \swift observations of \gx in the low/hard state found that the reflector seems to see a different continuum than the observer, i.e., a hotter part of the corona \citep{gx339}. This indicates a temperature gradient and a complex structure of the corona and seems to be independent of the spectral state \citep{parker16a}. It is clear from previous studies that the largest truncation radius is expected at the lowest luminosities, i.e., at the end and beginning of an outburst. High quality data in this state are traditionally difficult to obtain, given the low flux and necessary precise scheduling of the observations before the source vanishes into quiescence. With a combination of \xmm \citep{xmmref} and the \textsl{Nuclear Spectroscopy Telescope Array} \citep[\nustar,][]{harrison13a}, however, such observations are now possible. Here we report on \xmm and \nustar observations of the BH transient \grs in the declining phase of its very long outburst in 2014/2015 (Figure~\ref{fig:batlc}). \grs is a transient BH candidate, discovered by \textsl{Granat} \citep{paul96a, vargas97a}. It is most likely located close to the Galactic Center at a distance of $\approx8.5$\,kpc. The large extinction \citep[$A_V=14\pm2$,][]{greiner96a} makes a spectral identification of the companion difficult, but from photometric data, \citet{marti97a} and \citet{chaty02a} infer a late-type main-sequence star of at least F5~V or later. \grs was classified as a BH candidate given its similarity in spectral evolution to other transient BHs as well as the presence of a very strong 5\,Hz QPO in the soft-intermediate state \citep{borozdin98a,borozdin00a}. During the beginning of the 2014/2015 outburst, \nustar measured a strong reflection spectrum and a relativistically broadened iron line in a bright low/hard state (M15). These authors could constrain the size of the corona, assuming a lamppost model, to be $<22\,\rg$ and the truncation radius to $\rin = 5^{+3}_{-4}\,\rg$. In the lamppost geometry the corona is assumed to be a point-like source located on the spin axis of the BH and shining down onto the accretion disk \citep{matt91a, dauser13a}. The luminosity during this observation was around 8\%\ledd (assuming a canonical mass of 10\,\msun), at which no truncation of the accretion disk is expected. \begin{figure} \includegraphics[width=0.95\columnwidth]{batlc_soft_long.pdf} \caption{\swift/BAT \citep[15--50\,keV, orange;][]{swiftbatref} and MAXI/GSC \citep[2--20\,keV, green; ][]{maxiref} monitoring light curve of \grs. The \nustar observations (3--79\,keV) are marked by black diamonds, the one presented by \citet{miller15a} occurred around 150\,d, the one presented here around 680\,d. All data are shown in observed (i.e., absorbed) count-rates rescaled to mCrab fluxes in the respective energy band of the instrument. The right-hand $y$-axis gives the average measured \nustar count-rate of the observation. The inset shows a zoom-in on the 2015 data, including \swift/XRT \citep{swiftxrtref} data (3--9\,keV, blue triangles) and the \xmm observation (1--10\,keV, red square). Due to the crowded source region the MAXI data suffer from increased background of about 40\,mCrab and are therefore not shown in the inset. Note that the inset $y$-axes are scaled logarithmically. } \label{fig:batlc} \end{figure} After the first \nustar observation, the source continued with a typical outburst evolution and faded to very low luminosities around MJD~57000. However, it probably never reached quiescent levels and \swift/XRT and BAT monitoring indicated that it also did not switch back to a stable low/hard state. A detailed description of the evolution will be presented by Loh et al. (in prep.). Around MJD~57272 the monitoring data indicated a stable transition to the low/hard state had occurred, confirmed by a brightening in the radio. We then triggered simultaneous \xmm and \nustar observations to observe a very faint hard state, and found \grs at $\sim$0.02\%\,\ledd. The rest of the letter is structured as follows: in Section~\ref{sec:data} we describe the data reduction and calibration. In Section~\ref{sec:spec} we present the spectral analysis and compare it to results by M15. In the last section, Section~\ref{sec:disc}, we discuss our results and put them into context. | 16 | 9 | 1609.07530 |
|
1609 | 1609.09377_arXiv.txt | In the next decade, new astrophysical instruments will deliver the first large-scale maps of gravitational waves and radio sources. Therefore, it is timely to investigate the possibility to combine them to provide new and complementary ways to study the Universe. Using simulated catalogues appropriate to the planned surveys, it is possible to predict measurements of the cross-correlation between radio sources and GW maps and the effects of a stochastic gravitational wave background on galaxy maps. Effects of GWs on the large scale structure of the Universe can be used to investigate the nature of the progenitors of merging BHs, the validity of Einstein's General Relativity, models for dark energy, and detect a stochastic background of GW. The results obtained show that the galaxy-GW cross-correlation can provide useful information in the near future, while the detection of tensor perturbation effects on the LSS will require instruments with capabilities beyond the currently planned next generation of radio arrays. Nevertheless, any information from the combination of galaxy surveys with GW maps will help provide additional information for the newly born gravitational wave astronomy. | The detection by the LIGO instrument of gravitational waves (GW150914,~\citealp{GW150914} and GW151226,~\citealp{GW151226}) from the merger of binary black holes opened up a new window to study our Universe. In the first few months following the first detection, gravitational waves have been used to test General Relativity in a new way~\citep{LIGO:GR}, the speed of gravitational waves~\citep{Collett:2016} and alternative cosmological models such as the one where the dark matter is made of primordial black holes (e.g.~\citealt{Bird:2016}). Currently and for the foreseeable future, the main way to detect gravitational waves (GWs) is by the use of laser interferometers, on Earth and in space. Several alternatives have been proposed, and they involve detecting the effect of GWs on other observables, such as Pulsar timing arrays~\citep{PTA}, the effect of gravitational waves from inflation on the Cosmic Microwave Background~\citep{KK}, and the effect of GWs on the Large-Scale Structure (LSS) of the Universe~\citep{Guzzetti:2016}. The presence of tensor modes during the early epochs of the Universe modifies the power-spectrum of primordial scalar perturbations~\citep{Jeong:2012CF}, while at late times the presence of a GW background leads to several effects, including projection effects due to the perturbation of space-time by GWs on the galaxy distribution~\citep{Jeong:2012, Schmidt:2012}, the CMB~\citep{Dodelson:2003, Cooray:2005, Book:2011a} and the $21$-cm background~\citep{Book:2012, Pen:2003}. At the same time, radio surveys for cosmology are entering a new phase of exponential expansion on both quantity and quality of data available~\citep{sparcs}, with the construction of several instruments, including the Australian Square Kilometre Array Pathfinder (ASKAP,~\citealt{Johnston:2008}) and the design definition of the Square Kilometre Array (SKA\footnote{https://www.skatelescope.org}). Radio galaxy surveys with such instruments will be able to detect galaxies over a large redshift range, a wide area of the sky, and down to a very low flux limit. Radio surveys such as NVSS have been used in the past to perform cosmological analyses (see e.g.~\citealt{Nolta:2004, Raccanelli:2008, Xia:2010, Bertacca:ISW}); future surveys will have a wider redshift range and orders of magnitude more objects observed, so it is expected they will improve the precision of cosmological measurements~\citep{Raccanelli:radio}. All this, combined with the fact that effects of GWs on LSS are largest at very large scales, makes it very timely to start an investigation of the combination of GW with radio galaxy maps. This paper investigates the possibility to use future radio galaxy surveys to contribute to gravitational wave astronomy. By measuring the position and correlation of galaxies, or cross-correlating their number counts with GW maps, it will be possible to detect direct or indirect effects of GWs coming from the merger of massive compact objects or the early stages of the Universe. Gravitational wave astronomy is still in its infancy but it is predicted to grow quickly, and the coincidental exponential increase in radio survey capabilities makes it very interesting to analyze how to best combine the two fields. Therefore, it is timely to try to understand if the combination of observations of radio sources and GWs can give useful additional information about cosmological models and parameters currently investigated. We will present forecasts of the constraints on cosmological models and parameters that will be possible to obtain both by cross-correlating future GW maps with galaxy catalogs from a variety of planned radio surveys, and by analyzing the effect of GWs on position, distribution and correlation of such galaxy catalogs. Recently, ideas about cross-correlation of LSS with GW maps have been explored in e.g.~\cite{Camera:2013, Oguri:2016, Namikawa:2016, Raccanelli:2016PBH}. The structure of the paper is as follows. In Section~\ref{sec:radiosurveys} we introduce the radio galaxy surveys we consider. In Section~\ref{sec:ClgGW} we present the studies that will be enabled by cross-correlating GW with galaxy maps, in particular angular correlations to determine the progenitor of BBH mergers in Section~\ref{sec:ccf} and constraints on cosmic acceleration models by using lensing effects on radial correlations in Section~\ref{sec:cosmag}. In Section~\ref{sec:SGWB} we investigate the effects of GWs on the LSS; we predict measurements that will be possible to obtain by using cosmometry in Section~\ref{sec:cosmometry} and the cosmic rulers methodology in Section~\ref{sec:rulers}. We then summarize our findings and conclude in Section~\ref{sec:conclusions}. | \label{sec:conclusions} This work analyzed a few possible ways to achieve this goal: by cross-correlating radio galaxy catalogs with GW maps it is possible to determine properties of the progenitors of merging black hole binaries and forecast how the magnification of GWs by foreground radio sources allows to test models that explain cosmic acceleration. Furthermore, it is in principle possible to detect the effects of a background of gravitational waves, by measuring angular motion and large scale correlations of galaxy distribution and lensing. By using simulated catalogs resembling planned instruments, it was possible to show that the angular galaxy-GW cross-correlation can set stringent limits on properties of the progenitors of binary black holes, testing formation models and the possibility that primordial black holes are in fact the dark matter. Radial cross-correlations can be used to detect the magnification bias of GWs that are lensed by low-redshift galaxies, and future laser interferometers, paired with forthcoming radio galaxies, can provide constraints on dynamical dark energy and modified gravity parameters that are competitive with the ones obtained with galaxy surveys alone and in combination with the CMB. On the other hand, the detection of a stochastic gravitational wave background on galaxy position and distribution presents a much greater challenge. Tensor perturbation effects on galaxy clustering remain orders of magnitude below errors in measurements of galaxy power spectra, even in the case of very futuristic galaxy surveys. The situation is slightly more optimistic for the correlation of lensing effects: in the case of a deep, full-sky survey with very precise shape measurements, it will be possible to measure the SGWB (provided that the tensor-to-scalar ratio $r$ is not negligibly small). In any case, any measurements of gravitational wave effects coming from radio galaxy surveys or their correlation with GW detectors, would represent a valuable cross-check of other measurements and potentially provide new insights about cosmological models of current interest. In summary, radio galaxy surveys can be used to provide information useful for gravitational wave astronomy and contribute studying the Universe in a new and complementary way. | 16 | 9 | 1609.09377 |
1609 | 1609.05968_arXiv.txt | The XQ-100 survey has provided high signal-noise spectra of 100 redshift 3--4.5 quasars with the X-Shooter spectrograph. The metal abundances for 13 elements in the 41 damped Ly$\alpha$ systems (DLAs) identified in the XQ-100 sample are presented, and an investigation into abundances of a variety of DLA classes is conducted. The XQ-100 DLA sample contains five DLAs within 5000 \kms{} of their host quasar (proximate DLAs; PDLAs) as well as three sightlines which contain two DLAs within 10,000 \kms{} of each other along the same line-of-sight (multiple DLAs; MDLAs). Combined with previous observations in the literature, we demonstrate that PDLAs with logN(HI)$<21.0$ show lower [S/H] and [Fe/H] (relative to intervening systems with similar redshift and N(\HI{})), whilst higher [S/H] and [Si/H] are seen in PDLAs with logN(HI)$>21.0$. These abundance discrepancies are independent of their line-of-sight velocity separation from the host quasar, and the velocity width of the metal lines (\vninety{}). Contrary to previous studies, MDLAs show no difference in \alphafe{} relative to single DLAs matched in metallicity and redshift. In addition, we present follow-up UVES data of J0034+1639, a sightline containing three DLAs, including a metal-poor DLA with [Fe/H]$=-2.82$ (the third lowest [Fe/H] in DLAs identified to date) at \zabs{}$=4.25$. Lastly we study the dust-corrected [Zn/Fe], emphasizing that near-IR coverage of X-Shooter provides unprecedented access to Mg\sion{}, Ca\sion{} and Ti\sion{} lines (at redshifts 3--4) to provide additional evidence for subsolar [Zn/Fe] ratio in DLAs. | \label{sec:intro} Quasars (QSOs) exist at many different epochs, providing lines of sight through pockets of gas from the epoch of reionization to the present day. One of the classes of intervening absorbers towards QSOs are damped Lyman-$\alpha$ systems \citep[DLAs;][]{Wolfe05}, defined by their large \HI{} column densities \citep[N(\HI{})$\geq 2\times{}10^{20}$ atoms cm$^{-2}$;][]{Wolfe86}. DLAs are common probes to study the evolution of neutral gas and metals in the interstellar medium (ISM) of galaxies from \zabs{}$\sim5$ to the present day \citep{Wolfe95,Pettini97,Prochaska04DR1,Rao06,Rafelski14,SanchezRamirez16}. A large portion of DLA analyses has been concentrated on detailed abundance analyses of the host galaxies \citep[e.g.][]{Pettini94,Lu98,Centurion00,Wolfe03,Cooke11,Zafar14N, Berg15II}. As elements have unique physical properties and nucleosynthetic origins \citep{Woosley95,Mcwilliam97,Nomoto13}, different abundance ratios have been used to understand the star formation history and dust content of DLAs \citep{Ledoux02,Prochaska02II,Vladilo11}. The most common ratio to probe enrichment histories is \alphafe{}, which traces the star formation history due to the time-delayed contributions of Type II and Ia supernovae \citep{Tinsley79,Mcwilliam97,Venn04,Tolstoy09}. However elements such as Fe, Ni, and Cr are heavily depleted onto dust \citep{Savage96}, leading to overestimates of the measured gas-phase \alphafe{} in DLAs. These overestimates in \alphafe{} have led to the use of other undepleted elements that trace Fe (such as Zn) to better estimate the intrinsic \alphafe{} ratio \citep{Pettini97,Vladilo02b}. In the case of Zn, care must be taken as Zn does not necessarily trace Fe in all environments and metallicities \citep{Prochaska00disk,Chen04,Nissen07,Rafelski12,Berg15II}. The physical nature of DLAs also influences their gas phase abundances, including the role of ionizing sources \citep{Dodorico07,Ellison10,Zafar14Ar} or the amount of dust \citep[e.g.][]{Pettini94,Kulkarni97,DLAcat50,Krogager16}. There are many sub-classes of DLAs that provide opportunities to probe these differing physical environments. Proximate DLAs (PDLAs) are DLAs defined to be within $\Delta v\leq 5000$ \kms{} of the host QSO, and more frequently seen than intervening systems \citep{Ellison02,Russell06,Prochaska08}. PDLAs have shown increasing metal abundances with increasing N(\HI{}), in particular both [S/H] and [Si/H] are $\sim3\times$ larger in four PDLAs with logN(\HI{})$>21.0$ \citep{Ellison10,Ellison11}. Multiple DLAs (MDLAs) along the same line of sight within $500\leq \Delta v \leq 10000$ \kms{} of eachother have also shown different metallicity effects, with a low \alphafe{} relative to the typical DLA \citep{Ellison01L,Lopez03}; an effect attributed to truncated star formation from environmental effects. However, the analyses of \cite{Lopez03} and \cite{Ellison10} suffer from low numbers of MDLAs (seven absorbers) and PDLAs (16 absorbers). Recently there has been a significant effort to identify the first stars and galaxies \citep{Cayrel04,Beers05,Suda08,Spite11,Frebel12,Norris13,Frebel15} to constrain Population III nucleosynthesis \citep{Umeda02,Greif07,Heger10,Cooke13}. In tandem with the search for metal-poor stars in the Galaxy and its nearby companions \citep[e.g.][]{Jacobson15,Skuladottir15MP}, work at higher redshifts focused the identification and measurement of abundances in the most metal-poor DLAs \citep[MPDLAs; {[Fe/H]$\leq-2.5$};][]{Penprase10,Cooke11,Becker12,Cooke14}. As the explosion mechanism of the supernovae models is very uncertain, chemical abundances in these metal-poor regimes are required to constrain the models of Population III nucleosynthesis. In particular the supernovae explosion energy influences the mass cut of the supernovae, and thus which elements escape into the ISM \citep{Umeda02,Nomoto13}. To date, abundances in the most MPDLAs reflect first generation stars that have undergone moderate to low energy core-collapse supernovae \citep{Cooke11,Cooke13}, but remains to be tested for a large sample of DLAs with [Fe/H]$\leq-3$. The XQ-100 Large Programme survey \citep[PI: S. Lopez, ESO ID 189.A-0424;][]{Lopez16} has observed 100 QSOs at $z=$3.5--4.5 with the X-Shooter \citep{Vernet11} spectrograph on the Very Large Telescope (VLT). As the survey was primarily designed to study active galactic nuclei, the inter-galactic medium, and the Ly$\alpha$ forest; XQ-100 provides a near-random sample of intervening DLAs as the QSOs were selected without consideration of intervening absorbers. In this paper, we present the metal column densities for 14 species (O\textsc{i}, C\sion{}, Mg\textsc{i}, Mg\sion{}, Ca\sion{}, Si\sion{}, P\sion{}, S\sion{}, Ti\sion, Cr\sion{}, Mn\sion{}, Fe\sion{}, Ni\sion{}, Zn\sion{}) in the DLAs recently identified by \cite{SanchezRamirez16} in the XQ-100 survey. By combining the XQ-100 DLAs with a sample of DLA abundances in the literature \citep{Berg15II}, we investigate the elemental abundances of the XQ-100 sample and demonstrate the prospects of using X-Shooter to study absorption lines in the near infrared (NIR). | The sample of XQ-100 DLAs provides coverage of the relatively moderately-sampled redshift range \zabs{}= 3--4. We have computed the column densities for a variety of metals in the 41 DLAs in the XQ-100 sample. The additional coverage from the NIR arm of X-Shooter provides coverage of rarely detected lines at redshifts 3--4 in abundance studies such as Mg\sion{}, Ca\sion{}, and strong Ti\sion{} lines. With the addition of dust-depleted $\alpha$-elements, we are able to test the dust-corrected [Zn/Fe] to see if [Zn/Fe] is solar in DLAs. We have shown in Section \ref{sec:dust} that [Zn/Fe] is not necessarily solar in DLAs, and that [Zn/Fe] shows the same range of values as seen in the dSphs of the Local Group \citep[in agreement with][]{Berg15II}. In combination with a sample of DLAs drawn from the literature, we have provided a statistical analysis of PDLAs (within $\Delta v\leq 5000$ \kms{} of the host QSO) and MDLAs (two or more DLAs separated by $500\leq \Delta v \leq 10000$ \kms{}) by comparing to a control-matched sample of individual, intervening absorbers. We do not find any suppression in \alphafe{} in MDLAs, suggesting that there is no evidence for truncated star formation between nearby DLAs on their abundance. Relative to a control sample of DLAs, we note a mildly elevated [S/H] and [Si/H] for high logN(\HI{})$>21.0$ PDLAs at (AD test rejects the null hypothesis at 14\% and 26\% confidence; respectively), as previously seen by \cite{Ellison10}; however, we also detect a deficit in [S/H] and [Fe/H] (null hypothesis rejected at 6\% and 32\% confidence, respectively) for PDLAs with logN(\HI{})$<21.0$. These abundance discrepancies appear to be independent of velocity separation of the host QSO and the mass proxy \vninety{}. It is possible to explain the deficit of [S/H] at low logN(\HI{}) through ionization corrections, but not the deficit of [Fe/H]. We have also presented UVES observations of three DLAs towards J0034+1639 in order to investigate an MPDLA candidate at \zabs{}$\sim4.25$ with a [Fe/H]$=-2.82\pm0.11$. This MPDLA is consistent with abundances in the typical MPDLA \citep{Cooke11}. MPDLAs such as the one towards J0034+1639 prime targets for easily detecting Ni and other discriminating elements in future follow-up observations with 30-m class telescopes. | 16 | 9 | 1609.05968 |
1609 | 1609.03580_arXiv.txt | We find that $\sim 15-20$ per cent of A-type stars or red giants are bound with a massive companion ($M_{\rm secondary} > 1\Msun$) in an intermediate wide orbit ($0.5<P<5000\yr$). These massive binaries are expected to form wide-orbit, double-degenerate systems (WODDs) within $\lesssim10\Gyr$ implying that $\sim10$ per cent of white dwarfs (WDs) are expected to be part of a WODD with a lighter WD companion. These findings are based on an analysis of previous adaptive optics observations of A-type stars and radial velocity measurements of red giants and shed light on the claimed discrepancy between the seemingly high multiplicity function of stars and the rather low number of detected double degenerates. We expect that GAIA will find $\sim 10$ new WODDs within $20\pc$ from the sun. These results put a stringent constraint on the collision model of type Ia supernovae in which triple stellar systems that include a WODD as the inner binary are required to be abundant. | \label{sec:Introduction} Type Ia Supernovae (SNe) are among the most luminous and energetic events observed. Following decades of extensive observational surveys and modeling efforts, there is good evidence that these events are the result of thermonuclear explosions of carbon oxygen white dwarfs (CO-WDs) but it is still unknown what triggers $\sim 1$ per cent of them to explode \citep[for a recent review, see e.g.][]{maoz14}. One of the scenarios recently argued to be the progenitor of type Ia SNe is the direct collision (as opposed to merger) of two CO-WDs \citep{katz12, kushnir13, dong15}. Following previous demonstrations that colliding WDs explode \citep{rosswog09, raskin10, hawley12}, \cite{kushnir13} showed numerically that such collisions with the observed range of WDs masses robustly lead to thermonuclear explosions with the observed range of brightness and late time characteristics. \cite{dong15} reported observations of double peaks in the spectra of some events, a unique prediction (so far) of the collision model. Until recently, the rate of direct collisions was considered to be orders of magnitudes lower than the type Ia rate \cite[e.g.][]{rosswog09, raskin09}. \cite{thompson11} recently argued that the merger rate of WDs due to gravitational waves may be enhanced in triple systems by the Lidov-Kozai mechanism and noted that some direct collisions may also occur in such systems. It was later shown by \cite{katz12} that the rate of WD direct collisions may be as high as the type Ia rate if tens of percents of WDs reside in (mildly) heirarchical triple systems with a wide-orbit-double-degenerate (WODD hereafter) inner binary (semimajor axis $1\lesssim a_{\rm in} \lesssim 1000$AU), raising the possibility that most type Ia SNe are due to direct collisions. A critical requirement for the collision model is that a sufficient amount of triple systems with the required hierarchy exists. In particular, such systems should have an inner WODD. A first step to determine the abundance of such relevant triple systems is to find out the abundance of WODDs. In this paper we therefore attempt to answer the following question: \textbf{what is the fraction of CO-WDs that have a lighter CO-WD companion with a wide orbit ($\mathbf{P\gtrsim1\yr}$)?}. A straight forward approach to answer this question is to examine the population of WDs in the solar neighborhood. This approach was presented in \cite{holberg09} based on the local sample of WDs within $D<20\pc$ claimed to be $80$ per cent complete by the authors \citep{holberg08}\footnote{The sample has been updated to $136$ WDs without any new WODDs and its current completeness estimate by the authors is $86$ per cent \citep{holberg16}.}. In this sample, there are only $3$ WODDs\footnote{WD-0121-429 is an additional uncertain candidate. One should note that the separation of WD-2226-754 is slightly larger $\sim 1400$AU \citep{scholtz02} but is still counted as a WODD. There are $3$ additional double degenerate systems in the local sample \citep{holberg08}, however WD-0322-019 (G77-50) was found to be a single star \citep{farihi11} and two other systems are short period close binaries ($P\sim2$ days). WD-0532+414 which is newly entering the local ($D<20\pc$) sample in the current version is a short period close binary based on its radial velocity (RV) measurements \citep{zuckerman03}.} out of $136$ WDs in total. This count suggests that only $\mathbf{\sim 2}$ per cent of WDs have a (lighter, wide orbit) WD companion (and only $\sim 30$ per cent have any companion \citep{holberg16}). This result is very low compared to the binarity fraction ($\sim70-100$ per cent) of the progenitors of todays WDs - intermediate mass main sequence (MS) stars \citep[M $\sim1.5-8 \Msun$, e.g.][]{kobulnicky07, kouwenhoven07} and their supposed mass ratio distribution of $f(q)\propto q^{-0.5}$. Moreover, $4$ out of the closest $6$ WDs are in binary systems \citep{holberg16} and the two closest WDs - Sirius B and Procyon B have massive ($M\gtrsim 1.5 \Msun$) MS companions that will become WDs within $\sim 1\Gyr$ and are thus likely to become WODDs \citep{liebert05, liebert13}. If the fraction of WODDs is indeed $\sim2$ per cent, this is a strange (but possible) coincidence. Another option is that for some reason, many of the wide-orbit MS massive binaries do not end up as WODDs. Interaction during the stellar evolution is unlikely to play a significant role beyond separations of a few AU and we assume that bound systems remain bound (however see comment about this assumption in section \sref{sec:Discussion}). These puzzles have led to suggestions that \cite{holberg08} is not as complete as reported by the authors \citep{ferrario12, katz14}. In this paper we attempt to quantify the expected fraction of WODDs based on observations of the relevant WD progenitors - intermediate mass ($1<M<8\Msun$) MS stars that will become WDs within a Hubble time. An adaptive optics (AO) survey of A-type stars within $75\pc$ was recently conducted by \cite{DeRosa14} allowing the binarity fraction at long periods ($P\gtrsim50\yr$) to be established. In particular the relevant massive ($M_{\rm secondary}>1\Msun$) companions have sufficiently low contrast to be reliably detected. This is discussed in section \sref{sec:VAST_AO}. The fraction of companions with shorter periods is more challenging. Finding binaries with periods $P\sim 1-10\yr$ is currently best achieved by radial velocity (RV) surveys. However, the rapid rotation of the relevant intermediate mass stars broadens the lines and makes it very challenging \citep{verschueren99}. A way around this problem is to observe these stars when they are in the red giant phase in which the rotational broadening is greatly reduced. An extensive RV survey of red giant stars in open clusters was preformed by \cite{mermilliod08} providing an excellent sample. Again, the fact that only companions with significant mass are considered implies large signals increasing our confidence of detection. An analysis of the sample is done in section \sref{sec:RVs}. \emph{We find that $\mathbf{\sim15-20}$ per cent of massive stars have a (lighter) massive companion $M_{\rm secondary} > 1\Msun$ in the period range $0.5\lesssim P\lesssim 5000\yr$ with a uniform distribution in logarithmic space or equivalently $\mathbf{\sim4}$ per cent per dex in period (see Fig.~\ref{fig:massive_binaries_occurence_vs_period_compilation_M2_gt_1})}. A roughly flat distribution in log space is typical for wide binaries \citep[e.g.][]{raghavan10} and the fact that such a distribution is obtained increases our confidence in the estimate which is based on very different samples at the two ends of the period range which covers $4$ orders of magnitude. | \label{sec:Discussion} In this paper we analysed previous AO observations of A-type stars by \cite{DeRosa14} (section \sref{sec:VAST_AO}) and RV measurements of red-giants in open clusters by \cite{mermilliod08} (section \sref{sec:RVs}) to obtain a robust estimate of the fraction of massive stars $1<M<8 \Msun$ that have (lighter) $M > 1\Msun$ companions in a wide orbit ($P\gtrsim 1\yr$). Assuming that these systems will remain in-tact when the stars evolve to become WDs within $\lesssim 10\Gyr$, they will become wide orbit double degenerate systems (WODDs). The results for the two populations are shown in Fig.~\ref{fig:massive_binaries_occurence_vs_period_compilation_M2_gt_1}. As can be seen, the binaritiy fraction per logarithmic period bin is rather constant across $4$ orders of magnitude $0.5<P<5000\yr$ using different techniques. About $\sim15-20$ per cent of massive stars have such massive companions in this period range with about $\sim4$ per cent for each dex of period. The samples are likely close to being complete in this range given the high luminosity (for large separations) and large RV signal (for low separations) as demonstrated in sections \sref{sec:VAST_AO} and \sref{sec:RVs} (except for the $5<P<50\yr$ bin where we obtain a lower limit for the fraction $\sim 2$ per cent). The upcoming release by GAIA, expected in September 2016, should confirm the results based on the AO observations at large separations with much larger statistics. In particular, by providing parallax and proper motion for the Tycho 2 catalogue, main sequence (MS) stars with $M>1\Msun$ should be measured to over $100\pc$. \begin{figure} \includegraphics[scale=0.37]{massive_binaries_occurence_vs_period_compilation_M2_gt_1.eps} \caption{\label{fig:massive_binaries_occurence_vs_period_compilation_M2_gt_1} The fraction of massive stars that have lighter companions with $M_{\rm secondary}>1\Msun$ as a function of the orbital period. The red solid line and red dashed line represent lower and upper bounds respectively from RV measurements of red giants in open clusters in the logarithmic period bin $0.5<P<5\yr$. Blue solid lines with error bars (1$\sigma$ statistical) represent the fraction obtained from AO measurements of A-type stars in two logarithmic bins in the range $50<P<5000\yr$ (based on 5 detected systems in each bin). The blue line in the period bin $5<P<50\yr$ is a rough lower limit (based on the 2 systems detected) in this range which is only partly covered by the AO survey. } \end{figure} Based on these results we expect that \emph{$\mathbf{\sim15-20}$ per cent of WDs have wide orbit ($P\gtrsim 1\yr$) companions which are either (lighter) WDs or massive MS stars ($M>1\Msun$)}\footnote{This does not necessarily apply to low mass WDs, $M_{\rm WD}\lesssim 0.55 \Msun$ whose progenitors with mass $M \lesssim 1.5 \Msun$ were not probed by the samples presented here.}. In order to estimate the fraction of WDs that have a wide orbit WD companion, the fraction of stars with $M>1\Msun$ that have already evolved into WDs needs to be estimated. Assuming the age of our galactic disk is $\sim 9.5 \Gyr$ \citep{oswalt96}, a constant star formation rate (SFR), an initial mass function (IMF) of $dN/dm\propto m^{-2.3}$ \citep{kroupa01} and a MS lifetime of $t_{\rm MS}=10\Gyr(M/\Msun)^{-3}$, we simulate the population of WDs in the galactic disk where for every forming A-type or earlier star ($M>1.5 \Msun$) we assign a $0.17$ chance to be found in a wide orbit with another (lighter) MS companion with $M>1\Msun$ (independent of the companion's specific mass). We find that a fraction of $\sim 60$ per cent of the lighter companions in massive binaries in which the primary already evolved to a WD will also evolve to a WD implying that \emph{$\sim \mathbf{10}$ per cent of WDs have a wide-orbit WD companion.} These expectations can be directly compared with the statistics of observed companions to WDs. Out of the $\approx 120$ WDs with $M>0.5\Msun$ and $D<20\pc$ presented in \cite{holberg16} we would expect $\sim10$ WODDs and $\sim 5$ wide orbit systems with a WD and a MS companion with $M>1\Msun$. In the observed sample there are $3$ WODDs (WD-0727+482, WD-2226-754 and WD-0747+073) and $4$ WD-MS($M>1\Msun$) systems (Sirius B, Procyon B, WD-1544-377\footnote{The companion of WD-1544-377, HD 140901, mass's uncertainty includes $1\Msun$ \citep{pinheiro14}.} and WD-0415-594). The small number of detected WODDs compared to the expectation is unlikely to be due to a statistical fluctuation. This strengthen's previous suspicions that there are missing WDs in multiple systems in the local sample \citep{ferrario12}. \emph{We expect that about $\sim 10$ WODDs be detected within $20\pc$ in the future.} In particular, the GAIA astrometric mission should eventually detect most of these missing systems by resolving the systems with large separations $P\gtrsim 10\yr$ and finding astrometric solutions for the systems with close separations $P\lesssim 10\yr$. If the fraction of WODDs is established to be much smaller than $10$ per cent, this would raise the interesting possibility that many wide massive binaries become unbound before they become WDs. Our estimate of the WODD fraction places a tight constraint on the feasibility of the collision model as a primary channel for type Ia supernovae. Following the same assumptions made above and assuming delay time distribution of type Ia SNe of \cite{maoz12, graur13} we find that $\sim 10$ per cent of WODDs should end up with a collision of the WDs in order to account for the SNe rate. This result can be equivalently obtained by assuming production of $0.1$ WDs and $0.001$ type Ia SNe per $\Msun$ of star formation combined with our result that $\sim 10$ per cent of WDs end up in WODDs. This is in tension with the estimate that only a few percent of triple systems with WODDs having the right hierarchy \citep{katz12} lead to a collision. This suggests that in order for the collision model to work, either the majority of WODDs have a relevant tertiary (leaving a modest discrepancy of order $2$) or that other effects such as higher multiplicity \citep{pejcha13} or passing stars \citep{antognini16} substantially increase the chance for collisions in some of the systems. | 16 | 9 | 1609.03580 |
1609 | 1609.01299_arXiv.txt | Using kinematic maps from the Sloan Digital Sky Survey (SDSS) Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, we reveal that the majority of low-mass quenched galaxies exhibit coherent rotation in their stellar kinematics. Our sample includes all 39 quenched low-mass galaxies observed in the first year of MaNGA. The galaxies are selected with $M_{r} > -19.1$, stellar masses $10^{9}$~M$_{\sun} < M_{\star} < 5\times10^{9}$~M$_{\sun}$, EW$_{H\alpha} <2$~\textrm{\AA}, and all have red colours $(u-r)>1.9$. They lie on the size-magnitude and $\sigma$-luminosity relations for previously studied dwarf galaxies. Just six ($15\pm5.7$~per~cent) are found to have rotation speeds $v_{e,rot} < 15$~km~s$^{-1}$ at $\sim1$~$R_{e}$, and may be dominated by pressure support at all radii. Two galaxies in our sample have kinematically distinct cores in their stellar component, likely the result of accretion. Six contain ionised gas despite not hosting ongoing star formation, and this gas is typically kinematically misaligned from their stellar component. This is the first large-scale Integral Field Unit (IFU) study of low mass galaxies selected without bias against low-density environments. Nevertheless, we find the majority of these galaxies are within $\sim1.5$~Mpc of a bright neighbour ($M_{K} < -23$; or M$_{\star} > 5\times10^{10}$~M$_{\sun}$), supporting the hypothesis that galaxy-galaxy or galaxy-group interactions quench star formation in low-mass galaxies. The local bright galaxy density for our sample is $\rho_{proj} = 8.2\pm2.0$~Mpc$^{-2}$, compared to $\rho_{proj} = 2.1\pm0.4$~Mpc$^{-2}$ for a star forming comparison sample, confirming that the quenched low mass galaxies are preferentially found in higher density environments. | Identifying the processes which drive the quenching of star formation in the observed galaxy population (and therefore the general decline of star formation in our Universe; \citealt{1996MNRAS.283.1388M}) forms one of the most studied topics in modern extragalactic astrophysics. While it has been recognised for decades that both galaxies which are massive, and those found in higher density environments are more likely to reside on the red sequence and be passive/quenched \citep[][]{1998ApJ...504L..75B,2002MNRAS.334..673L,2003MNRAS.341...54K,2006MNRAS.373..469B,2010ApJ...721..193P,2010MNRAS.404.1775T,2016A&A...586A..23D,2016arXiv160503182D,2016ApJ...818..180C}, disentangling these two correlations has proven difficult. It is now generally recognised that both mass and environment play a role in driving the processes which turn off star formation, such that massive galaxies \citep[in any environment, including voids:][]{2015MNRAS.453.3519P} and galaxies in high density environments (of any mass) are observed to be likely to be quenched \citep[e.g.][]{2009MNRAS.393.1324B,2010ApJ...721..193P}. In high density environments (such as large groups or clusters), external processes such as ram-pressure stripping \citep{1972ApJ...176....1G}, tidal harassment \citep{1996Natur.379..613M} or gas strangulation \citep{1980ApJ...237..692L} are effective in shutting down global star formation. Observations of quenched massive galaxies ($M_{\star} > 3\times10^{10}$~M$_{\odot}$) even in voids demonstrate that internal stellar or halo mass-dependent processes such as supernovae or AGN feedback \citep{2008MNRAS.386.2285C}, and perhaps even processes of secular evolution \citep{2015MNRAS.453.3519P} are able to regulate and shut-off star formation in any environment. However, the degree to which such processes can shape the evolution of low mass galaxies is unknown. AGN feedback might help galaxies maintain quiescence \citep{2006MNRAS.365...11C}, and recently \citet{2016Natur.533..504C} demonstrated that low-powered AGN maintenance-mode feedback (``red geyers'') can heat accreted cold gas, preventing new star formation, even if the AGN feedback is not sufficient to initially quench the galaxy. Simulations have shown that supernova feedback can halt star formation in dwarf galaxies by driving out gas \citep[e.g.][]{1986ApJ...303...39D,2007ApJ...667..170S,2014ApJ...785...58G}, however this ejected gas can cool and re-accrete, resulting in bursty star formation histories in isolated dwarf galaxies \citep[e.g.][]{2007ApJ...667..170S}. Winds driven by star formation can also generate these bursty star formation histories \citep{2015MNRAS.454.2691M,2016ApJ...820..131E}. One promising method to isolate the roles in which various processes play in the cessation of star formation, is to identify a sample in which we can be sure that the effect of either environment or galaxy mass on the galaxy's evolution is negligible. In this work we focus our investigation on just the external, or environmental processes by identifying a sample in which internal processes should be unable to completely quench galaxies. Our selection will include low mass galaxies with stellar masses $10^{9} $~M$_{\sun} < M_{\star} < 5\times10^{9}$~M$_{\sun}$. There are few quenched galaxies with low mass found in isolation in the nearby Universe \citep[e.g.][]{2012ApJ...757...85G}, and so it seems clear that they are sufficiently low in mass that internal feedback is inefficient in driving their evolution from star-forming to passive. Galaxies in this mass range are sometimes referred to as dwarf galaxies \citep[e.g.][]{2012MNRAS.419.3167S}, although other studies restrict their dwarf samples to galaxies with $M_{\star} < 10^{9}$~M$_{\odot}$ \citep[e.g.][]{2012ApJ...757...85G}, so in this article we choose to refer to our sample as low mass galaxies rather than dwarf galaxies. Despite being the dominant galaxy population by number in groups and clusters, the formation timescale and mechanism of lower mass galaxies, including dwarf spheroidals (dSph, M$_{r} \gtrsim -14$) and dwarf ellipticals (dEs M$_{r} \gtrsim -19$) are unknown. Like massive galaxies, these lower mass galaxies are observed to follow a clear morphology density relation \citep{1990A&A...228...42B}. This relation is such that dwarf elliptical (dE) and dwarf spheroidal (dSph) galaxies are found primarily in galaxy clusters or at small distances from luminous galaxies in groups, whereas dwarf irregulars (dIrrs) are found in low density regions of the Universe \citep{1990A&A...228...42B}. It therefore seems likely that a large fraction of dE galaxies are late-type galaxies that have been quenched and morphologically transformed by environmental processes \citep{2012ApJS..198....2K,2012ApJ...745L..24J,2013MNRAS.428.2980R}. The majority of studies examining the origin of lower mass galaxies (excluding the Local Group dwarfs) are restricted to the Virgo Cluster \citep[e.g.][]{2001ApJ...559..791C,2006AJ....132..497L,2011A&A...526A.114T,2014ApJ...783..120T}, with a few studies extending to other clusters, or to the group environment \citep[e.g.][]{2014MNRAS.443.3381P,2015MNRAS.453.3635P}. \citet{2008MNRAS.383..247P} show that dEs in clusters exhibit a range of star formation histories, with some exhibiting old stellar populations consistent with them being part of the primordial cluster population, whereas other dEs within the same cluster ceased star formation much more recently, likely being a later accreted population. Using IFU spectroscopy of dEs in the Virgo Cluster, \citet{2015MNRAS.452.1888R} show that dEs can have complex star formation histories, with both old and young ($<5$~Gyr) stellar components contributing to their mass. In the Virgo Cluster, these objects show a strong environmental dependence, such that the slow rotators favour the cluster centre, whereas the fast rotators are typically found at large cluster-centric distances. The cluster dwarf galaxy population therefore appears to be a composite of two subpopulations: an old, non-rotating, pressure-supported population found primarily in the cluster core, and a younger, rotationally supported subpopulation, found to larger cluster-centric radii than the pressure-supported systems \citep{2009ApJ...706L.124L,2011A&A...526A.114T}. These fast-rotating systems are likely the low-mass end of the cluster infall population. Many show embedded discy substructure, as revealed by deep imaging and unsharp-masking techniques \citep[][]{2003A&A...400..119D,2003AJ....126.1787G,2006AJ....132..497L}. Several environmentally-driven mechanisms can quench low-mass star-forming galaxies. In galaxy clusters, ram-pressure stripping by the hot intra-cluster medium can rapidly remove gas from an infalling galaxy in $\sim100$~Myr \citep{1972ApJ...176....1G,1999MNRAS.308..947A,2000Sci...288.1617Q}. However, the effectiveness of this process depends on the gravitational potential of the infalling galaxy, and the size of the galaxy group/cluster, such that low-mass discs falling into massive clusters will be the most strongly stripped. Tidal processes can also drive the evolution of low-mass galaxies. Through frequent high-speed galaxy-galaxy interactions, galaxy harassment transforms the morphology of a galaxy from disc-like to spheroidal, and is again most efficient in the cluster environment \citep{1996Natur.379..613M}. Thus we might expect quenched dEs in groups to exhibit kinematic and morphological differences to those in rich clusters such as Virgo, Coma, and Perseus, making this study of quenched low mass galaxies selected independent of environment or morphology an important addition to the literature. For example, a dwarf galaxy in the core of a dense galaxy cluster will be subject to many more fast galaxy-galaxy interactions than a dE located in e.g. the Local Group. Harassment \citep[e.g.][]{1996Natur.379..613M} is likely more effective at erasing the rotation in the dE's progenitor disc in a rich galaxy cluster vs. a poor galaxy group. The kinematics of galaxies provide information on their assembly history and origins, with coherent rotation revealing a more quiescent merger history \citep[e.g.][]{2014MNRAS.444.3357N}, and/or monolithic collapse \citep{1962ApJ...136..748E}, while pressure supported systems can be created via frequent major mergers or collapse via violent relaxation. A rotationally supported system can be transformed into a pressure supported one through galaxy-galaxy interactions via processing including harassment \citep{1996Natur.379..613M}, while infall of cold gas is thought to be able to create new rotationally supported components in galaxies \citep[e.g.][]{2006MNRAS.373..906M}. This rotationally supported component is likely to be kinematically distinct or even counter-rotating from older components. It has been known for some time that massive galaxies show a range of rotational properties \citep[e.g.][]{1983ApJ...266...41D,1988A&A...202L...5B}, with S0-Sb galaxies exhibiting more rapid rotation than giant ellipticals \citep[e.g.][]{1982ApJ...256..460K}, which is in strong agreement with more recent work. For example, nearby massive galaxies have been divided into two classes based on their stellar angular momenta: fast and slow rotators \citep{2011MNRAS.414..888E}. As shown in \citet{1990A&A...239...97B} and \citet{2015ApJ...799..172T} this split extends to the faint galaxy regime ($M_{r} > -19$). However, the kinematics of dwarf galaxies have not been studied in a large or representative sample to date, nor examined with large IFU surveys. In this paper, we aim to construct a sample of low mass galaxies, with no pre-selection on morphology or environment, utilising data from the the Sloan Digital Sky Survey \citep[SDSS,][]{2000AJ....120.1579Y}. Our sample is selected from the Mapping Nearby Galaxies at APO \citep[MaNGA, ][]{2015ApJ...798....7B} multi-object IFU survey, which is in the process of observing a representative sample of $\sim10$k galaxies from the SDSS Main Galaxy Sample \citep{2002AJ....124.1810S}, elected to produce a roughly flat stellar mass distribution with $M_{\star}>10^9$~M$_{\sun}$ (calculated using a \citet{2003PASP..115..763C} Initial Mass Function). We define a low mass galaxy to be any galaxy with a luminosity or stellar mass comparable to, or smaller than, that of the Large Magellanic Cloud ($M_{r} \sim -18.6$, $\sim 3\times 10^{9}$~M$_{\odot}$, \citealt{2002AJ....124.2639V}). To compile our sample, we therefore select all galaxies in the first year of MaNGA observations that are low mass ($<5\times10^{9}$~M$_{\sun}$), low luminosity ($M_{r} > -19$), and have no evidence for ongoing star formation. A second paper (Penny et al., in prep.) will examine the stellar angular momentum of our faint quenched galaxy sample. This paper is organised as follows. In Section~\ref{sec:sampsel}, we discuss our sample selection, with a description of the MaNGA survey provided in Section~\ref{sec:manga}, the quenched low mass galaxy selection in Section~\ref{sec:qsamp}, and the local environment of each galaxy in Section~\ref{sec:lenv}. Our results are presented in Section~\ref{sec:results}, including results for two low mass quenched galaxies hosting kinematically distinct cores (Section~\ref{sec:kindes}). We discuss our results in Section~\ref{sec:discuss}, and conclude in Section~\ref{sec:conclude}. We will apply no environmental or morphological selection to our sample, which is selected from galaxies observed by the Sloan Digital Sky Survey (SDSS) galaxy integral field unit (IFU) survey MaNGA (Mapping Nearby Galaxies at Apache Point Observatory) purely on luminosity (as a proxy for mass) plus indicators of current star formation (a combination of optical colour and emission line strengths). This paper is therefore the first in which the origin of quenched low mass galaxies across a range of environments is studied with a large and representative IFU sample. The only previous IFU studies of low mass galaxies to date have been confined to Virgo \citep{2013MNRAS.428.2980R,2015ApJ...804...70G}, with the exception of \citet{2013MNRAS.428.2980R} who examine IFU spectroscopy for just three dEs selected from the field. Throughout this paper, we assume a cosmology with $\Omega_{\Lambda}=0.7$ and $\Omega_{M}=0.3$, and $H_{0} = 100h$~km~s$^{-1}$~Mpc$^{-1}$, unless otherwise noted. | \label{sec:conclude} We have examined the kinematics of 39 quenched low luminosity galaxies in the MaNGA survey with $M_{r} > -19.1$. The majority (37/39) are located within $\sim1.5$~Mpc and $\pm1000$~km~s$^{-1}$ of a luminous neighbour with $M_{K} > -23$, with a median separation of 184~kpc, confirming the result of \citet{2012ApJ...757...85G} that a massive neighbour is required to quench star formation in low mass galaxies. The faint quenched galaxies have half-light radii $0.64~\textrm{kpc} < R_{e} < 2.57$~kpc, and velocity dispersions ($<$)40~km~s$^{-1} < \sigma_{e} < 128$~km~s$^{-1}$. The majority of our sample lie on the size-magnitude and $\sigma$-luminosity relation for bright dwarf elliptical galaxies, though five objects with $\sigma > 100$~km~s$^{-1}$ are likely low-luminosity ``classical'' ellipticals rather than dwarf galaxies. Kinematic maps reveal the majority of the low-mass quenched MaNGA galaxies to be rotating, with clear disc-like structure seen in many dwarf galaxies of comparable magnitude. Given this result, and that the low mass quenched galaxies are primarily found in galaxy groups/clusters at small separation from a bright neighbour galaxy, we suggest that most of our sample are quenched/passive spiral galaxies that have been stripped of star forming material, but have not undergone sufficient tidal interactions to completely erase their substructure. This is in contrast to smooth dEs observed in clusters such as e.g. Virgo where galaxy harassment is able to operate more efficiently to morphologically transform low-mass disc galaxies into dEs. Two galaxies, MaNGA~1-113520 and MaNGA~1-255220 show counter-rotation in their stellar kinematics with their velocity profiles turning over at $<1$~$R_{e}$, and furthermore exhibit distinctive 2$\sigma$ peaks in their stellar velocity dispersion maps. These two objects host counter-rotating stellar discs, likely the result of a recent gas accretion event, but may have a tidal origin. As we have a relatively small sample size of 39 galaxies, this result suggests low mass galaxies hosting kinematically decoupled cores may be relatively common. While the majority of low-mass quenched galaxies in our sample are emission-line free objects, six exhibit weakly-ionised gas emission throughout their structures, with $H\alpha_{EW} < 2$~$\textrm{\AA}$. The two galaxies with KDCs exhibit rotation in their ionised gas component, and this the gas is kinematically misaligned with their stellar component. Four other dwarfs in our sample also have measurable rotation in their ionised gas component, again kinematically-offset from their stellar components. As this gas does not share the same angular momentum as the stellar component, we suggest this kinematic misalignment is the result of accretion. However, we also note that counter-rotating gas that is kinematically offset by $180^{\circ}$ can occur without the need for accretion due to relaxation. MaNGA has observed 39 quenched low mass galaxies in its first 12 months of observing, we can expect this sample size to grow to $\sim200$ galaxies upon completion of the project. For the first time, the spatially resolved dynamics and star formation histories of low mass galaxies will be examined using a statistically significant sample, and compared to their high-mass counterparts. In future work, for those low-mass galaxies with sufficiently high velocity dispersions, we will determine the fraction of fast vs. slow rotators in this mass regime, and compare these fractions to those found in high-mass galaxies. We will also examine the quenching timescales of the faint galaxy sample. | 16 | 9 | 1609.01299 |
1609 | 1609.08692_arXiv.txt | Most current high contrast imaging point spread function (PSF) subtraction algorithms use some form of a least-squares noise minimization to find exoplanets that are, before post-processing, often hidden below the instrumental speckle noise. In the current standard PSF subtraction algorithms, a set of reference images is derived from the target image sequence to subtract each target image, using Angular and/or Simultaneous Spectral Differential Imaging (ADI, SSDI, respectively). However, to avoid excessive exoplanet self-subtraction, ADI and SSDI (in the absence of a strong spectral feature) severely limit the available number of reference images at small separations. This limits the performance of the least-squares algorithm, resulting in lower sensitivity to exoplanets at small angular separations. Possible solutions are to use additional reference images by acquiring longer sequences, use SSDI if the exoplanet is expected to show strong spectral features, or use images acquired on other targets. The latter option, known as Reference Star Differential Imaging (RSDI), which relies on the use of reference images that are highly correlated to the target image, has been ineffective in previous ground-based high contrast imaging surveys. The now $>$200 target reference library from the Gemini Planet Imager Exoplanet Survey (GPIES) allows for a detailed RSDI analysis to possibly improve contrast performance near the focal plane mask, at $\sim$2-7 $\lambda/D$ separations. We present the results of work to optimize PSF subtraction with the GPIES reference library using a least-squares algorithm designed to minimize speckle noise and maximize planet throughput, thus maximizing the planet signal to noise ratio (SNR). Using December 2014 51 Eri GPI data in the inner 100 mas to 300 mas annulus, we find no apparent improvement in SNR when using RSDI and/or our optimization scheme. This result, while still being investigated, seems to show that current algorithms on ADI+SSDI data sets are optimized, and that limited gains can be achieved by using a PSF archive. | \label{sec: intro} In the search to detect and characterize exoplanets by direct imaging, the best achievable contrast requires suppression effects from both a realtime adaptive optics (AO) and coronagraphic system as well post-processing of these images to remove the residual point spread function (PSF). Current state of the art PSF subtraction algorithms are limited in sensitivity at small angular separations from the on-axis PSF, close to the coronagraph's focal plane mask (FPM). Exoplanet population predictions suggest that with the current generation of high contrast imaging instruments, more detections are possible at smaller separations\cite{gpi_planets}, or alternatively there could be additional planets in existing data that could be seen with better post-processing sensitivity. It is suggested that the distribution of radial-velocity detected planets as a function of separation follows an inverse power law\cite{rv_planets}, continuing to wider separations accessible by direct imaging\cite{gdps}, and thus improved post-processing performance at smaller angular separations is of great interest to the exoplanet community. The main factor limiting PSF subtraction performance near the inner working angle (IWA) is the selection criteria for angular differential imaging (ADI)\cite{adi} and simultaneous spectral differential imaging (SSDI)\cite{ssdi1,ssdi2,ssdi3}. This selection criteria requires that reference images, used in some form of a least-squares-based\cite{loci, klip} PSF subtraction algorithm, have a certain planet signal threshold (known as ``aggressiveness'') to limit planet self-subtraction in the target image. The amount of field of view (FOV) rotation or spectral magnification required with ADI or SSDI, respectively, usually between $\sim$1.5 and 3 $\lambda/D$, limits fewer available references from the target sequence at smaller separations (i.e., with SSDI, for a flat spectrum, compared to a larger separation, diffraction at a smaller separation moves speckles a smaller absolute radial distance as a function of wavelength\footnote{For a spectrum with strong spectral features like methane absorption, the selection criteria will allow many more references to include in the least-squares at the peak vs. trough of the spectrum, thus ``counteracting'' the small angular separation selection bias.}, and with ADI, at a set FOV rotation, arc length decreases with decreasing radial separation). Thus, this ADI+SSDI selection effect limits the optimal PSF subtraction sensitivity to planet detection at small angular separations near the instrument IWA. A solution to this problem is reference star differential imaging (RSDI), where PSF subtraction on a target image that may contain a hidden planet can access a large archive of ``planet-less'' references images. The key to increasing sensitivity at small IWA using RSDI, as with any PSF subtraction technique, is to use a set of reference images that are highly correlated to the target image. With this in mind, the archival legacy investigations of circumstellar environments (ALICE) pipeline\cite{alice} was recently developed for \textit{Hubble Space Telescope} (\textit{HST}) PSF subtraction, mostly to recover disks, but no ground-based first generation AO surveys, generally accessing a higher sensitivity and smaller IWA than \textit{HST}, have yet acquired enough data for RSDI in the $\sim$2-7$\lambda/D$ regime\footnote{Ground-based RSDI was initially attempted with pervious-generation generation high contrast imaging surveys beyond $\sim$7 $\lambda/D$, but with no performance gain, likely due to stability issues (e.g., Galicher et al. 2016, submitted)}. With the next generation of high contrast imaging instrument surveys such as the Gemini Planet Imager Exoplanet Survey (GPIES)\cite{gpies}, we can test the performance of RSDI down to $\sim$2 $\lambda/D$. Our initial work on this topic acts as demonstrator for RSDI performance gain in this regime with future high contrast imaging survey instruments. In this paper, we present an analysis using GPIES to increase planet sensitivity near the IWA with a least-squares-based RSDI algorithm. In \S\ref{sec: lib} we describe our procedure used to create PSF library reference images, in \S\ref{sec: algo} we outline the specifics of our algorithm, in \S\ref{sec: results} we present the results of our algorithm applied to December 2014 GPI 51 Eri data\cite{51eri}, and in \S\ref{sec: conclusion} we summarize our work and consider possible future improvements. This analysis is based entirely on GPI H band 51 Eri target sequence data from December 2014\cite{51eri} and an additional PSF library archive from the GPIES campaign through December 2015. We only consider performance close to the edge of the FPM ($\sim$125 mas)\cite{gpi_coron} in the inner 100 mas to 300 mas annulus. Matching the 51 Eri b detection, all of the following analysis is carried out using a methane (T8) dwarf spectrum. We use zero indexing to refer to frames and slices in the target sequence. We use a GPI pixel scale of 14.166 mas/spaxel, determined from all GPIES and lab astrometric data\cite{plate_scale}. We note that a similar RSDI procedure with GPIES was recently developed using the Karhunen-Lo{\`e}ve Image Projection (KLIP) algorithm\cite{klip}, mostly designed for broadband disk detection (M. Millar-Blanchaer et al., in prep) and broadband planet detection at wider separations (D. Vega et al, in prep), and so the work presented in this paper is complimentary, instead using a least-squares designed for small IWA planet detection and spectral extraction. | \label{sec: conclusion} ADI and SSDI limit PSF subtraction sensitivity to detect and characterize planets at small angular separations. This problem can be addressed using RSDI. RSDI on ground-based high contrast imaging instruments at $\sim$2-7 $\lambda/D$ has only recently become possible with sufficient campaign data from the Gemini Exoplanet Imaging Survey (GPIES)\cite{gpies}. Our main conclusions are as follows: \begin{itemize} \item We have developed a new method of optimized RSDI PSF subtraction using the SOSIE\cite{sosie} and TLOCI\cite{tloci} least-squares formalism, which includes \begin{enumerate} \item reference image selection based on an input spectral template and robust correlation to the target image, \item an ensemble of PSF library reference images that removes any planet signal through medianing, many of which are correlated enough to images in the target sequence to allow using RSDI, \item an improved planet throughput compared to the LOCI\cite{loci} formalism, based on an optimization and subtraction region masking scheme and a subsequent forward model (FM) throughput correction, and \item an optimization routine designed to maximize the planet SNR as a function of the number of reference images and aggressiveness. \end{enumerate} \item When running this PSF subtraction routine on the inner 100 to 300 mas annulus of the GPI December 2014 51 Eri dataset\cite{51eri}, we find \begin{enumerate} \item no obvious planet detection, \item when bootstrapping a fake methane planet into the raw datacubes, there is no apparent gain in planet SNR when adding the PSF library and/or using our FM optimization scheme compared to current non-RSDI-based PSF subtraction methods. \end{enumerate} \end{itemize} These results present the first attempt to improve planet SNR using RDSI in the $\sim$2-7 $\lambda/D$ regime. This method should be further explored in the context of current and future high contrast imaging survey instruments working near the diffraction limit. Future work on this initial study will proceed for a number of different topics. However, for any further adjustments to the optimized code, the first step is to parallelize the now serial Python-based optimization code so that it can reduce the full sequence in only a few hours on our 16 core machine rather than $\sim$24 hours. Afterwards, there are a number of different possible avenues to explore: \begin{itemize} \item Understand the discrepancy between input and output bootstrap signal near the T8 peak, perhaps originating from problems with applying our FM throughput correction in this regime. This throughput loss may also be affecting our FM SNR optimization scheme. \item Test performance of the three codes using additional spectral templates, such as a DUSTY\cite{dusty} spectrum, which should be less effective than a methane spectrum when using SSDI due to the lack of spectral features, thus more sensitive to increased performance with RSDI. \item Test performance of different optimization and subtraction region geometries, e.g., using all or portions of the adjacent, more outer annulus and/or portions of the inner annulus to define the optimization region geometry, still not overlapping with the subtraction region. The rational here is that there could be a more optimal geometry that samples the noise of the subtraction region rather than assuming azimuthal symmetry in the same annulus (e.g., assuming radial symmetry). \item To further investigate the performance tradeoff between a linear least-squares and a NNLS, include a loop in the linear least-squares to optimize the SVD cutoff. Although we found that using two subtraction regions consistently gave the highest FM SNR, we found that the optimal SVD cutoff varied between $10^{-3}$ and $10^{-4}$. We did not include a loop to optimize this parameter due to computational limits, which would have at minimum doubled the overall computation time in serial. However, there may be little or no gain from adding such a loop, since optimizing the SVD cutoff is similar to optimizing the number of references. \item Create PSF library images by medianing only across wavelength. This could allow for a greater ensemble of references from which to choose. However, medianing only in wavelength is also less effective at medianing out the planet flux in the inner annulus, and so there may be additional throughput effects from this. The rational here is that by median collapsing in time and wavelength, we could be missing a potentially more correlated PSF library image due to time instability. \item Run the tar+lib opt code on the all of the GPIES campaign data acquired thus far to search for any undetected planets already in the existing data, using multiple spectral templates. Most datasets are far less ideal than our 51 Eri data set, particularly in stability and FOV rotation, for which the former and the latter can be improved by using an SNR optimization scheme and a PSF library, respectively. Thus, RSDI and/or FM SNR optimization may show more improvement on other targets. \end{itemize} | 16 | 9 | 1609.08692 |
1609 | 1609.03639_arXiv.txt | Natures of progenitors of type Ia Supernovae (SNe Ia) have not yet been clarified. There has been long and intensive discussion on whether the so-called single degenerate (SD) scenario or the double degenerate (DD) scenario, or anything else, could explain a major population of SNe Ia, but the conclusion has not yet been reached. With rapidly increasing observational data and new theoretical ideas, the field of studying the SN Ia progenitors has been quickly developing, and various new insights have been obtained in recent years. This article aims at providing a summary of the current situation regarding the SN Ia progenitors, both in theory and observations. It seems difficult to explain the emerging diversity seen in observations of SNe Ia by a single population, and we emphasize that it is important to clarify links between different progenitor scenarios and different sub-classes of SNe Ia. | \label{aba:s1} There is almost no doubt that Type Ia Supernovae (SNe Ia) are thermonuclear explosions of a C+O white Dwarf (WD) in a binary system. SNe Ia are one of the most matured standardized candles that led to the discovery of the accelerating expansion of the Universe,\cite{phillips1999,permutter1999,riess1998} and further improvement as the cosmological distance indicator, to the level to constrain the `Dark Energy Equation of State' by SN Ia observational data, requires the better understanding of the progenitor system and the explosion mechanism. SNe Ia also play a key role in the chemical enrichment of galaxies and the Universe,\cite{matteucci1986,kobayashi1998} and our understanding of SNe Ia is directly linked to the origin of major chemical species. Involving the binary evolution as a major ingredient to form an immediate progenitor star, studying SNe Ia also provides a key input to clarify many unresolved issues in the binary evolution.\cite{ruiter2009} Several progenitor scenarios have been proposed for SNe Ia. There are many variants in details, but they are basically categorized into the following classes; the single-degenerate (SD), double-degenerate (DD), and core-degenerate (CD) scenarios. In the SD scenario, a C+O WD accretes materials from its non-degenerate companion star (either a main-sequence, MS, or a red giant, RG) and reach to the Chandrasekhar limiting mass.\cite{whelan1973,nomoto1982} The DD scenario involves a merger of two WDs,\cite{iben1984,webbink1984} and the CD scenario involves a merger of a WD and an asymptotic giant branch (AGB) star in a binary system.\cite{sparks1974,soker2015} | \label{aba:summary} There are variants of SN Ia progenitor and explosion models, and no single model seems to be perfect to satisfy all the observational constraints available to date. Given the large diversity of SNe Ia in various observables, it is indeed possible that SNe Ia are originating from multiple populations. Furthermore, there are always theoretical uncertainties to interpret the data, and indeed it is risky to rely on a single observational approach to discriminate different models. Keeping all of these caveats in mind, we hope that the summarizing list of the comparisons between the models and observations (Tab. 1) serves as a useful guide for future works. So far, assigning the progenitor paths to outliers seems like more straightforward than for normal SNe Ia, at least at a quick look. Possible detections of a companion star in a pre-SN image of SN Iax 2012Z and a possible companion or a left-over compact remnant in a post-SN image of SN Iax 2008ha indicate that these systems could be related to the SD channel. However, the difference in the natures of these detected objects is puzzling, i.e., a blue source for SN 2012Z and a red source in SN 2008ha, and it requires both theoretical investigation and further follow-up of these SNe. Also, we should stress that even if the blue source in the pre-SN image of SN 2012Z would be solidly identified as a He companion star, it should raise another important question regarding the link between the progenitor scenario and the explosion mode. Indeed, the most popular explosion model for SNe Iax, the failed deflagration model, is associated either with a RG/MS companion or no companion, in apparent contradiction to the blue source. For other classes of outliers, the inferred link is mostly based on the diagnostics through CSM. A strong argument for an association to the SD scenario exists for SNe Ia-CSM (but note that it is also consistent with the CD model). A huge mass loss before the explosion is required, pointing to an RG companion or an association to recurrent novae. It seems that a main fraction of SNe Ia-CSM are associated with SN 1991T-like SNe. A question then is if the opposite is a case -- namely, whether most (or all) SN 1991T-like SNe are associated with massive CSM. A recent work on Kepler SNR is very indicative, which suggests that SN 1991T-like SNe could be generally associated with massive CSM. This could be most naturally explained by a variant of the SD model in a system with a huge mass loss. As for over-luminous SNe (i.e., Super-Chandrasekhar candidates), recently there is a suggestion that at least one over-luminous SN Ia is associated with massive CSM, either an RG wind or nova shells. While there is still a single example, this could indicate that over-luminous SNe Ia might be related to the SD channel. The details of the explosion nature is however not yet clear. Finally, there are a number of observational constraints placed for normal SNe Ia, and the situation is less clear than for the outliers. Indeed, one has to take it in mind seriously that the apparent links between the outliers and the progenitor scenarios (as mentioned above) may merely reflect a small number of constraining observations for these outliers, and once the observational data are increasing the situation may well become more complicated than currently believed -- the same situation as normal SNe Ia have been encountered. Still, the advantages and disadvantages for different scenarios suggest (at least to the authors) that the delayed detonation is the best model for a mode of the explosion, while the information related to the environment (companion and CSM) generally prefers the DD scenario (or ones predicting the clean environment, e.g., a spin-up/down scenario in the SD model). So, if we simply rely on the score sheet for each scenario like Tab. 1, the explosion of Chandrasekhar mass WD through the secular evolution after the WD-WD merger could be a straightforward interpretation. However, this is still too early to make this strong conclusion, as many questions/challenges have been raised for this scenario from different directions as well, including whether the system can avoid the off-center deflagration (not to form an ONeMg WD), whether the number of such systems are sufficiently large to account for the main population of normal SNe Ia, and so on. Also, one should note that there is at least one normal SN Ia showing a possible signature of a non-degenerate companion, and at least a fraction of normal SNe Ia show the association with detectable CSM. Another important issue in the progenitor scenario of normal SNe Ia is that relations to the outliers must be considered self-consistently. One might jump onto the conclusion that normal SNe Ia are from the DD systems and outliers are from the SD systems, but this is probably an oversimplification. For example, the existence of at least a single path of the SD systems may indeed suggest that there must be other variants of the SD systems as well. Also, it is not trivial if the SD and DD can coexist to contribute to different populations of SNe Ia, since the evolutionary processes toward the SD and DD are coupled -- for example, the existence of the SD channel suggests that the common envelope evolution must be avoided for those systems while the DD generally requires the common envelope evolution. | 16 | 9 | 1609.03639 |
1609 | 1609.05912_arXiv.txt | A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither complement it by theoretical framework, nor provided satisfactory fit for their dependence on mutual inclinations. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations, which accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov-Kozai cycles and evection. We generalize the Hill-stability criteria to arbitrarily inclined triple systems, explain the existence of quasi-stable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numerical study, to test our analytic results. We find excellent correspondence up to high inclinations $(\sim120^{\circ}$), beyond which the agreement is marginal. At such high inclinations the stability radius is larger, the ratio between the outer and inner periods becomes comparable, and our secular averaging approach is no longer strictly valid. We therefore combine our analytic results with polynomial fits to the numerical results to obtain a generalized stability formula for triple systems at arbitrary inclinations. Besides providing a generalized secular-based physical explanation for the stability of non co-planar systems, our results have direct implications for any triple systems, and in particular binary planets and moon/satellite systems; we briefly discuss the latter as a test case for our models. | The three-body problem is an old topic in celestial mechanics, with wide astrophysical applications in the Solar system and beyond \citep{V08, I97, Holman97}. Hierarchical triple systems are systems in which an inner binary orbits a more distant object on an outer orbit, with some mutual given inclination between the inner and outer orbits. A fundamental aspect of a hierarchical triple system is its stability. A system is considered stable if no collision or escape of one of the bodies occurs after a large number of orbital periods. The natural length scale of stability is the mutual Hill radius $r_{H}=a_{out}(\mu/3)^{1/3}$, where $a_{out}$ is the distance from the distant outer body with mass $m_{out}$ to the center of mass of the binary and $\mu\equiv(m_{1}+m_{2})/m_{out}$ is the binary to perturber mass ratio. The Hill radius is centered on the center of mass of the inner binary. In the case of the test particle limit $m_1 \gg m_2$ the Hill radius is centered on $m_1$. If the inner binary semi-major axis (SMA) is larger than the Hill radius $a_{in}>r_{H}$, the binary is unstable, since tidal forces from the perturber shear apart the binary. Conversely, if $a_{in}\ll r_{H}$, then the binary is stable and the perturbations from $m_{\text{out}}$ are small. Early studies of \emph{co-planar} triple systems \citep{1967torp.book.....S,Henon70, HB91} have shown that prograde orbits are stable for $a_{in}\approx0.5r_{H}$ while retrograde orbits are stable for twice the distance. The first analytic study to explore the critical stability radius at \emph{arbitrary} inclination was done by Innanen \citep{1979AJ.....84..960I,I80}. He finds that the critical stability radius is an \emph{increasing} function of the inclination, thus the most stable orbits are retrograde, consistent with previous results of co-planar orbits. However, numerical simulations show that the critical radius is compatible with the analytical expectation only for moderately inclined orbits. For highly inclined orbits, the critical radius starts to decrease at $\sim60^{\circ}$, and increases again only at higher inclinations, forming form a bowl-like shape (see Fig. \ref{fig:1} and Fig. 15 of \citealp{HB91}). \begin{figure} \begin{centering} \includegraphics[width=0.45\textwidth]{fig1_revised} \caption{Numerical stability map. The initial conditions for stability map are described in sec. \ref{subsec:Numerical-set-up}. Left: Blue pixel indicates stable orbit, red pixel \label{fig:1} is unstable orbit. The stability map is morphologically similar to \protect\cite{HB91} (their Fig. 15).} \end{centering} \end{figure} The general equations of motion of the three-body problem cannot be solved analytically \citep{ValtonenBook2006}, however secular averaging analysis can be used to describe a wide range of cases. For hierarchical systems, pioneering works of \citet{Lidov62} and \citet{Kozai62} have shown that the torque of the outer binary can induce significant quasi-periodic oscillations in the inclination and eccentricity of the inner binary over long, secular timescales, under certain configurations. The Lidov-Kozai (LK) mechanism is obtained by double averaging (DA) over the orbits. The averaging process does not take into account short period terms that affect the secular evolution. \citet{CB04} considered corrections due to evection and Lunar theory for circular perturbers in the context of irregular moons around giant planets. Recently, a critical analysis of the DA technique and its correction, as well as generalization of \cite{CB04} for arbitrary inclination and eccentricity was studied by \cite{Katz16}. In previous analytic studies of Hill stability, the impact of secular evolution, and in particular Lidov-Kozai cycles were not fully addressed. Numerical studies provided insights and phenomenological mapping for the stability criteria of such systems \citep{HB91,Nesvorny03,Frouard10,Domingos06}, but did not explain their physical origin, nor provided analytic derivations and satisfactory fits for the the dependence of stability on the mutual inclinations. In this paper we account for secular evolution in exploring the stability of triple systems (namely the LK mechanism and evection), and provide a physical understanding of its behaviour. In addition, we perform an extensive numerical three-body study of the stability criteria, confirming our analytic solutions (finding excellent correspondence up to high inclinations) and complement them in regimes where the secular averaging approach we use is no-longer valid. For hierarchical two-planet systems, the Lagrange-stability using resonance overlap has been studied in \citet{Veras04, M08}, while empirical stability criteria are obtained in \citet{Ma2001} and more recently in \citet{P15}. In this paper we deal with the Hill-stability of hierarchical systems in mass. The paper is organized as follows. In Sec. \ref{sec:2} we briefly provide the background for previous analytic study of the instantaneous Hill stability at arbitrary inclinations based on \cite{I80}. In Sec. \ref{sec:Novel-Lidov-Kozai-Hill-secular} We first describe the LK mechanism, and then couple it to stability analysis. We then show how secular evolution affects the results, explaining the discrepancy between \cite{I80} and \cite{HB91}. In Sec. \ref{sec:Evection-and-Lunar} we explore how evection further improves the stability analysis. In Sec. \ref{sec:Numerical-parameter-space}, we numerically integrate the three-body problem to confirm and complement our analytic approach, providing a generally useful fitting formula for triple stability at arbitrary inclinations. Finally we discuss our results and their implications and summarize in Sec. \ref{sec:Discussion-and-summary}. | \label{sec:Discussion-and-summary} In this paper we have developed a generalized stability criteria for triple systems with arbitrary mutual inclination, and extended the Hill stability criteria to account for secular evolution and evection resonance. We used analytic arguments to derive the critical stability criteria and complemented them with extensive three-body simulations. Using these we also provided a convenient polynomial fitting formula for the stability criteria. The comparison between the analytical theory and numerical integrations is excellent, reproducing the morphology of the stability map, the amplitude and the "turn-off point" of the bowl-like-shaped stability region. In addition, the break up time-scales for highly inclined orbits is comparable with the quasi-secular Lidov-Kozai timescale, and much longer than the orbital period of the binary. This indicates that the mechanism that drives the highly inclined binaries to instability is indeed of secular nature, rather than a dynamical Hill instability. In addition, the maximal eccentricity attained in the numerical integrations is compatible to the maximal eccentricity predicted by the analytic theory. Though the analytic theory well describes prograde orbits, there is a significant discrepancy for retrograde orbits at high inclinations beyond $i\gtrsim120^{\circ}$. At sufficiently large separations of $a/r_{H}\gtrsim0.6$, the inner orbit of the triple is strongly perturbed by the outer companion and the orbit is no longer Keplerian. In addition, the timescales of the inner and outer binaries are comparable and the averaging method we use is no longer valid. The latter is evident in the eccentricity map of Fig. \ref{fig:e_max}, where co-planar retrograde orbits, far from the Lidov-Kozai oscillation regime, also evolve into large eccentricities. For retrograde inclinations close to $180^{\circ}$, the analytic critical stability radius poorly describes the critical stability radius. Properly sampling the parameter space yields a chaotic transition boundary, which width increases for retrograde orbits. In this regime the critical stability strongly depends on the initial phase and orientation of the binary, such that the transition from stable to unstable orbits stretches to the range of $0.7\lesssim a/r_{H}\lesssim1$. As an example we considered an application of our results for Solar System satellites. Our findings shed light on the binomial inclination distributions of irregular satellites \citep{2005AJ....129..518S,2015ARA&A..53..409W}. In particular, the largest inclinations of prograde satellites is near $\sim60^{\circ}$ ($57^{\circ}$ for Margaret, a moon of Uranus) and $\sim130^{\circ}$ for retrograde satellites ( $\sim136.5^{\circ}$ for Neso, a moon of Neptune). At least for prograde satellites, the critical angle of $\sim60^{\circ}$ is well explained by the evection corrections to the LK mechanism, as we show (see also \citealp{CB04}). | 16 | 9 | 1609.05912 |
1609 | 1609.00640_arXiv.txt | We present average $R$-band optopolarimetric data, as well as variability parameters, from the first and second \rbpl~observing season. We investigate whether gamma-ray--loud and gamma-ray--quiet blazars exhibit systematic differences in their optical polarization properties. We find that gamma-ray--loud blazars have a systematically higher polarization fraction (0.092) than gamma-ray--quiet blazars (0.031), with the hypothesis of the two samples being drawn from the same distribution of polarization fractions being rejected at the $3\sigma$ level. {We have not found} any evidence that this discrepancy is related to differences in the redshift distribution, rest-frame $R$-band luminosity density, or the source classification. The median polarization fraction versus synchrotron-peak-frequency plot shows an envelope implying that high synchrotron-peaked sources have a smaller range of median polarization fractions concentrated around lower values. Our gamma-ray--quiet sources show similar median polarization fractions although they are all low synchrotron-peaked. We also find that the randomness of the polarization angle depends on the synchrotron peak frequency. For high synchrotron-peaked sources it tends to concentrate around preferred directions while for low synchrotron-peaked sources it is more variable and less likely to have a preferred direction. We propose a scenario which mediates efficient particle acceleration in shocks and increases the helical $B$-field component immediately downstream of the shock. | % \label{sec:introduction} Active galactic nuclei (AGN) are the small fraction of galaxies ($\sim 7\,\%$, \citealt{1995PASA...12..273R}) that appear to have nuclear emission exceeding or comparable to the total stellar output. Of all members of the AGN class, ``blazars'' are both the most variable sources and the sources that are most common in the gamma-ray sky \citep{2012ApJS..199...31N,2015ApJS..218...23A}. With defining characteristic the close alignment of their confined plasma flow to our line of sight and the often relativistic speeds involved \citep{1979ApJ...232...34B}, their jet dominates the emission, generally outshining the host galaxy. Blazars emit radiation throughout the electromagnetic spectrum -- through synchrotron at lower frequencies, and through inverse Compton, and possibly hadronic processes, at high frequencies. Owing to its synchrotron character, the blazar jet emission at energies around and below optical frequencies is expected to be polarized. The polarization levels depend mostly on the degree of uniformity of the magnetic field at the emission element \citep{1970ranp.book.....P}. The mere detection of some degree of polarization already implies some degree of uniformity in the magnetic field \citep[e.g.][]{1972Ap&SS..19...25S} and provides a handle for understanding its topology and strength at the source rest-frame, assuming that the polarized radiation transmission can be modeled accurately. In blazars, both the linear polarization degree and angle can show variations over a range of time scales and magnitudes \citep{1972ApJ...175L...7S,1998AAS...19310714Y,2010PASJ...62...69U}. The polarization angle often goes through phases of monotonic transition (``rotations'') between two limiting values \citep{1988A&A...190L...8K}. The detection of such events that specifically appeared to be associated with episodic activity at high energies \citep{2008Natur.452..966M,2010ApJ...710L.126M, 2010Natur.463..919A,2014A&A...567A.135A} prompted the use of rotations as a tool to probe the inner regions of AGN jets and gave rise to a series of different scenarios about the physical processes that may be causing them. In order to pursue a systematic investigation of optical polarization properties and the polarization plane rotations of blazars, we initiated the \rbpl\ high cadence polarization monitoring program \citep{2014MNRAS.442.1706K,2014MNRAS.442.1693P}. The aim of the program is to study an unbiased subset of a photon-flux limited sample of gamma-ray--loud (GL) AGN, as well as smaller ``control'' sample of gamma-ray--quiet (GQ) blazars. The main scientific questions that the program was designed to address are: \begin{enumerate} \item Do temporal coincidences between activity at high energies and polarization rotations indeed imply a physical connection between the events? \item What is the temporal polarimetric behavior of blazars? \item Do the optical polarization properties of GL and GQ blazars differ in a systematic fashion? And are the optical polarization and gamma-ray emission independent, or driven by the same process and hence causally connected? \end{enumerate} First results on the first two questions have been presented in \citet{2015MNRAS.453.1669B} and \citet{2016MNRAS.457.2252B}. In this paper, we focus on the third question: the optopolarimetric differences between GL and GQ blazars. On the basis of the exploratory observations conducted during and shortly after the instrument commissioning, \cite[2013 May -- July,][hereafter: Survey Paper]{2014MNRAS.442.1693P}, we found a significant difference ($3 \sigma$ level) in the values of the polarization fraction between GL and GQ sources as measured in a single-epoch survey. The current paper uses data from the first two \rbpl~observing seasons to verify whether there is indeed a divergence between the two samples and investigate what may be causing it. The paper is organized as follows: \S \ref{sec:sample_descr} briefly discusses the blazar samples and observations used in this work. The higher-level data products that we use are presented in \S \ref{sec:products} along with the maximum likelihood methods used in the estimation of intrinsic mean values. In \S \ref{sec:analysis} we present a number of studies aiming at investigating the possible dependence of the polarization on other source properties. In the same section, we test for consistency of polarimetric properties between GL and GQ sources. Finally, in \S \ref{sec:discussion} we summarize and discuss our findings within the framework of a shock-in-jet model. | Summary of the GL and GQ sources that were observed at least once during the first two \rbpl~seasons. For each study we present here we use the subset of the table that satisfies the relevant requirements. Columns: (1) and (7) the \rbpl~ID; (2) and (8) source survey name; (3) and (9) mark whether the source is in the TeV \rbpl~or the F-GAMMA program; (4) and (10) the 2FGL classification; (5) and (11) source redshift; (6) and (12) number of measurements.} \begin{tabular}{llllrrcllllrr} \hline ID &Survey ID &Other$^1$ &Class$^2$ &\mc{1}{c}{z} &N & &ID &Survey ID &Other$^1$ &Class$^2$ &\mc{1}{c}{z} &N \\ (RBPL ...) & & & & & & &(RBPL ...) & & & & & \\ \hline \mc{6}{c}{\bf Monitored Gamma-ray-loud (GL) sources} & & & & & & &\\ J0045$+$2127 &GB6J0045$+$2127 & &bzb &\ldots & 23 & &J1121$-$0553 &PKS1118$-$05 & &bzq &1.2970 & 1 \\ J0114$+$1325 &GB6J0114$+$1325 & &bzb &2.025 & 20 & &J1132$+$0034 &PKSB1130$+$008 & &bzb &0.6780 & 2 \\ J0136$+$4751 &OC457 &F2 &bzq &0.859 & 24 & &J1159$+$2914 &Ton599 &F12 &bzq &0.7250 & 1 \\ J0211$+$1051 &BZBJ0211$+$1051 & &bzb &0.2 & 25 & &J1217$+$3007 &1ES1215$+$303 &TeV F2 &bzb &0.1300 & 16 \\ J0217$+$0837 &ZS0214$+$083 & &bzb &0.085 & 24 & &J1220$+$0203 &PKS1217$+$02 & &bzq &0.2404 & 1 \\ J0259$+$0747 &PKS0256$+$075 & &bzq &0.893 & 15 & &J1221$+$2813 &WComae &TeV F12 &bzb &0.1030 & 7 \\ J0303$-$2407 &PKS0301$-$243 & &bzb &0.26 & 6 & &J1221$+$3010 &PG1218$+$304 &TeV &bzb &0.1840 & 2 \\ J0405$-$1308 &PKS0403$-$13 & &bzq &0.571 & 5 & &J1222$+$0413 &4C$+$04.42 & &bzq &0.9660 & 1 \\ J0423$-$0120 &PKS0420$-$01 &F12 &bzq &0.915 & 6 & &J1224$+$2122 &4C21.35 &TeV F1 &bzq &0.4340 & 8 \\ J0841$+$7053 &4C71.07 &F12 &bzq &2.218 & 13 & &J1224$+$2436 &MS1221.8$+$2452 &TeV &bzb &0.2180 & 5 \\ J0848$+$6606 &GB6J0848$+$6605 & &bzb &\ldots & 14 & &J1229$+$0203 &3C273 &F12 &bzq &0.1580 & 1 \\ J0957$+$5522 &4C55.17 & &bzq &0.899 & 4 & &J1230$+$2518 &ON246 & &bzb &0.1350 & 1 \\ J0958$+$6533 &S40954$+$65 &F12 &bzb &0.367 & 9 & &J1231$+$2847 &B21229$+$29 & &bzb &0.2360 & 1 \\ J1037$+$5711 &GB6J1037$+$5711 & &bzb &0.8304 & 16 & &J1238$-$1959 &PMNJ1238$-$1959 & &agu &\ldots & 1 \\ J1048$+$7143 &S51044$+$71 & &bzq &1.15 & 7 & &J1245$+$5709 &BZBJ1245$+$5709 & &bzb &1.5449 & 1 \\ J1058$+$5628 &TXS1055$+$567 & &bzb &0.143 & 12 & &J1253$+$5301 &S41250$+$53 & &bzb &0.1780 & 2 \\ J1203$+$6031 &SBS1200$+$608 & &bzb &0.065 & 17 & &J1256$-$0547 &3C279 &F12 &bzq &0.5360 & 19 \\ J1248$+$5820 &PG1246$+$586 & &bzb &0.8474 & 13 & &J1314$+$2348 &TXS1312$+$240 & &bzb &2.1450 & 1 \\ J1512$-$0905 &PKS1510$-$08 &F12 &bzq &0.36 & 36 & &J1337$-$1257 &PKS1335$-$127 & &bzq &0.5390 & 1 \\ J1542$+$6129 &GB6J1542$+$6129 &F2 &bzb &0.117 & 31 & &J1354$-$1041 &PKS1352$-$104 &F2 &bzq &0.3320 & 1 \\ J1553$+$1256 &PKS1551$+$130 &F2 &bzq &1.308 & 30 & &J1357$+$0128 &BZBJ1357$+$0128 & &bzb &0.2187 & 2 \\ J1555$+$1111 &PG1553$+$113 &F1 &bzb &0.36 & 51 & &J1427$+$2348 &PKS1424$+$240 &TeV &bzb &0.1600 & 7 \\ J1558$+$5625 &TXS1557$+$565 & &bzb &0.3 & 34 & &J1510$-$0543 &PKS1508$-$05 & &bzq &1.1850 & 1 \\ J1604$+$5714 &GB6J1604$+$5714 & &bzq &0.72 & 25 & &J1512$+$0203 &PKS1509$+$022 & &bzq &0.2190 & 1 \\ J1607$+$1551 &4C15.54 & &bzb &0.496 & 25 & &J1516$+$1932 &PKS1514$+$197 & &bzb &1.0700 & 1 \\ J1635$+$3808 &4C38.41 &F12 &bzq &1.813 & 51 & &J1548$-$2251 &PMNJ1548$-$2251 & &bzb &0.1920 & 1 \\ J1642$+$3948 &3C345 &F12 &bzq &0.593 & 23 & &J1550$+$0527 &4C5.64 & &bzq &1.4170 & 2 \\ J1653$+$3945 &Mkn501 &F12 &bzb &0.034 & 52 & &J1608$+$1029 &4C10.45 & &bzq &1.2320 & 2 \\ J1725$+$1152 &1H1720$+$117 & &bzb &0.018 & 40 & &J1637$+$4717 &4C47.44 & &bzq &0.7350 & 3 \\ J1748$+$7005 &S41749$+$70 & &bzb &0.77 & 45 & &J1640$+$3946 &NRAO512 & &bzq &1.6660 & 1 \\ J1751$+$0939 &OT81 &F2 &bzb &0.322 & 49 & &J1643$-$0646 &FRBAJ1643$-$0646 & &bzb &\ldots & 1 \\ J1754$+$3212 &BZBJ1754$+$3212 & &bzb &\ldots & 31 & &J1649$+$5235 &87GB1648$+$5240 & &bzb &2.055 & 30 \\ J1800$+$7828 &S51803$+$784 &F12 &bzb &0.68 & 30 & &J1722$+$1013 &TXS1720$+$102 & &bzq &0.7320 & 1 \\ J1806$+$6949 &3C371 &F1 &bzb &0.05 & 39 & &J1727$+$4530 &S41726$+$45 & &bzq &0.7140 & 1 \\ J1809$+$2041 &RXJ1809.3$+$2041 & &agu &\ldots & 28 & &J1733$-$1304 &PKS1730$-$13 &F12 &bzq &0.9020 & 1 \\ J1813$+$3144 &B21811$+$31 & &bzb &0.117 & 27 & &J1745$-$0753 &TXS1742$-$078 & &bzb &\ldots & 1 \\ J1836$+$3136 &RXJ1836.2$+$3136 & &bzb &\ldots & 25 & &J1749$+$4321 &B31747$+$433 & &bzb &0.2150 & 1 \\ J1838$+$4802 &GB6J1838$+$4802 & &bzb &0.3 & 28 & &J1813$+$0615 &TXS1811$+$062 & &bzb &\ldots & 2 \\ J1841$+$3218 &RXJ1841.7$+$3218 & &bzb &\ldots & 24 & &J1824$+$5651 &4C56.27 &F1 &bzb &0.6640 & 2 \\ J1903$+$5540 &TXS1902$+$556 & &bzb &\ldots & 27 & &J1844$+$5709 &TXS1843$+$571 & &agu &\ldots & 1 \\ J1927$+$6117 &S41926$+$61 & &bzb &\ldots & 25 & &J1848$+$3244 &B21846$+$32B & &agu &\ldots & 1 \\ J1959$+$6508 &1ES1959$+$650 &F1 &bzb &0.049 & 35 & &J1849$+$6705 &S41849$+$67 &F2 &bzq &0.6570 & 1 \\ J2005$+$7752 &S52007$+$77 & &bzb &0.342 & 27 & &J1911$-$1908 &PMNJ1911$-$1908 & &agu &\ldots & 1 \\ J2015$-$0137 &PKS2012$-$017 & &bzb &\ldots & 27 & &J1923$-$2104 &TXS1920$-$211 &F2 &bzq &0.8740 & 1 \\ J2016$-$0903 &PMNJ2016$-$0903 & &bzb &\ldots & 22 & &J2000$-$1748 &PKS1958$-$179 & &bzq &0.6520 & 1 \\ J2022$+$7611 &S52023$+$760 & &bzb &0.594 & 28 & &J2030$+$1936 &87GB2028$+$1925 & &agu &\ldots & 1 \\ J2030$-$0622 &TXS2027$-$065 & &bzq &0.671 & 26 & &J2031$+$1219 &PKS2029$+$121 & &bzb &1.2130 & 1 \\ J2039$-$1046 &TXS2036$-$109 & &bzb &\ldots & 32 & &J2035$+$1056 &PKS2032$+$107 & &bzq &0.6010 & 1 \\ J2131$-$0915 &RBS1752 & &bzb &0.449 & 28 & &J2146$-$1525 &PKS2143$-$156 & &bzq &0.6980 & 1 \\ J2143$+$1743 &OX169 &F2 &bzq &0.211 & 29 & &J2147$+$0929 &PKS2144$+$092 &F2 &bzq &1.1130 & 1 \\ J2148$+$0657 &4C6.69 & &bzq &0.999 & 29 & &J2152$+$1734 &S32150$+$17 & &bzb &0.8740 & 1 \\ J2149$+$0322 &PKSB2147$+$031 & &bzb &\ldots & 23 & &J2217$+$2421 &B22214$+$24B & &bzb &0.5050 & 1 \\ J2150$-$1410 &TXS2147$-$144 & &bzb &0.229 & 20 & &J2253$+$1404 &BZBJ2253$+$1404 & &bzb &0.3270 & 1 \\ J2202$+$4216 &BLLacertae &F12 &bzb &0.069 & 77 & &J2321$+$2732 &4C27.5 & &bzq &1.2530 & 1 \\ J2225$-$0457 &3C446 &F1 &bzq &1.404 & 22 & &J2325$+$3957 &B32322$+$396 &F2 &bzb &\ldots & 1 \\ J2232$+$1143 &CTA102 &F12 &bzq &1.037 & 53 & & \mc{6}{c}{} \\ J2243$+$2021 &RGBJ2243$+$203 & &bzb &\ldots & 32 & & \mc{6}{c}{\bf Monitored Gamma-ray-quiet (GQ) sources} \\ J2251$+$4030 &BZBJ2251$+$4030 & &bzb &0.229 & 33 & & J0017$+$8135 &\ldots & &RL-FSRQ &\ldots & 11 \\ J2253$+$1608 &3C454.3 &F12 &bzq &0.859 &103 & & J0642$+$6758 &HB89$-$0636$+$680 & &RL-FSRQ &3.1800 & 11 \\ J2311$+$3425 &B22308$+$34 & &bzq &1.817 & 30 & & J0825$+$6157 &HB89$-$0821$+$621 & &RL-FSRQ &0.5420 & 8 \\ J2340$+$8015 &TXS2331$+$073 & &bzq &0.401 & 13 & & J0854$+$5757 &HB89$-$0850$+$581 & &RL-FSRQ &1.3191 & 6 \\ J2334$+$0736 &BZB J2340$+$8015 & &bzb &0.274 & 18 & & J1551$+$5806 &SBS1550$+$582 & &RL-FSRQ &1.3240 & 26 \\ \mc{6}{c}{} & & J1603$+$5730 &HB89$-$1602$+$576 & &RL-FSRQ &2.8580 & 15 \\ \mc{6}{c}{\bf Not monitored Gamma-ray-loud (GL) sources} & & J1624$+$5652 &SBS1623$+$569 &discontinued$^{3}$ &BL~Lac &0.4150 & 18 \\ J0136$+$3905 &B30133$+$388 &TeV &bzb &\ldots & 4 & & J1638$+$5720 &HB89$-$1637$+$574 &discontinued$^{3}$ &RL-FSRQ &0.7506 & 24 \\ J0221$+$3556 &S40218$+$35 &F2 &bzq &0.9440 & 1 & & J1800$+$3848 &HB89$-$1758$+$388 & &RL-FSRQ &2.0920 & 16 \\ J0222$+$4302 &3C66A & &bzb &0.4440 & 24 & & J1835$+$3241 &3C382 & &\ldots &0.0579 & 16 \\ J0238$+$1636 &AO0235$+$164 &F12 &bzb &0.9400 & 19 & & J1854$+$7351 &S5$-$1856$+$73 & &RL-FSRQ &0.4610 & 16 \\ J0340$-$2119 &PKS0338$-$214 & &bzb &0.2230 & 1 & & J1927$+$7358 &HB89$-$1928$+$738 & &RL-FSRQ &0.3021 & 13 \\ J0336$+$3218 &NRAO140 &F1 &bzq &1.2630 & 6 & & J1955$+$5131 &HB89$-$1954$+$513 &new$^{4}$ &RL-FSRQ &1.2200 & 2 \\ J0339$-$0146 &PKS0336$-$01 &F1 &bzq &0.8520 & 4 & & J2016$+$1632 &TXS2013$+$163 & &VisS &\ldots & 11 \\ J0407$+$0742 &TXS0404$+$075 & &bzq &1.1330 & 1 & & J2024$+$1718 &GB6J2024$+$1718 & &RL-FSRQ &1.0500 & 13 \\ J0442$-$0017 &PKS0440$-$00 & &bzq &0.8450 & 12 & & J2033$+$2146 &4C$+$21.55 &new$^{4}$ &QSO &0.1735 & 4 \\ J0510$+$1800 &PKS0507$+$17 & &bzq &0.4160 & 2 & & J2042$+$7508 &4C$+$74.26 & &QSO &0.1040 & 27 \\ J0721$+$7120 &S50716$+$71 &F12 &bzb &0.31 & 51 & & \mc{6}{c}{} \\ J0738$+$1742 &PKS0735$+$17 &F12 &bzb &0.4240 & 11 & & \mc{6}{c}{\bf Not monitored Gamma-ray-quiet (GQ) sources} \\ J0750$+$1231 &OI280 &F1 &bzq &0.8890 & 11 & & J0702$+$8549 &CGRaBSJ0702$+$8549& &RL-FSRQ &1.0590 & 1 \\ J0809$+$5218 &1ES0806$+$524 &TeV &bzb &0.1370 & 4 & & J0728$+$5701 &BZQJ0728$+$5701 & &RL-FSRQ &0.4260 & 2 \\ J0818$+$4222 &S40814$+$42 &F12 &bzb &0.5300 & 10 & & J0837$+$5825 &SBS0833$+$585 & &RL-FSRQ &2.1010 & 2 \\ J0830$+$2410 &S30827$+$24 &F1 &bzq &0.9420 & 6 & & J1010$+$8250 &8C1003$+$830 & &RL-FSRQ &0.3220 & 1 \\ J0854$+$2006 &OJ287 &F12 &bzb &0.306 & 26 & & J1017$+$6116 &TXS1013$+$615 & &RL-FSRQ &2.8000 & 2 \\ J0956$+$2515 &OK290 & &bzq &0.7080 & 1 & & J1148$+$5924 &NGC3894 & &BL~Lac - GD &0.0108 & 1 \\ J1012$+$0630 &NRAO350 & &bzb &0.7270 & 1 & & J1436$+$6336 &GB6J1436$+$6336 & &RL-FSRQ &2.0680 & 1 \\ J1014$+$2301 &4C23.24 & &bzq &0.5650 & 1 & & J1526$+$6650 &BZQJ1526$+$6650 & &RL-FSRQ &3.0200 & 2 \\ J1018$+$3542 &B21015$+$35B & &bzq &1.2280 & 1 & & J1623$+$6624 &\ldots & &RL-FSRQ &0.201 & 2 \\ J1023$+$3948 &4C40.25 & &bzq &1.2540 & 1 & & J1727$+$5510 &GB6J1727$+$5510 & &BL~Lac - GD &0.2473 & 4 \\ J1032$+$3738 &B31029$+$378 & &bzb &0.5280 & 3 & & J1823$+$7938 &S51826$+$79 & &BL~Lac - GD &0.2240 & 4 \\ J1033$+$6051 &S41030$+$61 & &bzq &1.4010 & 1 & & J1850$+$2825 &TXS1848$+$283 & &RL-FSRQ &2.5600 & 3 \\ J1054$+$2210 &87GB1051$+$2227 & &bzb &2.0550 & 1 & & J1918$+$4937 &BZQJ1918$+$4937 & &RL-FSRQ &0.9260 & 3 \\ J1058$+$0133 &4C1.28 & &bzb &0.8880 & 1 & & J1941$-$0211 &PMNJ1941$-$0212 & &RL-FSRQ &0.2020 & 5 \\ J1059$-$1134 &PKSB1056$-$113 & &bzb &\ldots & 1 & & J2022$+$6136 &S42021$+$61 & &RL-FSRQ &0.2270 & 6 \\ J1104$+$0730 &GB6J1104$+$0730 & &bzb &0.6303 & 1 & & J2051$+$1742 &PKS2049$+$175 & &Blazar U &0.1950 & 3 \\ J1104$+$3812 &Mkn421 &F12 &bzb &0.0300 & 3 & & & & & & & \\ \hline \multicolumn{11}{p{12cm}}{$^1$ Indicates whether a source is part of another monitoring sample. ``TeV'' marks sources that are in the TeV monitoring sample; ``F'' marks sources of the F-GAMMA sample. The designation ``1'' tags F-GAMMA sources before and ``2'' those after F-GAMMA sample change/revision in middle 2009.}\\ \multicolumn{11}{p{12cm}}{$^2$ Source classification. The tags ``bzq'', ``bzb'' and ``agu'' are taken directly from the 2FGL. ``RL-FSRQ''stands for ``QSO RLoud flat radio sp'', ``BL~Lac - GD'' stands for ``BL~Lac - galaxy dominated'' and ``Blazar U'' stand for ``Blazar Uncertain type'' of the Roma BZCAT - 5th edition \citep{2015ApSS.357...75M}. Other designations have been taken from NASA/IPAC Extragalactic Database (NED).}\\ \multicolumn{11}{p{12cm}}{$^3$ discontinued after the completion of the second season.}\\ \multicolumn{11}{p{12cm}}{$^4$ introduced after the second season (2014) in exchange of the 2 sources that appeared in the 3FGL.}\\ \end{tabular} \end{table*} The data sets presented here have been acquired during the first two \rbpl~monitoring seasons, which followed a brief commissioning phase \citep[2013 May -- July,][]{2014MNRAS.442.1706K,2014MNRAS.442.1693P}. The first season lasted from 2013 May 26 until 2013 November 27 with 67~per~cent of the observing time usable; the second season lasted from 2014 April 11 till 2014 November 19 with about 60~per~cent of the nights usable. Data-taking during each season is discussed in \citet{2015MNRAS.453.1669B} and \citet{2016MNRAS.457.2252B}, respectively, while our data processing and reduction pipeline is presented in detail in \cite{2014MNRAS.442.1706K}. The pipeline output includes fractional Stokes parameters $q$ ($q=\nicefrac{Q}{I}$) and $u$ ($u=\nicefrac{U}{I}$) and their uncertainties, from which the linear polarization fraction $p$ and the electric vector position angle (EVPA) $\chi$, for each source are calculated, with their uncertainties derived from error propagation (see Eqs. 5, 6 in \citealp{2014MNRAS.442.1706K}). The median uncertainties of $q$ and $u$ from all measurements in our data set that passed the quality criteria are both around 0.007 while that of the polarization angle $\chi$, is 4.7\degr. The median uncertainty in photometry based, for example, on PTF \citep[][]{2012PASP..124..854O} standard stars, is around 0.02~mag. A measure of the instrumental polarization is given by Table~1 in \cite{2014MNRAS.442.1706K}, where it is shown that the mean absolute difference between \rbpl-measured and catalogued degree of polarization for polarized standard stars is about $(3 \pm 5) \times 10^{-2}$ in terms of polarization fraction $p$. Finally, the instrumental rotation is $2.31\degr\pm0.34\degr$. After the pipeline operation and before any useful data product is processed, each measurement is subjected to post-reduction quality checks, which include: \begin{enumerate} \item Goodness of the astrometry; by comparing the expected source position to that recovered from the reversal of the ``1-to-4'' mapping of the source. The tolerance is 9~arcsec. \item Field ``crowdedness''; which affects the reliability of the aperture photometry. \item Central mask edge proximity, which may severely affect the photometry. \end{enumerate} All the data products discussed here are based on data sets that have passed all these checks. \label{sec:discussion} We have presented the average polarimetric and photometric properties and the variability parameters, of GL and GQ sources observed with \rbpl~during the first two observing seasons. Our analysis concentrated on (a) quantifying the possible difference in the polarization of the GL and GQ sources that was first found by \cite{2014MNRAS.442.1693P}; and (b) investigating its possible causes. We also examined whether the polarization variability shows a similar dichotomy for GL and GQ sources. We have found that: \paragraph*{{\it The average polarization does not depend on luminosity. }} While in the Survey Paper the un-polarized starlight contribution of the host galaxy was suggested as being possibly responsible for the apparent de-polarization of the brightest sources, a more detailed analysis in luminosity space revealed that sources that are both very luminous and highly polarized are possible (see Fig.~\ref{fig:PDvsL_k}). \paragraph*{{\it The average polarization fraction of GL and GQ sources differs. }} The two samples have different mean polarization fractions: the distributions of $\hat{p}$ are different at an almost $4\sigma$ level, while those of the intrinsic mean polarization fraction $p_0$ have yielded a significance of $\sim3\sigma$. A Gehan's generalized Wilcoxon test applied on a dataset including $2\sigma$ upper limits in $p_0$, produces a similar result (Fig.~\ref{fig:PD-GLoudns} lower panel). A log-normal distribution fit to the two distributions of $p_0$ gives the mean intrinsic polarization $\left<p_0\right>$ of $(9.2\pm0.8)\times 10^{-2}$ for GL and $(3.1\pm0.8)\times10^{-2}$ for GQ sources. \paragraph*{{\it The variability amplitude of the polarization fraction does not differ between GL and GQ sources. }} Unlike the polarization fraction, its variability amplitude does not show the same dichotomy between GL and GQ samples. However the sample consisted of 64 GL and 2 GQ sources (of which 19 have only upper limits), so small number statistics may limit our ability to establish a difference between the two populations. This makes any conclusion concerning the distributions of $m_p$ ambiguous. However, the very fact that for the majority of GQ sources we were able only to place upper limits on the amplitude of optical polarization variability may be seen as an indication that GQ sources are less variable. That is indeed the case in terms of radio and optical flux density modulation index as Fig.~\ref{fig:mPD_mi}~and~\ref{fig:mPD_miR}, show. \paragraph*{{\it The stronger the variability in radio or optical the larger the mean polarization. }} Figures~\ref{fig:mPD_mi}~and~\ref{fig:mPD_miR} suggest that the larger the amplitude of the radio and the $R$-band flux density variability, the higher is the median polarization. On the other hand, the polarization variability amplitude $m_p$ does not seem to influence the median polarization although there is even an indication that the two are anti-correlated (Fig.~\ref{fig:p0_mp}). We have also examined whether the high energy (2FGL) variability index is influencing the polarization fraction and found no evidence for such a dependence. \paragraph*{{\it The modulation index of the polarization fraction is redshift dependent. }} Contrary to the polarization fraction itself, its variability amplitude seems to be a function of redshift. \paragraph*{{\it Source class is not the reason for the GL-GQ dichotomy.}} The dominance of radio quasars in the GQ sample could explain the observed dichotomy, if BL~Lac objects and Flat Spectrum Radio Quasars were characterized by different distributions of $p$. A two-sample K-S test between quasars and BL~Lac objects has shown that the two distributions are indistinguishable. It must be noted however that the GQ sources reach larger redshifts (Fig.~\ref{fig:PDF-z}) which could potentially have an effect on the gamma-ray detectability given the maximum redshift that {\it Fermi} can probe. Our findings however cannot be influenced by this; (a) because GQ sources for which $\hat{p}$ values are available and hence are included in our plots, are limited to $z< 1.5$; and (b) as can be seen in Fig.~\ref{fig:mPD_z.eps}, the degree of polarization is independent of the source cosmological distance. \paragraph*{{\it The optical polarization fraction and the randomness of the polarization angle, depend on the synchrotron peak frequency.}} Figure~\ref{fig:PD_peak} revealed a synchrotron-peak-dependent envelope limiting the polarization fraction: the fractional polarization $\hat{p}$ of LSP sources is on average higher {than that} for HSP ones, while their polarization spreads over a broader range extending to considerably higher values of $\hat{p}$. We {have shown} that if we exclude the GQ sources (for which the synchrotron peak is severely under-sampled), there is a significant anti-correlation between $\hat{p}$ and the rest-frame frequency of the synchrotron peak, $\nu_\mathrm{s}$. The anti-correlation {becomes} clearer and more significant when only the ``bzb'' subset of the GL sample {is} considered. A similar relation between the fractional polarization of the VLBA core and the synchrotron peak frequency {has been found} by \cite{2011ApJ...742...27L}. When they { have focused} only on LSP and HSP BL~Lac objects that span similar redshift ranges, they observe the same trend. They explain the observed correlation as a result of the balance between the intrinsic gamma-ray loudness and the Doppler boosting of the sources given the general association of high polarization to highly Doppler-boosted jets. Myserlis et al. (in prep.) look at the fractional polarization of roughly 35 {\it Fermi} sources and find that at 2.64 and 4.85~GHz the same relation is apparent. Specifically at 4.85~GHz they find that Spearman's $\rho=-0.35$. We also {show} that apart from the polarization fraction, the randomness of the EVPA depends on the synchrotron peak frequency. LSP sources tend to show a random orientation of their, unlike HSP sources which tend to show a preferred direction. \subsection{A qualitative interpretation of the observed trends} In this section, we propose a simple, qualitative explanation for the various trends of the average degree of polarization found in this study. It is based on a basic shock-in-jet scenario, as sketched in Fig.~\ref{fig:shock}. The jet is expected to be pervaded by a helical magnetic field structure, on which a turbulent $B$-field component is superposed. A mildly relativistic shock, caused either by a static disturbance in the environment of the jet (i.e. a standing shock), or by the collision of plasmoids propagating along the jet with different Lorentz factors (internal shock), mediates efficient particle acceleration due to diffusive shock acceleration (DSA) or magnetic reconnection in a small volume, concentrated in the immediate downstream environment of the shock. As particles are advected away from the shock, they cool, primarily due to the emission of synchrotron and Compton radiation. Consequently, the highest-energy particles, responsible for the emission near and beyond the peak of the synchrotron (and Compton) SED components, are expected to be concentrated in a small volume immediately downstream of the shock, where the shock-compressed magnetic field is expected to have a strong ordered (helical) component, in addition to shock-generated turbulent magnetic fields. Substantial degrees of polarization are thus expected near and beyond the peak of the synchrotron SED component. Due to progressive cooling of shock-accelerated electrons as they are advected downstream, the volume from which lower-frequency synchrotron emission is received, is expected to increase monotonically with decreasing frequency. One therefore expects a lower degree of polarization with decreasing frequency due to de-polarization from the superposition of radiation zones with different $B$-field orientations. First of all, the general trend of a higher degree of polarization for GL compared to GQ AGN, may be explained as follows: GL AGN (i.e., primarily blazars) are known to be highly variable, indicating a strong jet dominance throughout most of the SED due to a high degree of Doppler boosting \citep[e.g.][]{2010A&A...512A..24S,2015ApJ...810L...9L} and the frequent occurrence of impulsive particle acceleration events, such as the shock-in-jet scenario described above. On the other hand, GQ AGN appear to represent objects in which Doppler boosting is less extreme and/or impulsive particle acceleration episodes are less efficient, thus not accelerating particles to the energies required for gamma-ray production at measurable levels. Consequently, optical synchrotron emission is likely to be produced on larger volumes than in the more active GL objects, thus naturally explaining the lower degree of polarization. This scenario also naturally explains the dependence of the degree of polarization on the synchrotron peak frequency: In LSP blazars, such as FSRQs and low-frequency peaked BL~Lacs (LBLs), the synchrotron peak frequency is typically located in the infrared. Thus, the optical regime represents the high-frequency portion of the synchrotron emission, for which -- as elaborated above -- one expects a high degree of polarization. On the contrary, in HSP blazars, such as high-frequency peaked BL~Lacs (HBLs), the synchrotron peak tends to be located at UV or X-ray frequencies. Thus, here the optical regime represents the low-frequency part of the synchrotron SED, for which one expects a lower degree of polarization. \begin{figure} \centering \includegraphics[trim=0pt 0pt 0pt 0pt ,clip,width=0.38\textwidth]{figures/shock_in_jet_sketch_sk.eps} \caption{Cartoon representation of the shock-in-jet scenario. The downstream directions is towards the left.} \label{fig:shock} \end{figure} Finally, this scenario also explains the tendency of the optical EVPA rotation events to occur preferentially in LSP sources as we present elsewhere (Blinov et al. in prep.). In the case of LSP sources the optical emission originates at the small volume in the immediately downstream environment of the shock, where the magnetic field has a strong helical component. In HSP sources on the other hand, the optical emission originates in a larger region farther downstream of the shock, where the electrons have already lost part of their energy and the turbulent $B$-field component becomes more significant. It has been shown by \cite{2015MNRAS.453.1669B} and \cite{2016arXiv160300249K} that two types of EVPA rotations may coexist in blazars. The smooth deterministic EVPA rotations may occur preferentially when plasmoids propagate through regions where the helical field component is dominant \citep[e.g.][]{2008Natur.452..966M,2010ApJ...710L.126M, 2014ApJ...789...66Z, 2015ApJ...804...58Z}, {whereas} further downstream the EVPA variability is more likely to be driven by stochastic processes. Consequently, smooth rotations are more likely to occur in LSP than HSP sources. Indeed, all five rotations in Fig. 8 of \cite{2015MNRAS.453.1669B} associated with strong gamma-ray flares and short time lag from the flare, which are hence considered deterministic, have occurred in LSP sources. Moreover, the optical emission region in LSP sources is smaller than in HSP sources and thus expected to be more variable. In the context of stochastic variations, larger emitting region implies an increased number of cells, which decreases the variability \citep[e.g.][]{2016arXiv160300249K}. Also, the larger emission region in HSP sources increases the variability time scale. Assuming the superposition of a helical magnetic field component and a turbulent one, LSP and HSP sources may have an underlying, stable EVPA component due to the helical field component. In LSP sources the stable component may not be clearly visible owing to stronger variability and shorter variability time scales. In HSP sources, in which the variability amplitudes are lower and variability time scales are longer, the stable component may be more dominant. There, the combination of local turbulence that keeps the global magnetic field structure intact can explain a preferred, though slightly variable EVPA. Only long term observations can confirm whether the EVPA has a truly preferred orientation on time scales longer than the \rbpl~observing periods. If the difference between LSP and HSP sources in terms of polarization is indeed caused merely by the fact that observations in the optical band probe (a) regions of different size and (b) different parts of the particle distribution, then we would expect the same polarization variability in HSP sources at X-ray bands as in LSP sources in optical bands. It is worth noting that in this scenario the rotations of the EVPA are expected to be happening downstream the shock in contrast to earlier suggestions \citep[e.g.][]{2010ApJ...710L.126M} that the region responsible for these events was just upstream of the shock. | 16 | 9 | 1609.00640 |
1609 | 1609.07851_arXiv.txt | { Modified Gravity (MOG) and Non-Local Gravity (NLG) are two alternative theories to General Relativity. They are able to explain the rotation curves of spiral galaxies and clusters of galaxies without including dark matter \citep{rahvar1,rahvar2,rahvar3}. In the weak-field approximation these two theories have similar forms, with an effective gravitational potential that has two components: (i) \mbox{Newtonian} gravity with the gravitational constant enhanced by a factor $(1+\alpha)$ and (ii) a Yukawa type potential that produces a repulsive force with length scale $1/\mu$. In this work we compare the rotation curves of dwarf galaxies in the LITTLE THINGS catalog with predictions of MOG, NLG and Modified Newtonian Dynamics (MOND). We find that the universal parameters of these theories, can fit the rotation curve of dwarf galaxies with a larger stellar mass to the light ratio compared to the nearby stars in the Milky Way galaxy. Future direct observations of mass function of stars in the dwarf galaxies can examine different modified gravity models.} | At the scales of galaxies and clusters of galaxies, observations show a systemic discrepancy between dynamical mass models and the mass distributions inferred from the luminous matter~\citep{zw,rubin1,rubin2}. One proposal for resolving this discrepancy is dark matter---so-called missing mass of the Universe. Cosmological dark matter is a fluid composed of massive particles that interact gravitationally with each other, with the possibility of very weak non-gravitational interaction with themselves and with ordinary (baryonic) matter. {The most accurate and acceptable model of dark matter is $\Lambda CDM$ which by having six parameters explains CMB data~\citep{CDM}, large scale structure of the universe~\citep{StFormation} and Baryonic Acoustic Oscillations \citep{BAO}. It should be noted that it is hard for any alternative theory to explain such a wide range of observations that $\Lambda CDM$ do. While dark matter is successful in interpretation of observations, no explicit signal of dark matter particle interaction with the ordinary matter has yet been found \citep{moore,gal,ang,ake}.} {Recent observations of 153 galaxies with different morphology, mass, size and gas fraction shows that there is a strong correlation between observed radial acceleration and acceleration results from the baryonic matter ~\citep{McGaugh}, which maybe suggests new dynamical laws rather than dark matter. Moreover in the gravitational lensing, \cite{Sanders} showed that mass derived from the lensing within the Einstein ring has linear correlation with the surface brightness.} An alternative approach to interpret the dynamics of large structures is to analyze observations using a modified law of gravity, with no dark matter. One well known model is Modified Newtonian Dynamics (MOND), which changes the Newtonian dynamics at small accelerations in a way that produces flat rotation curves for spiral galaxies \citep{milgrom}. MOND was extended to a relativistic theory by \citet{beken}. Some challenges facing MOND and other modified gravity theories are to explain the gravitational lensing of systems like the bullet cluster \citep{bullet} and the large scale structure formation in the Universe without using dark matter. { Although it seems that MOND can not be made consistent with the detailed shape of the CMB and matter power spectra, there are some works on hybrid models which include both DM and MOND phenomena \citep{hybrid1,hybrid2} and explain both the dynamic of galaxies and cosmological observations.} Another modification to the gravity is done by \citet{mashhoon} where they introduced Non-Local Gravity (NLG), with a modified gravitational acceleration, to solve the missing mass problem. NLG extends non-local special relativity to the accelerating frames. In the weak-field, non-relativistic limit of NLG, the effective gravitational potential of a point mass adds to a Newton-like potential a new term that gives a repulsive, Yukawa-like force \citep{mashhoon}. Predictions of this theory have been compared with the rotation curves of spiral galaxies and the temperature profiles of hot gas for clusters of galaxies in the Chandra database. With the fixed values for the parameters of NLG, the dynamics of spiral galaxies and clusters of galaxies are consistent with the baryonic distribution of matter in these systems, with no need for dark matter \citep{rahvar3}. Modified Gravity (MOG) theory---a covariant extension of General Relativity---also avoids the need for dark matter \citep{moffat06}. In MOG, gravity is described by the tensor metric field in combination with new scalar and vector fields. An important feature is that each particle has a fifth force charge, proportional to its inertial mass, through which it couples to the massive vector field. Similar to the Lorentz acceleration of charged particles in electrodynamics, test particles in MOG deviate from geodesics due to coupling of their fifth force charge with the vector field. In the weak-field approximation a modified Poisson equation is obtained, which for a point-like mass has a Yukawa repulsive term in addition to a conventional Newtonian potential. Comparison with the dynamics of spiral galaxies in the THINGS catalog results in universal values for the parameters of this model, with reasonable fits to the rotation curves of galaxies and clusters of galaxies \citep{rahvar1,rahvar2}. { For all the modified gravity models, the crucial observational tests would be predicting (i) the angular power spectrum of CMB (ii) the power spectrum of large scale structures and the other consequences of structure formation as the Baryonic acoustic oscillations. } Although NLG and MOG have completely different physical axioms, they have almost same behaviour in the weak-field approximation limit. To test the universality of parameters of modified gravity models at intermediate scales, we use the dynamical and luminosity data of dwarf galaxies in the LITTLE THINGS catalog and interpret them in the effective potentials of MOG, NLG, and MOND. The observational data in the LITTLE THINGS catalog are the density distributions of stars and gas of each galaxy as well as the dynamics in form of galaxy rotation curves. In Section \ref{mogfield}, we review three alternative theories of gravity of (i) Modified Gravity (MOG) and its weak field approximation (ii) Non-Local Gravity (NLG) and the corresponding weak field approximation (iii) and Modified Newtonian Dynamics (MOND). In Section \ref{rotcurve}, we introduce the LITTLE THINGS catalog and apply the results of weak field approximation of alternative models of gravity to the dwarf galaxies. We determine the best-fitting values for the stellar mass to light ratio for our three model. { The conclusion is given in Section \ref{conc} where we discuss the universality of parameters of modified gravity theories and a larger stellar mass to light ratio for dwarf galaxies which can be used to examine the modified gravity models with the future direct observations of stellar mass function in these galaxies.} | {To test MOG, Non-Local Gravity and MOND models as the alternative models for the dark matter, we compared the theoretical rotation curves predicted by these three gravity models with the observed data for sixteen dwarf galaxies in the LITTLE THINGS catalog. The gravitational acceleration due to a point source in the weak field limit of MOG and Non-Local Gravity involves two parameters: $\alpha$ determines the gravitational coupling strength via $G=G_N(1+\alpha)$ and $\mu$ as the inverse of the characteristic length of the repulsive Yukawa force. At distances much greater than $\mu^{-1}$, the repulsive term is negligible. For each of MOG and Non-Local Gravity, we fix the parameters of $\mu$ and $\alpha$ with the universal values that has been reported in \citep{rahvar1,rahvar3} and analyze the rotation curve of dwarf galaxies, using $\Upsilon_{*}$ at $3.6\mu m$ as the only free parameter of model. The same procedure for MOND has been done like the other gravity models. We fixed $a_{0}=1.0\times10^{-10}\,\mathrm{m\,s}^{-2}$ as the universal value which is consistent with the value obtained previously by fitting to spiral galaxies \citep{sanders and McG}. } { For the two modified gravity models of MOG and NLG, the value of $\Upsilon_{*}$ in the dwarf galaxies is larger than the conventional value in the Milky Way while for MOND we obtain a compatible value with the spiral galaxies. The stellar mass to the light ratio is a function of stellar population inside a galaxy where for population with larger mass stars this parameter would be smaller and for small mass population of stars, that will be larger. For diffused mediums as the dwarf galaxies, the history of star formation might be different and produce small mass stars. The result would be a larger stellar mass to the light ratio. On the other hand the remnant of heavy stars also can produce a larger stellar mass to the light ratio. This phenomenon can be examined by direct observations of stellar populations in the dwarf galaxies. Future telescope may resolve stars in the nearby dwarf galaxies and can rule out either MOG/NLG models or MOND. } \label{conc} | 16 | 9 | 1609.07851 |
1609 | 1609.02042.txt | { Magnetic fields, which play a major role in a large number of astrophysical processes can be traced via observations of dust polarization. In particular, {\it Planck} low-resolution observations of dust polarization have demonstrated that Galactic filamentary structures, where star formation takes place, are associated to well organized magnetic fields. A better understanding of this process requires detailed observations of galactic dust polarization on scales of 0.01 to 0.1 pc. Such high-resolution polarization observations can be carried out at the IRAM 30 m telescope using the recently installed \nikad\ camera, which features two frequency bands at 260 and 150 GHz (respectively 1.15 and 2.05 mm), the 260~GHz band being polarization sensitive. \nikad\ so far in commissioning phase, has its focal plane filled with $\sim$ 3300 detectors to cover a Field of View (FoV) of 6.5 arcminutes diameter. The \nika\ camera, which consisted of two arrays of 132 and 224 Lumped Element Kinetic Inductance Detectors (LEKIDs) and a FWHM (Full-Width-Half-Maximum) of 12 and 18.2 arcsecond at 1.15 and 2.05~mm respectively, has been operated at the IRAM 30 m telescope from 2012 to 2015 as a test-bench for \nikad. \nika\ was equipped of a room temperature polarization system (a half wave plate (HWP) and a grid polarizer facing the \nika\ cryostat window). The fast and continuous rotation of the HWP permits the quasi simultaneous reconstruction of the three Stokes parameters, $I$, $Q$, and $U$ at 150 and 260 GHz. This paper presents the first polarization measurements with KIDs and reports the polarization performance of the \nika\ camera and the pertinence of the choice of the polarization setup in the perspective of \nikad. We describe the polarized data reduction pipeline, specifically developed for this project and how the continuous rotation of the HWP permits to shift the polarized signal far from any low frequency noise. We also present the dedicated algorithm developed to correct systematic leakage effects. We report results on compact and extended sources obtained during the February 2015 technical campaign. These results demonstrate a good understanding of polarization systematics and state-of-the-art performance in terms of photometry, polarization degree and polarization angle reconstruction. } \titlerunning{\NIKA\ polarization performance} \authorrunning{A. Ritacco, N. Ponthieu, A. Catalano et al.} | \label{sec:introduction} \vspace{0.2cm} Magnetic fields have been proven to play a predominant role in a large number of astrophysical processes from galactic to cosmological scales. In particular, recent observations obtained with {\it Herschel} and {\it Planck} \citep{planck2013mission} satellites have provided us with sensitive maps of the star-forming complexes in the galaxy. These maps reveal large-scale filamentary structures as the preferential sites of star formation \citep{2010A&A...518L.100M,arzoumianian}. These filamentary structures are associated with organized magnetic field topology at scales larger than 0.5 pc \citep{2014prpl.conf...27A} and indicate that magnetic field must be explored on scales of 0.01 to 0.1 pc \citep{2004ApJ...603..584P,planckXXXIII}. At millimeter and sub-millimeter wavelengths, the magnetic field orientation can be explored using the polarized thermal dust emission \citep{2015A&A...576A.104P,2016arXiv160100546P}. Dust grains are generally prolate. The polarization emission of a grain depends on the orientation and acceleration of its magnetic dipole moment and is stronger along the major axis of the grain that aligns orthogonally to the magnetic field \citep{2009ASPC..414..482L}. This results in coherently polarized dust emission in the plane perpendicular to the magnetic field lines. Thus, polarized dust emission permits us to recover the direction of the magnetic field lines projected on the plane of the sky \citep[{\it e.g.,}][]{2015A&A...576A.106P}. The {\it Planck} satellite has mapped the polarized dust emission at 353 GHz on large angular scales over the entire sky \citep{2014A&A...571A...8P,2015arXiv150201587P} and suggests a high degree of polarization, up to 15 \% \citep{planckdust}, confirming previous {\it Archeops} results \citep{2004A&A...424..571B}. This opens a new window on the understanding of galactic magnetic fields. Unfortunately, the 5 arcminutes resolution of the {\it Planck} 353~GHz data limits the study of the galactic magnetic field at scales of 0.2 to 0.5 pc even for the closest clouds. For a detailed exploration of the magnetic field lines in the star-forming filamentary structures we need to perform high-resolution observations (10-20 arcsec resolution) of the polarized dust emission \citep{2014ApJ...792..116Z}. The \nikad\ dual-band millimeter camera \citep{Calvo2016,2016arXiv160508628C}, recently (October 2015) installed at the IRAM 30 m telescope in Pico Veleta (Spain), is particularly well adapted to such high-resolution observations of the polarized thermal dust emission. \nikad\ features two frequency bands at 260 (polarized) and 150 (non polarized) GHz for a total of 3300 Lumped Element Kinetic Inductance Detectors (LEKIDs). \nikad\ has expected to have 12 (resp.~18.2) arcsec Full Width Half Maximum (FWHM) resolution at 260~GHz (resp.~150~GHz) and a 6.5 arcmin diameter Field of View (FoV) at both frequencies. Between 2012 and 2015, a prototype version of \nikad\ named \nika\ \citep{monfardini2010,catalano2014} was operated at the IRAM 30 m telescope as a test-bench. \nika\ was also a dual-band camera at 150 and 260 GHz with a total of 356 LEKIDs, 12 and 18.2 arcsec resolution, but a 1.8~arcmin diameter FoV. Thanks to a specifically designed polarization setup \nika\ has provided polarized observations at both frequency bands \citep{Ritacco2015}. This polarization setup includes an analyzer and a half-wave plate (HWP). Experiments such as {\it Planck} \citep{planck_mission}, BICEP \citep{bicep}, ACTPol \citep{ACTPOL}, QUaD \citep{QUAD}, QUIET \citep{QUIET} and QUIJOTE \citep{QUIJOTE} rotate the instrument with respect to the sky. This modulates the input polarization signal providing the required angular coverage to reconstruct the $I$, $Q$, and $U$ Stokes parameters. By contrast, other experiments rotate a HWP in front of an analyzer to modulate the incoming sky polarization. HERTZ \citep{1997PASP..109..307S}, SCUPOL \citep{2003MNRAS.340..353G}, SHARP polarimeter \citep{2008ApOpt..47..422L}, PILOT \citep{PILOT}, BLASTPol \citep{BLASTPol}, SPIDER \citep{SPIDER}, POLARBEAR \citep{polarbear}, and SMA \citep{2008SPIE.7020E..2BM} change the HWP orientation step by step and maintain it fixed during some periods of observation. EBEX \citep{ebex}, POLKA \citep{polka_apex}, ABS \citep{2016arXiv160105901Er}, \nika, and \nikad\ take another option, that is, to rotate the HWP continuously. We discuss in this paper the polarization performance of the \nika\ camera and the implications for the \nikad\ design. The paper is organized as follows: Sect.~\ref{nika instrument} presents the \nika\ instrument and the polarization setup. Sect.~\ref{lab_characterization} discusses the laboratory characterization of the polarization setup. Sect.~\ref{data_analysis} presents the observational strategy and the dedicated polarization-data-reduction pipeline. Sect.~\ref{polcalibration} discusses observations on quasars; Sect.~\ref{sec:extended} presents the polarization maps of few extended sources, Orion OMC-1, M87 and Cygnus~A. We draw conclusions in Sect.~\ref{conclusions}. \begin{figure*} \begin{center} \includegraphics[width=7cm, keepaspectratio]{figures/Lab_test_config.pdf} \includegraphics[width=7cm, keepaspectratio]{figures/setup_polar_telescope.pdf} \caption{{\it Left} Laboratory instrumental setup: the \nika\ cryostat, the HWP in a fixed position, the polarizer mounted inside the cryostat and a Martin-Puplett interferometer. {\it Right} Instrumental setup for polarization measurements at the telescope with the last two mirrors of the optics chain and the polarization module with the HWP and the stepper motor mounted in front of the entrance window of the cryostat. The polarizer is tilted by approximately 10 degrees with respect to the optical axis to avoid standing waves.} \label{polarsetup} \end{center} \end{figure*} | This paper presents the first astrophysical polarization measurements with KIDs. For these measurements, we have adopted a simplified polarization system consisting of an achromatic, continuously rotating HWP at approximately 3~Hz, an analyzer, and arrays of KIDs not sensitive to polarization. The fast modulation of the input polarization signal with the HWP allowed us to significantly reduce the atmospheric emission in the polarized signal. Instrumental polarization in the form of intensity to polarization leakage with a non-trivial-point-spread function has been observed at the level of 2\% to 3\% peak to peak for point- like and extended sources, respectively. We have successfully developed an algorithm to correct for this systematic effect. We are then left another kind of instrumental polarization that generates a polarized signal directly proportional to intensity at the level of 0.7\% and 0.6\% at 1.15 and 2.05~mm, respectively, that can be corrected. We have observed 3C286, a quasar used as a standard polarization calibrator in the literature and have found a total flux, a polarization degree, and orientation in agreement with existing data. These results confirms findings for other quasars, such as 3C279, 3C273, and 0923+392, for which we either comparable results in the literature or performed simultaneous measurements with XPOL. We have also observed compact and extended sources such as Cygnus~A, OMC-1, and M87, and, again, found consistent results with existing polarization maps at approximately the same wavelength ({\it e.g.} OMC-1 \cite{scubapol}). All these observations establish the accuracy of our system and analysis on astronomical sources with fluxes of approximately one Jansky and degrees of polarization as low as 3\%. On extended sources such as OMC-1, \nika\ observations confirm that polarization vectors align well with the intensity structures indicating the presence of well ordered magnetic fields. To our knowledge, our observations of Cygnus~A and M87 are the first ones in polarization at millimetric wavelengths. \nika\ has been a successful test-bench for the \nikad \footnote{http://ipag.osug.fr/nika2} camera, which shares the same polarization system, although limited to the 260~GHz channel. \nikad\ will observe the sky at the same frequencies with ten times more detectors and a FOV of 6.5 arcminutes. The \nikad\ camera has been installed at the IRAM 30 meter telescope in Spain on October 2015 to start its commissioning phase for unpolarized observations. A polarization dedicated commissioning will follow, during which we will improve our understanding of the observed instrumental polarization and our ability to correct for it. This paper shows the potentialities of an instrument based on KIDS and a fast and continuously rotating HWP to measure polarization, especially from the ground, where atmosphere is a nuisance, even more at low temporal frequencies and large angular scales. It opens the way to forthcoming observations with \nikad\ that will undoubtedly provide advances in the field of Galactic emission and interactions with the magnetic field. | 16 | 9 | 1609.02042 |
1609 | 1609.03475_arXiv.txt | Observations of pre-transitional disks show a narrow inner dust ring and a larger outer one. They are separated by a cavity with no or only little dust. We propose an efficient recycling mechanism for the inner dust ring which keeps it in a steady-state. No major particle sources are needed for replenishment. Dust particles and pebbles drift outwards by radiation pressure and photophoresis. The pebbles grow during outward drift until they reach a balanced position where residual gravity compensates photophoresis. While still growing larger they reverse their motion and drift inwards. Eventually, their speed is fast enough that they get destroyed in collisions with other pebbles and drift outwards again. We quantify the force balance and drift velocities for the disks LkCa15 and HD135344B. We simulate single particle evolution and show that this scenario is viable. Growth and drift timescales are on the same order and a steady state can be established in the inner dust ring. | \label{sec:intro} Protoplanetary disks with optically thin gaps (pre-transitional disks) have been observed frequently \citep{Calvet2002,Najita2007,Sicilia-Aguilar2008, Bruderer2014,Marel2015}. The basic structure of these disks is as follows. \begin{itemize} \item There is an inner disk up to a gap opening distance from the star $r_{\rm gap}$ which is usually on the order of about one AU. \item This inner ring contains dust in a significant amount. Radiation from the central star can cross the inner dust disk depending on the dust density but with intensity loss up to several orders of magnitude. \item There is a cavity from $r_{\rm gap}$ to $r_{\rm cav}$, where the disk contains (nearly) no dust. \item The inner edge of the outer disk $r_{\rm cav}$ is usally several tens of AU from the star. \item The inner disk up to $r_{\rm cav}$ is not gas-free. As accretion partly goes on and as recent CO measurements show, the gas content can be very significant. \item Compared to the gas the solid fraction of the disk is strongly reduced. This explicitly includes small sub-micron dust in the warmer inner parts of the gap. \end{itemize} Considering this basic setup, one would expect the inner dust ring to vanish quickly since there is no dust reservoir outside the ring to drift inwards and replenish particle losses that might be assumed due to accretion or particle growth. In this paper we introduce a recycling mechanism which takes place in the inner dust ring and keeps a self-sustained dust distribution. It prevents particle accretion by the star and it prevents dust to vanish due to unlimited growth to larger sizes no longer observable. Classic calculations of dust movement (e.g. by \cite{Weidenschilling1977a} which is adopted frequently) do not include additional radial forces. Therefore in our model we included radiation pressure and photophoretic forces. Photophoresis has long been known and applied in atmospheric science \citep{Rohatschek1995,Cheremisin2005,Beresnev2003c}. It was only introduced to protoplanetary disks by \citet{Krauss2005} and \citet{Wurm2006} as potential candidate to drive dust particles and chondrules and concentrate them in specific locations. Since then the quantiative description of photophoresis has been improved based on numerical simulations and laboratory experiments \citep{Wurm2010,VonBorstel2012, Loesche2014, Matthews2016, Loesche2016b}. Futher applications of photophoresis to the inner edge of full protoplanetary disks considered the separation of different materials or local concentration \citep{Haack2007, Wurm2013, Cuello2016}. Also large scale particle transport by photophoresis in an optical thin disk or over the surface of the disk have been calculated, i.e. to explain how high temperature minerals forming close to the sun can be found further out in the disk, for example in asteroids or comets \citep{Wurm2009, Mousis2007, Moudens2011a}. Currently, photophoresis is being explored as source of particle motion in a disk with temperature fluctuations (Loesche et al. submitted) which is work ongoing. Photophoresis by thermal radiation might also be important in the context of (hot) giant planet accretion \citep{Teiser2013}. Related to this more accurate treatments of photophoretic forces in radiation fields of optical thick disks have already been worked out \citep{McNally2015}. The motion of dust in optical thin disks explicitly includes transitional disks which were considered by \cite{Takeuchi2008} and \cite{Herrmann2007}. \cite{Dominik2011} looked for an explanation why the gap is so clean of dust. They studied the influence of radiation pressure which pushes the dust outwards but come to the conclusion that this is not a viable mechanism for keeping the gap clean of small dust coming from the outer disk. They consider photophoresis shortly but discard it due to the fact that photophoretic motion is small for sub micron particles. We do not consider in detail here why dust from the outer disk is not crossing the inner edge of the outer disk. This might be a particle trap due to the pressure drop or an embedded planet. We consider radiation pressure and photophoresis for the inner dust ring here. For one thing we show later that, in fact, photophoresis can dominate the particle movement even for $10^{-6}$ m sized particles at least in the inner parts of the disk. In addition though the small grains are embedded in a cloud of larger grains and cannot be regarded as isolated. While effects of photophoresis on small grains might be low photophoretic drift is significant for larger grains which in turn influences the small grain fraction. As detailed below, mm-sized particles can set off with velocities up to 10 m/s close to the star and cross a wide distance easily on a short timescale. If they encounter smaller grains on their way outwards they can partly collect them and grow bigger. Photophoretic drift decreases in efficiency with increasing size and a stability point will be reached while feeding further on any small dust particles. This prevents further outward drift of large grains and of small grains which are intercepted by the large particles. Therefore the gap can be kept clean at its inner edge and the dust will stay in the inner ring. Once the large particles reach a critical size they switch their drift direction and move back inwards. Close to the star they meet their equals in size with high velocities and get destroyed in collisions. This produces some dust and pebble size particles again, which -- once more -- move outwards efficiently, scavenge small dust, get back and so on. This principle of cleaning is actually not unheard of. Cleaning of the Earth's atmosphere works in a similar way. Sub-micron grains (smog) easily accumulate under dry conditions. However, if it rains, eventually, the raindrops collect the small dust and clean the atmosphere. In that case gravity is the driving force for the large particles instead of photophoresis. The same concept is used technically to clean airflows from small particles as droplets are introduced and capture fine dust. A sketch of the protoplanetary version of photophoretic sweep up cleaning is shown in fig. \ref{fig:diskclearing}. \begin{figure*} \figurenum{1} \plotone{ppdGROWTH_PREV.pdf} \caption{Scheme of the disk structure and sketch of the self-sustained recycling process which keeps the mass inside the inner disk by photophoretic sweep up. Inside the inner disk (between $r_{\rm sub}$ and $r_{\rm cav}$) small particles generally tend to drift outwards. Due to the collisional behaviour, the larger particles sweep up the smaller particles and grow. Once they reach a critical size the drift direction switches and they move inwards which further supports the sweep up process. Eventually, the large particles get destroyed in collisions with particles of (more or less) the same size and the whole process can start again. The disks contains only little dust inside the gap (between $r_{\rm cav}$ and $r_{\rm gap}$) but gas is still present, although less than in the outer disk ($ > r_{\rm gap}$). For small particles the drift is positive for $r \lesssim r_{\rm gap}$ and negative for $r \gtrsim r_{\rm gap}$ while larger particles always drift inwards for large distances.} \label{fig:diskclearing} \end{figure*} In the following sections we calculate the drift of particles in the disks LkCa15 and HD135344B and perform single particle evolution simulations showing that a self sustained recycling process can be established where large particles drift outwards up to $r_{\rm gap}$, grow beyond a certain mass and fall back inwards where they get destroyed again. | We calculated size and distance dependent drift velocities for dust particles in the inner dust ring of pre-transitional disks including photophoretic forces and radiation pressure. For the disks LkCa15 as well as HD135344B the resulting outer edge of the dust ring reachable by larger particles is in good agreement with the disk models (see fig. \ref{fig:drift3DLK}, \ref{fig:drift3DLKM2} and \ref{fig:drift3DHD}). Using the calculated velocities, we showed that a self sustained collisional recycling mechanism can be established in the inner dust ring of a pre-transitional disk. | 16 | 9 | 1609.03475 |
1609 | 1609.06857_arXiv.txt | We use the Low Frequency Array to perform a systematic high spectral resolution investigation of the low-frequency 33-78~MHz spectrum along the line of sight to Cassiopeia A. We complement this with a 304-386~MHz Westerbork Synthesis Radio telescope observation. In this first paper we focus on the carbon radio recombination lines. We detect Cn$\alpha$ lines at -47 and -38~km~s$^{-1}$ in absorption for quantum numbers n=438-584 and in emission for n=257-278 with high signal to noise. These lines are associated with cold clouds in the Perseus spiral arm component. Hn$\alpha$ lines are detected in emission for n=257-278. In addition, we also detect Cn$\alpha$ lines at 0~km~s$^{-1}$ associated with the Orion arm. We analyze the optical depth of these transitions and their line width. Our models show that the carbon line components in the Perseus arm are best fit with an electron temperature 85~K and an electron density 0.04~cm$^{-3}$ and can be constrained to within 15\%. The electron pressure is constrained to within 20\%. We argue that much of these carbon radio recombination lines arise in the CO-dark surface layers of molecular clouds where most of the carbon is ionized but hydrogen has made the transition from atomic to molecular. The hydrogen lines are clearly associated with the carbon line emitting clouds, but the low-frequency upper limits indicate that they likely do not trace the same gas. Combining the hydrogen and carbon results we arrive at a firm lower limit to the cosmic ray ionization rate of 2.5$\times$10$^{-18}$~s$^{-1}$, but the actual value is likely much larger. | Since the study by PAE89 there have been two other detailed investigations of the CRRLs along the Cas~A line of sight by \citet{Pa94} and KAP98. Neither of these studies were able to fit both the integrated optical depths and the line widths of the CRRLs for a single set of physical parameters. This is likely due to the reasons outlined in Sect.~\ref{s_compare_prev}. With the more detailed models by S16a,b we have shown in Sect.~\ref{s_combine_constraint} that we are now able to obtain a satisfactory fit to both the linewidth and the optical depths. The derived electron densities of $\sim$0.04~cm$^{-3}$ translate into a density of hydrogen nuclei of 286~cm$^{-3}$, adopting the gas phase carbon abundance of 1.4$\times$10$^{-4}$ \citep{Ca96,So97}. This density is high compared to the typical density of diffuse clouds traced by the 21~cm HI line \citep[n$_{\rm{H}}\sim$50~cm$^{-3}$; ][]{Wo03}. However, they are quite comparable to densities derived for the well studied diffuse sight-lines of $\zeta$~Oph, $\zeta$~Per, and $\omicron$~Per where simultaneous modeling of the observations of many atomic and molecular species result in densities in the range of 200--400~cm$^{-3}$ \citep*[e.g.][]{Di86,Vi88}. The derived temperature of 85~K is well in the range of temperatures derived by the same studies as well as temperatures derived from HI 21~cm line studies \citep*[e.g.][]{Me75,Di82,Di90,He03}. The derived thermal pressure of 2$\times$10$^{4}$~K~cm$^{-3}$ agrees, of course, well with those measured towards $\zeta$~Oph, $\zeta$~Per, and $\omicron$~Per but they are an order of magnitude larger than the typical gas pressures derived from UV absorption lines measuring the CI fine structure line excitation ($\sim$4$\times$10$^{3}$~K~cm$^{-3}$; e.g. \citet{Je11}). Finally, our sizes are comparable to the sizes of typical HI diffuse clouds \citep[$\sim$10~pc, e.g.][]{Sp78} but the derived column densities are an order of magnitude higher. These differences may merely reflect that we are probing clouds in the Perseus and Orion spiral arms rather than diffuse clouds in the local Solar neighborhood. Specifically, the clouds probed by the CRRLs may be the atomic/CO-dark surfaces of molecular clouds. As our clouds are situated in spiral arms and molecular clouds have been detected along the same sight line at the same velocities \citep{Bi86,Li99,Mo06,Ki14}, this is quite reasonable. We note that it is difficult to keep CII ionized over the large path lengths inferred here, unless we are viewing the Cas~A clouds from a preferred angle. It is therefore likely that the clouds we are observing are sheet-like structures. Filamentary spurs springing off spiral arms are a common characteristic of a turbulent ISM and these are dominated by atomic and CO-dark molecular gas \citep{Sm14}. The inferred pressures are also in line with measured pressures of molecular cloud surfaces \citep[e.g.][]{Bli80,He01}. Moreover, the very similar sight-lines towards $\zeta$~Per and $\omicron$~Per traverse the atomic HI surfaces associated with the B3/B4/B5 molecular clouds \citep*{An92}. On the other hand, the high HI 21~cm column densities and the implied high visual extinction of these clouds (N$_{HI}\sim$2$\times$10$^{22}$~cm$^{-2}$; A$_{V}\sim$10 magnitudes) are very high for atomic clouds (N$_{HI}\lesssim$~2$\times$10$^{21}$~cm$^{-2}$; A$_{V}\lesssim$~1; e.g. \citet{Di90}). Indeed, for visual extinctions in excess of 1 magnitude, much of the gas phase carbon is expected to be in CO (and to a lesser extent in CI) rather than CII \citep[e.g.][]{Di86,Vi88}. This may just be a matter of geometry as the clouds probed by the CRRL may be arranged into thin sheets as is common for large scale HI structures \citep{Sp75,Sa74,He84}. Future observations will be instrumental in settling the relationship between the CRRL gas and the molecular clouds in the direction of Cas~A. \subsection[]{Gas pressure}\label{s_pressure} In the previous sections we found that we can constrain the electron temperature and density for both components to better than 15 percent. If we consider T$_{e}$ and n$_{e}$ to be independent variables then this translates to an uncertainty of up to 20 percent for the electron pressure at the 1$\sigma$ confidence level. One would expect the uncertainty on the pressure to increase at the 2 and 3$\sigma$ levels, however this is not observed in Figs.~\ref{f_47_crrl_comb} and \ref{f_38_crrl_comb}. These figures show that T$_{e}$ and n$_{e}$ are not independent and that the electron pressure remains to be constrained to better than 20 percent at the 3$\sigma$ confidence level. This tight relation ship between T$_{e}$ and n$_{e}$, along lines of almost constant pressure, is driven primarily by our constraints on the range in n where the CRRL emission to absorption transition takes place (Fig.~\ref{f_nt_emabsp}). Although the electron pressure itself is well constrained by our measurements there is still an uncertainty in translating this to a thermal gas pressure due to the unknown abundance of carbon in these clouds. The typical gas phase carbon abundance in the interstellar medium has been found to be [C/H]$\sim$1.4$\times$10$^{-4}$ \citep[e.g.][]{Ca96}. It is possible to derive the carbon abundance [C/H] by comparing CRRL measurements with HI 21~cm absorption measurements, under the assumption that the lines arise from the same gas and that within this gas singly ionised carbon is the dominant state of carbon, i.e. N(CII)/N(HI)$\approx$N(C)/N(H)=[C/H] \citep[e.g.][PAE89]{Oo15}. HI 21~cm absorption measurements have been carried out by e.g., \citet{Me75,Bi91,Sc97}. These studies find three main HI absorbing components at -47, -38 and 0~km~s$^{-1}$. These HI 21~cm components, in terms of velocity and FWHM, are in good agreement with our CRRL measurements and indicate that it is likely that the HI 21~cm absorption and our CRRL measurements spatially trace the same gas structures. A similar conclusion was reached by KAP98 (and references therein). However, these studies also find that the HI 21~cm absorption measurements are heavily saturated for the -47~km~s$^{-1}$ component and mildly saturated for the -38~km~s$^{-1}$ component. This means that from these measurements we can only obtain a lower limit to true cold HI column density. Following \citet{Sc97} find N(HI)~$>$~4$\times$10$^{21}$~cm$^{-2}$ and N(HI)~$>$~3$\times$10$^{21}$~cm$^{-2}$ for the -47 and -38 component respectively. An upperlimit to the HI column density can be obtained by considering the total hydrogen column N(H) from X-ray observations. The maximum total N(H) reported by \citet{Hw12} is about 3.5$\times$10$^{22}$~cm$^{-2}$. From these measurements we can only constrain the carbon abundance to be in the range [C/H]=1.3-11$\times$10$^{-4}$ for the -47 component and [C/H]=0.7-7.7$\times$10$^{-4}$ for the -38 component. This range in [C/H] allowed by the RRL and HI measurements is large and especially the upper limits of this range are likely not realistic. We therefore adopt the gas phase abundance by \citet{Ca96} here and then we find a thermal pressure p$_{thermal}$/k=2.4$\times$10$^{4}$~K~cm$^{-3}$. This is consistent with the model prediction of p$_{thermal}$/k$\sim$1$\times$10$^{4}$~K~cm$^{-3}$ by \citet[][their Fig.~7]{Wo03} for densities n$_{H}\sim$286~cm$^{-3}$ at a Galactocentric radius of about 10.5~kpc. It is also consistent with measurements and simulations of the external pressure for molecular clouds in the Galactic midplane \citep[e.g.][]{Bli80,He01,Gi16}. The turbulent pressure in the gas can be obtained from the observed FWHM of the turbulent (Doppler) line broadening. We calculate the turbulent velocity dispersion as $\sigma_{turbulent}$=3$^{0.5}\times$FWHM/2.355 and find p$_{turbulent}$/k=1.9$\times$10$^{5}$~K~cm$^{-3}$ for the -47 component and p$_{turbulent}$/k=7.6$\times$10$^{5}$~K~cm$^{-3}$ for the -38 component. We thus find that the turbulent pressure dominates over the thermal pressure in both clouds as is typical in the interstellar medium of the Milky Way \citep[e.g.][ and references therein]{Wo03}. Another contribution to the pressure in the clouds are magnetic fields. Using OH measurements \citet{He86} infer an average magnetic field strength B$\sim$8~$\mu$G. HI 21~cm Zeeman splitting measurements by \citet{Sc86} indicate an average parallel component of the magnetic field B$_{\rm{||}}\sim$20~$\mu$G. The reason for the difference between these measurements is not clear. This range in measurements indicates a magnetic field pressure p$_{magnetic}$/k=(1.8-4.5)$\times$10$^{4}$~K~cm$^{-3}$. This shows that the magnetic field pressure is of the same order as the thermal pressure and less than the turbulent pressure, although the HI measurements do allow for higher magnetic field pressures that may rival the turbulent pressure. \subsection[]{Hydrogen RRLs}\label{s_ionisation} We have detected two HRRL emission lines in our stacked WSRT spectrum, see Fig.~\ref{f_app_wsrt_full_stack}. This is the second detection of HRRLs along this line of sight. The first detection of HRRL emission at n=250 and associated with the -47 component was made by SS10 at 420 MHz. Our n=267 detection of this component at 344~MHz agrees well with theirs. For the -38 component, SS10 do not claim a detection, but they do see a feature in their spectrum. We confirm this feature here at the 4$\sigma$ level. The main peak of our -38 HRRL line agrees well with the feature seen in the spectrum by SS10, however we do find that our line is narrower than theirs. Our -47 HRRL line is also narrower than the detection reported by SS10, but not as much as for the -38 component. Line broadening of RRLs typically increases with increasing n, as discussed above, and this therefore does not explain the difference. The difference between our spectrum and SS10 is close to the noise level of the SS10 spectrum and their broader feature may be caused by a noise peak. Deeper observations are necessary to investigate this further. The HRRL velocity centroids in our WSRT spectrum, in the rest-frame for hydrogen, are at -47.4 and -38.6~km~s$^{-1}$. This agrees very well with the corresponding CRRL lines and shows that both the carbon and hydrogen lines likely originate in the same clouds, see Fig.~\ref{f_wsrt_hcrrl_overlay}. The line width of the CRRL and HRRL lines agree well for the -47 component, but the same is not true for the -38 component where our HRRL feature is significantly narrower than the corresponding CRRL feature (Fig.~\ref{f_wsrt_hcrrl_overlay}). This could indicate that only part of the -38 CRRL emitting gas is traced by the corresponding HRRL line. \subsubsection{Gas ionization} Low frequency HRRLs can be used to trace the hydrogen ionization rates in the CRRL emitting clouds, if they trace the same gas. For the -47 component this is possible and two methods have been proposed to derive the total hydrogen ionization rate from HRRL measurements. The first method, proposed by Shaver (1976), uses the ratio between the HI 21~cm and the HRRL integrated optical depths. It is important to use the integrated and not the peak optical depths here, as the HRRL emission at sufficiently low frequencies can be affected by line broadening due to the Stark effect \citep[e.g. S16b; ][]{Sh75}. In the previous section we saw that the HI~21cm absorption measurements are saturated and thus underestimate the true HI optical depth. This method therefore only provides an upperlimit to the ionization rate $\zeta_{\rm{H}}$(-47)~$<$~5$\times$10$^{-17}$~s$^{-1}$. A second method to obtain $\zeta_{\rm{H}}$ was first proposed by \citet{So87}, later modified by \citet{So90} and SS10, and uses the ratio between the CRRL and the HRRL integrated optical depths. For convenience we repeat the equation here; \begin{eqnarray} \begin{aligned} \zeta_{\rm{H}}&=&\alpha_{\rm{H}^(2)}[C/H]\left(\frac{\tau_{\rm{H_{n}}}\Delta\nu_{\rm{H_{n}}}}{\tau_{\rm{C_{n}}}\Delta\nu_{\rm{C_{n}}}}\right)\left(\frac{\Phi_{\rm{2}}n_{e}}{T_{e}^{0.5}}\right)\left(\frac{(b_{\rm{n}}\beta_{\rm{n}})_{\rm{C}}}{(b_{\rm{n}}\beta_{\rm{n}})_{\rm{H}}}\right) \end{aligned} \end{eqnarray} Here we have reformulated it in terms of the hydrogen (gas phase) recombination coefficient $\alpha^{(2)}$=$\alpha_{\rm{H}}^{(2)}\Phi_{\rm{2}}T_{\rm{e}}^{-0.5}$, where captures to the n=1 level are excluded \citep{Sp82}. $\alpha_{\rm{H}}^{(2)}$=2.06$\times$10$^{-11}$ and $\Phi_{\rm{2}}$ is an integral over gaunt factors that is tabulated in table 5.2 in \citet{Sp82}. We use the b$_{\rm{n}}$ and $\beta_{\rm{n}}$ values from S16a. For the gas phase abundance of carbon we find that $\zeta_{\rm{H}}$(-47)=3$\times$10$^{-18}$~s$^{-1}$. Following PAE89 we can also use the ratio of the HRRL to CRRL optical depth to estimate the volume density ratio of ionised carbon to protons (n$_{\rm{CII}}$/n$_{p}$) and electrons (n$_{\rm{CII}}$/n$_{e}$). Using our WSRT measurements at n=267 and the b$_{\rm{n}}$, $\beta_{\rm{n}}$ values from S16a we find n$_{\rm{CII}}$/n$_{p}$~=~15.5 and n$_{\rm{CII}}$/n$_{e}$~=~0.94 This shows that 94 percent of the free electrons are donated by carbon and that the proton to electron ratio is n$_{\rm{p}}$/n$_{e}$=0.06. The HRRL to CRRL hydrogen ionization rate we derive for the -47 component is an order of magnitude lower than reported by SS10. We find that this is entirely due to a difference in models used to compute the departure coefficients. We have also computed $\zeta_{\rm{H}}$(-47) from their n=250 measurement using our models and find that it is consistent with our measurement at n=267. Our hydrogen ionization rate for the -47 component is a factor of a few lower than the modeled cosmic ray ionization rate ($\zeta_{\rm{CR,10~kpc}}\sim$1$\times$10$^{-17}$~s$^{-1}$) and the EUV plus X-ray ionization rate ($\zeta_{\rm{XR,10~kpc}}\sim$8$\times$10$^{-18}$~s$^{-1}$) at a Galactocentric radius R$_{c}$=10~kpc \citep{Wo03}. Recent measurements of the cosmic ray ionization rate in diffuse clouds, through H$_{3}^{+}$ observations, by \citet{In12} have shown that the cosmic ray ionization rate is higher by almost an order of magnitude (i.e. $\zeta_{\rm{C}R}\sim$10$^{-16}$-10$^{-15}$~s$^{-1}$) for total hydrogen column densities N$_{\rm{H}}\leq$10$^{22}$~cm$^{-2}$. This would be inconsistent with our measurement. However, Indriolo et al. made only a few measurements in the range l=90-130~deg, most of which are upper limits, and for N$_{\rm{H}}>$2$\times$10$^{22}$~cm$^{-2}$ they find a steep drop to about 2$\times$10$^{-17}$~s$^{-1}$ for the cosmic ray ionization rate. \subsubsection {Grain neutralization} \citet{Li03} has pointed out that interactions with small grains may lower the RRL derived ionization rates. In this case our RRL measurement would provide a firm lower limit to the actual ionization rate. Atomic ions can not just be neutralized through gas phase recombination, but gas-grain interactions may also play a role through a process best called mutual neutralization \citep[e.g.][]{Dr87,LD88,Le88,Li03,Wo08}. In the literature this process is sometimes also referred to as grain neutralization. In this process large molecules and very small grains, or polycyclic aromatic hydrocarbons (PAH), can become negative charged by acquiring (free) electrons \citep{Ba94}. The models by \citet{Li03} show that mutual neutralization becomes increasingly important for regions that are more heavily shielded. At the gas density observed here these models show that, for the case of depleted gas phase abundances ([C/H]=1.4$\times$10$^{-4}$), mutual neutralization can decrease the proton density by up to a factor of $\sim$100 relative to gas phase recombination. While this process will affect the neutral atomic carbon abundance \citep{Ba98}, C$^{+}$ remains the main reservoir of carbon and the dominant free electron donor and \citet{Li03} show that at these gas densities the free electron density is very close to the singly ionized carbon density. In equation 1 only gas phase recombination is taken in to account \citep[e.g.][]{So87}. Below we have modified this equation by specifically including a factor $\eta_{GN}$ which is the ratio of the total (gas and grain) recombination rate to the gas phase recombination rate (i.e. this is the inverse of value plotted in Fig.~1 in \citet{Li03}); \begin{eqnarray} \begin{aligned} \zeta_{\rm{H}}&=&\eta_{GN}\alpha_{\rm{H}^(2)}[C/H]\left(\frac{\tau_{\rm{H_{n}}}\Delta\nu_{\rm{H_{n}}}}{\tau_{\rm{C_{n}}}\Delta\nu_{\rm{C_{n}}}}\right)\left(\frac{\Phi_{\rm{2}}n_{e}}{T_{e}^{0.5}}\right)\left(\frac{(b_{\rm{n}}\beta_{\rm{n}})_{\rm{C}}}{(b_{\rm{n}}\beta_{\rm{n}})_{\rm{H}}}\right) \end{aligned} \end{eqnarray} We find that upon including grain neutralization that the above hydrogen ionization rate, as derived from the HRRL over CRRL ratio, may need to be corrected upwards to a maximum of $\zeta_{\rm{H}}$(-47)$\sim$3$\times$10$^{-16}$~s$^{-1}$, if this process dominates within the environment in which the RRL emission arises. Similarly the upperlimit on $\zeta_{\rm{H}}$(-47) derived from the HRRL over HI 21~cm ratio would also have to be corrected upwards. Currently there are no direct observational constraints on the importance of mutual neutralization for the clouds studied here. \subsubsection{HRRL vs. CRRL gas conditions} In the above calculations for the hydrogen ionization rate we have implicitly assumed that the CRRLs and HRRLs trace gas with the same physical conditions and the same geometry. To test this we plot in Fig.~\ref{f_wsrt_hcrrl spectra} the HRRL optical depth as a function of n with the HRRL models from S16a for the best-fit CRRL conditions overplotted. In order to fit the model to the data we allow the ionized hydrogen column density N$_{\rm{HII}}$=n$_{\rm{HII}}$$\times$L$_{\rm{HII}}$ to differ from the singly ionized carbon column density N$_{\rm{CII}}$=n$_{\rm{CII}}$$\times$L$_{\rm{CII}}$. If we demand HII and CII to follow the same geometry, i.e. L$_{HII}$=L$_{\rm{CII}}$, then the HRRL to CRRL optical depth ratio directly traces n$_{HII}$/n$_{\rm{CII}}$ i.e. the relative fraction of free electrons donated by hydrogen and carbon. In agreement with above we find n$_{\rm{HII}}$/n$_{\rm{CII}}$=0.06. Fig.~\ref{f_wsrt_hcrrl spectra} shows that for the -47 component the HRRL model with the best-fit CRRL gas conditions can match the high frequency detections by us, \citet{Oo15} and SS10, but not our low frequency 3$\sigma$ LBA HRRL limits. This indicates that for the -47 component the CRRL and HRRL do not trace the same gas. To determine whether any other HRRL model can fit the HRRL measurements we ran a full HRRL grid search with the same parameters as done for the CRRLs above. We constrain the model fits by demanding that the model must be able reproduce all the detections within their 1$\sigma$ errors and provide low frequency values that fall within the 3$\sigma$ LBA limits. For the -47 component we find that only some significantly colder and higher density models, i.e. T$_{e}$=30-50~K, n$_{e}$=0.065-0.11~cm$^{-3}$ and EM$_{H}$=0.0007-0.002, are able to fit the measurements. This comparison of the HRRL and CRRL models suggests that the HRRL and CRRL emission may not originate in the same region with the same physical conditions. Alternatively, it is possible that the CRRLs probe CO-dark molecular gas (Sect.~\ref{s_discuss}). In such gas carbon is ionized but hydrogen is in molecular form, a large contribution to the CRRL emission from CO-dark gas may then be expected. Spatially resolved investigations at higher frequencies (1-8~GHz) of dense PDRs have shown that in some cases narrow HRRL and CRRL lines do not trace the same gas \citep[e.g.][ and references therein]{Ro89}. Deeper and higher spatial resolution measurements are necessary to investigate this in cold clouds at low frequencies (Salas et al. in prep.). \subsection{CRRL modeling uncertainties}\label{s_model_uncertainties} The modeling approach that we used here has a number of uncertainties that we will discuss below. \subsubsection{Spatial structure} We have used a homogenous slab model with a constant temperature and density and a filling factor of unity to model the clouds in front of Cas~A. This approach is likely a simplification of the true situation for these clouds. There have been a number of studies performed to explore the physical conditions and spatial structure in the cool atomic and molecular gas of the Cas~A clouds \citep[e.g.][]{Ki14,Mo06,Li99,Sc97,An94,Bi91,Ba84,Ba83,dJ78}. These studies show: (i) that the cool gas extends over most of the face of the remnant, (ii) that the cool gas has spatial structure on arcmin-scales and peaks in a filamentary-like structure over the southern part of the remnant running from the western hotspot to the south-east of the remnant, and (iii) the -38 component is more localized and shifted towards the western part of the remnant, as compared to -47 component, although this could be a sensitivity issue. The observed CRRL emission is consistent with this arcmin-scale picture and \citet{An94} argue that on 2.7$\times$2.4 arcmin$^{2}$ scales the CRRL emission shows a better spatial and velocity correlation with HI 21~cm absorption than with $^{12}$CO emission, although they also note that there are differences between all three tracers. Observations of $^{12}$CO on larger scales show that the southern filamentary structure seen in absorption against Cas~A is likely the edge of a larger molecular cloud complex that is located to the south of the remnant \citep[e.g.][]{Ki14,Ba84}. Higher spatial resolution studies have been performed in HI 21~cm absorption and in several molecular tracers \citep[e.g.][]{Bi91,Ba83,Ba84}. The HI 21~cm study by \citet{Bi91}, with a spatial resolution of 7 arcsec, shows that the HI absorption extends over the entire face remnant and that there is great complexity within it. They find several morphological structures identified based on velocity cuts and describe these structures as filaments, arcs, loops and irregular with typical sizes varying from about 0.5 to 3 arcmin. Molecular absorption line studies are consistent with these sizes. Additional substructure may be present and \citet{Ba84} based on the low filling factor (f=0.04) they derive for one of their ammonia clouds find that the molecular clouds may contain structure as small as 8 arcsec. They interprete this as evidence for dense, high pressure clumps with physical sizes of 0.12~pc and pressures p$_{thermal}$/k$\sim$7$\times$10$^{4}$~K~cm$^{-3}$. Given the available data we recognize that our CRRL measurements likely measure an average which is weighted towards the southern part of the remnant. By assuming a unity filling factor we average over a range in physical conditions that may be in present in the gas. On arcmin-scales the total, i.e. the sum of the -38 and -47 component, CRRL optical depth does not vary by more than about a factor of 2 across the remnant \citep{An94}. \citet{As13} shows that, except for an overall increase in optical depth, there are no significant differences for the total CRRL integrated optical depth as function of n (albeit over a very limited range in n) observed against the western hotspot as compared to the sum over the entire remnant. The low-frequency CRRLs observed here likely trace gas intermediate between the atomic and molecular phase (e.g. Sect~\ref{s_discuss}) and a substantial filling factor seems reasonable. Low filling factors for the CRRL emitting gas would imply even larger, and likely unrealistic, CII column densities given the required beam dilution corrections. The physical conditions derived here may therefore represent a reasonable average of the true physical conditions. If higher spatial resolution observations find evindence for low filling factors of the CRRL emitting gas then this can effect the observed optical depths as a function of n as the underlying continuum emission from Cas~A is also highly structured in terms of the surface brightness and spectral index \citep[e.g.][]{Ka95}. In particular this may effect the measurements for the potentially more localized -38 component. A more detailed analysis of the spatial structure for the CRRLs along the line of sight to Cas~A will be presented elsewhere (Salas et al. in prep.). \subsubsection{Radiation field \& radiative transfer} In this work we have assumed that the clouds are embedded within an isotropic radiation field. At the distance of of Cas A an angular scale of 1~arcmin corresponds to 1~pc. Over these small spatial scales we feel it is reasonable to expect that the low-frequency Milky Way synchrotron radiation field is isotropic. Comparison of our LOFAR interferometric data with existing single dish radio surveys \citep[e.g.][]{Ha82,La70,Ro99} shows that the bulk ($\gtrsim$80\%) of the low-frequency Milky Way synchrotron emission is emitted on scales larger than about 10 wavelengths, or equivalently on angular scales larger than of about 6 degrees. The existing low-frequency Milky Way single dish measurements do not allow for a diffuse Milky Way contribution that is less than about 800~K at 100~MHz \citep[e.g.][]{Ha82,La70,Ro99} and our measured linewidths do not allow for a total contribution greater than about 1600~K at 100~MHz. Given the above constraints we have investigated lowering the Milky Way contribution and adding a contribution from Cas~A to the radiation field. For the data presented here we find that this does not provide a better fit. As discussed in S16b the equations used here to calculate the line widths and optical depths are approximations. These approximations are valid at sufficiently high n levels. This is especially true in the case of a bright background source such as Cas~A. Following the prescription in S16b we have, for a few representative cases, calculated the exact solutions to the radiative transfer equation for the CRRLs along the line of sight to Cas~A. We find that the differences between the approximate and exact solutions in the case of Cas~A are less than one percent for n$>$225 and as such do not affect our results. \subsubsection{Collision rates} Our CRRL models depend on the ratio of the $^{2}$P$_{3/2}$ over the $^{2}$P$_{1/2}$ population, also referred to as the R value \citep{Wa82,Po92}. We have used the formulation by \citet{S16a} who give R in terms of collisions with electrons and hydrogen atoms using the rates given in \citet*{Ti85} and \citet*{La77}. The \citet{S16a} model does not include collisions with molecular hydrogen. We have investigated adding these collisions, using the rate given in \citet{Ti85}, and we find a small systematic effect on the computed b$_{n}\beta_{n}$ values that are shifted by about 5\%, for n$_{\rm{H_{2}}}$=n$_{\rm{HI}}$, towards lower values upon including these collisions, see Fig.~\ref{f_cmp_bbn_h2}. A more important effect on the CRRL models, in terms of b$_{n}\beta_{n}$, is the choice in $\ell$-changing collisions. S16a uses rates by \citet{Vr12}. These rates were the most up to date rates for the $\ell$-changing collisions at the time of writing. S16a also investigated rates by \citet{Pe64}. These rates give qualitatively similar b$_{n}\beta_{n}$ behavior, but quantitatively the results can differ substantially. The \citet{Pe64} rates are not suitable for this work as they diverge for densities n$_{e}<$0.05~cm$^{-3}$. Very recently there has been renewed interest in these rates by \citet*{Gu16a} and \citet*{Gu16b}. In a future paper we will address the influence of the $\ell$-changing rates on the Cas~A clouds in more detail. | 16 | 9 | 1609.06857 |
|
1609 | 1609.04580_arXiv.txt | The determination of the resolution of cosmological N-body simulations, i.e., the range of scales in which quantities measured in them represent accurately the continuum limit, is an important open question. We address it here using scale-free models, for which self-similarity provides a powerful tool to control resolution. Such models also provide a robust testing ground for the so-called stable clustering approximation, which gives simple predictions for them. Studying large N-body simulations of such models with different force smoothing, we find that these two issues are in fact very closely related: our conclusion is that the accuracy of two point statistics in the non-linear regime starts to degrade strongly around the scale at which their behaviour deviates from that predicted by the stable clustering hypothesis. Physically the association of the two scales is in fact simple to understand: stable clustering fails to be a good approximation when there are strong interactions of structures (in particular merging) and it is precisely such non-linear processes which are sensitive to fluctuations at the smaller scales affected by discretisation. Resolution may be further degraded if the short distance gravitational smoothing scale is larger than the scale to which stable clustering can propagate. We examine in detail the very different conclusions of studies by \cite{smith2003stable} and \cite{widrow_etal2009} and find that the strong deviations from stable clustering reported by these works are the results of over-optimistic assumptions about scales resolved accurately by the measured power spectra, and the reliance on Fourier space analysis. We emphasise the much poorer resolution obtained with the power spectrum compared to the two point correlation function. | % \label{sec:introduction} Numerical simulations using the N-body method are the primary instrument used to probe the non-linear regime of structure formation in cosmology and provide the basis for all theoretical predictions for the distribution of dark matter at the corresponding physical scales. Over the last few decades, such simulations have gained in refinement and complexity and have allowed the exploration of an ever larger range of scales (for a review see e.g. \cite{bertschinger_98,springel2005simulations,dehnen+reed_2011}). Nevertheless, the understanding of their precision and their convergence toward the continuum limit remains, at very least, incomplete, in particular for smaller scales (see e.g., \cite{splinter_1998, knebe_etal_2000, romeo_etal_2008, discreteness3_mjbm,power2016spurious}). In this context ``scale-free" cosmological models, in which both the expansion law and the power spectrum characterizing the initial fluctuations are simple power laws, have the advantage of relative simplicity, and they have for this reason been studied quite extensively in the literature (see e.g. ~\cite{efstathiou1988gravitational,colombi_etal_1996,bertschinger_98,jain+bertschinger_1998,smith2003stable,knollmann_etal_2008, widrow_etal2009,orban2013keeping,diemer+kravtsov_2015}). More specifically these models provide a testing ground for the numerical method through the predicted ``self-similarity" of the clustering: the temporal evolution of the clustering statistics must be equivalent to a rescaling of the distances. This follows from the fact that there is only one characteristic length scale (derived from the amplitude of the fluctuations) and one characteristic time scale in the model. Further the exact rescaling function can be determined from the evolution in the linear regime of arbitrarily small fluctuations. However, discreteness and numerical effects typically introduce additional characteristic scales (e.g., force regularization at small scales, particle density, finite box size, etc.) which lead directly to a breaking of such self-similarity. Thus the self similarity of clustering provides a potentially powerful tool to separate the scales affected by such non-physical effects from the physical results representing the continuum limit. The focus of this study is to exploit self-similar models to better understand the resolution at small scales of N-body simulations. In particular we will use simulations with a very small force smoothing which allow us to follow carefully the propagation of self-similarity to small scales in the course of a simulation. A further motivation for studying scale-free models is that they provide a very simple analytical prediction for non-linear clustering which is the stable clustering hypothesis (\cite{davis+peebles_1977,peebles}). This corresponds to the assumption that once a structure is strongly non-linear it no longer evolves in physical coordinates, i.e., structures behave as though they were isolated virialized structures. While this hypothesis can be made in any cosmological model, for scale-free initial cosmologies it implies, when combined with self-similarity, that the strongly non-linear regime of the two point correlation function (and also of the power spectrum) should be a power law function of the separation, i.e. $\xi(x) \propto x^{-\gsc}$ where the exponent $\gsc$ is a simple function of $n$, the exponent characterizing the power law behaviour of the initial fluctuations (with power spectrum $P(k) \sim k^n$). The stable clustering hypothesis can, at best, be a good approximation because it neglects in principle the evolution of structures due to their interaction in general (and their merging in particular). It is, nevertheless, a fundamental question about non-linear clustering to understand how good an approximation stable clustering in fact provides. Indeed, the assumption of the validity of this approximation at sufficiently small scales provided the basis of the assumed functional form of non-linear clustering at small scales in phenomenological approaches, like that of \cite{hamilton_etal_1991, peacock} (hereafter PD), which were widely used to compare galaxy data to cosmological models until a few years ago. Historically there have been numerous numerical studies of the validity of the stable clustering hypothesis in scale-free models, with, for a long time, inconclusive results. While, for example, \cite{padmanabhan1995pattern} and \cite{colombi_etal_1996} reported deviations from stable clustering, ~\cite{jain1997does}, \cite{bertschinger_98} and \cite{valageas_etal_2000} found results apparently in agreement with this hypothesis in the strongly non-linear regime. A subsequent larger study, by \cite{smith2003stable}, reported clear deviations from the stable clustering predictions at smaller scales. These results, confirmed also by the larger study of \cite{widrow_etal2009}, appeared thus to unambiguously detect the inadequacy of the stable clustering hypothesis, and more specifically of the PD fits to the non-linear clustering based on it. The latter have then been superseded by fits with ``halo models" which generically break stable clustering. Indeed these models are explicitly based on the assumption of smooth virialized structures which are built up through merging, which is qualitatively different from stable clustering which instead implies a hierarchy of virialized structures~\footnote{Nevertheless it is possible, as shown in \cite{ma+fry_2000a}, to write down very specific halo models which have the exponents predicted by stable clustering at asymptotically small scales.}. In this paper we closely re-examine the issue of the breakdown of stable clustering in scale-free cosmological models, which is, as we will see, inseparable from the issue of the resolution of N-body simulations of these models. We have been prompted to carry out the simulations and analysis reported here by results we obtained using smaller simulations, reported in a previous paper \citep{benhaiem2013self} in which we explored clustering in scale free models in a broader class than usually considered in cosmology. The conclusions of this study appeared to be discrepant with those of \cite{smith2003stable}, which, as discussed above, have been widely assumed in the literature to establish definitively clear {deviations} of non-linear clustering from that predicted by the stable clustering hypothesis. Indeed our conclusion --- using simulations somewhat smaller than those of \cite{smith2003stable}, but with higher resolution --- was that the resolved (i.e. self-similar) non-linear clustering was in good agreement with the stable clustering hypothesis. Moreover, while we observed apparent deviations from the stable clustering predictions like those reported by \cite{smith2003stable}, these were not in the self-similar regions. Further we have detected a clear dependence on force smoothing $\varepsilon$, by comparing simulations with different $\varepsilon$, precisely in the range of scales which has been considered by \cite{smith2003stable} in their fits. This would imply that the assumptions made by \cite{smith2003stable}, when obtaining their fits to the power spectrum, are strongly affected by force smoothing. The results of \cite{smith2003stable} for non self-similar cosmologies, and notably the standard $\Lambda$CDM cosmology, given in terms of the parameters of the ``halofit'' model, have been very extensively used in the literature. These have been revisited by other authors. In particular, \cite{takahashi_etal_2012} found that the results of \cite{smith2003stable} for the power spectrum at small scales (large wave-numbers) are indeed incorrect, due to the underestimation of the power generated by the effect of smoothing. \cite{takahashi_etal_2012} have corrected the halofit power spectrum, and this change has then been widely adopted in the literature. While the correction of the halofit power spectrum was taken into account for the $\Lambda$CDM simulations, the consequences for the results of \cite{smith2003stable} for scale-free simulations, and in particular for the issue of the validity of stable clustering, have not been examined in the literature other than in one other study \citep{widrow_etal2009}. In the present work we thus choose our simulations to allow a detailed comparison with the results of \cite{smith2003stable} for scale-free models, and to assess, in particular, the role of the force smoothing length in limiting their resolution. Specifically we present the study of six simulations, for the cases $n=-2$, $n=-1$ and $n=0$, and for $N=256^3$ particles (as \cite{smith2003stable}) and an Einstein-de Sitter (EdS) cosmology. For each case, we have run simulations with exactly the same initial conditions and numerical parameters, changing only the force smoothing. On the one hand we have used the same smoothing used by \cite{smith2003stable}, and, on the other hand, a smoothing as in \cite{benhaiem2013self}, smaller by a factor of six. The detailed analysis of these simulations allows us to draw clear conclusions concerning the results of \cite{smith2003stable} (and also \cite{widrow_etal2009}) and in particular the issue of the validity of stable clustering. It also reveals that there is in fact an intimate connection between the breakdown of this same approximation and the resolution of N-body simulations. Our study also allows us to address in detail the important issue of optimal choice of smoothing in a cosmological simulation. The paper is organized as follows. We first recall, in Sect.\ref{sec:a_family_of_scale_free_cosmologies}, the equations of motion in an expanding universe, the self-similar evolution of scale-free models and the prediction obtained in the stable clustering hypothesis for the two point correlation function. In Sect.\ref{Numerical_simulations} we describe the numerical simulations, and in Sect.\ref{sec:results} we present our results. Finally in Sect.\ref{sec:stable_clustering} we summarise our main conclusions. | % \label{sec:stable_clustering} We have revisited the study of scale-free models, with a focus on using them as a tool to understand better what the resolution of cosmological N-body simulations {truely are, i.e.,} how reliably such simulations can reproduce the clustering in the continuum physical limit. \subsection{Resolution in the strongly non-linear regime} Our main finding is that the measures of two point statistics in the strongly non-linear regime of our scale-free simulations, represent accurately the physical limit only in the range of scales in which stable clustering remains a good approximation. Indeed we have found a very clear and robust association between the real-space scale at which the two point {CF} deviates from the behaviour predicted by stable clustering and the scale at which self-similarity breaks down. We have explained that such an association is natural because the breakdown of stable clustering is indeed associated with physical processes which may intrinsically be much more sensitive to fluctuations at scales affected by the ultra-violet cut-offs --- notably the grid scale and force softening --- introduced by the N-body discretisation. Let us underline, firstly, that our conclusion is not that strongly non-linear physical clustering which is not stable {\it cannot} be resolved accurately in an N-body simulation, but just that in practice it is {\it not} accurately resolved in those we have done, nor in those of \cite{smith2003stable} and of \cite{widrow_etal2009}, which are fairly typical of current cosmological simulations. Conversely the physical processes such as merging which violate the stable clustering approximation are, in our simulations and those of \cite{smith2003stable}, apparently polluted by discreteness effects, and the corresponding clustering, which is measured in some cases over a significant range of scale, cannot be assumed to represent accurately the physical limit. Secondly, we cannot and do not conclude that {\it all} N-body simulations in the literature of realistic cosmological initial conditions fail to resolve the regime in which stability of clustering is not a good approximation. We believe, however, that our results place in serious question, at least, the accuracy of all such results. As a consequence they place in doubt the accuracy in particular of popular phenomenological fits to the strongly non-linear regime based on halos models. Indeed \cite{smith2003stable} is one of the reference studies in the literature for such fits (in particular the``halofit" model), and the fact that we have found its results to be not only quantitatively, but also qualitatively, incorrect for the case of scale-free initial conditions logically places in doubt the correctness of its interpretation of its simulation results for the case of spectra which are not scale free. As we have noted in the introduction, higher resolution simulations by \cite{takahashi_etal_2012} for these cases have in fact shown that the results of \cite{smith2003stable} at small scales to be manifestly resolution dependent. Our analysis of the scale-free models leads us to the conclusion that the real limits on resolution imply that, rather than adjustment of the best fit parameters of the phenomenological halofit model, it is the correctness of fitting to any such model breaking stable clustering in the strongly non-linear regime which should be placed in question. \subsection{Real space vs. reciprocal space analysis} One important aspect of our analysis is that we studied always in parallel the two point correlation properties in both real and reciprocal space. It is very clear from our results that, to understand the issue of spatial resolution, and also indeed that of stable clustering, is it absolutely essential to consider carefully the real space quantities: the physical phenomena are expected to be characterized fundamentally by real space scales and the mixing of real space scales in reciprocal space makes it much more difficult to identify the essential dependencies. Indeed we believe that the erroneous conclusion of \cite{smith2003stable} are essentially due to the use of a k space analysis only. \subsection{Choice of force smoothing} As we have noted, the question of what is the optimal smoothing for an N-body simulation of a cosmological model is an important open one, and we now summarise what conclusion we draw from our study about it. There are two different, but related, aspects to this question of optimisation. On the one hand, there is consideration of numerical cost: the smaller the smoothing, the greater the numerical cost to integrate accurately the $N$ body system. On the other hand, the use of a large smoothing bounds below the length scale which can be resolved, while too small a value can potentially amplify discrete effects --- most evidently, two body collisions --- which do not represent the physical collisionless limit. The question of its optimisation can thus be phrased as follows: how small a value of the force smoothing should be taken to maximize the range of scales over which physical clustering can be accurately simulated? Our results show clearly that {\it reducing} force smoothing, down to the values we have considered, somewhat smaller than those typically used in cosmological simulation, never decreases the range in which non-linear clustering is self-similar (i.e. physical) to a good approximation, but can, depending on the model, increase this range. In other words in no case have we found evidence that using higher resolution produces any significant degradation of the lower resolution result, and can, on the other hand, signicantly extend the range of resolved clustering (most strongly for $n=0$). In particular we infer from this that any associated additional two body scattering does not sensibly affect the quantities we measure. This is reasonable as we have indeed, as detailed in Sect. \ref{Simulation parameters}, increased numerical accuracy specifically to ensure accurate integration of the consequent less soft two body collisions (and the rate of two body collisionality is in fact only weakly dependent on $\varepsilon$, remaining finite even at $\varepsilon=0$). We have, on the other hand, found clear evidence that using a force smoothing which is larger than the scale down to which self-similarity can potentially propagate in the duration of the simulation (i.e. as seen in the higher resolution simulation) can lead to a significant degrading of the results, for the PS in particular. In summary our results indicate that there is no apparent reason for using a finite smoothing in cosmological simulations other than a consideration of numerical cost: provided the numerical accuracy is sufficient, we have not found any evidence of adverse effects of using a small smoothing. Such effects may of course exist, and manifest themselves at yet smaller values of $\varepsilon/\Lambda$, but we have not found them. We note that, for what regards two body effects, this is quite consistent with the conclusion of other detailed studies (e.g. \cite{knebe_etal_2000, joyce+syloslabini_2012}). Taking numerical cost into account, our conclusion is then that the optimal smoothing for scale-free simulations --- at least for the determination of the two point statistics we have studied --- is that which allows the resolution of the scale down to which self-similar clustering would propagate in the duration of the simulation if $\varepsilon$ were zero. In a non scale-free simulation, the equivalent would be expected to be the scale down to which the non-linear clustering is dominated by the density fluctuations initially modelled well in the initial conditions. In any model, if strongly non-linear clustering is stable to a good approximation, this minimal scale fixing the optimal softening can easily be estimated: it is $\sim L_v^0 (a_v/a_f)$ where $L_v^0$ is the average comoving size of the first resolved non-linear structures (containing e.g. $10^2$ particles) when it virializes, at a scale factor $a_v$, and $a_f$ is the final scale factor. Let us consider just how this depends, in a given model, on the size of the simulation (i.e. $N$). In units of the interparticle separation $\Lambda$ it just decreases as the inverse of the final scale factor (assuming fixed amplitude of power at the scale $\Lambda$), which is fixed just by $N$. Specifically, for a scale-free simulation, assuming simulations are stopped when the non-linear scale is a fixed fraction of the box size, we have $a_f \propto N^\frac{3+n}{6}$. For our $N=256^3$ simulations we have seen (cf. Fig.~\ref{fig-SS}) that the low resolution value (used also by \cite{smith2003stable}) appears to be close to optimal for the case $n=-2$, but larger than the optimal value for the other two cases. In the latter cases our results do not allow us to conclude whether our high resolution values are optimal either: to do so we would need to simulate with yet smaller $\varepsilon/\Lambda$ to see whether we can extend the range of measured self-similar clustering. Concerning the simulations of \cite{widrow_etal2009}, which use an $\varepsilon/\Lambda$ half that of \cite{smith2003stable}, and $N$ up to a factor of $4^3$ larger, the resolution appears also close to optimal for $n=-2$ but again significantly larger than optimal for $n=-1$. \subsection{Future studies} Our final conclusion from the present study is that further larger, studies of scale-free models should be undertaken to try to establish whether the breaking of stable clustering can be unambiguously detected in an N-body simulation, ideally of comparable sizes to the largest simulations currently performed in the community. As we have discussed, such simulations at larger particle number should be performed over a range of resolution (i.e. values of the parameter $\varepsilon/\Lambda$) which extends to the limit in which the range of self-similar clustering observed becomes independent of its value, i.e., in the case of stable clustering a resolution high enough to follow the stable evolution of the first virialized structures through to the end of the simulation. Unless it can be shown unambiguously in scale-free models, using a combined analysis both in real and reciprocal space, that self-similarity extends into the non-linear region where the predictions of the stable clustering hypothesis are clearly wrong, we conclude that one can have little confidence that realistic cosmological simulations, where the test of self-similarity is not available, can in fact accurately trace the physical clustering into the same regime. We note that large ($N=1024^3$) scale-free simulations with quite high resolution have in fact been performed recently by \cite{diemer+kravtsov_2015}, but analysed only to determine the properties of halos extracted from them and without detailed consideration of tests for self-similarity (or indeed tests for stable clustering). In a forthcoming study, using simulations similar to those presented here, we will also explore in detail the clustering in scale-free simulations in terms of halo properties, and address in details the question of which of the measured properties in simulations can be shown to be self-similar and therefore physical). In particular we will aim to determine which scales are resolved within the halos, and how their properties are related to that of the CFs. \bigskip {Our numerical simulations have been run on the HPC resources of The Institute for Scientific Computing and Simulation financed by Region Ile de France and the project Equip@Meso (reference ANR-10-EQPX- 29-01) overseen by the French National Research Agency (ANR) as part of the Investissements d'Avenir program.} {We are indebted to Bruno Marcos for his collaboration in the first phase of this project, and specifically for his contribution to the development of modified version of the Gadget code. We thank E. Bertschinger, S. Colombi, B. Diemer, C. Orban, R. Sheth and J. V$\ddot{\rm a}$liviita for useful conversations or remarks.} \setlength{\bibhang}{2.0em} \setlength\labelwidth{0.0em} | 16 | 9 | 1609.04580 |
1609 | 1609.04063_arXiv.txt | {The infrared Calcium Triplet and its nearby spectral region have been used for spectral and luminosity classification of late-type stars, but the samples of cool supergiants (CSGs) used have been very limited (in size, metallicity range, and spectral types covered). The spectral range of the \textit{Gaia} Radial Velocity Spectrograph (RVS) covers most of this region but does not reach the main TiO bands in this region, whose depths define the M sequence.}{We study the behaviour of spectral features around the Calcium Triplet and develop effective criteria to identify and classify CSGs, comparing their efficiency with other methods previously proposed.}{We measure the main spectral features in a large sample (almost 600) of CSGs from three different galaxies, and we analyse their behaviour through a principal component analysis. Using the principal components, we develop an automatised method to differentiate CSGs from other bright late-type stars, and to classify them.}{The proposed method identifies a high fraction ($0.98\pm0.04$) of the supergiants in our test sample, which cover a wide metallicity range (supergiants from the SMC, the LMC, and the Milky Way) and with spectral types from G0 up to late-M. In addition, it is capable to separate most of the non-supergiants in the sample, identifying as supergiants only a very small fraction of them ($0.02\pm0.04$). A comparison of this method with other previously proposed shows that it is more efficient and selects less interlopers. A way to automatically assign a spectral type to the supergiants is also developed. We apply this study to spectra at the resolution and spectral range of the \textit{Gaia} RVS, with a similar success rate.}{The method developed identifies and classifies CSGs in large samples, with high efficiency and low contamination, even in conditions of wide metallicity and spectral-type ranges. As this method uses the infrared Calcium Triplet spectral region, it is specially useful for surveys looking for CSGs in high-extinction regions. In addition the method is directly applicable to the \textit{Gaia} spectra.} | Red supergiants (RSGs) are evolved high-mass stars, characterised by very high luminosities $\log(L/L_{\sun})\sim4.5$\,--\,5.8 \citep{hum1979} and late spectral types (K and M). They are the result of the evolution of moderately high-mass stars with masses from $\sim8$ to $\sim40\:$M$_{\sun}$, which represent the overwhelming majority of high-mass stars \citep{eks2013}. Since this phase is short ($\lesssim10$\% of their lifetime), evolutionary models for high-mass stars find a strict test-bed in the RSG phase. The interest of RSGs goes beyond their role as evolutionary model constraints. Due to their high luminosity and low temperature, RSGs appear very bright in the infrared, and thus are easily observable at very large distances, even if they are affected by high extinction. Thanks to this, in the past few years, several massive and highly reddened clusters have been discovered in the inner Galaxy \citep[for example][]{dav2007,neg2012}, in the region where the tip of the Galactic bar is believed to touch the base of the Scutum arm, revealing recent widespread massive star formation in this part of the Milky Way. Stars massive enough to pass through the RSG phase are expected to end their lives as core-collapse supernovae (SNe). In fact, RSGs are the progenitors of type-IIP SNe \citep{gro2013, sma2015}, which is the most frequent SN type. Thus, the characterisation of RSGs (individually and as population) has an obvious interest for SN studies. From a theoretical point of view, high- and intermediate-mass stars are easy to tell apart because of their very different evolutionary paths. High-mass stars are those with enough mass ($\gtrsim8\:M_{\sun}$) to end their lives as SNe after a few million years of life, while intermediate-mass stars will go through the asymptotic giant branch (AGB) phase, lose their envelopes, and finally become white dwarfs (except in a few cases, close to the limit with high-mass stars, where an electron-capture SN is possible). Despite their different natures, RSGs are hard to distinguish from other late type stars, such as AGB or red giant branch (RGB) stars, by using only photometry. The intrinsic colours of all these stars are the same, as their temperatures are similar. Of course, the bolometric magnitude, $M_{\mathrm{bol}}$, of RSGs is much higher than that of RGB and most AGB stars, but this is not really helpful when the distances and extinctions are unknown, and there are many less luminous but closer foreground stars, as is the case of the Galactic plane. To break this degeneracy, spectroscopic studies are necessary. Classical spectral classification criteria were originally defined for the optical range \citep[e.g.][and references therein]{tur1985,kee1987}. However, as has been mentioned before, late stars are more easily accessible in the near infrared (NIR) than in the optical. The Calcium Triplet (CaT) spectral region, from $\sim8400\:$\AA{} to $\sim8900\:$\AA{}, has many advantages for a spectral study of RSGs. Firstly, this region is close to the emission peak of stars with temperatures typical of RSGs, and it is less affected by extinction than the optical range. Secondly, it is not affected by strong telluric absorption, as it is inside an atmospheric window. Thirdly, it is rich in spectral features that can be used for spectral classification, and many works have already studied them \citep{kir1991,gin1994,car1997,mun1999}. In fact, the CaT itself is a well-known luminosity discriminator \citep[e.g.][]{dia1989}. There are still some unresolved issues related to the spectral type and luminosity classification of RSGs. The number of standard stars of the MK system classified as RSGs is very limited, and some of them are not very reliable standards because they present spectral variations of a few subtypes. Even more dramatic is the situation among the M-type RSGs: only a handful of them have been sufficiently well-characterised. Thus, the number of RSGs studied in works dealing with cool stars in general \citep[e.g.][]{kir1991,gin1994,car1997} is really low, and they cover only the K sequence. In their spectral atlas of the CaT region at moderately-high resolution, \cite{mun1999} reach later spectral types, but only for dwarf and giant stars, never supergiants (SGs). In fact, the number of SGs considered by Munari~\&~Tomasella is extremely low. For M1 and later types, there are TiO molecular bands growing deeper in this wavelength range. Classical criteria define the M sequence by the presence and depth of the TiO bands in the optical spectral range. In the CaT range there are two main TiO bands (with bandheads at $8432+8442+8452\:$\AA{} and $8859\:$\AA{}), plus a weak VO band (at $8624\:$\AA{}), which are used for the same purpose (see Fig.~\ref{sec_spt}). However, these bands represent a major complication for luminosity classification. At low and mid-resolutions these bands erode the continuum, weakening other spectral features, and even erasing them \citep{dor2013}. Therefore, the bands affect the line ratios and other measurements used as luminosity class (LC) criteria, rendering most of them useless except for the earliest M subtypes (those earlier than M3). Being so, extrapolation of the classification scheme from earlier types cannot be used. Even the CaT becomes unable to separate clearly LC~I from LC~II and LC~III \citep{neg2011}. However, the classification is still roughly possible if the spectral type (SpT) is known, as this will predict the TiO bandhead depths, and therefore warn about the erosion suffered by other spectral features \citep{neg2011,neg2012}. Interest in the CaT range has grown in recent years because this is the spectral range that is being observed by the \textit{Gaia} space telescope. \textit{Gaia} uses its Radial-Velocity Spectrometer (or RVS) to observe the centre of the CaT range (from $8470\:$\AA{} to $8740\:$\AA{}) at medium resolution \citep[R$=\lambda/\Delta\lambda=11\,500$;][]{kat2004}. Unfortunately, the spectral range observed does not cover any of the two main TiO bandheads in the region. Thus, for all M stars observed, all the spectral features in the RVS spectral range are affected by molecular band erosion, while the corresponding bandheads are not seen (and therefore their depth cannot be measured). In consequence, a strong degeneracy between SpT and luminosity appears for all bright late stars. Given the high extinction towards the inner Galaxy, many of the stars observed by the RVS in this area of the sky will be luminous cool stars. Because of their brightness in the CaT region, they will be excellent tracers of structure in these obscured regions. A good luminosity classification, however, will be necessary to make use of this information. In this paper, we set out to derive spectral and luminosity classification criteria making use of the spectral features available in the spectra of cool luminous stars. These criteria will be useful for the analysis not only of \textit{Gaia} spectra, but also of the products of forthcoming spectroscopic surveys, such as those that will be conducted with William herschell telescope Enhanced Area Velocity Explorer (WEAVE). | In this work, we have developed criteria based on PCA and SVM methods to separate SGs from non-SGs through their spectral features in the CaT spectral region, using a statistically significant sample from the SMC, the LMC, and the Galaxy. We obtained an efficiency identifying SGs of $0.98\pm0.04$, and a contamination of $0.02\pm0.04$. We also revisited those criteria used in the past to identify SGs (the sum of the EWs of the CaT, the blend at $8468$\:\AA{}, and the ratio between Fe\,{\sc{i}}~$8514\:$\AA{} and Ti\,{\sc{i}}~$8518\:$\AA), studying their behaviour for a significantly larger sample. We have evaluated their limitations and compared their efficiency and contamination with those obtained through our PCA/SVM method. We show that all classical methods present efficiencies similar to (strength of the CaT and the Fe\,{\sc{i}}~$8514\:$\AA{} to Ti\,{\sc{i}}~$8518\:$\AA{} ratio) or significantly lower (the blend at $8468$\:\AA{}) than the PCA method. However, their contaminations are significantly worse. In conclusion, the PCA method is more reliable than the classical ones. Furthermore, as the PCA uses information from many different spectral features, it is more robust than those criteria which are based on a few lines. The PCA method can also be applied to spectra taken with the RVS on board \textit{Gaia}. These spectra cover a spectral region shorter than our spectra, but in Appendix~\ref{gaia} we repeat the same analysis, using only those lines that lie inside the RVS spectral range. In spite of the good results obtained, we must highlight the fact that the efficiency and contamination depend on the typical SpTs in the sample (the mid- and late-M stars are hard to identify even with our PCA method), which depends on the metallicity of the population. We tested the PCA method for a sample from the Galaxy alone, obtaining a good efficiency ($0.94\pm0.13$) and a low contamination ($0.03\pm0.13$), statistically equivalent to the results from the three-galaxy sample. In addition, we also investigated the behaviour of a number of features depending on SpT (TiO bandhead at $8859$\:\AA{}, the EW of the Ti lines, and the calculated PC2). From this we developed a method to estimate the SpT of CSGs. Finally, we have also developed criteria to identify veiled RSGs, or at least good candidates for being such objects. | 16 | 9 | 1609.04063 |
1609 | 1609.08598_arXiv.txt | Fast magnetic reconnection may occur in different astrophysical sources, producing flare-like emission and particle acceleration. Currently, this process is being studied as an efficient mechanism to accelerate particles via a first-order Fermi process. In this work we analyse the acceleration rate and the energy distribution of test particles injected in three-dimensional magnetohydrodynamical (MHD) domains with {large-scale} current sheets where reconnection is made fast by the presence of turbulence. {We study the dependence of the particle acceleration time with the relevant parameters of the {embedded turbulence}, i.e., the Alfv\'en {speed} $V_{\rm A}$, the injection power $P_{\rm inj}$ and scale $k_{\rm inj}$ ($k_{\rm inj} = 1/l_{\rm inj}$). We find that the acceleration time follows a power-law dependence with the particle {kinetic} energy: $t_{acc} \propto E^{\alpha}$, with $0.2 < \alpha < 0.6$} for a vast range of values of $c / V_{\rm A} \sim 20 - 1000$. The acceleration time decreases with the {Alfv\'en speed} {(and therefore with the reconnection velocity)} as expected, having an approximate dependence $t_{acc} \propto (V_{\rm A} / c)^{-\kappa}$, {with $\kappa \sim 2.1- 2.4$ {for particles reaching kinetic} energies between {$1 - 100 \, m_p c^2$}, respectively. Furthermore, we find that the acceleration time is only weakly dependent on the $P_{\rm inj}$ and $l_{\rm inj}$ parameters} of the turbulence. The particle spectrum develops a high-energy tail {which can be fitted by a hard power-law already in the early times of the acceleration, in consistency with the results of kinetic studies of particle acceleration by magnetic reconnection in collisionless plasmas}. | Magnetic reconnection occurs when two magnetic fluxes of opposite polarity encounter each other. Under finite magnetic resistivity conditions a current sheet is formed at the discontinuity surface, where the field lines annihilate. Direct evidence of magnetic reconnection in astrophysical and space environments like the solar corona and the Earth magnetotail indicate that in some circumstances reconnection can be very fast, with rates which are a substantial fraction of the Alfv\'en speed $V_{\rm A}$. Fast reconnection breaks the magnetic field topology releasing magnetic energy explosively thus explaining the bursty emission, for instance, in solar flares. Relativistic particles are always observed in connection with these flares suggesting that magnetic reconnection can lead to direct particle acceleration \citep[see e.g., the reviews ][and references therein]{degouveia14, degouveia15, uzdensky2011}. In analogy to diffusive shock acceleration (DSA), in which particles confined between the upstream and downstream flows undergo a first-order Fermi acceleration, \citet{degouveia05} (hereafter GL05) proposed a similar process occurring within the current sheet where trapped particles bounce back and forth between the converging magnetic fluxes of opposite polarity in the {large-scale} reconnection region. The particles gyrorotate around a reconnected magnetic field \citep[see Figure 2b in][]{kowal11}, gaining energy due to collisions with magnetic irregularities at a rate $\Delta E/E \propto V_{\rm rec}/c$ (where $V_{\rm rec}$ is the reconnection speed) {implying} a first-order Fermi process with an exponential energy growth after several round trips (GL05, \citealt{degouveia15}). {A similar process was also invoked by \citet{drake06} who investigated particles accelerated inside two-dimensional contracting magnetic islands (or loops). In \citet{kowal11} it has been demonstrated the equivalence between the two mechanisms for driving first-order Fermi acceleration. This process has been extensively tested numerically mainly through two-dimensional (2D) particle-in-cell (PIC) simulations of collisionless electron-ion or electron-positron plasmas \citep[e.g.,][]{drake06,zenitani01,zenitani07, zenitani08,lyubarsky08,drake10,clausen-brown2012, cerutti14, li15}, and more recently also through three-dimensional (3D) PIC simulations \citep{sironi14,guo15, guo16}. However, these simulations can probe acceleration only at the kinetic scales of the plasma, of a few hundreds of the inertial length ($\sim 100 c/\omega_p$, where $\omega_p$ is the plasma frequency). To assess the first-order Fermi process in the large scales of the collisional MHD flows commonly observed in astrophysical systems, \citet{kowal11, kowal12a} have also successfully tested it in 2D and 3D MHD simulations injecting test particles in the reconnection domain. } Currently, fast magnetic reconnection is regarded as a potentially important mechanism to accelerate particles not only in the solar system context \citep[e.g.,][]{drake06, drake09, gordovskyy10, gordovskyy11, zharkova11, lazarian09, drake10, lazarian10,li15}, but also beyond it, in galactic and extragalactic environments such as jet-accretion disk systems \citep[e.g.,][]{degouveia05,degouveia10a,degouveia10b, giannios10,delvalle11, kadowaki14,khiali15a,khiali15b}, pulsar {winds} and GRBs \citep[e.g.,][]{lazarian03,zenitani07, zhang11,uzdensky2011,clausen-brown2012,cerutti14, sironi14,guo14,guo15,singh16}. It has been also related to the production of {ultra-high-energy} cosmic rays \citep[e.g.,][]{degouveia00, degouveia01, kotera2011}. Besides, the accelerated particles may produce detectable non-thermal emission in a wide range of energies, specially at gamma rays \citep[e.g.,][]{delvalle11,vieyro12,cerutti14,khiali15a,khiali15b,kadowaki14, singh14} or neutrinos \citep[e.g.,][]{khiali16}, {therefore, studies of} the acceleration rate and the particle power-law index are fundamental for understanding and modelling this emission. As remarked above, in order to obtain an efficient acceleration process, reconnection has to be fast. {In collisioneless plasmas, this is usually ensured by kinetic instabilities or by the Hall effect (in the case of an electron-ion plasma), both relevant only at plasma kinetic scales. In {large-scale} collisional MHD systems, fast reconnection can be driven either by anomalous resistivity \citep[][]{parker79,biskamp_etal97,zenitani09} or by turbulence} \citep[][]{lazarian99, kowal09, kowal12b,lazarian12}\footnote{Alternative descriptions of fast reconnection in a collisional MHD scenario have been proposed also by \citet{loureiro07,shibata01}.}. In a weak turbulent medium, the wandering of the magnetic field lines allows for many simultaneous events of reconnection {to happen at the same time}. {Moreover, the reconnected flux is more efficiently removed due to turbulence which broadens the outflow channel \citep[see Figure 1 in][for example]{kowal09}. These two factors make such reconnection fast.} According to \citet{lazarian99}, $V_{\rm rec} \sim V_{\rm A} (l/L)^{1/2} (v_l/V_{\rm A})^2$, where $v_l$ and $l$ are the injection velocity {and scale} of the turbulence, respectively. It is easy to see that for {the upper limit, i.e.} $l \sim L$ and $v_l \sim V_{\rm A}$, {the maximum reconnection rate is} $V_{\rm rec} \sim V_{\rm A}$. Both features, the simultaneous reconnection events and the broadened reconnection layer, are very important for accelerating particles, as demonstrated in \citet{kowal11, kowal12a}. In this work we extend the earlier numerical studies of \citet{kowal11, kowal12a} of the acceleration of test particles in collisional, non-relativistic\footnote{Recent studies \citep{takamoto15} indicate that in relativistic domains turbulent driven magnetic reconnection behaves similarly to the non-relativistic case \citep[see][for reviews]{lazarian15, degouveia14}.} three-dimensional MHD domains of reconnection having {large-scale} current sheets {with embedded turbulence, in order to assess the dependence of the particles acceleration time and power spectrum with the parameters involved in the process, namely, the reconnection speed which in turn is directly correlated with the Alfv\'en velocity ($V_{\rm A}$), and the turbulence injection power ($P_{\rm inj}$) and scale ($k_{\rm inj} = 1/l_{\rm inj}$) {using the same methodology as described in \citet{kowal12a}}.} \footnote{We note that in an earlier pioneering work, \citet{kobak2000} also studied the role of MHD turbulence in the particle acceleration process in a volume with a reconnecting magnetic field. However, they did not consider a real turbulent cascade developed self-consistently to affect the reconnection at the current sheet, as performed in \citet{kowal11,kowal12a} and in the present work. They instead, employed a Monte Carlo method and mimicked the effects of the turbulence with small-amplitude pitch angle scatterings. Their approach did not allow them to detect any Fermi process. Besides, the limitations of their method did not allow them to explore the dependence of the acceleration rate with the parameters of the turbulence, or the Alfv\'en (and reconnection) velocity, as we do in the present work.} In the next section we summarize the main aspects of the theory of first-order Fermi acceleration within current sheets with fast reconnection driven by turbulence. In Sec.~\ref{sec:methods}, we describe the numerical methodology used in this work to perform the calculations. In Sec.~\ref{sec: time} we show the computed acceleration time for different models. In Sec. ~\ref{sec:acc_dist} we analyse the distribution of the accelerated particles. In Sec.~\ref{sec:concl} we discuss the results and draw our conclusions. | \label{sec:concl} In this work we have investigated the first-order Fermi acceleration of particles {within {large-scale} current sheets with fast magnetic reconnection driven by turbulence, using 3D collisional MHD simulations with the injection of test thermal particles, following the same approach as in \citep{kowal12a}. We extended here this earlier study \citep[see also][]{kowal11,degouveia14,degouveia15} by examining the effects of the parameters of the reconnection on the effective acceleration rate and the evolution of the spectrum of the particles.} We considered models with different values of $V_{\rm A} / c $ and {different turbulence injection scale and power.} The main results can be summarized as follows. \begin{itemize} \item The acceleration time follows a power-law dependence with the particle energy, $t_{acc} \propto E^{\alpha}$, with 0.2 $<\alpha < 0.6$ {which is weakly sensitive to the magnetic reconnection parameters {of the injected turbulence}, tested for a large range of values of $ c / V_{A} \sim 20 - 1000$. } \item The acceleration time {dependence with} the Alfv\'en velocity is $t_{acc} \propto (V_{\rm A} / c)^{-\kappa}$,{ with $\kappa \sim 2.1 - 2.4$ {for particle kinetic} energies between $E= (1 - 10^2)\,m_{p}c^2$, respectively and keeping the same trend approximately for larger energies (tested for model I).} \item {For a given value of} the $V_{\rm A}/c$ ratio, the acceleration time {is shorter for larger values of the turbulence injection parameters,} i.e. $l_{\rm inj}$ and $P_{\rm inj}$, as expected from theory. Nonetheless, the maximum differences between the models are generally less than an order of magnitude and are within the error bars {due} to the uncertainties in the evaluation of the acceleration times from the numerical simulations, {so that we can conclude that these dependences are not relevant.} \item In all the cases studied here, the number of particles being accelerated in the perpendicular direction to the local magnetic field is larger than the ones being accelerated in the parallel direction. This unbalancing is important to ensure the effectiveness of the acceleration process (see below). \item The particle spectrum of the accelerated particles develops a high-energy tail, which can be fitted by a hard power-law index {$\propto$ $E^{p}$, with $p$ $\sim$ $-1.3$ to $-1$} (or even a little smaller) in the early times of the acceleration and is independent of the initial thermal energy of the injected particle distribution. \end{itemize} {These results} have important implications for studies of particle acceleration specially in magnetically dominated regions of astrophysical environments like the surrounds of GRBs, black holes in AGNs and microquasars, and the relativistic jets associated to these sources. {As remarked,} most studies of first-order Fermi particle acceleration by magnetic reconnection have been performed considering PIC simulations \citep[e.g.,][]{zenitani07,lyubarsky08, drake10,cerutti13,sironi14,guo14,guo15}, which apply only to the kinetic scales of the flow. In order to probe the {large-scale} properties of the acceleration by magnetic reconnection beyond the kinetic scales in collisional astrophysical systems like those mentioned above, an MHD description is required. The 2D and 3D studies undertaken by \citet{kowal11,kowal12a} and in this work have explored exactly these macroscopic scales of the acceleration by magnetic reconnection and thus are complimentary to the former kinetic studies. It should be noticed also that, contrary to what has been found in PIC simulations \citep[e.g.,][]{guo14}, \citet{kowal11} demonstrated that the acceleration of energetic particles in 2D and 3D reconnection domains shows substantial differences, being more efficient in the second case. This justifies why our analysis here has focussed on 3D geometries of reconnection only. {The earlier collisional numerical studies (\citealt{kowal11, kowal12a}; see also \citealt{dmitruk03}) {and most of the ones presented here} have neglected the time evolution of the MHD environment. This is in general expected to be valid since this time is much longer than the particle time scales, particularly when considering a first-order Fermi process in a statistically steady state turbulent domain. {In Sec.~\ref{time-evol}, we explored the particle acceleration considering different snapshots} of the reconnection domain and found no significant changes, as predicted. Nonetheless, this evolution may be important when considering more realistic non-steady flows and when calculating the spectra and loss effects in real astrophysical systems. Preliminary steps in this direction have been performed in studies like, e.g. \cite{lehe09, khiali15a, khiali16, khiali15b}.} {Earlier analytical studies of the first-order Fermi process in {large-scale} current sheets \citep[e.g., GL05;][]{drury12} predicted that the acceleration time would be similar to that of shock acceleration, and the energy power-law spectrum of the accelerated particles could be {either steeper or harder } than the one predicted for shock acceleration and nearly independent on the reconnection velocity}. These predictions, although based on rather simplified assumptions have been at least qualitatively confirmed by the results of this work. For a broad range of reconnection velocities represented by a fiducial parametric space encompassing $V_{\rm A}/c \sim 1/1000- 1/20$, the acceleration time dependence with the {kinetic} particle energy is found to be $\propto E^{\alpha}$, with $\alpha \simeq 0.2-0.6$. Furthermore, the minimum analytically estimated acceleration time according to Eq.~(\ref{eq:threshold}) is comparable to the values found in the simulations when the particles reach the maximum energy during} the first-order Fermi acceleration in the reconnection zone (the saturation energy). As we have seen, this maximum energy is attained when the particle Larmor radius becomes comparable to the size of the acceleration zone. It is also remarkable {that} the power-law indices obtained for the particles distribution in the high-energy tail from our collisional MHD simulations in the large scales are comparable to the values obtained from the PIC simulations in the kinetic scales of the plasma} \citep[e.g.,][]{zenitani01,drake13,sironi14,guo14,guo15,li15}. \footnote{It should be stressed that, as in our model, the Fermi acceleration and resulting particle power-law spectrum obtained by \citet{guo14, guo15, li15} is due to the electric field produced by the magnetic fluctuations ($-{\bf u}\times{\bf B}$), while in the case of \citet{sironi14}, it is argued that the acceleration is dominated by the resistive electric field component, which in our case is absent (see also \citealt{kowal12a}).} We should stress that the acceleration process in magnetic reconnection sites with turbulence theory depends on $V_A$, $P_{\rm inj}$ and $l_{\rm inj}$) that determines the first-order energy gain; (ii) the thickness of the turbulent region which improves the particle scattering probability; and (iii) the strength and maximum scale of the velocity and magnetic field fluctuations within the turbulent region, which control the scattering mean free path (or time) which in turn depend on both $P_{\rm inj}$ and $l_{\rm inj}$. Therefore, the overall acceleration process is very complex. In this work we analysed only the dependence of $V_{\rm rec}$ {with $V_A$ and the turbulence injection parameters. Both, $V_{\rm rec}$ and the acceleration efficiency are clearly dominated by the $V_A$ dependence, as one should expect for any process driving the fast reconnection, though we also obtained some weak dependencies of the acceleration time with the turbulent parameters.} For instance, the scattering should happen at scales equal or smaller than $l_{\rm inj}$, this might be the reason why only the dependence on the injection power and not on injection scale is manifested at lower energies in our results ($E_p < 10^2$, compare Figures~\ref{fig:t-pinj} and ~\ref{fig:t-kinj}). Moreover, at these scales particles can be scattered many times on the same side of the current sheet, with the energy gain {temporarily} independent of the value of $V_{\rm rec}$ until they are scattered back across the magnetic discontinuity again {to complete the first order Fermi cycle.} {Having the points above in mind, we should remember that the turbulence is essentially the physical mechanism that drives fast reconnection in the {large-scale} current sheets studied here. This is a potentially very important driving mechanism because turbulence is very common in astrophysical sources and environments. Nevertheless, the first order Fermi could in principle operate in current sheets with fast reconnection driven by other possible processes and the results should not {differ} substantially {from} the present ones. This is compatible with the results found above that show only a weak dependence of the acceleration rate with the parameters of the turbulence. This may also explain why our results are similar to those of kinetic PIC simulations, where the driving mechanisms of fast reconnection are generally very distinct.} {It should be also stressed that the collisional MHD simulations shown here focussed on proton acceleration. Although applicable to electrons too, the numerical integration of the electron trajectories is much longer in MHD domains with test particles. Nevertheless, such tests are also needed. Hybrid simulations combining both the PIC and the MHD approach may be a good approach to this problem \citep[e.g.,][]{bai15}.} We further remark that we have tried to establish a link with the results of the PIC studies which probe only the kinetic scales up to 1000 skin depth scales. But in our collisional study only the injected particles with Larmor radii near the MHD scales are effectively accelerated. This {limitation} can be also solved using hybrid codes able to resolve both the kinetic and the MHD scales {and make a smooth transition between them} \citep{degouveia15}. {Another note is in order. This work should be distinguished from studies that examined particle acceleration in pure turbulent environments (which are not embedded in {large-scale} current sheets, see e.g., \citealt{dmitruk03,zharkova11,dalena14,kowal12a,degouveia15,brunetti16}). For instance, \citet{kowal12a} have compared the two cases and concluded that in the cases with pure turbulence particle acceleration is probably dominated by a second order Fermi process, but further studies must be carried out in order to disentangle the processes.} {Finally, cosmic-ray acceleration investigation in magnetic reconnection sites has still many challenges to overcome, particularly in collisional MHD and relativistic regimes. The present study has tried to advance a little in the first of these topics. With regard to the second one, i.e., the study of acceleration in relativistic domains of reconnection, there has been some recent advances both in collisionless descriptions \citep[e.g.,][and references therein]{cerutti13,sironi14,guo14,guo15}, and in collisional relativistic MHD fast reconnection involving turbulence (e.g., \citealt{degouveia15, lazarian15, singh16,takamoto15}; see also \citealt{degouveia14} for a short review of both approaches). These are important issues to be explored further, specially for building more realistic models of flares and variability in the spectrum of compact sources to help in the interpretation of current high energy observations and in making predictions for upcoming new generation of instruments, like the Cherenkov Telescope Array \citep{cta11, cta13, sol13} and the ASTRI CTA Mini-Array \citep{astri15}.} | 16 | 9 | 1609.08598 |
1609 | 1609.04255_arXiv.txt | The breaks and truncations in the luminosity profile of face-on spiral galaxies offer valuable insights in their formation history. The traditional method of deriving the surface photometry profile for face-on galaxies is to use elliptical averaging. In this paper, we explore the question whether elliptical averaging is the best way to do this. We apply two additional surface photometry methods, one new: principle axis summation, and one old that has become seldom used: equivalent profiles. These are compared to elliptically averaged profiles using a set of 29 face-on galaxies. We find that the equivalent profiles match extremely well with elliptically averaged profiles, confirming the validity of using elliptical averaging. The principle axis summation offers a better comparison to edge-on galaxies. | The surface photometry of a galaxy is the relationship of the radius $R$, seen from the centre of a galaxy, with the surface brightness $\mu(R)$. To first order, light is tracing mass in a galaxy. It is therefore an interesting tool for the study of galaxy dynamics and evolution. The first studies on the subject are by \citet{Patterson1940A} and \citet{Vaucouleurs1948A,Vaucouleurs1959A}, who noted that the surface brightness of the disc of spiral galaxies followed an exponential decline. The exponential nature was studied in more detail by \citet{Freeman1970A}, who found that there was a second type of profiles that exhibits a break, beyond which the brightness decreases more rapidly. The lines-of-sight in an edge-on galaxy are typically longer than in a face-on galaxy. Thus, more stars are sampled by a single line-of-sight through an edge-on than through a face-on galaxy at that same (projected) radius. Because of this, it is easier to detect light at larger radii in edge-on galaxies than in face-on galaxies. This allowed \citet{vdk79} to note that in three edge-on galaxies, the radius of the stellar disc did not increase with deeper photograp000hic exposures. This work was later expanded to a set of eight edge-on galaxies for which the three-dimensional light distribution was studied in detail. Each of these galaxies has a truncated disc, beyond which the intensity rapidly drops to zero, on average after $4.2\pm0.6$ radial scale lengths \citep{vanderKruit1981A,vanderKruit1981B,vanderKruit1982A,vanderKruit1982B}. The presence of truncations was confirmed by \citet{2000PDL}, who found however a ratio of trunction radius to exponential scale length of only $2.9\pm0.7$. Truncations in face-on galaxies have, at least in our view, not been unambiguously identified. \citet{pt06} used the Sloan Digital Sky Survey (SDSS) to study a set of 90 face-on late-type galaxies. \citet{pt06} identified 14 face-on galaxies with truncations. This result has been disputed by \citet{vanderKruit2008A}, who argued that these are in fact breaks similar to those found by \citet{Freeman1970A}. \citet{Erwin2008A} studied 66 barred, early-type galaxies and \citet{GEAB11} another sample of 47 early-type non-barred spirals. Many of these inclined systems are classified as having `truncations' (increasingly among later types), but we remain unconvinced that these are equivalent to those in edge-ons and not breaks at higher surface brightness levels. Combining Spitzer and near-IR observations seems to indicate that the break radii correlate with those of rings, lenses or spiral arms, and not with a sharp outer decline \citep{2014Laineetal}. \citet{2008BakTruPo} found from a study of radial colour profiles that breaks in the light profiles often do not correspond to breaks in the apparent total stellar mass surface density, in fact leaving no feature whatsoever. Recently \citet{2013HHE,2016HHE} have initiated studiss of a large sample of dwarf galaxies; they find many cases of breaks that (unlike spirals) remain in stellar surface density profiles. Exponential gas disks can have a double exponential star formation rate, the break radius being related to the instability \citep{2006EH}. \citet{Com12} studied 70 edge-on galaxies from the Spitzer Survey of Stellar Structure in Galaxies (S$^4$G) and found that many edge-ons have truncations, while often more inward breaks could be identified, that occured at similar positions as those measured in face-on galaxies by \citet{pt06}. The view of breaks and truncations as two separate features was put forward by \citet{mbt12}. In a study of 34 highly inclined spiral galaxies, they found that the innermost break occurs at $\sim\!8\pm1$ kpc and truncations at $\sim\!14\pm2$ kpc in galaxies. It should be stated that not all workers agree with this point of view. In particular \citet{Erwin2008A}, but also \citet{Erwin2005A} and \citet{pt06}, argue that the breaks really correspond to the truncations in edge-on galaxies. We disagree, but will return to this subject more extensively in the next paper in our studies \citep{Peters2015G}. Anti-truncated profiles, in which the intensity drops less quickly beyond the break than it did before the break, have also been discovered \citep{Erwin2005A}. We no further address this issue in this paper, but will discuss it in more detail in the next paper \citep{Peters2015G}. Part of the problem in detecting truncations originates in the different ways profiles from edge-ons and face-ons are extracted. In edge-on galaxies, the surface photometry is defined as the surface brightness along the major axis of the galaxy. This light comes from a variety of radii as the line-of-sight crosses through the galaxy. In face-on galaxies, the most common way to derive profiles is by performing elliptical averaging, such as that offered by the \textsc{IRAF} package \texttt{ellipse} \citep{Jedrzejewski1987,Busko1996}. Light in such a profile only comes from structures at a single radius. The averaging cancels out any local structure, which might be causing the truncations in edge-ons \citep{kf11}. We believe that these local structures are of importance when looking for disc truncations. It is therefore interesting to see what the impact of ellipse averaging is on profiles, and to explore alternative ways to derive such profiles. We use two different methods for deriving surface brightness profiles in face-on galaxies that should be less sensitive to local structure and deviations from circular symmetry: the Principle Axis Summation and the Equivalent Profiles. In Section \ref{sec:PASmethods}, we will detail the inner workings of these methods. We will present our sample of face-on galaxies, based on a sub-sample of the work by \citet{pt06}, in Section \ref{sec:PASdata}. In Section \ref{sec:PASanalysis}, the data will be analyzed and discussed, followed by the conclusions in Section \ref{sec:PASdiscussion}. In order to conserve trees, the online Appendix contains tables and figures for individual galaxies. | \label{sec:PASdiscussion} We have developed two new approaches for extracting the surface photometry of a face-on galaxy. The Equivalent Profiles (EP) work under the assumption that the surface brightness of a galaxy decreases as the radius increases. By starting with the brightest pixel and moving to lower brightness levels, each level can be assigned an equivalent area ellipse containing the surface of all pixels that are at or brighter than that level. The equivalent ellipse then gives the equivalent radius. The other method is the Principle Axis Summation (PAS), which work by summing the light onto the principle axis of the galaxy. This method then gives the equivalent of the profile as if the galaxy was seen edge-on. We have then tested this method on a sub-sample of the galaxies from \citet{pt06}. Seen overall, we find that both our methods perform well. Considering the fundamentally different method used to derive them, a detailed comparison that we have made (not illustrated) shows to us that the EP are remarkably similar to the ellipse-fit profiles as measured by \citet{pt06}. We also point out that the classical method of elliptical averaging compares very well with results of equivalent profiles, \citep{vdk79}. There are some differences. The ellipse-fit profiles have the ability to measure local upturns in the profiles, for example due to a local bar or ring feature. By design, the EP is unable to cope with this. This can lead to slightly different scale lengths. Beyond such a bump however, the EP profile and ellipse-fit join up again, as for example in Figure \ref{fig:IC1067}. Overall, we see that the EP behaves worse at lower brightness levels than the ellipse-fit profiles. For practical purposes, the ellipse therefore remains the preferred method. The PAS method turns out to be a very interesting approach. Compared to the EP profiles, breaks and truncations often look sharper. A good example of this can be seen in galaxy IC1158, seen in Figure \ref{fig:IC1158}, where the PAS profiles starts to drop quite rapidly beyond $\sim65''$, much stronger than the ellipse-fit profiles. We find that the inner scale length as measured with the PAS is on average 10\% longer than the same scale length in either of the other methods. We also find a negative correlation with the inclination as expressed by the ratio $a/b$. As the inclination increase, the outer scale length of the PAS profiles get smaller. This leads to sharper breaks $h_0/h_f$ than is seen in ellipse-fit profiles or in the EP profiles. Although beyond the scope of this project, it would be interesting to test if $h_0/h_f$, rather than $R_b/h_f$ is a good way to distinguish between breaks and truncations. In edge-on galaxies, there is a well-observed correlation of the radius of the truncations with the maximum rotation velocity $v_\mathrm{rot}$ \citep{vanderKruit2008A}. This was confirmed by \citet{mbt12}, who also found a correlation with the absolute magnitude of the galaxy $M_\textrm{B,abs}$. Various studies of face-on samples, starting with \citet{pt06} and more recently for example \citep{2013mm} have looked for and sometimes reported similar relations (e.g. their fig.~8), but in those cases it is not clear that the break radii used are referring to the equivalent features of edge-on truncations. We do not find any correlation of the surface brightness at the feature, difference in brightness between various bands at the feature, and the feature radius, with the absolute brightness $M_\textrm{B,abs}$ nor with the maximum rotation $v_\textrm{rot}$. \citet{mbt12} divide their samples up into truncations and breaks based on the criteria $R_f/h_0=5$, with the galaxy belonging to breaks if the ratio was below five and truncations if it was above it. We have split our sample into these two subsets using the same criteria and have inspected the data for correlations. We do not reproduce these correlations. We are therefore skeptical of the galaxies in our truncations subsample constituting true truncations in the edge-on sense. It more likely that we are still only observing breaks. Truncations can likely only be found by using deeper imaging, such as that used by \citet{Bakos2012a}. We will explore the use of deeper imaging to detect truncations further in \citet{Peters2015G}. | 16 | 9 | 1609.04255 |
1609 | 1609.06120_arXiv.txt | An accurate line list, VOMYT, of spectroscopic transitions is presented for hot VO. The 13 lowest electronic states are considered. Curves and couplings are based on initial {\it ab initio} electronic structure calculations and then tuned using available experimental data. Dipole moment curves, used to obtain transition intensities, are computed using high levels of theory (e.g. MRCI/aug-cc-pVQZ using state-specific or minimal-state CAS for dipole moments). This line list contains over 277 million transitions between almost 640,000 energy levels. It covers the wavelengths longer than 0.29 $\mu$m and includes all transitions from energy levels within the lowest nine electronic states which have energies less than 20,000 \cm{} to upper states within the lowest 13 electronic states which have energies below 50,000 \cm{}. The line lists give significantly increased absorption at infrared wavelengths compared to currently available VO line lists. The full line lists is made available in electronic form via the CDS database and at www.exomol.com. | Vanadium oxide (VO) plays an important role in astrophysical chemistry, particularly of cool stars, and is expected to also be present in brown dwarfs and hot Jupiter exoplanets. However, no comprehensive, high quality line list has been published for this molecule, limiting the potential information that can be obtained. The ExoMol project \citep{jt528,jt569} aims to produce high temperature line lists of spectroscopic transitions for key molecular species likely to be significant in the analysis of the atmospheres of extrasolar planets and cool stars. The molecular data is crucial for accurate astrophysics models of the opacity, as discussed by \citet{sb07} and \citet{09Bexxxx.exo}, and the spectroscopy of the object. However, from a chemistry perspective, vanadium is a transition metal in terms of its electronic structure and spectroscopic properties. This makes the electronic structure calculations much more difficult and gives higher uncertainties \citep{jt632}. VO absorption bands are generally present in cool late M class stars with effective temperature on order 2500-3000 K, mass less than 0.1 \Msol\ and are also expected to be observed in hot Jupiter exoplanets \citep{08FoLoMa.VO}. VO is generally present simultaneously with TiO and has similar spectroscopic and thermodynamic properties, though its abundance is about an order of magnitude less than TiO. VO tends to be more important in classifying slightly cooler (i.e. late) M dwarfs \citep{93KiKeRi.VO,04McKiMc.dwarfs}. VO is one of the dominant species in the spectra of young hot brown dwarfs \citep{04McKiMc.dwarfs,06KiBaBu.dwarfs,08PeMeLu.dwarfs}. \begin{figure} \includegraphics[width=0.5\textwidth]{AllPES.eps} \caption{\label{fig:PES} Potential Energy Curves. Curves in ascending order are: solid; \X, \Ap, \A, \B, \C, \D; dashed; \Da, \Db, \Dc, \Dd, \De, \Df, \Dg. The short horizontal lines above the full curves are indicative of the next highest known quartet (solid) and doublet (dashed) states based on experimental data; there are many extra doublets believed to exist above 20,000 \cm{} not shown on this graph.} \end{figure} \begin{table*} \def\arraystretch{1.2} \caption{\label{tab:Morse} Specifications for extended Morse oscillator parameters (see Eq \ref{eq:EMO}) for the fitted potential energy curves in {\Duo}. The dissociation energy, $D_e$, is 52288.4 \cm{} and the reduced mass of $^{51}$V$^{16}$O is 12.17296118 Da. } \begin{tabular}{lrrrrrrr}% \toprule State & \mc{5}{c}{{Morse parameters}} & \mc{1}{c}{Properties} \\ \cmidrule(r){2-6} \cmidrule(r){7-7} & \mc{1}{c}{$T_e$/\cm}&\mc{1}{c}{$r_e$/\AA} & \mc{1}{c}{$b_0$} & \mc{1}{c}{$b_1$} & \mc{1}{c}{$b_2$} & \mc{1}{c}{$\omega_e$/\cm} \\%& \omega_e \\%{$T_e$} & {$a$} & {$r_e$} & {$b_1$} & {$\omega_e$} \\ \midrule \X & 0.000 & 1.589443 & 1.87974 & 0 & 0 & 1011.8\\%968751044 \\ \Ap &7293.270 & 1.622990 & 1.89529 & 0 & 0 &946.4\\%617881040 \\ \A & 9561.867 &1.633621 & 1.8200$^*$ & 0 & 0 & 890.3\\%380101477 \\ \B &12655.372 & 1.640253 & 1.94733 & 0 & 0 & 912.4\\%453567789 \\ \C & 17487.690 & 1.670620 & 1.94674 & -0.359 & 0.540 & 864.9\\%027071872\\ \D & 19229.786 & 1.683170 & 1.96500 & 0.060 & 0.900 & 840.9\\%28132755\\ \Da & 5630.00$^*$ & 1.58200$^*$ & 2.0100$^*$ & 0 & 0 & 1041.7\\%541524475 \\ \Db &8551.49$^*$ & 1.57700$^*$ & 2.0900$^*$ & 0 & 0 & 1009.0\\%392188275 \\ \Dc & 9860.107 & 1.582247 & 2.07538 & 0 & 0 & 1006.1\\%090896098 \\ \Dd &10343.630 & 1.578560 & 2.16131 & 0 & 0 & 1041.7\\%330489496\\ \De & 15440.547 & 1.628968 & 2.0900$^*$ & 0 & 0 & 985.2\\%724865906 \\ \Df & 17115.919 & 1.629330 & 2.12146 & 0.226 & 0.471 & 937.2\\%886948828 \\ \Dg & 18108.500 & 1.635810 & 2.17648 & 1.157 & -1.850 &947.5\\%905619239 \\ \bottomrule \end{tabular} $*$: Fixed based on theory or low-resolution experiment. \end{table*} The A-X transition of VO, which occurs at approximately 1.05 $\mu$m in the infrared, was first observed in the red giant Mira-type variable stars Mira Ceti and R Leonis by \citet{47KuWiCa.VO}, and subsequently studied more extensively by \citet{52KeShxx.VO,66SpYoxx.VO,67WiSpKu.VO,69SpWixx.VO,98AlPexx.VO} and \citet{00CaLuPi.VO}. VO has also been observed in M red-dwarf stars \citep{98AlPexx.VO,09Bexxxx.exo,14RaReAl.VO}. Molecular lines of VO have been detected in sunspot umbral spectra \citep{08SrBaRa.VO}. \citet{08DeViLe.VO} found non-definitive evidence for VO in the atmosphere of the hot Jupiter HD209458b. Tentative detection of VO and TiO in the hot atmosphere of the hot exoplanet WASP-121b were recently reported by \citet{16EvSiWa.exo}. There has been considerable recent debate \citep{09SpSiBu.VO,10FoShSo.VO,10BoLiDu.VO,10MaSexx.VO,12HuSiVi.VO,13SpBuxx.VO,13GiAiBa.VO,13PaShLi.VO,14AgPaVe.VO,15HoKoSn.VO,15ScBrKo.VO,15HaMaMa.VO,15WaSixx.VO} about a possible temperature inversion in hot Jupiters, potentially caused by the presence of TiO and VO. \citet{15HoKoSn.VO} highlight the need for more accurate line lists to resolve this issue; though they specifically mention TiO in this paper, VO usually coexists, although it is generally thought to have a lower abundance. Line lists for TiO \citep{98Plxxxx.TiO,98Scxxxx.TiO,VALD3}, despite their shortcomings, are still significantly more developed than those for VO. \citet{Kurucz} and \citet{99Plxxxx.VO} have both circulated VO line lists. Both these line lists contained only transitions in the main A-X, B-X and C-X bands (in particular, no infrared X-X transitions were included). These line lists have been used extensively in stellar and planetary models. \citet{89BuHuLu.VO} give an early study based on a simple model atmospheres incorporating TiO and VO opacities. In particular, VO is an important component of model atmospheres for M dwarfs \citep{95AlHaxx.VO,12RaReSc.VO,14RaReAl.VO}. The more complex T Tauri atmosphere models have also incorporated VO absorption bands \citep{14HeHixx.VO}. A good VO line list is especially important in light of the new generation of proposed and planned satellites with the ability to take high quality spectra of hot Jupiters. These are required both for missions purpose-designed for studying exoplanet spectroscopy \citep{jt523,jt578,11TiChGr.exo} or more general purpose satellites such as James Webb Space Telescope (JWST) which will also have the capability to study atmospheres of hot Jupiters in 0.6-- 28 \um\ region \citep{14BeBeKn.Sa,15WaSixx.VO,15BaAiIr.Sa}. % VO is generally critical in modelling oxygen-rich astronomical objects with temperatures between 1500-3000 K: at lower temperatures, it condenses to more complex oxides while at higher temperatures it partially dissociates. VO may continue to be a non-negligible source of opacity and absorption up to 5000 K; therefore, we aim for a 90\% complete line list up to this temperature. The resulting line list should automatically be valid for any lower temperatures. Due to its astronomical importance in the spectroscopic analysis of M-dwarfs, the spectroscopy of diatomic VO has been well studied experimentally \citep{68Kaxxxx.VO,68LaKaxx.VO,68RiBaxx.VO,68RiBaxy.VO,69HaNixx.VO,81ChHaLy.VO,81HoMeMi.VO,82ChHaMe.VO,82ChTaMe.VO,87MeHuCh.VO,89Mexxxx.VO,92HuMeCl.VO,94ChHaHu.VO,95AdBaBe.VO,02RaBeDa.VO,05RaBexx.VO,09HoHaMa.VO}. A good summary of previous experimental results is given by \citet{07MiMaxx.VO} and \citet{09HoHaMa.VO}. Generally, only the ground and first vibrational energy levels are well characterised for observed electronic states. Fortunately, transitions between quartet and doublet electronic states have been observed; this enables the relative positioning of the quartet and doublet manifold to be fixed with reasonably accuracy (limited by the fact that the absolute value of some spin-orbit terms is unknown experimentally). The dipole moment of the ground state has been measured by \citet{91SuFrLo.VO}. There is no information on the transition dipole moments of VO. However, lifetime measurements for levels in the A, B and C states were performed by \citet{97KaLiLu.VO}. The spectroscopy of VO has also been well studied theoretically \citep{66CaMoxx.VO,77WoFaSh.VO,86BaLaxx.VO,87DoWeSt.VO,95BaMaxx.VO,96BaStTs.VO,00BrRoxx.VO,01BrBoxx.VO,03DaDeYa.VO,03PyWuxx.VO,04MaMiOw.VO,06DuWaSh.VO,07YaGuSo.VO,08DuWaSh.VO,08BaLuxx.VO,10KuMaxx.VO,11PrGuWe.VO}. However, the challenging nature of theoretical treatments of excited states in transition metal diatomics means that achieving quantitative accuracy is very difficult, particularly for excitation energies \citep{jt632}. Generally, multi-reference configuration interaction (MRCI) approaches are essential. The most detailed \abinitio\ electronic structure study was performed by \citet{07MiMaxx.VO}, who looked at the lowest nine electronic states, and also reviewed previous theoretical studies. The quality of these calculations is high, but quantitative results are only given for equilibrium values. Another important study was performed by \cite{15HuHoHi.VO}, who calculated the energetics of a much larger number of electronic states, but did not consider dipole moment or spin-orbit couplings (except for the X equilibrium dipole moment). They investigate the effect of including $3p$ correlation on the internally-contracted (ic) MRCI results; however, the accuracy of the potential energy surface parameters does not show significant (if any) improvement. Their icMRCI calculations incorrectly predict the ordering of the \C{} and \D{} states; we find similar difficulties in reproducing the correct ordering of these states. The goal of this paper is to produce a comprehensive line list for the main isotopologue of VO accounting for all of the lowest 13 electronic states of VO. The structure of this article is as follows. In Section \ref{sec:SMforVO}, the spectroscopic model for VO is developed. In Section \ref{sec:LL}, the line list for VO, named VOMYT, is constructed based on the spectroscopic model developed here and earlier \citep{jt623}. In Section \ref{sec:comparisons}, we compare cross-sections using the new VOMYT linelist against laboratory, observational, and previous line list spectra. % | Transition metal diatomics are important species in cooler stars and hot Jupiters. However, the difficulty of the \abinitio\ calculations and the relative lack of experimental data mean that it is difficult to construct high quality line lists for these species. Here we present the first ExoMol line list for a transition metal diatomic species of astrophysical relevance. Work on CrH, MnH and TiH is in advanced stages and will be published shortly. Using the lessons from the construction of the VO line list, we are now actively working on an improved high quality line list for TiO to address much discussed shortcomings in the existing line list in terms of intensities and at very high resolution. This new TiO line list will use high quality \abinitio\ results and be fitted to all available experimental data. Furthermore, a {\sc Marvel}-type analysis \citep{jt412} is currently underway to extract high quality experimental energies from experimental frequencies. Our VOMYT rovibronic line list for VO, containing over 277 million transitions, can be accessed online at www.exomol.com in the extended ExoMol format described by \citet{jt631}. It includes the transition energies and Einstein coefficients, partition functions, lifetimes and temperature-dependent cross-sections. Land\'{e} g factors to describe the splitting of the energy levels due to the Zeeman effect will be added shortly. We have also included the Duo input file with our spectroscopic model for VO. | 16 | 9 | 1609.06120 |
1609 | 1609.03019_arXiv.txt | {The composition of a planet's atmosphere is determined by its formation, evolution, and present-day insolation. A planet's spectrum therefore \rt{may} hold clues on its origins. We present a ``chain'' of models, linking the formation of a planet to its \rt{observable} present-day spectrum. The chain links include (1) the planet's formation and migration, (2) its long-term thermodynamic evolution, (3) a variety of disk chemistry models, (4) a non-gray atmospheric model, and (5) a radiometric model to obtain simulated spectroscopic observations with JWST and ARIEL. In our standard chemistry model the inner disk is depleted in refractory carbon as in the Solar System and in white dwarfs polluted by extrasolar planetesimals. Our main findings are: (1) Envelope enrichment by planetesimal impacts during formation dominates the final planetary atmospheric composition of hot Jupiters. We investigate two, under this finding, prototypical formation pathways: a formation inside or outside the water iceline, called ``dry'' and ``wet'' planets, respectively. (2) Both the ``dry'' and ``wet'' planets are oxygen-rich (C/O$<$1) due to the oxygen-rich nature of the solid building blocks. The ``dry'' planet's C/O ratio is $<$0.2 for standard carbon depletion, while the ``wet'' planet has \rt{typical} C/O values between 0.1 and 0.5 \rt{depending mainly on the clathrate formation efficiency}. Only non-standard disk chemistries without carbon depletion lead to carbon-rich C/O ratios $>$1 for the ``dry'' planet. (3) \rt{While we consistently find C/O ratios $<$1, they still vary significantly. To link a formation history to a specific C/O,} a better understanding of the disk chemistry is \rt{thus needed}.} | \label{sec:introduction} One of the most fascinating aspects of the recent observational progress in exoplanet science are the first spectra of planets around other stars. Spectra probe the atmosphere which is a window into the composition of a planet. This composition, in turn, may give critical insights into the formation and migration history of the planet. A planet's composition depends on the composition of the host star, the structure and chemistry of the protoplanetary disk, the locations where the planet accreted, the composition of the accreted gas and solids, the properties (size, strength) of the accreted bodies like planetesimals or pebbles, the mixing or separation of the different materials inside the planet, the interaction and exchange between the interior and the atmosphere, the stellar radiation field, etc. Therefore, each formation track of a planet will leave - potentially in a convoluted way - an imprint in the atmospheric composition. This means that atmospheric spectra might contain a multitude of clues to planetary formation that cannot be provided by other observational techniques. For the Solar System planets atmospheric observations show that Jupiter is enriched in carbon by about a factor four relative to the sun, Saturn by a factor $\sim$10, while Uranus and Neptune are enriched by a factor $\sim$90 \citep{guillotgautier2014}. This trend of decreasing enrichment with increasing mass was recently found to apply also to WASP-43b \citep{kreidbergbean2014}. For the core accretion formation model \citep[e.g.,][]{alibertmordasini2005} such a trend is a natural prediction \citep[for a quantification, see][]{mordasiniklahr2014}, but not necessarily for the competing direct collapse model. Thus, spectra can help to distinguish formation models of the Solar System. Regarding exoplanets, the atmospheric composition may in particular also give clues on the formation of hot Jupiters, which are currently the best characterized class of exoplanets. The discovery of a Jovian planet at an orbital distance of only 0.05\cu\AU \ from its star by \cite{1995Natur.378..355M} was a surprise. Theoretical planet formation models had rather predicted \citep[e.g.,][]{1995Sci...267..360B} that giant planets should be found several AU away. The mechanism that was underestimated was orbital migration \citep{1980ApJ...241..425G}. As a reaction, orbital migration due to gravitational interaction with the protoplanetary gas disk was included in planet formation theory as a key mechanism \citep[e.g.,][]{linbodenheimer1996}. Disk migration predicts that planetary orbits are coplanar with the stellar equatorial plane (but see also \citealt{batygin2012}). The subsequent discovery of highly inclined or even retrograde hot Jupiters has therefore again challenged theory \citep[e.g.,][]{2010ApJ...718L.145W}. Alternative scenarios bringing giant planets close to the host star were developed. The most important scenarios are planet-planet scattering in unstable systems of planets and Kozai migration due to the presence of an outer perturber \citep[e.g.][]{2010A&A...524A..25T}. These mechanism take place after the dispersal of the protoplanetary disk and can lead to highly inclined planets. To date, it is debated if disk migration or scattering/Kozai is the dominant mechanism leading to close-in planets \citep[e.g.,][]{cridabatygin2014}. An interesting novel approach of constraining which migration processes acted on the planet during or after its formation is to evaluate whether the formation process, chiefly the planet's location(s) in the disk during its formation, leaves an observable spectral signature. If one could, e.g., deduce from the spectrum that a hot Jupiter has accreted exclusively outside the water iceline, this would make disk migration through the inner part of the disk unlikely as the processes that brought this planet close to the star. The reason is that the planet would accrete matter while migrating through the inner disk \citep{foggnelson2007a}. Apart from being able to constrain possible migration scenarios a successful link between a planet's formation and its spectrum would be very interesting on its own, providing a historical record of the formation of individual planets. \rcp{The first attempts to link the planetary formation process to \rch{exo}planetary compositions have in part been sparked by a retrieval analysis which suggested that WASP-12b, a hot Jupiter around a G0 main-sequence star, is carbon-rich\footnote{In this work we define oxygen-rich and carbon-rich as C/O$<$1 and $>$1 by number, respectively. This is different from the absolute enrichment level in C and O \rt{and the sub/super-stellar C/O distinction}.} with C/O $\gtrsim$ 1 \citep{madhusudhanharrington2011}. Further claims of a C/O$>$1, and a corresponding carbon rich chemistry including absorbers such as HCN and C$_2$H$_2$, have been made by \citet{stevensonbean2014}. Both of these assessments rely on \emph{Spitzer} eclipse photometry, impeding the conclusive detection of a carbon-bearing molecule in the atmosphere of this planet thus far. Studies contesting the claim of a carbon-rich WASP-12b include \citet{crossfieldbarman2012,swainderoo2013,lineknutson2014,benneke2015,kreidbergline2015}. In these studies the retrieved C/O ratio may reach super-solar ($\gtrsim$0.56) values, but the (7 $\sigma$) detection of H$_2$O firmly rules out an atmosphere with a carbon-rich chemistry (C/O$>$1), if equilibrium chemistry is assumed \citep{kreidbergline2015,benneke2015}. As stated in \citet{stevensonbean2014}, an oxygen-rich atmosphere would require unrealistically large CO$_2$ abundances to fit the planet's photometric emission data. In this case higher SNR dayside emission spectroscopy may resolve these inconsistencies.} \rcp{Even though the data quality thus can currently still inhibits conclusive statements about atmospheric compositions, the question of how the formation process constrains the planetary composition is interesting and should be studied in any case for the reasons outlined above.} \rch{It is important to note that the existing studies attempting to link planetary formation and composition can be divided into two classes: in the first class the planetary formation process itself is included in the analysis. In the second class the planet formation process is not modeled. Here the disk gas and solid composition as a function of time and location in the disk is investigated and the results are used to infer the composition of gaseous planets forming at this location and time. In this second class planets with C/O~$>$~1 may only be formed if the planet's metal enrichment is dominated by the accreted gas.} \rch{In the study presented here we will show that planets formed under the core accretion paradigm, with masses typical of hot Jupiters and below, have an enrichment dominated by planetesimal accretion. We show this by explicitly modeling the planetary formation process and the planetesimal accretion process. We further show that this trend predicted by core accretion agrees well with measurements of the bulk and atmospheric abundances of exoplanets and Solar System planets.} The studies which exist to this day include \rch{\citet{MousisMarboeuf2009,MousisLunine2009}}; \citet{obergmurray-clay2011,ali-dipmousis2014,thiabaudmarboeuf2014,hellingwoitke2014,marboeufthiabaud2014a,marboeufthiabaud2014b,madhusudhanamin2014,thiabaudmarboeuf2015}; \rch{\citet{CridlandPudritz2016}}. These studies vary widely in their scopes: \rch{In the context of Jupiter and Saturn, \citet{MousisMarboeuf2009} combine the planet formation model of \citet{alibertmordasini2005} with a model for the formation of clathrates and pure condensates. They assume that the observed atmospheric enrichment in volatiles originates from the vaporization of icy planetesimals entering the envelopes of the growing planets. They show that for Jupiter this leads to an enrichment of both the atmosphere and interior that is in agreement with observations. Their results indicate that large amounts of icy solids have been incorporated into Jupiter's and Saturn's envelope.} \rch{In the context of exoplanets,} \citet{obergmurray-clay2011} constrain possible planetary C/O ratios based on the disk volatile ice lines but do not model the planet formation process. \rch{In this work the possibility of planets with C/O~$\rightarrow$1 may only arise for planets which have their enrichment dominated by gas accretion and only if they form between the CO$_2$ and CO icelines.} \citet{hellingwoitke2014} carry out a more detailed analysis of the volatile components within a pre-stellar core and protoplanetary disk, modeling the volatile gas and ice abundances as a function of time in static core and disk models. They also model how cloud formation ensues in planetary atmospheres of various abundances and C/O ratios, but do not model the formation of the planets in the disk. \rch{Similar to \citet{obergmurray-clay2011}} they find that super-\rch{stellar} C/O ratios (but $\lesssim$ 1) in the disk gas are possible, mainly between the CO$_2$ and CO icelines. The first studies to more self-consistently link the planet formation process to the final elemental abundances within the planet \rch{in the context of exoplanets} were performed by \citet{thiabaudmarboeuf2014,marboeufthiabaud2014a,marboeufthiabaud2014b} and \citet{thiabaudmarboeuf2015}. They modeled planetesimal formation by assuming refractory and volatile condensation in an initial protoplanetary disk, and then let the gas disk evolve viscously while modeling the planet formation via the core accretion paradigm. \citet{thiabaudmarboeuf2015} find that the gas giants forming in their models have low C/O ratios\footnote{The solar C/O ratio is $\sim$ 0.56 \citep{asplundgrevesse2009}.} unless there is a lack of mixing between the envelope and the accreted solids. \rch{They also find that if icy planetesimals fully sublimate into the planets' gaseous envelope, then their effect on the planetary C/O ratio is dominant compared to the contribution of the accreted gas.} \citet{madhusudhanamin2014} use a simplified description of a planetary population synthesis forming 1 M$_{\rm Jup}$ planets by both core accretion and gravitational instability with final semi-major axes of 0.1 AU. They study whether migration mechanisms might be constrained by the resulting planetary compositions. Disk migration and disk-free migration processes for a planet forming within a viscously evolving disk are treated, keeping track of the matter accreted at various orbital distances in both planetesimal (rocky and/or icy) and gaseous form (including volatiles). Only type II disk migration is modeled and the growth of the planet before opening the gap in type II migration is neglected. This could be a non-trivial assumption, as the planets are possibly strongly enriched before opening of the gap and prior to runaway gas accretion \citep{fortneymordasini2013}. \rch{Therefore, planets in this study which form via core accretion, but have a sub-\rch{stellar} enrichment, are likely caused by the lack of modeling the planet's formation before the type II migration sets in.} Furthermore, rapid type I migration could result in a strong enrichment which originates farther outside in the disk where different planetesimal and gas compositions are likely present. \citet{madhusudhanamin2014} consider two different compositional models for the volatiles and refractory disk, one including carbon grains based on protoplanetary disk observations and one without carbon grains. They find that planets which formed in the outer regions of the disk \rch{may} have sub-\rch{stellar} C and O abundances \rch{if the planets are dominated by gas enrichment} and C/O ratios ranging from \rch{stellar} to super-\rch{stellar} values. This class of planets, if found close to its star at 0.1 AU must therefore have moved in after disk dispersal, suggesting a disk-free migration mechanism. Planets which formed in the inner regions of the disk are found to have super-\rch{stellar} C and O abundances and \rch{stellar} and sub-\rch{stellar} C/O ratios. \rch{In the work presented here we take the previous approaches a step further and} directly investigate whether the formation process leaves visible imprints in the planetary spectra and whether these can be used to constrain planetary formation and migration theory. This is achieved by constructing a ``chain'' of models directly linking the formation, evolution, and present-day spectral appearance of the planets, where the output of one chain link serves self-consistently as input for the next one. With this ``chain'' we furthermore want to study the range of resulting planetary C/O ratios. There are five chain links in our model: In the \textit{first chain link} we fully model the planet's formation via core accretion in a gas and planetesimal disk, yielding the planetary core and envelope masses. The viscous evolution of the disk is modeled as well as type I and II disk migration. The fate of planetesimals during infall into the protoplanet is also directly treated, so that it is known which solids enrich the H/He envelope, and which ones reach the solid core. In the \textit{second chain link}, after the planet has formed, we evolve it to 5 Gyr using a planet evolution model that describes the thermodynamic evolution with the initial conditions given by the formation model. We solve the planetary structure equations including atmospheric escape and using a double-gray atmospheric model with appropriately scaled solar opacities given the envelope's bulk enrichment from formation. As the composition of volatiles and refractories in the disk in- and outside of the iceline is currently not well understood, the planetary formation model merely tracks the mass fractions of accreted volatiles and refractories. Then, at 5 Gyr, in the \textit{third chain link}, a chemistry model translates these bulk compositions yielded by the formation model into elemental abundances in the planet's atmosphere. Combining various volatile and refractory compositional models and turning on or off effects such as clathrate formation or volatile flushing inside of icelines we have 152 different compositional models outside of the iceline and 54 inside. In the \textit{fourth chain link} we use the planetary elemental abundances from the chemistry model and the radius and luminosity from the evolutionary model to calculate the planet's emission and transmission spectra with self-consistent non-gray atmospheric models. Finally, in the \textit{fifth chain link} we use the spectra to simulate secondary eclipse observations with the JWST and ARIEL using the EclipseSim package to see whether the different spectral imprints can be distinguished. With this linked approach, we want to make the aforementioned earlier predictions regarding the imprint of formation on the planetary composition and its expression in spectra more comprehensive and coherent and take a step towards exoplanetology which will be at the focus of upcoming observational studies on extrasolar planets. To demonstrate this we apply our chain model to the example of two \rch{prototypical} planets that eventually become hot Jupiters. First, a ``dry Jupiter'', a Jovian-mass planet that forms exclusively inside of the water iceline and migrates close to its host star by disk migration. Second, a ``wet Saturn'', a Saturnian-mass planet that forms fully outside of the water iceline, and gets to its final positions close to the host star by a dynamical interaction like planet-planet scattering or Kozai mechanism. \rch{As we find that the enrichment of planets with masses typical for hot Jupiter and below is dominated by planetesimal accretion it is important to study the two under this result fundamentally different, and prototypical, cases of how a planet's enrichment can vary as a function of the planet's formation location. This lead to the choice of looking at the ``dry'' and ``wet'' planet.} We find that for some assumptions for the disk chemistry, clear imprints \rch{on the spectra} exist, while for others, it is difficult to distinguish the formation histories. We introduce our model in Section \ref{sec:methods} and show our calculations and results in Section \ref{sec:results}. A discussion and summary can be found in Section \ref{sec:discussion}. | \label{sec:discussion} In this work we present a ``chain'' of models linking directly the formation of a planet to its spectrum. The spectrum of a planet represents a window into its composition. This composition depends on the planet's formation history, its subsequent evolution, and the present-day irradiation. This opens the possibility to use spectra of extrasolar planets as a novel way to better understand planetary formation. However, due to the multitude of physical processes affecting the outcome, the link between formation and spectrum is complex. To make it tractable, we construct a chain of simple but linked models where the output of one model serves self-consistently as the input for the next one. Our chain consists of five chain links: (1) a core accretion formation model that describes the accretion history of a giant planet, its interaction with the disk, the evolution of the disk, and the internal structure of the forming planet. It follows in particular which materials are accreted at what time and location in the disk, and whether the accreted refractory and icy material is added to the solid core or gets mixed into the gaseous H/He envelope. This is achieved by simulating \rch{explicitly} the planetesimal impacts into the protoplanetary envelope\rch{, a new aspect relative to previous similar studies}. This yields the bulk composition of the planetary envelope as inherited from the formation process. (2) In the second chain link, we use a planet evolution model to calculate the thermodynamic evolution of the planetary structure including cooling, contraction, and atmospheric evaporation. This yields the planet's mass, luminosity, and radius at an age of 5\cu Gyrs. (3) In the third link we assign a range of elemental compositions to the refractory, icy, and gaseous components that result from the formation model. We use a large number of models for the disk chemistry to obtain the associated elemental composition of the planet's atmosphere, assuming that the bulk elemental composition of the envelope is representative for the atmospheric composition. We explore various assumption on the composition of the gaseous, refractory, and volatile material that represent extremes of the plausible parameter space. (4) Using a fully-non gray radiative-convective model of the atmosphere and given the planet's physical properties and elemental composition, we calculate in the fourth chain link the atmospheric $p$-$T$ structure and molecular composition yielding also the planet's emission and transmission spectrum. (5) In the fifth chain link, we simulate spectroscopic observations of the planet's eclipse \rch{and transit with JWST and ARIEL}. We apply this chain of models to two hot Jupiters with very different formation histories to investigate whether this leads to visible spectral imprints: (1) a ``dry'' planet that formed completely in the warm inner disk inside of the water iceline, and (2) a ``wet'' planet that formed completely in the colder outer disk, outside of the water iceline. \rch{Because we find that the enrichment of hot Jupiters is dominated by planetesimal accretion, these two planet formation pathways represent two extremes of the possible scenarios, intermediate cases could occur when a planet crosses the iceline during its formation.} The first planet becomes a hot Jupiter by disk migration. We assume that also the second planet is moved close to the central star, but this time due to dynamical interactions (Kozai migration or planet-planet scattering), without accreting ``dry'' material in the inner disk. This leads to the following main results: \\ \\ (1) \textit{Planetesimals play a dominant role for the planetary atmospheric composition \rch{of hot Jupiters}.} An important difference between our model and some previous efforts to predict the planetary composition from the parent disk properties (e.g., \citealt[][]{obergmurray-clay2011,hellingwoitke2014}\rch{; \citealt{ali-dipmousis2014}}) is that in our model the planetesimals, for which we explicitly calculate their atmospheric dissolution, form the prime source of heavy elements in the planetary envelope\rt{. They are dominant over the heavy elements accreted with the gas}, at least for the giant planets of low\rch{er} mass that we study \rch{here} (Saturnian to Jovian mass)\rch{, in agreement with \citet{MousisMarboeuf2009}}. Core accretion models predict that the planetary enrichment due to planetesimal accretion is a decreasing function of planet mass \citep{mordasiniklahr2014}, in good agreement with observations \rch{of the interior and atmospheric enrichment of Solar System and extrasolar giant planets \rt{with an equilibrium temperature of less than $\sim$1000 K}} \rch{\citep{millerfortney2011,kreidbergbean2014,guillotgautier2014,thorngrenfortney2015}}. Thus, there should be a transition from a planetesimal-dominated composition for lower mass planets like the ones considered here to a composition that is dominated by the composition of the accreted gas at large masses (above \rch{2}-10 Jovian masses, \rch{as estimated in Sect. \ref{sect:importanceplanetesimals}). Since the large majority of known transiting hot Jupiters have lower masses than these values, planetesimal-dominated compositions should \rt{likely} apply to most hot Jupiters. More massive planets like those detected by direct imaging may in contrast have different, gas-dominated abundances}. In this work, the bulk elemental composition of the envelope is taken to be representative for the atmosphere of the mature planet. This is valid only if the envelope remains well mixed during the formation phase where most heavy elements are accreted earlier than most gas (Figure\cs\ref{fig:mass_vs_Time} and \cs\ref{fig:mass_vs_aPlanet}) leading \rch{potentially} to compositional gradients in the interior, as well as during the subsequent evolution. As in most planet formation and evolution models, a fully convective interior is a fundamental assumption in our model, but we note that the compositional gradients (Fig. \ref{fig:zenvejupsat}) may halt large scale convective mixing \citep{lecontechabrier2012}. If the envelope does not remain well mixed during formation, then the final atmospheric composition will depend primarily on the heavy element abundances in the gas acquired during gas runaway accretion, rather than on material supplied by planetesimals during the early formation phase \citep{thiabaudmarboeuf2015}. A similar situation arises regarding the compositional mixing across the deep radiative zone that develops during a hot Jupiter's evolution. This could also decouple the observable atmospheric composition from the bulk composition. \rch{Simple estimates indicate (Sect. \ref{sec:methods:atmosphere}) that the latter effect should not be important, but t}he detailed mixing processes in the envelope during runaway gas accretion remain to be investigated, as well as the long-term evolution of the relation between the bulk interior and atmospheric composition. {\it (2) Hot Jupiters are most likely oxygen-rich, i.e., have C/O$<$1, except for non-standard disk chemistries that have no depletion of refractory carbon in the inner disk.} Our result for the planetary C/O depends critically on the assumptions made for the refractory composition in the inner disk. We adopt a composition that is inherited from the ISM \citep{gaidos2015}, in contrast to the approach often used that initially all material is hot and gaseous, and that solids are formed along the condensation sequence as the disk cools. The actual disk composition could lie between these extremes and will most likely resemble one or the other depending on location in the disk and evolutionary stage \citep{pontoppidansalyk2014}. We allow the disk chemistry to alter the ISM refractory composition only in a single, however crucial, pathway: namely that carbon grains initially present in the ISM material can be destroyed in the inner parts of the disk by oxidizing reactions at the carbon grain-gas interface \citep{2001A&A...378..192G,leebergin2010}. \rch{This is based on the observation that the inner part of the Solar System is very carbon poor \citep{1988RSPTA.325..535W,2001E&PSL.185...49A,2015PNAS..112.8965B}, and that freshly polluted white dwarf atmospheres are also carbon poor \citep{2013MNRAS.432.1955F,Wilson01072016} which points towards a generality of carbon depletion.} Then, the result is that all hot Jupiters are oxygen-rich (i.e. C/O $<$1): \rch{as their composition is planetesimal dominated}, a planet forming inside of the water iceline is oxygen-rich because silicates from the dissolved rocky planetesimals add high amounts of oxygen atoms to the planet's envelope. Some carbon is accreted in the form of C-depleted planetesimals and as CO and CH$_{4}$ gas, but the amount is small compared to the oxygen that is accreted in the form of planetesimals. A planet forming outside of the water iceline is also oxygen rich. Its envelope gets enriched via the planetesimals by refractory and volatile material that contains both oxygen and carbon, but due to the oxygen-dominated composition of these building blocks containing water ice, they also end up with a C/O$<$1. Thus, both the ``dry'' planet formed inside of the water iceline and the ``wet'' one formed outside of it are dominated by oxygen, and with our assumed inner disk carbon depletion profile (Fig. \ref{fig:Cdef}) the ``dry'' planets \rch{sometimes} have an even lower C/O than the ``wet'' ones. For the former, we find C/O$<$0.2, for the latter, C/O$<$0.9 with most values clustering around 0.1-0.3. Only in disk chemistry models without carbon depletion in the inner disk (i.e., an ISM-like composition) we robustly find that planets forming inside of the water iceline can have a C/O$>$1: in the accreted planetesimals, the refractory carbon now dominates over the oxygen in the silicates, leading to planetary C/O ratios of $\sim$1.2 for an approximately ISM refractory composition with a 2:1 mass ratio of silicates:carbon, and correspondingly higher or lower values (between 0.5 and 2.5) for different assumption of this ratio. However, as outlined above, disks without carbon depletion in the inner regions appear unlikely, rendering the formation of carbon-rich hot Jupiters \rch{via this channel} unlikely. \rt{In our model, we include a planet's enrichment by both planetesimal impacts, and by the heavy elements that are accreted in gaseous form together with the H/He gas. Our finding that a planetesimal-dominated enrichment (usally) leads to O-rich compositions is in good agreement with earlier works that merely assumed planetesimal domination to be the case. The new aspect that is added by our study is that we explicitly calculate the planetesimal dissolution and then directly find that planetesimal enrichment is really the dominant enrichment pathway for hot Jupiters, at least within the fundamental assumptions of our model. The fundamental reason for this is that already relatively modest planetesimal contributions are sufficient to move from the gas to the planetesimal-dominated regime.} \rch{This probably planetesimal-dominated nature of the enrichment of most hot Jupiters furthermore means that other mechanisms that were proposed to lead to high C/O in previous studies \citep{obergmurray-clay2011,hellingwoitke2014,ali-dipmousis2014} appear unlikely for most hot Jupiters. The reason is that they rely on the accretion of gas of different C/O ratios such that they only apply to gas-dominated enrichments. They may be applicable to planets more massive than 2-10 $\mj$.} We neglect the effect of a moving iceline which could condense ice on grains and planetesimals otherwise consisting of refractories. If all condensible volatiles are trapped in solids outside of the initial iceline position and the inner disk is cleared from volatiles due to the diffusive disk evolution \citep[see, e.g.,][]{ali-dipmousis2014}, this might be a viable assumption. If we would allow for ice condensation on grains, and therefore planetesimals, inside the initial iceline at later times our main result would not be changed: The planets stay oxygen-rich, as water ice only adds more oxygen. \rch{Regarding the impact of model parameters and settings, the carbon depletion model has the biggest impact on the possible outcome of the ``dry'' planet's C/O ratios. We found that introducing a partially ad hoc model of the actual carbon depletion function is sufficient, as already relatively modest carbon reduction factors ($10^{-1}$ instead of the nominal $10^{-4}$) do not change the result that carbon-rich hot Jupiters cannot form under carbon-depleted conditions. For the ``wet'' planet the clathrate formation can have a non-negligible impact on the C/O ratio if a significant amount of carbon-bearing volatiles is trapped in the water ice planetesimals (this requires a volatile abundance model with a non-negligible carbon-fraction). Under no circumstances do we find ``wet'' planets with C/O ratios bigger than 1, however. In the ``dry'' cases without carbon depletion, the silicate-to-carbon mass ratio has the biggest influence on the planetary C/O ratio, leading to C/O values of $\sim 2.8$ for the maximum value considered in the paper (C/Silicate mass ratio = 1).} {\it (3) \rch{Constraining a hot Jupiter's formation location and migration mechanism based on the spectral imprint of a C/O higher or lower than 1 alone appears difficult because hot Jupiters are expected to be oxygen-rich for a formation both inside and outside of the water iceline, at least for our nominal disk chemistries.}} \rch{The ``dry'' and the ``wet'' planets have oxygen-rich envelopes such that their atmospheres both show strong water features and are dominated by oxygen-rich chemistry. For the example shown in sections \ref{sec:results:spectra} and \ref{sec:results:spectra_transm} the ``dry'' planet has a much lower C/O ratio than the ``wet'' planet and it has been shown that both the water and the CO abundance may be retrieved with high SNR in hot Jupiter emission spectra, and thus the C/O ratio \citep{greeneline2016}. Therefore a distinction of the formation location may be possible for this specific disk chemistry. However, in Section \ref{sec:results:stoichiometry} we show that depending on the details of the carbon depletion and clathrate formation model other scenarios may arise where the ``dry'' and ``wet'' planet have overlapping C/O$<$1 ratios, usually $<$ 0.3. Thus an important step to improve the link between planet formation and spectra would be a detailed and quantitative treatment of the carbon depletion and clathrate formation chemistry in exoplanet disks.} \rch{Nonetheless, we find some secondary features distinguishing the two classes:} Planets forming outside of the water iceline are at a fixed total mass more enriched in C and O relative to H/He because of the larger reservoir of planetesimals in the outer disk. This can result in a higher CO$_{2}$ abundance. Next, planets forming outside of the water iceline are more strongly enriched in C and O relative to Si and Mg because of the accretion of icy planetesimals (Fig. \ref{fig:stoichiometry}). \rch{This is generally true for O; for C it is true only if efficient trapping of C-rich ices as clathrates occurs.} In the case where carbon depletion is neglected in the inner parts of the disk, albeit favored by neither observation nor theory, carbon-rich planets can form. \rch{A complete inheritance of carbon-rich ISM-like grains into the solid building blocks of hot Jupiters forming inside of the water iceline thus represents a planetesimal-driven, but probably unlikely pathway towards high C/O$>$1. A related formation path to C-rich planets was suggested for solid planets \citep{gaidos2000,carter-bondobrien2010} around stars which have intrinsically themselves a C/O$>$1. However, such carbon-rich stars are probably very rare \citep[e.g.,][]{fortney2012,gaidos2015}.} In this case there is a clear dichotomy between planets having accreted exclusively inside or outside the iceline, leading to C/O-ratios~$>$~1 or $<$~1, respectively. Carbon-rich (C/O $>$ 1), ``dry'' hot Jupiters would be dominated by methane absorption, rather than water, leading to a distinctively different spectrum when compared to the water-rich, ``wet'' planet. It is interesting to link these findings to predictions by formation models. Giant planet formation models based on the core accretion paradigm predict that around low-metallicity stars, giant planets form only outside of the water iceline, while around high-metallicity stars, giant planets can form both outside and entirely inside of the water iceline (Fig.\,5 in \citealt{idalin2004}; Fig.\,8 in \citealt{mordasinialibert2012a}). The reason is that around high metallicity stars, the amount of refractories alone is high enough to form a critical core of $\sim$10 $\mearth$ triggering runaway gas accretion, while at low [Fe/H], the extra mass provided by the condensation of ice is needed to form such a massive core. Here it is implicitly assumed that the stars have a scaled solar composition. This leads to two predictions: (1) that around low [Fe/H] stars, hot Jupiters with the signs of having accreted only inside of the iceline should be rare, while around high [Fe/H] stars, hot Jupiters with the signs of an accretion inside as well as outside of the iceline are predicted. (2) for stars where tidal interactions have not damped high obliquities, hot Jupiters that show signs of an accretion only beyond the iceline should have a wide range of obliquities including high ones, at least if a high obliquity is a sign of a dynamical interaction, and if this interaction does not lead to the accretion of solids originating from inside of the water iceline, contrarily to disk migration. Using our chain of models we were able to predict the planets' spectra based on their formation \rt{history}. The most striking of our results described above is that the formation of carbon-rich \rch{hot Jupiters} with C/O $>$ 1 is unlikely. \rcp{This result is in good agreement with observations, because the \rch{hot Jupiters recently} characterized appear to be oxygen-rich \citep{lineknutson2014,benneke2015,singfortney2015}. \citet{lineknutson2014} do not find any conclusive evidence for super-solar C/O ratios. The study by \citet{benneke2015} allows for super-solar C/O ratios, while robustly excluding cases with C/O$>$1. The latter is due to the fact that a water detection in {HST WCF3} firmly rules out a carbon-rich chemistry for the considered hot Jupiters. \citet{singfortney2015} further show that the low water abundance in some hot Jupiters is due to the presence of clouds and hazes, and not to a water depletion during formation. Such a primordial depletion would be in contradiction to our results.} Tentative evidence for planets with carbon-rich atmospheres exists \rch{for types of planets other than hot Jupiters like HR8799b} \citep{lee2013} \rch{or 55 Canc e} \citep{tsiarasrocchetto2015}. In our paper we also discuss the possibility of a carbon sweet spot in the disk which lies outside of the region of carbon depletion, but still inside of the iceline \citep{lodders2004}. Planets which would form exclusively within this region could attain carbon-rich envelopes and atmospheres. If such planets end up close to their stars they should be easily distinguishable due to their methane-dominated spectra. While the exact location and processes which give rise to this carbon sweet spot are specific to our model assumptions, the existence and formation of carbon-rich planets is therefore not downright refutable, but should be the exception, rather than the rule. At least under the assumptions made in this work, the majority of hot Jupiters should be oxygen-rich. | 16 | 9 | 1609.03019 |
1609 | 1609.06316_arXiv.txt | \par We present ALMA observations of the inner 1' (1.2 kpc) of the Circinus galaxy, the nearest Seyfert. We target CO (1--0) in the region associated with a well-known multiphase outflow driven by the central active galactic nucleus (AGN). While the geometry of Circinus and its outflow make disentangling the latter difficult, we see indications of outflowing molecular gas at velocities consistent with the ionized outflow. We constrain the mass of the outflowing molecular gas to be 1.5$\times$10$^{5}$ --5.1$\times$10$^{6}$ M$_{\odot}$, yielding a molecular outflow rate of 0.35--12.3 M$_{\odot}$ yr$^{-1}$. The values within this range are comparable to the star formation rate in Circinus, indicating that the outflow indeed regulates star formation to some degree. The molecular outflow in Circinus is considerably lower in mass and energetics than previously-studied AGN-driven outflows, especially given its high ratio of AGN luminosity to bolometric luminosity. The molecular outflow in Circinus is, however, consistent with some trends put forth in \citet{2014A&A...562A..21C}, including a linear relation between kinetic power and AGN luminosity, as well as its momentum rate vs.\ bolometric luminosity (although the latter places Circinus among the starburst galaxies in that sample). We detect additional molecular species including CN and C$^{17}$O. | \par A primary source of feedback in galaxies are galactic outflows/winds \citep{2005ARA&A..43..769V}. They potentially expel material into the intergalactic medium (IGM), enriching the surrounding environment, and constituting a reservoir of material that can be reaccreted to fuel later star formation in galaxies \citep{2010MNRAS.406.2325O}. Galactic winds play also an important role in driving bubbles into the ISM that allow radiation to propagate further \citep{2000ApJ...531..846D}. Galactic winds are invoked to explain the observed paucity of massive galaxies in the local universe (e.g.\ \citealt{2008MNRAS.391..481S}) and the quenching of star formation in massive galaxies (e.g.\ \citealt{2013MNRAS.430.3213B}). Thus, it is imperative to gauge the total outflow rate and compare it to the accretion rate in order to understand the evolution of galaxies. While a recent emphasis has been placed on researching galactic winds (e.g.\ \citealt{2005ARA&A..43..769V}, \citealt{2010ApJ...711..818S}, \citealt{2010A&A...518L.155F}, \citealt{2013Natur.499..450B}, \citealt{2014A&A...562A..21C}, \citealt{2015ApJ...798...31A}, \citealt{2015A&A...574A..85A}), the degree to which they regulate these evolutionary processes is still poorly constrained, largely due to insufficient observational data. With the advent of instruments such as ALMA, the molecular phases of galactic winds may now be mapped in detail and with superb velocity resolution. \par A fundamental question is the relative importance of starburst- and AGN-driven winds in the feedback process. Both tend to suppress star formation by removing molecular gas, but the efficiency with which they do it is unknown. Both affect the surrounding ISM, but their respective impacts may differ based on their energetics and distributions within the host galaxies. Simulations and observations indicate that AGN-driven winds are more energetic and concentrated near the center, resulting in a higher chance for material to escape the galaxy and a lower likelihood of it fueling future star formation \citep{2012ApJ...750...55S}. Starburst-driven winds, however, are more widely distributed and may eject material at larger galactocentric radii, producing a greater effect on the ISM. When both are present, the two types of outflows may work to amplify their respective contributions \citep{2009MNRAS.396L..46P}, but can also counteract each other's effects \citep{2013NatSR....E1738B}. Fundamentally, their impact depends on their efficiency at entraining and ejecting material of the various phases of the ISM from in the disk. \par Molecular outflows are seen in several starburst galaxies, including M 82 (\citealt{2002ApJ...580L..21W}, \citealt{2015ApJ...814...83L}), Arp 220 \citep{2009ApJ...700L.104S}, NGC 253 \citep{2013Natur.499..450B}, NGC 1808 \citep{2016ApJ...823...68S} among others. The molecular mass outflow rates in these galaxies indicate that starburst-driven molecular outflows can indeed regulate star formation (SF), particularly in NGC 253 where the molecular mass outflow rate was determined to be $>$3 times the global star formation rate (SFR) in that galaxy, and likely higher. \par During the past five years there have been a number of studies focusing on AGN-driven outflows, summarized in \citet{2011ApJ...733L..16S}, \citet{2013ApJ...776...27V}, \citet{2014A&A...562A..21C}, \citet{2015A&A...583A..99F}, and \citet{2015ApJ...811...15L}. These studies show that an increase in AGN luminosity (L$_{AGN}$) typically results in stronger outflows, with some reaching values of over 1000 M$_{\odot}$ yr$^{-1}$ for the molecular component. There are also indications that stronger outflows may also be tied to a high ratio of L$_{AGN}$ to the bolometric luminosity (L$_{bol}$), but that appears to be less important. \par Other results by \citet{2015ApJ...798...31A} indicate a molecular outflow of $\sim$100 M$_{\odot}$ yr$^{-1}$ with an average velocity of 177 km s$^{-1}$ within a radius of $\sim$225 pc in NGC 1266, and \citet{2016A&A...590A..73A} determine a molecular mass outflow rate for NGC 1377 of 9--30 M$_{\odot}$ yr$^{-1}$, showing a strong jet potentially entraining the cold gas extending out to $\sim$150 pc in projection, with velocity estimates from 240 to 850 km s$^{-1}$. \citet{2015A&A...580A...1M} and \citet{2014Natur.511..440T} characterize the AGN-driven molecular outflow in IC 5063, a radio-weak Seyfert galaxy, that the multiphase outflow components (ionized, {\sc H\,i}, warm H$_{2}$, cold molecular gas) share similar kinematics. The molecular mass outflow rate they determine is sufficiently high and the AGN sufficiently weak, that the radio jet within that galaxy is likely the primary driver of the outflow - not radiation from the AGN. However, in Mrk 231, \citet{2016A&A...593A..30M} find that it is unlikely that a jet is driving its multiphase ({\sc Na\,i}, {\sc H\,i}, OH, and CO) outflow. \par In contrast with those massive molecular outflows, \citet{2007A&A...468L..49M} detect a more modest molecular outflow of $\sim$4 M$_{\odot}$ yr$^{-1}$ in M 51 - a galaxy that is neither starbursting nor a ULIRG. They conclude that the molecular outflow is likely mechanically-driven by a radio jet as opposed to SF (which is spread throughout the disk) or radiation from the AGN (which is too weak). The bulk of the molecular outflow they detect is within 1" (34 pc) of the center of M 51 -- quite small by comparison to the molecular outflows observed in other systems and unlikely to impact SF throughout M 51. \citet{2014A&A...565A..97C} observe NGC 1566, a galaxy with a low-luminosty AGN, with ALMA and find no evidence for a molecular outflow or AGN-driven feedback. \par In the current sample of molecular outflows there appears to be a correlation between AGN luminosity and powerful outflows. There is however, (as noted in \citealt{2014A&A...562A..21C}), a bias in that, with a few exceptions (e.g.\ ULIRGs in the Herschel sample presented in \citealt{2010A&A...518L..36S} for which the molecular outflows were investigated by \citealt{2013ApJ...776...27V}), only galaxies with previously-detected, high-velocity molecular outflows are considered. It is necessary to observe molecular outflows in host galaxies with a range of AGN luminosities at high spatial resolution in order to see if these trends hold. \subsection{The Circinus Galaxy} \par At an adopted distance of 4.2 Mpc (1"$=$20.4 pc, \citealt{2009AJ....138..323T}), the nearest Seyfert 2 \citep{1994A&A...288..457O} is The Circinus galaxy \citep{1977A&A....55..445F}. An ionized outflow is clearly observed emerging from the nuclear region of Circinus, with blue-shifted velocities (receding components are likely obscured by the intervening disk) of approximately $-$150 km~s$^{-1}$ (e.g.\ \citealt{1994Msngr..78...20M}, \citealt{1997ApJ...479L.105V}, \citealt{2000AJ....120.1325W}, Figure~\ref{halpha_muse}). The ionized component extends for at least 30" along the minor axis and farther. \citet{1997ApJ...479L.105V} also observe what look like bow-shocked features resembling Herbig-Haro objects at the ends of these filaments suggesting a strong interaction with the surrounding ISM. \citet{1998MNRAS.297.1202E} detect an outflow in the radio continuum, most prominently in the north-eastern direction, but with a counter-jet to the southeast. This counter-jet shows that the outflow is not entirely one-sided, and observations of the molecular phase (which suffers less from extinction effects) may indeed uncover a counter-jet closer to the disk -- a possibility we explore in this work. Observational parameters of Circinus are listed in Table~\ref{tbl_circ}. \begin{deluxetable}{lcc} \tabletypesize{\scriptsize} \tablecaption{The Circinus Galaxy \label{tbl_circ}} \tablewidth{0pt} \tablehead { \colhead{Parameter} & \colhead{Value} & \colhead{Reference} } \startdata \phd Distance &4.2 Mpc&\citet{2009AJ....138..323T}\\ \phd SFR &4.7 M$_{\odot}$ yr$^{-1}$&\citet{2008ApJ...686..155Z}\tablenotemark{a}\\ \phd L$_{bol}$ &1.7$\times$10$^{10}$ L$_{\odot}$ &Maiolino et al.\ (1998)\tablenotemark{b}\\ \phd L$_{AGN}$ &10$^{10}$ L$_{\odot}$ &Moorwood et al.\ (1996)\\ \phd Type &Seyfert 2&Oliva et al.\ (1994)\\ \phd Black Hole Mass &1.7$\times$10$^{6}\pm0.3$M$_{\odot}$&Tristram et al.\ (2007)\\ \phd Eddington Luminosity &5.6$\times$10$^{10}$L$_{\odot}$&Tristram et al.\ (2007) \tablenotetext{a}{Multiple values from the literature for the star formation rate are listed in \citet{2012MNRAS.425.1934F}. We adopt the value derived using L$_{TIR}$.} \tablenotetext{b}{Originally derived by \citet{1997A&A...325..450S} and modified by \citet{1998ApJ...493..650M}.} \enddata \end{deluxetable} \begin{figure} \includegraphics[width=80mm]{halpha_muse.eps} \caption{\textit{An H$\alpha$ image of Circinus created with MUSE data (full presentation of the MUSE data in Venturi at al. (\textit{in prep}) and Marconi et al. (\textit{in prep})). Multiple filaments extend from the central regions of the disk (center marked with a cross). The approximate width of the H$\alpha$ outflow cone is shown by the two large arrows. Regions referred to throughout the text are introduced here for reference although their molecular components are not visible. The slanted rectangle near the center marks the molecular ``overdense region", the circle marks the ``NW cloud", and the rectangle to the west marks the ``far W cloud". Assuming our adopted distance of 4.2 Mpc, 1" = 20.4 pc.} \label{halpha_muse}} \end{figure} \par This paper is organized as follows: In $\S$~\ref{observations}--~\ref{data} we present the observations, calibration, and the data. In $\S$~\ref{results} we present our analysis and results followed by a discussion in $\S$~\ref{discussion}. We provide a summary of our results in $\S$~\ref{summary}. The Appendix includes details on our kinematic modeling. | \label{discussion} \subsection{Energetics of the Outflow} \par We now consider how the AGN and star formation in Circinus may be affecting the outflow properties. \par Circinus hosts a 10$^{10}$ L$_{\odot}$ AGN \citep{1996A&A...315L.109M} and has a bolometric luminosity (L$_{bol}$) of 1.7$\times$10$^{10}$ L$_{\odot}$ (\citealt{1997A&A...325..450S}, \citealt{1998ApJ...493..650M}). These values yield $L_{AGN}$/$L_{bol}$ of around 0.6 (closer to 0.9 if using values derived in \citealt{2016ApJ...826..111S}). L$_{AGN}$ for Circinus is comparable to that of NGC 1266, NGC 1068, and NGC 1377 (\citealt{2014A&A...562A..21C} and references therein), and thus on the lower-end of AGN luminosities for the molecular outflows observed to date. $L_{AGN}$/$L_{bol}$ for Circinus, however, is 2--3 times higher than for those galaxies. \par Relevant to the launching mechanism of the outflow are its kinetic power and momentum rate. Observations show that these properties, when associated with AGN-driven outflows, show some correlation with L$_{AGN}$ (e.g.\ \citealt{2014A&A...562A..21C}, \citealt{2015A&A...583A..99F}). Such connections have also resulted from simulations (e.g.\ \citealt{2012ApJ...745L..34Z}, \citealt{2012MNRAS.425..605F}). \par The kinetic power of 1.0$\times$10$^{39}$--1.1$\times$10$^{41}$ erg s$^{-1}$ that we determine for the molecular outflow is generally lower than that of the \citet{2014A&A...562A..21C} sample, especially the outflows assumed to be driven by AGN. In that work, a relation was established between the kinetic power of the outflows and the L$_{AGN}$ of the host galaxies (generally finding that the P$_{kin,OF}$ is $\sim$5$\%$ of L$_{AGN}$). Circinus has a substantially lower P$_{kin,OF}$/L$_{AGN}$ ratio (on the order of 0.01--0.3$\%$ of L$_{AGN}$) compared to the ULIRGs and other Seyferts. However, this range is consistent with the linear fit expressed in Equation 3/Figure 12 of \citet{2014A&A...562A..21C}. We directly duplicate Figure 12 from that work here with the addition of Circinus (Figure~\ref{cicone_all_mod}, panel A). In that relation, P$_{kin,OF}$/L$_{AGN}$ decreases for lower L$_{AGN}$, indicating that the trends derived from that sample may indeed apply to lower luminosity galaxies as well. The relation does not, however, appear to be consistent with the high ratio of L$_{AGN}$ to L$_{bol}$ in Circinus. % \begin{figure*} \begin{centering} \includegraphics[width=180mm]{cicone_all_mod.eps} \caption{\textit{Figures 12 (panel A), 13 (panel B), 14 (panel C), and 16 (panel D) reproduced directly from \citet{2014A&A...562A..21C} (with permission), but with the addition of Circinus here. Symbols labeled in panel A correspond to Seyfert 1 (Sy1), Seyfert 2 (Sy2), LINER and starburst (SB) galaxies. The ranges for P$_{kin,OF}$ and $v\dot{M}_{H_{2}, OF}$ for Circinus have been added where applicable. It is important to note that $\alpha_{CO}$=0.8 was assumed for the galaxies in the \citet{2014A&A...562A..21C} work (upper end of range shown for Circinus). In all cases, P$_{kin,OF}$ and $v\dot{M}_{H_{2}, OF}$ for Circinus is significantly lower than that of the AGN-driven outflows, especially those with high $L_{AGN}$/$L_{bol}$. However, when considering the upper-limit of $\alpha_{CO}$=0.8 (typically used for ULIRGs) in the case of Circinus, it appears to follow the relation indicated by the Seyfert 2 galaxies when extrapolated to lower $L_{AGN}$.} \label{cicone_all_mod}} \end{centering} \end{figure*} \par The kinetic power due to supernovae (P$_{kin,SF}$) is also useful to consider. Equation 2 from \citet{2005ARA&A..43..769V} indicates that P$_{kin,SF}$=7$\times$10$^{41}$ SFR(M$_{\odot}$ yr$^{-1}$), yielding a value of 3.5$\times$10$^{42}$ erg s$^{-1}$ for Circinus -- again low given its AGN properties. When P$_{kin,OF}$ is plotted against P$_{kin,SF}$, P$_{kin,OF}$ for Circinus is well below that of the AGN-driven outflows with $L_{AGN}$/$L_{bol}$ summarized in Figure 13 of \citet{2014A&A...562A..21C}, which we show here in panel B of Figure~\ref{cicone_all_mod}. Instead, Circinus falls within the LINER and starburst population. \par We find the momentum rate of the molecular outflow is 2.0$\times$10$^{32}$ --1.3$\times$10$^{34}$ g cm s$^{-2}$. With these values, we find a ratio of $v\dot{M}_{H_{2}, OF}$ to L$_{AGN}$/$c$ of 0.1--10.3. \citet{2014A&A...562A..21C} found this ratio to be $\sim$20 (and often significantly higher) for outflows in host galaxies having L$_{AGN}{\geq}$10$\%$ of L$_{bol}$. The ratio found in that work is consistent with simulations presented by \citet{2012ApJ...745L..34Z}. Circinus is well below this ratio, again indicating that it does not have similar outflow properties to other galaxies with high values of $L_{AGN}$/$L_{bol}$. However, if one considers only the ratio of $v\dot{M}_{H_{2}, OF}$/L$_{AGN}$, the upper-limit for Circinus derived using $\alpha_{CO}$=0.8 (typically used for ULIRGs) is again consistent with the \citet{2014A&A...562A..21C} trend seen in the galaxies with presumed AGN-driven outflows if one extrapolates to lower L$_{AGN}$ (Figure 14 of \citealt{2014A&A...562A..21C} or panel C of Figure~\ref{cicone_all_mod} here). When $v\dot{M}_{H_{2}, OF}$ is considered only in relation to $L_{bol}$, Circinus again appears to be consistent with starburst galaxies and LINERS (Figure 16 of \citealt{2014A&A...562A..21C} or panel D of Figure~\ref{cicone_all_mod} shown here). \par In summary, when considering the kinetic power and momentum rate, Circinus appears to be consistent with trends put forth in \citet{2014A&A...562A..21C}, with the exception of those connected to its high AGN luminosity (and $L_{AGN}$/$L_{bol}$). \subsection{The Multiphase Structure of the Wind} \par While there is a clear ionized outflow in Circinus, the existence of one in molecular phase is ambiguous. In the preceding sections we have presented the strongest evidence for one within the ALMA data: 1) There is an overdensity to the northwest of the nucleus. This overdense region coincides with the location of the ionized outflow cone. 2) There is a cloud to the northwest (NW cloud) that appears to be traveling away from the disk. The NW cloud is also blue-shifted by approximately the same amount as the ionized outflow. This feature is the clearest outflow signature in the ALMA data. Based on the NW cloud, the molecular outflow is driven $\sim$35" in projection from the center, or 1.5 kpc when deprojected. 3) A similar, but less prominent cloud is seen to the west (far W cloud). The far W cloud is directly along one of the ionized filaments, with velocities that coincide with that filament. \par The ionized outflow to the northwest in Circinus is well-known, manifesting as a $\sim$1.5 kpc blue-shifted outflow cone (e.g.\ \citealt{1994Msngr..78...20M}, \citealt{1997ApJ...479L.105V}, \citealt{2000AJ....120.1325W}, \citealt{2010ApJ...711..818S}). All of these studies have noted the wide opening angle of the outflow cone, as well as filamentary structures. \citealt{1997ApJ...479L.105V} note the presence of bow-shocked features, indicating strong interactions with the ISM. \citealt{2010ApJ...711..818S} found evidence for a filled ionized gas cone and velocity gradients along filaments. The current resolution of the molecular data does not allow for a direct comparison with the ionized outflow, but the features that we see have similar velocities. Like the ionized component, it is possible that there exists unidentifiable molecular outflow material is kinematically indistinct from disk emission. \par While we detect outflow signatures only on the near-side of the galaxy (also consistent with ionized observations), a counter-jet indeed exists as shown by \citet{1998MNRAS.297.1202E} in the radio continuum. If the aformentined overdense region is truly due to a molecular outflow, the lack of a molecular component to the counter-jet is somewhat intriguing as it was previously thought that the lack of a symmetric ionized component was due to absorption. The counter-jet presented in \citet{1998MNRAS.297.1202E}, however, shows a substantial gap ($\sim$2' or 5--6 kpc taking projection effects into account) between the main disk and the radio emission on that side, indicating that perhaps any molecular component is either weaker on that side, or no longer present. There is also the possibility of asymmetries in the disk that could hinder the expulsion of material on one side. \par Interestingly, \citet{2016ApJ...826..111S} search for OH outflows in more than 50 low-luminosity Burst Alert Telescope (BAT) detected AGN, including Circinus. In the case of Circinus, they find an unambigous OH \textit{inflow} in the form of an inverted P-Cygni profile within the innermost $\sim$10" from the center. Most of this region is omitted from our analysis due to resolution limitations. Thus, a valid comparison must wait for higher resolution data. \subsection{Implications for the Evolution of Circinus} \par As demonstrated, it is difficult to detect outflowing molecular gas in Circinus. The kinematics of the disk and any potential outflow are largely overlapping as demonstrated in Figure~\ref{channel_maps_muse} for the ionized outflow. We see multiple indications of a molecular outflow in the ALMA data, including the overdense region, the NW cloud and far W clouds, and the northern stripe. Still, there is no indication in the molecular phase of a prominent outflow such as what is seen in the ionized component (which is clearly seen even without kinematic information). Furthermore, even when we consider all potential outflowing molecular gas, its mass, mass outflow rate, and energetics are substantially lower than what is seen in AGN-driven outflows \citep{2014A&A...562A..21C}, especially when considering its high L$_{AGN}$/L$_{bol}$ ratio. We now consider possible explanations for this result. \par Circinus has one of the most highly-ionized narrow-line regions, which is visible in the optical, near-infrared, and mid-infrared (e.g.\ \citealt{1998ApJ...505..621C}, \citealt{2010MNRAS.402..724P}). \citealt{1997ApJ...479L.105V} find evidence that the higher-resolution ionized component is launched from the region containing AGN. The ionized component of the outflow outflow from the central regions of Circinus is prominent (e.g.\ \citealt{1994Msngr..78...20M}, \citealt{1997ApJ...479L.105V}, \citealt{2010ApJ...711..818S}). Thus, it is likely that a majority of the gas in the outflow cone of Circinus is in the ionized phase, resulting in a weak detection of outflowing CO. \par It is difficult to say whether the molecular component of the outflow is entrained gas, or if the ionized component condenses and forms molecular gas in-situ. Higher resolution observations (especially on a level comparable to the MUSE data) and additional CO transitions, as well as shock tracers will help to answer this question. | 16 | 9 | 1609.06316 |
1609 | 1609.01714_arXiv.txt | \qquad Fiber-fed multi-object spectroscopic surveys, with their ability to collect an unprecedented number of redshifts, currently dominate large-scale structure studies. However, physical constraints limit these surveys from successfully collecting redshifts from galaxies too close to each other on the focal plane. This ultimately leads to significant systematic effects on galaxy clustering measurements. Using simulated mock catalogs, we demonstrate that fiber collisions have a significant impact on the power spectrum, $P(k)$, monopole and quadrupole that exceeds sample variance at scales smaller than $k\sim0.1~h/{\rm Mpc}$. \qquad We present two methods to account for fiber collisions in the power spectrum. The first, statistically reconstructs the clustering of fiber collided galaxy pairs by modeling the distribution of the line-of-sight displacements between them. It also properly accounts for fiber collisions in the shot-noise correction term of the $P(k)$ estimator. Using this method, we recover the true $P(k)$ monopole of the mock catalogs with residuals of $<0.5\%$ at $k=0.3~h/{\rm Mpc}$ and $<4\%$ at $k=0.83~h/{\rm Mpc}$ -- a significant improvement over existing correction methods. The quadrupole, however, does not improve significantly. \qquad The second method models the effect of fiber collisions on the power spectrum as a convolution with a configuration space top-hat function that depends on the physical scale of fiber collisions. It directly computes theoretical predictions of the fiber-collided $P(k)$ multipoles and reduces the influence of smaller scales to a set of nuisance parameters. Using this method, we reliably model the effect of fiber collisions on the monopole and quadrupole down to the scale limits of theoretical predictions. The methods we present in this paper will allow us to robustly analyze galaxy power spectrum multipole measurements to much smaller scales than previously possible. | Cosmological measurements such as galaxy clustering statistics are no longer dominated by uncertainties from statistical precision, but from systematic effects of the measurements. This is a result of the millions of redshifts to distant galaxies that have been obtained through redshift surveys such as the 2dF Galaxy Redshift Survey (2dFGRS; \citealt{Colless:1999aa}) and the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (SDSS-III BOSS; \citealt{Anderson:2012aa, Dawson:2013aa}). Current surveys, such as the Extended Baryon Oscillation Spectroscopic Survey (eBOSS; \citealt{Dawson:2015aa}), and future surveys such as the Dark Energy Survey Instrument (DESI; \citealt{Schlegel:2011aa, Morales:2012aa, Makarem:2014aa}), and the Subaru Prime Focus Spectrograph (PFS; \citealt{Takada:2014aa}), will continue to collect many more million redshifts, extending our measurements to unprecedented statistical precision. These completed and future surveys, all use and will use fiber-fed spectrographs. For each galaxy, a fiber is used to obtain a spectroscopic redshift. However, the physical size of the fiber housing and other physical constraints limit how well any of these surveys can observe close pairs of galaxies. In the SDSS, if two galaxies are located within the fiber collision angular scale from one another on the sky, separate fibers cannot be placed adjacently to observe them simultaneously (\citealt{Yoon:2008aa}). In these situations, only a single redshift is measured. With redshifts of galaxies in close angular proximity missing from the sample, any clustering statistic probing these scales will be systematically affected. As our cosmological surveys extend further to higher redshifts, the systematic effect becomes more severe. The fiber collision angular scale corresponds to a larger comoving scale at higher redshift, thereby affecting our measurements on larger scales. BOSS, in particular, has an angular fiber collision scale of $62\arcsec$. This corresponds to $\sim 0.43 \;\mathrm{Mpc}/h$ at the center of the survey's redshift range; fiber-collided galaxies account for $\sim 5\%$ of the galaxy sample (\citealt{Anderson:2012aa, Reid:2012aa, Guo:2012aa}). While this may seem like a relatively small fraction of redshifts, its effect on clustering measurements such as the power spectrum and bispectrum is significant and needs to be accounted for in order to probe mildly non-linear scales. Unfortunately, future spectroscopic surveys such as DESI, which will use robotic fiber positioner technology, will be subject to similar effects. Therefore, accounting for the effects of fiber collisions will remain a crucial and unavoidable challenge for analyzing clustering measurements. To correct for fiber collisions, one common approach used in clustering measurements is the nearest neighbor method (\citealt{Zehavi:2002aa, Zehavi:2005aa, Zehavi:2011aa, Berlind:2006aa, Anderson:2012aa}). For fiber-collided galaxies without resolved redshifts, the method assigns the statistical weight of the fiber-collided galaxy to its nearest angular neighbor. This provides a reasonable correction for the fiber collision effects at scales much larger than the fiber collision scales; however the correction falls short elsewhere. In fact, as \cite{Zehavi:2005aa} find, fiber collisions affect the two-point correlation function (2PCF) measurements even on scales significantly larger than the fiber collision scale ( $> 1\;\mathrm{Mpc}/h$). For power spectrum measurements in BOSS, the nearest neighbor method has recently been supplemented with adjustments in the constant shot-noise term of the power spectrum estimator to correct for fiber collisions~\citep{Beutler:2014aa, Gil-Marin:2014aa, Gil-Marin:2015aa, Gil-Marin:2016ab, Beutler:2016aa, Grieb:2016aa, Gil-Marin:2016aa}. More specifically, methods like the one used in \cite{Gil-Marin:2014aa} obtain the value of the shot-noise term from mock catalogs and thus rely entirely on their accuracy to correct for fiber collisions. This is concerning since, as we shall demonstrate in detail, fiber collisions depend systematically on the small-scale power spectrum, and mock catalogs used for large scale structure analyses are typically not based on high resolution N-body simulations. In addition, there is no way to validate and calibrate the shot-noise term independently for observations. A more reliable approach is to marginalize over the value of the shot-noise term, and this is the approach that has recently become more popular ~\citep{Beutler:2014aa, Gil-Marin:2016ab, Beutler:2016aa, Grieb:2016aa, Gil-Marin:2016aa}. However, adjustments to the shot-noise term are limited to the power spectrum monopole, since higher order multipoles do not have a shot-noise term. However, as we shall discuss in detail below, {\em fiber collisions affect all multipoles in a $k$-dependent way}, not just adding a constant for the monopole power. \cite{Guo:2012aa}, focusing on SDSS-III BOSS like samples, proposed a fiber collision correction method for the 2PCF that is able to reasonably correct for fiber collisions above and below the collision scale. \cite{Guo:2012aa} estimates the total contribution of fiber-collided galaxies to the 2PCF by examining the pair statistics in overlapping tiling regions of the survey, where a smaller fraction of galaxies suffer from fiber collisions. Unfortunately, applying an analogous method in Fourier space proves to be more difficult. The \cite{Guo:2012aa} method in Fourier space would involve measuring the power spectra for individual overlapping regions. Given the complex geometry of these regions, the systematic effect introduced by the window function makes measuring the power spectrum at larger scales intractable. Meanwhile, galaxy redshift-space power spectrum models from perturbation theory continue to reliably model higher $k$ in the weakly non-linear regime \citep{Taruya:2010aa, Sato:2011aa, Taruya:2012aa, Okumura:2012aa, Taruya:2013aa, Taruya:2014aa, Beutler:2014aa, Okumura:2015aa, Beutler:2016aa, Grieb:2016aa, Sanchez:2016aa}. Recent analyses of galaxy power spectrum multipoles (\citealt{Zhao:2013aa, Beutler:2014aa, Gil-Marin:2014aa, Gil-Marin:2016ab, Beutler:2016aa, Grieb:2016aa, Gil-Marin:2016aa}) use scales up to $k_{\rm max}=0.15-0.2 h$/Mpc for BOSS galaxies, and this limit will for sure move towards smaller scales in upcoming analyses. As statistical errors decrease the importance of systematics due to fiber collisions plays an increasingly important role. The main goal of this paper is to quantify this systematic effect for the power spectrum multipoles and to provide ways to overcome it; for this purpose we develop two distinct approaches. The first approach improves upon the nearest neighbor method by modeling the distribution of the line-of-sight displacement between resolved fiber collided galaxies to statistically reconstruct the clustering of fiber-collided galaxies. This uses information on resolved fiber collided galaxies that is available from the data themselves (e.g. in tiling overlap regions). The difficulty with this method is that it works statistically, i.e. we cannot reconstruct the {\em actual} galaxy by galaxy line of sight displacement due to collisions. As a result of this, while the method works very well to recover the true power spectrum monopole from fiber collided galaxy catalogs, it does not work sufficiently well for the power spectrum quadrupole which is far more sensitive to the precise structure of ``fingers of god''. The second approach addresses the shortcomings of the first one by modeling the effects of fiber collisions on the {\em predictions} instead of trying to undo their effect on the data before computing power spectrum statistics. It approximates the effect of fiber collisions on the 2PCF as a 2D top hat function. Then it derives the effect of fiber collisions on the galaxy power spectrum as a convolution of the true power spectrum with the top hat function. Therefore the theoretical predictions for the power spectrum are fiber collided and then can be compared directly to the observed fiber collided power spectrum in clustering analyses. This paper is organized as follows. In Section \ref{sec:catalog}, we briefly describe the simulated mock catalogs with realistic fiber collisions and the power spectrum estimator used throughout the paper. We then demonstrate the impact of fiber collisions on power spectrum measurements and how the nearest neighbor method does not adequately account for fiber collisions in Section \ref{sec:fc_pk}. We present our two methods of accounting for fiber collisions along with the results for mock catalogs in Section \ref{sec:dlospeak} and Section \ref{sec:fourier}, respectively. Finally in Section \ref{sec:summary} we summarize our results and conclude. | \label{sec:summary} Using simulated mock catalogs designed specifically for interpreting BOSS clustering measurements with realistically imposed fiber collisions, we demonstrate that the Nearest Neighbor method (NN), most common used for dealing with fiber collisions, is insufficient in accounting for the effect of fiber collisions on the galaxy power spectrum monopole and quadrupole. Although fiber collisions have little significant effect on the power spectrum at large scales, their effect quickly overtakes sample variance on scales smaller than $k \approx 0.1 \;h/\mathrm{Mpc}$. At $k \sim 0.3 \;h/\mathrm{Mpc}$ fiber collisions have over a $7.3\%$ and $73\%$ impact on the power spectrum monopole and quadrupole, respectively. The effect is equivalent to $7.3$ and $2.5$ times the sample variance of CMASS for $\delta k \approx 0.01\;h/\mathrm{Mpc}$, leading to a binning-independent scale of validity of the NN method of $k_{\chi^2}=0.068\;h/\mathrm{Mpc}$ for the monopole and $k_{\chi^2}=0.17\;h/\mathrm{Mpc}$ for the quadrupole (see bottom panel of Figure~\ref{fig:dlospeak_norm_resid}). Consequently at these scales, measurements of the power spectrum becomes dominated by the systematic effects of fiber collisions. Some recent methods (\citealt{Beutler:2014aa,Gil-Marin:2014aa,Beutler:2016aa,Grieb:2016aa,Gil-Marin:2016aa}) have supplemented the NN method with adjustments to the constant shot noise term in the power spectrum estimator. While these methods improve the overall residual for the monopole, e.g. $k_{\chi^2}=0.17\;h/\mathrm{Mpc}$ for the method by \cite{Gil-Marin:2014aa}, they fail to account for the $k$-dependence of the systematic effect on smaller scales. Furthermore, since the quadrupole does not have a shot noise term, these methods provide no improvements for $l \geq 2$. In this paper, we first model the distribution of the line-of-sight displacement between fiber collided pairs using mock catalogs. From the model, we statistically reconstruct the clustering of fiber collided galaxies that reside in the same halo. This, combined with the actual shot noise subtraction of the power spectrum estimator that accounts for chance alignments, leads to our LOS Reconstruction method that recovers very well the true power spectrum monopole from fiber collided data. As an added advantage, the method only relies on parameters ($\sigma_\mathrm{LOS}$ and $f_\mathrm{peak}$) measured from the actual observations. This makes the performance of the method independent from the accuracy of the mock catalogs, which are known to be unreliable at small scales. Using the LOS Reconstruction method, we can recover the true power spectrum monopole to scales well beyond previous methods. The LOS Reconstruction monopole power spectrum residuals remain within sample variance until $k \sim 0.53\;h/\mathrm{Mpc}$ and $k_{\chi^2}$ extends to $0.29\;h/\mathrm{Mpc}$. However, for the power spectrum quadrupole at $k = 0.2\;h/\mathrm{Mpc}$, the LOS Reconstruction method only reduces the discrepancy between the fiber collided $P_2(k)$ and the true $P_2(k)$ to roughly the sample variance. Therefore, the true monopole power spectrum estimate from the LOS reconstruction method can be compared to the systematics free predicted power spectrum monopole to infer the cosmological parameters of interest without biases from fiber collisions, but for the quadrupole power spectrum the method is not a substantial improvement over previous methods. We trace this problem to the fact that the quadrupole is more sensitive to the object by object finger of god effect, while the LOS reconstruction works only statistically starting from the distribution of close pairs. To improve on the LOS reconstruction results we develop the effective window method which, rather than attempting to correct the data before making measurements, computes theoretical predictions of the fiber-collided power spectrum multipoles. In this approach, we approximate the effect that fiber collisions have on the two-dimensional configuration space two-point correlation function of the NN method as a scaled top-hat function. Then the effect of fiber collisions can be written as the sum of two contributions: 1) that of uncorrelated chance collisions, with an amplitude proportional to the the effective survey area affected by fiber collisions times the wavelength of perturbations, and 2) that of correlated collisions, which is also proportional to the effective survey area affected by fiber collisions and to the integral of the power spectrum over 2D modes perpendicular to the line of sight smoothed at the fiber collision scale. Using high resolution mock catalogs, we demonstrate that our analytic prescription accurately models the power spectrum residuals from the NN method to within sample variance of BOSS volumes at $k < 0.83\;h/\mathrm{Mpc}$ for both the monopole and quadrupole when the true power spectrum is known down to small scales from simulations, allowing to compute the fiber-collided predictions. Since typically we do not have fast reliable ways of computing the small scale power spectrum, we develop a practical approach when the power spectrum predictions are reliable up to some scale $k_\mathrm{trust}$. We split the contributions of the correlated fiber collisions effect into a piece that can be calculated reliably as it depends on large-scale modes, and an unreliable piece that depends on modes that are not under control. We show that the latter piece can be written as polynomials in $k$, and demonstrate that for scales up to $k \sim 0.3\;h/\mathrm{Mpc}$, the unreliable contribution can be accurately estimated by a quadratic polynomial in $k$. In principle, this method can be applied to larger $k_\mathrm{trust}$ than used here as a reasonable example ($k_\mathrm{trust} = 0.3\;h/\mathrm{Mpc}$). Therefore, using the effective window method we can model the fiber collided power spectrum as the systematics-free power spectrum plus three contributions due to fiber collisions: an uncorrelated piece (independent of the model power spectrum), a calculable piece (which involves integrating the model power spectrum over 2D long-wavelength modes perpendicular to the line of sight), and an unreliable contribution that is a quadratic polynomial, $C_{l,0} + C_{l,2}\, k^2$. While the precise values of $C_{l, n}$ cannot be robustly predicted in practice because of its dependence on small scale power, the coefficients can be treated as nuisance parameters in the analysis. Typically a constant shot noise term is already included as a nuisance parameter, while the constant contribution vanishes for higher multipoles, therefore only one extra parameter per multipole is required (the $k^2$ corrections). For cosmological parameter inference, the fiber collided model power spectrum can be compared directly to the observed fiber collided power spectrum. Then by marginalizing over these free coefficients, we marginalize over the effect of small-scale power induced fiber collisions on the power spectrum, which allows us to robustly infer the cosmological parameters of interest. The fiber collision correction methods we present will enable us to robustly account for the effects of fiber collisions in galaxy clustering analyses to the smallest scales allowed by theoretical predictions. They can also be extended to future surveys such as eBOSS or any other large fiber-fed surveys that suffer from systematic effects of fiber collisions. Our fiber collision correction method can also be extended to higher order clustering statistics such as bispectrum (Hahn et al., in prep.). We will use the methods presented in this paper to analyze the galaxy power spectrum and bispectrum multipoles in future work. \bigskip | 16 | 9 | 1609.01714 |
1609 | 1609.08635_arXiv.txt | The Pluto-Charon system has come into sharper focus following the fly by of \emph{New Horizons}. We use $N$-body simulations to probe the unique dynamical history of this binary dwarf planet system. We follow the evolution of the debris disc that might have formed during the Charon-forming giant impact. First, we note that in-situ formation of the four circumbinary moons is extremely difficult if Charon undergoes eccentric tidal evolution. We track collisions of disc debris with Charon, estimating that hundreds to hundreds of thousands of visible craters might arise from 0.3--5 km radius bodies. \emph{New Horizons} data suggesting a dearth of these small craters may place constraints on the disc properties. While tidal heating will erase some of the cratering history, both tidal and radiogenic heating may also make it possible to differentiate disc debris craters from Kuiper belt object craters. We also track the debris ejected from the Pluto-Charon system into the Solar System; while most of this debris is ultimately lost from the Solar System, a few tens of 10--30 km radius bodies could survive as a Pluto-Charon collisional family. Most are plutinos in the 3:2 resonance with Neptune, while a small number populate nearby resonances. We show that migration of the giant planets early in the Solar System's history would not destroy this collisional family. Finally, we suggest that identification of such a family would likely need to be based on composition as they show minimal clustering in relevant orbital parameters. | \emph{New Horizon's} arrival at Pluto has brought a new spotlight to the \sols's largest Kuiper belt dwarf planet and most well-known binary. Pluto and its largest moon, Charon, have a mass ratio of about 0.12 \citep{Brozovic2015}. Thus, the barycentre of the system lies between the two objects, and the regime of binary dynamics is most applicable. Four circumbinary moons, Styx, Nix, Kerberos, and Hydra, have also been identified. With the better characterisation of the \pc\ system stemming from the high-resolution view of \emph{New Horizons}, we can gain deeper insight into this system. This work aims to investigate two tracers of Pluto and Charon's formation: craters on the surface of Charon and debris that escaped into the Kuiper belt. \cite{McKinnon1989}, \cite{Canup2005,Canup2011}, and others have proposed and refined a giant impact origin for the \pc\ binary. \cite{Canup2011} studied a variety of collisions between Pluto and an impactor. The bodies can be either differentiated or non-differentiated; different incoming trajectories are simulated to understand the variations in the resultant system. A giant collision of this type will typically form a moon, a disc, or both. This study finds that a body one third to half the mass of the primordial Pluto will form Charon when it collides, although the newly formed moon tends to form with high eccentricity and a pericentre close to Pluto (within a few Pluto radii). If the impactor is differentiated, a disc is very likely and will have mass anywhere from 0.001\% of Pluto's mass to Charon's mass. A post-collision disc may extend out to about 30 Pluto radii. After the Charon forming impact, Charon is thought to migrate to its current position via tidal evolution. This tidal evolution can either be eccentric \citep{Cheng2014} or circular \citep{Dobrovolskis1989,Dobrovolskis1997,Peale1999} and should take at most a few million years. Charon concludes its migration tidally locked to Pluto with a 6.4 day period (semi-major axis of roughly 17 Pluto radii) and has eccentricity $\le 5\times10^{-5}$. \subsection{Pluto's Moons} Despite a compelling explanation for the formation of Charon, a theory for the emplacement of the four small circumbinary moons remains elusive. Many works, such as \cite{Ward2006}, \cite{Lithwick2008a,Lithwick2008}, \cite{Canup2011}, \cite{Cheng2014a}, \cite{Kenyon2014}, and \cite{Walsh2015}, have tried to explain the location of the small moons. Dynamical stability studies by \cite{Youdin2012} predicted low masses and high albedos for the moons, which were confirmed by \cite{Brozovic2015}, and \emph{New Horizons} \citep{Stern2015}. They find that the moons have masses of about $<1\times10^{-6}$, $3.1\times10^{-6}$, $1.1\times10^{-6}$, and $3.3\times10^{-6}$ relative to Pluto for Styx, Nix, Kerberos, and Hydra, respectively. These limits suggest that the circumbinary moons are icy, consistent with an origin in the disc from the Charon-forming impact. Nevertheless, many features of these moons remain difficult to explain when accounting for the tidal history of Charon. Specifically, the migration of Charon would easily destroy the extreme coplanarity ($<0.5$\deg), low eccentricity ($<0.006$), and the nearness to resonance (nearly 3:1, 4:1, 5:1, and 6:1 with Charon) \citep{Brozovic2015}. The dynamical properties of the moons listed above are most consistent with in-situ disc formation, yet the discs in the \cite{Canup2011} simulations simply do not have enough material at the moons' current locations to form them. Many proposed solutions have invoked resonant transport from the inner disc (where bodies form) to the outer disc, but these methods often pump the eccentricities and/or inclinations of the small moons well above the observed values. The corotation resonance from \cite{Ward2006} would not excite eccentricities, but this method requires different Charon eccentricities to transport each moon. Thus, \cite{Lithwick2008a} and \cite{Cheng2014a} suggest that this mechanism is unlikely. \cite{Cheng2014a} show a method to capture and transport disc material outward in a low (albeit non-zero) eccentricity orbit though capture into multiple Lindblad resonances while Charon is tidally evolving; however, they are unable to migrate material at the 3:1 and 4:1 commensurability with Charon (the locations of Styx and Nix). \cite{PiresdosSantos2012} suggests that the current moons could come from collisions of other bodies near Pluto in the Kuiper belt, but the collision time-scales for massive enough objects are too long. \cite{Walsh2015} suggest that the moons could form from disruption of an existing satellite in the system. This would provide a secondary disc, possibly at larger orbital radii, from which the moons can form, but still struggles to account for the wide range of circumbinary moon semi-major axes. \subsection{The Kuiper Belt and Collisional Families} The history of the \pc\ system is tied to the history of the Kuiper belt and Kuiper belt objects (KBOs). A plethora of works beginning from \cite{Malhotra1993,Malhotra1995} have explored the early history of the \sols\ and the sculpting of the Kuiper belt via giant planet migration. In these scenarios, Neptune and Pluto begin closer to the Sun than they are today. Neptune then migrates outward to its current orbit and Pluto is captured into the 3:2 resonance. During this process, Pluto's orbit gains both eccentricity and inclination. It is likely that the Charon-forming collision occurred early in the history of the \sols\ because the density of planetesimals was higher and thus collisional time-scales shorter. Additionally, works such as \cite{Levison2008} propose that there may be large numbers of larger objects (Pluto-sized) in the primordial Kuiper belt, which means that the cross section for giant impacts was larger. Therefore, Pluto and Charon have likely existed in their current state for most of the Kuiper belt's history and should record information about the surrounding population of KBOs through cratering. \cite{Greenstreet2015} simulates the expected crater size distribution on the surfaces of Pluto and Charon for both ``divot'' \citep[discontinuous double power law, e.g.][]{Shankman2016} and ``knee'' \citep[broken power law, e.g.][]{Bernstein2004,Fraser2014} Kuiper belt populations. The true size distribution is still uncertain due to small samples and the likely presence of multiple populations. Another interesting feature of massive KBOs is the presence of collisional families. Many KBOs, including the \pc\ system, show evidence of giant impacts that would produce a collisional family. The Haumea collisional family originally reported by \cite{Brown2007} is the only identified collisional family in the Kuiper belt. This family consists of roughly a dozen objects with similar compositions and orbits to the dwarf planet Haumea. In Haumea's case, the collisional family was easily identified because the members share a striking spectral feature and because the velocity dispersion of family members is about an order of magnitude lower than expected \citep{Schlichting2009}. The typical collisional family, however, should have velocity dispersions closer to the escape velocity from the parent system, which is closer to one \kms. \cite{Marcus2011} find that collisional families in the Kuiper belt are difficult to distinguish using the same method of low velocity dispersion used to find the Haumea family, but these families may be possible to pick out using other methods, such as clustering in inclination. They also estimate that there should be, at most, a handful of collisional families from massive collisions and a few tens of families from progenitors of 150 km in size. The Haumea collisional family is suggested to be old (from less than 1Gyr after \sols\ formation) and therefore may be primordial \citep{Ragozzine2007}. Thus, the majority of collisional families might stem from a time when the Kuiper belt was more dense, before dynamical stirring by Neptune. \cite{Leinhardt2010} note that collisional families in the Kuiper belt and the main asteroid belt have different characteristics due to Kuiper belt giant collisions tending to be slower and more massive. \medskip In this work, we investigate the evolution of a debris disc resulting from the Charon-forming collision. We look at collisions onto Charon's surface that might leave visible craters. This crater population may contaminate measurements of the KBO size distribution. We also look at the population of debris ejected into the \sols\ that might manifest as a Pluto collisional family in the Kuiper Belt. In Section~\ref{CBD}, we discuss the circumbinary dynamics in the \pc\ system. Section~\ref{method} presents our simulation methodology. Section~\ref{charon} presents results for collisions onto Charon's surface, while Section~\ref{sols} shows the properties of ejected particles. | \label{disc} This work aims to investigate the impact of a debris disc from the Charon-forming giant impact in both the \pc\ system and in the Kuiper belt. We present \nb\ simulations of the isolated \pc\ binary to follow the fates (collisions and ejections) of debris in the disc, and we also present simulations of the evolution of this debris in the \sols. We find the following: \begin{enumerate} \item The current circumbinary moons, Styx, Nix, Kerberos, and Hydra, did not form in situ if Charon has an eccentric tidal evolution history. The \cite{Holman1999} instability boundary crosses at least one of the moons' current positions if Charon has $e>0.048$ at its current semi-major axis; many realisations of the Charon-forming impacts from \cite{Canup2005,Canup2011} have the moon forming with eccentricity from 0.1--0.8. Thus, circumbinary moon formation mechanisms must either invoke a circular tidal evolution for Charon (or one that leaves Charon on a circular orbit long before it reaches its current semi-major axis) or involve forming the moons after Charon reached its current orbit (through capture, disruption of other bodies, or some other mechanism). \item The predominant loss mechanisms in a debris disc around \pc\ are collisions with Charon and ejections. The amount of clearing is a strong function of Charon's eccentricity. Collisions are most common from particles that begin close to Charon, while ejections begin to dominate in the outer disc. Including migration in the simulations causes ejections to increase dramatically because the binary instability boundary interacts with previously unperturbed disc material as the \pc\ orbit expands. \cite{Walsh2015} find that including collisional evolution in the disc may stabilise material on shorter time-scales, but interactions with the instability boundary will always cause particle loss. \item Collisions with Charon are most common for a wide orbit, eccentric Charon, such as may have existed near the end of the tidal evolution process. Collisions with Charon are the least common if migration is included. Ejections dominate exterior to Charon's orbit in the wide, eccentric case when Charon undergoes eccentric tidal evolution because the instability boundary is large. Ejections dominate the majority of the disc in the migration case because of the moving instability boundary. \item Assuming a reasonable, realistic (albeit optimistic) disc from \cite{Canup2011} and accounting for a surface solidification time-scale of a few hundred to a few thousand years, we predict hundreds to thousands of craters visible by \emph{New Horizons} on the surface of Charon that stem from the disc and not incident KBO collisions. It would be difficult to disentangle these populations from size alone as crater-to-impactor size ratios (collisional velocities) are similar. It is probable that the debris has a different size distribution than KBOs, in addition to a different average impact velocity, so the presence of two distinct crater populations on the surface of Charon might give insight into the disc. The apparent lack of small craters on Charon noted by \cite{Singer2016} already has implications on the extent or composition of a debris disc. \item Violent tidal heating during the early tidal evolution of Charon may prevent craters from forming on the surface. If the surface solidifies while tidal heating is still warming the interior, craters should form but may relax. Radiogenic heating later in the system's history (Gyrs after formation) may contribute to more surface relaxation and/or cryovolcanic resurfacing. While neither process should cause the oldest craters to disappear, old craters, such as those originating from the debris disc, may appear to be filled in or have indistinct crater walls. The physical appearance of old craters may help distinguish craters from the disc and craters from KBOs. \item About 80--90\% of material ejected into the \sols\ is lost within 1.5 Gyr, regardless of initial Pluto position or inclusion of migration. The material that remains tends to reside in the 3:2 resonance with Neptune, thereby maintaining a similar orbit to Pluto. Some material populates nearby resonances, especially the 5:4, 4:3, 5:3, and 7:4 resonances. The material that remains does not show any strong correlation at the end of the simulations with the initial position of Pluto or the other planets. The objects in resonances, especially in the 3:2, have resonant angles consistent with librating orbits. \item Using the same methodology that was used to calculate crater numbers and the most optimistic ejection profile, we estimate anywhere from 14--42 icy bodies greater than 10 km in radius could be produced through ejections from the \pc\ disc, forming a ``Pluto disc collisional family.'' Larger, more easily observable members of a Pluto collisional family may originate from the Charon-forming impact itself, such as is seen with the Haumea collisional family. Members of the collisional family should have similar icy composition to the original disc and a low velocity dispersion. We find no evidence that a collisional family will be disrupted by the migration of the giant planets in the early \sols, nor will it be disrupted through secular or resonant effects over Gyr time-scales. \end{enumerate} The formation of the \pc\ binary and its moons remains both a fascinating and frustrating problem, especially with the enhanced view of the system provided by the \emph{New Horizons} flyby in July 2015. Through potentially observable tracers such as craters from the debris disc on the surface of Charon or the presence of a Pluto collisional family, we might be able to better constrain the formation and early evolution of this intriguing system. | 16 | 9 | 1609.08635 |
1609 | 1609.01522_arXiv.txt | { We enhance the Syer \& Tremaine made-to-measure (M2M) particle method of stellar dynamical modelling to model simultaneously both kinematic data and absorption line strength data thus creating a `chemo-M2M' modelling scheme. We apply the enhanced method to four galaxies (NGC 1248, NGC 3838, NGC 4452, NGC 4551) observed using the SAURON integral-field spectrograph as part of the ATLAS$^{\rm{3D}}$ programme. We are able to reproduce successfully the 2D line strength data achieving mean $\chi^2$ per bin values of $\approx 1$ with $>95\%$ of particles having converged weights. Because M2M uses a 3D particle system, we are also able to examine the underlying 3D line strength distributions. The extent to which these distributions are plausible representations of real galaxies requires further consideration. Overall we consider the modelling exercise to be a promising first step in developing a `chemo-M2M' modelling system and in understanding some of the issues to be addressed. Whilst the made-to-measure techniques developed have been applied to absorption line strength data, they are in fact general and may be of value in modelling other aspects of galaxies. | \label{sec:introduction} The creation and evolution of galaxies is a significant research topic involving, for example, an understanding of galaxy mergers and in situ star formation. A galaxy's construction and evolution are imprinted in its kinematics and chemistry but require significant analysis to identify the contributing componentry. IFU-based galaxy surveys, providing spatially dense spectral data cubes from which complementary measurements of kinematics and spectral line strength can be obtained, offer major opportunities to investigate the underlying componentry and its assembly, provided appropriate techniques can be developed. Included are surveys such as ATLAS$^{\rm{3D}}$ \citep{AtlasI}, SAMI \citep{SAMI2015} and MaNGA \citep{Bundy2015}. The made-to-measure (M2M) method proposed by \citet{Syer1996} for modelling stellar dynamical systems has been used on a variety of research projects by a number of different research groups (for example, \citealt{DL2007}, \citealt{Morganti2012}, \citealt{Portail2015}; \citealt{Dehnen2009}; \citealt{Long2010, Long2012}, \citealt{Zhu2014}; \citealt{Hunt2013}; \citealt{Malvido2015}). With projects \begin{itemize} \item covering elliptical and lenticular galaxies, dwarf spheroidals, and the Milky Way, \item using IFU data, long slit data, velocity measurements of individual stars, globular clusters and planetary nebulae, \item employing self-gravitation of particles (with particle weights affecting the gravitational mass of particles) and potentials from N-body simulations, multi-Gaussian expansions as well as theoretical formulae, and \item utilising both inertial and rotating frames, \end{itemize} the M2M method has demonstrated itself to be very flexible and well able to handle a wide variety of applications. Whereas previous papers utilised the M2M method to model stellar kinematic data, the method is capable of being used to model other types of data. The current short investigation applies the M2M method to model simultaneously spectral absorption line strength data and kinematic data. We believe that this is the first time in which line strength data has been employed in M2M modelling. Our objectives in performing this investigation are four-fold, \begin{enumerate} \item to extend the M2M method to model absorption line strength data as well as kinematic data and to create a software implementation of the revised method, \item to apply the method to a selection of external galaxies and confirm that the usual criteria for a successful M2M run can be met (particle weight convergence and observable reproduction), \item to understand the limitations of the extensions and to identify areas for future work, and \item to promote further research by bringing the potential chemo-modelling capabilities of the M2M method to the attention of the astrophysical community. \end{enumerate} The structure of the paper broadly follows the objectives. In Sections \ref{sec:m2m} and \ref{sec:external}, we describe the M2M method together with our enhancements, and apply the enhanced method to four galaxies taken from the ATLAS$^{\rm{3D}}$ survey. In Sections \ref{sec:discuss} and \ref{sec:conclusions}, we discuss our results and draw conclusions identifying areas for further examination. | \label{sec:conclusions} We have met the objectives we set out in the Introduction, Section \ref{sec:introduction}. We have extended the M2M method into a chemo-dynamical method which is able to handle both kinematic and absorption line constraints simultaneously, and have applied the extended method to four ATLAS$^{\rm{3D}}$ galaxies. We see signs that the extended method may enable us to start understanding the 3D line strength distribution. However, as anticipated in the objectives, and as can be seen from the Discussion, Section \ref{sec:discuss}, much remains to be investigated to understand the limitations of the deprojected line strength maps, and to analyse the chemical footprint of orbits, before we are able to make robust predictions. Clearly, a second paper is needed after this `investigation of concept' paper, and it is now in preparation (Li et al.). Overall, we believe a promising first step has been taken in enhancing Syer \& Tremaine's made-to-measure method to perform chemo-dynamical modelling. | 16 | 9 | 1609.01522 |
1609 | 1609.08290_arXiv.txt | This work focuses on a sample of seven extremely late-time X-ray flares with peak time $t_{\rm p} > 10^4 {\rm s}$, among which two flares can be confirmed as the late-time activity of central engine. The main purpose is to investigate the mechanism of such late-time flares based on the internal origin assumption. In the hyper-accreting black hole (BH) scenario, we study the possibility of two well-known mechanisms as the central engine to power such X-ray flares, i.e., the neutrino-antineutrino annihilation and the Blandford-Znajek (BZ) process. Our results show that the annihilation luminosity is far below the observational data. Thus, the annihilation mechanism cannot account for such late-time flares. For the BZ process, if the role of outflows is taken into consideration, the inflow mass rate near the horizon will be quite low such that the magnetic field will probably be too weak to power the observed X-ray flares. We therefore argue that, for the late-time flares with internal origin, the central engine is unlikely to be associated with BHs. On the contrary, a fast rotating neutron star with strong bipolar magnetic fields may be responsible for such flares. | \label{sec:Introduction} In the past twenty years, great progress has been achieved on the understandings of gamma-ray bursts (GRBs). In particular, Swift has opened a new window to understand the nature of GRB phenomenon (e.g., \citet{Meszaros2006,Zhang2007,Liang2010}). The onboard X-Ray Telescope (XRT; \citealp{Burrows2005a}) opened an exciting era for GRB researches. It has established a large sample of X-ray light curves from tens of seconds to days, sometimes even months (e.g., GRB 060729; \citealp{Grupe2006}). It is interesting to find that X-ray flares are common in GRBs, which occur well after the initial prompt emission \citep{Romano2006,Falcone2007, Chincarini2007,Margutti2010,Margutti2011,Bernardini2011}. X-ray flares have been observed both in long and short GRBs \citep{Romano2006,Falcone2006,Campana2006,Margutti2011}. Based on the observations from Swift/XRT, four power-law light-curve segments together with a flaring component are identified in the X-ray afterglow phase \citep{Zhang2006,Nousek2006,OBrien2006}. The temporal analysis and spectral property suggest that the X-ray flare is from a distinct emission mechanism, since the temporal behavior of flares is quite similar to the prompt emission pulses, whereas different from the other four components in the canonical light-curves. Thus, X-ray flares may have a common physical origin as the prompt pulses \citep{Burrows2005b,Falcone2006,Falcone2007, Liang2006,Nousek2006,Zhang2006,Chincarini2007,Chincarini2010, Wu2013,Hou2014a,Yi2015}, and are probably related to the late time activity of the central engine \citep{Romano2006,Bernardini2011}. The central engine of GRBs remains an open question \citep{Zhang2011}. A hyper-accreting stellar-mass black hole (BH) or a millisecond magnetar \citep{Usov1992,Dai1998,Zhang2001,Metzger2011} is usually invoked as possible GRB central engine. In the BH hyper-accretion scenario, the photons generated in the accretion flow can hardly escape due to the extremely large optical depth. On the contrary, a large amount of neutrinos can escape from the flow and therefore the neutrino cooling may be the most important mechanism to balance the viscous heating. Such a flow is named as the neutrino-dominated accretion flow (NDAF). The structure and radiation of an NDAF has been extensively studied (e.g., \citet{Popham1999,Di2002,Gu2006,Kawanaka2007, Liu2007,Liu2013,Liu2014,Lei2009,Zalamea2011,Pan2012,Janiuk2013,Xue2013,Cao2014}. In the hyper-accretion scenario, the relativistic jet may be powered by the following two mechanisms. The first one is related to the annihilation of neutrino-antineutrino pairs. Such an annihilation process was previously investigated by several works (e.g., \citet{Popham1999,Di2002,Gu2006,Birkl2007,Liu2007,Xue2013,Liu2016}. The second one is related to the Blandford-Znajek (BZ) process \citep{Blandford1977}, which can effectively extract the rotational energy of the central BH through large-scale magnetic fields. The physical origin of X-ray flares remains mysterious, including internal dissipation and external shock mechanisms. \citet{Falcone2007} showed that many X-ray flares are from late-time activity of the internal engine that spawned the initial GRB, not from an afterglow-related effect. Moreover, \citet{Chincarini2010} and \citet{Margutti2010} made analyses of the flare temporal and spectral properties of a large sample of early-time flares and of a subsample of bright flares, which revealed close similarities between them and the prompt emission pulses, and therefore pointing to an internal origin. \citet{Margutti2011} investigated the relation between flares and continuum emission, and suggested the variability to be established as a consequence of different kinds of instabilities. On the other hand, from the theoretical view, \citet{Ioka2005} proposed a criterion to separate the internal and external origin of flares. \citet{Curran2008} concluded that the late-time flares ($t_{\rm p}\ga 10^{4}{\rm s}$) are not different from the early-time ones, where the majority of the flares can be explained by either internal or external shock. However, due to the small number of flares (a sample of 7 GRBs), the conclusion may require further investigation. Moreover, \citet{Bernardini2011} focused on the late-time flares ($t_{\rm p} \ga 10^{3}$~{\rm s}) of a larger sample than \citet{Curran2008} and found that a large fraction of late-time flares are also compatible with afterglow variability. In addition, \citet{Lazzati2007} showed internal dissipation and external shock mechanisms of X-ray flares, and concluded that at least a sizable fraction of the flares cannot be related to the external shock mechanism, since external shock flares evolve on much longer timescales than observed. Then, some late-time flares in our sample may be related to late-time central engine activity rather than a slower outflow produced simultaneously with the prompt emission. Moreover, the steep decay of X-ray flares is more likely to originate from the internal dissipation (e.g., \citep{Kumar2000}). In the present work, we will adopt two criteria to examine the internal or external origin of the flares in our sample, and then study the possible mechanisms for those flares probably related to internal origin. Several mechanisms and models were proposed to explain the episodic phenomenon of X-ray flares \citealp{King2005,Dai2006,Meszaros2006,Perna2006,Lazzati2008,Lee2009, Lazzati2011,Yuan2012,Luo2013,Hou2014b}. According to the internal origin of X-ray flares, the central engine that powers the prompt gamma-ray emission also powers the X-ray flares. Thus, the long-duration flares require the long-lasting activity of the central engine. For the neutrino annihilation mechanism, as pointed out by \citet{Luo2013}, although such a mechanism may work well for the central engine of the gamma-ray emission, it may encounter difficulty in interpreting the X-ray flares. By considering a possible magnetic coupling between the inner disk and the central BH, \citet{Luo2013} showed that the annihilation mechanism can also work for the X-ray flares with duration $\tau \la 100{\rm s}$. However, the annihilation mechanism is unlikely to be responsible for those long flares with duration $\ga 1000{\rm s}$, even the role of magnetic coupling is included. On the other hand, according to the analyses of \citet{Luo2013}, the BZ mechanism may work well even for the long duration flares. However, outflows were not taken into consideration in \citet{Luo2013}, which can be of importance particularly for relatively low accretion rates where the neutrino cooling is inefficient. There is a positive correlation for the X-ray flares between the duration $\Delta t$ and the peak time $t_{\rm p}$ (e.g., \citealp{Margutti2010,Yi2016} ). In the present work, we will focus on the extremely late-time X-ray flares with $t_{\rm p} > 10^4$~s and study the corresponding central engines. The remainder of this paper is organized as follows. Our sample and data analyses are presented in \S~2. The different mechanisms for the central engine are investigated in \S~3. Conclusions and discussion are made in \S~4. | The present work focuses on the central engine of extremely late-time X-ray flares ($t_{\rm p} > 10^4 {\rm s}$) with the internal origin assumption. We have investigated the possibility of the two well-known mechanisms related to BHs for the central engine, i.e., the neutrino-antineutrino annihilation and the BZ process. Our results show that the annihilation luminosity is far below the observational data, which indicates that the annihilation mechanism cannot account for the extremely late-time X-ray flares. On the other hand, for the BZ process, if the role of outflows is taken into consideration, the inflow mass rate near the horizon will be quite low such that the magnetic field will probably be too weak to power the observed X-ray flares. We therefore argue that, for such late-time X-ray flares, the central engine is unlikely to be associated with BHs. On the contrary, a fast rotating NS with strong bipolar magnetic fields may be responsible for such flares. We would stress that this work only considered bright flares. Some dim flares at late-time may be missed since the underlying continuum is too bright for their detection. These dim flares may occupy the lower part of Figures~\ref{F:BZ luminosity} and \ref{F:NS energy}, which are possibly consistent with the BZ mechanism and the magnetic origin in the magnetar context \citep{Margutti2011}. In this work, the existence of outflows is a key point to draw the conclusion that the BZ mechanism is unlikely to power the extremely late-time X-ray flares. In recent years, outflows have been found to be significant in accretion systems of different scales by theories \citep[e.g.,][]{Jiao2011,Gu2015}, simulations \citep[e.g.,][]{Ohsuga2005,Ohsuga2011,Yuan2012a,Yuan2012b,Jiang2014, Sadow2015,Sadow2016}, and observations \citep[e.g.,][]{Wang2013}. Based on the balance of heating and cooling, \citet{Gu2015} shows that the outflow is inevitable for the accretion flows that the radiative cooling is far below the viscous heating, no matter the flow is optically thin or thick. In the current work for accretion rates $\dot M \la 10^{-4} M_{\sun} {\rm s}^{-1}$, neither the photon radiative cooling nor the neutrino one is efficient to balance the viscous heating. Thus, the outflows ought to be significant. Actually, \citet{Liu2008} studied this issue and proposed that there exists a lower critical $\dot M$ varying with radius, below which outflows have to occur. From the observational view, taking our Galactic center as an example, \citet{Wang2013} reveals that more than 99\% of the accreted mass escape from the accretion flow by outflows. Therefore, it is reasonable to assume less than 1\% of the supplied mass can enter the BH in the present work. The present work focuses on the late-time X-ray flares with $t_{\rm p} > 10^4 {\rm s}$. On the other hand, a previous work \citep{Luo2013} focused on the X-ray flares with rest duration $\Delta t\la 100{\rm s}$, and found that the neutrino annihilation mechanism cannot account for the flares except for including the magnetic coupling between the inner disk and the BH. However, such a coupling and corresponding distribution of magnetic fields have not been found in simulations yet. Thus, we would argue that, in general, the annihilation mechanism may not work as the central engine for X-ray flares. For the BZ mechanism, the output power is larger than that of the annihilation mechanism, particularly for relatively low accretion rates. From the energy argument, the BZ mechanism may be responsible for X-ray flares with duration $\Delta t_{\rm res} \la 10^4~{\rm s}$ in the case that outflows are not significant. | 16 | 9 | 1609.08290 |
1609 | 1609.09069_arXiv.txt | {Heavy neutrinos with masses below the electroweak scale can simultaneously generate the light neutrino masses via the seesaw mechanism and the baryon asymmetry of the universe via leptogenesis. The requirement to explain these phenomena imposes constraints on the mass spectrum of the heavy neutrinos, their flavour mixing pattern and their $CP$ properties. We first combine bounds from different experiments in the past to map the viable parameter regions in which the minimal low scale seesaw model can explain the observed neutrino oscillations, while being consistent with the negative results of past searches for physics beyond the Standard Model. We then study which additional predictions for the properties of the heavy neutrinos can be made based on the requirement to explain the observed baryon asymmetry of the universe. Finally, we comment on the perspectives to find traces of heavy neutrinos in future experimental searches at the LHC, NA62, BELLE II, T2K, SHiP or a future high energy collider, such as ILC, CEPC or FCC-ee. If any heavy neutral leptons are discovered in the future, our results can be used to assess whether these particles are indeed the common origin of the light neutrino masses and the baryon asymmetry of the universe. If the magnitude of their couplings to all Standard Model flavours can be measured individually, and if the Dirac phase in the lepton mixing matrix is determined in neutrino oscillation experiments, then all model parameters can in principle be determined from this data. This makes the low scale seesaw a fully testable model of neutrino masses and baryogenesis.} | \label{sec:introduction} All fermions in the Standard Model (SM) of particle physics are known to exist with both left handed (LH) and right handed (RH) chirality, with the exception of neutrinos. RH neutrinos could, if they exist, generate the light neutrino masses $m_a$ via the type I seesaw mechanism \cite{Minkowski:1977sc,GellMann:1980vs,Mohapatra:1979ia,Yanagida:1980xy,Schechter:1980gr,Schechter:1981cv}. Traditionally it is assumed that the Majorana masses $M_i$ of the RH neutrinos are much larger than the masses of any known particles. However, a \emph{low scale seesaw} with Majorana masses below the electroweak scale is in perfect agreement with all known experimental and cosmological constraints \cite{Atre:2009rg,Ibarra:2011xn,Asaka:2013jfa,Abada:2013aba,Drewes:2013gca,Abada:2014vea,Hernandez:2014fha,Antusch:2014woa,Gorbunov:2014ypa,Drewes:2015iva,deGouvea:2015euy,Abada:2015oba,Fernandez-Martinez:2016lgt,Abada:2016awd,Blennow:2016jkn,Ge:2016xya}. A strong theoretical motivation for this choice is provided by the observed values of the Higgs boson and top quark masses, which lie in the region in which the SM could be a viable effective field theory valid up to the Planck scale. While the existence superheavy RH neutrinos would destabilise the Higgs mass \cite{Vissani:1997ys}, this problem is alleviated if the RH neutrinos have masses below the electroweak scale \cite{Bezrukov:2012sa}. Hence, in absence of any other New Physics, a low seesaw scale $M_i$ is required to preserve the technical naturalness of the SM with RH neutrinos. This scenario is technically natural if the difference between baryon number $B$ and lepton number $L$, which is conserved in the SM due to an accidental symmetry, is an approximately conserved quantity in Nature. % This allows to explain the smallness of the light neutrino masses even for comparably large values of the neutrino Yukawa couplings $Y$ (slightly smaller than the electron Yukawa coupling for $M_i$ below the electroweak scale). The probably most studied model that invokes the low scale seesaw is the \emph{Neutrino Minimal Standard Model} ($\nu$MSM) \cite{Asaka:2005pn,Asaka:2005an}, a minimal extension of the SM by three RH neutrinos that aims to address several problems in particle physics and cosmology.\footnote{Detailed descriptions of the $\nu$MSM are e.g. given in refs.~\cite{Boyarsky:2009ix,Canetti:2012kh}.} Other frameworks that can accommodate a low scale seesaw include the possibility that the scale(s) $M_i$ and the electroweak scale have a common origin \cite{Iso:2009ss,Iso:2012jn,Khoze:2013oga,Khoze:2016zfi}, minimal flavour violation \cite{Cirigliano:2005ck,Gavela:2009cd} and left-right-symmetric models \cite{Pati:1974yy,Mohapatra:1974hk,Senjanovic:1975rk,Wyler:1982dd} in which the complete breaking of GUT symmetry happens near the TeV scale, and the possibility that $B-L$ is a spontaneously broken symmetry \cite{Chikashige:1980ui,Gelmini:1980re,GonzalezGarcia:1988rw} and/or is approximately conserved \cite{Branco:1988ex,Gluza:2002vs,Shaposhnikov:2006nn,Kersten:2007vk,Gavela:2009cd,Racker:2012vw}. Two of the most popular classes of scenarios are often referred to as ``inverse seesaw models'' \cite{Mohapatra:1986bd,Mohapatra:1986aw,GonzalezGarcia:1988rw} and ``linear seesaw models'' \cite{Akhmedov:1995vm,Akhmedov:1995ip,Barr:2003nn,Malinsky:2005bi} (see also \cite{Bernabeu:1987gr,Pilaftsis:1991ug,Abada:2007ux,Sierra:2012yy,Fong:2013gaa}). In addition to the generation of light neutrino masses via the seesaw mechanism, RH neutrinos with masses below the electroweak scale could also generate the baryon asymmetry of the universe (BAU) via low scale leptogenesis.\footnote{A short review of the observational evidence for a matter-antimatter asymmetry in the observable universe and its theoretical implications is given in ref.~\cite{Canetti:2012zc}.} In contrast to thermal leptogenesis in scenarios with superheavy RH neutrinos \cite{Fukugita:1986hr}, the BAU in these scenarios is not generated in the decay of the heavy neutrinos, but via $CP$ violating oscillations during their production \cite{Akhmedov:1998qx,Asaka:2005pn}. The minimal number $n_s$ of RH neutrinos that is required to explain the two observed light neutrino mass differences is $n_s=2$. This is the scenario on which we focus in the following. The same choice also effectively describes baryogenesis in the $\nu$MSM, where it was first shown that leptogenesis from neutrino oscillations is feasible for $n_s=2$ \cite{Asaka:2005pn}. Two of the three RH neutrinos in the $\nu$MSM generate the light neutrino masses and the BAU, while the third one is a Dark Matter (DM) candidate. The constraints on the mass and lifetime of the DM candidate imply that its mixing with ordinary neutrinos must be extremely tiny, see \cite{Adhikari:2016bei} and references therein, so that its effect on the magnitude of the light neutrino masses and the BAU is negligible. Hence, one can effectively describe the seesaw mechanism and baryogenesis in the $\nu$MSM by setting $n_s=2$. An attractive feature of the $\nu$MSM is that it could in principle be an effective field theory up to the Planck scale \cite{Shaposhnikov:2007nj}, i.e. , all known phenomena in particle physics and cosmology may be explained without adding any new particles other than the RH neutrinos to the SM. From an experimental viewpoint this scenario is very attractive because the new particles (or traces of them) could be found in the laboratory \cite{Shrock:1980ct,Shrock:1981wq,Langacker:1988ur}, and there is a realistic possibility of solving two of the most important puzzles in particle physics and cosmology. The goal of this work is to derive constraints on the properties of the RH neutrinos from the requirement to simultaneously explain the light neutrino flavour oscillations and the BAU. If any heavy neutral leptons are discovered in future experiments, then it will be possible to use these constraints in order to assess whether these particles can indeed be the common origin of light neutrino masses and the baryonic matter in the universe. In the present analysis, we focus on the heavy neutrino mass range $100 \,\MeV < M_i < 40\,\GeV$. In the context of the seesaw mechanism, masses below $100 \,\MeV$ are disfavoured by cosmological constraints \cite{Hernandez:2014fha}. For masses larger than $40 \,\GeV$ our treatment of leptogenesis in the early universe requires some refinements because the underlying assumption that the heavy neutrinos are fully relativistic while the BAU is generated is not justified. This paper is organised as follows: In section~\ref{Sec:Osc} we introduce the seesaw mechanism, define the active-sterile mixing and discuss the allowed parameter region that can be explained by neutrino oscillation data. Further constraints emerge by simultaneously imposing that the heavy neutrinos generate the experimentally observed BAU. The discussion of these constraints and corresponding plots are presented in section~\ref{Sec:Lepto}. Future improvements of flavour predictions are listed in section~\ref{Sec:Future}, and appendix~\ref{App:Mixing} summarises analytic expressions for the heavy neutrino mixing angles. | The extension of the SM by two RH neutrinos with masses below the electroweak scale can simultaneously explain the observed neutrino masses via the seesaw mechanism and the BAU via low scale leptogenesis. An attractive feature of this scenario is the possibility to discover heavy neutrinos $N_i$ in direct search experiments, such as SHiP, NA62, similar facilities at LBNF or T2K, LHCb, BELLE II, ATLAS, CMS or a future lepton collider. In addition to the light neutrino masses $m_a$ and the angles and phases in the mixing matrix $U_\nu$, this model adds only four new parameters to the SM. These can be chosen as the masses $M_1$ and $M_2$ of the heavy neutrinos and the real and imaginary part of a complex angle $\omega$. $\omega$ determines both, the misalignment between the heavy neutrino mass and interaction basis as well as the overall strength $U^2=\sum_{a=e,\mu,\tau} U_a^2$ of the mixing of the heavy neutrinos with the SM neutrinos. Here $U_a^2=\sum_i U_{ai}^2$ is the sum of the mixings of both heavy neutrino states $N_i$ with the SM flavour $a$. An experimental discovery is most likely in the regime where $U^2$ is large. Large $U^2$ can be made consistent with small $m_a$ if the heavy neutrino masses are quasi-degenerate. In addition, leptogenesis with two heavy neutrinos also requires a mass degeneracy. From a model building viewpoint, the region with large $U^2$ and small $\Delta M$ can be motivated by a approximate $U(1)_{B-L}$ symmetry. Because of this, it is convenient to use the average mass $\bar{M}$ and mass splitting $\Delta M$ of the two heavy neutrinos instead of their individual masses $M_1$ and $M_2$. In most of the parameter region where the observed BAU can be reproduced by two heavy neutrinos, their masses are required to be too degenerate to be resolved experimentally. This does not only make a direct determination of $\Delta M$ impossible, but also implies that the mixings $U_{a1}^2$ and $U_{a2}^2$ of the two heavy neutrinos with the different SM generations cannot be measured individually. Instead, experiments can only constrain their sum $U_a^2$. Moreover, values of $U^2$ that lie within reach of existing experiments require comparably large values of ${\rm Im}\omega$. In the parameter region with $\Delta M/\bar{M}\ll 1$ and ${\rm Im}\omega>1$, the sensitivity of $U^2$ to ${\rm Re}\omega$ is practically lost. The two parameters $\Delta M$ and ${\rm Re}\omega$, which are crucial for leptogenesis, cannot be determined by neutrino oscillation data and direct searches for the $N_i$ alone. Hence, leptogenesis in this scenario is not fully testable even if the $N_i$ are discovered and the Dirac phase $\delta$ in $U_\nu$ is measured (testable in the sense that all observables, including the BAU, can be calculated uniquely from measured quantities). However, our analysis shows that the parameter space of the model can be severely constrained, and testable predictions can be made based on the requirement to explain light neutrino oscillation data and the observed BAU. \begin{itemize} \item In the limit $\Delta M/\bar{M}\ll 1$ and ${\rm Im}\omega\gg 1$, the flavour mixing pattern $U_a^2/U^2$ of the heavy neutrinos is determined by light neutrino parameters alone. With the exception of one Majorana phase, all of these may be measured in foreseeable time. The precise relations are given in appendix \ref{App:Mixing}. This point has recently also been made in ref.~\cite{Hernandez:2016kel}. \item By combining the negative results of various direct and indirect search experiments with lifetime constraints from the requirement not to disturb BBN, one can impose considerably stronger bounds on the $U_a^2$ than by simply superimposing them. We present the results of the first global analysis of this kind in figures~\ref{Fig:Flavor_Plots_NH} and \ref{Fig:Flavor_Plots_IH}. \begin{itemize} \item The combined constraints rule out most of the parameter region below $\bar{M}\simeq350$ MeV. Moreover, they impose a much stronger lower bound on $U_\mu^2$ and $U_\tau^2$ than BBN and the seesaw relation alone for $\bar{M}<m_K$. However, before completely disregarding the mass region $\bar{M}<350$ MeV, a careful re-analysis of the lower bounds on $U_a^2$ from BBN should be performed in the regime $\bar{M}>m_\pi$.\footnote{For masses $\bar{M}<m_\pi$ a revised calculation has recently been presented in ref.~\cite{Ruchayskiy:2012si}, where the authors also perform a comparison to earlier results in the literature.} In this work, we used the simple estimate that the heavy neutrino lifetime should be shorter than $0.1$s, which may be too simplified. Moreover, there exist different interpretations of the results of the PS191 experiment in the literature \cite{Bernardi:1987ek,Ruchayskiy:2011aa,Artamonov:2014urb}, and the combined constraints strongly depend on these differences. In our analysis we have chosen to use the results of ref.~\cite{Ruchayskiy:2011aa}. Finally, we have fixed the known neutrino masses and mixing angles to their best fit values in figures~\ref{Fig:Flavor_Plots_NH} and \ref{Fig:Flavor_Plots_IH}. The error bars on these quantities should slightly relax the exclusion bounds presented there. \item In the regime $m_K<\bar{M}<m_D$ the combined constraints impose a much stronger upper bound on $U_\tau^2$ than those from direct searches alone. For normal hierarchy, they impose a stronger upper bound on $U_e^2$. \item Any improvement in the measurement of light neutrino properties will tighten the combined constraints. In particular, a measurement of the Dirac phase $\delta$ and the light neutrino mass hierarchy would be highly desirable. \end{itemize} It should be pointed out that the combined constraints are specific to the minimal scenario with two mass degenerate heavy neutrinos or models that can effectively be described in this way (e.g.\ the $\nu$MSM). They are considerably weaker if more heavy neutrinos exist in the mass range we consider or the masses are not degenerate \cite{Drewes:2015iva}. \item As shown in section~\ref{Sec:Future}, future experiments can either discover the $N_i$ or impose much stronger constraints on their properties. For $\bar{M}$ below $1-2$ GeV, a measurement of neutrinoless double $\beta$ decay can provide information about ${\rm Re}\omega$. Moreover, various processes that are sensitive to the oscillations of heavy neutrinos in the laboratory and the degree of lepton number violation they mediate can be used to extract information about $\Delta M$. However, as pointed out in section~\ref{Higgs}, a quantitative analysis requires careful inclusion of $\mathcal{O}[U^2]$ corrections to the heavy neutrino mass spectrum at tree level as well as loop corrections. \item In figures~\ref{Fig:Flavor_Plots_tot}, \ref{Fig:Flavor_Plots_e}, \ref{Fig:Flavor_Plots_mu} and \ref{Fig:Flavor_Plots_tau} we present estimates for the range of allowed values for the mixings $U_a^2$ of heavy neutrinos with individual SM flavours that are consistent with successful leptogenesis, and compare these to the expected sensitivity of planned experiments. These results may be used to estimate the discovery potential of experiments that are only sensitive to one or two SM flavours, or which have very different sensitivities to the individual flavours. \item Our results shown ~\ref{Fig:Flavor_Plots_tot}, \ref{Fig:Flavor_Plots_e}, \ref{Fig:Flavor_Plots_mu} and \ref{Fig:Flavor_Plots_tau} may be compared to those found in ref.~\cite{Hernandez:2016kel}, which appear much more pessimistic. The reason for the apparent discrepancy may lie in the fact that the authors of that study performed a Bayesian analysis to estimate the likelihood that heavy neutrinos with given parameters are responsible for the BAU. While such analysis in principle allows to different information about the parameter space, this additional information in the present case clearly depends on the choice of the choice of parametrisation and priors. In contrast, our analysis aims at identifying the largest and smallest $U_a^2$ that are consistent with neutrino oscillation data and successful leptogenesis, without imposing any theoretical prejudice about the model parameters. In this sense, the two analyses should be viewed as complementary. \item As discussed in section~\ref{Sec:Testability}, the model is fully testable if the experimental resolution is sufficient to determine $\Delta M$. Independent measurement of all $U_{ai}^2$ would, in combination with a determination of the Dirac phase $\delta$ in the light neutrino mixing matrix $U_\nu$, in principle allow to determine all model parameters and fully reconstruct the Lagrangian (\ref{eq:Lagrangian}). This would allow to predict the BAU and the outcome of other future experiments, such as searches for neutrinoless double $\beta$ decay. In practice, the finite experimental sensitivity would of course imply that the error bars on some quantities (in particular ${\rm Re}\omega$) will be sizeable in foreseeable time. \item Even in the case $\Delta M/\bar{M}\ll 1$ and ${\rm Im}\omega\gg 1$, in which the values of $\Delta M$ and ${\rm Re}\omega$ cannot be extracted from measurements of the $U_{a i}^2$, a measurement of the individual $U_a^2$ still provides a powerful test of the minimal low scale leptogenesis scenario. As shown in section~\ref{Sec:Lepto}, the requirement to explain the observed BAU allows to make predictions for the flavour mixing pattern $U_a^2/U^2$ for given $\bar{M}$ and $U^2$, cf. figures \ref{Fig:Lepto_NH} and \ref{Fig:Lepto_IH}. Finding heavy neutral leptons with flavour mixing patterns within these regions will provide circumstantial evidence for leptogenesis. \end{itemize} The low scale seesaw and leptogenesis provide a simple explanation for at least two of the most studied questions in fundamental physics, the origin of neutrino masses and the origin of the baryonic matter in the universe. A significant fraction of the parameter space can be tested in existing or proposed experiments, and in a part of this region, the model is fully testable. The global constrains and estimates of the cosmologically relevant parameter space presented here are state of the art, but still suffer from order one uncertainties. In the wake of upcoming experiments, further theoretical work will be necessary to reduce these to a level that would be required for a comparison with experimental data if any heavy neutral leptons are discovered. \subsection*{Acknowledgements} We would like to thank Elena Graverini, Nicola Serra, Walter Bonivento, Gaia Lanfranchi, Oliver Fischer and Jilberto Antonio Zamora Saa for helpful discussions about experimental aspects. We would also like to thank Dmitry Gorbunov and Stefan Antusch for pointing out errors in the experimental sensitivities shown in the first version of this manuscript and Mikhail Shaposhnikov for general comments. This research was supported by the DFG cluster of excellence 'Origin and Structure of the Universe' (www.universe-cluster.de). \appendix | 16 | 9 | 1609.09069 |
1609 | 1609.09858_arXiv.txt | The bulk of the rare earth elements are believed to be synthesized in the rapid neutron capture process or $r$ process of nucleosynthesis. The solar $r$-process residuals show a small peak in the rare earths around $A\sim 160$, which is proposed to be formed dynamically during the end phase of the $r$ process by a pileup of material. This abundance feature is of particular importance as it is sensitive to both the nuclear physics inputs and the astrophysical conditions of the main $r$ process. We explore the formation of the rare earth peak from the perspective of an inverse problem, using Monte Carlo studies of nuclear masses to investigate the unknown nuclear properties required to best match rare earth abundance sector of the solar isotopic residuals. When nuclear masses are changed, we recalculate the relevant $\beta$-decay properties and neutron capture rates in the rare earth region. The feedback provided by this observational constraint allows for the reverse engineering of nuclear properties far from stability where no experimental information exists. We investigate a range of astrophysical conditions with this method and show how these lead to different predictions in the nuclear properties influential to the formation of the rare earth peak. We conclude that targeted experimental campaigns in this region will help to resolve the type of conditions responsible for the production of the rare earth nuclei, and will provide new insights into the longstanding problem of the astrophysical site(s) of the $r$ process. | \label{sec:intro} One of the most intriguing open problems in nuclear astrophysics is the astrophysical site or sites of the production of the heaviest elements in the rapid neutron capture process, or $r$ process, of nucleosynthesis \cite{NRC03, NRC13}. The final elemental and isotopic abundances of the nuclei produced in the $r$ process can be seen in stars and found in meteorites \cite{Marti+85}. From these observations one tries to determine the astrophysical conditions under which the $r$ process occurs. Complicating this endeavor is a dearth of measurements of the properties of nuclei that participate in the $r$ process. The study of the $r$ process is therefore inherently an inverse problem - the output is known and the input must be determined. The output, the observed isotopic and elemental abundance patterns, e.g. \cite{Arlandini+99}, show a number of interesting features. There exists evidence of both a `weak' component to the $r$ process \cite{Qian+01, Travaglio+04, Aoki+05, Montes+07}, which produces material up until the region of atomic mass number $A\sim120$, and a `main' component which produces the rest of the heavier elements, $A\gtrsim120$ \cite{Wasserburg+96, Qian+07, Shibagaki+16}. A distinguishing factor between these two components is the scatter found in the elemental patterns of the weak component \cite{Sneden+08}, suggesting either variable conditions within a single type of astrophysical event or contributions from multiple sites. Here we focus on the main component, which is characterized by the robustly-produced heavier $r$-process peaks found at $A\sim160$ and $A\sim195$, and likely also $A\sim130$ \cite{Roederer+12, Roederer+14}. One component of the input, the astrophysical conditions, must be such that there is a high neutron flux \cite{Burbidge+57, Cameron+57}. However, the precise amount of neutron-richness has not been established and neither has the degree of heating, or the range of outflow timescale, temperature or density. This has lead to a number of suggestions for the main $r$ process site, which include the traditional core collapse supernova and the merging of compact objects; see \cite{Arnould+07, Thielemann+11, Mumpower+16r} and references therein. Proposed $r$ process sites show marked differences in the evolution of the last stage of the $r$ process when nuclei slow their capture of neutrons and begin to decay back to stability, a phase known as `freeze-out'. Though many variations are possible, conditions during the final of the $r$ process can be generally classified as `hot' or `cold'. A hot $r$ process evolution goes through an extended equilibrium between neutron captures and its inverse reaction photodissociation, often written, \nggn. The freeze-out from equilibrium and the decay back to stability are triggered by an exhaustion of free neutrons. A cold $r$ process \cite{Wanajo+07} evolution has a short or non-existent \nggn \ phase where equilibrium fails due to the drop in temperature, followed by competition between neutron captures and $\beta$-decays. The other component of the input for the $r$ process is the yet to be measured nuclear properties of unstable neutron-rich nuclei. Theoretical nuclear models used in $r$-process calculations are well constrained and are mostly in agreement where data exists, however, the model predictions diverge as one approaches the driplines \cite{Kortelainen+12,Erler+13,Mumpower+15a}. Where there is disagreement between models, there is no experimental data and the majority of nuclei that have substantial impact on the final $r$-process abundances are in this category, see Refs.~\cite{Mumpower+15b, Liddick+16, Martin+16} for recent examples. The most important nuclear physics inputs for the $r$ process are masses, $\beta$-decays and neutron capture rates near closed neutron shells and in the rare earth region \cite{Mumpower+16r}. To solve an inverse problem, it is helpful to have the output as well determined as possible. The solar isotopic $r$-process abundances are defined by a residual procedure from the well constrained $s$-process abundances \cite{Kappeler+11}. In particular, the abundances of the rare earth elements, the peak at $A\sim160$, are some of the most precisely known in the solar system and in very metal-poor stars \cite{Lodders+09}. Further, the $r$-process rare earths are expected to be produced only in the main $r$ process, i.e. they don't have a weak component \cite{Sneden+08}. Therefore, the rare earth elements and the associated peak is an ideal choice for exploration of an $r$ process inversion technique \cite{Mumpower+16a}. Two distinct mechanisms have been previously proposed to explain rare earth peak formation. The first mechanism is dynamic formation of the peak during freeze-out \cite{Surman+97, Mumpower+12a}. In this scenario, material becomes hung up in the rare earth region during the decay back to stability. This mechanism requires a nuclear physics feature in this region responsible for the hangup and is sensitive to the late-time evolution of astrophysical conditions. The second mechanism is the formation of the peak by the deposition of fission fragments \cite{Schramm+71}. This possibility requires both multiple fission cycles from higher to lower atomic mass number and precisely tuned fission fragment distributions \cite{Goriely+13}. While a less aesthetically pleasing solution, it is also possible that the rare earth peak is formed by a combination of the two mechanisms. Experimental campaigns to produce the appropriate neutron-rich heavy isotopes and study their fission fragments are not possible now or in the foreseeable future. However, measurements of nuclei that are populated during the decay back to stability are possible in some cases currently and for others in near future. Ergo, the most sensible path forward is to try to confirm or eliminate the purely dynamical mechanism. In this manuscript, we take the observed rare earth abundance pattern and, for different types of astrophysical conditions, invert this abundance pattern to determine nuclear properties. We use common Bayesian inference techniques to find the region of the $NZ$-plane which dictates the shape and location of rare earth abundance pattern. The feedback provided by the observed rare earth abundances allows us to \textit{reverse engineer} the required trends in the nuclear masses that are responsible for the production of the rare earth peak. The larger strategy is to compare predictions of this type with future measurements, moving us closer toward an understanding of the astrophysical site of the main $r$ process. In section \ref{sec:method} we introduce this methodology and discuss all of the assumptions that go into our calculations. The propagation of nuclear model input changes is also covered in detail. In section \ref{sec:results} we give the results of these calculations and report the most favorable mass surface trends for each type of astrophysical conditions. In section \ref{sec:summary} we summarize. | \label{sec:summary} While there are large uncertainties in the inputs to $r$-process nucleosynthesis, the output---the pattern of solar $r$-process residuals---is relatively well known. This opens up the $r$ process to treatment as an inverse problem. Here we have developed a Monte Carlo framework to reverse engineer unknown nuclear properties using a quantitative match to the solar isotopic pattern, starting from a range of different astrophysical conditions. Ultimately, we aim to correlate engineered nuclear structure features to characteristics of possible $r$-process environments, such that future experiments can search for these features and thus help to constrain the $r$-process site. In this work, we have applied our reverse-engineering framework to the neutron-rich rare earth region in an attempt to understand the mass trends responsible for the formation of the rare earth peak. Our procedure starts with Duflo-Zuker masses, which are featureless in the rare earth region and produce flat abundance predictions, and finds solutions with mass modifications to Duflo-Zuker that reproduce the rare earth peak to within the solar isotopic pattern uncertainties. We look for two types of solutions: those that result in a persistent feature in the mass surface that spans a large range in proton number $Z$, and those which produce a feature more localized in $Z$. In both cases, the trends found in the mass surface responsible for rare earth peak production depend on the adopted astrophysical conditions. When a persistent feature is assumed, we find traditional, hot $r$-process trajectories that go through a long duration \nggn \ equilibrium require trends in masses near $Z=60$ neodymium isotopes that have local minimums at even-$N$ nuclei near $N\sim100$ and span a change of no more than $0.8$ MeV. Colder $r$-process trajectories that have a short duration \nggn \ equilibrium are found to require trends in the mass surface that have local minimums at odd-$N$ and span a change of over $1$ MeV. We find that the depth of the feature in the masses near $N\sim100$ is directly related to how far the $r$-process path proceeds towards the neutron dripline and how fast it moves back to stability. In all cases, the trends in the predicted masses are extended in neutron number and are not the abrupt changes that might be expected, e.g., from a subshell closure. Nuclear deformation is a possible source of these smooth trends. When we look for a localized feature, we find solutions that depend more sensitively on the details of the astrophysical conditions. This is most pronounced in the case of hot trajectories where we find a larger deviation between the resultant mass surfaces. Our results suggest that a wealth of information can be obtained from new measurements in the rare earth region. If a sizable region of enhanced stability is found, its characteristics could point to the nature of the $r$-process site: hot, cold, or very neutron-rich cold. More detailed information about freeze-out conditions could potentially be extracted from the location and depth of a small, localized region of enhanced stability. The absence of any significant feature would disfavor the dynamical method of rare earth peak formation. This would point instead to a rare earth peak composed of fission fragments, which would argue for neutron star mergers as the main $r$-process astrophysical site. It would also be possible to use this method to consider partial fission / partial dynamical solutions for any given prediction of fission rates and daughter distributions. The past few years has seen a dramatic increase in the quantity and quality of experimental data for neutron-rich nuclei important for the $r$ process, e.g., \cite{Hakala+12, Madurga+12, VanSchelt+13, Kurtukian+14, Caballero-Folch+14, Spyrou+14, Sun+15, Atanasov+15, Klawitter+15, Lascar+15, Lorusso+15, Cizewski+15, Mazzocchi+15, Jones+15, Dunlop+16, Alshudifat+16, Liddick+16, Domingo+16, Miernik+16, Caballero-Folch+16, Hirsh+16, Wu+16}. Future measurement campaigns at current and planned experimental facilities such as the Facility for Rare Isotope Beams, will offer an unprecedented access to the production of short-lived isotopes \cite{Horowitz+16r}. Our study has pinpointed nuclei in the rare earth region which have a substantial impact on the formation of the rare earth peak. A combined theoretical and experimental effort will help to distinguish between astrophysical conditions, thus providing an avenue for moving forward with the solution of the site(s) of the $r$ process. | 16 | 9 | 1609.09858 |
1609 | 1609.00524_arXiv.txt | We present the first linear polarimetric survey of white dwarfs (WDs). Our sample consists of WDs of DA and DC spectral types in the SDSS \textit{r} magnitude range from 13 to 17. We performed polarimetric observations with the RoboPol polarimeter attached to the 1.3-m telescope at the Skinakas Observatory. We have 74 WDs in our sample, of which almost all are low polarized WDs with polarization degree (PD) smaller than 1\%, while only~2 have PD higher than 1\%. There is an evidence that on average the isolated WDs of DC type have higher PD (with median PD of 0.78\%) than the isolated DA type WDs (with median PD of 0.36\%). On the other hand, the median PD of isolated DA type WDs is almost the same, i.e. 0.36\% as the median PD of DA type white dwarfs in binary systems with red dwarfs (dM type), i.e. 0.33\%. This shows, as expected, that there is no contribution to the PD from the companion if the WD companion is the red dwarf, which is the most common situation for WDs binary systems. We do not find differences in the polarization degree between magnetic and non-magnetic WDs. Because 97\% of WDs in our sample have PD lower than 1\%, they can be used as faint zero--polarized standard star in the magnitude range from 13 up to 17 of SDSS \textit{r} filter. They cover the Northern sky between 13 hour to 23 hour in right ascension and from \ensuremath{-11}$\dg$ to 78$\dg$ in declination. Additionally, we found that for low extinction values (< 0.04) the best model that describes the dependence of PD on E(B--V) is given by the equation: $\rm{PD_{max, ISM}}[\%] = 0.65~\rm{E(B-V)}^{0.12}$. | \label{sec:introduction} In the last years the interest in optical polarimetry has grown significantly \citep[e.g.][]{Marscher2010}. The reason for this boom is that polarimetric measurements give an invaluable additional constrain on theoretical models that neither the photometry, astrometry nor spectrometry can provide. These studies include all kinds of astrophysical objects. There are regular monitoring campaigns to study the polarization changes of AGNs in the optical domain, as for example the optical monitoring of selected blazars with the RoboPol polarimeter \citep{Pavlidou2014}. There are also optical polarization studies of isolated neutron stars including pulsars \citep[e.g.][]{Slowikowska2009, Lundqvist2011, Moran2013, Moran2014, Mignani2015} and magnetars \citep[e.g.][]{Wang2015}, as well as neutron stars in high mass X-ray binaries \citep[e.g.][S\l{}owikowska et al. in preparation]{Reig2014} and low mass X-ray binaries \citep[e.g.][]{Baglio2014}, not to mention polarization studies of GRBs \citep{Mundell2013} and of polarized light from exoplanets for which a dedicated detector, i.e. Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) at VLT has been recently built\footnote{\url{https://www.eso.org/sci/facilities/paranal/instruments/sphere.html}}. The scientific community has started to use polarimetric measurements extensively to study stellar and non-stellar objects. However, reaching fainter objects by using infrastructure with larger mirror introduced a serious problem, namely, the lack of faint polarization standards of both types --- the zero-polarized and polarized ones. Each measurement using a polarimeter or spectropolarimeter needs to be properly calibrated. Thus, the polarized standards are necessary to establish the intrinsic depolarization caused by the instrument, while the zero-polarized standards are necessary to get the instrumental polarization (e.g. the RINGO3 polarmeter at the Liverpool Telescope, see \citet{Slowikowska2016}). The aim of our work is twofold: {\em i)} to perform a statistical analysis of the linear polarization properties of white dwarfs sample and {\em ii)} to provide observers with new faint linear polarimetric standard sources. There are more than 23,000 WDs known up to date (see Sec.~\ref{sec:sample}). For many of them their spectral type is known. Most of of WDs atmospheres are hydrogen-rich atmospheres (DA), while almost all the rest are helium-rich (DB). However, a significant fraction of WDs also contain trace elements in their atmospheres and therefore they are labelled with Z for metals or Q for carbon, as for example DZ or DQ. There are also cases when the WD spectrum does not show any strong lines, but still their atmospheres are helium-rich. Such WDs are classified as DC type WDs. WDs with magnetic fields stronger than 1MG can be detected via Zeeman splitted lines, while weaker magnetic fields can be detected using spectropolarimetry. However, because DC type WDs spectra do not have strong spectral lines, therefore it is not possible to use the Zeeman effect to measure their magnetic field strength. Previous studies showed that around 10\% up to 20\% of all WDs are magnetised with strong magnetic field \citep[][and references therein]{Ferrario2015}. The PD of magnetised WDs is between a fraction of a percent up to a few percent, as for example in case of GD~229 that has almost $8\%$ of linear PD in R band \citep{Berdyugin1999}. The population of magnetised WDs can be even larger because the magnetic field of many sources is unknown. Linear polarimetric population study can help to select WDs as good candidates for stable polarimetric calibration sources. Moreover, for each WD we have information about whether it is an isolated WD or WD in a binary system. In most cases the companion is a low mass red dwarf. Magnetised WDs in binary systems with low mass star that are in contact are classified as the magnetic cataclysmic variables (MCVs, i.e. polars and intermediate polars) and they represent one fourth of the whole CVs population \citep{Wickramasinghe2000}. There are also binary systems composed of WD and low mass star that are close but are not in contact, i.e. pre-CVs, however none of such systems with magnetic WD is known so far \citep{Liebert2015}. There are close double degenerate systems and common proper motion binaries as well. This allows us to study the dependence of WD polarimetric properties on singularity or binarity, taking into account the type of the binary. White dwarfs are commonly used as zero polarization standard stars. In the literature we can find eleven white dwarfs used for this purpose. Two of them, i.e. G191-B2B (PD=0.09\%) and GD319 (PD=0.045\%), were proposed by \cite{Turnshek1990} as the HST polarimetric standards, whereas another nine were proposed by \cite{Fossati2007} as main zero polarization standards for the FORS1 instrument on the VLT. The main goal of \cite{Fossati2007} was to find a group of faint polarized and non-polarized standard stars that can be used for calibration of big telescopes. His sample consists of 30 stars of different types in the magnitude range from 6 to 14. However, WDs given by \cite{Fossati2007} are in the magnitude range from 11 to 13, with only one exception of 14 mag. In our work we propose to extend existing standard lists with additional 74 WDs as low linear polarization standards. The biggest advantage of WDs from our sample is that they are even fainter, i.e. in the SDSS $r$ magnitude range from 13.2 (WD2149+021) up to 17 (WD2213+317), than those already available in the literature. In this way our sample is complementary to the earlier work. A larger group of zero polarization standards allows to find visible standard in convenient time of the night and position on the sky. There were many polarization studies of large samples of white dwarfs conducted so far, for example: \citet{Angel1981}; \citet{Schmidt1995}; \citet{Putney1997}; \citet{Kawka2007}; \citet{Jordan2007}; \citet{Kawka2012}; \citet{Landstreet2015}. Recently, \citet{Bagnulo2015} published a spectropolarimetric catalogue of 809 objects, obtained with the FORS/VLT instrument, that includes 70 WDs. However, there is only one WD common in both lists, ours and \citet{Bagnulo2015}, i.e. WD2149+021. The crucial difference between above mentioned studies and our work is that our observations are the first WDs linear polarization survey, whereas the others measured the circular polarization. We describe the selection method in Sec.~\ref{sec:sample}, the observations in Sec.~\ref{sec:obs}, while the data analysis in Sec.~\ref{sec:data}. Results and conclusions are given in Sec.~\ref{sec:results} and Sec.~\ref{sec:summary}, respectively. | \label{sec:summary} We conclude that most of the measured WDs, being of DA and DC spectral types and in the SDSS \textit{r} magnitude range from 13 to 17, have low PD below 1\%. Only WD1440$-$025 and WD2213+317 have PD higher than 1\%. We found out that there is a correlation between the measured PD and \textit{r} brightness, as well as between the $\sigma_\mathrm{PD}$ and \textit{r} brightness. Moreover, the DC type white dwarfs on average have higher PD (with the median PD of 0.78\%) than DA type WDs (with the median PD of 0.36\%). The significance of the difference (p--value of the null hypothesis) is on the level of 0.01. Taking into account that the PD and PD uncertainties show the dependence on the brightness the difference between those two WD types can be attributed to the fact that the DC type WDs are fainter than DA. However, there are only 4 DC type WDs in our sample, so we can not state this without any doubts. On the other hand, there seems to be no difference between PD of isolated DA type WDs (0.36\%) and binary systems that include DA type WDs (0.35\%). Our sample constitutes a set of good candidates of faint linear polarimetric standard stars with SDSS \textit{r} magnitudes ranging from 13 up to 17. They are well distributed in the right ascension range from 13 hour up to 24 hour mostly on the Northern sky with declination form \ensuremath{-11}$\dg$ up to 78$\dg$. Moreover, we enrich the present low linear polarization WDs standard list by a factor of five. Reaching fainter objects with infrastructure with larger mirror introduced a serious problem, namely, the lack of faint polarization standards of both types, the zero-polarized and polarized ones. The presented list of WDs addresses this need with respect to zero-polarized standard stars and is complementary to the previous work done by \cite{Fossati2007}, which includes nine WDs in the magnitude range from 11 to 13, with only one exception of 14 mag. Additionally, we found that for low extinction values (< 0.04) the best model that describes the dependence of PD on E(B--V) is given by the equation: $\rm{PD_{max, ISM}}[\%] = 0.65~E(B-V)^{0.12}$. Even in cases of highly MWDs, as well as in the cases of low magnetic field WDs, we do not detect significant linear polarization degree. This is likely caused by the fact of the polarization dilution over broad band. Therefore, we conclude that even the MWDs of our sample can be very well used as polarimetric standards. It will be very useful to perform deeper and longer observations on the DC type WDs to obtain measurements with higher accuracy and to expand the test sample. It is worth mentioning that Gaia satellite will discover around 100,000 WDs. Assuming the same ratio of around 300/23,000 (WDs brighter than 17 mag visible from the Skinakas Observatory to the total number of known WDs), there will be around 1,300 Gaia WDs brighter than 17 mag visible at Skinakas, therefore we will be able to continue our study in the future on much bigger sample. | 16 | 9 | 1609.00524 |
1609 | 1609.02693.txt | Motivated by the significant interaction of convection, rotation and magnetic field in many astrophysical objects, we investigate the interplay between large-scale flows driven by rotating convection and an imposed magnetic field. We utilise a simple model in two dimensions comprised of a plane layer that is rotating about an axis inclined to gravity. It is known that this setup can result in strong mean flows; we numerically examine the effect of an imposed horizontal magnetic field on such flows. We show that increasing the field strength in general suppresses the time-dependent mean flows, but in some cases it organises them leading to stronger time-averaged flows. Further, we discuss the effect of the field on the correlations responsible for driving the flows and the competition between Reynolds and Maxwell stresses. A change in behaviour is observed when the (fluid and magnetic) Prandtl numbers are decreased. In the smaller Prandtl number regime, it is shown that significant mean flows can persist even when the quenching of the overall flow velocity by the field is relatively strong. | Many astrophysical flows are turbulent and contain systematic large-scale (mean) flows that reside alongside smaller-scale turbulent eddies. Well-known examples of such large-scale flows are the zonal jets evident at the surface of the gas giants (e.g., \citet{Porcoetal2003, VasavadaShowman2005}) and the strong zonal and meridional flows in the interior of the Sun which are understood as the observed differential rotation and meridional circulations (\cite{Schou1998}). It is widely accepted that the dynamics of these flows is often further complicated by the presence of a magnetic field. Techniques such as spectropolarimetry, asteroseismology, and photometric monitoring have allowed observers to probe differential rotation in stars and its interaction with magnetism. For example, \cite{Reinholdetal2013} use precision photometry to obtain surface differential rotation that varies with spectral type in a large sample of Kepler stars. Meanwhile, spectropolarimetric measurements of surface differential rotation in very low-mass stars (see e.g., \cite{Donati2003, DonatiLandstreet2009}) often suggest that such objects rotate nearly as solid bodies, with quenching of zonal flows by magnetic fields being a possible cause. Asteroseismology of red giants (e.g., \cite{Becketal2012, Deheuvelsetal2012}) has also revealed strong internal differential rotation, with the cores of some objects rotating multiple times faster than their envelopes. Separately, global simulations of turbulent convection under the influence of rotation have suggested multiple regimes of zonal flows are possible, particularly in the presence of magnetic fields: in some cases angular velocity contrasts persist even in the presence of relatively strong magnetic fields while in others the large-scale flows are largely eliminated. What delineates these regimes, and determines the amplitude and direction of the large-scale flows, is still not known (see e.g., \cite{Brunetal2005, Kapylaetal2011, Gastineetal2014, Karaketal2015}). It is clear then, that in addition to understanding the interaction between the smaller-scale turbulence and the large-scale flows, it is important to determine the role of a magnetic field in such a system. Such interactions are complicated, and although much progress has been made (as discussed briefly below) there is still much that is not understood. In order to evaluate the effects of a magnetic field on mean flows, here we consider flows driven by convection resulting from an imposed temperature gradient. Such is the complexity of modelling the interactions of convection, rotation and magnetic fields, a starting point has often been the hydrodynamic problem whereby the effects of magnetic fields are neglected. Mean flow generation in hydrodynamic models, in both local and global geometries, has received significant attention in the literature: (see e.g., \cite{HS1983, HS1986, HS1987, JulienKnobloch1998, SaitoIshioka2011} (local) and \cite{Mieschetal2000, Elliottetal2000, Christensen2001, Christensen2002, BrunToomre2002, Browningetal2004, GastineWicht2012, Gastineetal2013} (global).) The mechanism for the generation of such large-scale flows is dependent upon the system of study, and in particular the geometry. In rotating spherical shell models zonal flow is thought to be driven by Reynolds stresses resulting from the curvature of the boundaries (\cite{Busse1983}); although density variations may also provide a source of vorticity that can help to sustain mean flows (e.g., \cite{Evonuk2008, Gastineetal2014a, VerhoevenStellmach2014}). In order to capture some important geometrical effects of a spherical body but whilst maintaining a relative simplicity, \cite{Busse1970} introduced an annulus model. This setup has since been implemented in models of the zonal flow on Jupiter. For example, \cite{Jonesetal2003} used a two-dimensional (2d), rotating annulus setup which allowed for more realistic jet solutions to be found when boundary friction was included. \cite{RotvigJones2006} explored this annulus model further and identified a bursting mechanism that occurs in the convection in some cases. In a local Cartesian geometry, \cite{HS1983, HS1986, HS1987} studied the flows generated when the rotation vector was oblique to gravity in a number of different models. The plane layer geometry, when the axis of rotation is allowed to vary from the direction of gravity, is often used to approximate a local region of fluid located at different latitudes of a spherical body; this introduces an asymmetry into the system. This asymmetry is enough to drive significant mean flows within the system. As an additional mechanism, \cite{Currie2014} examined mean flow generation when a thermal wind (driven by the presence of horizontal temperature gradients) was present. \cite{CT2016} extended the work of \cite{HS1983} to include the effects of a background density stratification. Furthermore, strong shear flows can be driven in 2d models of Rayleigh-B\'enard convection that employ horizontally periodic, and vertically stress-free, boundary conditions (see \cite{Goluskinetal2014}). The effect of a magnetic field on convection has received less attention. Whilst there is a vast body of literature on magnetic field generation in astrophysical objects through dynamo action (e.g., \cite{Moffatt1978}, \cite{Parker1979}, \cite{Tobias2002}, \cite{BrandenburgSubramanian(2005)}, \cite{Jones2011}), there is less relating to the effect of the magnetic field on the convection and in particular, the effect of an imposed field on the driving and maintaining of mean flows seen in hydrodynamic systems. In this paper we impose a horizontal magnetic field and assess its effect on the system; we do not address the question of how the field got there. The difficulties in solving the full dynamo problem make magnetoconvection in an imposed magnetic field an important tool for studying the basic principles which influence the interactions between convection and magnetic fields. Early studies of magnetoconvection include the linear analyses of \cite{Chandrasekhar1961}, \cite{Eltayeb1972, Eltayeb1975}. Eltayeb derived a bound for which rotational effects dominate over magnetic effects in a plane layer system with rotation and magnetic field both in the horizontal direction. \citet{Arter} studied 2d nonlinear convection in an imposed horizontal magnetic field in a plane layer but without rotation. He found that, in general, stronger horizontal magnetic fields resulted in time-dependent convection and, as the thermal driving was increased, the oscillations grew in amplitude until the flow direction reversed. An analogous problem to the one studied by \cite{Arter} involves convection in an imposed vertical field; this topic was comprehensively reviewed by \citet{PW}. \citet{Arter} highlighted that an imposed horizontal magnetic field results in convective motions which are significantly different to those in a vertical field, since in the latter case, flux can separate out from the flow. Later studies of magnetoconvection (often motivated by the need to understand convection in the Sun) looked to include compressibility effects. For example, \cite{LantzSudan1995} used numerical simulations to solve anelastic equations in an imposed horizontal magnetic field but without the effects of rotation. \cite{HurlburtToomre1988} considered nonlinear fully compressible convection in an imposed vertical field, again without rotation. They found the convection sweeps the initially vertical field into concentrated flux sheets and, for strong enough imposed fields, the Lorentz force can suppress the flows. In global calculations, a main focus of study has been dynamo theory and so much of the existing literature does not examine convection in an imposed field (e.g., \cite{Brunetal2005}, \cite{Browning2008}, \cite{Brownetal2011}, \cite{FanFang2014}). However, the early global simulations of \cite{OlsonGlatzmaier1995} did consider convection in an imposed toroidal field under the Boussinesq approximation. In this paper we focus on mean flows driven by convection in a 2d rotating plane layer in which rotation is oblique to gravity and the layer is permeated by an imposed horizontal magnetic field. It is believed that large-scale magnetic fields that emerge in sunspots or in active regions on the Sun originate near the base of the convection zone where the field is mostly azimuthal (see e.g., \cite{GallowayWeiss1981}) and therefore we chose to impose a horizontal (and not, as is often done, a vertical) magnetic field. As described above, the tilted plane layer geometry has been shown to be capable of sustaining mean flows, and here we assess the impact of an imposed horizontal field on such flows. For simplicity, we will consider Boussinesq fluids only. The simplicity of this setup, compared to other more complicated (and realistic) geometries, allows us to study some parameter regimes more easily and to identify key physical interactions between magnetic field and mean flows driven by rotating convection. The main aim of this article then is to elucidate the role of magnetic field in modifying the mean flows driven self-consistently by convection. In section \ref{model}, the model and governing equations are presented. In sections \ref{results1} and \ref{results2}, we present results from numerical simulations, highlighting the role of magnetic field in different parameter regimes. Finally, in section \ref{conc} we offer conclusions and a discussion of the results and how they may be developed in future. %%%%%%%%% %% MODEL SETUP AND EQUATIONS %%%%%%%%% | \label{conc} The main aim of this paper was to examine the effect of a horizontal magnetic field on mean flow generation by rotating convection in two dimensions. In general, the field acts to suppress the fluid velocity but we have showed it has more complicated interactions with the processes that drive mean flows. We focussed on two sets of examples: one at $Pr=1$ and $\zeta=1.1$ (case (i)) and one at $Pr=0.1$ and $\zeta=0.5$ (case (ii)) whilst approximately maintaining the rotational constraint through fixing $Ro$. In both cases (i) and (ii), at small to moderate $Q$ (i.e., small to moderate magnetic field strengths), we illustrated that the field acts to reduce the average magnitude of the time-dependent, horizontally-averaged flows but that the field also organises these flows so that they are more systematic in time. We also demonstrated the effect of decreasing $Pr$ and $\zeta$. In case (i), increasing the imposed field strength affects the processes driving $\bar v$ as much (if not more) than it did $v$ itself, but in case (ii), where $Pr$ and $\zeta$ were decreased, the magnetic field suppresses $v$ much more than it did $\bar v$. In other words, the magnetic field appears to be less effective at suppressing the mean flow (as opposed to the overall flow) when $Pr$ and $\zeta$ are small. However, this change in behaviour is also accompanied by a difference in the type of solution observed at small to moderate $Q$ in cases (i) and (ii). In case (i), the solutions are chaotic, whereas in case (ii), the solutions, whilst chaotic, also exhibit bursting tendencies. Further investigation is required to establish if it is solely the small $Pr$ and $\zeta$ that result in $\bar v$ being able to persist as the imposed field strength is increased, or if the change to a bursting regime that coincided with the decrease in $Pr$ and $\zeta$ is responsible. Any clear trends in the differences in the effect of the imposed magnetic field on $\bar u$ were harder to establish. By analysing the horizontally-averaged (mean) equations we revealed what was responsible for the size and vertical structure of the mean flows at different $Q$. In general, a balance between the MS and RS terms drives the flows, though at the relatively modest values of $Ra$ and $Ta$ considered here, the viscous term plays a role when $Pr=1$. At small $Q$, magnetic flux is expelled to the boundaries causing the field to have a significant effect on the behaviour close to the boundaries but almost no effect on the bulk fluid. These effects lead to the size and structure of the bulk mean flows being dominated by the RS terms and, in some cases, modified by the viscous terms. However, in case (i), as $Q$ is increased, the RS terms are suppressed by the field and the MS terms have a larger impact; these two processes act together to suppress the mean flows in this regime. In case (ii), the smaller $Pr$ means that the viscous terms are much less important. Furthermore, the small $Pr$ and $\zeta$ result in the RS terms dominating the flows at larger $Q$, as the MS terms do not contribute as they do in case (i). Indeed, a much larger $Q$ has to be reached in the smaller Prandtl number regime (case (ii)) than is required in case (i) for the MS terms to dominate. In case (ii), at small to moderate $Q$, the time-averaged RS terms actually increase with field strength and so this, coupled with the fact the MS terms contributed less, leads to mean flows that are able to persist even though the velocity field is being suppressed by the field. Our results emphasise that the interaction between mean flows and magnetic fields is quite complex and, in particular, they highlight the crucial role of the Prandtl numbers. Our results show strong dependence on these parameters: in case (i) it is clear that magnetic field influences the balance between the Reynolds and Maxwell stresses; however, how robust this behaviour is is still unclear as shown by the results at smaller Prandtl numbers (case (ii)). Whilst our model is a crude simplification of the full problem, the demonstration that large-scale flows may be able to persist in the presence of a magnetic field has potential applications to astrophysical flows (e.g., differential rotation in stars). To conclude, we recognise the limitations of our crude model. Firstly, in two dimensions, correlations may be amplified resulting in strong mean flows and flow suppression. We are therefore currently examining how extending the model to three dimensions affects the driving of mean flows and their suppression by magnetic fields. Furthermore, the periodic boundary conditions we imposed are likely to be unrealistically enhancing the meridional flows relative to the zonal flows. The modest parameters used in this work were for illustrative purposes and are orders of magnitude below astrophysically relevant values ($Ra$, $Ta> 10^{10}$). However, with modern-day computing facilities, there is the potential to probe more realistic regimes; this forms an avenue for prospective follow-up work. Finally we note that, throughout this study, we imposed a uniform horizontal magnetic field. In reality, magnetic fields are generated and sustained by dynamo action; an obvious problem to address then is whether the mean flows generated in our system are capable of sustaining a magnetic field through dynamo action, this is something we address in a future paper. | 16 | 9 | 1609.02693 |
1609 | 1609.01302_arXiv.txt | Lindsay 1 is an intermediate age ($\approx 8$ Gyr) massive cluster in the Small Magellanic Cloud (SMC). Using VLT FORS2 spectra of 16 probable cluster members on the lower RGB of the cluster, we measure CN and CH band strengths (at $\simeq 3883$ and $4300 $ \AA~respectively), along with carbon and nitrogen abundances and find that a sub-population of stars has significant nitrogen enrichment. A lack of spread in carbon abundances excludes evolutionary mixing as the source of this enrichment, so we conclude that this is evidence of multiple populations. Therefore, L1 is the youngest cluster to show such variations, implying that the process triggering the onset of multiple populations must operate until at least redshift $\sim 1$. | \label{sec:intro} Globular clusters (GCs) have been found to host multiple populations (MPs) of stars, an indication that they are not the simple stellar systems once thought to be. These MPs are characterised by abundance variations between stars that can be seen in both photometry (from splits and spreads in the Main Sequence (MS) or Red Giant Branch (RGB) in appropriate filters, for example (e.g. \citet{piotto13})) and spectroscopy (from chemical abundance anti-correlations (e.g. \citet{gratton12b})). Abundance variations have been observed for light elements such as C, N, O, Na, Al and Mg, which are often paired in anti-correlations. Iron has been found to exhibit very little variation in these clusters, which would be expected if supernovae were not responsible for the enrichment of the second population of stars. Old GCs (>10 Gyr) in both the Milky Way and the LMC have been found to host MPs \citep{mucciarelli09, mateluna12}, while similarly aged, less massive open clusters have not. Therefore, it was traditionally thought that the main cluster property contributing to the presence, or lack thereof, of MPs is the cluster's mass. However, this has recently been called into question as younger ($\sim 1.5$ Gyr) clusters of comparable mass to GCs do not appear to host them (e.g. NGC 1806; \citet{mucciarelli14}). This indicates that age could also be a controlling parameter, and is what we aim to test here. The differences between the populations in younger clusters and old GCs is crucial for GC formation scenarios. It is currently accepted that the enrichment process must be external to the stars, as main sequence stars are also found to exhibit abundance variations, excluding processes such as evolutionary mixing within stellar interiors \citep{harbeck03}. Many scenarios describing the origin of MPs invoke multiple generations of stars in order to explain said features in the Colour Magnitude Diagrams (CMDs) of clusters and chemical variations. The AGB \citep[e.g.][]{dercole08}, FRMS (Fast Rotating Massive Star; e.g. \citet{decressin07} and interacting massive binaries \citep[e.g.][]{demink09} scenarios use the ejecta of evolved stars to pollute a second generation of stars forming later than the first, with age spreads of up to $\sim 300$ Myr. The early disc accretion scenario alternatively uses the ejecta of stars of the same generation to pollute pre-MS stars \citep{bastian13}. However, these scenarios cannot reproduce all light element abundance variations \citep{bastian15b} without succumbing to significant issues, such as the mass budget problem \citep[e.g.][]{larsen12,bastianlardo15,kruijssen15}. Additionally, sufficient gas reservoirs have not been found in Young Massive Clusters (YMCs) at the ages required for formation of a second generation with the proposed age spreads \citep{ivan15, longmore15}. The gap between the single population 1-3 Gyr clusters and those >10 Gyr with MPs is therefore an important age range to study to provide insight into exactly when and how MPs originate. This is the aim of this study into Lindsay 1 (hereafter L1), an intermediate age cluster in the SMC. At $\approx 8$ Gyr \citep{mighell98, glatt08}, it fits well into the unexplored age region for GCs. Additionally, it has low metallicity ([Fe/H] $\approx -1.35$, \citet{mighell98}) and is massive \citep[$\approx 1.7 - 2.6\times 10^5$ \msun ;][]{glatt11}, so is comparable with old GCs. In this study we obtain CN and CH band strengths \citep{kayser08,pancino10, lardo12} and C and N abundances to look for MPs in L1. In \S~\ref{sec:data} we discuss our data and its reduction, \S~\ref{sec:index} our measurement of CN and CH band strengths and C and N abundances, \S~\ref{sec:refine} discusses our determination of cluster members and \S~\ref{sec:results} and \S~\ref{sec:discussion} our results and discussion respectively. \vspace{-0.6cm} | \label{sec:discussion} We obtained spectroscopy for 34 targets towards L1, and have determined through various methods that 15 of these sources are true cluster members and reliably lower RGB stars. Out of these 15 stars, 6 show enriched [N/Fe] compared to a fairly constant [C/Fe] throughout all sources, which is evident in Fig.~\ref{fig:cnch}. This is strongly indicative of the presence of MPs in L1, the youngest cluster to show abundance variations, though not the least massive \citep[NGC 6362 at $5 \times 10^4$ \msun,][]{mucciarelli16}. This indicates that the unknown mechanism responsible for MPs operated more recently than previously thought, though sample size is currently very small and more intermediate age GC targets can be studied in the SMC. Niederhofer et al, in prep, have also found evidence in support of MPs in L1 using HST photometry. In certain filter combinations the RGB splits into two sequences, in support of our findings using FORS2 spectroscopy. Stars in our study that overlap with their catalogue also lie on the correct RGB branch depending on whether they are N-enriched or not. Evolutionary mixing can be disregarded as an explanation for elevated N abundances, as the C abundances show no variation. This indicates that our abundance estimates for the main N-poor population should be similar to those of the stars' original gas cloud (apart from some small evolutionary effects due to internal stellar mixing). Additionally, as our sources are lower RGB stars, they are fainter than the bump in the LF \citep[$V_{BUMP} = 19.30 \pm 0.05$;][]{alcaino03} meaning that any evolutionary mixing should have had minimal impact on the C and N abundances \citep[e.g.][]{gratton00}. We have also visually examined the N-enhanced stars using HST ACS F555W band images (proposal ID 10396, P.I Gallagher) taken from the Hubble Legacy Archive (HLA). Though the ACS image was smaller than our coverage, 3 of the 6 enriched stars were within ACS field of view, including 0709, the most enriched star. All of these targets appeared to be reliable sources, isolated single stars without contamination from nearby objects. Based on evidence for a lack of evolutionary mixing, the quality of the sources and our stringent membership tests, we believe the spread in [N/Fe] to be real. It is important to note, however that we are only sampling the outer regions of L1, as the centre of the cluster is too crowded to obtain spectra of single stars with the slits on FORS2. Therefore, the observed ratios (N-enriched/N-normal) cannot be used to derive $F_{enriched}$. This may have affected previous studies of young and intermediate age LMC clusters (e.g \citet{mucciarelli08,mucciarelli14}), hence, HST imaging of these clusters in filters sensitive to MPs should also be undertaken. In order to investigate other light elements, time-consuming, high resolution spectroscopy is necessary, however, our method can be regarded as a promising way to identify and study MPs on shorter timescales. \vspace{-0.5cm} | 16 | 9 | 1609.01302 |
1609 | 1609.08223_arXiv.txt | We present elemental abundances for all seven stars in Moving Group W11450 (Latham 1) to determine if they may be chemically related. These stars appear to be both spatially and kinematically related, but no spectroscopic abundance analysis exists in literature. Abundances for eight elements were derived via equivalent width analyses of high resolution (R$\sim$60,000), high signal--to--noise ratio ($\langle$SNR$\rangle\sim$100) spectra obtained with the Otto Struve 2.1m telescope and Sandiford Echelle Spectrograph at McDonald Observatory. The large star--to--star scatter in metallicity, -0.55 $\leq$ [Fe/H] $\leq$ 0.06 dex ($\sigma$= 0.25), implies these stars were not produced from the same chemically homogeneous molecular cloud, and are therefore not part of a remnant or open cluster as previously proposed. Prior to this analysis, it was suggested that two stars in the group, W11449 \& W11450, are possible wide binaries. The candidate wide binary pair show similar chemical abundance patterns with not only iron, but with other elements analyzed in this study, suggesting the proposed connection between these two stars may be real.\\ | Astronomers have long used star clusters as empirical testbeds for the purposes of understanding both the kinematic properties of the Galaxy as well as its chemical evolution. These bound stars share a common formation history, and as a result, share a common age, distance from us, relative speed, and spatial relationship on the sky. Open clusters are loosely bound, relatively young star clusters that reside almost exclusively in the plane of the Milky Way, making them particularly useful systems, in aggregate, for investigating Galactic dynamical and chemical evolutionary processes. Having been formed from the same well--mixed giant molecular cloud (GMC), they are also thought to be fairly homogeneous in their chemical composition \citep[e.g][]{2006AJ....131..455D, 2007AJ....133.1161D}. For many elements, the observed star--to--star abundance variations for constituent members within open clusters show a remarkably small spread, $\sim$0.01 to 0.05 dex \citep[see][]{2010A&A...511A..56P, 2011MNRAS.415..563D, 2012MNRAS.427..882T, 2012MNRAS.419.1350R, 2013MNRAS.431.3338R, 2013MNRAS.431.1005D, 2016A&A...590A..74B}. These common attributes acquired from a shared formation history allow astronomers to differentiate stars that may belong to a particular cluster from those that happen to share the same field of view. It also allows for an examination of chemical evolutionary patterns that may emerge among these stars. \\ Even though the vast majority of stars, if not all, are born in clusters \citep{2003ARA&A..41...57L}, the array of stars we see in the night sky are either single stars or binary systems, suggesting some disruption of clusters must have occurred on a relatively short timescale \citep{2003ARA&A..41...57L,2005A&A...443...79B,2005A&A...443...41M}. The Galactic disk is a dynamic environment where close encounters or interactions with other clusters, stars in the field, or GMCs can disrupt a cluster and cause it to lose members to the disk. Perturbations due to spiral arm rotation and the central Galactic bar may cause orbital variations that can disperse cluster members, and orbital resonances that may trap dispersed member stars \citep{1998AJ....115.2384D}. Both internal star formation dynamics \citep[see][for a review]{2010RSPTA.368..713L} and external Galactic perturbations can oust cluster member stars where they migrate to the disk as unbound stars, or moving groups, and become part of the general stellar population. While Galactic orbital parameters may change for these stars their chemical composition is preserved, as well as the small star--to--star elemental scatter \citep[see][]{2007AJ....133..694D, 2010AJ....140..293B}. High resolution, high SNR spectroscopic abundance analyses can reveal the chemical signatures necessary for identifying such stellar associations for the purpose of ``chemically tagging" them to either the thick or thin disk of the Galaxy \citep{2002ARA&A..40..487F}. While beyond the scope of this study, chemically tagging stars to their Galactic zip code, in the interest of reconstructing the chemical evolution of the Galaxy, is an intriguing proposition for near field cosmology.\\ In a systematic radial velocity survey centered on ``Selected Area 57"\footnote{The term is an historical holdover from a plan originally proposed by Jacobus Cornelius Kapteyn in 1906 to determine the structure of the Galaxy by taking samples at regularly spaced intervals.\citep[see][]{1906BuAsI..23..480.}.}(SA 57; \emph{l}=66$\degr$, \emph{b}=+86$\degr$) near the North Galactic Pole, \citet[hereafter LMS91]{1991AJ....101..625L} noted seven specific stars, referred to as Group W11450, located within a circle of radius $0.5 ^{\circ}$ near the edge of the survey region with a small velocity dispersion of $\sim$0.27 km s$\rm ^{-1}$. The group gets its name as a consequence of a high--probability bound pair residing within the stellar association, W11450AB--W11449, the `AB' indicating a possible tertiary system \citep{1988Ap&SS.142..131M}. As described by \citet{1984ApJ...281L..41L}, distances for four LMS91 stars are estimated by calibrating absolute magnitudes \emph{v.} spectral types, which the study also provides. LMS91 affirms the distances found are consistent with all stars being within 2 pc of each other, commensurate with an open cluster tidal radius of $\sim$10 pc \citep{1998A&A...331...81P, 1998A&A...329..101R, 1999A&A...345..471R}. By extrapolating masses down to late M stars, and applying the angular diameter of the ``cluster" together with the velocity dispersion, the study concludes that the moving group is virialized and therefore bound, or close to being bound. \\ Listed as Latham 1, and hereafter referred to as such, in the current Dias catalog of open clusters \citep{2002A&A...389..871D}\footnote{The catalog can be found online at http://www.astro.iag.usp.br/ocdb}, a search of current literature reveals few details about these stars. Interestingly, a study of blue horizontal branch (BHB) halo stars in SA 57 from \citet{1994AJ....108.1722K} considers a Latham 1 star, W13284 identified as Case A-F 860, in the initial star sample. All seven Latham 1 stars have reliable 2MASS \citep[The Two Micron All Sky Survey;][]{2006AJ....131.1163S} \emph{JHK} photometry and $B_TV_T$ colors from the Tycho-2 catalog \citep{2000A&A...355L..27H}. By leveraging both 2MASS and Tycho surveys, \citet{2006ApJ...638.1004A} produced photometric estimates of stellar parameters, including metallicities for four stars and effective temperatures for all stars considered in this study. Utilizing the same surveys, \citet{Casagrande} contributes a metallicity estimate for one star, W23375, which is common to both studies. This star also appears in the \emph{Hipparcos} catalog \citep{1997A&A...323L..49P} with a parallax distance consistent with LMS91, 108 pc and 101 pc, respectively. While both \citet{2006ApJ...638.1004A} and \citet{2010PASP..122.1437P} provide distances for all Latham 1 stars, the two studies show considerable differences in their estimates. \citet{2010PASP..122.1437P} also provide spectral and luminosity classes, revealing all seven stars are dwarfs ranging in temperature from F0 to G8. We summarize the estimates of distances, metallicities and spectral types from these earlier studies in Table \ref{tab1}. \\ Withal, Latham 1 has a number of essential parameters that remain unmeasured. In an effort to remedy this deficiency we conducted a study of Latham 1 stars to derive their metallicities. Therefore, we present the first high resolution spectroscopic study for abundances of Fe I \& Fe II (neutral and singly ionized iron, respectively), Na I, Mg I, Si I, Ca I, Ni I and Ba II in an effort to determine whether Latham 1 stars have individual chemical compositions consistent with the group being defined as a cluster, or remnant cluster.\\ In \S{2} we describe the observations and data reduction sequence for program stars in this study. Radial velocity measurements are presented in \S{3}. In \S{4} we take up the procedure for estimating model stellar atmospheres and for measuring the chemical abundances. We state results and provide some discussion in \S{5}, and conclude with a summary of this study in \S{6}.\\\\ | We have derived chemical abundances for seven stars that constitute Moving Group W11450, or Latham 1, in an effort to determine whether they may be chemically related. All measured abundances can be found in Table \ref{tab6}. The large star--to--star scatter in metallicity, -0.55 $\leq$ [Fe/H] $\leq$ 0.06 ($\sigma$= 0.25), precludes all stars being formed from the same chemically homogeneous GMC. Ad hoc examination of the $>\,\sim$0.60 dex spread in [Fe/H] values displayed in Figure \ref{f3} appears to segregate the stars into three distinct groups: [Fe/H]$\sim$ -0.17, [Fe/H]$\sim$ -0.50, and [Fe/H] = 0.06. Since no elemental abundances beyond [Fe I \& II/H] have been determined for W23375 ([Fe/H] = -0.18), we draw no conclusions for any relationship that may exist between that star and W12388. Turning to the three stars in the [Fe/H]$\sim$ -0.50 range, with the exception of [Ni/Fe] Figure \ref{f4} shows $\sim$0.25 $\leq$ [X/Fe] $\leq$ 0.61 dex dispersion in measured abundance ratios for all other elements considered in this study. This large element--by--element abundance scatter is incompatible with these stars being chemically related.\\ \subsection{W11449 \& W11450} The two metal--rich stars in this study, W11449 \& W11450, were first noted by \citet{1932ngcd.book.....A} in a catalog of double stars located about the North Galactic pole. LMS91 lists an 8.0$^{\prime\prime}$ angular separation on the sky for the stars, with a physical separation of $\sim$600 AU and $P_{bound}$ = 0.85. The detailed kinematic study proposes these stars are wide binary candidates. Although beyond the scope of this study, \citet{2010MNRAS.404.1835K} suggests that wide binaries may be formed during the dissolution of a star cluster, leaving open the prospect of finding isolated, chemically related wide binaries in the Galactic field. \\ Beyond the near solar metallicity for these stars, [Fe/H] = 0.06 for both W11449 \& W11450, we find a notable similarity in abundance ratios for all other elements considered in this study and displayed in Figure \ref{f5}. We see the greatest difference between the two stars in Na I. [Na/Fe] is noticeably enhanced by $\langle$0.33$\rangle$ dex for both stars with $\Delta_{\rm [Na/Fe]}$ = 0.08. Both \citet{1993A&A...275..101E} and \citet{2000A&A...363..692T} cite an increase in Na I with [Fe/H], which can be seen in the ``upturn" in the first panel of Figure \ref{f6}. A compilation of Galactic cluster abundances by \citet{2006cams.book....3F} reveals this is not a peculiar over--abundance for stars in the solar neighborhood. The $\alpha$-- elements, Mg, Si and Ca appear to follow the same abundance trends as disk field stars as well \citep[see also][for field star trends in Ca at this metallicity]{2004MmSAI..75..267S}. We conclude these two stars show a striking similarity in abundances for all elements presented in this study, and may very well have shared the same stellar formation history.\\ | 16 | 9 | 1609.08223 |
1609 | 1609.06008_arXiv.txt | We carry out an ALMA $\rm N_2D^+$(3-2) and 1.3~mm continuum survey towards 32 high mass surface density regions in seven Infrared Dark Clouds with the aim of finding massive starless cores, which may be the initial conditions for the formation of massive stars. Cores showing strong $\rm N_2D^+$(3-2) emission are expected to be highly deuterated and indicative of early, potentially pre-stellar stages of star formation. We also present maps of these regions in ancillary line tracers, including C$^{18}$O(2-1), DCN(3-2) and DCO$^+$(3-2). Over 100 $\rm N_2D^+$ cores are identified with our newly developed core-finding algorithm based on connected structures in position-velocity space. The most massive core has $\sim70\:M_\odot$ (potentially $\sim170\:M_\odot$) and so may be representative of the initial conditions or early stages of massive star formation. The existence and dynamical properties of such cores constrain massive star formation theories. We measure the line widths and thus velocity dispersion of six of the cores with strongest $\rm N_2D^+$(3-2) line emission, finding results that are generally consistent with virial equilibrium of pressure confined cores. | Massive star formation remains an important unsolved problem in astrophysics. Here we seek to obtain improved observational constraints on the initial conditions and early stages of the process. If there is a universal star formation mechanism so that massive stars ($>$ 8 M$_\odot$) are born via a scaled-up version of the low-mass Core Accretion mechanism \citep[e.g.,][hereafter MT03]{1997ApJ...476..750M,2003ApJ...585..850M}, then the initial conditions, i.e., at the time just before protostar formation, should be massive starless cores. Here the term ``core'' is defined to be the self-gravitating structure that will collapse to a single central rotationally supported disk that eventually forms a single star or small $N$ multiple. Early stages of massive star formation by this mechanism would include a low-mass protostar undergoing relatively ordered accretion fed by quasi-monolithic collapse near the center of a massive core. The existence of such cores is a key difference between this model and Competitive Accretion \citep[e.g.,][]{2001MNRAS.323..785B,2010ApJ...709...27W}, which involves fragmentation of gas into protostellar seeds with initial masses only of order the thermal Jeans mass---typically much less than a solar mass in the high mass surface density, high pressure clumps where massive stars form. Note that the term ``clump'' is defined to mean the self-gravitating cloud that eventually fragments into a star cluster. Only later do some of these seeds accumulate further material, fed from the collapsing clump, to become massive stars. Thus finding and characterizing massive starless and early-stage cores is a key way to distinguish between massive star formation theories. However, since massive stars are rare, massive starless/early-stage cores, even if they exist, would also be rare and thus typically far away and relatively small in angular size. Furthermore, they would likely be surrounded by much larger quantities of cold, dense molecular clump gas, with most mass going into lower mass stars or being dispersed back into the diffuse interstellar medium. Finding massive starless/early-stage cores is thus a challenging problem. We have developed a strategy to overcome this challenge. We target regions based on mid-infrared extinction mapping of Infrared Dark Clouds (IRDCs) \citep[][hereafter BT09, BT12]{2009ApJ...696..484B,2012ApJ...754....5B}, which probes mass surface densities up to $\Sigma~\sim~0.5\:{\rm g~cm}^{-2}$ and with angular resolution of 2\arcsec. This allows detailed study of the structure of dense clumps: BT12 characterized 42 high $\Sigma$ clumps selected from 10 IRDCs (A-J), which had themselves been chosen to be relatively nearby and dense. The 42 clumps were checked to make sure they are free of 8 and $24\:\mu m$ (Spitzer-IRAC \& MIPS) sources. We note that this method of sample selection differs from that based on following up strong mm continuum sources and then selecting those that are IR, including $70\:{\rm \mu m}$, dark \citep[e.g.][]{2012A&A...540A.113T,2015MNRAS.451.3089T,2016ApJ...822...59S}. Our goal, which we carry out in this paper, is to search the majority of these sources for \ntdpns(3-2) line emission. The abundance of this species is known to increase in cold, dense conditions of low-mass starless cores \citep[e.g.,][]{2005ApJ...619..379C,2007ARA&A..45..339B,2012A&ARv..20...56C}, where CO is largely frozen-out onto dust grain ice mantles and thus depleted from the gas phase. The enhanced abundance of \ntdp with respect to \nthp is relatively well-understood from the astrochemical point of view, and we have developed a comprehensive spin-state, gas phase reaction network to model this deuteration process \citep[][hereafter K15]{2015ApJ...804...98K}. It is this high abundance of \ntdp that acts as a signpost for the presence of a starless core on the verge of collapse or an early-stage core just after protostar formation, allowing us to find these relatively rare locations in IRDCs. We tested this method by observing 4 target regions centered on IRDC clumps with ALMA in Cycle 0, detecting 6 \ntdpns(3-2) cores at 2\arcsec resolution ($\geq$ 1 from each region) \citep[][hereafter T13]{2013ApJ...779...96T}. The two most massive cores were found in the IRDC clump C1: C1-N and C1-S. We estimated the masses of the cores, defined by projection of their 3$\sigma$ $l-b-v$ space \ntdpns(3-2) contour, in two ways: (1) from the MIREX map, finding C1-N has $61\pm30\:M_\odot$ and C1-S has $59\pm30\:M_\odot$ with the $\sim$50\% systematic uncertainty due to assumed distance ($5\pm1$~kpc) and dust opacity ($\sim$30\%) uncertainties; (2) from mm dust continuum emission, finding C1-N has $16_7^{33}\:M_\odot$ and C1-S has $63_{27}^{129}\:M_\odot$, with uncertainties mostly due to the adopted dust temperature of $T = 10 \pm3$~K, together with distance and dust emissivity uncertainties. Note that it is possible that in general the ``core'' may extend beyond the observed \ntdpns(3-2) contour, so these may be lower limits on the core mass. On the other hand, it is also possible the \ntdpns(3-2) structure may actually contain more than one core, i.e., it may be resolved into two or more separate cores if observed at higher angular resolution. Thus of the six T13 cores, C1-S and C1-N are the most promising examples of a massive starless/early-stage cores, i.e., with $\ga20\:M_\odot$ that may allow formation of a $\ga10\:M_\odot$ star, given expected outflow regulated formation efficiencies $\sim$50\% \citep{2014ApJ...788..166Z}. C1-S appears monolithic, centrally-concentrated in both \ntdpns(3-2) and mm continuum emission, and rounded (most likely by self-gravity). C1-N appears to be less centrally concentrated and potentially fragmented. Follow-up observations of other \ntdp and \nthp lines allowed measurement of $D_{\rm frac}\equiv [{\rm N_2D^+}]/[{\rm N_2H^+}]$ in the cores, with values of 0.2-0.7 \citep{2016ApJ...821...94K}. For most chemodynamical models, such high values that are orders of magnitude greater than the cosmic [D]/[H] ratio of $\sim 10^{-5}$, imply relatively old astrochemical ages and thus relatively slow collapse rates, $\lesssim 1/3$ of the rate of free-fall collapse. Further follow-up with ALMA in Cycle 2 of the C1 region found the presence of a very collimated protostellar outflow, traced by $^{12}$CO(2-1), from a source within C1-S (in both position and velocity space), so that this is most likely to be an example of an early-stage massive core \citep{2016ApJ...821L...3T}. A second protostellar outflow source also overlaps spatially with C1-S, although its association with the core in velocity space is less certain. No outflows were seen from C1-N. T13 used the \ntdpns(3-2) line-width to study the dynamics of the cores. For the sample of 6 sources, the velocity dispersions were on average consistent (within a factor of $\sim 0.8$) with those expected from virial equilibrium of the fiducial MT03 Turbulent Core model. However, for C1-S the observed velocity dispersion is about a factor of two smaller than the fiducial virial equilibrium prediction. If virial equilibrium is being maintained, as would be expected if the astrochemical age is larger than the dynamical time, then relatively strong magnetic fields, $\sim$1~mG, are needed. We see that larger samples of starless and early-stage cores are needed to better test the different theoretical models. This has motivated the observations and analysis presented in this paper. | \label{sec:dc} We have carried out a survey of 32 IRDC clumps designed to detect cores with strong \ntdpns(3-2) emission. Such cores may be massive analogs of low-mass pre-stellar or early-stage protostellar cores. This work follows on from the pilot study of T13, which identified six such cores in 4 IRDC clumps. Our current survey has a lower line sensitivity level than T13, but a similar 1.3~mm continuum sensitivity. The spectral set-up includes several ancillary line tracers, including DCO$^+$(3-2), DCN(3-2), C$^{18}$O(2-1) and SiO(5-4). We have also utilized the MIREX maps of these regions developed by \citet{2014ApJ...782L..30B} and BT12. In order to process the larger number of target regions, we have presented a new way to automatically identify \ntdpns(3-2) cores as connected structures in PPV space using Graph theory methods. In total 141 \ntdpns(3-2) core candidates were identified via these automated methods, although many of the weakest sources are likely to be noise fluctuations. The locations of these sources are identified in our maps of the clump-scale regions. We have presented properties of the strongest 50 cores, including their mean velocities and velocity ranges, and their \ntdpns(3-2) line fluxes. We have presented zoom-in maps of the top 15 of these cores and a dynamical analysis of the best 6 amongst these sources. The main results are the identification of the very massive (up to $\sim 170\:M_\odot$) C9A \ntdpns(3-2) ``core,'' i.e., a connected structure in ppv space, which shows complex structure and kinematics. Several other $\sim10\:M_\odot$ cores are found. The \ntdpns(3-2) velocity dispersions are consistent with the predictions of the turbulent core model of MT03, based on quasi virial equilbrium of such structures. Further follow-up work is needed to test for the starless nature of these cores, especially examining outflow tracers. The methods presented in this study should also be applied to larger samples of clumps to identify their \ntdpns(3-2) core populations, which may be key for understanding the origin of the stellar initial mass function and the formation of star clusters. | 16 | 9 | 1609.06008 |
1609 | 1609.04527_arXiv.txt | We present long term H$\alpha$ monitoring results of five Be/X-ray binaries to study the Be disc size variations and their influence on Type \rom{2} (giant) X-ray outbursts. The work is done in the context of the viscous decretion disc model which predicts that Be discs in binary systems are truncated by resonant torques induced by the neutron star in its orbit. Our observations show that type \rom{2} outbursts are not correlated(nor anti-correlated) with the disc size, as they are seen to occur both at relatively small and large Be disc radii. We discuss these observations in context of alternate interpretation of Be disc behaviour, such as precession, elongation and density effects, and with cognisance of the limitations of our disc size estimates. | \label{sec:introduction} Be/X-ray binaries (BeXBs) are binary stellar systems which make up the largest subclass of the high mass X-ray binary (HMXB) population (about two-thirds of the identified systems, \citealt{2011BASI...39..429P}). These systems are primarily composed of a massive, early-type donor (an Oe or Be star) and a neutron star accretor. The rapidly rotating Oe/Be primary is surrounded by a geometrically thin, Keplerian circumstellar disc in the equatorial regions. The presence and variations of the disc are detected observationally through infrared excess and Balmer emission lines in the optical spectra, the strongest and best-studied of these being the H$\alpha$ emission line \citep{2003PASP..115.1153P}. The neutron star is generally in an eccentric orbit ($e \geq 0.3$) around the massive companion and a correlation in the $P_\mathrm{orb} - P_\mathrm{spin}$ diagram is observed, across a wide range of orbital periods (24.3 $\leq P_\mathrm{orb} \leq$ 262.6 days, \citealt{Corbet1984,Corbet1986}). The interaction of the neutron star with the material in the circumstellar disc results in transient X-ray behaviour. The transient nature of BeXBs is characterised by two types of outburst events \citep{1986ApJ...308..669S}:\\ \indent (\Rom{1}) Type \rom{1} (normal outbursts), which have moderate luminosities ($L \leq 10^{37} \mathrm{erg\,s^{-1}}$) and occur regularly, separated by the orbital period.\\ \indent (\rom{2}) Type \Rom{2} (giant outbursts), which display larger luminosities ($L \geq 10^{37} \mathrm{erg\,s^{-1}}$). They are less frequent and are not modulated on the orbital period. The extent to which the circumstellar disc grows is restricted by the neutron star in its orbit. The viscous decretion disc model explains how circumstellar discs interact with the neutron star, resulting in disc truncation \citep{1991MNRAS.250..432L, 2001A&A...377..161O}. Angular momentum is added to the inner regions of the disc by the Be star and the material is then transported to the outer parts via viscosity (Shakura-Sunyaev $\alpha$-prescription for viscous stress is applied: \citealt{ShakuraSunyaev1973}). The disc is truncated at particular radii, where the ratio between the angular frequency of the disc rotation and that of the orbit is an integer. In BeXBs, the maximum observed H$\alpha$ equivalent width correlates with the orbital period \citep{ReigFabregatCoe1997,ReigNersesianZezas2016}, and this is interpreted as evidence for truncation of the circumstellar disc at a radius resonant with the neutron star orbit. This truncation is an expected outcome of the viscous disc model \citep{1991MNRAS.250..432L, OkazakiBateOgilvie2002} and its effect on mass transfer has been explored by \citet{NegueruelaOkazaki2001} and \citet{NegueruelaOkazakiFabregat2001}. Except for this tidal truncation, the neutron star, being much less massive than the Be star, has very little effect on the circumstellar disc. However, when the circumstellar disc is truncated at a radius close to the inner Lagrangian point at periastron mass transfer to the neutron star can occur, resulting in an X-ray outburst (see Fig. 6 in \citealt{NegueruelaOkazaki2001} for an illustration of the geometry). This truncation suggests that the inner parts of Be star discs may be vertically thicker and/or denser than those of their isolated Be star counterparts, while the outer disc density drops much more rapidly \citep{OkazakiBateOgilvie2002}. While the physical extent of a Be star disc is very difficult to determine, the H$\alpha$ emission line in Be stars is often used to provide an estimate. The Balmer lines are optically thick and produced through recombination. They are also formed in a large part of the disc, giving a much better idea of the physical extent than some of the helium or metal lines which are formed closer to the central star. Balmer line equivalent widths have been shown to correlate with estimates from optical interferometry \citep{2006ApJ...651L..53G}. \citet{1972ApJ...171..549H} show that the peak separation in double-peaked emission lines resulting from a disc can be used to gauge the size of an emitting region, providing reliable sizes in the case of optically thin discs \citep{Hummel1994}. Interferometric measurements suggest that disc emitting areas in the various bands are as large as a few tens of stellar radii, with disc sizes larger in the $K$ band -- in rough agreement with the dynamic estimates from Huang \citep{2007ApJ...654..527G}. \citet{SilajJonesTycner2010} show the dependence of Be star line profiles and equivalent widths on inclination angles, density and different power law indices of the radial density dependence. In these models the H$\alpha$ equivalent width correlates inversely with the peak separation, meaning both of these parameters are sensitive to changes in the disc size and/or density. While the work of \citet{2006ApJ...651L..53G} and \citet{SilajJonesTycner2010} pertains to isolated Be stars, it is not clear how this translates to a case where the disc is truncated. \citet{ZamanovReigMarti2001} show a rough inverse correlation between H$\alpha$ equivalent width and peak separation for Be stars in BeXBs, and this seems to suggest that the situation is not so different in the case of the truncated disc. However, a degeneracy between the disc density and disc radius appears to persist. Our goal in this paper is to investigate how the circumstellar disc size variations, through studying different properties of the H$\alpha$ emission line, influence X-ray outbursts in BeXBs in the context of the viscous decretion disc model. The objects under study are Galactic Be/X-ray transients \hbox{1A~0535+262}, \hbox{4U~0115+634}, \hbox{V~0332+53}, \hbox{EXO~2030+375} and \hbox{1A~1118$-$61}. The article is structured as follows: in section \ref{sec:observations} we present the observations and analysis of the data, while our method of estimating the circumstellar disc radius is addressed in section~\ref{sec:radius}. The results are presented in section~\ref{sec:results} and implications of the results are discussed in section~\ref{sec:discussion}. | We have presented results from long term spectroscopic monitoring of five BeXB systems to study the evolution of Be disc radius and look at its influence on X-ray outbursts, in the context of the viscous decretion disc model. The H$\alpha$ emission line was used to obtain an estimate of the disc size and the main result is that type I outbursts generally occur when the Be disc radius is truncated at radii close to/larger than the critical lobe radius at periastron passage. This provides additional evidence (cf. \citealt{ReigNersesianZezas2016}) for the viscous disc model. Type \rom{2} outbursts, however, are difficult to predict solely based on disc size information, as these are seen to occur when the apparent disc size is large (larger than R$_\mathrm{crit}$), as well as when the disc is smaller than R$_\mathrm{crit}$. As is becoming clear from other recent analyses of H$\alpha$ data \citep{MoritaniNogamiOkazaki2013} and disc simulations \citep{2014ApJ...790L..34M}, the circumstellar disc behaviour is more complex than just growth, decay and truncation. The large disc sizes estimated on this assumption are unphysical and more complex behaviours such as warping, ellipticity or increases in the base density must be invoked to explain the observations presented here. | 16 | 9 | 1609.04527 |
1609 | 1609.01072_arXiv.txt | We present the observations and first results from the FIGGS2 survey. FIGGS2 is an extension of the earlier Faint Irregular Galaxies GMRT survey (FIGGS) towards faint luminosity end. The sample consists of 20 galaxies of which 15 were detected in \HI 21cm line using the Giant Meter-wave Radio Telescope (GMRT). The median blue band magnitude of our sample is $\sim -11.6$, which is more than one magnitude fainter than earlier FIGGS survey. From our GMRT observations we find that, for many of our sample galaxies, the \HI disks are offset from their optical disks. The \HI diameters of the FIGGS2 galaxies show a tight correlation with their \HI mass. The slope of the correlation is 2.08$\pm$0.20 similar to what is found for FIGGS galaxies. We also find that for almost all galaxies, the \HI disks are larger than the optical disks which is a common trend for dwarf or spiral galaxies. The mean value of the ratio of \HI to optical diameter is $\sim$ 1.54. | There are a number of issues that make systematic studies of dIrr galaxies particularly interesting. Firstly, in hierarchical models of galaxy formation, small objects form first and merge together to form larger objects. In that sense, nearby dwarf galaxies are the closest analogues to the galaxies in the early universe. Secondly, the ISM of dwarf galaxies have low metallicity. In this sense too, they are analogous to high redshift galaxies, and serve as a nearby laboratory for the study of gas and star formation in environments with low dust and low metallicity \citep{roychowdhury09, roychowdhury11}. This is in part responsible for the increasing number of recent surveys of dwarf galaxies, e.g. FIGGS \citep{begum08c}, SHIELD \citep{cannon11}, VLA-ANGST \citep{ott12}, LITTLE-THINGS \citep{hunter12}. In this paper we describe an extension to the FIGGS \citep{begum08c} survey. This extension focuses on galaxies with fainter luminosities and smaller \hi\ masses. We present here the results of our \HI observations of 20 very faint galaxies with the Giant Meterwave Radio Telescope (GMRT). In \S 2 we describe our sample, in \S 3 we explain the main science drivers of the survey, in \S 4 we present the observations and data analysis and finally in \S 5 we present the results and discussion. | \label{resultsanddiscussion} In Figure~\ref{ovrplot} we show the integrated \HI distribution (contours) overlayed on the optical images for the detected galaxies. The lowest contour levels are quoted at the upper left corners of each panel in the unit of \acc. We used optical images from SDSS survey (`g' band) whenever available or else we use images from DSS survey (`B' band). We quote the source of the optical images at the top right corner of each panel. To compare the \HI and optical extents and to show large scale \HI structures of our sample galaxies, we choose to overlay low resolution (higher SNR) \HI maps on top of the optical images in Fig.~\ref{ovrplot}. However, due to non-uniform sampling of the visibility plane across our sample, the synthesised beams vary considerably for galaxy to galaxy even after setting the same maximum range of visibility (5 kilo $\lambda$) during imaging. The synthesised beams are shown at the left bottom corner of every panel. We note that the optical center and the \HI center of many galaxies do not coincide (e.g U4879, KKH86, LVJ1243+4127). We speculate that feedback from star formation could be a possible cause of these offsets. In Figure~\ref{spec} we plot the \HI global spectra of our detected galaxies (red solid line). As the detected galaxies are very faint, the global spectra at $\sim$ 1.8 \kms\ resolution some times has a very low SNR. Hence adjacent channels were collapsed together to increase SNR wherever necessary. The velocity resolutions used for different galaxies are quoted at the upper left corner of the respective panels in Figure~\ref{spec}. We also over-plot the single-dish spectra (blue dashed line) for comparison. For KKH37 and UGC04879 we could not find single dish spectra from literature. For BTS146, we note that there is a difference in the central heliocentric velocity ($V_{sys}$) between single dish spectra and the GMRT spectra. However, \cite{kovac09} observed the same galaxy using WSRT and found a central velocity of 446 $\pm$ 17 \kms which matches well what we found ($\sim$ 440 \kms). The parameters derived from the global spectra are listed in Table \ref{table3_figgs}. The columns are as follows: column (1) the galaxy name, column (2) The integrated \HI flux, column (3) systematic velocity ($V_{sys}$), column (4) the velocity width at 50 percent of the peak flux ($\Delta_{50}$), column (5) The \HI diameter derived by ellipse fitting at a column density, $\rm N_{HI}= 0.3 \ M_{\odot} /pc^{2}$, column (6) the ratio of the \HI diameter to the optical diameter, column (7) the derived \HI mass, column (8) mass to light ratio ($M_{HI}/L_B$), column (9) the ratio of GMRT flux to single-dish flux, column (10) \HI inclination assuming an intrinsic thickness of 0.6 \citep{roychowdhury10}. The associated errors are quoted along with the derived parameters. The $V_{sys}$ and the $\Delta_{50}$ were derived by fitting a Gaussian profile to the global \HI spectra. The quoted errors on $V_{sys}$ and $\Delta_{50}$ represent fitting errors only. We estimate the \HI diameter by fitting an ellipse to the iso-\HI column density contour at $\rm N_{HI}= 0.3 \ M_{\odot} /pc^{2}$. The errors in the estimation of \HI diameter ($D_{HI}$) is expected to be dominated by the errors in the \HI map. To account this, we first compute an error map by using the knowledge of the rms in the \HI cube and the number of channels used to make the \HI map. We then estimate a typical error involved in measured column density at $\rm N_{HI}= 0.3 \ M_{\odot} /pc^{2}$ contours (i.e. the mean error along the $\rm N_{HI}= 0.3 \ M_{\odot} /pc^{2}$ contour from the error map). We then construct 1000 realization of \nh~which are consistent with $\rm N_{HI}= 0.3 \ M_{\odot} /pc^{2}$ within the error. We use these \nh~values for \HI isophotes and fit ellipses to these isophotes. We use the standard deviation as an estimate of the errors in the fit parameters. The errors in $\rm D_{HI}$, $\rm D_{HI}/D_{opt}$ and $\rm i_{HI}$ were estimated in this way. \begin{table*} \centering \caption{Results from the GMRT observations of FIGGS2 sample galaxies} \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|} \hline Galaxy & $\rm FI_{GMRT}$ & $\rm V_{sys}$ & $\rm \Delta V_{50}$ & $\rm D_{HI}$ & $\rm D_{HI}/D_{opt}$ & $\rm M_{HI}$ & $\rm M_{HI}/L_B$ & $\rm FI_{GMRT}/FI_{SD}$ & $\rm i_{HI}$\\ & (Jy \kms) & (\kms) & (\kms) & (arcmin) & & $(\times 10^{7} \ M_{\odot})$ & & & ($^o$) \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) \\ \hline AGC112521 & $0.44 \pm 0.34$ & $270.4 \pm 0.2$ & $25.0 \pm 3.8$ & $1.12 \pm 0.14$ & $ 1.9 \pm 0.2$ & $0.38 \pm 0.29$ & $0.67 \pm 0.51$ & $ 0.7 \pm 0.5$ & $44 \pm 7$ \\ KK15 & $0.52 \pm 0.19$ & $371.3 \pm 1.3$ & $23.8 \pm 3.1$ & $0.93 \pm 0.14$ & $ 1.6 \pm 0.2$ & $0.92 \pm 0.34$ & $1.12 \pm 0.42$ & $ 0.6 \pm 0.2$ & $63 \pm 6$ \\ KKH37 & $0.70 \pm 0.13$ & $17.4 \pm 0.1$ & $17.2 \pm 0.9$ & $1.46 \pm 0.12$ & $ 1.3 \pm 0.1$ & $0.20 \pm 0.04$ & $0.29 \pm 0.05$ & $ 0.4 \pm 0.1$ & $64 \pm 4$ \\ KKH46 & $1.96 \pm 0.47$ & $598.2 \pm 0.3$ & $21.2 \pm 0.8$ & $1.88 \pm 0.23$ & $ 3.1 \pm 0.4$ & $2.07 \pm 0.49$ & $1.59 \pm 0.38$ & $ 0.8 \pm 0.2$ & $39 \pm 4$ \\ UGC04879 & $1.35 \pm 0.66$ & $-13.2 \pm 0.2$ & $14.2 \pm 1.2$ & $1.36 \pm 0.37$ & $ 0.4 \pm 0.1$ & $0.06 \pm 0.03$ & $0.06 \pm 0.03$ & $ 0.5 \pm 0.3$ & $46 \pm 7$ \\ LeG06 & $0.22 \pm 0.37$ & $1005.9 \pm 2.6$ & $16.3 \pm 6.6$ & $0.54 \pm 0.31$ & $ 0.9 \pm 0.5$ & $0.56 \pm 0.94$ & $0.62 \pm 1.04$ & $ 0.8 \pm 1.3$ & $54 \pm 17$ \\ KDG073 & $0.40 \pm 0.18$ & $114.6 \pm 0.5$ & $14.2 \pm 1.2$ & $1.23 \pm 0.30$ & $ 1.0 \pm 0.2$ & $0.13 \pm 0.06$ & $0.39 \pm 0.18$ & $ 0.4 \pm 0.2$ & $71 \pm 14$ \\ VCC0381 & $1.07 \pm 0.30$ & $479.8 \pm 0.2$ & $22.9 \pm 1.3$ & $1.45 \pm 0.11$ & $ 1.9 \pm 0.1$ & $0.56 \pm 0.16$ & $0.74 \pm 0.21$ & $ 0.4 \pm 0.1$ & $38 \pm 5$ \\ KK141 & $0.43 \pm 0.18$ & $576.0 \pm 0.8$ & $14.5 \pm 1.8$ & $0.98 \pm 0.19$ & $ 2.4 \pm 0.5$ & $0.61 \pm 0.26$ & $0.98 \pm 0.41$ & $ 0.4 \pm 0.2$ & $45 \pm 11$ \\ KK152 & $1.78 \pm 0.37$ & $834.7 \pm 0.9$ & $30.5 \pm 2.0$ & $1.63 \pm 0.18$ & $ 1.5 \pm 0.2$ & $2.00 \pm 0.42$ & $0.80 \pm 0.17$ & $ 0.6 \pm 0.1$ & $66 \pm 4$ \\ UGCA292 & $11.67 \pm 0.62$ & $309.2 \pm 0.1$ & $24.6 \pm 0.3$ & $3.12 \pm 0.22$ & $ 3.1 \pm 0.2$ & $4.08 \pm 0.22$ & $4.51 \pm 0.24$ & $ 1.3 \pm 0.1$ & $37 \pm 4$ \\ BTS146 & $0.39 \pm 0.15$ & $440.5 \pm 1.8$ & $25.5 \pm 4.3$ & $1.00 \pm 0.15$ & $ 2.9 \pm 0.4$ & $0.66 \pm 0.26$ & $0.56 \pm 0.22$ & $ 0.7 \pm 0.3$ & $59 \pm 7$ \\ LVJ1243+4127 & $0.62 \pm 0.53$ & $403.2 \pm 0.0$ & $16.5 \pm 2.6$ & $1.22 \pm 0.20$ & $ 0.9 \pm 0.1$ & $0.54 \pm 0.46$ & $0.66 \pm 0.56$ & $ 0.5 \pm 0.4$ & $68 \pm 5$ \\ KK160 & $0.51 \pm 0.53$ & $301.6 \pm 0.1$ & $20.0 \pm 3.4$ & $1.45 \pm 0.31$ & $ 2.5 \pm 0.5$ & $0.22 \pm 0.23$ & $0.62 \pm 0.65$ & $ 0.6 \pm 0.6$ & $71 \pm 8$ \\ KKH86 & $0.45 \pm 0.16$ & $285.0 \pm 0.7$ & $15.1 \pm 1.5$ & $1.11 \pm 0.22$ & $ 1.3 \pm 0.3$ & $0.07 \pm 0.03$ & $0.35 \pm 0.13$ & $ 0.9 \pm 0.3$ & $59 \pm 9$ \\ \hline \end{tabular} \label{table3_figgs} \end{table*} In Figure~\ref{momnt1} we present the velocity fields of the detected galaxies. We note that in many cases emission has been detected only across a few channels. As the SNR is poor, we did not take a Gaussian-Hermite polynomial fitting approach to derive the velocity field. Instead we adopted the intensity weighted first moment of the spectral cube as the velocity field. From Figure~\ref{momnt1}, we can see that, there are ordered velocity fields which is an indication of rotation in many galaxies (e.g. AGC112521, LeG06, KDG73, VCC381). But at the same time there are a few galaxies in the sample which show chaotic velocity fields, for example, KKH86, KK160, KKH37. The chaotic appearance of the velocity field could be due to the low SNR and low spatial resolution in the spectral cube. For the same reasons, the PV diagrams are noisy and do not bring out kinematics of the galaxies and hence we do not present them here. \begin{figure} \begin{center} \resizebox{85mm}{!}{\includegraphics{hist_dh1_dopt.pdf}} \end{center} \caption{Histogram of \HI diameters of our sample galaxies normalized to optical diameter. One can see that almost all our galaxies have \HI diameter larger than the optical diameter except one (UGC4879). See the text for more discussion.} \label{dh1_dopt} \end{figure} In Figure~\ref{dh1_dopt} we plot the histogram of \HI diameters of our sample galaxies. To compare the extent of \HI disks with their optical counterparts, we normalised the \HI diameter by the optical diameter ($\rm D_{opt}$) of the galaxies. Isophotal radii e.g. $R_{Holm}$ or $R_{25}$ have limited meaning for dwarf galaxies having low surface brightness. These radii estimates could be prone to systematic under-estimation of their optical extent. Hence we perform photometric analysis of B-band image of our galaxies, and fit the surface brightness profiles with an exponential profile. Adopting a convention by \citep{swaters02}, we define optical radii as 3.2 times exponential scale length. However for four of our detected galaxies (KKH37, LeG06, KDG073 and KKH86), optical photometry (in B band) could not be performed due to poor quality of available data. For these galaxies, we considered Holmberg radius as optical radii. In many previous \HI surveys \citep{broeils97,verheijen01,swaters02,noordermeer05} an isophote of $\rm 1 \ M_{\odot} pc^{-2}$ was adopted for ellipse fitting and estimating the \HI radii. However, most of our detected galaxies, fall short of \HI surface density of $\rm 1 \ M_{\odot} pc^{-2}$ even at the center. We have used an face-on \HI surface density of $\rm 0.3 \ M_{\odot} pc^{-2} \ (3.75 \times 10^{19} \ atoms \ cm^{-2})$ isophote to estimate the \HI diameter. The mean value of normalised \HI diameter is 1.54 which is somewhat lower than the value found for the FIGGS \citep{begum08c} sample which is 2.40. This may be in part to the very faint outer emission being resolved out. From our data, we found that for all our sample galaxies, \HI disk extends more than the optical disk except one. For the galaxy UGC4879, the \HI disk found to be smaller than its optical counterpart. From Figure~\ref{ovrplot} (5th image) we note that, a faint extended \HI emission is seen in the south-east corner, which may be indicative of diffuse emission not picked up in our observations. It is worth noting that for UGC04879 the GMRT observation picks up only about 50\% of the single dish flux. \begin{figure} \begin{center} \resizebox{85mm}{!}{\includegraphics{mh1_dh1.pdf}} \end{center} \caption{The \HI mass (single-dish) of the FIGGS2 sample as a function of \HI diameter (measured at a column density of $\rm 0.3 \ M_{\odot} pc^{-2} \ (3.75 \times 10^{19} \ atoms \ cm^{-2})$ ). The black solid line represents a straight line fit to the FIGGS2 data whereas the magenta dashed line represents a fit to the FIGGS data taken from \citep{begum08c}. The empty symbols in the plot represent data for spiral galaxies taken from literature. As the large spiral galaxies are bright in \HI the $\rm D_{HI}$ for them is defined at a column density of $\rm 1 \ M_{\odot} pc^{-2} \ (1.25 \times 10^{20} \ atoms \ cm^{-2})$. } \label{mh1_dh1} \end{figure} The \HI diameter and the \HI mass of different types of galaxies exhibits a tight correlation. In Figure~\ref{mh1_dh1} we plot the correlation between the \HI diameter and the \HI mass of our sample galaxies (filled blue triangles). As the GMRT resolves out a significant amount of \HI at low column densities at the outer radii (as noted in \S4), we use single-dish \HI flux measurements in Fig.~\ref{mh1_dh1}. To compare the correlation with larger galaxies, we over plot data for spiral galaxies (\HI diameter defined at an \HI surface density of $\rm 1 \ M_{\odot} pc^{-2}$) from various previous \HI surveys \citep{broeils97,verheijen01,swaters02,noordermeer05}. The solid black line represents a linear fit to our (FIGGS2) data whereas the dashed magenta line represents a linear fit for FIGGS survey. It can be seen that due to the small size of our sample galaxies, our study extended this correlation to low mass and low diameter end. From the figure it can be noted that our data points follow the trend for spiral galaxies (hollow points) or for the FIGGS galaxies (magenta dashed line). However, we note that our data points might be affected by the facts that the $\rm D_{HI}$ were measured at a different \HI column density for FIGGS2 and for the spiral galaxies. The best linear fit of $D_{HI}$ vs $M_{HI}$ correlation (black solid line) could be represented by \begin{equation} \log(M_{HI}) = (2.08 \pm 0.20) \log(D_{HI}) + (6.32 \pm 0.07) \label{eq:mh_md} \end{equation} \noindent In Fig.\ref{mh1_dh1} the dashed magenta line represents the correlation for FIGGS galaxies. The slope and the intercept for FIGGS2 galaxies (i.e. $2.08 \pm 0.20$ and $6.32 \pm 0.07$) roughly matches with that of the FIGGS galaxies. In Figure~\ref{mh_mb} we show the $\rm \log (M_{HI}/L_B)$ as a function of $\rm M_B$. Our sample galaxies are shown by filled (GMRT \HI mass) and hollow (Single dish \HI mass) blue triangles, whereas the red hollow asterisks represent the FIGGS sample. The blue hollow squares are from \citet{warren07} and green hollow pentagons are for galaxies from \citet{verheijen01a}. The solid line represents an empirically derived upper limit to the $\rm (M_{HI}/L_B)$ from \citet{warren07}. It can be thought of as a minimum fraction of the baryonic mass to be converted into stars in order to be stable under thermal equilibrium with gravity \citep{warren07} for a galaxy of given baryonic mass. It is interesting to note that all our sample galaxies lies well below the solid line (even with single-dish \HI mass). It implies that these small dwarf galaxies converted much more gas into stars than the minimum required to be stable under the balance of gravity and thermal energy. \begin{figure} \begin{center} \resizebox{85mm}{!}{\includegraphics{logmh_mb.pdf}} \end{center} \caption{The log of \HI-mass-to-light ratio as a function of $\rm M_B$. Blue filled (GMRT \HI mass) and hollow (Single dish \HI mass) triangles are from FIGGS2, red hollow asterisks represent data from FIGGS survey whereas blue hollow squares and green hollow pentagons represent \citet{warren07} and \citet{verheijen01a} respectively. The solid line represents an empirically derived upper limit to $\rm M_{HI}/L_B$ from \citep{warren07}. See text for more details.} \label{mh_mb} \end{figure} In summary we have observed 20 faint galaxies with the GMRT to extend the FIGGS sample towards the low luminosity end. We detected \hi emission from 15 of the galaxies. We find that these galaxies have the similar \hi\ mass to \hi\ diameter relation as the brighter dwarfs. These data will be useful for a host of studies of dwarf galaxies, including the interplay between gas and star formation, the phase structure of the atomic ISM, the structure and distribution of the dark matter halos, etc. | 16 | 9 | 1609.01072 |
1609 | 1609.07181_arXiv.txt | We have conducted a search for L subdwarf candidates within the photometric catalogues of the UKIRT Infrared Deep Sky Survey and Sloan Digital Sky Survey. Six of our candidates are confirmed as L subdwarfs spectroscopically at optical and/or near-infrared wavelengths. We also present new optical spectra of three previously known L subdwarfs (WISEA J001450.17-083823.4, 2MASS J00412179+3547133 and ULAS J124425.75+102439.3). We examined the spectral type and metallicity classification of subclasses of known L subdwarfs. We summarized the spectroscopic properties of L subdwarfs with different spectral types and subclasses. We classify these new L subdwarfs by comparing their spectra to known L subdwarfs and L dwarf standards. We estimate temperatures and metallicities of 22 late-type M and L subdwarfs by comparing their spectra to BT-Settl models. We find that L subdwarfs have temperatures between 1500 and 2700 K, which are higher than similar-typed L dwarfs by around 100--400 K depending on different subclasses and subtypes. We constrained the metallicity ranges of subclasses of M, L, and T subdwarfs. We also discussed the spectral-type and absolute magnitude relationships for L and T subdwarfs. | Metal-deficient very low-mass stars (VLMS) and brown dwarfs (BDs) are primeval populations in the Galaxy's ancient halo, and represent extremes in low metallicity and old age among Galactic populations. They can reveal the fundamental interior structure physics around the substellar mass limit, and are crucial to our understanding of complex ultra-cool atmospheres and the star formation mechanisms of the early Universe. VLMS \citep[$M \loa$ 0.5 M$_{\sun}$;][]{gros74,bara95} are red dwarfs at the low-mass end of the Hertzsprung--Russell diagram's stellar main sequence. BDs are substellar objects with masses below the hydrogen burning minimum mass, which ranges from 0.075 to 0.092 M$_{\sun}$ for solar to primordial metallicities according to theoretical models \citep{bur01}. Primeval VLMS with $M \loa$ 0.1 M$_{\sun}$ and BD have subsolar metallicity and are generally referred to as ultra-cool subdwarfs (UCSDs). VLMS and BDs are classified as M, L, T, and Y types according to spectral morphology that is dominated by temperature-dependent chemistry and thermal emission \citep{kir91,kir99,mart99,bur02,cus11}. A massive BD could be a late-type M dwarf when it is about 0.1 Gyr old, but then cools becoming a late-type L dwarf after about 10 Gyr. L subdwarfs represent the lowest mass stars with subsolar metallicity and also include massive metal-poor BDs \citep[e.g. 2MASS J05325346+8246465, referred to as 2M0532;][]{bur08b}. L subdwarfs \citep[e.g. 2M0532; ][]{bur03} exhibit characteriztic spectral signatures due to strong metal hydrides (e.g. FeH), weak or absent metal oxides (e.g. VO and CO), and enhanced collision-induced H$_2$ absorption \citep[CIA H$_2$;][]{bat52,bor89,bor01,abe12,sau12} in the near-infrared (NIR). Modern large-scale optical and NIR surveys have the capability to identify L subdwarfs, although they are very rare compared to L dwarfs. About 22 L subdwarfs have been reported in the literature from different surveys (see Section \ref{ssspt}). The Two Micron All Sky Survey \citep[2MASS;][]{skr06} observed in three NIR filters ($J, H$, and $Ks$), and searches therein have yielded eight L subdwarfs \citep{bur03,bur04,bur04b,bur08c,cus09,kir10}. \citet{sch04} discovered an L subdwarf by its high proper motion, measured across 2MASS and SuperCOSMOS Sky Survey epochs \citep{hamb01}. The Sloan Digital Sky Survey \citep[SDSS; ][]{yor00} has imaged 14555 deg$^2$ of the sky in five optical bands ($u, g, r, i, z$), yielding several L subdwarfs with $i$ and $z$ band detections. In addition two L subdwarfs have been identified using the SDSS spectroscopic survey \citep[e.g. ][]{siv09,bowl10,sch10,bur10}. The UKIRT Infrared Deep Sky Survey \citep[UKIDSS; ][]{law07} Large Area Survey (hereafter ULAS) has imaged 3500 deg$^2$ of sky in four NIR filters ($Y, J, H$, and $K$), and is about three magnitudes deeper than 2MASS (thus being sensitive to a volume of about 5.5 times larger). UKIDSS has yielded three L subdwarfs to date \citep[e.g. ][]{lod10,lod12}. Most recently the Wide-field Infrared Survey Explorer \citep[WISE;][]{wri10} has revealed eight L subdwarfs \citep{luhm14,kir14,kir16}. Model atmospheres \citep{all95,wit09} have been developed and used to characterize VLMS and BD \citep[e.g.][]{bur09}. The BT-Settl models \citep{alla11,alla13,alla14} cover a wide range of metallicity, and their success at reproducing observed L subdwarf spectral energy distributions (SEDs) suggests that they are an effective means to estimate their atmospheric parameters. The classification scheme for L subdwarfs has not been fully established due to the small number of confirmed objects. A method is proposed to assign spectral types for L subdwarfs by comparing their optical spectra to those of L dwarfs \citep{bur07}. Metallicity subclasses for L subdwarfs are also unclear; however, d/sdL (mildly metal-poor), sdL, and esdL (extremely metal-poor) subclasses have been proposed \citep[e.g.][]{bur07,kir10}, and metallicity-sensitive signatures are observed in a number of L subdwarf spectra \citep[e.g. Fig 29 of][]{kir10}. To properly understand and characterize L subdwarfs, it is necessary to identify a sample that covers a wide range of effective temperature ($T_{\rm eff}$) and metallicity. In this paper we present the discovery of six new L subdwarfs. Our candidate selection process is presented in Section \ref{ssele}. Section \ref{sspec} presents the follow up spectroscopic observations. Section \ref{sclas} describes our spectral classification and characterization of L subdwarfs. Atmospheric properties of UCSDs derived through model comparison are presented in Section \ref{smodel}. Finally, Sections \ref{sdisc} and \ref{ssumm} present further discussion and a summary. \begin{figure*} \begin{center} \includegraphics[angle=0,width=\textwidth]{ijk_sdl_purple1d.pdf} \caption[]{The $i-J$ versus $J-K$ colours of L subdwarfs compared to M and L dwarfs. Filled circles are 14 known L subdwarfs (with updated metallicity subclasses from this paper, red for sdL, blue for esdL, and black for usdL) from the literature with SDSS detections. Filled squares are the six new L subdwarfs (red for sdL, and blue for esdL) from this paper. Red, blue, and black crosses are sdM5-8.5, esdM5-8, and usdM5-7.5 subdwarfs confirmed with SDSS spectra and classified based on \citet{lep07}. A diamond filled with blue is 2MASS J014231.87+052327.3 \citep[2M0142;][]{bur07}. SSSPM 1013-1356 \citep[SSS1013;][]{sch04b} is indicated with a black filled circle and a larger open circle. 2MASS photometry of some known L subdwarfs has been converted into the MKO system according to \citet{hew06}. Some objects do not show error bars because these are smaller than the symbol size. Grey dots are 5000 point sources selected from a 10 deg$^2$ area of UKIDSS with $14<J<16$. Yellow dots are 1820 spectroscopically confirmed late-type M dwarfs (for which mean spectral types are indicated) from \citet{wes08}. Black asterisks are L dwarfs from DwarfArchives.org with UKIDSS and SDSS detections. The BT-Settl model grids \citep{alla14,bara15} with log $g$ = 5.5 (magenta) are over plotted for comparison, with $T_{\rm eff}$ and metallicity being indicated. The dashed cyan lines indicate our $i-J$ and $J-K$ colour selection criteria [equations (3) and (4)].} \label{ijk} \end{center} \end{figure*} \begin{table*} \centering \caption[]{Photometry of six new and five known L subdwarfs in our sample. References: 1 -- this paper; 2 -- \citet{lod12}; 3 -- \citet{kir10}; 4 -- \citet{lod12}; 5 -- \citet{bowl10} and \citet{sch10}. } \label{tsdlm} \begin{tabular}{c c c c c c c c c} \hline Name & SpT & SDSS \emph{i} & SDSS \emph{z} & UKIDSS \emph{Y} & UKIDSS \emph{J} & UKIDSS \emph{H} & UKIDSS \emph{K} & Ref \\ \hline ULAS J021642.97+004005.6 & sdL4~ & 22.14$\pm$0.15 & 20.03$\pm$0.10 & 18.41$\pm$0.05 & 17.30$\pm$0.03 & 16.96$\pm$0.04 & 16.51$\pm$0.04 & 1 \\ ULAS J124947.04+095019.8 & sdL1~ & 20.39$\pm$0.04 & 18.66$\pm$0.04 & 17.62$\pm$0.02 & 16.83$\pm$0.02 & 16.40$\pm$0.03 & 16.12$\pm$0.04 & 1 \\ SDSS J133348.24+273508.8 & sdL1~ & 20.51$\pm$0.05 & 18.75$\pm$0.04 & 17.47$\pm$0.02 & 17.47$\pm$0.02 & 16.62$\pm$0.01 & 16.00$\pm$0.02 & 1 \\ ULAS J133836.97$-$022910.7 & sdL7~ & 22.47$\pm$0.26 & 20.06$\pm$0.14 & 18.56$\pm$0.06 & 17.37$\pm$0.03 & 16.81$\pm$0.04 & 16.37$\pm$0.05 & 1 \\ SDSS J134749.74+333601.7 & sdL0~ & 19.87$\pm$0.03 & 18.06$\pm$0.02 & 16.66$\pm$0.01 & 15.85$\pm$0.01 & 15.46$\pm$0.01 & 15.27$\pm$0.02 & 1 \\ ULAS J151913.03$-$000030.0 & esdL4~~ & 21.46$\pm$0.09 & 19.33$\pm$0.06 & 18.19$\pm$0.03 & 17.21$\pm$0.02 & 17.07$\pm$0.03 & 16.97$\pm$0.04 & 1 \\ \hline ULAS J033350.84+001406.1 & sdL0~ &19.24$\pm$0.02&17.87$\pm$0.02&16.81$\pm$0.01&16.11$\pm$0.01&15.77$\pm$0.01&15.50$\pm$0.02 & 2\\ 2MASS J11582077+0435014 & sdL7~ &21.02$\pm$0.08&18.15$\pm$0.03&16.61$\pm$0.01&15.43$\pm$0.00&14.88$\pm$0.01&14.37$\pm$0.01 & 3\\ ULAS J124425.90+102441.9 & esdL0.5 &19.48$\pm$0.02&18.01$\pm$0.02&16.98$\pm$0.01&16.26$\pm$0.01&16.00$\pm$0.01&15.77$\pm$0.02 & 2 \\ ULAS J135058.86+081506.8 & usdL3 &21.25$\pm$0.08&19.52$\pm$0.06&18.66$\pm$0.05&17.93$\pm$0.04&18.07$\pm$0.10&17.95$\pm$0.15 & 4 \\ SDSS J141624.08+134826.7 & sdL7~ &18.37$\pm$0.02&15.89$\pm$0.02&14.26$\pm$0.00&12.99$\pm$0.00&12.47$\pm$0.00&12.05$\pm$0.00 & 5 \\ \hline \end{tabular} \end{table*} | \label{sdisc} \subsection{Metallicity ranges of the subclasses of M and L subdwarfs} \label{smetal} Metallicity plays an important role in shaping the spectra of VLMS and BD, causing shifts in the spectral types and temperature scale. L subdwarfs are a natural extension of M subdwarfs into lower mass and $T_{\rm eff}$ regimes. M subdwarfs are brighter and more numerous than L subdwarfs, and relatively well characterized; thus, they provide a useful comparison and possible reference for the characterization of L subdwarfs. To determine the metallicity subclasses of M dwarfs and subdwarfs LRS07 used the metallicity index $\zeta_{\rm TiO/CaH}$, and defined four metallicity subclasses: ultra subdwarf (usdM; $\zeta_{\rm TiO/CaH} < 0.2$), extreme subdwarf (esdM; $0.2 < \zeta_{\rm TiO/CaH} < 0.5$), subdwarf (sdM; $0.5 < \zeta_{\rm TiO/CaH} < 0.825$) and dwarf (dM; $\zeta_{\rm TiO/CaH} > 0.825$). The metallicity distributions of these four subclasses became clear when metallicity measurements were made based on optical high-resolution spectra \citep[e.g.][]{wool09}. This allowed a relationship (albeit with a scatter) to be established between $\zeta_{\rm TiO/CaH}$ and iron abundance, which was recently refined by \citet{pavl15} who combined data from \citet{wool06} and \citet{wool09} to give \begin{equation} {\rm [Fe/H]} = 2.00 \times \zeta_{\rm TiO/CaH} - 1.89 \end{equation} with an rms of 0.26. However, equation (8) is valid only for early-type M subdwarfs, because all the objects in the Woolf sample are M0--M3 subdwarfs. We calculated approximate metallicity ranges for the four LRS07 subclasses of M0--M3 subdwarfs using the $\zeta_{\rm TiO/CaH}$ ranges from LRS07 and equation (8) (these are presented in the left-hand side of Table \ref{tmetal}). As we discussed in Section \ref{ssmsd}, the metallicity consistency of $\zeta_{\rm TiO/CaH}$ is tested only for early-type M subdwarfs. The $\zeta_{\rm TiO/CaH}$ index is not a consistent indicator of metallicity across all M subtypes and L types. \begin{figure} \begin{center} \includegraphics[width=\columnwidth]{metallicity_feh_teff3.pdf} \caption[]{[Fe/H] and $T_{\rm eff}$ of M, L, and T subdwarfs. Black dashed lines indicate the boundaries between K, M, L, and T types. Horizontal red, blue, and black dotted lines indicate [Fe/H] boundaries (Table \ref{tmetal}) between early-type dM, sdM, esdM, and usdM derived from fig. 9 of \citet{pavl15}. Objects with $T_{\rm eff} >$ 3500 K (yellow, red, blue and black crosses are for dM, sdM, esdM, and usdM, respectively) are from \citet{wool06} and \citet{wool09}. Objects labelled with numbers `1--6' have metallicity measurements inferred from their primary stars. `1' is G224-58 B \citep{pavl15}; `2' is HD 114762 B \citep{bow09}; `3' is GJ 660.1 B \citep{agan16}; `4' is Hip 73786 B \citep[T6p;][]{murr11}; `5' is WISE 2005+5424 \citep[sdT8;][]{mac13}; and `6' is BD+01$^{\circ}$ 2920 B \citep[T8p;][]{pin12}. The remaining $T_{\rm eff} <$ 3000 K objects are provided in Table \ref{tmodel}. The shaded area indicates the rough [Fe/H] range for the thick disc population, with the thin disc population above and the halo population below. The $T_{\rm eff}$ of some objects has been offset by $\pm$15 K for clarity, if they share the same $T_{\rm eff}$ and [Fe/H] as another object.} \label{mostmp} \end{center} \end{figure} Fig. \ref{mostmp} explores how metallicity subclass distributions map on to the metallicity-$T_{\rm eff}$ plane for M, L and T types. Three black dashed lines indicate the boundaries between K, M, L and T dwarfs/subdwarfs which are derived from spectral type--$T_{\rm eff}$ relationships of late-type M and L dwarfs \citep{fili15} and subdwarfs [equation (7)] augmented with data from \citet{mann15}. Different symbol shapes/colours indicate different spectral subclasses (see caption of Fig. \ref{mostmp}). These late M and L subdwarf subclasses are modified from the literature in Section \ref{ssclass}. We note that there are no L subdwarf benchmark companions currently known, and although there are additional known T subdwarfs in the literature, none have metallicity constraints as robust as the objects shown in the plot. The approximate metallicity ranges of the subclasses of M0--M3 defined by LRS07 are shown as dotted lines in the left side of the plot. It can be seen that these metallicity ranges reasonably bracket the four LRS07 metallicity subclasses (d, sd, esd, and usd), though there is some scatter that leads to each LRS07 subclass spreading into adjacent metallicity ranges (this will be discussed further later in this section). We also establish the approximate metallicity ranges for the subclasses of L subdwarfs (or more generally the $T_{\rm eff} \lid$ 3000 K population). The metallicity range for these UCSDs is [Fe/H] $> -0.3$ and is $-1.0 <$ [Fe/H] $\lid -0.3$ for the sd subclass. These are very similar to the metallicity ranges of the LRS07 dM0-3 and sdM0-3 subclasses. At lower metallicity (for $T_{\rm eff} \lid$ 3000 K), the metallicity range is $-1.7 <$ [Fe/H] $\lid -1.0$ for the esd subclass and is $[Fe/H] \lid -1.7$ for the usd subclass. These cover slightly different metallicity ranges than the (M0--M3) LRS07 esdM and usdM subclasses. By comparison, the kinematic halo population of F, G, and K stars have $[Fe/H] \loa -0.9$ and a metallicity distribution function peaks at $[Fe/H] \approx -1.7$ \citep{lair88,spa10,an13}, well matched to the two lowest metallicity ranges for both classification schemes. And thin disc stars generally have $[Fe/H] > -0.3$ \citep[e.g. from APOGEE; ][]{hay15}, well matched to the highest metallicity range for both schemes. Although the metallicity ranges for the two subclass schemes appear reasonably consistent, there is some evidence that they may not be consistent in the late M regime. The metallicity ranges of the LRS07 subclasses were estimated using M0--M3 subdwarfs, and we note three later dwarfs in the LRS07 esdM subclass that have metallicity well below the approximate range expected from M0-M3 dwarfs. G224-58 B (esdM5.5 according to LRS07) has a significantly lower metallicity than earlier esdM dwarfs, and APM0559 and LEHPM 2-59 have similarly low metallicity and are classified as esdM by LRS07 and usdM in this paper. Changing metallicity ranges within a metallicity subclass is not ideal, and attempts to mitigate against this were made by LRS07 through the use of wide binary systems (whose components should have common metallicity) to help define subclass divisions. However, the lack of subdwarf binaries with early and late M components could have led to metallicity gradients across the LRS07 subtypes. Any such gradients appear to be largely absent from the $T_{\rm eff} <$ 3200 K subclasses scheme. Clearly more binary systems like SDSS J210105.37--065633.0 AB \citep[esdM1.5+esdM5.5;][]{zha13,pavl15} would be very useful if the metallicity subclasses of early-late M subdwarfs are to be refined. Table \ref{tmetal} summarises both subclass schemes, and indicates approximate links between subclasses, metallicity and kinematic populations. \begin{table*} \centering \caption[]{Metallicities ranges of subclasses of early-type M and L dwarfs/subwarfs. } \begin{tabular}{r c c c c r c} \hline\hline $^{a}$Subclass & [Fe/H] & | & Kinematics & | & Subclass & [Fe/H] \\ \hline dM0-3 & $ > -$0.24 & | & Thin disc &| & dL & $ > -$0.3 \\ sdM0-3 & $ (-0.9, -0.24]$ & |& Thick disc &| & sdL & $ (-1.0, -0.3]$ \\ esdM0-3 & $ (-1.5, -0.9]$ & |& Halo &| & esdL & $ (-1.7, -1.0]$ \\ usdM0-3 & $\lid -$1.5 & |& Halo &| & usdL & $\lid -$1.7 \\ \hline \end{tabular} \begin{list}{}{} \item[$^{a}$] Metallicity subclasses of M dwarfs/subdwarfs are based on the classification scheme of LRS07. \end{list} \label{tmetal} \end{table*} \subsection{Absolute magnitudes of L and T subdwarfs} \begin{figure} \begin{center} \includegraphics[width=\columnwidth]{spt_mjmh5.pdf} \caption[]{The relationship between spectral type and $J$- and $H$-band absolute magnitudes (MKO) for L and T subdwarfs. The red solid line is for M--L--T dwarfs \citep{dup12}. The shaded area shows the fitting rms. Three numbers to the left of three sdT companions indicate that [Fe/H] was inferred from their bright primary stars \citep{cena07,roja12,pin12}. Note that sdL7 and sdT7.5 are components of a wide binary SD1416 AB. Error bars for some objects are similar to or smaller than the plotting symbols. } \label{fsptmj} \end{center} \end{figure} In Fig. \ref{fsptmj} we plot $M_J$ and $M_H$ absolute magnitude against spectral type relationships for L and T dwarfs and subdwarfs. The dwarf sequence (red line) comes from \citet{dup12}. These six L subdwarfs with parallax distances are: 2M0532 \citep{bur08b,sch09}, 2M0616 \citep{fah12}, SSS1013, 2M1256, and 2M1626 \citep{sch09}, and SD1416 A \citep{dup12}. To extend the subdwarf sequence into the T dwarf regime, we collected T subdwarfs with direct or indirect parallax measurements from the literature. They are either single objects with parallax distances or companions to bright stars which have parallax distances. The parallax of 2MASS J09373487+2931409 \citep[T6p;][]{bur02} was measured by \citet{sch09}. The parallax of SD1416 B \citep[T7.5p;][]{bur10} was from SD1416 A \citep{dup12}. The parallaxes of Hip 73786 B \citep[T6p;][]{murr11}, BD+01$^{\circ}$ 2920 B \citep[T8p;][]{pin12}, and WISE 2005+5424 \citep[sdT8;][]{mac13} are measured from their primary stars \citep{van07}. It is interesting to compare the dwarf and subdwarf sequences. M0-M5 dwarfs are brighter in the $J$ band than subdwarfs of the same spectral type, while M7-L7 dwarfs are fainter in the $J$ band (see Fig. \ref{fmjh}). Fig. \ref{fsptmj} shows that T dwarfs are brighter in $J$ and $H$ band than sdT subdwarfs of the same spectral type. A larger sample of L and T subdwarfs with parallax distances would allow us to have a better idea of how and why they are different from dwarfs. The sdT subdwarfs have $M_J$ and $M_H$ that are fainter by 1--2 mag when compared to T dwarfs with the same NIR spectral type. Distances of isolated late-type T subdwarfs will be over estimated by 2$\pm$0.5 times, if they are based on relationships between spectral type and $J$ or $H$ absolute magnitude \citep[e.g.][]{dup12,fah12}. \citet{pin14} also noted that the distance constraints (estimated from T dwarf absolute magnitude versus spectral type relations) for two highly $K$ band suppressed fast moving T subdwarfs are much greater when using NIR bands than for mid-infrared bands. | 16 | 9 | 1609.07181 |
1609 | 1609.07148_arXiv.txt | We present new \textit{Chandra X-ray Observatory} and \textit{Hubble Space Telescope} observations of eight optically selected broad-line AGN candidates in nearby dwarf galaxies ($z<0.055$). Including archival \textit{Chandra} observations of three additional sources, our sample contains all ten galaxies from Reines et al. (2013) with both broad H$\alpha$ emission and narrow-line AGN ratios (6 AGNs, 4 Composites), as well as one low-metallicity dwarf galaxy with broad H$\alpha$ and narrow-line ratios characteristic of star formation. All eleven galaxies are detected in X-rays. Nuclear X-ray luminosities range from $L_{0.5-7 \rm{keV}}\approx5\times10^{39}$ to $1\times10^{42}$ $\rm{erg}\rm{s^{-1}}$. In all cases except for the star forming galaxy, the nuclear X-ray luminosities are significantly higher than would be expected from X-ray binaries, providing strong confirmation that AGN and composite dwarf galaxies do indeed host actively accreting BHs. Using our estimated BH masses (which range from $\sim7\times10^{4}-1\times10^{6}~M_{\odot}$), we find inferred Eddington fractions ranging from $\sim0.1-50\%$, i.e. comparable to massive broad-line quasars at higher redshift. We use the \textit{HST} imaging to determine the ratio of ultraviolet to X-ray emission for these AGN, finding that they appear to be less X-ray luminous with respect to their UV emission than more massive quasars (i.e. $\alpha_{\rm OX}$ values an average of 0.36 lower than expected based on the relation between $\alpha_{\rm OX}$ and $2500{\rm \AA}$ luminosity). Finally, we discuss our results in the context of different accretion models onto nuclear BHs. | In the last few years, the number of active galactic nuclei (AGN) identified in dwarf galaxies (i.e., $M_{\ast}\lesssim3\times10^{9}M_{\odot}$) has grown from a handful of quintessential examples (e.g., NGC 4395; \citealt{1989ApJ...342L..11F}, and POX 52; \citealt{2004ApJ...607...90B}) to a body of several hundred candidates (see \citealt{2016arXiv160903562R} for a review). This has largely been possible thanks to large scale optical spectroscopic surveys (e.g., the Sloan Digital Sky Survey; SDSS), which have facilitated the search for AGN signatures in samples of tens of thousands of galaxies (see e.g. \citealt{2004ApJ...610..722G, 2007ApJ...670...92G, 2012ApJ...761...73D}), with the most recent studies concentrating on \textit{bona-fide} dwarf galaxies \citep{Reines:2013fj, 2014AJ....148..136M, 2015MNRAS.454.3722S}. In particular, the most successful searches for AGN in dwarf galaxies have used narrow emission line diagnostics (e.g., the BPT diagram; Baldwin, Phillips \& Terlevich 1989\nocite{1981PASP...93....5B}) to search for photo-ionized gas consistent with the presence of an AGN (see also \citealt{2003MNRAS.346.1055K, 2006MNRAS.372..961K} for commonly used diagnostics). For AGN exhibiting broad H$\alpha$ emission, assuming that the broad line region gas is virialized, it is possible to estimate the mass of the central BHs. Note that, for AGN in dwarf galaxies, this also relies on the assumption that the scaling relation between BH mass and host stellar velocity dispersion \citep{2000ApJ...539L...9F, 2000ApJ...539L..13G} holds in this mass regime \citep{2016arXiv160803893B}. The velocity of the broad line region gas is estimated from the width of the H$\alpha$ line, and the radius to the broad line region is estimated from the luminosity of the broad emission (\citealt{2000ApJ...533..631K, 2004ApJ...613..682P, 2005ApJ...630..122G,2009ApJ...705..199B, 2013ApJ...767..149B}). BH masses in dwarf AGN are typically $\sim10^{5}-10^{6}M_{\odot}$ solar masses (see e.g., \citealt{Reines:2013fj}, \citealt{2016arXiv160505731B}), with the lowest reported having a mass of just $\sim50,000 M_{\odot}$ \citep{2015ApJ...809L..14B}. Despite these recent advances in the identification of AGN in dwarf galaxies, the radiative properties of this population of AGN as a whole are largely unconstrained. Much work has been done exploring the X-ray properties of $\sim10^{6}M_{\odot}$ optically selected AGN from the Greene \& Ho samples \citep{:kx, 2012ApJ...761...73D, 2016ApJ...825..139P}, but these host galaxies tend to be more massive than the dwarf galaxies considered here. Stacking analyses have been used to detect X-ray emission in dwarf galaxies out to z $\approx$ 1.5 \citep{2016ApJ...817...20M, 2016ApJ...823..112P}. Additionally \cite{2016arXiv160301622P} used X-ray observations to search for AGN in dwarf galaxies at z $<1$, finding an AGN fraction of $\sim1\%$. However, we are concerned with following up individual systems in order to obtain a detailed look at the radiative properties of this relatively unexplored population. Determining the radiation properties of actively accreting BHs at the cores of dwarf galaxies is important for several reasons. Firstly, the BHs at the centers of dwarf galaxies may provide clues about galaxy nuclei in the early universe, since they are expected to be similar (to first approximation; see, e.g., \citealt{2011ApJ...742...13B, 2016arXiv160509394H}). With current instrumentation, it is not possible to detect $10^{5}M_{\odot}$ BHs in the earliest galaxies. A BH of this size accreting at its Eddington limit has a bolometric luminosity of $\sim10^{43}~{\rm erg~s^{-1}}$. Assuming it releases $\sim10\%$ of its energy in hard X-rays, the flux reaching us would be an order of magnitude below the detection limit of the 4 Ms Chandra Deep Field South (which has a 2-8 keV flux limit of $5.5\times10^{-17}~{\rm erg~s^{-1}~cm^{-2}}$; \citealt{2011ApJS..195...10X}). Furthermore, searches for AGN at high redshift (z $>6$) find fewer sources than expected based on relations at lower redshift \citep{2015MNRAS.448.3167W}, possibly due to the lower normalization for low-mass galaxies in the BH mass-galaxy stellar mass relation \citep{2015ApJ...813...82R, 2016ApJ...820L...6V}. As an alternative, present-day dwarf galaxies can serve as useful local analogs \citep{2011ApJ...731...55J, Reines:2011fr, 2014ApJ...787L..30R}. Present day dwarf galaxies have likely not undergone any major mergers, and are thus relatively undisturbed and ``pristine" compared to more massive systems. Moreover, studying AGN in dwarf galaxies is useful for understanding the interplay between AGN activity and star formation on all galaxy scales. AGN feedback is expected to have an effect on galaxy scale star formation, particularly in more massive systems (e.g., \citealt{2015ARAA..53..115K}). Feedback from massive stars and/or supernovae is expected to be particularly relevant for dwarf galaxies, but it is unclear what (if any) influence AGN can have on star formation in these smaller systems \citep{2005ApJ...618..569M, 2010MNRAS.401L..19H, 2014MNRAS.445..581H, 2016MNRAS.458..816H}. Studying radiation from AGN in dwarf galaxies is also useful for understanding whether BH accretion had any influence on star formation in the earliest galaxies (see e.g., \citealt{2012MNRAS.423.1325A}), as well as for investigating the contribution of low luminosity AGN to reionization \citep{2009ApJ...698..766M, 2015ApJ...813L...8M}. High resolution X-ray and UV follow-up of these systems is essential for understanding the accretion properties of AGN in dwarf galaxies. If detected, sufficiently bright, point-like nuclear UV/X-ray emission provides strong confirmation of the presence of an AGN (e.g., \citealt{1994ApJS...95....1E}). Additionally, X-ray studies can be used to determine the distribution of Eddington ratios for AGN in dwarf galaxies. Furthermore, the relative strength of the UV and X-ray emission is important for learning about the structure and properties of the accretion disk and corona (\citealt{1979ApJ...234L...9T,2016ApJ...819..154L}). Finally, studies of the broad-band spectra of these objects is necessary for determining the bolometric correction for this class of AGN. Reines et al. (2013) identified 151 dwarf galaxies with narrow and/or broad emission line signatures indicating the presence of an AGN. With the above goals in mind, we analyze \textit{Chandra X-ray Observatory} observations of a sub-sample of these objects, focusing on the most promising broad-line AGN candidates. The paper is organized as follows. In Section 2, we discuss our sample, X-ray and UV observations, and data reduction and analysis. In Section 3, we report on properties of the X-ray and UV emission, including the ratio of X-ray to UV emission. In Section 4, we discuss the origin of the X-ray emission, and compare the properties of our galaxies to more massive quasars. | We analyze \textit{Chandra X-ray Observatory} of 11 broad-line AGN candidates in dwarf galaxies identified in Reines et al. (2013). These include all ten objects with broad and narrow emission line AGN signatures (6 BPT AGN, 4 BPT composite), plus one low-metallicity dwarf galaxy with broad H$\alpha$ but narrow-emission lines dominated by star formation. Three out of eleven objects had \textit{Chandra} observations analyzed in the literature. We analyze new \textit{Chandra} observations of the remaining eight, supplemented by joint HST/WFC3 F275W imaging. Nuclear X-ray emission is detected in all galaxies, i.e. we find a 100\% detection rate. We also find that: \begin{itemize} \item{The detected X-ray nuclei are bright, with $L_{0.5-7\rm{keV}}\approx5\times10^{39} - 1\times10^{42}~\rm{erg~s^{-1}}$. Galaxies in our sample have BH masses in the range of $\sim10^{5-6}M_\odot$; we infer Eddington fractions ranging from $\sim0.1-50\%$, i.e., consistent with the range of Eddington fractions found for massive broad-line quasars. } \item{The observed X-ray emission in broad-line objects falling in either the AGN or composite region of the BPT diagram is brighter than would be expected from HMXBs. We conclude an AGN is the most likely source of the detected X-ray emission.} \item{We emphasize that the observations presented here provide strong evidence that the BPT composite objects (i.e., those thought to have contributions to the narrow-line flux from both star formation and an AGN) do indeed host actively accreting BHs.} \item{Our targets tend to have $\alpha_{\rm OX}$ values lower than expected based on relationships defined by classical quasars. If the measured UV emission is not significantly enhanced by nuclear star formation, AGN in dwarf galaxies seem to be X-ray weak relative to their UV emission.} \end{itemize} | 16 | 9 | 1609.07148 |
1609 | 1609.09363_arXiv.txt | {In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron$-$proton ($e^{-}-p^{+}$) and electron$-$positron ($e^{\pm}$) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of ``global'' jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the $e^{-}-p^{+}$ jet simulation a recollimation-like instability occurs and jet electrons are strongly perturbed. In the $e^{\pm}$ jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields. } \keyword{relativistic jets; particle-in-cell simulations; global jets; helical magnetic fields; kinetic~instabilities; kink instability} % \begin{document} | Relativistic jets are collimated plasma outflows associated with active galactic nuclei (AGNs), gamma-ray bursts (GRBs), and pulsars. Among these astrophysical systems, blazars and GRB jets produce the most luminous phenomena in the universe% ~{(}e.g., \cite{peer14} {)}. Despite extensive observational and theoretical investigations (including simulation studies), our understanding of their formation, % interaction, and evolution in the ambient plasma% ---and consequently their observable properties, such~as time-dependent flux and polarity% ---remains quite limited. One of the key open questions in the study of relativistic jets is how they interact with the immediate plasma environment on the microscopic scale. In particular, we wish to examine how relativistic jets containing helical magnetic fields evolve under the influence of kinetic and {MHD}-like ~instabilities that occur within and at the jet boundaries, with consequences such as flares due to reconnection. Jet outflows are commonly thought to be dynamically hot (relativistic) magnetized plasma flows launched, accelerated, and collimated in regions where Poynting flux dominates over particle (matter) flux \cite{blanz77,mck14}. This scenario involves a helical large-scale magnetic field structure in some AGN jets, which~provides a unique signature in the form of observed asymmetries across the jet width, particularly in the polarization \cite{laing81, aloy00,Clausen11}. Large-scale% ~ordered magnetic fields have been invoked to explain the launching, acceleration, and collimation of relativistic jets from the central nuclear region of an active galaxy \cite{meier08}, and from coalescing and merging compact objects (neutron stars and black holes)% ; e.g., \cite{piran04}. The magnetic field structure and particle composition of the jets are still not well constrained observationally. Circular~polarization (CP; measured as Stokes parameter V) in the radio continuum emission from AGN jets provides a~powerful diagnostic for {the deduction of}% ~magnetic structure and particle composition, because% {---}unlike linear polarization (LP)% {---}CP is expected to remain almost completely unmodified by external screens (e.g.,~\cite{OS13}). Jet particle composition has remained an unresolved issue ever since the discovery of jets. The~two~main candidates are a ``normal'' plasma consisting of relativistic electrons and protons (an~$e^{-}$% {--}$p^{+}$ jet), and a ``pair'' plasma consisting only of relativistic electrons and positrons (an $e^{\pm}$~jet)~\cite{wardle98}. The~detection of circular polarization from the violently variable quasar 3C\, 279 at several epochs, using the Very Long Baseline Array (VLBA) at 15 GHz, has been used by Wardle et al. \cite{wardle98} to argue that the circular polarization is produced by Faraday conversion of linear to circular polarization in the jet plasma. This conversion requires that the energy distribution of the radiating particles extends down to $\gamma_{\min} \ll 100$, and that should imply an $e^{\pm}$ jet. Over the past few years, we have been using a fully self-consistent relativistic particle-in-cell (RPIC) simulation method to investigate collisionless shocks, and the kinetic Kelvin--Helmholtz instability (kKHI) at relativistic jet--sheath shear boundaries, and to calculate the resulting synthetic emission spectra. The RPIC code used in these studies is a modified version of the TRISTAN code~\cite{buneman93}, parallelized with MPI and utilized for various research projects% ~(e.g., \cite{niem08,nishi09,nishi16}). To date, RPIC simulations of the kKHI have been performed in slab \cite{Alves12,Alves14,Alves15,Gris13a,Gris13b, nishi13a,nishi13b,nishi14a,liang13a,liang13b} and cylindrical geometries using periodic boundary conditions \cite{Alves10,nishi14b}. Previously, full-scale shock simulations have not incorporated velocity shear interactions at the jet boundary with the ambient plasma (interstellar medium)% ~(e.g.,~\cite{nishi09}), and~global shock simulations including velocity shear interactions performed to date used only very small simulation boxes \cite{nishi03,nishi05,ng06}. Recently, we performed ``global'' jet simulations involving {the} injection of a~cylindrical unmagnetized jet into an ambient plasma in order to investigate shock (Weibel instability) and velocity shear instabilities (kKHI and {Mushroom instability (MI))} simultaneously \cite{nishi16}. Here we report preliminary results of our new studies of global relativistic jets containing helical magnetic~fields. | Our initial global jet simulations containing helical magnetic fields show new types of growing instabilities for both electron--proton and pair plasma jets. Preliminary results indicate that the presence of helical fields suppresses the growth of the kinetic instabilities, such as the Weibel instability, kKHI, and MI. Instead, new instabilities appear, associated with recollimation shocks and current-driven kink instability. The $e^{-}$ {--}$p^{+}$% ~helically magnetized jet shows recollimation-like shock structures in the current density $J_{x}$, similar to recollimation shocks observed in RMHD simulations containing helical magnetic fields \cite{mizuno15}. The observed modulations in the kinetic energy of jet electrons shown in Figure \ref{px-v}a might correspond to the modulations in the Lorentz factor reported in RMHD studies (see Figure~\ref{singhf4f}a). Additionally, while not shown here, the electron density in the $e^{-}$ {--}$p^{+}$% ~jet shows pile-ups which correspond to recollimation shock structures seen in RMHD simulations. Evidence for {the} growth of a~kink-like instability in the $e^{\pm}$ jet is seen in the $y$-component of magnetic field $B_{y}$ in Figure \ref{ByBxz}b, and is similar to that seen in Figure \ref{singhf4f}b, where helical magnetic fields carried by the jet are disrupted by the growth of the kink instability. Finally, we see evidence that reconnection is taking place in the jets. However, larger-scale and higher-resolution simulations are required to fully resolve the reconnection phenomena and to understand the nature of the new instabilities. Future simulations will be combined with calculations of radiation signatures and polarity, along with variations in space and time \cite{Zhang15,Zhang16}. \vspace{6pt} \supplementary{The following are available online at www.mdpi.com/link, Video S1: Evolution of $J_{x}$ for the $e^{-}-p^{+}$ jet.}% | 16 | 9 | 1609.09363 |
1609 | 1609.07238_arXiv.txt | Since the first confirmed detection of exoplanets in 1992, more than 3500 exoplanets have been found, with the 1000th detection by the $Kepler$ mission announced\footnote{{\tt http://science.nasa.gov/science-news/science-at-nasa\\/2015/06jan\_kepler1000}.} by NASA on January 6th, 2015. With the number of discoveries sky-rocketing, it is adequate to continue studying exoplanets, as well as searching for exomoons, besides identifying habitable zones (HZs). It is also well-known that binary (as well as higher order) systems occur frequently in the local Galactic neighborhood (e.g., Duquennoy \& Mayor 1991, and subsequent studies). Observations show that exoplanets can also exist in binary systems, and might also be orbitally stable for millions or billions of years. There are two types of possible orbits (e.g., Dvorak 1982): planets orbiting one of the binary components are said to be in S-type orbits, while planets orbiting both binary components are said to be in P-type orbits. For example, Kepler-413~b (Kostov et al. 2014) is in a P-type orbit, indicating that the planet is orbiting both stellar components of the binary system. Kepler-453~b (Welsh et al. 2015) also constitutes a transiting circumbinary planet. Planetary S-type orbits have more confirmed detections, such as Kepler-432~b (Oritz et al. 2015). Some of these planets are located within the stellar HZs, as, for example, Kepler-62~f (Borucki et al. 2013); those cases typically receive significant attention due to their potential of hosting alien life. In previous studies, focusing on habitable zones in stellar binary systems, presented by Cuntz (2014, 2015), denoted as Paper I and II, respectively, henceforth, a joint constraint of radiative habitable zones (RHZs, based on stellar radiation) and orbital stability was considered. Moreover, Paper~II also takes into account the eccentricity of binary components. RHZs, including conservative, general and extended habitable zones (therefore referred to as CHZ, GHZ, and EHZ, respectively), are defined in the same way as for the solar system (see Section 2.1). Our paper is structured as follows. In Section~2, we briefly describe the theoretical approach for the calculation of HZs adopted from Paper I and II; however, our work also takes into account revised HZ limits for the Solar System from updated climate models. In Section~3, we present some case studies with fitting equations for identifying the existence of HZs. Our summary will be given in Section~4. | In this study, we explore the requirements for HZs to exist for selected examples of binary systems based on the method given in Paper I and II with updated results for terrestrial climate models obtained by Kopparapu et al. (2013, 2014). Thus, we developed fitting equations to efficiently determine the existence of HZs. Utilizing the fitting equations allows us to identify if the respective HZs is able to exist without the need for cumbersome calculations. Future work will deal with improving the fitting equations for enhanced accuracy. We also plan to have $M_{1}$ and $M_{2}$ as parameters in the fitting equations instead of being fixed values as for now. This will make the fitting equation more useful and applicable. | 16 | 9 | 1609.07238 |
|
1609 | 1609.03154_arXiv.txt | We have obtained simultaneous photometric and spectroscopic observations of the cataclysmic variable 1RXS J064434.5+334451. We have calibrated the spectra for slit losses using the simultaneous photometry allowing to construct reliable Doppler images from H$\alpha$ and \ion{He}{ii} 4686 \AA\@ emission lines. We have improved the ephemeris of the object based on new photometric eclipse timings, obtaining $HJD = 2453403.759533 + 0.26937446E$. Some eclipses present a clear internal structure which we attribute to a central \ion{He}{ii} emission region surrounding the white dwarf, a finding supported by the Doppler tomography. This indicates that the system has a large inclination angle $i=78 \pm 2^{\circ}$. We have also analyzed the radial velocity curve from the emission lines to measure its semi--amplitude, $K_1$, from H$\alpha$ and \ion{He}{ii} 4686 and derive the masses of the components: $M_1=0.82\pm0.06$~M$_{\odot}$, $M_2=0.78\pm0.04$ M$_{\odot}$ and their separation $a=2.01\pm0.06$ $R_{\odot}$. The Doppler tomography and other observed features in this nova-like system strongly suggests that this is a SW Sex-type system. | Cataclysmic variables (CV) are semi-detached binary systems which consists of a white dwarf (WD) primary surrounded by a Keplerian disc accreted from a Roche Lobe-filling late-type secondary star. In systems where the mass transfer is high \citep[$\dot{M}\sim10^{-8}$~M$_{\odot}$~yr$^{-1}$,][]{tow09}, the disc will become steady and remain bright for longer periods, suppressing the typical outbursts of CVs with lower mass transfer. These systems are commonly referred as \textit{nova-like variables} (NL). \citet{tho91} constructed an initial qualitative description of NL systems which possess V-shaped eclipses, single-peaked lines and lags between the photometric and spectroscopic ephemeris, known as SW Sex stars. Recently, this list of properties had been revised in order to account for an increasing variety of systems (including non-eclipsing) that share similar traits\footnote{See D.~W.\ Hoard's Big List of SW Sextantis Stars at \url{http://www.dwhoard.com/biglist}.}. Furthermore, SW Sex stars seem to be the dominant population of systems with orbital periods around 3-4 hr \citep{rod07} and their possible connection to nova eruptions may provide information in the general context of CV evolution \citep{pat13}. 1RXS J064434.5+334451 (hereinafter J0644) is a bright object ($V\sim$13.3), discovered during the Northern Sky Variability Survey by \citet{wea04} (NSVS 7178256), was initially identified as a $\beta$ Lyrae object by \citet{hea08}, but they point out that \citet{sea07} (hereinafter S07) have identified the object as a deep-eclipsing CV with an orbital period of nearly 6.5 hr. The latter authors present the first spectroscopic and photometric study of this object and derive radial velocity semi-amplitudes for the primary and secondary stars, from which they obtained a mass ratio $q=0.78$, and individual stellar masses in the range 0.63-0.69 $M_{\odot}$ for the white dwarf and 0.49-0.54 $M_{\odot}$ for the late--type star. They found that this nova--like resembles a UX UMa or a SW Sex type object. In this paper, we present new spectroscopic and simultaneous photometry of J0644. We revisit the ephemeris of the system based on new observed eclipses, whose shapes are discussed in detail. We discuss the radial velocity measurements of the Balmer H$_{\alpha}$ and the high-excitation \ion{He}{ii} $\lambda 4686$ emission line. We present Doppler tomography reconstructions, calibrated with the simultaneous photometry. Finally, a discussion is made on the classification of the object among the CVs, which point out towards the group of the SW Sex--type stars. | \label{sec:conclusions} We have improved the ephemeris of the object through differential photometry. A slow and short brightening of $\sim$~0.4~mag was observed in 2008. Our radial velocity analysis allowed us to obtain values for the semi-amplitudes of both components of the system. Doppler tomography revealed the \ion{He}{ii} emission arises from the WD and is a good indicator of its radial velocity semi-amplitude. From our adopted values for $K_1$, $K_2$ and $i=78\pm 2^{\circ}$, we find $M_1 = 0.82 \pm 0.06$~M$_\odot$; $M_2 = 0.78 \pm 0.04$~M$_\odot$ and a separation of the binary $a = 2.05 \pm 0.06$~R$_\odot$. We found that the general characteristics of J0644 are consistent with a SW Sex nova-like CV. Follow--up observations, specially simultaneous spectroscopy and photometry, are needed to better understand the nature of this object. | 16 | 9 | 1609.03154 |
1609 | 1609.02222_arXiv.txt | I analyze statistics of the stellar population properties for stellar nuclei and bulges of nearby lenticular galaxies in different environments by using panoramic spectral data of the integral-field spectrograph SAURON retrieved from the open archive of Isaac Newton Group. I estimate also the fraction of nearby lenticular galaxies having inner polar gaseous disks by exploring the volume-limited sample of early-type galaxies of the ATLAS-3D survey. By inspecting the two-dimensional velocity fields of the stellar and gaseous components with running tilted-ring technique, I have found 7 new cases of the inner polar disks. Together with those, the frequency of inner polar disks in nearby S0 galaxies reaches 10\%\ that is much higher than the frequency of large-scale polar rings. Interestingly, the properties of the nuclear stellar populations in the inner polar ring hosts are statistically the same as those in the whole S0 sample implying similar histories of multiple gas accretion events from various directions. | The outer gas accretion is now recognized as a main driver of disk galaxy evolution: neither prolonged star formation observed in disks of spiral galaxies, nor observed chemical abundances in their stars can be explained without continuous gas supply from outside. Indeed, the gas depletion time in nearby spirals is found to concentrate tightly around the value of only 2--3~Gyr \citep{bigiel} while the solar abundance ratios of the disk stellar populations imply the duration of the continuous star formation of more than 3~Gyr. The `G-dwarf paradox' and the absence of the age-metallicity correlation in the thin stellar disk of our own Galaxy \citep{tosi,chiosi} as well as the lowered effective oxygen yield in the disks of other spiral galaxies \citep{pilyugin,dalcanton} require such accretion. However, direct observational findings of outer-gas accretion signatures are rather rare despite we expect these events to happen daily. Perhaps, it would be easier to search for consequences of outer gas accretion in early-type disk galaxies, namely, in S0s, where own gas of the galaxies, usually absent, does not prevent rather long-lived kinematical misalignments between the stellar disks and the accreted gaseous subsystems. One of the most bright phenomena betraying the outer-gas accretion events are {\it inner} polar rings/disks of ionized gas which are embedded deeply into the bulge-dominated area. The presence of some minor species with a decoupled momentum can be explained only by such accretion. The first finding of the inner polar disk was noted by \citet{bettoni} in SB0-galaxy NGC~2217 from the multiple long-slit cross-sections of this barred galaxy; the complex gas kinematics was explained by a strong warp of the gas rotation plane in the center of the galaxy, such that the central gas rotation proceeded in the plane orthogonal to the stellar rotation plane and also to the bar major axis. After the rise of the era of integral-field spectroscopy, the inner polar disks were found also in many unbarred galaxies, in particular: in Sb-galaxy NGC~2841 \citep{silvb97}, in Sb galaxy NGC~7742 \citep{n7742we}, and in isolated Sa-galaxy NGC~7217 \citep{we7217}. They were detected exclusively through the kinematical analysis: the integral-field spectroscopy allowed to determine spatial orientations of the rotation axes both for the stellar and ionized-gas components, and if these rotation axes appeared to be mutually orthogonal, the presence of the inner polar disk could be claimed. Sometimes inner polar rings of the ionized gas could be seen as dust lanes aligned along the minor axes of the isophotes -- in such a way we found 8 inner polar disks in lenticular galaxies whose high-resolution images were provided by the Hubble Space Telescope (HST) \citep{polars0}. The first list of 17 galaxies which were claimed to possess inner polar disks was presented by \citet{inpoldisk}. Now a few dozen of the inner polar gaseous disks are already known, and the time for their statistics has come. \citet{moisrev} has assembled a list of 47 inner polar disks reported by various authors before 2012, and has presented some general properties of the inner polar disks and their host galaxies. Firstly, these disks are indeed polar: though all the gaseous rings whose rotation axes are inclined to the stellar rotation axes by more than 50 deg have been considered, the distribution of the mutual inclinations peaks strongly at 90 deg. Secondly, they can be met mostly in early-type galaxies: more than the half of all known inner polar disks belong to (mostly) lenticular and elliptical galaxies; however a few ones belonging to very late-type dwarfs are also known. Typical radii of the inner polar disks range from 0.2 to 2.0 kpc; the outer boundary is quite real betraying the relation of the inner polar disks to bulge-dominated areas, while the inner limit results from finite spatial resolution of the ground-based integral-field spectroscopy. However, the review by \citet{moisrev} operated with a very heterogeneous sample of casual observational findings. A particular question remains unanswered: what is a frequency of the inner polar disks/rings in the whole ensemble of nearby lenticular galaxies? The answer would help to specify the geometry of the outer-gas accretion and so to identify its sources. In the case of isotropic accretion we would be able to estimate the theoretical fraction of inner polar rings by taking into account their dynamical evolution -- precession and sinking to the main symmetry planes. If the theoretical estimates diverge with the observational statistics, it may be a hint to anisotropic accretion-source distribution -- e.g. accretion from a single neighbor galaxy or multiple minor mergers from the satellite plane. I have undertaken a further attempt to increase the number of the known inner polar disks by using the possibility provided by the integral-field spectral data for a sample of early-type galaxies which have been obtained with the IFU SAURON \citep{sauron} in the frame of the ATLAS-3D survey \citep{atlas3d_1}. The ATLAS-3D sample was volume-limited and complete above the absolute magnitude of $M_K=-21.5$, so I hoped to estimate reliably the frequency of inner polar disks in nearby lenticular galaxies from these data. The data of the ATLAS-3D survey are free for retrieving from the Isaac Newton Group (ING) Archive (CASU Astronomical Data Centre at the Institute of Astronomy, Cambridge) after the end of the proprietary period, and I have retrieved the raw data for about 150 lenticular galaxies, to analyze the kinematics of the stellar and ionized-gas components in the central parts of these galaxies and to search for new cases of the inner polar disks. | I have inspected the central stellar population properties and also the gaseous and stellar kinematics of the volume-limited sample of nearby S0 galaxies observed with the IFU SAURON in the frame of the ATLAS-3D project. I have found seven (7) new cases of nearly polar rotation of the circumnuclear warm-gas disks with respect to the stars. Together with these new findings, I report the presence of 21 inner polar disks among the complete sample of 200 nearby S0s. It means that the frequency of the inner polar gas rotation is about 10\%\ for the early-type disk galaxies in the local Universe that is much higher than the incidence of large-scale polar rings which is $<1$\% \citep{pringcat}. Perhaps, this difference reflects the natural difference between frequencies of minor and major mergers. To my surprise, the properties of the nuclear stellar populations of the inner polar disk hosts are strictly the same as those of the whole sample of nearby S0s. In particular, the age distributions are quite similar, with the most galaxies concentrated around the value of the nuclear stellar age of 1--4~Gyr. It means that despite proposed stability of polar orbits, the gas reached the very centers and provoked recent star formation bursts in the nuclei of the inner polar disk hosts, as it took place in the majority of S0 galaxies. It remains to be understood if the S0 galaxies suffered multiple gas accretion events, with only a single one of them from a polar orbit. | 16 | 9 | 1609.02222 |
1609 | 1609.02152_arXiv.txt | We used ultra-deep $J$ and $K_s$ images secured with the near-infrared GSAOI camera assisted by the multi-conjugate adaptive optics system GeMS at the GEMINI South Telescope in Chile, to obtain a ($K_s$, $J-K_s$) color-magnitude diagram (CMD) for the bulge globular cluster NGC 6624. We obtained the deepest and most accurate near-infrared CMD from the ground for this cluster, by reaching $K_s$ $\sim$ 21.5, approximately 8 magnitudes below the horizontal branch level. The entire extension of the Main Sequence (MS) is nicely sampled and at $K_s$ $\sim$ 20 we detected the so-called MS ``knee'' in a purely near-infrared CMD. By taking advantage of the exquisite quality of the data, we estimated the absolute age of NGC 6624 ($t_{age}$ = 12.0 $\pm$ 0.5 Gyr), which turns out to be in good agreement with previous studies in the literature. We also analyzed the luminosity and mass functions of MS stars down to M $\sim$ 0.45 M$_{\odot}$ finding evidence of a significant increase of low-mass stars at increasing distances from the cluster center. This is a clear signature of mass segregation, confirming that NGC 6624 is in an advanced stage of dynamical evolution. | Globular Clusters (GCs) are complex systems hosting $10^{4}-10^{6}$ gravitationally bound stars, distributed with an approximately spherical geometry. In the central regions of these stellar systems, where stars are forced to live in an extremely dense environment, the probability of stellar encounters is highly enhanced. Such collisions lead to the formation of peculiar objects like Cataclysmic Variables, Low Mass X-ray Binaries (LMXBs), Millisecond Pulsars and Blue Straggler Stars \citep[e.g.][]{Ba92,Pa92,Fe01,Fe09a,Fe12,Ra05,PH06} and they influence the time scales on which mass segregation, core collapse and other dynamical processes occur \citep{Mey97}. The large stellar concentration in the central regions of high density GCs prohibited to resolve individual stars for many years, until the launch of Hubble Space Telescope (HST), which allowed exquisite resolution over a relatively large (a few square arcmin) field of view (FOV) mainly in the optical bands. The investigation of the stellar content of GCs in the bulge of the Galaxy has the additional complication of the presence of thick clouds of dust along the line of sight that almost totally absorb the optical light, and/or the presence of a heavy field star contamination. The exploration of such clusters requires near-infrared (NIR) observations \citep[e.g.,][]{Fe00,Fe09b,Va04a,Val07,Or97,Or11}, a wavelength range where the foreground extinction significantly drops. The observations of such stellar systems in the NIR have tremendously improved with the advent of instrumentation assisted by the new adaptive optics (AO) facilities. These systems, in fact, mainly work in the NIR, where the spatial and temporal coherence of the corrugated wavefront is larger \citep{DK12}, and they are able to compensate the blurriness of the astronomical images due to the Earth's atmosphere by using one or more deformable mirrors and, as reference, natural and/or laser guide stars. The Gemini South Telescope, on Cerro Pach\'on in Chile, currently is the only facility equipped with a Multi-conjugate Adaptive Optics System (named GeMS), which uses three natural guide stars, a constellation of five laser guide stars and two deformable mirrors conjugated at the ground and at an altitude of 9 km \citep[see][]{Rig14,Nei14}. This allows GeMS to (almost) reach the diffraction limit of the telescope. By exploiting the unprecedented capabilities of this system, which works in combination with the NIR high-resolution camera Gemini South Adaptive Optics Imager (GSAOI), we started an observing campaign of a set of GCs located in the Galactic bulge. After the encouraging results obtained for Liller 1 \citep{Sar15}, a heavily obscured cluster located very close to the Galactic plane and center, here we present the results for NGC 6624. This GC is located just at the edge of the inner bulge, at a distance of 7.9 Kpc from Earth (\citealp{Har96}, 2010 edition) and it is characterized by only a moderate foreground extinction for a bulge GC, $E(B-V) = 0.28$ (\citealp{Va04a, Har96}, 2010 edition). These features also make NGC 6624 an ideal target to investigate the sky performance of the GeMS+GSAOI system. NGC~6624 is a well-studied cluster, but mainly in the optical bands \citep[see][]{Sar07,Dal14}. In the NIR it was observed with the following instruments: \begin{itemize} \item[{\it (i)}] IRCAM, mounted at the 2.5 m Du Pont telescope. These observations provided the first ($K_s$, $J-K_s$) CMD of the cluster sampling the brightest portion of the red giant branch (RGB; see \citealp{KF95}) down to the Horizontal Branch (HB) level. \item[{\it (ii)}] IRAC-2 mounted at the ESO 2.2 m telescope MPI. The NIR CMD derived from these observations was deeper than the previous one, reaching the cluster sub-giant branch ($K_s$ $\sim$ 17), and thus allowing to study the RGB features (RGB bump and tip; see \citealp{Va04a, Va04b,Val07,Fer06b}). \item[{\it (iii)}] Within the {\it VISTA Variables in the Via Lactea} (hereafter VVV) survey. The NIR CMD obtained from the VVV catalog was deep enough ($K_s$ $\sim$ 19) to sample the main sequence turn-off (MS-TO) only in the external regions of the cluster \citep{Min10,Cat11}. \end{itemize} NGC 6624 is quite compact and it has been catalogued as a dynamically evolved cluster, which already experienced core collapse \citep{Tra95}. It has been found to harbour six millisecond pulsars \citep[][]{Lyn12,Tam11,Fre11} and at least an ultra-compact LMXB \citep{Dib05}, thus confirming that its dense environment efficiently boosts the formation of exotic objects. In this paper we present ultra-deep NIR observations of NGC 6624 obtained by using the powerful combination of the GeMS+GSAOI devices mounted at the Gemini South Telescope. The paper is organized as follows: in Section \ref{obs} we discuss the observations and the data analysis. In Section \ref{cmd} we present the CMD of the cluster. Section \ref{age} is focused on the determination of the age of the cluster and in Section \ref{luminosity} we discuss the Luminosity (LF) and Mass Functions (MF) of the cluster MS. In Section \ref{concl} we present our conclusions. | \label{concl} This work is focused on NGC 6624, a metal-rich globular cluster located in the Galactic bulge. By combining the exceptional capabilities of the adaptive optics system GeMS with the high resolution camera GSAOI on the GEMINI South telescope, we obtained the deepest and most accurate NIR ($K_s, J-K_s$) and ($J, J-K_s$) CMDs ever obtained from the ground for NGC 6624. The quality of the photometry turns out to be fully competitive with the optical photometry from the HST. The derived CMDs span a range of more than 8 magnitudes, allowing to identify all the well known evolutionary sequences, from the HB level to the MS-TO point down to below the MS-K (detected at $K_s$ $\sim $ 20), a feature observed so far only rarely in the optical band and identified for the first time here in a purely infrared CMD. We took advantage of our high-resolution photometry to get an accurate estimate of the absolute age of NGC 6624, which is still quite debated in the literature. By adopting the MS-TO fitting method, we determined an absolute age of about 12.0 $\pm$ 0.5 Gyr for the cluster. Taking advantage of this high-quality sample, we studied the MS-LF and MF at different distances from the cluster center. The level of completeness of the MS sample has been evaluated from artificial star experiments and turns out to be larger than 50\% down to $K_s\sim 20.3$ at any distance from the cluster center. The completeness-corrected and field-decontaminated LFs and MFs show significant signatures of mass segregation. In fact, moving from the innermost region of the cluster to the outskirts, the number of low-mass stars gradually increases compared to high-mass stars. This result confirms that NGC~6624 is a dynamically old cluster, already relaxed. The data obtained for NGC 6624 clearly show that, under favorable conditions (for example the seeing of the observing night or the NGSs magnitude), the GeMS/GSAOI system is able to provide images with similar spatial resolution and photometric quality as HST in the optical bands. \begin{appendices} | 16 | 9 | 1609.02152 |
1609 | 1609.09076_arXiv.txt | A planet orbiting in the "habitable zone" of our closest neighboring star, Proxima Centauri, has recently been discovered, and the next natural question is whether or not Proxima~b is``habitable". Stellar winds are likely a source of atmospheric erosion that could be particularly severe in the case of M dwarf habitable zone planets that reside close to their parent star. Here we study the stellar wind conditions that Proxima~b experiences over its orbit. We construct 3-D MHD models of the wind and magnetic field around Proxima Centauri using a surface magnetic field map for a star of the same spectral type and scaled to match the observed $\sim 600$~G surface magnetic field strength of Proxima. We examine the wind conditions and dynamic pressure over different plausible orbits that sample the constrained parameters of the orbit of Proxima~b. For all the parameter space explored, the planet is subject to stellar wind pressures of more than 2000 times those experienced by Earth from the solar wind. During an orbit, Proxima~b is also subject to pressure changes of 1 to 3 orders of magnitude on timescales of a day. Its magnetopause standoff distance consequently undergoes sudden and periodic changes by a factor of 2 to 5. Proxima~b will traverse the interplanetary current sheet twice each orbit, and likely crosses into regions of subsonic wind quite frequently. These effects should be taken into account in any physically realistic assessment or prediction of its atmospheric reservoir, characteristics and loss.\\ | \label{s:intro} The recent discovery of the planet Proxima~b orbiting in the nominal ``habitable zone" of our nearest stellar neighbor \citep{Anglada-Escude.etal:16} presents a unique opportunity to further study and infer the properties and the evolutionary path of exoplanets. It has been pointed out that it is sufficiently close to Earth as to be directly observable by the next generation of space telescopes such as WFIRST and JWST, in addition to planned 30-meter class ground-based telescopes \citep{Barnes.etal:16,Kreidberg.Loeb:16}. Proxima b is estimated to be of at least 1.3 Earth masses ($M\sin i=1.3 M_\Earth$) and have an orbital period of 11.2 days with a semi-major axis of only 0.049~AU---twenty times closer to Proxima than the Earth is to the Sun \citep{Anglada-Escude.etal:16}. Apart from its approximate mass and orbital parameters, rather little is currently known about Proxima~b itself, although a handful of studies have already examined its likely irradiation history and possible climate and evolution in relation to potential habitability \citep{Ribas.etal:16,Turbet.etal:16,Barnes.etal:16,Meadows.etal:16}. The current view of the ``habitable" zone of a star is limited to a rather narrow definition of the range of orbital distances over which a planet might have liquid surface water (e.g., \citealt{Kasting.etal:93}). Of special additional importance for planets around M dwarfs such as Proxima (M5.5V) is the potential for such a habitable zone planet to retain any surface atmosphere at all over a sufficiently long period of time that renders habitability of practical interest. M dwarfs are potentially awkward places for atmospheres to survive because their UV, EUV and X-ray (hereafter UEX\footnote{We purposely avoid the acronym XUV that has sometimes been adopted as a shorthand for the UV to X-ray bands due to potential confusion with its common historical use to describe the extreme ultraviolet band covering approximately 100 to 912~\AA.}) radiation that can drive atmospheric photoevaporation \citep[e.g.][]{Lammer.etal:03,Penz.Micela:08,Owen.Jackson:12} stays proportionally larger in relation to their bolometric luminosity for much longer than higher mass Sun-like stars \citep[e.g.][]{Wright.etal:11,Jackson.etal:12}. While photoevaporation of planetary atmospheres due to parent stellar radiation has been relatively well-studied in limited regimes, the stellar magnetic activity responsible for the corrosive UEX radiation also drives stellar winds and coronal mass ejections (CMEs) that could be even more perilous to atmospheric survival \citep[e.g.][]{Khodachenko.etal:07,Lammer.etal:07}. In earlier work, we have applied a state-of-the-art magnetohydrodynamic (MHD) stellar wind and magnetosphere models to begin to investigate the space environment and its atmospheric impact for planets in the habitable zones of active M dwarf stars \citep{Cohen.etal:14,Cohen.etal:15}. These studies introduced generic magnetized and non-magnetized terrestrial planets. Here, we perform the first step in this process and apply similar stellar wind modeling to estimate the space weather conditions experienced at the orbit of Proxima b. | We illustrate the wind structure resulting from our simulations in Figure~\ref{fig:3d} for each magnetic field scaling: the first one with 600~G field amplitude and the second one with 600~G average field. The blue surface shows the Alfv\'en surface, while the plane corresponds to the current sheet with a color coding that reflects the dynamic wind pressure $\rho \cdot v^{2}$ normalized to that of the typical solar wind pressure at 1~AU ($\sim 10^{-8} gr/( cm \cdot s^2) $ or 1 nanoPascal). Only one of the modeled orbits is shown illustratively in each plot to avoid confusion, and selected magnetic field lines are plotted in gray. The wind speeds obtained by our model are not dramatically different to the solar wind ones---up to 1300~km~s$^{-1}$ for the lower magnetic field case and up to 1600~km~s$^{-1}$ for the higher magnetic field case compared to 800--900~km~s$^{-1}$ for the fast solar wind \citep{McComas.etal:07}. However, the densities at Proxima b's orbital distance are 100 to 1000 times larger than the densities for the solar wind at 1~AU (1--10~cm$^{-3}$). Consequently, the dynamic pressure at the orbital distance of Proxima~b is very high, and three to four orders of magnitude higher than that experienced by the Earth. The wind dynamic pressure exceeds the magnetic pressure by about an order of magnitude at high latitudes and by up to three orders of magnitude close to the current sheet. \begin{figure*}[][h] \center \includegraphics[trim = 1in 2.5in 0.9in 2.5in,clip, width = 0.48 \textwidth]{3d_centaury_orbit10_025} \includegraphics[trim = 1in 2.5in 0.9in 2.5in,clip, width = 0.48 \textwidth]{3d_centaury_orbit10_05} \caption{Three-dimensional stellar magnetosphere and wind for Proxima corresponding to a maximum (left) and mean (right) magnetic field of $600$~G (see text). The Alfv\'en surface is shown in blue and the plane corresponds to the current sheet, which is colored according to the wind dynamic pressure normalized to that of the sun at $1$~AU. An orbit with Proxima b's semi-mayor axis of $0.049$~AU, $10$~deg inclination, and eccentricity of $0.1$ is shown in black while selected magnetic field lines are gray.} \label{fig:3d} \end{figure*} Figure~\ref{fig:planes} shows the dynamic wind pressure in the plane of the different orbits considered. In all cases, the planet resides in dynamic wind pressures reaching over a thousand times the one we experience at Earth and passes through large pressure variations over an orbit. In Figure~\ref{fig:pressure} we quantify the pressure as a function of orbital phase for the different orbits examined and for each magnetic field strength. For the lower magnetic field strength case, all orbits go through a wind pressure change of at least a factor of 1000, while for the stronger magnetic field the variability is smaller but still of at least a factor of 10. In 7 out of 8 cases, the orbits reside close to, but outside of, the Alfv\'en surface. For the stronger magnetic field, the orbit of $i = 60$~deg and $e = 0.2$ touches, and maybe crosses, the Alfv\'en surface for a small fraction of its orbital period. The true Alfv\'en surface will be fairly dynamic and depend on the exact wind conditions at any given time. The strong dependence of the Alfv\'en surface size on the magnetic field strength and the likely variation of this, together with the recently detected magnetic cycles \citep{Wargelin.etal:16}, suggest Proxima~b is likely to encounter transitions between subsonic and supersonic wind conditions quite frequently. \citet{Cohen.etal:14} found that the lack of a bow shock in subsonic conditions leads to much deeper penetration of the wind into the magnetosphere than in supersonic conditions. Proxima~b is then likely to experience episodes of deep wind penetration. While even the Earth can occasionally experience short periods of time under sub-Alfv\'enic wind conditions \citep[e.g.,][]{Chane.etal:15}, the extreme dynamic pressure of the wind conditions for Proxima~b renders the potential effects much more drastic. \citet{Vidotto.etal:14b} also found changes in the ambient dynamic pressure in their investigation of M~dwarf winds in planetary habitable zones. However, the dynamic pressure changes we find are orders of magnitude greater than the factor of 3 variations they found. Their wind models were based on an initially spherically-symmetric Parker-type thermally-driven wind \citep{Parker:58} with which the magnetic field subsequently interacts and are quite spatially smooth with densities and pressure variations of factors of only a few. The models employed here are instead driven by a magnetic field dependent energy deposition that results in a much more spatially variable wind. \begin{figure*}[][h] \center \includegraphics[trim = 1in 0.2in 0.9in 0.1in, clip, width = 0.49 \textwidth]{2d_GJ51_B025_10deg_hr} \includegraphics[trim = 1in 0.2in 0.9in 0.1in,clip, width = 0.49 \textwidth]{2d_GJ51_B025_60deg_hr}\\ \includegraphics[trim = 1in 0.2in 0.9in 0.1in,clip, width = 0.49 \textwidth]{2d_GJ51_B05_10deg_hr} \includegraphics[trim = 1in 0.2in 0.9in 0.1in,clip, width = 0.49 \textwidth]{2d_GJ51_B05_60deg_hr} \caption{Wind pressure normalized to the solar wind at $1$~AU for two different orbits of Proxima~b ($e=0.1, 0.2$) with $i=10$~deg (left panel) and $i=60$~deg (right panel) for a maximum (top panel) and mean (bottom panel) magnetic field of $600$~G. The white line represents the Alfv\'en surface.} \label{fig:planes} \end{figure*} The salient effect of the extreme wind pressure at the location of Proxima~b is a compression of its magnetosphere. As we show below, the magnetopause of Proxima~b lies at a distance between 1 and 5 planetary radii, with average distances likely being 2 to 3 radii. This is very close to the planet compared with the Earth's magnetopause at about 10 planetary radii, and creates conditions for potentially strong atmospheric stripping by the stellar wind \citep{Cohen:15}. The variations in the magnetopause location due to secular dynamic pressure variations are also expected to drive strong currents in the magnetosphere and ionosphere, and cause heat deposition and particle precipitation down to the upper atmosphere \citep{Kivelson.Russell:95}. In order to better understand how the changes in wind pressure might impact the magnetosphere of Proxima~b, we computed the approximate magnetopause standoff distance as a function of orbital phase for the different orbits considered (see Figure~\ref{fig:standoff}), assuming pressure equilibrium between the stellar wind and the planet's magnetic field \citep[e.g.,][]{Schield:69,Gombosi:04} $$R_{mp}/R_{planet}=[B_p^2/(4\pi P_{SW})]^{1/6},$$ where $R_{mp}$ is the radius of the magnetopause, $R_{planet}$ is the radius of the planet, $B_p$ refers to the planet's equatorial magnetic field strength, and $P_{SW}$ is the ram pressure of the stellar wind. We find that for all the modeled orbits and for both stellar magnetic field scalings, the magnetopause distance changes over the orbit by a factor $>2$ for an Earth-like magnetic field and a factor $> 4$ for a magnetic field of 0.1~G consistent with the \cite{Zuluaga.Bustamante:16} assessment for Proxima~b. These rapid changes happen twice each orbit as the planet passes through the equatorial streamer regions of dense wind and high dynamic pressure on a timescale as short as a day. The magnetopause standoff distance also depends on the strength and orientation of the interplanetary magnetic field relative to that of the planetary field \citep[e.g.][]{Dungey:61,Schield:69,Holzer.Slavin:78}. The magnetopause is eroded by the transfer of magnetic flux from the day side magnetosphere into the magnetotail through interaction with interplanetary field of opposite polarity. In the case of the Earth's magnetosphere, \citet{Holzer.Slavin:78} found that flux transfer resulted in magnetopause changes similar to those caused by solar wind pressure variations. Proxima~b is likely to traverse the current sheet twice each orbit (see Figure~\ref{fig:3d}), and the consequent polarity change in the interplanetary magnetic field will add an additional magnetopause change term with a timescale of several days. \citet{Cohen.etal:14} found that large variations in dynamic pressure like those we find for Proxima~b lead to Joule heating at the top of the atmosphere at a level of up to a few percent of the stellar irradiance. The heating was also enhanced in their time-dependent planetary magnetosphere model because of the additional current generated by the temporal changes in the magnetic field. The timescale of the variations for Proxima~b are only of the order of a day. Further detailed and physically realistic modeling is needed in order to asses the full impact of these geomagnetic effects on a planetary atmosphere. \begin{figure*} \center \includegraphics[ width = 0.78\textwidth]{GJ51_B025_pressure_orbangle} \includegraphics[width = 0.78\textwidth]{GJ51_B05_pressure_orbangle} \caption{Stellar wind pressure for the four modeled orbits ($e=0.1, 0.2$ and $i=10, 60$~deg) for GJ 51 with a maximum (top panel) and mean (bottom panel) magnetic field of $600$~G.} \label{fig:pressure} \end{figure*} \begin{figure*} \center \includegraphics[ width = 0.8\textwidth]{GJ51_B025_rmp_orbtime} \includegraphics[width = 0.8\textwidth]{GJ51_B05_rmp_orbtime} \caption{Magnetosphere radius normalized to the planet's radius for the four modeled orbits ($e=0.0, 0.2$ and $i=10, 60$~deg for GJ 51 with a maximum (top panel) and mean (bottom panel) magnetic field of $600$~G. The solid line corresponds to a planetary magnetic field like the earth's of $0.3$~G while the dashed line corresponds to a planetary magnetic field of $0.1$~G, expected for Proxima b.} \label{fig:standoff} \end{figure*} \citet{Wargelin.etal:16} have recently detected a magnetic cycle with a period of 7 years in Proxima. The nature of the detection in the form of secular changes in $V$ magnitude implies that the cycle modulates the surface starspots. \citet{Garraffo.etal:15} have shown that spots can close down what would have been open magnetic field, altering the wind mass and angular momentum loss. It is likely that Proxima~b's space environment will then also be subject to associated changes in the magnetic field of its host star. \cite{Ribas.etal:16} and \citet{Barnes.etal:16} have performed a detailed study based on the orbital evolution and estimated irradiation history pf Proxima~b and concluded that different formation scenarios could lead to a range of situations from dry planets to Earth-like water contents to waterworlds. \cite{Turbet.etal:16} studied two likely rotation modes (tidally locked and 3:2 resonances) reaching the conclusion that, for both synchronous and non-synchronous rotation, there are scenarios which would allow liquid water to be present. Other studies have aimed at understanding the likely climate, photosynthetic properties and observational discriminants of the atmosphere of Proxima~b \citep{Goldblatt:16,Lopez.etal:14, Meadows.etal:16,Kreidberg.Loeb:16}. We have shown here that space weather conditions of Proxima~b are extreme and very different to those experienced on Earth. Further work is needed in order to investigate the atmospheric loss processes and rates of Proxima~b and to assess the likelihood that the planet has retained an atmosphere at all. | 16 | 9 | 1609.09076 |
1609 | 1609.09289_arXiv.txt | A generalized teleparallel cosmological model, \\$f(T_\mathcal{G},T)$, containing the torsion scalar $T$ and the teleparallel counterpart of the Gauss-Bonnet topological invariant $T_{\mathcal{G}}$, is studied in the framework of the Noether Symmetry Approach. As $f(\mathcal{G}, R)$ gravity, where $\mathcal{G}$ is the Gauss-Bonnet topological invariant and $R$ is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, $f(T_\mathcal{G},T)$ contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether Symmetry Approach allows to fix the form of the function \\ $f(T_\mathcal{G},T)$ and to derive exact cosmological solutions. | \label{uno} Extended theories of gravity are semi-classical approaches where the effective gravitational Lagrangian is modified, with respect to the Hilbert-Einstein one, by considering higher order terms of curvature invariants, torsion tensor, derivatives of curvature invariants and scalar fields (see for example \cite{RepProgPhys,PhysRepnostro, OdintsovPR, annalen}). In particular, taking into account the Ricci, Riemann and Weyl invariants, one can construct terms like $R^2,$ $R^{\mu\nu}R_{\mu\nu},$ $R^{\mu\nu\delta\sigma}R_{\mu\nu\delta\sigma}$, $W^{\mu\nu\delta\sigma}W_{\mu\nu\delta\sigma},$ that give rise to fourth-order theories in the metric formalism \cite{stelle,arturo}. Considering minimally or nonminimally coupled scalar fields to the geometry, we deal with scalar-tensor theories of gravity \cite{faraoni,maeda}. Considering terms like $R\Box R,$ $R\Box^k R$, we are dealing with higher-than fourth order theories \cite{schmidt,lambiase}. $f(R)$ gravity is the simplest class of these models where a generic function of the Ricci scalar $R$ is considered. The interest for these extended models is related both to the problem of quantum gravity \cite{PhysRepnostro} and to the possibility to explain the accelerated expansion of the universe, as well as the structure formation, without invoking new particles in the matter/energy content of the universe \cite{annalen,stelle,arturo,faraoni,maeda,schmidt,lambiase,cianci,greci,supernovae1,supernovae2,quintessence}. In other words, the attempt is to address the dark side of the universe by changing the geometric sector and remaining unaltered the matter sources with respect to the Standard Model of Particles. However, in the framework of this "geometric picture", the debate is very broad involving the fundamental structures of gravitational interaction. Just to summarize some points, gravity could be described only by metric (in this case we deal with a metric approach), or by metric and connections (in this case, we are considering a metric-affine approach \cite{francaviglia}), or by a purely affine approach \cite{purely}. Furthermore, dynamics could be related to curvature tensor, as in the original Einstein theory, to both curvature and torsion \cite{hehl}, or to torsion only, as in the so called {\it teleparallel gravity} \cite{teleparallel}. Starting from these original theories and motivations, one can build more complex Lagrangians, by using different combinations of curvature scalars and their derivatives, or topological invariants, such us the Gauss-Bonnet term, $\mathcal{G}$, as well as the torsion scalar $T$. Many theories have been proposed considering generic functions of such terms, like $f({\cal G})$, $f(T)$, $f(R, {\cal G})$ and $f(R, T)$ \cite{FGRgravity,17,18, 21,antonio,felixquint, double,ft,Kofinas:2014owa,fRT,sebastian,cimento,hamilton,pla2,marek, Capozziello:2009te, 2011GReGr..43.2807S, stabile1, zerb}. However, the problem is {\it how many} and {\it what kind} of geometric invariants can be used, and furthermore what kind of physical information one can derive from them. For example, it is well known that $f(R)$ gravity is the straightforward extension of the Hilbert-Einstein which is $f(R)=R$ and $f(T)$ is the extension of teleparallel gravity which is $f(T)=T$. However, if one wants to consider the whole information contained in curvature invariants, one has to take into account also combinations of Riemann, Ricci and Weyl tensors\footnote{Clearly, this means that we are not considering higher-order derivative terms like $\Box R$, or derivative combinations of curvature invariants.}. As discussed in \cite{double}, assuming a $f(R, {\cal G}$ theory means to consider the whole curvature budget and then all the degrees of freedom related to curvature. Assuming the teleparallel formalism, a $f(T_{\cal G},T)$ theory, where $T_{\cal G}$ is the torsional counterpart of the Gauss-Bonnet topological invariant, means to exhaust all the degrees of freedom related to torsion and then completely extend $f(T)$ gravity. It is important to stress, as we will show below, that the Gauss-Bonnet invariant derived from curvature differs from the same topological invariant derived from torsion in less than a total derivative and then the dynamical information is the same in both representations. According to this result, the topological invariant allows a regularization of dynamics also in the teleparallel torsion picture (see \cite{double, PhysRevD.28.1876} for a discussion in the curvature representation). The layout of the paper is the following. In Sec.\ref{tre}, we sketch the basic ingredients of the $f(T_{\cal G},T)$ theory showing, in particular, the equivalence between $T_{\cal G}$ and $\cal G$. Sec.\ref{noether} is devoted to derive the cosmological counterpart of the theory and to the derivation of the Noether symmetry. The specific forms of $f(T_{\cal G},T)$ function, selected by the Noether symmetry, are discussed in Sec. \ref{selection}. Cosmological solutions are given in Sec. \ref{solutions}. Conclusions are drawn in Sec.\ref{conclusion}. | \label{conclusion} In this paper, we discussed a theory of gravity where the interaction Lagrangian consists of a generic function $f(T_{\mathcal{G}},T)$ of the teleparallel Gauss-Bonnet topological invariant, $T_{\mathcal{G}}$, and the torsion scalar $T$. The physical reason for this approach is related to the fact that we want to study a theory where the full budget of torsional degrees of freedom are considered. Furthermore, it is easy to show that, from a dynamical point of view, the Gauss-Bonnet invariant, derived from curvature, $\cal G$, and the Gauss-Bonnet invariant, derived from torsion, $T_{\mathcal{G}}$, are equivalent and then we can consider a $f({\mathcal{G}},T)$ theory. After these considerations, we searched for Noether symmetries in the cosmology derived from this model. We showed that specific forms of $f(\mathcal{G},T)$ admit symmetries and allow the reduction of the dynamical system. In particular, the class $f(\mathcal{G},T)= f_0 \mathcal{G}^kT^{1-k}$ results particularly interesting and, depending on the value of $k$, it is possible to achieve all the behaviors of standard cosmology as particular solutions. Clearly, other cases can be considered and a systematic approach to find out other solutions can be pursued. This will be the argument of a forthcoming paper where a general cosmological analysis will be developed. | 16 | 9 | 1609.09289 |
1609 | 1609.08185_arXiv.txt | Recent observations of exoplanets have shown that Super-Earths are common \citep{Batalha2014,Dressing2015}, and water is expected to be a major bulk constituent for many of them. Water and CO$_2$ have been found to be common both in protoplanetary disks \citep{Pontoppidan2014} and in comets in our own solar system \citep{Bockelee2004} so it is natural to assume that they will be important components in water planets as well. Geochemically, CO$_2$ in water planets has largely been treated in the framework of silicate weathering, representing direct analogies to the Earth \citep[e.g.][]{Abbot2012,Alibert2013,Wordsworth2013}. However, for a planet to be analogous to the Earth, its water mass fraction must be kept very small. Therefore the majority of water planets are probably not Earth-like, and the geochemistry of CO$_2$ needs further study. We consider water planets with masses similar to the Earth and lacking a substantial hydrogen atmosphere. For such bodies, if the mass fraction of water is greater than $\sim 1\%$ the pressure at the bottom of the water layer will be high enough so that high-pressure ice polymorphs will form \citep{Levi2014}. As a result there would be no direct contact between the liquid ocean and the silicate interior \citep[as in Type $1$ planets discussed by][for modelling the Kepler-$62$e,f exoplanets]{Kaltenegger2013}, and the ocean would have very low total alkalinity. This would limit the formation of bicarbonate and carbonate ions \citep{CarbonCycle}, making dissolved CO$_2$ the dominant carbon bearing molecule in the water planet's ocean. In this paper we consider the case of a secondary atmosphere outgassing, in particular the outgassing of CO$_2$. In section $2$ we discuss the solubility of freely dissolved CO$_2$ in water, in the entire pressure-temperature domain expected in water planet oceans. The solubility is derived both outside the SI CO$_2$ clathrate hydrate thermodynamic stability field and when in equilibrium with this phase. In section $3$ we model the thermodynamic stability field for the SI clathrate hydrate of CO$_2$, for the entire parameter space relevant to water planet oceans, and compare it with the most up to date data. In section $4$ we explore the different potential reservoirs for CO$_2$ at the ocean bottom in water planets. In section $5$ we calculate the power required to maintain an oceanic overturning circulation, and estimate the feasibility of vertical ocean mixing in water planets. In section $6$ we investigate the ocean-atmosphere flux of CO$_2$, and derive steady state values for the partial atmospheric pressure of CO$_2$. The effect of the wind-driven circulation is the subject of subsection $6.1$ and the effect of sea-ice forming at the poles is quantified in subsection $6.2$. The results are discussed in section $7$ and a summary is given in section $8$. | Our model for the SI CO$_2$ clathrate hydrate yields cage occupancies as a function of pressure and temperature. For the pressure range of a few tens of bars some experiments suggest that the small cage occupancy is lower than predicted by our model (see figs.\ref{fig:OccupPorb} and \ref{fig:CO2AbundClath}). Cage occupancies are part of our model for the solubility of CO$_2$ in water while in equilibrium with the clathrate hydrate phase. This possible discrepancy at a few tens of bars suggests our derived solubility may be exaggerated by approximately $8$\%, for this pressure range. However, our geophysical model relies more on the solubility in equilibrium with the clathrate phase for pressures above hundreds of bars. Hence we do not expect this uncertainty to introduce a considerable error into the geophysical model. Recent experiments \citep{Bollengier2013,Tulk2014} indicate that rather then separating to CO$_2$ ice and water ice under high pressure the SI clathrate hydrate of CO$_2$ transforms into a new phase with a similar crystallographic structure as of the filled ice of methane. This new phase is probably stable up to $1$\,GPa. Since at the moment little is known of this new phase quantifying its influence is impossible and more experimental data is needed. Because this new filled ice phase becomes unstable at pressures above $1$\,GPa it probably does not play a significant role in the transport of CO$_2$ from the deep mantle outward. It may play a role in setting the mechanical properties of the upper boundary layer of the ice mantle convection cell, and thus the dynamics of the ocean bottom. A filled ice sub-layer may act as extra storage for CO$_2$, in addition to the clathrate layer. CO$_2$ that may become available to the ocean if it tries to unsaturate. In the $\beta$ domain (see fig.\ref{fig:alphabetagamma}), if the ocean's bottom is composed of filled-ice of CO$_2$, then one should ask what solubility of CO$_2$ is enforced in the overlying ocean due to this new phase. If this solubility is higher than the value we estimate for the equilibrium with the clathrate hydrate phase, then an elevated clathrate layer should still form. This clathrate layer then controls the solubility in the ocean, clearing any supersaturation by forming clathrate grains. Only if the newly discovered filled-ice phase enforces a lower solubility, then supersaturation with respect to clathrates will not be achieved and a mid-ocean clathrate layer will not form. It is interesting to note here that for the case of CH$_4$ when going from a cage clathrate to filled-ice the guest to water-host abundance ratio increases \citep{lovedaynat01}. This is also true for the filled-ice of hydrogen, though with more complexity at intermediate pressures due to multiple cage occupancies \citep[see][and references therein]{Qian2014}. If this trend is also true for CO$_2$ it may suggest the necessary supersaturation required for clathrate formation within the ocean can be achieved. A full dynamical investigation of this hypothesized mid-ocean clathrate layer is beyond the scope of this work. However, if such a layer can form and become thick and stable it may isolate internal processes from the upper ocean. As a consequence, atmospheric observations may predominantly act as probes into the nature of this layer. Thus potentially severing connections between the deep mantle and atmospheric observations. In subsection \ref{subsec:FluxesWindDriven} we also introduce a possible loss of atmospheric CO$_2$ due to erosion. This is measured in bars lost per Myr, and denominated in the text as $Q_c$. \cite{Pierrehumbert2010principles} has suggested that a high flux of energetic photons in a close orbit around an M-dwarf star could result in some loss of CO$_2$ from the planetary atmosphere. A small planet the size of Mars could be stripped off entirely of its primordial CO$_2$ atmosphere due to the action of solar winds. In the latter case $8$\,bar of CO$_2$ could be lost in a $1$\,Gyr \citep{Pierrehumbert2010principles}, giving $Q_c\approx 0.01$\,bar\,Myr$^{-1}$. The efficiency of erosion of CO$_2$ out of the atmosphere must be compared with the efficiency of the internal reservoirs of CO$_2$ in the deep ocean to replenish what is lost. For $Q_c$ in bars Myr$^{-1}$ and a deep ocean vertical eddy diffusion coefficient, $D_{eddy}$, in cm$^2$ s$^{-1}$ we find that only when $Q_c/D_{eddy}>40$ the effect of atmospheric erosion becomes prominent. For $Q_c/D_{eddy}>100$ the atmosphere can be completely eroded of its CO$_2$ content. A value larger than $100$ for $Q_c\approx 0.01$\,bar\,Myr$^{-1}$ is only possible if the deep ocean vertical eddy diffusion coefficient is close to its minimal possible value. One should also consider that very high values for the ratio $Q_c/D_{eddy}$ are probably more likely for a young M-dwarf star while it is still very active. Therefore, for more mature planetary systems the internal outgassing of CO$_2$ should control the pressure of CO$_2$ in the planet's atmosphere. We note that if cometary composition is a good approximation for the primordial composition of a water planet's ice mantle, then a $20$\,bar CO$_2$ atmosphere, around a $2$M$_E$ planet with a $50$\% ice mass fraction, represents a very small fraction of about $0.01-0.1$\% of the total ice mantle budget of CO$_2$. A caveat to this approximation is the possibility that high-pressure chemistry in the deep ice mantle may change the primordial partitioning of carbon between the different carbon bearing molecules, according to the redox state of the mantle. This issue was not yet addressed and may change the given percentage margin we estimate here. Partial filling of the sea-ice composite pore space by water would expel back into the atmosphere the pore space gaseous content. These are the molecular species that while in the pore space did not experience any forcing to become enclathrated. For example, this includes O$_2$ and N$_2$, which have clathrate dissociation pressures much higher than that for CO$_2$ \citep{Kuhs2000}. Therefore, removal of atmospheric gas by the sinking of sea-ice works selectively on CO$_2$. As we explain in subsection \ref{subsec:FluxesSeaIce} the partial atmospheric pressure of CO$_2$ likely has a minimum value as a function of the subpolar surface temperature (see fig.\ref{fig:SteadyStateWithIce} and its related text for more detailed information). The minimum in the atmospheric pressure of CO$_2$ and the subpolar surface temperature corresponding to this minimum depend on the sea-ice grain morphology. This is clearly seen in figs.\ref{fig:TspTsbtCold1}-\ref{fig:TspTsbtHot1} where we have plotted atmospheric isobars of CO$_2$ as a function of the subtropic and subpolar surface temperatures. Whether this intricate behaviour produces a negative or a positive feedback mechanism requires coupling our model to a radiative-convective atmospheric model. We will address this issue quantitatively in future work. The greenhouse effect increases the surface temperature when more CO$_2$ enters the atmosphere. However, increased Rayleigh scattering takes over at some threshold causing cooling of the surface when more CO$_2$ is added. Therefore, the greenhouse effect has a maximum \citep{Kasting1993}. Various investigations of this phenomenon place the threshold at about $8$\,bar of CO$_2$ \citep{Kasting1993,Kopparapu2013,Kitzmann2015}. This does not include the effect of clouds which are difficult to account for in 1-D radiative-convective models for the atmosphere \citep{Kopparapu2013}. The threshold also depends on the type of star, and other molecular species in the atmosphere. Nevertheless, it is interesting to note that the threshold may fall somewhat above the minimal value we find for the partial atmospheric pressure of CO$_2$, versus the subpolar surface temperature, for initial ice Ih grains smaller than $400\mu$m (see figs.\ref{fig:TspTsbtCold1}-\ref{fig:TspTsbtHot1}). Thus a water rich planet experiencing a reduction in stellar irradiation, causing a drop in high latitude surface temperatures, may respond by increasing the abundance of CO$_2$ in its atmosphere while the greenhouse effect is still dominant. If the drop in high latitude surface temperatures is too big, so as to cause a shut down of the sea-ice sink mechanism, the abundance of CO$_2$ in the atmosphere may spiral to values where Rayleigh scattering becomes dominant causing further cooling of the surface. In this work we find there are two end scenarios for the steady state atmospheric pressure of CO$_2$: one controlled by the polar sea-ice and the other by the wind-driven circulation and the deep ocean CO$_2$ saturation values. The transition between these two end scenarios happens when the initial sea-ice grain sizes are on the order of hundreds of micrometers (see fig.\ref{fig:SwReal}). This grain size is not unreasonable, and is found in natural environments \citep[e.g.][]{klapp2007}. Therefore, experiments for our studied system are required in order to resolve this issue. The likely SI CO$_2$ clathrate hydrate bottom of the ocean has a mass density allowing it to sit stably at the deep ocean, and moderate the abundance of CO$_2$ dissolved in the ocean. In other words, it makes sure the ocean stays saturated if it tries to unsaturate. We therefore conclude that a sub-bar CO$_2$ atmosphere around water-rich ocean exoplanets is less likely. Our results suggest the atmosphere has two discrete states: one of a few bars of CO$_2$, probably no less than $2$\,bar and a second discrete state where the planet is surrounded by tens of bars of CO$_2$. Which state is materialized depends on what ocean-atmosphere flux mechanism is dominant, polar sea-ice in the first case and wind-driven circulation in the second case. The pressure-temperature conditions within the ice mantle of a $2$M$_E$ planet are probably not high enough to induce the dissociation of CH$_4$. The incorporation of CH$_4$ in filled-ice aids in its transport across the ice mantle, if solid state convection is established \citep{Levi2014}. Therefore, it is likely that CH$_4$ locked in the deep ice mantle would reach the bottom of the ocean, in ocean exoplanets, and then the atmosphere. This outgassed CH$_4$ may potentially effect our model. For example, its existence in the atmosphere may effect the composition and dynamics of the sea-ice. If the partial atmospheric pressure of CH$_4$ exceeds the dissociation pressure of SI CH$_4$ clathrate hydrate for the subpolar surface temperature (e.g. $8.2$\,bar for $240$\,K), then CH$_4$ as well may become enclathrated within the sea-ice. Because the mass density of SI CH$_4$ clathrate hydrate \citep[$0.912$\,g\,cm$^{-3}$, see][]{cox} is less than that of liquid water it will contribute to the buoyancy of the sea-ice. Thus, sea-ice migration to warmer climate may become enhanced, resulting in an increased abundance of CO$_2$ in the atmosphere. Such a mechanism may limit the CH$_4$/CO$_2$ ratio in the atmosphere. Such an analysis may help astronomers pinpoint ocean exoplanets. Another way in which CH$_4$ may influence our model is by becoming a part of the clathrate layer in the deep ocean. This will effect the abundance of CO$_2$ in this layer. Now, some clathrate hydrate cages will be filled with CO$_2$ and others with CH$_4$. As a consequence the solubility of CO$_2$ in equilibrium with the clathrate phase may change, influencing the solubility of CO$_2$ in the overlying ocean, and its atmospheric abundance. It would also be important to know how the addition of CH$_4$ varies the mass density of the ocean's bottom clathrate layer, especially, whether this decreases its mass density below that of the water-rich liquid. We hope to address this ternary system in the future. | 16 | 9 | 1609.08185 |
|
1609 | 1609.03542_arXiv.txt | Using high dispersion high quality spectra of HD 30963 obtained with the echelle spectrograph SOPHIE at Observatoire de Haute Provence in November 2015, we show that this star, hitherto classified as a B9 III superficially normal star, is actually a new Chemically Peculiar star of the HgMn type. Spectrum synthesis reveals large overabundances of Mn, Sr, Y, Zr , Pt and Hg and pronounced underabundances of He and Ni which are characteristic of HgMn stars. We therefore propose that this interesting object be reclassified as a B9 HgMn star. | HD 30963 (V =7.23 mag) ,currently assigned an B9 III spectral type, is one of the slowly rotating late B we are currently observing. This star has been little studied: one only finds 10 references in SIMBAD for HD 30963. The incentive of this project is to reclassify the late B stars in the northern hemisphere brighter than V=7.5 mag with low apparent projected velocities (less than 60 $\kms$). We have previously undertaken a similar survey of the slowly rotating early A stars,.whose results are published in \cite{Royer14}. An abundance analysis of high resolution well exposed spectra of these objects has sorted out the sample into 17 chemically normal stars (ie. whose abundances do not depart more than $\pm$ 0.20 dex from solar values), 12 spectroscopic binaries and 13 Chemically Peculiar stars (CP). Among the new CP stars, \cite{Monier15} and \cite{Monier2016} have identified 5 new HgMn stars. We present here new abundance determinations for HD 30963, a slowly rotating late B star and show that this star is another new HgMn late B star. | Whereas it was up to now classified as a normal late B9 III star, our analysis of HD 30963 shows that it has very peculiar over and underabundances. The overabundances in Mn, Sr, Y, Zr, Pt and Hg are characteristic of an HgMn star. It displays large overabundances of the Sr, Y and Zr triad which is however inverted compared to the solar system triad. The synthesis of the Hg II and Pt II lines reveals large overabundances of Pt and Hg. We are currently performing a detailed abundance analysis of HD 30963 to complement the first abundances presented here. | 16 | 9 | 1609.03542 |
1609 | 1609.04823_arXiv.txt | The Milky Way (MW) and M31 both harbor massive satellite galaxies, the Large Magellanic Cloud (LMC) and M33, which may comprise up to 10 per cent of their host's total mass. Massive satellites can change the orbital barycentre of the host-satellite system by tens of kiloparsecs and are cosmologically expected to harbor dwarf satellite galaxies of their own. Assessing the impact of these effects depends crucially on the orbital histories of the LMC and M33. Here, we revisit the dynamics of the MW-LMC system and present the first detailed analysis of the M31-M33 system utilizing high precision proper motions and statistics from the dark matter-only Illustris cosmological simulation. With the latest {\em Hubble Space Telescope} proper motion measurements of M31, we reliably constrain M33's interaction history with its host. In particular, like the LMC, M33 is either on its first passage ($\rm t_{inf}$ < 2 Gyr ago) or if M31 is massive ($\geq2 \times 10^{12}$ \Msun), it is on a long period orbit of about 6 Gyr. Cosmological analogs of the LMC and M33 identified in Illustris support this picture and provide further insight about their host masses. We conclude that, cosmologically, massive satellites like the LMC and M33 are likely completing their first orbits about their hosts. We also find that the orbital energies of such analogs prefer a MW halo mass $\sim$$1.5\times10^{12}$ \Msun and an M31 halo mass $\geq1.5\times10^{12}$ \Msun. Despite conventional wisdom, we conclude it is highly improbable that M33 made a close (< 100 kpc) approach to M31 recently ($\rm t_{peri}$ < 3 Gyr ago). Such orbits are rare (< 1 per cent) within the 4$\sigma$ error space allowed by observations. This conclusion cannot be explained by perturbative effects through four body encounters between the MW, M31, M33, and the LMC. This surprising result implies that we must search for a new explanation for M33's strongly warped gas and stellar discs. | \label{sec:intro} Both the Milky Way (MW) and M31 host systems of satellite dwarf galaxies that are relics of their assembly history. These satellite galaxies are typically assumed to exert minimal gravitational forces on their hosts or on each other. As such, satellites are often considered point mass tracers of their host potentials. However, this assumption breaks down if the total mass of the satellite is a significant fraction of the host mass. The MW and M31 both host such massive satellites, the Large Magellanic Cloud (LMC) and M33, respectively. With stellar masses of 3-5 $\times 10^9$ \Msun, both galaxies are cosmologically expected to have dark matter masses of order $10^{11}$ \Msun, roughly 10 per cent of the total mass of the MW or M31 \citep{moster13}. While we generally think of satellites as being heavily affected by their hosts (via tides, ram pressure, etc.), massive satellites can in turn affect the dynamics and structure of their hosts as well. They can induce warps in the host galactic disc \cite[e.g. ][]{weinberg98,weinberg06}, shift the orbital barycentre of the host-satellite system by tens of kiloparsecs \cite[e.g. ][hereafter G15]{gomez15}, and are cosmologically expected to host dwarf satellite galaxies of their own \citep{sales13, deason15}. The past orbital trajectory of these galaxies is critical to understanding the origin of and magnitude to which these effects play a role in the dynamical history of the Local Group. More specifically, the accretion time, number of pericentric approaches, and the host-satellite separation at those pericentric passages are key determinants for these phenomena. The survivability of satellites in the environment of their host haloes is also directly connected to the time-scale over which satellites approach and potentially interact with their hosts. Knowledge of warps in the gas discs of the MW and M31 date back to the mid-20$\rm^{th}$ century \citep[e.g. ][]{oort58, roberts75, newton77}. Both warps reach heights up to several kiloparsecs above the disc plane. Several authors have argued that the LMC could be responsible for inducing the warp in the MW's disc \citep[e.g. ][]{weinberg98, weinberg06, tsuchiya02} or whether the influence of other satellites, such as the Sagittarius dSph, also play a role in this phenomena \citep{laporte16, gomez13}. Similarly, M31 satellites are suspects in the formation of the warp in M31's gas disc and other prominent substructures, such as its star forming ring \citep{block06, fardal09}. M33 being the most massive of those satellites may contribute to the current structure of M31's warped disc if it once reached a similar pericentric distance as the LMC ($\sim$50 kpc). On a lower mass scale, satellites of massive satellite galaxies could have similar impacts on their dwarf hosts if their orbits allow for close passages \citep[e.g. the LMC's disc may be warped owing to interactions with the Small Magellanic Cloud;][]{besla12,besla16}. In 2015, a slew of ultra-faint dwarf galaxy candidates were discovered in the Southern hemisphere, many of which are located in close proximity to the LMC \citep{bechtol15, koposov15, martin15, dwagner15, kim15a, kim15b}. Several studies have suggested that the new ultra-faint dwarfs are dynamical companions of the LMC \citep[e.g. ][]{deason15, jethwa16, martin15}. This association depends directly on the orbital history of the LMC and its purported system of satellites about the MW \citep{sales11}. For example, in a first infall scenario for the LMC, there has not been enough time for the MW's tides to disrupt the infalling system and consequently remove traces of common orbital trajectories and similar kinematics. Whether M33 may harbor faint satellite companions today will similarly depend sensitively on its orbital history about M31. As massive satellites approach distances within tens of kpc from their hosts, the high mass ratio of the system becomes exacerbated. For example, at a separation of 50 kpc, the total mass of the LMC may be up to 25 per cent of the MW mass enclosed within a similar radius. G15 illustrate that the MW experiences a strong gravitational influence due to the massive LMC residing nearby. As a result, the orbital barycentre of the MW-LMC sloshes back and forth over Gyr time-scales--this effect can also modify the orbital planes of other MW satellites like the Sagittarius dSph (G15). The M31-M33 system is similarly susceptible to this gravitational effect, as \citet{dierickx14} have shown for the past M31-M32 orbital history. Thus a constraint on the closest passage of M33 about M31 is crucial to understanding the current and future dynamics of M31 and its satellites. Furthermore, the host-satellite separation determines the morphological impact that processes such as tidal stripping will have on the satellite. The time-scales over which satellite galaxies deplete their gas reservoirs and cease forming stars (quenching) is also sensitive to the orbital histories of the satellites about their hosts \citep[e.g. ][]{wetzel14, wetzel15}. It is curious that the MW and M31 both host a massive, gas-rich satellite at distances where other satellites are gas poor. These abundant gas reservoirs suggest that the LMC and M33 have only recently been accreted by their hosts. A recent accretion scenario is consistent with proper motion measurements of the LMC \citep{k13,b07} and cosmological expectations \citep{bk11, busha11, gonzalez13}. However, to date the orbital history of M33 about M31 has not been similarly examined. A scenario under which M33 makes a close passage to M31 is presented by \cite{mcconnachie09} and \citet{putman09}. The gas and stellar discs of M33 are substantially warped. These studies require that M33 made a close (50-100 kpc) encounter with M31 in the past 3 Gyr. We will use these models as a foundation to our assessment of M33's orbital history in analytic models and cosmological simulations. To date, a rigorous, simultaneous study of the orbital history of M33, both numerically and cosmologically, has not been conducted. The major missing component for such an analysis has been a precise measurement of M31's proper motion. Recent {\em Hubble Space Telescope (HST)} observations have constrained the tangential velocity of M31 to $\rm v_{tan}=17\pm17$ \kms \citep{sohn12,vdm12ii}. Others have inferred the tangential velocity component of M31 by using the kinematics of M31 satellites \citep{vdmG08, salomon16}, and the latter reports a value as high as $\rm v_{tan}\!\sim\!150$ \kms. The discrepancy between these values has severe implications for the history and current state of the Local Group. Depending on its orbital history, M33 may help minimize this discrepancy or it may simultaneously impact the motions of other M31 satellites, further complicating such analyses. M33's proper motion was measured recently by \cite{brunthaler05} using the {\em Very Long Baseline Array (VLBA)}. Together, the proper motion measurements of M33 and M31 allow us to constrain the relative motion of the two galaxies, enabling us to quantify the plausibility of a recent, close M31-M33 encounter for the first time. In this study we develop a self-consistent picture linking the observed morphological structure of M33 and the LMC with their numerically derived orbital histories and statistics from the {\em Illustris} cosmological simulation \citep{nelson15, vogelsberger14B, vogelsberger14A, genel14}. We will constrain the orbit of M33 using the latest astrometric data and place it in a cosmological context for the first time. We also compare the similarities and differences in the orbital properties of the two most massive satellite galaxies in the Local Group. Using orbits extracted for massive satellite analogs in the dark matter-only Illustris simulation, we will not only place their present-day kinematics in a cosmological context, but also their full orbital histories. Finally, we assess the impact of massive satellites on the structure of their hosts, on other satellites, and discuss implications of this picture regarding their own morphological evolution. This paper is structured as follows. Section~\ref{sec:observed} highlights the observed properties of the LMC and M33 including their morphology, proper motions, and mass estimates. In Sections~\ref{sec:analyticmethods} and~\ref{sec:orbitanalysis}, we develop and analyse orbital histories for each host-satellite system based on astrometric data. Section~\ref{sec:illustris} describes the Illustris simulation and our sample selection methods for host-satellite analogs. Section~\ref{sec:orbitalprops} compares the average dynamical properties of the LMC and M33 to the cosmological sample of massive satellite analogs. Section~\ref{sec:discussion} assesses the viability of a close M31-M33 encounter in both a cosmological context and in light of the astrometric data. Finally, Section~\ref{sec:conclusions} contains our final remarks on the link between proper motions, analytic orbital models, and cosmological analogs for massive satellite galaxies and their hosts. This is the first in a pair of affiliated papers. In Paper II (Patel et al. 2016b), the orbits of massive satellite analogs in cosmological simulations are used to constrain the halo mass of the MW and M31. While this has been previously done for the MW-LMC by \citet{bk11,busha11,gonzalez13}, we will constrain the mass of M31 for the first time in this fashion. | \label{sec:conclusions} The orbital evolution of massive satellite galaxies, and specifically those of the LMC and M33, have been explored in three contexts in this work: by numerically integrating their orbits backwards in time using astrometric data, by studying a large sample of massive satellite analogs in the Illustris-Dark simulation \citep{nelson15, vogelsberger14A, vogelsberger14B, genel14}, and by determining their consistency with orbital expectations informed by morphology. We have explored plausible orbital histories for the LMC and M33 about the MW and M31, respectively, using their observationally constrained velocity error space and backward integration schemes (e.g. B07, G15). The recently determined proper motion of M31 (S12) has enabled the study of M33's orbital history for the first time in this fashion. We find consistency with previous studies of LMC's orbital history. If the MW's total mass is < $1.5 \times 10^{12}$ \Msun, the LMC is on its first approach to the MW and only recently completed its first pericentric passage. Surprisingly, we find that M33 is either also completing its first orbit about M31, or if M31 is massive (>$2 \times 10^{12}$ \Msun) then it is on a long period orbit. Note that in this study we have adopted a new dynamical friction approximation \citep{vdm12iii}, which reduces the orbital decay of satellite trajectories as their gravitational softening lengths and masses increase. From our sample of massive satellite analogs in Illustris-Dark, we find that the orbital energetics and eccentricities of the LMC and M33 are generally consistent with a recent infall scenario (\tcross < 4 Gyr). Comparing the kinematics from recently updated LMC proper motion measurements to the orbital energies of the massive satellite analogs in Illustris-Dark, we find that a MW halo mass of $\sim$1.5$\times 10^{12}$ \Msun is preferred for recently accreted satellites. Early accretion for an LMC analog is cosmologically likely only if the MW's halo mass is >$3\times 10^{12}$ \Msun. Applying the same analysis using M33's kinematics favors an M31 halo mass $\geq1.5\times10^{12}$ \Msun if M33 is accreted recently. Early accretion of M33 is only plausible at the 20 per cent level if M31's halo mass is $\sim\!3\times10^{12}$ \Msun. Therefore, first infall is certainly favored from energetics alone. These results are generally consistent with the results of the numerical orbit integrations. We conclude that both the LMC and M33 are most likely completing their first orbits about their hosts. The MW's halo mass is likely $\sim1.5 \times 10^{12}$ \Msun. M31's halo mass is likely $\geq1.5\times10^{12}$ \Msun. Paper II will focus on estimating the most typical halo masses for the MW and M31 based on the LMC and M33's present-day orbital angular momentum. We will apply Bayesian inference methods to analogs in the Illustris-Dark simulation to compute the posterior distribution of halo mass from satellite properties via importance sampling and kernel density estimation. The orbital eccentricities of LMC and M33 cosmological analogs were extracted directly from the merger trees and also computed using the instantaneous position and velocity of the satellite, treating the satellite as a point mass. We find markedly different results in the correlation between eccentricity and infall time. In particular, the weak correlation between infall time and eccentricity computed from orbital trajectories implies that eccentricity should not be used to characterize satellites by early and late infall times. Our orbital analysis further reveals that M33 is unlikely to have reached closer than 100 kpc to M31, regardless of its orbital history. This is at odds with conventional models, where M33 is expected to have approached within 50-100 kpc of M31 in order to reproduce its observed warped morphology (P09, M09). We find that orbits recovering this scenario are $\sim$2.5$\sigma$ outliers from the mean $v_Y$ and $v_Z$ components of M33's velocity vector relative to M31 (representing only 0.14 per cent of orbits recovered by sampling the full error space 10,000 times in a Monte Carlo fashion). Upon testing these conclusions when M31 is modeled with a total mass near its predicted upper limit of $3\times10^{12}$ \Msun, we still find that the orbits suggested by M09 and P09 are rare within the proper motion error space explored in this paper. Furthermore, high mass host haloes (>$2.5\times 10^{12}$ \Msun) are cosmologically rare in this orbital configuration. Cosmologically, recently accreted massive satellite are about equally likely to have made recent (< 3 Gyr), close (< 100 kpc) encounters as recent wide encounters (> 100 kpc). There is no cosmological preference for either case. 32.42 per cent of such recently accreted massive satellite analogs have encounters < 55 kpc--i.e. the LMC's orbit, which brings it within 50 kpc of the MW, is not cosmologically rare. From the combined numerical integration and cosmological analysis of M33's orbit, we propose that other sources of its warped disc should be investigated (i.e. other M31 satellites, ram pressure stripping, etc.). While the proper motions generally do not support a recent, close interaction between M33 and M31, the few numerically integrated orbits that do support this scenario are not consistent with the M31 tangential velocity components measured directly with HST (S12) or inferred by satellite kinematics (S16). More precise M31 proper motion measurements are necessary to disentangle M33's true orbital history. The orbital histories of the four most massive members of the Local Group are computed simultaneously to demonstrate that the LMC's trajectory has not been significantly perturbed by M31, nor M33 by the MW during the last 6 Gyr. Allowing the MW and M31 to move freely in these integrations also demonstrates that the LMC and M33 change the velocity of their hosts by tens and sometimes up to a hundred kilometers per second in just the last 2 Gyr, which may have important implications for the inferred orbital histories of their other satellites (e.g. G15), such as those used in S16 to infer properties of M31. We conclude that the third and fourth most massive members of the Local Group, M33 and the LMC, respectively, are recent interlopers in the environment of their hosts. Such recent infall scenarios suggest they should both still contain a majority of their cosmological infall masses ($\sim$10 per cent of their host's mass) today. Therefore, we must account for their dynamical influence on all other MW and M31 satellites. | 16 | 9 | 1609.04823 |
1609 | 1609.03210.txt | Data Release 5 (DR5) of the Radial Velocity Experiment (RAVE) is the fifth data release from a magnitude-limited ($9< I < 12$) survey of stars randomly selected in the southern hemisphere. The RAVE medium-resolution spectra ($R\sim7500$) covering the Ca-triplet region (8410-8795\,\AA) span the complete time frame from the start of RAVE observations in 2003 to their completion in 2013. Radial velocities from 520\,781 spectra of 457\,588 unique stars are presented, of which 255\,922 stellar observations have parallaxes and proper motions from the Tycho-Gaia astrometric solution (TGAS) in {\it Gaia} DR1. For our main DR5 catalog, stellar parameters (effective temperature, surface gravity, and overall metallicity) are computed using the RAVE DR4 stellar pipeline, but calibrated using recent K2 Campaign 1 seismic gravities and Gaia benchmark stars, as well as results obtained from high-resolution studies. Also included are temperatures from the Infrared Flux Method, and we provide a catalogue of red giant stars in the dereddened color $(J-Ks)_0$ interval (0.50,0.85) for which the gravities were calibrated based only on seismology. Further data products for sub-samples of the RAVE stars include individual abundances for Mg, Al, Si, Ca, Ti, Fe, and Ni, and distances found using isochrones. Each RAVE spectrum is complemented by an error spectrum, which has been used to determine uncertainties on the parameters. The data can be accessed via the RAVE Web site or the Vizier database. | The kinematics and spatial distributions of Milky Way stars help define the Galaxy we live in, and allow us to trace parts of the formation of the Milky Way. In this regard, large spectroscopic surveys that provide measurements of fundamental structural and dynamical parameters for a statistical sample of Galactic stars, have been extremely successful in advancing the understanding of our Galaxy. Recent and ongoing spectroscopic surveys of the Milky Way include the RAdial Velocity Experiment \citep[RAVE,][]{steinmetz06}, the Sloan Extension for Galactic Understanding and Exploration \citep[SEGUE,][]{yanny09}, the APO Galactic Evolution Experiment \citep[APOGEE,][]{eisenstein11}, the LAMOST Experiment for Galactic Understanding and Exploration \citep[LAMOST,][]{zhao12}, the Gaia--ESO Survey \citep[GES,][]{gilmore12} and the GALactic Archaeology with HERMES \citep[GALAH,][]{desilva15}. These surveys were made possible by the emergence of wide field multi-object spectroscopy (MOS) fibre systems, technology that especially took off in the 1990s. Each survey has its own unique aspect, and together form complementary samples in terms of capabilities and sky coverage. Of the above mentioned surveys, RAVE was the first, designed to provide stellar parameters to complement missions that focus on astrometric information. The four previous data releases, DR1 \citep{steinmetz06}, DR2 \citep{zwitter08}, DR3 \citep{siebert11} and DR4 \citep{kordopatis13} have been the foundation for a number of studies which have advanced our understanding of especially the disk of the Milky Way \citep[see review by][]{kordopatis14}. For example, in recent years a wave-like pattern in the stellar velocity distribution was uncovered \citep{williams13} and the total mass of the Milky Way was measured using the RAVE extreme-velocity stars \citep{piffl14a}, as was the local dark matter density \citep{bienayme14, piffl14b}. Moreover, chemo-kinematic signatures of the dynamical effect of mergers on the Galactic disk \citep{minchev14}, and signatures of radial migration were detected \citep{kordopatis13b, wojno16}. Stars tidally stripped from globular clusters were also identified \citep{kunder14, anguiano15, anguiano16}. RAVE further allowed for the creation of pseudo-3D maps of the diffuse interstellar band at 8620~\AA~\citep{kos14} and high-velocity stars to be studied \citep{hawkins15}. RAVE DR5 includes not only the final RAVE observations taken in 2013, but also earlier discarded observations recovered from previous years, resulting in an additional $\sim30\,000$ RAVE spectra. This is the first RAVE data release in which error spectrum was generated for each RAVE observation, so we can provide realistic uncertainties and probability distribution functions for the derived radial velocities and stellar parameters. We have performed a recalibration of stellar metallicities, especially improving stars of super-solar metallicity. Using the Gaia benchmark stars \citep{jofre14, heiter15} as well as 72 RAVE stars with Kepler-2 asteroseismic $\log g$ parameters (Valentini et~al. submitted, hereafter V16), the RAVE $\log g$ values have been recalibrated, resulting in more accurate gravities especially for the giant stars in RAVE. The distance pipeline \citep{binney14} has been improved and extended to process more accurately stars with low metallicities (${\rm [M/H]} < -0.9\dex$). Finally, by combining optical photometry from APASS \citep{munari14} with 2MASS \citep{skrutskie06} we have derived temperatures from the Infrared Flux Method \citep{c10}. Possibly the most unique aspect of DR5 is the extent to which it complements the first significant data release from {\it Gaia}. The successful completion of the Hipparcos Mission and publication of the catalogue \citep{esa97} demonstrated that space astrometry is a powerful technique to measure accurate distances to astronomical objects. Already in RAVE-DR1\citep{steinmetz06}, we looked forward to the results from the ESA cornerstone mission {\it Gaia}, as this space-based mission's astrometry of Milky Way stars will have $\sim$100 times better astrometric accuracies than its predecessor, Hipparcos. Although {\it Gaia} has been launched and data collection is ongoing, a long enough time baseline has to have elapsed for sufficient accuracy of a global reduction of observations \citep[e.g., five years for {\it Gaia} to yield positions, parallaxes and annual proper motions at an accuracy level of 5 -- 25 $\rm \mu$as,][]{michalik15}. To expedite the use of the first {\it Gaia} astrometry results, the approximate positions at the earlier epoch (around 1991) provided by the Tycho-2 Calalogue \citep{hog00} can be used to disentangle the ambiguity between parallax and proper motion in a shorter stretch of Gaia observations. These TGAS stars therefore contain positions, parallaxes, and proper motions earlier than the global astrometry from Gaia can be released. There are $215\,590$ unique RAVE stars in TGAS, so for these stars we now have space-based parallaxes and proper motions from {\it Gaia} DR1 in addition to stellar parameters, radial velocities, and in many cases chemical abundances. The Tycho-2 stars observed by RAVE in a homogeneous and well-defined manner can be combined with the released TGAS stars to exploit the larger volume of stars for which milliarcsecond accuracy astrometry exists, for an extraordinary return in scientific results. We note that in a companion paper, a data-driven re-analysis of the RAVE spectra using {\it The Cannon} model has been carried out (Casey et~al. 2016, in prep, hereafter C16), which presents the derivation of $T_{\rm eff}$, surface gravity $\log{g}$ and $\rm [Fe/H]$, as well as chemical abundances of giants of up to seven elements (O, Mg, Al, Si, Ca, Fe, Ni). In \S\ref{sec:SF}, the selection function of the RAVE DR5 stars is presented -- further details can be found in Wojno et~al. submitted, hereafter W16. The RAVE observations and reductions are summarised in \S\ref{sec:S}. An explanation of how the error spectra were obtained is found in \S\ref{sec:ES}, and \S\ref{sec:RV} summarises the derivation of radial velocities from the spectra. In \S\ref{sec:P}, the procedure used to extract atmospheric parameters from the spectrum is described and the external verification of the DR5 $T_{\rm eff}$, $\log g$ and [M/H] values is discussed in \S\ref{sec:EV}. The dedicated pipelines to extract elemental abundances, and distances are described in \S\S\ref{chemicalpipeline} and \ref{sec:D}, respectively -- DR5 gives radial velocities for all RAVE stars but elemental abundances and distances are given for sub-samples of RAVE stars that have SNR $>$ 20 and the most well-defined stellar parameters. Temperatures from the Infrared Flux Method are presented in \S\ref{sec:IRFM}. In \S\ref{sec:AC} we present for the red giants gravities based on asteroseismology by the method of V16. A comparison of the stellar parameters in the RAVE DR5 main catalog to other stellar parameters for RAVE stars (e.g., those from C16) is provided in \S\ref{sec:BP}. The final sections, \S\ref{sec:diff} and \S\ref{sec:conclude} provide a summary of the difference between DR4 and DR5, and an overview of DR5, respectively. | \label{sec:conclude} The RAVE DR5 presents radial velocities for 457\,589 individual stars in the brightness range $9< I< 12\,$mag, obtained from spectra with a resolution of 7\,500 covering the CaT regime. This catalog can be accessed by \doi{10.17876/rave/dr.5/001} and in the supplemental online data. The typical SNR of a RAVE star is 40 and the typical uncertainty in radial velocity is $<2\kms$. Stellar parameters are derived from the DR4 stellar parameter pipeline, based on the algorithms of MATISSE and DEGAS, but an updated calibration improves the accuracy of the DR5 stellar parameters by up to 15\%. This pipeline is valid for stars with temperatures between 4000~K and 8000~K. The uncertainties in $T_{\rm eff}$, $\log g$ and \mh~are approximately 250\,K, 0.4\,dex and 0.2\,dex, respectively, but vary with stellar population and SNR. The best stellar parameters have {\tt Algo\_Conv}=0, SNR $>$ 40, and {\tt c1}=n, {\tt c2}=n and {\tt c3}=n. An error spectrum has been computed for each observed spectrum, and is then used to assess the uncertainties in the radial velocities and stellar parameters. Temperatures from the Infrared Flux Method are derived for $>95$\% of all RAVE stars, and for a sub-sample of stars that can be calibrated asteroseismically ($\sim45$\% of the RAVE sample), the asteroseismically calibrated $\log g$ is provided. The RAVE stars in the asteroseismically calibrated sample are given in \doi{10.17876/rave/dr.5/002} and described in Table~8 of the Appendix. As in \citet{matijevic12}, binarity and morphological flags are given for each spectrum. Photometric information and proper motions are compiled for each star. The abundances of Al, Si, Ti, Fe, Mg and Ni are provided for approximately 2/3 of the RAVE stars. These are generally good to $\sim0.2\,$dex, but their accuracy varies with SNR and, for some elements, also of the stellar population. Distances, ages, masses and the interstellar extinctions are computed using the methods presented in \citet{binney14}, but upgraded, especially for the more metal-poor stars. %For 80\% of the stars in the RAVE volume, space velocities can be derived to %better than $20\kms$ by combining DR5 distances, radial velocities and the %UCAC4 proper motions listed in DR5. The astrometry and parallaxes from the first Gaia data combined with the RAVE DR5 radial velocities ensure that $10\kms$ uncertainties in space velocities for 70\% of the RAVE-TGAS stars can be derived. Further, because Gaia astrometry provides completely new constraints on distances and tangential velocities, we can now use the RAVE pipelines to derive yet more accurate stellar parameters and distances for the TGAS stars, and even improve the parameters and distances of RAVE stars that are not in TGAS. The RAVE stars that have TGAS counterparts are provided in \doi{10.17876/rave/dr.5/004}. | 16 | 9 | 1609.03210 |
1609 | 1609.02919_arXiv.txt | text{ The Gaia-Tycho release, scheduled for 14 September, is forecast to yield parallax errors of $\sigma(\pi)\sim 300\,\mu$as for about 2 million Tycho stars. We show analytically that the actual performance should be $$ \sigma(\pi) = {\rm max}(\sigma_{1991}/96,20\,\mu{\rm as}) $$ where $\sigma_{1991}$ is the positional error from the Hipparcos mission. For typical Tycho stars, $\sigma_{1991}\sim 30\,$mas, so this reproduces the usual claims. However, for the 100,000 star Hipparcos subset of this sample, $\sigma_{1991}$ is a factor 15 or more smaller. These much lower Hipparcos positional errors apply even to stars at the Hipparcos-Tycho limit, $V\sim 12$. This is especially important for RR Lyrae stars, as well as other special classes, that were systematically included in the Hipparcos catalog down to this limit because of their exceptional scientific importance. This predicted performance will provide an early test of the Gaia algorithms. } \begin{document} \jkashead % | } On 14 September, Gaia will release parallax and proper motion measurements for roughly 2 million stars in the Tycho catalog. The release will be based on about 9 months of Gaia data, which normally would not be enough to disentangle the correlations between the three quantities, position $P$, proper motion $\mu$, and parallax $\pi$. However, for Tycho stars, these degeneracies can be broken by the 1991 position measurements of the Hipparcos satellite. The ``anticipated'' parallax precision (no doubt highly influenced by the fact that the actual precisions are already known to the Gaia team) is $\sigma(\pi)\sim 300\,\muas$. This release will enable a huge range of science, and also facilitate community preparation for the subsequent full Gaia releases. However, as we show here, the information content of these observations is potentially much greater for the subset of these stars with Hipparcos data. These stars have much smaller positional errors than typical Tycho stars, even when they are at similar $V$ magnitudes. We ourselves are motivated by the problem of calibrating RR Lyrae period-luminosity relations, a project that will greatly benefit from the much higher precision that we predict. This calibration will also pave the way to measuring the Gaia parallax zero point \citep{gk2016}. However, the same improved precision would greatly aid many other investigations as well. | \label{sec:discuss}} It may well be that when the Gaia-Tycho catalog is released, the reported errors will be roughly as predicted here. In this case, the main value of the present work will be to alert the community to the fact that much higher-precision science is possible than was thought based on pre-release advertisements. For example, typical Hipparcos RR Lyrae stars have parallaxes $\pi\sim 800\,\muas$ (e.g., \citealt{popow98b}). If the parallax measurements have errors of $\sigma(\pi)\sim 300\,\muas$, then it will be possible to determine the zero-point of the period-luminosity (PL) relation to a precision of $(5/\ln 10)(300/800)/\sqrt{100}= 0.08\,$mag from a sample of 100 stars. This is really not qualitatively better than a number of previous determinations dating back more than 20 years \citep{longmore90,layden96,popow98a,gould98,benedict11,kollmeier13,madore13,dambis14}. On the other hand, if the precisions can be improved a factor 10, then the PL zero points will experience similar improvements. Moreover, such improvements would allow qualitatively different questions can be addressed. For example, the scatter about the PL relation could be investigated in field RR Lyrae stars, whereas currently this is only possible in (presumably more homogeneous) clusters. On the other hand, if the errors reported in the Gaia-Tycho catalog are at the $300\,\muas$ level even for Hipparcos stars, then the analytic arguments presented here can be used to track down the discrepancy between these reports and our predictions. This may lead either to an improved catalog or to a deeper understanding of issues that will impact future Gaia releases. | 16 | 9 | 1609.02919 |
1609 | 1609.07157_arXiv.txt | We present a Bayesian algorithm to combine optical imaging of unresolved objects from distinct epochs and observation platforms for orbit determination and tracking. By propagating the non-Gaussian uncertainties we are able to optimally combine imaging of arbitrary signal-to-noise ratios, allowing the integration of data from low-cost sensors. Our Bayesian approach to image characterization also allows large compression of imaging data without loss of statistical information. With a computationally efficient algorithm to combine multiple observation epochs and multiple telescopes, we show statistically optimal orbit inferences. | \label{sec:introduction} The Geosynchronous Earth Orbit (GEO) is an increasingly crowded environment requiring regular monitoring for orbit determinations and refinements in catalog maintenance. When using optical telescopes to monitor GEO, many observations are needed to measure sufficient arc length to constrain an orbit. The exposure time for a single exposure is often limited by the requirement to avoid detector saturation from bright stars. Or, in the case of non-sidereal tracking, the exposure time is limited by the avoidance of star streaks covering too much detector area. The telescope aperture then limits the faintest magnitudes that can be tracked, which are correlated with satellite or debris size~\cite{schildknecht2004}. We present an algorithm for characterization of streaks in optical CCD imaging of arbitrary signal-to-noise ratio (assuming an initial detection has been made \cite{dawson_amos2016}) and subsequent orbit determinations including uncertainty propagation and combinations of information from multiple observing epochs or telescopes. We characterize streak information (position, length, and flux) via a statistical model that allows statistical compression of image information. | \label{sec:conclusions} Using a simulation study, we demonstrated a new algorithm to combine images of a satellite from multiple telescopes or exposures for orbit determination and refinement. Our algorithm uses a probabilistic forward model for satellite images in sidereal tracking optical observations. The output of a probabilistic fit to an image is samples of streak image model parameters from an interim posterior distribution. These samples constitute a form of statistical image compression. Because we propagate all uncertainties in the streak fitting process we can select images of arbitrary signal-to-noise ratio. Given interim posterior samples of streak image parameters from an image, we perform a preliminary orbit determination (POD) using a `statistical ranging' algorithm from \cite{virtanen2001,schneider12} to transform image positions to probabilistic samples of osculating Keplerian elements. This is a flexible approach to image processing that allows trivial parallelization of computations across distinct images. Given the PODs from all images of a satellite (over all times and telescopes), we can combine the statistical samples of orbit parameters with a new importance sampling algorithm. The importance sampling requires new evaluations of the likelihood functions of each exposure, but can again be massively parallelized unlike Markov Chain algorithms~\cite{schneider12}. In our simulation study we found distinct advantages in orbit determination in the combination of ground- and space-based observing deriving from the geometry of separate observatories. To perform similar orbit inferences from a single ground-based telescope requires a higher cadence of tracking observations, which we expect to become impractical as more sources and larger areas of the sky are monitored. | 16 | 9 | 1609.07157 |
1609 | 1609.09183_arXiv.txt | A stellar mass black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) has been discussed in a number of works as the central engine of gamma-ray bursts (GRBs). It is widely believed that NDAF cannot liberate enough energy for bright GRBs. However, these works have been based on the assumption of ``no torque" boundary condition, which is invalid when the disk is magnetized. In this paper, we present both numerical and analytical solutions for NDAFs with non-zero boundary stresses, and reexamine their properties. We find that NDAF with such boundary torque can be powerful enough to account for those bright short GRBs, energetic long GRBs and ultra-long GRBs. The disk becomes viscously unstable, which makes it possible to interpret the variability of GRB prompt emission and the steep decay phase in the early X-ray afterglow. Finally, we study the gravitational waves radiated from a processing BH-NDAF. We find that the effects of the boundary torque on the strength of the gravitational waves can be ignored. | \label{sect:intro} The leading model of Gamma-ray burst (GRB) central engine is a hyper-accreting stellar-mass black hole (BH). The typical accretion rate is extremely high (e.g., $0.01 - 1 M_\sun s^{-1}$), leading to a much dense and hot flow. Under such condition, photons become trapped and are inefficient in cooling the disk. The gravitational energy in the accretion flow is mainly carried by neutrino and anti-neutrinos, which annihilate and power GRB jets. These disks are therefore named ``neutrino-cooling-dominated accretion flows'', or NDAFs (e.g., \citealt[hereafter PWF99]{P99}; \citealt{KM02}). The NDAF has been extensively investigated and usually compared with the magnetic mechanism (e.g.,\citealt[hereafter NPK01]{N01}; \citealt{KM02}; \citealt[hereafter DPN02]{D02}; \citealt{CB07,J04,J07,J10,G06,Liu07,Lei08,Lei09,Lei13a}). It was for a long time considered as an inefficient model for GRBs. This conclusion was first made by Popham et al. (1999), and enhanced by Di Matteo et al. (2002). Fan et al. (2005) found that NDAF model was disfavour in explaining the X-ray flares of GRB afterglows. Recently, detailed studies by Liu et al. (2015) show that some bright short GRBs (SGRBs) are hard to be explained with NDAF. More recently, Song et al. (2016) argued that NDAF may not be the central engine for some extremely high energy long GRBs (LGRBs). It is worth pointing out that these works are based on the assumption of zero-torque at the inner edge of the accretion disk. This condition has been argued based on the fact that small amount of mass in the plunging region could hardly be expected to exert a force on the far heavier disk proper, or rapidly becomes causally disconnected from the disk (\citealt[hereafter NT73]{NT73}). However, as recognized by \citet[hereafter PT74]{PT74}, neither of these arguments applies to magnetic stress. This issue has become increasingly important with the realization that angular momentum transport in disk is entirely due to turbulence generated via the magnetorotational instability (MRI) (\citealt{BH91}). \citet{K99} and \citet{G99} argued that the dominant role of this magnetic stresses in angular momentum transport in the disk body should actually lead to stresses near the marginally stable orbit. Based on these considerations, \citet{AK00} studied a relativistic thin disk with non-zero torque at its inner edge. As a consequence, the additional magnetic stresses have strong effects that change the fundamental properties of the accretion flow. A more complete magnetohydrodynamical (MHD) model of a magnetized thin disk has been developed by \citet{G99}, a numerical MHD simulation has been carried out by \citet{RA01} using ZEUS code \citep{SN92}, and they verified the existence of torque at marginally stable radius due to the coupling of the plunging region to the disk through magnetic fields. The accretion of a magnetized torus in Kerr metric has been studied by \citet{G03} and \citet{D03} by using general relativistic magnetohydrodynamical (GRMHD) codes. It is found that the disk would be significantly altered by the additional stress, with wide-ranging observational consequences (\citealt{AK00}; Zimmerman et al. 2005). Some authors suggested that the episodic jets in GRBs could be reproduced by magnetized NDAF (e.g. \citealt{YZ12, Cao14}). The magnetic energy within an episodic jet is possibly dissipated via internal-collision-induced magnetic reconnection and turbulence (ICMART, \citealt{ZY11}). These works motive us to investigate the NDAF with boundary stresses. We refer this model as non-zero torque NDAF (nztNDAF), and the previous NDAF model with zero boundary torque as NDAF. This paper is organized as follows: In section 2, we describe the NDAF model with boundary stress and general relativistic corrections. A free parameter $\eta$ is introduced to account for the magnitude of the unknown stress at the inner edge of nztNDAF. In section 3, we study the properties of the disk by solving the set of equations. Based on the solutions, we investigate the stability and total neutrino annihilation luminosity of nztNDAF. In section 4, we apply the nztNDAF model to GRBs. In section 5, we find that the variability of the GRB prompt emissions and the steep decay phase in the early X-ray afterglow can be well explained by the viscous instability in nztNDAF. In section 6, we investigate the effect of inner boundary torque on the gravitational waves radiated from a processing disk. We summarize and discuss the results of this work in section 7. | \label{sect:Discussion} We revise the NDAF model by including a boundary stress. Based on numerical and analytical solutions, we study the properties of nztNDAF. The disk becomes much hotter and denser due to the non-zero boundary torque. The properties in inner region are significantly different from those of NDAF. As a result, we find that the disk becomes unstable if $\dot{m}$ and $\eta$ are great enough (e.g., when the parameter $\eta>0.45$ for $\dot{m}=1.0$). The neutrino annihilation luminosity is greatly enhanced by the boundary stress. The luminosity of nztNDAF varies from $7.8\times10^{48}\rm{erg\, s^{-1}}$ to $2.4\times10^{54}\rm{erg\, s^{-1}}$ for $0.01<\dot{m}<10$ with $\eta=1$, which is much greater than NDAF (its range is from $2.3\times10^{45}\rm{erg\, s^{-1}}$ to $4.6\times10^{53}\rm{erg\, s^{-1}}$). We then apply nztNDAF model to GRBs. For some bright short GRBs and powerful long GRBs, NDAF model is challenged when interpreting the limited mass of the accretion disk after the compact binaries coalescence or massive collapsar \citep{Liu15, Song16}. For the same reason, NDAF is not expected to explain ULGRBs. However, in this paper we argued that the NDAF could still be a feasible model for those issued GRBs, as long as the inner boundary torque is considered. In addition, we extend the method of \cite{Liu15} to ultra-long GRBs and find that the nztNDAF model is also suitable under the frame of BSG-progenitor. Viscous instability may occur nztNDAF in the inner region. When it happens, the disk will transit between two stable brunch with different accretion rates, leading to a variable jet luminosity. The timescale for the instability is about 10 ms (estimated by the viscous timescale at the inner disk). These results can explain the variability in GRB lightcurves. The steep decay following the prompt emission occurs when the mass feeding rate at the outer edge of the disk reduces to a value lower than a critical accretion rate. Finally, we find that the effects of boundary torque on gravitational wave can be ignored. In this work, we describe the boundary torque with a parameter $\eta$. The properties of nztNDAF strongly depend on the value of $\eta$. However, there is no characteristic or ``natural'' magnitude that one can select for the torque \citep{ZNMM05}. Numerical simulation performed by \citet{PSM12} indicated the stress at the inner edge to be directly proportional to the disk thickness. They then argued that zero-stress boundary condition is valid for thin disk in the limit $h\rightarrow 0$. However, the GRMHD simulations by \citet{Noble10} with different thickness found a large stress at the inner edge even in the limit of vanishing disk opening angle $h\rightarrow 0$. The GRMHD simulations by \citet{K05} and \citet{B08} also found that the torque can reach a very high value in the plunging region. Due to these uncertainties, we take $\eta$ as a free parameter in the calculations. In these works, the magnetic stress in the plunging region is likely the origin of the non-zero torque at inner disk edge. For simplicity, we roughly take the magnetic coupling torque exacted by BH as the upper limit of such boundary torque \citet{Lei09}. Nonetheless, there are two differences at least between the nztNDAF model in this work and the MCNDAF model in \citet{Lei09}. Firstly, the MCNDAF essentially adopted the zero stress assumption at the inner edge of the disk, and the MC torque is a resultant effect of the magnetic stresses differentially distributed in a limited disk region which is coupled with the BH by ordered large scale magnetic field lines (see the integrated angular momentum equation (18) in \citet{Lei09}). While in the nztNDAF model, the non-zero stress is just exerted on the inner edge rather than any location else, this inner edge stress originates from the angular momentum transport between the plumping region and the disk through magnetized turbulence. Secondly, for the same magnitude of the two different types of extra torque, the extra viscous heating rate in the inner region caused by the inner edge torque in nztNDAF is much higher than that of the MCNDAF, consequently, the structure near the inner edge of the nztNDAF will be changed with a more significant extent than MCNDAF. Those arguments deserve further studying by GRMHD simulation. For simplicity, we just consider radial direction in this work, with adopting the one-zone approximation in the vertical direction. Our current results show that the inner side of the disk will expand a lot due to the extra heating by the non-zero torque (Figure 1d). Especially when $\eta \gtrsim 1$, the ratio of height to radius $h/r$ can approach unity. The larger disk height will aggravate the extent to which the neutrinos are trapping in the disk, this is one of the reason why the innermost disk become advection cooling dominated. In addition, the increment of the disk height due to the inner edge torque indicates the necessity of the further consideration of the vertical structure. According to \cite{G07}, when $h/r \gtrsim 0.2$, the H\={o}shi form of the gravitational potential \citep{H77} used for deriving the vertical static equilibrium can not be satisfactory any more. There are a number of works on the vertical structure of NDAF (e.g., \citealt{Saw03, Liu10, Liu12a, Liu13, Liu14, Liu15a, PY12}). We may further explore the effects of the inner edge torque by considering the vertical structure in future. Another widely discussed GRB central engine model is Blandford-Znajek mechanism \citep{BZ77, Lee00, Lei13a}. \citet{Lei13a} studied the baryon loading in NDAF and Blandford-Znajek jets. It is found that Blandford-Znajek mechanism can produce ``clean'' jet. NDAF-driven ``fireball'' is typically too ``dirtier'' to account for GRBs. In our nztNDAF model, however, the existence of the magnetic filed may help to suppress baryons from disk, and thus lead to a clean central engine. | 16 | 9 | 1609.09183 |
1609 | 1609.02544_arXiv.txt | We use a spherical model and an extended excursion set formalism with drifting diffusive barriers to predict the abundance of cosmic voids in the context of general relativity as well as $f(R)$ and symmetron models of modified gravity. We detect spherical voids from a suite of N-body simulations of these gravity theories and compare the measured void abundance to theory predictions. We find that our model correctly describes the abundance of both dark matter and galaxy voids, providing a better fit than previous proposals in the literature based on static barriers. We use the simulation abundance results to fit for the abundance model free parameters as a function of modified gravity parameters, and show that counts of dark matter voids can provide interesting constraints on modified gravity. For galaxy voids, more closely related to optical observations, we find that constraining modified gravity from void abundance alone may be significantly more challenging. In the context of current and upcoming galaxy surveys, the combination of void and halo statistics including their abundances, profiles and correlations should be effective in distinguishing modified gravity models that display different screening mechanisms. | The large scale structure of the Universe offers a promising means of probing alternative gravity theories \cite{Brax2, deMartino}. Many models of modified gravity can be parameterized by a scalar degree of freedom that propagates an extra force on cosmologically relevant scales. Viable gravity theories must produce a background expansion that is close to that of a Lambda Cold Dark Matter ($\Lambda$CDM) model in order to satisfy current geometry and clustering constraints, and reduce to general relativity (GR) locally in order to satisfy solar system tests. The first feature may be imposed by construction or restriction of the parameter space whereas the latter feature relies on a nonlinear screening mechanism operating e.g. on regions of large density or deep potentials \cite{Brax3}. Examples include $f(R)$ models with the chameleon mechanism \cite{Khoury04, Khoury04b, shaw, gan, Gubser, Navarro}, braneworld models which display the Vainshtein mechanism \cite{Vainshtein72, Babichev, Falck}, and the symmetron model with a symmetry breaking of the scalar potential \cite{Hinterbichler10, Hinterbichler11, Hammami, Davis}. Most viable models of cosmic acceleration via modified gravity are nearly indistinguishable at the background level and may be quite degenerate, even when considering linear perturbation effects. However, different screening mechanisms operating on nonlinear scales are quite unique features of each model. It is therefore highly desirable to explore observational consequences that help expose these differences, despite the fact that nonlinear physics and baryonic effects must also be known to similar accuracy at these scales. Investigating the nonlinear regime of modified gravity models requires N-body simulations \cite{Oyaizu08, Oyaizu08b, Schmidt09, Schmidt09b, Schmidt09c,clifton, Khoury09, Li2, Schmidt10, Ferraro11, Zhao11, Li1, Li13, Wyman13, Arnold, Brax4, Candlish, Hagala, Achitouv4, Hammami, Winther, Barreira}, in which one must solve nonlinear equations for the extra scalar field in order to properly account for screening mechanisms. From simulations one may extract the matter power spectrum on linear and non-linear scales \cite{Oyaizu08b, Schmidt09b, Schmidt09c, Khoury09, Li11, Wyman13, Taruya} as well as properties of dark matter halos, such as their abundance \cite{Schmidt09, Schmidt09b, bour, Schmidt09c, Li11, Zhao11, Lombriser13, Wyman13}, bias \cite{Schmidt09, Schmidt10, Zhao11, Wyman13} and profiles \cite{Schmidt09, Schmidt09b, Zhao11, Lombriser12}. From the theoretical perspective, estimating e.g. the power spectrum in the nonlinear regime is non-trivial even for GR, and more so for modified gravity \cite{Koyama09, Taruya}, as the screening mechanisms must be properly accounted for in the evolution equations \cite{Brax1}. The halo model \cite{Cooray} provides an alternative to study these nonlinearities \cite{Schmidt09, Schmidt10}, but it has its limitations even in standard GR. Moreover it requires accurate knowledge of various halo properties, including abundance, bias and profiles. In GR the halo mass function may be estimated from the linear power spectrum and spherical collapse within the Press-Schechter \cite{Press} formalism and its extensions \cite{Sheth2, Bond} or from empirical fits to simulations for higher precision \cite{Tinker, Jenkins}. However for modified gravity screening mechanisms operate effectively within the most massive halos, and must be properly accounted for \cite{Li11}. In addition, massive clusters have observational complications such as the determination of their mass-observable relation \cite{Lima05}, which must be known to good accuracy in order for us to use cluster abundance for cosmological purposes. These relations may also change in modified gravity \cite{Arnold}. Cosmological voids, i.e. regions of low density and shallow potentials, offer yet another interesting observable to investigate modified gravity models \cite{Clampitt}. Screening mechanisms operate weakly within voids, making them potentially more sensitive to modified gravity effects \cite{Pisani}. One of the main issues for using voids is their very definition, which is not unique both theoretically and observationally. Compared to halos, the properties of voids have not been discussed in as much detail, although there have been a number of recent developments on the theory, simulations and observations of voids \cite{Sanchez, Pisani, Massara, Cai2, Wojtak, Pollina, Nadathur1, Nadathur2, Nadathur3}. Despite ambiguities in their exact definition, it has been observed in simulations that voids are quite spherical \cite{Sheth1}, and therefore it is expected that the spherical expansion model for their abundance must work well (differently from halos, for which spherical collapse alone is not a very good approximation \cite{Achitouv2}). In this work, we use N-body simulations of $\Lambda$CDM as well as $f(R)$ and symmetron models of modified gravity in order to identify cosmic voids and study their abundance distribution. In order to interprete the simulation results, we use a spherical model and an extended excursion set formalism with underdense initial conditions to construct the void distribution function. Our extended model includes two drifting diffusive barriers in a similar fashion to the work from \cite{Maggiore1, Maggiore2} to describe halo abundance. As a result, our model accounts for the void-in-cloud effect and generalizes models with static barriers \cite{Jennings}. We start in \S~\ref{sec:perturbation} describing the parametrization of perturbations in $f(R)$ and symmetron gravity as well as the spherical model equations. In \S~\ref{sec:void_dist} we use the excursion set formalism to model void abundance and in \S~\ref{sec:void_sim} we describe the procedure for void identification from simulations. Importantly, we define spherical voids in simulations with a criterium that is self-consistent with our predictions. In \S~\ref{sec:res} we present our main results, using simulations to fit for the model free parameters and studying constraints on modified gravity from ideal dark matter voids. We also study the possibility of using our model to describe galaxy voids. Finally, in \S~\ref{sec:discussion} we discuss our results and conclude. | \label{sec:discussion} We have used a suite of N-body simulations from the Isis code \cite{Llinares} for GR and modified gravity models to define spherical voids from underdensities detected by {\tt ZOBOV} \cite{Neyrinck}, a void-finder based on Voronoi tesselation. We find that the void abundance in modified gravity and $\Lambda$CDM may differ by $\sim 100\%$ for the largest void radii in our simulations. We interpreted the void abundance results through a spherical expansion model and extended Excursion Set approach. The most general theoretical model considered has two drifting diffusive barriers, with a linear dependence on the density variance (2LDB, see \S~III). This model depends on the theory linear power spectrum $P(k)$ and in principle has multiple parameters, namely $\delta_c$ and $\delta_v$ (the critical densities for collapse and expansion), $\beta_c$ and $\beta_v$ (the barrier slopes for halos and voids) and $D_c$ and $D_v$ (the diffusion coefficients for halos and voids). Fixing $\delta_c$ and $\delta_v$ to their GR values and under the simplifying assumption that $\beta=\beta_c=\beta_v$, the model depends on two free parameters: $\beta$ and $D=D_c+D_v$. Interestingly, our model accounts for the void-in-cloud effect and generalizes previous models for void abundance based on static barriers \cite{Jennings}. The generalizations proposed here are similar to those made by \cite{Maggiore1, Maggiore2} in the context of halos. Since our model requires the linear power spectrum in modified gravity, we have implemented a numerical evolution of the linear perturbation equations for general theories of modified gravity parametrized by Eq.~\eqref{delta_lin}. We compared our computation to that from {\tt MGCAMB} for $f(R)$ gravity and found very good agreement. We then use this implementation to compute the linear spectrum for both $f(R)$ and symmetron gravity. We also considered approximate equations for spherical collapse and spherical expansion and derived the spherical collapse parameters $\delta_c$ and $\delta_v$ as a function of scale, recovering in particular the values in the strong and weak field regimes of $f(R)$ gravity -- the latter corresponding to the GR solution. We then estimated the dependence of barriers $B_c$ and $B_v$ with the variance $S$ and derived values for $\beta_{c,v}$ and $\delta_{c,v}$. The values found did not however seem to correctly describe the void abundance from simulations, which may be due to the approximated equations used to study the expansion/collapse. We also found that the variations on $P(k)$, $\beta$ and $D$ as a function of modified gravity were much stronger than those from $\delta_c$ and $\delta_v$. Therefore, in our modeling of void abundance we kept $\delta_c$ and $\delta_v$ fixed to their GR values, and took $\beta$ and $D$ as free parameters to be fit from simulations. Although beyond the scope of this work, we envision that it should be possible to derive the model parameters from first principles in the future. By comparing the measured void abundance from the simulations to the theoretical models considered, we found the best fit values for $\beta$ and $D$ in each gravity theory and each abundance model. In particular, we found that these parameters were best-fit for models with linear diffusive barriers (see Figs.~\ref{Distribution_fofr},~\ref{Distribution_symm} and Table~\ref{chi2}), indicating that the addition of these features is important to describe modified gravity effects on void abundance. This allowed us to then fit for $\beta$ and $D$ as a function of modified gravity parameters, namely $|f_{R0}|$ in the case of $f(R)$ gravity, and $z_{SSB}$ in the case of symmetron. Next we used these fits to check how well the calibrated models could recover the modified gravity parameters from hypothetical and idealized void abundance observations. We compared the void abundance measured in simulations to the model predictions and performed an MCMC search for the gravity parameters. Since the predictions were calibrated from the simulations themselves, our results may be highly optimistic. Nonetheless, we found that the models with linear diffusive barriers recover the modified gravity parameters better than the model with static barriers for all gravity theories (see Figs.~\ref{Posterior_fofr},~\ref{Posterior_symm} and Table~\ref{Best_and_mean}). We also found that when using voids found in the GR simulation to fit for modified gravity parameters, we seem to properly recover the GR limit at the $2\sigma$ level. Since we only used one simulation for each gravity model considered, our results have considerable uncertainties. We expect these to improve significantly with the use of multiple and larger simulations. Finally, we populated the dark matter halos found in the simulations with galaxies in order to access the possibility of modeling the abundance of galaxy voids. For the GR case, we found that the same model with linear diffusive barriers properly describes the abundance of galaxy voids, provided we use the galaxy bias to correct for the effective overdensity $\Delta$ used for void detection. However, the error bars were too large to allow for any signal in the modified gravity case relative to GR. Again since we used a single simulation for each gravity, our results for galaxy voids are even more affected by shot noise and unknown sample variance effects. Current and upcoming spectroscopic and photometric galaxy surveys will produce large catalogs of galaxies, clusters and voids. Observed void properties from real data are affected by nontrivial effects such as surveys masks and depth variations in the sky. One could partially characterize these effects from realistic simulations and understand their possible consequences, such as inappropriately breaking large voids into multiple smaller ones or vice-versa (i.e. merging small voids into larger ones). Assuming that such effects can be understood and characterized, we expect that the properties of voids, including their abundance, clustering properties and profiles, will be very important to constrain cosmological models, especially modified gravity. In particular, since voids and halos respond differently to screening effects present in viable modified gravity theories, a combination of voids and halo properties should be particularly effective in constraining and distinguishing alternative gravity models. | 16 | 9 | 1609.02544 |
1609 | 1609.05478_arXiv.txt | {We present the first single-burst stellar population models which covers the optical and the infrared wavelength range between 3500 and ${\rm 50000 \, \AA}$ and which are exclusively based on empirical stellar spectra. To obtain these joint models, we combined the extended MILES models in the optical with our new infrared models that are based on the IRTF (Infrared Telescope Facility) library. The latter are available only for a limited range in terms of both age and metallicity. Our combined single-burst stellar population models were calculated for ages larger than 1 Gyr, for metallicities between ${\rm [Fe/H] = -0.40}$ and 0.26, for initial mass functions of various types and slopes, and on the basis of two different sets of isochrones. They are available to the scientific community on the MILES web page. We checked the internal consistency of our models and compared their colour predictions to those of other models that are available in the literature. Optical and near infrared colours that are measured from our models are found to reproduce the colours well that were observed for various samples of early-type galaxies. Our models will enable a detailed analysis of the stellar populations of observed galaxies. } | Single-burst stellar population (SSP) models mimic uniform stellar populations of fixed age and metallicity, and are an important tool to study unresolved stellar clusters and galaxies. They are created by populating theoretical stellar evolutionary tracks with stars of a stellar library, according to a prescription given by a chosen initial mass function (IMF). Thus, the quality of the resulting SSP models depends significantly on the completeness of the used input stellar library in terms of evolutionary phases represented by the atmospheric parameters temperature, $T{\rm _{eff}}$, surface gravity, ${\rm log(g)}$, and metallicity. A sufficiently large spectral coverage is equally crucial when constructing reasonable SSP models. Theoretical stellar libraries like, e.g. BaSeL \citep{Kurucz92, Lejeune97, Lejeune98, Westera02}, or PHOENIX \citep{Allard12, Husser13} are generally available for both a large range in wavelength and in stellar parameters, whereas empirical libraries are found to be more incomplete in both respects. However, the advantage of the latter ones is that they are not hampered by the still large uncertainties in the calculation of model atmospheres. Examples of empirical stellar libraries in the optical wavelenth range encompass the Pickles library \citep{Pickles98}, ELODIE \citep{Prugniel01}, STELIB \citep{LeBorgne03}, Indo-US \citep{Valdes04}, MILES \citep{Sanchez06}, and CaT \citep{Cenarro01, Cenarro07}. In the near-infrared (NIR) and mid-infrared (mid-IR)\footnote{Note that throughout this paper, we refer to the wavelength range until the end of the $K$-band as NIR, and the range between 2.5 and ${\rm 5 \, \mu m}$ as mid-IR.}, only very few empirical libraries have been observed so far \citep[e.g.][]{Lancon00, Cushing05, Rayner09}. The NASA Infrared Telescope Facility (IRTF) spectral library, described in the latter two papers, is to date the only empirical stellar library in the NIR and mid-IR which offers a sufficiently complete coverage of the stellar atmospheric parameter space to construct SSP models. In the future, the X-Shooter stellar library, which contains around 700 stars, and which covers the whole optical \citep[see][]{Chen14} and NIR wavelength range until ${\rm 2.5 \, \mu m}$, will clearly improve the current situation in the NIR. In the optical range, many different sets of SSP models have been developed, based on the abovementioned libraries \citep[e.g.][]{Worthey94, Vazdekis99, Bruzual03, LeBorgne04, Maraston05, Maraston09, Conroy09, Vazdekis10}. Other models cover the NIR and mid-IR ranges, like those by \citet{Maraston05}, \citet{Conroy12}, \citet{Meneses15b}, and \citet[][hereafter R15]{Roeck15}. In the current work, we combine our IRTF-based SSP models in the NIR and mid-IR with the MIUSCAT models \citep{Vazdekis12, Ricciardelli12} in the optical range. Thus we end up with combined SSP models, which are based on empirical stellar spectral libraries and encompass the spectral range from 3465 to ${\rm 50000 \, \AA}$. Moreover, we analyse and validate our new models in the NIR wavelength range between 1 and ${\rm 2.5 \, \mu m}$. | \label{summary} We present the first evolutionary stellar population models covering the wavelength range from 3465 to ${\rm 50000 \, \AA}$ which are -- apart from two gaps which were covered with the help of theoretical libraries -- based on empirical stellar spectra. We obtained this large wavelength coverage by combining the extended MILES models \citepalias{Vazdekis10, Vazdekis12} in the optical range with the models based on the IRTF library \citep{Cushing05, Rayner09} in the NIR and mid-IR between 8150 and ${\rm 50000 \, \AA}$ \citepalias{Roeck15}. The actual matching was carried out between 8950 and ${\rm 9100 \, \AA}$ (see Section \ref{models_joining}). Thanks to the excellent flux calibration of the stellar spectra of both the MILES and the IRTF library, we had to adjust only slightly the fluxes in the joining region. Nevertheless, due to this slight artificial modification of the flux one should refrain from measuring line strength indices in this matching region. However, it is completely safe to obtain all kinds of optical and NIR/mid-IR colours by integrating the model spectra over the respective filter bandpasses. When determining line strength indices from our combined SSP models, one should be aware that the MILES-based part of the models is kept at the FWHM resolution of ${\rm 2.5 \, \AA}$, while the IRTF-based part redwards of ${\rm 8950 \, \AA}$ is given at the constant spectral resolution of ${\rm R \approx 2000}$. We calculated our models based on both BaSTI \citep{Pietrinferni04} and Padova00 \citep{Girardi00} isochrones. Our models are available for a large range of underlying IMFs, like Kroupa, revised Kroupa and unimodal and bimodal of slopes varying between ${\rm \Gamma = 0.3}$ and 3.3. We conclude that our SSP models are internally consistent due to the close agreement of optical and NIR colours obtained from them with the colours originating from the predictions based on extensive photometric libraries published on our web page (http://miles.iac.es). Even colours composed of filters encompassing the joining region between our two sets of models usually do not deviate more than the photometric limit of ${\rm 0.02 \, mag}$ from the ones obtained from the photometric predictions. We also compared the predictions of our SSP models to those of other models which are available in the literature for the optical and NIR wavelength range. The observed differences between the theoretical Maraston, Marigo and the semiempirical CvD models and our two sets of Padova00 and BaSTI based SSP models are rather small in the case of the pure optical ($V - R$) colour. For a NIR colour like ($J - K$), some differences between the various sets of models arise from the different treatment of the TP-AGB evolutionary phase. Compared to our newly combined SSP models, the models of Marigo and in particular those of Maraston show a much more pronounced contribution of AGB stars which gets reflected in significantly redder colours with respect to our models for ages younger than 2 Gyr. For ages older than 3 Gyr, our SSP models agree best with the Marigo models, while the Maraston models show bluer colours compared to our models. The Meneses-models which are based on a comparable sample of stars from the IRTF library yield slightly redder colours in the case of underlying BaSTI andPadova00 isochrones. Their set of models calculated using the isochrones by \citet{Marigo08}, however, results in too red colours over the whole age range with respect to our models and in too low metallicities for the ETGs compared to what we know from the optical range. Moreover, our models offer the additional advantage of a much larger wavelength coverage. Different optical and NIR colours measured from our SSP models are in good agreement with the observed colours from ETGs. Like in the optical spectral range, we are able to fit these galaxies with just one, old single-burst like stellar population and we do not need to assume an additional young component as is the case for other models in the literature. Our combined models are available on the MILES webpage (http://miles.iac.es). Future work will focus on achieving a better understanding of the poorly analyzed absorption line features in the NIR from both a modeling and observational point of view. | 16 | 9 | 1609.05478 |
1609 | 1609.09073.txt | Broadband photometry of galaxies measures an unresolved mix of complex stellar populations, gas, and dust. Interpreting these data is a challenge for models: many studies have shown that properties derived from modeling galaxy photometry are uncertain by a factor of two or more, and yet answering key questions in the field now requires higher accuracy than this. Here, we present a new model framework specifically designed for these complexities. Our model, \mname{}, includes dust attenuation and re-radiation, a flexible attenuation curve, nebular emission, stellar metallicity, and a 6-component nonparametric star formation history. The flexibility and range of the parameter space, coupled with MCMC sampling within the \prospector{} inference framework, is designed to provide unbiased parameters and realistic error bars. We assess the accuracy of the model with aperture-matched optical spectroscopy, which was excluded from the fits. We compare spectral features predicted solely from fits to the broadband photometry to the observed spectral features. Our model predicts \halpha{} luminosities with a scatter of $\sim$0.18 dex and an offset of $\sim$0.1 dex across a wide range of morphological types and stellar masses. This agreement is remarkable, as the \halpha{} luminosity is dependent on accurate star formation rates, dust attenuation, and stellar metallicities. The model also accurately predicts dust-sensitive Balmer decrements, spectroscopic stellar metallicities, PAH mass fractions, and the age- and metallicity-sensitive features \dn{} and \hdelta{}. Although the model passes all these tests, we caution that we have not yet assessed its performance at higher redshift or the accuracy of recovered stellar masses. | One of the primary goals of galaxy evolution studies is to understand how galaxies assembled their stars over time. The most straightforward way to accomplish this is to measure star formation rates (SFRs) and stellar masses as a function of redshift for representative samples of the galaxy population. This has now been done by many studies out to high redshift, both for the stellar mass function (e.g., {Marchesini} {et~al.} 2009; {Muzzin} {et~al.} 2013; {Ilbert} {et~al.} 2013; {Moustakas} {et~al.} 2013; {Davidzon} {et~al.} 2013; {Tomczak} {et~al.} 2014) and for the SFR-mass relationship (e.g., {Brinchmann} {et~al.} 2004; {Noeske} {et~al.} 2007; {Daddi} {et~al.} 2007; {Peng} {et~al.} 2010; {Karim} {et~al.} 2011; {Whitaker} {et~al.} 2012; {Speagle} {et~al.} 2014; {Whitaker} {et~al.} 2014; {Ilbert} {et~al.} 2015). The star-forming sequence and stellar mass function are derivative-integral pairs, and as a consistency check, the stellar mass growth rates as a function of mass and redshift implied by each can be compared. This approach minimizes systematics by using star formation rates and masses derived from the same data sets, and in contrast to techniques which integrate over mass, is largely insensitive to the mass completeness limits ({Leja} {et~al.} 2015; {Tomczak} {et~al.} 2016). This technique finds broad consistency at $z < 1$ ({Bell} {et~al.} 2007; {Weinmann} {et~al.} 2012): however, at $z = 1 - 3$, the observed star formation rates and stellar masses are systematically incompatible with one another by a factor of $\sim$2 ({Leja} {et~al.} 2015; {Tomczak} {et~al.} 2016; {Contini} {et~al.} 2016). The most straightforward explanation is that these systematics are arise from the models used to convert observed fluxes into stellar masses and/or SFRs. Compilations of galaxy star formation rates and masses in the literature tell a more complex story. Comparisons of observed star formation rate densities to the evolution of the stellar mass density show systematic differences of a factor of $1.5-2$ ({Madau} \& {Dickinson} 2014; {Yu} \& {Wang} 2016). Empirical abundance matching models can appear able to reconcile these two measurements (e.g., {Behroozi}, {Wechsler}, \& {Conroy} 2013; {Moster}, {Naab}, \& {White} 2013). These models contain a greater degree of complexity, which may be important in reconciling SFRs and stellar mass densities, but some of these additional model ingredients are yet to be thoroughly tested. Part of the challenge associated with interpreting literature compilations is that systematic uncertainties vary across techniques, and so combining literature results likely washes away substantial systematic offsets. The apparent inconsistencies in observational quantities make it difficult for simulations of galaxy evolution to simultaneously satisfy observed SFR and mass constraints. Hydrodynamical simulations (e.g., {Genel} {et~al.} 2014; {Torrey} {et~al.} 2014; {Furlong} {et~al.} 2015), semi-analytical models (e.g., {Mitchell} {et~al.} 2014; {Henriques} {et~al.} 2015), and pure analytic models (e.g., {Lilly} {et~al.} 2013; {Dekel} \& {Burkert} 2014) are all systematically offset from observations of masses, SFRs, or both at the level of $0.2-0.5$ dex. This is a particularly interesting comparison because simulated star formation rates and stellar masses are self-consistent by definition. This systematic factor of two uncertainty in basic galaxy properties has direct implications for our understanding of how galaxies assemble their stars. Massive galaxies are thought to double in stellar mass from $z = 2$ to the present epoch (e.g., {van Dokkum} {et~al.} 2010; {Patel} {et~al.} 2013a). It is not possible to assess the uncertainty in this result without accurate models, nor in the evolution (or lack thereof) of the massive end of the mass function (e.g. {Moustakas} {et~al.} 2013). Milky Way-mass galaxies are thought to grow by a factor of $\sim$5 since $z = 2$, and M31-mass galaxies by $\sim$3, with most of the growth occurring between $z = 1$ and $z = 2$ ({van Dokkum} {et~al.} 2013; {Patel} {et~al.} 2013b; {Papovich} {et~al.} 2015). Systematic adjustment of stellar masses and star formation rates at $z = 1 - 3$ could change these results significantly. Furthermore, in order to convert dynamical measurements into the dark matter fractions within galaxies, it is critical to know the stellar masses to within a factor of two (e.g., {Cappellari} {et~al.} 2012). A systematic factor of two uncertainty in stellar mass results in no constraint for the dark matter fraction within the average quiescent ({van de Sande} {et~al.} 2015) or star-forming ({Wuyts} {et~al.} 2016) galaxy at $z = 1 - 3$. In order to advance the field, basic stellar mass and star formation rate estimates must be improved. The dominant source of uncertainty in stellar populations fitting is no longer instrumental noise, sample size, or sample selection, but instead are the degeneracies and limitations in synthesizing and fitting complex stellar populations to spectral energy distributions (SEDs) ({Conroy}, {Gunn}, \& {White} 2009; {Wuyts} {et~al.} 2009; {Behroozi}, {Conroy}, \& {Wechsler} 2010; {Walcher} {et~al.} 2011; {Mobasher} {et~al.} 2015; {Santini} {et~al.} 2015). These parameter degeneracies arise because galaxy SEDs are the result of many complex physical variables, and it is challenging to uniquely determine these variables in individual galaxies with only broadband photometry. The age-dust-metallicity degeneracy is a well-known example of this ({Bell} \& {de Jong} 2001), and uncertainty in these parameters can result in systematic changes to both stellar mass and SFR estimates. Another example is the shape of the dust attenuation curve, which is thought to change from galaxy to galaxy based on both dust geometry and composition ({Witt} \& {Gordon} 2000). Since the effect of extinction is strongest at blue wavelengths, there is a strong degeneracy between the shape of the attenuation curve and the total column density of dust, with most studies requiring spectra or infrared photometry to separate the two ({Johnson} {et~al.} 2007; {Wild} {et~al.} 2011; {Reddy} {et~al.} 2015). These parameter degeneracies complicate comparisons between different codes, because the outputs are strongly dependent on the priors in each SED fitting routine. The prior of a model parameter is the probability distribution which expresses the belief about the distribution of a parameter before the observations are fit: priors can either be explicitly applied in the likelihood calculation, or implicitly applied in the chosen parameterization of the variable, e.g. by using a decaying $\tau$ model to fit star formation histories. Complicating the situation further, the priors for each model are often not clearly defined or explored. There are also substantial uncertainties in the underlying stellar populations synthesis models. One challenge is the difficulty in sourcing accurate spectra for short-lived phases of stellar evolution and nonsolar stellar metallicities. For example, the contribution of thermally-pulsing asymptotic giant branch stars (TP-AGB) may or may not dominate the near-IR emission of galaxies of intermediate age galaxies ({Maraston} 2005; {Marigo} {et~al.} 2008; {Conroy} \& {Gunn} 2010). This uncertainty alone can result in systematic differences of a factor of two in both stellar mass and age estimates ({Bruzual} 2007), though recent analysis imply that the data favor a relatively low TP-AGB contribution (e.g., {Kriek} {et~al.} 2010). Galaxy SED-fitting routines thus far have largely used simple models to derive stellar masses, with fixed or discrete dust attenuation curves, limited or fixed stellar metallicities, simple parameterized star formation histories (SFHs), and simple chi-squared minimization routines ({Bolzonella}, {Miralles}, \& {Pell{\'o}} 2000; {Brammer}, {van Dokkum}, \& {Coppi} 2008; {Kriek} {et~al.} 2009). Yet, observed galaxies show significant variation in stellar metallicity ({Tremonti} {et~al.} 2004) and attenuation curves ({Reddy} {et~al.} 2015; {Salmon} {et~al.} 2016), and neglecting this variation can bias the parameters determined from SED fitting ({Mitchell} {et~al.} 2013). SFH recovery is critical to accurate recovery of stellar masses ({Lee} {et~al.} 2009; {Maraston} {et~al.} 2010; {Pforr}, {Maraston}, \& {Tonini} 2012), and simple exponentially declining SFHs fail to reproduce the mass function of galaxies at earlier epochs by several orders of magnitude ({Wuyts} {et~al.} 2011b). They also fit simulated SFHs poorly, leaving significant biases in stellar mass estimates ({Simha} {et~al.} 2014). Simple chi-squared fitting routines cannot properly estimate the uncertainties when there are substantial degeneracies, as is the case when fitting broadband photometry of galaxies. Progress has been made in fitting SEDs with nonparametric SFHs (e.g., STECMAP ({Ocvirk} {et~al.} 2006), VESPA ({Tojeiro} {et~al.} 2007), LITTLE THINGS ({Zhang} {et~al.} 2012), CSI ({Kelson} 2014; {Dressler} {et~al.} 2016)); however, this practice is not yet widespread, as nonparametric SFHs require either very high signal-to-noise data or a fitting algorithm which can handle significant degeneracies. It has also been shown that the SFRs derived from fitting the UV-NIR SED are often biased low for highly star-forming galaxies ({Wuyts} {et~al.} 2011a), largely because they cannot account for star formation obscured by dust. SFRs are instead often derived separately, with simple ``recipes'' to convert observed UV, MIR, or emission line fluxes into SFRs (e.g., {Kennicutt} 1998). This approach also suffers from known biases: the conversion from emission line fluxes to SFRs is affected by the ionization state of the gas, extra dust attenuation towards HII regions, and stellar metallicity. Inferring total IR luminosities with only MIR broadband photometry can be strongly affected by galaxy-to-galaxy variability in polycyclic aromatic hydrocarbon (PAH) emission in the MIR ({Draine} {et~al.} 2007) and by AGN contribution ({Kirkpatrick} {et~al.} 2015). The interpretation of \lir{} itself is complicated by the contribution of evolved stars to the IR luminosity ({Cortese} {et~al.} 2008; {Hayward} {et~al.} 2014; {Utomo} {et~al.} 2014). UV luminosities are sensitive to stellar metallicity and recent SFH and very sensitive to the amount of dust attenuation, which can be estimated from the UV slope $\beta$ but with serious limitations ({Viaene} {et~al.} 2016). Many of the issues in estimating SFRs with ``recipes'' can be avoided by instead performing a full-SED fit, which consolidates all available information regarding the physical condition of the stars, dust, and gas. Parameter degeneracies can be marginalized over with Bayesian inference techniques and physically motivated priors. Some codes have begun to take advantage of Bayesian approaches in fitting SEDs: \texttt{CIGALE} ({Burgarella}, {Buat}, \& {Iglesias-P{\'a}ramo} 2005; {Noll} {et~al.} 2009), \magphys{} ({da Cunha}, {Charlot}, \& {Elbaz} 2008), \texttt{GALMC} ({Acquaviva}, {Gawiser}, \& {Guaita} 2011), \texttt{BAYESED} ({Han} \& {Han} 2014), and \texttt{BEAGLE} ({Chevallard} \& {Charlot} 2016). Yet due to the complexity in choosing fit parameters, priors, and stellar population synthesis techniques, SED fitting codes with multiple, degenerate parameters often produce different solutions for key physical parameters like stellar mass and star formation rates ({Santini} {et~al.} 2015). This motivates a thorough investigation into the accuracy of the posteriors in SFRs, stellar masses, and other key physical parameters determined from broadband photometry. In this paper, we create and test the \mname{} model within the \prospector{} inference framework (Johnson et al. in prep) using the Flexible Stellar Populations Synthesis (\fsps{}) stellar populations code ({Conroy} {et~al.} 2009). The \mname{} model includes many of the advances mentioned above in a single, self-consistent framework. The model is fit to the broadband photometry from the {Brown} {et~al.} (2014) spectral atlas, which is unique in that it has optical spectra which are aperture-matched to the photometry. These data allow us to probe the accuracy of our model fits by comparing posterior probability functions (i.e., probability distributions for parameters of interest after the data are taken into account) for diagnostic spectral features to the observed features from the aperture-matched spectroscopy. This posterior check is a strong test of the output star formation rates, star formation history, dust attenuation model, and stellar metallicities derived from fitting the \mname{} model to broadband photometry. In Section \ref{section:data}, the galaxy sample is described, along with the available broadband photometric and spectroscopic observations. In Section \ref{section:features}, the \mname{} model is introduced, and the \prospector{} sampling procedure is described. In Section \ref{section:results}, the comparison between the \mname{} model posteriors and the observed spectroscopic quantities is shown, including the \halpha{} and \hbeta{} luminosities, Balmer decrements, \dn{}, \hdelta{} absorption, and stellar metallicities. In Section \ref{section:discussion}, the implications of the posterior checks are discussed, and past and future changes to the \mname{} model are discussion in Section \ref{section:future}. The conclusion is presented in Section \ref{section:conclusion}. A WMAP9 cosmology ({Hinshaw} {et~al.} 2013) and a {Chabrier} (2003) initial mass function (IMF) are adopted for all relevant calculations. | \label{section:conclusion} In this paper, we present the \mname{} model for fitting the SEDs of galaxies, based on the \fsps{} stellar populations code and built in the \prospector{} inference framework. The \mname{} model includes a 6-component nonparametric star formation history, nebular emission, a variable attenuation curve, and dust attenuation and re-radiation. It uses the on-the-fly model generation and MCMC implementation within the \prospector{} framework to explore the model posteriors in a thorough, unbiased manner. We demonstrate the power of this framework by fitting the {Brown} {et~al.} (2014) broadband photometry, and comparing the model predictions to aperture-matched optical spectroscopy. \mname{} predicts observed \halpha{} luminosities from fits to the photometry with a scatter of 0.18 dex and an offset of $\sim$0.1 dex, a strong verification of the model star formation rates, dust attenuation, and stellar metallicities, across a wide range of galaxy types and stellar masses. We also find good agreement in SFH indicators (\dn{} and \hdelta{} absorption), direct tests of the reddening curve (Balmer decrements), stellar metallicities, and PAH mass fractions. The accurate prediction of \halpha{} luminosities is a key component of these results, and it is explored in some detail. The \halpha{} luminosities are sensitive to the recent SFR, the stellar metallicities, and the dust attenuation in the \mname{} model. It is demonstrated that including stellar metallicities is key to achieving the tight scatter in \halpha{} comparisons. It is shown that the remaining scatter of 0.18 dex is consistent with the width of the model posteriors to within 20-30\% for \halpha{} and \hbeta{}, and that it is not dominated by errors in the reddening curve. The low scatter in this comparison implies that SFRs do not vary strongly over 100 Myr timescales. The accuracy of recovered trends in the dust attenuation and re-emission model is also explored. In Section \ref{section:dustcurve}, it is shown that the \mname{} model, using flat priors, naturally recovers the relationship between the dust optical depth and the shape of the attenuation curve predicted in dust radiative transfer models. In Section \ref{section:pah}, it is demonstrated using stacked \spitzer{} IRS spectra that the PAH mass fractions are well constrained by the full-SED fits. We test the extent to which the model posteriors describe the spread in true galaxy properties by performing mock tests (Appendix \ref{appendix:mock_tests}). It is demonstrated that the \mname{} model produces accurate posteriors with well-estimated error bars, even for model parameters which are poorly constrained by the data. The \mname{} model performs better at predicting \halpha{} luminosities than SED-fitting codes of similar complexity (Appendix \ref{appendix:magphys}), largely due to different choices in the dust and SFH implementation. It is also shown that the far-infrared \herschel{} fluxes can be predicted from fits to the UV to MIR photometry alone after applying reasonable physical priors to the shape of the IR SED (Appendix \ref{section:herschel}). Broadband galaxy SEDs are composed of a complex mix of stellar populations, gas, and dust, but models which contain this complexity are often only somewhat constrained by the data. Thus, the parameters derived from these SEDs can be highly sensitive to the model parameterization. Model posterior checks for SED fitters are the key ingredient necessary to move the field forward towards precise, unbiased estimates of stellar masses and SFRs across a variety of redshifts. Here we have performed these tests for the stellar metallicities, star formation rates, star formation histories, dust reddening, and PAH emission, and found excellent agreement with the data. However, important components of the \mname{} model remain untested, in particular the stellar masses and the behavior of the model at higher redshifts. These aspects will be explored in future work. The demonstrated flexibility and accuracy of the \prospector{} framework strongly motivates a fresh look at basic properties of the galaxy population, such as the stellar mass function and star-forming sequence as a function of redshift. Furthermore, \prospector{} allows broadband photometry to describe galaxy properties to a level of detail that was previously only reserved for spectra. The stellar mass-metallicity relationship, systematic variations in SFH with stellar mass and SFR, variations in the PAH fraction with stellar mass and metallicity, and variations in the total dust attenuation and attenuation curve with galaxy properties can all now be accurately explored with broadband photometry alone. This tremendously increases the sample sizes available to these types of studies. Going even further, the simultaneous fitting of broadband photometry and spectra can put tight constraints on quantities that would otherwise be highly degenerate, such as the timescale of SFH variations and the ratio between stellar and nebular attenuation. We plan to re-examine SFR-mass relations and the evolution of the stellar mass function to see if this framework is capable of producing self-consistent SFRs and masses over most of cosmic time. | 16 | 9 | 1609.09073 |
1609 | 1609.07143_arXiv.txt | { We consider various models realizing baryogenesis during the electroweak phase transition (EWBG). Our focus is their possible detection in future collider experiments and possible observation of gravitational waves emitted during the phase transition. We also discuss the possibility of a non-standard cosmological history which can facilitate EWBG. We show how acceptable parameter space can be extended due to such a modification and conclude that next generation precision experiments such as the ILC will be able to confirm or falsify many models realizing EWBG. We also show that, in general, collider searches are a more powerful probe than gravitational wave searches. However, observation of a deviation from the SM without any hints of gravitational waves can point to models with modified cosmological history that generically enable EWBG with weaker phase transition and thus, smaller GW signals. } | \label{sec:intro} Discovery of the Higgs boson, with a mass of $125$ GeV at the Large Hadron Collider (LHC) \cite{Aad:2012tfa,Chatrchyan:2012xdj} finally confirmed that the electroweak symmetry is broken due to a vacuum expectation value of an elementary scalar. This discovery also marks the beginning of a new era of precision measurements of the Higgs properties as a probe for physics beyond the standard model. Another very important recent discovery of the first gravitational wave signal \cite{Abbott:2016blz} opened a new way of probing violent events in the history of our universe through observation of the gravitational waves they would leave behind. With these experimental prospects it is very interesting to re-examine paradigms that predict observable effects in both these areas. In this paper, we wish to study electroweak baryogenesis \cite{Kuzmin:1985mm,Cohen:1993nk,Riotto:1999yt,Morrissey:2012db} in which a strong first order electroweak phase transition (EWPT) is responsible for the observed baryon asymmetry of the universe. In the Standard Model (SM) the phase transition is second order with the observed Higgs mass \cite{Arnold:1992rz,Kajantie:1996qd} and so a modification is required. We will study a simple toy model where a single new scalar is added to the SM, and we will consider several possible charge assignments for this new particle \cite{Curtin:2014jma,Cohen:2012zza,Katz:2014bha}. Such a modification creates a barrier between the symmetric minimum and the new electroweak symmetry breaking minimum which develops as the temperature of the universe drops, making the phase transition more strongly first order. This has two effects. First, modification of the high temperature potential inevitably leads to a modification of the zero temperature Higgs potential which we can probed in colliders. And second, a more violent phase transition (i.e., stronger first order) results in larger production of gravitational waves The main point we wish to make comes from the fact that early cosmological evolution of the universe is rather poorly constrained by experiments. To be more specific, in our discussion we will include the possibility that the early universe energy density was dominated by a new contribution not interacting with the SM which red-shifted away before nucleosynthesis. This scenario is much different from the standard assumption that the universe was dominated by radiation; however, as we will show, no currently available experimental data can exclude this possibility. The necessary condition for baryogenesis we will address comes from the fact that the same sphaleron processes that can be responsible for creation of the asymmetry can also wash it away when the universe goes back to thermal equilibrium and the sphalerons are not sufficiently decoupled. As mentioned already we will discuss not only how generating a larger potential barrier helps in damping the sphaleron processes but also discuss how their cosmological freeze-out can help ameliorate the situation \cite{Joyce:1996cp,Joyce:1997fc,Lewicki:2016efe,Servant:2001jh}. While we will not discuss generation of the baryon asymmetry during the phase transition, additional problems can appear when considering the CP violation that is also needed for the asymmetry. Helpful sources of CP violation are limited by increasingly accurate experimental EDM constraints~\cite{Hudson:2011zz,Harris:1999jx}, which in turn requires a stronger first-order phase transition for the asymmetry to develop~\cite{Konstandin:2013caa}. This problem, however, is very model dependent and in some models can be completely decoupled from the sphaleron bound. Thus we will only discuss the latter as a more robust requirement. Gravitational waves were widely discussed as a possible probe of electroweak baryogenesis \cite{Grojean:2006bp} including their interplay with collider signals \cite{Huang:2016cjm,Kakizaki:2015wua,Hashino:2016rvx,Hashino:2016xoj,Kobakhidze:2016mch,Chala:2016ykx} and possible non standard cosmological events during the phase transition \cite{Chung:2010cb,Addazi:2016fbj}. We reinvestigate these signals in our model. Strength of the GW signal drops quickly as the transition becomes weaker and generically modification of precision Higgs observables probes a larger part of the parameter space. In regions where baryogenesis is allowed due to our cosmological modification the GW signal is too weak for observation in planned searches even before considering the diminishing of the signal due to the modification. The simplest possible origin of our additional energy component is an oscillating homogeneous scalar field with non-renormalizable potential, i.e.\ with $V(\phi) \propto \phi^{2n}$. In that case the energy density of $\phi$ would redshift as $a^{-6n/(1+n)}$, which in the $n \gg 1$ limit gives $a^{-6}$. Such a field could originally play the role of one of the inflatons, which is very weakly coupled to the SM particles and therefore has not contributed significantly to the process of reheating. It is not to be confused with the new scalar that modifies the SM Higgs potential to produce a first order phase transition. Note, that non-renormalizable potentials are perfectly consistent with the CMB data assuming that the inflaton was non-minimally coupled to gravity \cite{Kallosh:2013tua}. | In this paper we studied detection possibilities for simple EWBG models that include only one new scalar with a possible modified cosmological history. To this end we used a very generic model to modify the cosmological history, which introduced a new energy density constituent which redshifted away before nucleosynthesis. We carefully computed the details of the EW phase transition going beyond the oft-used critical temperature approximation. This allowed us to accurately compute the gravitational wave signal produced during the phase transition as the degeneracy of the minima of the potential during the transition plays a critical role there. We also described the modification of $SU(2)$ sphalerons of the Standard Model due to the modified cosmological history. The main effect comes from cosmologically modified freezout of the sphaleron processes after the phase transition. This has a severe impact on the corresponding detection range for collider experiments changing the exclusion range by as much as a few hundred GeV. Next we computed the gravitational wave signals produced during the phase transition in our model. These turn out important only in the region where the phase transition is strong enough to allow baryogenesis without a cosmological modification. Thus we conclude that observation of a modification of the Higgs observables in future collider experiments without a corresponding gravity wave signal could point to scenarios with a modified cosmological history. | 16 | 9 | 1609.07143 |
1609 | 1609.09197_arXiv.txt | We study the effects of Horndeski models of dark energy on the observables of the large-scale structure in the late time universe. A novel classification into {\it Late dark energy}, {\it Early dark energy} and {\it Early modified gravity} scenarios is proposed, according to whether such models predict deviations from the standard paradigm persistent at early time in the matter domination epoch. We discuss the physical imprints left by each specific class of models on the effective Newton constant $\mu$, the gravitational slip parameter $\eta$, the light deflection parameter $\Sigma$ and the growth function $\fs$ and demonstrate that a convenient way to dress a complete portrait of the viability of the Horndeski accelerating mechanism is via two, redshift-dependent, diagnostics: the $\mu(z)-\Sigma(z)$ and the $\fs(z)-\Sigma(z)$ planes. If future, model-independent, measurements point to either $\Sigma-1<0$ at redshift zero or $\mu-1<0$ with $\Sigma-1>0$ at high redshifts or $\mu-1>0$ with $\Sigma-1<0$ at high redshifts, Horndeski theories are effectively ruled out. If $\fs$ is measured to be larger than expected in a $\Lambda$CDM model at $z>1.5$ then Early dark energy models are definitely ruled out. On the opposite case, Late dark energy models are rejected by data if $\Sigma<1$, while, if $\Sigma>1$, only Early modifications of gravity provide a viable framework to interpret data. | \label{sec_1} Current and future observations aiming at understanding the nature of cosmic acceleration offer the unique possibility of testing predictions of general relativity (GR) on scales well beyond those of the solar system, where GR has received its most impressive confirmations. Upcoming galactic surveys such as DES \cite{DES}, Euclid \cite{Euclid,Amendola:2016saw,Taddei:2016iku}, DESI \cite{DESI}, LSST \cite{LSST}, WFIRST \cite{WFIRST} and SKA \cite{SKA,Bull:2015lja,Camera:2015fsa} are expected to provide unprecedented datasets with which to investigate, in an accurate way, how structures form and grow, and how light rays bend in the presence of local gravitational potentials. Anticipating interesting signals of non-standard gravity that could be potentially detected by such future surveys of the large-scale structure (LSS) of the universe is a crucial task. Any deviation from the standard $\Lambda$CDM paradigm will imply some anomalous relation among the curvature perturbation $\Psi$, the Newtonian potential $\Phi$ and the comoving density contrast of non relativistic matter $\Delta$. These effects can be encoded in time and scale modifications to the effective Newton's constant parameter $\mu$ and to the gravitational slip parameter $\gsp$~\cite{Pogosian:2010tj}. The former quantity describes how fluctuations of the matter fields interact in the universe, while the latter encapsulates non-standard relation between the Newtonian potential $\Phi$ (time-time part of the metric fluctuations) and the curvature potential $\Psi$ (space-space part). From $\mu$ and $\eta$ one can derive a further parameter, $\Sigma$, of more direct relevance for lensing surveys~\cite{Song:2010fg,Simpson:2012ra}. $\Sigma$ relates the matter over-density with the lensing (or Weyl) potential $\Phi_+ = (\Phi+\Psi)/2$. Another convenient quantity to describe the gravitational clustering of matter is the product of the linear growth factor $f$ and the $rms$ density fluctuations on a scale of $8h^{-1}$ Mpc ($f \sigma_8$). This quantity, which can be optimally estimated from the analysis of the redshift space distortions induced by the large-scale, coherent, in-falling(/out-flowing) of matter into(/out of) high(/low) density regions, is another key quantity turning galaxy redshift surveys into gravity probes. While any observed deviation would represent a major discovery in itself, it is important to understand what type of signals are implied by concrete alternatives to the standard model and interpret them in terms of fundamental theoretical proposals. In particular, theories containing one extra scalar degree of freedom and leading to equations of motion of at most second order---\emph{Horndeski theories}~\cite{Horndeski:1974wa,Deffayet:2009mn}---despite the freedom in the choice of their free functions and the richness of their potential phenomenology, have proven to share common features and universal behaviours. The exclusion of pathologies and instabilities imposes tight constraints and well defined patterns for the time scaling of relevant observables of the LSS in the universe~\cite{Piazza:2013pua,Perenon:2015sla,Perenon:2016itr}. For instance, it was pointed out in~\cite{Perenon:2015sla} that the linear growth rate of Horndeski theories is systematically lower, at low redshift, than the value predicted by the standard $\Lambda$CDM model. In~\cite{Song:2010rm} it was shown that Brans-Dicke theories, clustering and interacting dark energy models follow characteristic paths in the $\mu $ - $\Sigma$ plane. It has also been argued~\cite{Pogosian:2016pwr} that Horndeski theories are expected to display a systematic sign agreement in the $\mu $ - $\Sigma$ plane across all cosmic epochs. Investigating the existence of further general patterns displayed by LSS observables is the main goal of the present work. To this purpose, we present a complete study of the Horndeski phenomenology that generalizes in many respects that presented in~\cite{Perenon:2015sla}. First of all, we explore accelerating cosmologies in which the presence of dark energy is not confined to the late times ~\cite{Wetterich:1987fm,Ratra:1987rm,Caldwell:1997ii,Hebecker:2000zb,Doran:2001rw,Wetterich:2001jw,Bean:2001wt,Wetterich:2004pv,Doran:2006kp,PhysRevD.83.123504,Reichardt:2011fv,Tsujikawa:2013fta,Sievers:2013ica,Archidiacono:2014msa,Pettorino:2013ia,Shi:2015tje,Pu:2014goa,Brax:2013fda,Lima:2016npg }. At first sight, this is counter intuitive, as the acceleration is a recent phenomenon and there is no need to invoke dark energy effects at early times. Truth is that, although such effects are not needed, not to say wanted, they are allowed within the context of Horndeski theories, therefore they must be thoroughly investigated and systematised. In particular, we find convenient to highlight three novel possibilities of increasing generality. \begin{itemize} \item \emph{Late-time dark energy} {\bf (LDE)}: \ This is the reference class of models (explored at length in~\cite{Perenon:2015sla}), in which both the dark energy momentum tensor and the possible modifications of gravity (\emph{i.e.} the non-minimal gravitational couplings) become negligible at early times. \item \emph{Early dark energy} {\bf (EDE)}: \ In these scenarios dark energy can contribute to the total energy momentum tensor even at early times, while non-minimal gravitational couplings are kept as a late-time phenomenon. \item \emph{Early modified gravity} {\bf (EMG)}: \ Horndeski theories in their full generality. Not only does dark energy always contribute to the total energy momentum tensor, but modified gravity effects are also persistent at early times, during matter domination. \end{itemize} On top of singling out the specific phenomenological features of the Horndeski sub-classes listed above, in this work we extend the analysis of~\cite{Perenon:2015sla} by including different background expansion histories than the $\Lambda$CDM model. Beside an effective equation of state parameter $w=-1$ (roughly, the value preferred by current observations, \emph{e.g.}~\cite{Betoule:2014frx,Ade:2015xua,Aubourg:2014yra}), we also consider models with $w = -0.9$ and $w = -1.1$. In~\cite{Perenon:2015sla} it was found that viability priors do impose tight constraints and well defined patterns for the time scaling of relevant observables of the LSS in the universe. As such, viability criteria can be effectively used to complement data and observational information in statistical inferences~\cite{Salvatelli:2016mgy}. Testing the consequences of relaxing some of these restrictions is also a goal of the present study. The main results of the paper are recapped in Figure~\ref{fig_diag} as exclusion regions in the parameter space of LSS observables. In the $\mu$-$\Sigma$ plane we highlight regions where the eventual presence of data would rule out the entire class of Horndeski theories. On the other hand, specific regions in the $f\sigma_8$-$\Sigma$ allow to rule out specific subclasses of models (LDE and/or EDE) presented above. A ``complete diagnostic" of Horndeski theories is presented in the other figures of the paper. The paper's structure is as follows: in Sec.~\ref{sec_2} we introduce the formalism adopted for the description of the background cosmic evolution, the non-minimal gravitational couplings and their relations with the LSS observables. In Sec.~\ref{sec_4} we present our results in the case of a cosmic expansion history identical to that of $\Lambda$CDM, for the three classes of models described above. In Sec.~\ref{sec_4bis} we verify the robustness of our conclusion by considering different equations of state for dark energy and by relaxing some of our viability conditions. The synthesis of our results as well as some digressions on future prospects are in Sec.~\ref{sec_5}. | \label{sec_5} What Horndeski theories have to say about early dark energy? This is the original question motivating the analysis presented in this paper. Early modifications of GR are found to have non-negligible, lasting and potentially detectable effects in the LSS observables of the local and recent universe. In Figure~\ref{fig_diag} we summarize our main findings. By tracing the time evolution, from early epochs ($z=100$) down to present day, of fundamental LSS observables such as the reduced effective Newton constant $\mu$, the gravitational slip parameter $\eta$, the lensing parameter $\Sigma$ and the linear growth function of LSS $\fs$ we have found that GR extensions contemplating an additional scalar degree of freedom with second order equations of motion can be definitely ruled out if one of the following conditions apply (Figure~\ref{fig_diag}, left panel): \begin{itemize} \item The observables $\mu$ and $\Sigma$ have opposite sign for $z>1.5$\, \item $\mu<1$ at $z=0$\, \end{itemize} Specific sub-classes of such theories in which the modified gravity effects are limited to late times could be discriminated if data at redshift $z>1.5$ eventually become available for both redshift and lensing surveys. Indeed, we find that above that critical redshift (Figure~\ref{fig_diag}, right panel): \begin{itemize} \item LDE will be ruled out if $\fs < (f \sigma_{8})_{\Lambda CDM}$ at $z>1.5$ \item EDE will be ruled out if $\fs > (f \sigma_{8})_{\Lambda CDM}$ at $z>1.5$ or $\fs > (f \sigma_{8})_{\Lambda CDM}$ and $\Sigma>1$ at $z>1.5$ \end{itemize} These results are insensitive to the background dark energy $e.o.s$ parameter within the reasonable range $\wb \in [-1.1,-0.9]$. Indeed, we have found the diagnostic tool does not lose predictability when progressively less constraining requirements are imposed. \begin{figure}[H] \begin{center} \hskip4mm \includegraphics[scale=0.55]{correl_schematics_musigma.pdf} \hskip8mm \includegraphics[scale=0.55]{correl_schematics_fsigsigma.pdf} \end{center} \caption{Schematics of the fundamental observable planes allowing to discard Horndeski theories (left diagram) and the type of dark energy embedded (right diagram).} \label{fig_diag} \end{figure} Two complementary strategies allow to estimate the likelihood of data given the Horndeski class of theories. A model-dependent analysis is optimal if one is to exploit theoretical priors about the physical viability of specific Horndeski models to complement the discriminatory power of data. Indeed, \cite{Salvatelli:2016mgy} have shown that by this approach the region of the parameter space that is not rejected by observations is significantly reduced. An orthogonal approach consists in implementing model-independent likelihood analysis, parametrising LSS observables in a purely phenomenological way, blindly of any gravitational theory. The diagnostics developed in this paper are meant to facilitate theoretical interpretation in these cases. Interestingly, model-independent analyses have been pursued for example in~\cite{Simpson:2012ra} and more recently in~\cite{Ade:2015rim} and preliminary results are suggestive of a negative value of $\mu-1$ at redshift z = 0. Should future, higher precision data strengthen the statistical significance of these findings, the Horndeski landscape would face hard times. \vv Exploring beyond standard GR, and notably the functional space of scalar-field extension of GR will eventually become less disorienting than previously suspected. However, much must still be accomplished and a number of improvements would be desirable. We have focused on scales much smaller than the Hubble radius in this paper. As data improve on ever larger scales, our analysis should be extended to include possible scale dependent effects coming from mass terms of the scalar field that are of the order of Hubble. On the contrary, it would be interesting to evaluate, on small scales, how many models survive once solar system tests are applied. Lastly, it would be useful to study to which level our diagnostic plots are stable to the inclusions of more general scenarios in which, for instance, the scalar field is allowed to satisfy larger than second order equation of motions (the so called beyond Horndeski theories \cite{Gleyzes:2014qga,Gleyzes:2014dya}, see also~\cite{Zumalacarregui:2013pma} for early studies in this direction), or when conformal-disformal couplings of matter to gravity are considered (the so called effective field theory of interacting dark energy~\cite{Gleyzes:2015pma}). | 16 | 9 | 1609.09197 |
1609 | 1609.09649.txt | \noindent We present high--resolution (0.16$''$) 870$\mu$m Atacama Large Millimeter/submillimeter Array (ALMA) imaging of 16 luminous ($L_{\rm IR} \sim 4 \times 10^{12} L_{\odot}$) submillimeter galaxies (SMGs) from the ALESS survey of the Extended \textit{Chandra} Deep Field South. This dust imaging traces the dust--obscured star formation in these $z\sim2.5$ galaxies on $\sim$1.3\,kpc scales. The emission has a median effective radius of $R_e=0.24$$''$$\pm$0.02$''$, corresponding to a typical physical size of $R_{e}=1.8\pm$0.2\,kpc. We derive a median S\'ersic index of $n=0.9$$\pm$0.2, implying that the dust emission is remarkably disk-like at the current resolution and sensitivity. We use different weighting schemes with the visibilities to search for clumps on 0.12$''$ ($\sim$1.0\,kpc) scales, but we find no significant evidence for clumping in the majority of cases. Indeed, we demonstrate using simulations that the observed morphologies are generally consistent with smooth exponential disks, suggesting that caution should be exercised when identifying candidate clumps in even moderate S/N interferometric data. We compare our maps to comparable--resolution \textit{HST} \textit{H}$_{\rm 160}$-band images, finding that the stellar morphologies appear significantly more extended and disturbed, and suggesting that major mergers may be responsible for driving the formation of the compact dust disks we observe. The stark contrast between the obscured and unobscured morphologies may also have implications for SED fitting routines that assume the dust is co-located with the optical/near--IR continuum emission. Finally, we discuss the potential of the current bursts of star formation to transform the observed galaxy sizes and light profiles, showing that the $z\sim0$ descendants of these SMGs are expected to have stellar masses, effective radii, and gas surface densities consistent with the most compact massive (M$_{*}\sim$ 1--2$\times$10$^{11}$ M$_{\odot}$) early--type galaxies observed locally. \noindent\textit{Key words:} galaxies: starburst -- galaxies: high-redshift -- submillimeter -- catalogs | \label{Intro} How high--redshift galaxies formed their stars remains an open question. Deep (rest--frame) UV/optical surveys have yielded large samples of high--redshift ($z$$\sim$1.5--3.5) star--forming galaxies selected based on magnitude/color properties \citep[BM/BX, $BzK$; e.g.,][]{2004ApJ...604..534S, 2004ApJ...617..746D, 2007ApJ...670..173D, 2007ApJ...670..156D}, the study of which has provided a basic picture of their formation. In particular, studies of the ionized gas kinematics in such galaxies have uncovered a high fraction of large rotating disks among the massive, optically--bright systems \citep[e.g.,][]{2006ApJ...645.1062F, 2008ApJ...682..231S, 2012MNRAS.426..935S}. These studies suggest that secular processes within star--forming galaxies are driving their gas and stars into the central regions, building up exponential disks and massive bulges without the need for major mergers \citep[e.g.,][]{2008ApJ...688...67E, 2008ApJ...687...59G, 2009ApJ...703..785D, 2013MNRAS.435..999D, 2016ASSL..418..355B}. The most luminous galaxies at high--redshift are the dusty star--forming galaxies originally detected in the submillimeter and known as submillimeter galaxies \citep[SMG; e.g.,][]{2002PhR...369..111B, 2005ARA&A..43..677S, 2013ARA&A..51..105C, 2014arXiv1402.1456C}. Their large luminosities ($L_{\rm IR} > 10^{12-13}$ L$_{\odot}$, qualifying them as ultra-- or even hyper--luminous infrared galaxies) make them easier to observe in the distant universe, in principle, though whether their star formation process differs from less extreme galaxies is still debated. The canonical picture is that the majority of SMGs are scaled--up ultra-luminous infrared galaxies \citep[ULIRGs;][]{1996ARA&A..34..749S} -- i.e., starburst--dominated major mergers \citep[e.g.,][]{2010MNRAS.401.1613N}, although non-cosmological hydrodynamic simulations have suggested that SMGs could be a heterogeneous population: a mix of pre-merger pairs of disk galaxies, merger--induced starbursts, and isolated gas--rich disk galaxies undergoing a secular burst \citep[e.g.,][]{2011ApJ...743..159H, 2012MNRAS.424..951H}. Still other models posit that the submillimeter-luminous phase is long-lived and associated with the bombardment of a central halo by numerous sub-halos in early Universe proto-clusters \citep{2015Natur.525..496N}. Finally, some models propose that SMGs may simply represent the most massive extension of the normal $z>2$ star--forming galaxy population \citep[e.g.,][]{2005MNRAS.363....2K, 2009MNRAS.395..160K, 2009MNRAS.396.2332K, 2010MNRAS.404.1355D}. This last theory may be at odds with claims that normal (BM/BX, $BzK$) high--redshift star--forming galaxies seem to follow a different sequence than SMGs on the $M_{\rm gas}$/$L_{\rm IR}$ plane (\citealt[e.g.,][]{2010MNRAS.407.2091G, 2010ApJ...713..686D, 2015ApJ...798L..18H}; although see \citealt{2011MNRAS.412.1913I}). In order to better understand how SMGs fit into the larger evolutionary picture -- and, more broadly, how star formation occurred in high--redshift galaxies in general -- resolved observations of the spatial distribution of the star formation are essential. However, studies based solely in the (rest--frame) optical/UV \citep[e.g.,][]{2003ApJ...599...92C, 2005ApJ...622..772C, 2010MNRAS.405..234S, 2015ApJ...799..194C} must contend with dust--obscuration, which can make such emission challenging to detect in the most highly star--forming galaxies, and where patchy reddening could potentially affect the apparent morphology, particularly in the rest--frame UV. Some studies therefore use the Plateau de Bure Interferometer (PdBI) and Karl G. Jansky Very Large Array (VLA) to target radio synchrotron emission, a potential proxy for star formation, or molecular line emission (CO), which traces the gas reservoirs required to fuel star formation, at sub-arcsecond resolution \citep[$\gtrsim$0.2$^{\prime\prime}$; e.g.,][]{2010Natur.463..781T, 2010ApJ...724..233E, 2010MNRAS.405..219B, 2012ApJ...760...11H, 2013ApJ...776...22H, 2013ApJ...768...74T, 2013ApJ...773...68G, 2014MNRAS.442..558A, 2015ApJ...809..175B, 2015A&A...584A..32M}. The molecular gas studies in particular reveal large clumpy disks in both the more `normal' high--redshift galaxies and even in some SMGs \citep{2012ApJ...760...11H}, in apparent agreement with claims of $\sim$kpc-scale star-forming regions in high-redshift galaxies from the rest-frame optical/UV \citep[e.g.,][]{2004ApJ...603...74E, 2011ApJ...739...45F, 2012ApJ...757..120G, 2015ApJ...800...39G} and H$\alpha$ line emission \citep{2011ApJ...733..101G}. Such massive kpc--scale clumps are thought to form in--situ by gravitational instability due to the gas--richness of these high--redshift galaxies \citep[e.g.,][]{2009ApJ...703..785D, 2014ApJ...780...57B}. Moreover, molecular gas observations can also provide valuable information on the kinematics of the systems. For example, based on observations of continuum and various CO transitions (up to CO[7--6]) in a sample of 12 SMGs, \citet{2010ApJ...724..233E} suggested that practically all SMGs are major mergers. However, such studies have been very expensive observationally, and in many cases at best marginally resolve the sources (see \citealt{2013ARA&A..51..105C} for a review). A more direct way to trace the obscured star--forming regions in high--redshift galaxies is through observations of the dust continuum emission in the rest--frame far-infrared (FIR), corresponding to observed submillimeter wavelengths for sources at $z>1$. The FIR dust continuum is dominantly powered by recently--formed, massive stars, making it an excellent tracer of the bolometric luminosity -- and thus star formation -- in dusty starbursts such as SMGs. While the resolution achievable by early submillimeter interferometric observations \citep[e.g.,][]{2008ApJ...673L.127D, 2011ApJ...726L..18W, 2012A&A...548A...4S, 2013ApJ...768...91H} was too poor ($>$1$^{\prime\prime}$) to sufficiently resolve high--redshift galaxies except for in a handful of cases \citep[e.g.,][]{2008ApJ...688...59Y, 2012ApJ...760...11H}, recently there have been some first attempts to constrain the sizes of larger samples of SMGs -- as well as massive dusty star--forming galaxies selected as likely progenitors of $z\sim2$ compact quiescent galaxies -- in the submillimeter \citep[e.g.,][]{2015ApJ...799...81S, 2015ApJ...810..133I, 2016ApJ...827L..32B}, revealing compact ($R_{e}\sim1$\,kpc) dusty starbursts. However, how this star formation is distributed within the sources -- e.g., whether it lies in clumpy disks or is strongly centrally peaked due to the violent and dissipative collapse expected from major merger remnants \citep{2011ApJ...730....4B} -- is still unknown. Moreover, only in rare cases of gravitational magnification \citep{2010Natur.464..733S, 2015PASJ...67...93H} or case studies of single extreme sources \citep{2015ApJ...798L..18H, 2016ApJ...827...34O} have individual star--forming regions in an SMG -- or any high--redshift galaxy -- been potentially resolved in the FIR. While seemingly consistent with the kpc--scale clumps observed in the rest--frame optical/UV and H$\alpha$/CO line emission, the reality of these low--S/N ``clumps'' -- which are argued to play a key role in high--redshift galaxy formation and evolution -- has not yet been confirmed. With ALMA, the situation is now fundamentally changed. The long baselines and large number of antennas make it possible to resolve the star-forming regions in galaxies on scales of $\lesssim$1 kpc, similar to the resolution achievable for nearby galaxies with \emph{Herschel}, and at a sensitivity sufficient to map the morphology of the emission. We therefore used ALMA to conduct high--resolution ($\sim$0.16$''$ FWHM) Band 7 (344\,GHz) mapping of the (rest--frame) FIR--continuum in 17 SMGs selected from our ALMA Cycle~0 compact configuration survey of single--dish 344\,GHz LABOCA sources detected in the Extended \textit{Chandra} Deep Field South (ECDFS) by \citet{2009ApJ...707.1201W}, constituting the largest, most homogenous, and highest--sensitivity sample of interferometrically observed SMGs to date \citep[ALESS;][]{2013ApJ...768...91H, 2013MNRAS.432....2K}. We begin in \S\ref{data} with the details of the observations. Our results are presented in \S\ref{results}, followed by a discussion in \S\ref{discussion}. We summarize our conclusions in \S\ref{summary}. Where applicable we assume a concordance, flat $\Lambda$CDM cosmology of H$_0$=71 km\,s$^{-1}$ Mpc$^{-1}$, $\Omega_{\Lambda}$=0.73, and $\Omega_{M}$=0.27 \citep{2003ApJS..148..175S, 2007ApJS..170..377S}. All magnitudes are on the AB system. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | \label{discussion} The ALMA imaging presented here allows us to resolve the dust-obscured star formation in a sample of luminous high-redshift dusty star-forming galaxies on scales of $\sim$1\,kpc. S\'ersic profile fits reveal that the galaxies have a median effective radius of $R_e=0.24$$''$$\pm$0.02$''$ at a rest wavelength of $\lambda\sim250\mu$m (for a typical source redshift of $z\sim2.5$), corresponding to a typical physical size of $R_{e}=1.8\pm$0.2\,kpc. In contrast, \textit{Herschel} 70--160$\mu$m imaging of 400 local galaxies and QSO hosts suggests that ULIRGs are exclusively found with very compact ($R_e\sim0.5$ kpc) morphologies \citep[albeit at shorter rest wavelengths of $\lambda\sim70\mu$m;][]{2016A&A...591A.136L}. This confirms earlier suggestions from CO observations and marginally resolved radio and submillimeter data \citep[e.g.,][]{2004ApJ...611..732C, 2010MNRAS.404..198I, 2011MNRAS.412.1913I, 2010ApJ...714.1407C, 2013ApJ...776...22H, 2015ApJ...799...81S, 2015ApJ...810..133I, 2015A&A...584A..32M} that high-redshift dusty star-forming galaxies are indeed larger than similarly luminous local galaxies. In addition to the observed sizes, the observations presented here resolve the dust emission over many beams at relatively high S/N, allowing us to constrain the more detailed morphology. In particular, there have been a number of claims in the literature that, when observed at high--resolution, the gas reservoirs of SMGs break up into sub--kpc or kpc--sized clumps \citep[e.g.,][]{2010Natur.463..781T, 2011ApJ...742...11S, 2012ApJ...760...11H, 2015PASJ...67...93H}. Assuming a constant dust--to--gas ratio -- i.e., that the dust follows the gas -- the dust distribution should then be similarly clumpy. Such clumpy dust within a rotating gas disk was potentially observed in, for example, the strongly lensed ``Eyelash'' galaxy by \citet{2010Natur.464..733S}, seeming to confirm this theory. In contrast, we find that the SMGs observed here appear (within the limits of our current resolution and sensitivity) to be smooth and disk--like on kpc--scales, with a median S\'ersic index of $n=0.9\pm0.2$. Combined with the measured sizes ($R_{e}=1.8\pm$0.2\,kpc), this seems to rule out the sort of extended, clumpy disk galaxies predicted by simulations of violent disk instability \citep[e.g.,][]{2009ApJ...703..785D, 2014ApJ...780...57B} and observed in optically--bright systems \citep[e.g.,][]{2006ApJ...645.1062F} and potentially even in the ultraluminous $z\sim4$ SMG GN20 \citep{2012ApJ...760...11H, 2015ApJ...798L..18H}. The relative uniformity of the dust morphologies observed here also seems to contradict models where SMGs are a heterogenous population \citep[e.g.,][]{2011ApJ...743..159H, 2012MNRAS.424..951H}, although larger sample sizes covering a larger range of flux densities are required to more thoroughly test this conclusion. It is, of course, still possible that there is clump--like structure below our current resolution limits. The clumps in the Eyelash and SDP.81 are reported to have physical sizes of only a couple hundred pc \citep{2010Natur.464..733S, 2015PASJ...67...93H}. Similarly, the dust continuum in the most well-studied local ULIRG, Arp 220, is concentrated in two very compact ($\sim$30--50\,pc) nuclei situated $\sim$300\,pc apart \citep[although at longer rest-frame wavelengths; e.g.,][]{2008ApJ...684..957S, 2015ApJ...799...10B, 2016arXiv160509381S}. We would not be able to resolve the nuclei of Arp 220 at a redshift of $z\sim2.5$ with the present observations, and indeed, we may find a hint of clump--like structure in one of our SMGs when we push down to (sub--)kpc scales. However, the simulations and analysis in \S\ref{clumps} suggest that caution should be exercised when identifying candidate clumps in even moderate S/N interferometric data. Indeed, the sizes we measure from the high--resolution images are consistent with those predicted from the Stefan--Boltzmann law based on the the measured dust temperatures and FIR luminosities, another indication that the emission is relatively smooth. The measured sizes also agree with those estimated from fitting models assuming power--law mass--temperature distributions, again assuming smooth disk emission \citep{2010ApJ...717...29K}. Significantly higher--S/N observations at higher resolution are required to determine whether the dust emission in these SMGs retains a disk--like appearance on sub--kpc scales. In contrast to the smooth appearance of the obscured star formation, the matched--resolution \textit{HST} WFC3 imaging of these SMGs -- tracing the unobscured rest--frame optical light -- appears clumpy and irregular. The median half--light radius observed for the unobscured stellar emission in these sources corresponds to $R_e=4.1\pm0.8$\,kpc at $z\sim2.5$, implying that the pre--existing stellar distributions of the SMGs are also significantly more extended than the dust emission. A similar conclusion was drawn regarding the morphology and extent of the stellar component for the larger sample of 48 ALESS SMGs presented by \citet{2015ApJ...799..194C}, indicating that stellar morphologies observed in our sources are representative of the parent population. The current study reveals that this unobscured stellar emission is largely uncorrelated with the obscured star-forming regions in individual sources. This observation implies that SED fitting routines assuming a simple dust screen over a single or even composite stellar population may be too simplistic. The difference observed between the morphology of the obscured star formation and unobscured stellar emission in these SMGs also leads us to consider their formation scenario. \citet{2015ApJ...799..194C} use the apparently disturbed rest--frame optical morphologies, along with the short expected lifetimes of SMGs, to argue that the majority of $z\sim2-3$ SMGs are early/mid--stage major mergers, as has been argued previously on the basis of, e.g., radio and submillimeter multiplicity and kinematics \citep[e.g.,][]{2006MNRAS.371..465S, 2010ApJ...724..233E}. Theoretically, the profiles of merger remnants are expected to be relatively compact and strongly centrally peaked due to the violent and dissipative collapse expected in turbulent and clumpy gas \citep[e.g.,][]{2011ApJ...730....4B}. The small sizes of the dust disks we measure could be consistent with this scenario, though the observed S\'ersic indices are lower than expected in the simulations. If the starbursts in these galaxies are major merger driven, we are likely observing the result of the gas/dust more rapidly (re--)forming disk structures than the existing stellar component. Assuming a typical gas consumption timescale for SMGs of $\sim$100 Myr \citep{2013MNRAS.429.3047B}, and based on the apparent dynamical (orbital) timescales ($\sim$20 Myr) implied assuming velocity widths of $\sim$500 km s$^{-1}$ \citep{2013MNRAS.429.3047B} and the effective radii measured here, it is possible that the disks have settled while the burst of star formation is still ongoing. It is possible that the more compact stellar counterparts observed in some sources (Figure~\ref{fig:PRthumbs}) then correspond to more evolved systems. Simulations show that the old stars present in the existing stellar component may also contract due to the turbulent dissipation of the gas and young stars, which can contain a large fraction of the total mass \citep{2011ApJ...730....4B}. The current bursts of star formation thus have the potential to transform both the observed galaxy sizes and the overall light profiles as they evolve. This transformation could also help establish the connection between SMGs and local elliptical galaxies, their proposed descendants \citep[e.g.,][]{1999ApJ...515..518E, 2006MNRAS.371..465S, 2015ApJ...810..133I}. In Figure~\ref{fig:atlas3d}, we compare the properties of the ALESS SMGs studied in this work with the volume--limited ATLAS$^{\rm 3D}$ sample of nearby early--type galaxies \citep{2011MNRAS.413..813C}. The stellar masses, effective radii, and mass surface densities for the ATLAS$^{\rm 3D}$ galaxies are discussed in \citet{2013MNRAS.432.1862C}. The median properties\footnote{We show the median properties of the ALESS SMGs as there can be significant scatter among individual galaxies.} of the ALESS SMGs from this work are overplotted, where we use the average gas mass surface densities (Figure~\ref{fig:Td_FIR}). If we assume an average stellar mass of M$_{*}\sim$ 8$\times$10$^{10}$ M$_{\odot}$ \citep{2014ApJ...788..125S} and a gas mass of M$_{\rm gas}\sim$ 5$\times$10$^{10}$ M$_{\odot}$ (\citealt{2013MNRAS.429.3047B}; consistent with that derived from the dust masses for our sources), then the $z\sim0$ descendants of these SMGs would have total masses of M$_{*}\sim$ 1--2$\times$10$^{11}$ M$_{\odot}$ (assuming $\sim$100\% star formation efficiency in the disk). If we then assume $z\sim0$ sizes of $R_{\rm e} \sim$ 2--3 kpc \citep[taking the weighted average of the submillimeter and optical sizes, and assuming the stellar components may also contract further;][]{2011ApJ...730....4B}, we can estimate how the descendants of SMGs may compare to local early--type galaxies. We find that the SMG descendants have stellar masses, effective radii, and average gas surface densities consistent with the most compact massive (M$_{*}\sim$ 1--2$\times$10$^{11}$ M$_{\odot}$) early--type galaxies -- with the highest M/L ratios -- observed locally (Figure~\ref{fig:atlas3d}). %%%%%%%%%%%%%%%%%%%%%%%%%% | 16 | 9 | 1609.09649 |
1609 | 1609.08534_arXiv.txt | {In this paper we carry out a preliminary study of the dependence of the Tully-Fisher Relation (TFR) with the width and intensity level of the absolute magnitude interval of a limited sample of 2411 galaxies taken from Mathewson \& Ford (1996). The galaxies in this sample do not differ significantly in morphological type, and are distributed over an $\sim11$-magnitude interval ($-24.4 < I < -13.0$). We take as directives the papers by Nigoche-Netro et al. (2008, 2009, 2010) in which they study the dependence of the Kormendy (KR), the Fundamental Plane (FPR) and the Faber-Jackson Relations (FJR) with the magnitude interval within which the observed galaxies used to derive these relations are contained. We were able to characterise the behaviour of the TFR coefficients $(\alpha, \beta)$ with respect to the width of the magnitude interval as well as with the brightness of the galaxies within this magnitude interval. We concluded that the TFR for this specific sample of galaxies depends on observational biases caused by arbitrary magnitude cuts, which in turn depend on the width and intensity of the chosen brightness levels.} | \label{sec:intro} There are studies published in the literature (Nigoche-Netro et al. 2008, 2009, 2010) in which the authors carry out studies of the dependence of the parameter values of structural relations of elliptical galaxies on the size and brightness of the magnitude interval in which the observed galaxies are contained. The structural relations which are studied in these papers are: the Kormendy Relation (KR), the Fundamental Plane Relation (FPR) and the Faber-Jackson Relation (FJR). The authors point out that it may not be possible to reach conclusions on the physical properties of groups of galaxies when comparing the values of the slopes of the structural relations if these values were obtained with galaxy samples contained in magnitude intervals of different width or in different magnitude intervals. If the magnitude intervals are narrow, the differences encountered are negligible, whereas, if the interval is wide, the geometric form of the galaxy distribution on a plane formed by the structural relations parameters is dominated by the magnitude cuts induced by the observations, and this could mask the differences produced by the galaxies intrinsic properties. A study similar to the ones described above for spiral galaxies has not been performed. This paper presents a preliminary study of whether these effects are also present in the TFR of a limited sample of galaxies which do not differ significantly in morphological type (Sb-Sc). In this paper we investigate whether arbitrary observational magnitude cuts to spiral galaxy samples produce biases on the TFR parameter values. If this is so, these parameter values may not be used in calculations of the distance of spiral galaxies using the TFR. It is important to stress at this point that the aim of this paper is not so much obtaining the true values of the coefficients of the TFR, but rather showing that these values may change depending on the way the data used in calculating the parameters are collected. In 1977 R. Brent Tully and J. Richard Fisher (Tully \& Fisher, 1977) published a paper in which they established a relation between the total luminosity and the rotational velocity ($L=\beta V_{rot}^{\alpha}$) for several samples of spiral galaxies. From this relation, and the maximum value of the rotational velocity, it is possible to estimate the absolute magnitude of the entire galaxy, and hence, by comparison with the apparent magnitude, calculate its distance. Therefore the TFR is a very important tool to map the large scale structure of the universe, and the Hubble flow. For nearby galaxies the TFR requires $HI$ observations (recessional velocity $\leq10,000$ $km/s$), whereas for larger recessional velocities we use $H\alpha$ observations, although when the recessional velocities are larger that $60,000$ $km/s$ $(z=0.2)$, $H\alpha$ appears with wavelength longer than $7875\mathring{A}$ where it may be confused with $OH$ sky emission lines. For larger distances the use of other emission lines, such as: [OII] (3727 \AA ) and [OIII] (5007 \AA ) is normal (Vogt et al., 1996). These authors point to the fact that the TFR may be used to study the structure and evolution of spiral galaxies with large systemic velocities, due to the fact that their luminosities (found using the TFR) do not vary much $(\Delta B_{M}\leq0.6)$ with respect to those found by spectroscopic means for more distant galaxies (Bamford et al, 2006). The observations of spiral galaxies used for establishing the parameters $(\alpha, \beta)$ of the TFR must be corrected for a variety of effects, among which some of the most important ones are the correction for inclination, the correction for internal absorption and also the correction for dust extinction within our own galaxy. If we consider, as it is usually done, that spiral galaxies may be represented by oblate spheroids, the inclination may be calculated from the disc projection using the following equation: \bigskip \bigskip \begin{center} $\cos^{2}i=\frac{\left( \frac{b}{a}\right) ^{2}-\alpha^{2}}{1-\alpha^{2}}$ \end{center} \bigskip where $i$ represent the angle of inclination, $\frac{b}{a}$ the minor to major axis ratio of the best fitted ellipse, and $\alpha$ is the intrinsic axial ratio for an edge-on system. There are some problems, however, because some galaxies do not have perfectly circular isophotes when viewed face-on, so we must restrict our galaxy sample to inclinations of at least $35^{o}-45^{o}$ in order to minimise the uncertainties on the deprojected values of rotational velocity. To determine the internal extinction in galaxies has always been very difficult. However, at present, the use of CCD and IR detectors allows very precise multiwavelength surface photometry for galaxies, which in turn, permits the statistical determination of reddening. The extinction corrections are expressed in terms of the axial ratio \ (Tully et al, 1998, Masters, Giovanelly \& Hanes, 2003): \bigskip \begin{center} $A_{\lambda}^{i}=\gamma_{\lambda}\log(\frac{a}{b})$ \end{center} \bigskip where \bigskip $A_{\lambda}^{i}$ represents the extinction at wavelength $\lambda$ as a function of the inclination angle $i$, and $(\frac{a}{b})$ \ the observed axial ratio. This correction depends on the dust content of galaxies as variations of the coefficient $\gamma_{\lambda}$ as a function of the rotational velocity corrected for inclination effects $\left( W_{R}^{i}\right) $. Recently Shao et al. (2007) have made an extensive study of a sample of more than 60,000 galaxies from the second Data Release of the SDSS. They find that the Luminosity Function (LF) of spiral galaxies appears to be consistent with a simple obscuration model; for which the optical depth $\tau$ results to be proportional to the cosine of the inclination angle $(i)$. This cosine function is multiplied by a coefficient $(\gamma)$ which turns out to be independent of the luminosity of the galaxy in question in any one of the bands studied, giving a power law of wavelength as an extinction curve $(\tau \sim \lambda^ {-n})$ where the exponent takes a value of $n=0.96 \pm 0.04$. The characteristic magnitudes $(M^*)$ of the LF are made dimmer by $0.5$ mags in the $z$ band and $1.2$ mags in the $u$ band. Since the Mathewson \& Ford (1996) sample that we use for this paper has already been corrected for a variety of effects, including inclination corrections, we do not attempt any further corrections in order to preserve the consistency of the data we are using. Apparent magnitudes also require corrections for dust effects in our own galaxy. Using the $HI$ and dust maps (IRAS 100 $\mu m$) we know that the amount of $HI$ and that of dust are well correlated. Extinction due to this components has been calibrated with observations of distant stars in different colours. As a result the galactic extinction for any galaxy may be estimated given its position on these maps (Schlegel, Finkbeiner \& Davis, 1998). If the galactic latitude is lower than $25^{o}-30^{o}$, corrections for galactic extinction become larger as well as the associated uncertainties (Schlafly \& Finkbeiner, 2011). This is why the samples of galaxies to which the TFR is applied are usually restricted to those with $l\geq25^{o}$. However, there is a recent paper (Said, Kraan-Korteweg \& Jarrett, 2015) in which the authors have found a correction in the Near Infrared (NIR) that allows the inclusion of galaxies located at lower galactic latitudes, in the so-called Zone of Avoidance (ZoA). \bigskip The TFR has been absolutely calibrated by the use of Cepheids in external galaxies, observed with the Hubble Space Telescope (HST), whose distances extend out to $\sim20$ $Mpc$ (see Freedman, 1990 and Pierce \& Tully, 1992.). One such study is the \textit{Hubble Key Project of Extragalactic Distances}, which obtained distances, using Cepheids, to galaxies that contain type Ia Supernovae. \bigskip In Vogt et al. (1996), the TFR has been used to calculate the distance to many spiral galaxies with systemic velocities smaller than $8,000$ $km/sec$, the results of this paper show a very good linear relation between the distance in $Mpc$ and the receding velocity of the galaxies in $km/sec$, showing quite clearly the Hubble flow and producing a value for the Hubble constant of 80 $kms^{-1}$ $Mpc^{-1}$. \bigskip Since its discovery in 1977, the TFR has been a very powerful tool, used to calculate the distance to galaxies whose position very far from our vantage point makes it difficult to obtain their distances using other more conventional methods, as well as to provide insight into the formation and evolution of galaxies. As mentioned above, the TFR is a relation between the brightness of a spiral galaxy and its rotational velocity, this brightness is measured in different passbands. Due to this fact, there are TFRs in the radio for HI and CO observations as well as for optical and infrared bands. The general form of the TFR is the same for all passbands but the values of its coefficients and scatter may vary. Although it appears that the TFR is valid for spiral galaxies at different redshifts, a change of the values of its parameters has been detected and is referred to as evolution of the TFR, Ziegler et al. (2002) have studied 60 late-type galaxies in the redshift interval $0.1-1$. They find that the more distant sample presents a flatter TFR than that for the local galaxies, being the values they find $-5.77 \pm 0.45$ and $-7.92 \pm 0.18$, thus finding evidence of evolution of the TFR at $3\sigma$ levels. Weiner, et al. (2006) measure the evolution of the TFR in the optical and infrared using kinematic measurements of a large sample of galaxies from the Team Keck Redshift Survey on the GOODS-N field. They detect evolution in both the slope and the intercept of the TFR, this results suggest differential luminosity evolution. With the aid of the multi-integral field spectrograph GIRAFFE at the VLT, Puech, et al. (2008) have derived the K-band TFR at $z \sim 0.6$ for a sample of 65 galaxies. They conclude that both the slope and the scatter of the TFR do not appear to evolve with redshift. Fern\'andez, et al. (2009) study the $B$, $R$ and $I$ TFR at $z=1.3$. Their results are not conclusive in suggesting evolution of the TFR, since the possible luminosity evolution is contained within the scatter of the relation. Their study, however, shows a clear tendency for all bands studied favouring a luminosity evolution where galaxies were brighter in the past for the same rotational velocity. Fern\'andez, et al. (2010) study the evolution of the TFR in the $B$, $V$, $R$, $I$, and $K_s$ bands. They detect a clear evolution of the TFRs in the sense that galaxies were brighter in the past at the same rotational velocity. The luminosity change is more noticeable for shorter wavelengths. Russell (2004) has found that the TFR pre\-sent a dependence on galactic morphology. Sc I and Seyfert galaxies are more luminous at a given rotational velocity than galaxies of other morphological types. Not taking into account this difference may lead to the distances to Sc I galaxies to be systematically underestimated, whereas distances to Sb/Sc III galaxies are overestimated. He concludes that using type-dependent TFR improves significantly the determination of distances to galaxies. Masters, et al. (2008) have investigated the dependence of the NIR TFR with morphological type and have shown that for the $J$, $H$, and $K$ bands the TFR is shallower for earlier-type spirals which also have a brighter TFR zero-point than the later-type spirals. Shen, at al. (2009) show that the TFR of spiral galaxies is very morphological-type dependent, where earlier-type spirals have systematically lower luminosities at a fixed maximum rotational velocity. This difference is more pronounced at shorter wavelengths. As we said above, the TFR was discovered in 1977 (Tully \& Fisher, 1977) and since this date, it has been widely utilised to study peculiar velocities and cosmography (e.g. Han, 1992; Mould et al., 1993; da Costa et al., 1996; Theureau et al., 2007; Courtois \& Tully, 2012; Courtois et al., 2013; Tully et al., 2014). The rotational velocity, which is distance independent, may be measured using either optical rotation curves or $HI$ profiles line-width, and the absolute magnitude of these galaxies may be obtained through photometric measurements. Once this is done in a consistent way, a truly reliable TF survey is obtained. This is exactly what was done by Mathewson \& Ford, (1996) for a particular sample of more than 2,000 galaxies perfectly suited for the TFR. This sample is the one we use in this preliminary study (see Section \ref{sec:sample}). If the results obtained in this paper look promising we plan to extend this preliminary study to a much larger statistically significant study using suitable spiral galaxies from the Sloan Digital Sky Survey (SDSS). \bigskip In this paper we shall report the results of a preliminary study of the dependence of the value of the coefficients of the TFR with the size and width of the magnitude interval within which the observed galaxies are contained. In \S2 we present a sample of 2411 galaxies which we use for this study, in \S3 and the Appendix we perform a series of analysis for the data which may be conceptualised as different observational arrangements for the galaxies used in the calculation of the TFR coefficients, \S4 presents a non-parametric statistical analysis with which we prove that the variation of the values of the coefficients is not due to statistical fluctuations and therefore, may be ascribed to the way the galaxies have been grouped together, \S5 and the Appendix present an analysis of the values of the TFR coefficients with apparent magnitude, and \S6 presents our conclusions. | \label{sec:conclusions} In this preliminary work we have performed an investigation on the variation of the coefficients $(\alpha, \beta)$ of the TFR due to the way the galaxies used for this determination are grouped together. Again, we would like to stress the fact that the aim of this paper is not to obtain the true values of the coefficients of the TFR, but rather to show that their values may vary significantly due to observational restrictions. In order to do this, we have followed the directives presented in previous papers (Nigoche-Netro et al. 2008, 2009 \& 2010) and have grouped a sample of 2411 galaxies taken from the literature (Mathewson \& Ford, 1996) in several different ways which may be conceptualised as different observational groups of data. This sample of galaxies was chosen to perform this investigation because it consisted only of spiral galaxies which Mathewson \& Ford had already identified as good candidates to be used in the TFR, and for which they presented all the necessary data required for our calculations; besides all the multiple corrections which are usually applied to samples of galaxies had already been applied, making this sample an ideal one for a straight forward use in our investigation. In all the cases reported we found that the values of the coefficients vary more than the typical size of their corresponding error bars. A non-parametric statistical analysis of our results shows that we may reject the $null$ $hypothesis$, that states that the variations of the values of the coefficients is simply due to statistical fluctuations, with a high degree of confidence (see Table \ref{tab:hypothesis}) considering the size of the sample and the nature of our study. In this preliminary, first-approach work, we have only shown that the values of the TFR may vary depending on how the sample of galaxies is collected. We do not, as yet, know whether these variations imply different physical properties between the alternate groups of galaxies used in the calculation of the TFR coefficients. However, we feel this not to be the case, because it appears that the differences in parameter values are due to three main causes: i) the way the different samples of galaxies are collected, here we certainly have the effects of observational cuts, ii) the form of the galaxy-distribution on the plane defined by the parameters of the relation in question (Tully-Fisher, Faber-Jackson, Fundamental Plane, and Kormendy). This point is fully explained in the Nigoche-Netro et al. (2008, 2009, 2010) papers and iii) the size of the intrinsic scatter of the relation. A detailed study with a larger sample of galaxies would shed more light into these points. We also advanced the idea that the correct way of calculating the values of the coefficients of the structural relations for early type galaxies (KR, FPR, and FJR), as well as those for the TFR would be following the second iterative procedure presented in Section \ref{sec:magnitudecases} which accumulates galaxies in {\bf apparent magnitude} starting with the brightest ones and adding fainter ones in convenient steps of apparent magnitude. | 16 | 9 | 1609.08534 |
1609 | 1609.01623_arXiv.txt | Protogalactic environments are typically identified using quasar absorption lines, and these galactic building blocks can manifest as Damped Lyman-Alpha Absorbers (DLAs) and Lyman Limit Systems (LLSs). We use radio observations of Faraday effects to test whether DLAs and LLSs host a magnetised medium, by combining DLA and LLS detections throughout the literature with 1.4~GHz polarization data from the NRAO VLA Sky Survey (NVSS). We obtain a control, a DLA, and a LLS sample consisting of 114, 19, and 27 lines-of-sight respectively -- all of which are polarized at $\ge8\sigma$ to ensure Rician bias is negligible. Using a Bayesian framework, we are unable to detect either coherent or random magnetic fields in DLAs: the regular coherent magnetic fields within the DLAs must be $\le2.8$~$\muup$G, and the lack of depolarization is consistent with the weakly magnetised gas in DLAs being non-turbulent and quiescent. However, we find mild suggestive evidence that LLSs have coherent magnetic fields: after controlling for the redshift-distribution of our data, we find a 71.5\% probability that LLSs have a higher RM than a control sample. We also find strong evidence that LLSs host random magnetic fields, with a 95.5\% probability that LLS lines-of-sight have lower polarized fractions than a control sample. The regular coherent magnetic fields within the LLSs must be $\le2.4$~$\muup$G, and the magnetised gas must be highly turbulent with a typical scale on the order of $\approx5$--20~pc, which is similar to that of the Milky Way. This is consistent with the standard dynamo pedagogy, whereby magnetic fields in protogalaxies increase in coherence and strength as a function of cosmic time. Our results are consistent with a hierarchical galaxy formation scenario, with the DLAs, LLSs, and strong magnesium~II (Mg\,{\sc ii}) systems exploring three different stages of magnetic field evolution in galaxies. | \label{introduction} The evolution of magnetism in galaxies is of fundamental interest \citep{1982ApJ...263..518K}. In particular, the magnetic fields in young protogalaxies remain essentially completely unexplored \citep{1992ApJ...388...17W,1995ApJ...445..624O}. These protogalaxies are expected to have not yet experienced significant dynamo activity, and therefore constitute ``missing links'' in our understanding of the dynamo process and the evolution of cosmic magnetic fields \citep{2004NewAR..48.1003G}. The dynamo process describes how weak ``seed'' magnets in the early Universe were amplified and ordered throughout cosmological history by large-scale rotation and turbulence within galaxy disks and halos \citep[e.g.][]{2014MNRAS.443.1867C,2015ApJ...808...28C}. This suggests that the magnetic field strength should be weaker in protogalaxies than in normal galaxies. Furthermore, the coherence of the typical protogalactic magnetic field should also be less, with significant field disorder expected to be present. Measuring these magnetic fields would have implications for the cosmological growth of magnetism, and would constrain dynamo mechanisms \citep[e.g.][]{2013MNRAS.435.3575B}. Such studies are highly challenging, as at radio wavelengths, the protogalactic environment is typically of such low-luminosity that directly imaging the emission due to magnetic fields will likely not even be possible with ultra-sensitive (sub-$\muup$Jy) data from the Square Kilometre Array (SKA) \citep{2015aska.confE..92J}. We therefore suggest an alternative approach to study magnetic fields in these galactic building blocks now, using radio polarization observations. \begin{figure*} \centering \includegraphics[trim=0cm 0.0cm 0cm 0.0cm, clip=true, width=15.8cm]{DLA_NEWIMAGE.pdf} \caption{A cartoon of a ``back-lit'' experiment towards a polarized background source. This is merely an illustratory cartoon, and is not to scale. The observer, on the left of the cartoon, measures properties (such as Faraday rotation) along the line-of-sight towards a bright, polarized, background radio source. Along the line-of-sight, an intervening foreground cloud is known to be present via quasar absorption lines. The physical nature of the foreground cloud can vary based upon the absorption line used, and in this cartoon is a primeval galaxy. The image is derived from original works in the public domain: the image of the protogalaxy is courtesy of Adolf Schaller for STScI, and the image of Cygnus A is courtesy of NRAO/AUI/NSF.} \label{DLAcartoon} \end{figure*} Radio polarization observations are the best available probe of cosmic magnetic fields, as they allow us to measure both the polarized fraction towards distant background radio sources (which is related to the degree of ordering of magnetic fields), and the Faraday rotation located along the entire line-of-sight. Faraday rotation is a powerful tool for measuring the magnetic field strength towards astrophysical objects. The combination of cosmic magnetic fields and charged particles distributed along the sightline towards a background radio source causes rotation of the polarization angle of linearly polarized synchrotron emission \citep[e.g.][]{2011hea..book.....L}. Along a line of sight, the observed polarization angle is altered by an amount equal to \begin{equation} \Phi = \Phi_{\textrm{0}} + \textrm{RM}\lambda^2 \,, \end{equation} where $\lambda$ is the observing wavelength, $\Phi$ and $\Phi_{\textrm{0}}$ are the measured and intrinsic polarization angles respectively, and the constant of proportionality RM, the `rotation measure', is generally related to the integrated product of the electron number density, \(n_{\rm e}\), and the strength of the component of the magnetic field parallel to the line of sight, \(B_{\parallel}\). The observed RM is also related to the redshift at which the Faraday rotating medium is located, but as it is generally not known where all of the rotating media are distributed along the line of sight, this relation is typically not simple. Nevertheless, measurements of the RM can be used to infer the presence of magnetic fields somewhere along the line of sight between an observer and a source. Using a ``back-lit'' quasi-stellar object (QSO, which we will use interchangably with quasar) as a flashlight shining through foreground intervening material, it has previously been suggested that there is a correlation between metal-line absorption and the Faraday rotation/RM of distant polarized sources \citep[e.g.][]{1984ApJ...279...19W,1992ApJ...387..528K}. The experimental setup of a typical back-lit experiment is shown in Fig.~\ref{DLAcartoon}. Previous studies have already begun using the correlations seen in back-lit experiments to indirectly test dynamo theory in normal galaxies using strong magnesium~II (Mg\,{\sc ii}) absorption lines \citep[e.g.][]{2008Natur.454..302B,2013ApJ...772L..28B,2014ApJ...795...63F} located in the spectra of QSOs. This analysis can be extended to use Damped Lyman-Alpha Absorption systems and Lyman Limit Systems in the spectra of QSOs, and thereby probe the distribution of gaseous matter throughout the Universe, particularly in the protogalactic and the intergalactic medium \citep{1998ARA&A..36..267R,2005ARA&A..43..861W,2009RvMP...81.1405M}. In this paper, we are therefore interested in two types of absorption systems, and define these systems via their neutral hydrogen column densities, with $1.6\times10^{17} <$ $N$(H\,{\sc i}) $< 2\times10^{20}$~cm$^{-2}$ being Lyman Limit Systems (LLSs), and $N$(H\,{\sc i}) $\ge 2\times10^{20}$~cm$^{-2}$ being Damped Lyman-Alpha Absorbers (DLAs) \citep{2005ARA&A..43..861W,2015MNRAS.451..904E}. There is a fundamental difference between both systems: hydrogen is mainly neutral in DLAs, while it is mainly ionised in LLSs. This characteristic separates the DLAs from both the LLSs and other intervening absorbers seen in QSO sightlines, such as the Ly-alpha forest ($N$(H\,{\sc i}) $\le10^{17}$~cm$^{-2}$), where the neutral gas is a minor or non-existent phase. The presence of neutral, cold, and molecular gas is crucial to link the DLAs to star-forming galaxies \citep{2003ApJ...593..215W,2003MNRAS.346..209L,2005ARA&A..43..861W,2005ApJ...622L..81H,2008A&A...481..327N}, although the exact nature of the DLAs and LLSs and their relation to present-day galaxies is still under debate and study \citep{2005ARA&A..43..861W,2006ApJ...652..981W,2008ApJ...681..856R,2009RvMP...81.1405M}. Although the nature of these absorption systems remains poorly understood, they possibly provide the only example of an interstellar medium in the high-redshift Universe. Both types of system are important, as they are known to be some of the biggest intervening neutral-hydrogen gas reservoirs in the Universe and thereby constitute the building blocks of galaxies. The combination of both DLAs and LLSs provides a large range in column density that allows us to explore and contrast the difference between these relative ends of the absorption system extrema. Importantly, both DLAs and LLSs are generally believed to correspond to similar features in the intergalactic medium with both systems probing the progenitors of current massive galaxies \citep[e.g.][]{2010ApJ...721.1448S}, and with DLAs corresponding to extended disks \citep[e.g.][]{1998ApJ...507..113P} and LLSs corresponding to extended gaseous haloes \citep[e.g.][]{2015MNRAS.451..904E}. The column density of these absorbers has been found to be correlated to the mass of the nearest galaxy, with the correlation more pronounced for DLAs, and similar correlations found between the star-formation rate, halo mass, and H\,{\sc i} content of the associated galaxies \citep[e.g.][]{2014MNRAS.438..529R}. Similarly, LLSs display a correlation between $N$(H\,{\sc i}) and halo mass, with lower column density systems more likely to be found near lower mass halos \citep[e.g.][]{2012MNRAS.421.2809V}. However, only two studies to-date have attempted to look for connections between protogalaxies themselves and magnetic fields. The first study of \citet{1992ApJ...388...17W} used Mg\,{\sc ii} systems with H\,{\sc i} column densities above $2\times10^{20}$~cm$^{-2}$, and classified these as DLAs. They found 5 background sources with Faraday rotation higher than 3 times the 1$\sigma$ uncertainty in RRM. The second study of \citet{1995ApJ...445..624O} used DLAs along the line of sight towards 11 background sources with known Faraday rotation. This data-limited study provided inconclusive results, with a ``tentative'' indication of higher Faraday rotation associated with the DLAs. Neither study attempted to measure the LLSs. This is a similar scenario to the previously weak correlations reported between |RM| and the number of strong Mg\,{\sc ii} absorption lines along the line of sight \citep{1982ApJ...263..518K,2012ApJ...761..144B}, which have more recently been expanded into definitive connections \citep{2014ApJ...795...63F}. The next step in understanding the magnetised structure, strength, and coherence in low-luminosity galaxies, is therefore to expand from studies of Mg\,{\sc ii} absorption lines to new studies of DLAs and LLSs. We can attempt to use polarization measurements to measure the magnetic fields in the ionized gas component of these systems \citep[e.g.][]{2015ApJ...808...38R}. This paper is structured as follows: we present our observational data in Section~\ref{data}, which details and justifies how we created our sample and its properties. Our results, including a quantitative analysis of our main sample is detailed in Section~\ref{results}. A discussion of our results and the estimation of magnetic properties from our data is presented in Section~\ref{discussion}, while our conclusions are summarised in Section~\ref{conclusions}. We refer to `polarization' on multiple occasions, in all cases we are referring to linear radio polarization. Unless otherwise specified, all quantities are presented as measured in the observed-frame. | \label{conclusions} We have studied samples of QSOs with intervening DLAs or LLSs identified somewhere along their line-of-sight, and compared these samples to a control sample of QSOs with no intervening DLAs or LLSs. We have compared these data using a Bayesian analysis, and it is the first time that such a statistical method has been applied to Faraday rotation and fractional polarization data in this way. The new application of this statistical tool opens a new method for quasar absorption line studies, in which many absorption lines have only a few quasar candidates and hence small sample sizes. This Bayesian analysis remains robust in the small sample regime, and therefore opens up previously restrictively-sized samples for analysis. This also presents a new way to more rigorously assess claimed correlations from previous studies of strong \citep[e.g.][]{2008Natur.454..302B,2014ApJ...795...63F} and weak \citep[e.g.][]{2016arXiv160400028K} Mg\,{\sc ii} absorbers. Given our data, we have found that: \begin{enumerate} \item It is unlikely that DLAs have coherent magnetic fields, with a 32.1\% probability that DLA lines-of-sight have a higher RM than a control sample. It is also unlikely that DLAs have random magnetic fields, with a 45.2\% probability that DLA lines-of-sight have a lower polarized fraction than a control sample. \item There is mild suggestive evidence that LLSs have coherent magnetic fields, and when controlling for the redshift distribution of our data, we find a 71.5\% probability that LLS lines-of-sight have a higher RM than a control sample. However, it is extremely likely that LLSs have random magnetic fields, with a 95.5\% probability that LLS lines-of-sight have a lower polarized fraction than a control sample. \item We model our data to show that there is a 90\% probability that the regular coherent magnetic fields within the DLAs must be $\le2.8$~$\muup$G, and within the LLSs must be $\le2.4$~$\muup$G. \item We also model the turbulent magnetic fields, and find that our data is most consistent with the DLAs having weak random magnetic fields which suggests that the magnetised gas in DLAs is non-turbulent and quiescent. We also find that the LLSs must have an incoherent magnetic field present, and that the magnetised gas must be highly turbulent with a turbulent scale on the order of $\approx5$--20~pc, which is similar to the measured turbulent scale within the Milky Way. \end{enumerate} Overall, a clear picture consistent with typical expectations of dynamo evolution is beginning to emerge from these absorption line studies. Our data are entirely consistent with the conventional interpretation of DLAs as protogalaxies, combined with the paradigm that dynamo action acts on weak disordered magnetic fields to generate coherent strong fields. Such studies hold promise for charting out dynamo evolution over cosmic time. Understanding the environment of different physical systems such as DLAs, LLSs, and other absorption lines will be first steps in beginning to directly map the evolution of cosmic magnetism. Using the combination of strong Mg\,{\sc ii} absorbers, LLSs, and DLAs, we have begun to chart out magnetic fields out to $z\approx2$. Our data allows us to see the first observational picture of magnetic field evolution in galaxies. Protogalaxies that lack a coherent magnetic field, and which maintain significant random magnetic fields, are evolving into normal star-forming galaxies with strong coherent fields. This reaffirms the role that magnetic fields play in the formation and evolution of galaxies. This is also the first time that the magnetic fields of LLSs have ever been studied, and the first time that DLAs or LLSs have been shown to have different magnetic field properties to those of a control sample. This also lends evidence for us to conclude that the seeding of magnetic fields by supernovae and subsequent amplification during structure formation are able to build up strong magnetic fields of $\muup$G strength within short timespans. This leads to detectable magnetic fields within the very first collapsing and starforming protohalos at high redshifts, which are the building blocks for the very first galaxies. The developed techniques can also allow us to slowly push back towards the seed field and magnetogenesis era. Seed fields could have been generated in protogalaxies in the early Universe, e.g.\ at phase transitions, or in shocks in protogalactic halos (via the Biermann battery), or in fluctuations in the protogalactic plasma. Nevertheless, these seed fields will remain observationally out of reach for a long time, and remain 6 orders of magnitude below current observational thresholds, and so are expected to remain undetectable even with the SKA. However, with the introduction of a more refined Bayesian analysis for such studies, this work has created a quantitative gateway towards accessing and constraining magnetic fields in the IGM via quasar absorption line experiments. Future studies will be able to use the lowest column density Lyman systems, the Lyman-alpha forest at $\le10^{17}$~cm$^{-2}$, in order to constrain magnetism in the IGM. We are currently lacking a large sample size in our study. This prevents us from subdividing the sample further, in order to explore other connections between the absorbers based on redshift, column density, and other intervenor parameters. In the future, with larger samples of sources with high polarized signal--to--noise so as not to be affected by Rician bias, we will be able to explore evolution based on the redshift of the absorbers, to definitively rule out evolution based on the redshift of the quasars, and to explore the evolution in magnetic and ionisation properties based on column density alone. Other subdivisions such as the spectral index are also of importance and has been shown to be important for studies of strong Mg\,{\sc ii} absorbers. Nevertheless, the spectral index is far less important for the DLAs and LLSs, which are known to be smoothly-distributed with a higher covering fraction compared to the clumpy partially-ionised medium with low-covering fraction that is associated with strong Mg\,{\sc ii}. It is therefore to be expected that the magnetic environment extends to larger scales in the DLAs and LLSs than in the Mg\,{\sc ii} absorbing systems. Furthermore, the DLA and LLS sample also include a very tight cross-matching criterion of 2~arcsec, which is equal to 25~kpc at $z=1$, and therefore less than typical estimates for the DLA/LLS size. Increased sample sizes with higher angular resolution will allow us further subdivide our data, and to test these attributes. Future studies will therefore be able to subdivide the data into flat- and steep- samples with high angular resolution, allowing for direct tests of the requirement for single-component compact sources, and also providing a unique way to measure the ionised size of these absorbers. Future data that will become available as DLAs and other absorption features are identified in the SDSS DR10 or DR12 will also improve our sample size, and allow for further subdivision into smaller sub-populations \citep{2016arXiv160806483P,2016arXiv160805112R}. Finally, future studies will also be able to refine the Bayesian analysis of Faraday rotation data introduced here for quasar absorption lines. Testing other distributions, alongside the normal distributions assumed in this paper, will provide improvements and will refine future results with larger samples. Such an analysis will most likely be unable to use conjugate priors, and so will require more sophisticated sampling techniques to be used. We also discuss our model selection in Appendix~\ref{modelchoice}. If there is substantial deviation from these model choices, then there would be implications for most previous magnetic field studies throughout the literature, as our chosen models have often been used either explicitly via model-fitting or the calculation of standard deviations, or implicitly via the use of frequentist tests. While we have been able to model the coherent magnetic fields using the RMs and GRMs, further analysis of the distribution of these statistical samples will allow us to ensure that our implicit assumption, that $\sigma_{\textrm{RM}}^2 = \sigma_{\textrm{GRM}}^2 + \sigma_{\textrm{RRM}}^2$ (see Section~\ref{faradaybayes}), is correct. Expansion of our Bayesian technique may also allow us to incorporate modelling of the error terms that currently inhibit use of RRMs, and thereby allow a statistical measurement with the RRMs directly. While this could have implications for our coherent magnetic field estimates in both DLAs and LLSs, our primary result of depolarization associated with the LLSs would of course remain unaffected. The application of these Bayesian techniques offers the opportunity to remove the systematic effects that frequently affect correlation-based studies, and to provide a thorough rigourous framework for testing connections between other absorption line systems. | 16 | 9 | 1609.01623 |
1609 | 1609.01848_arXiv.txt | In the present work, we have studied the collective behaviour of a chiral plasma with first and second order dissipative corrections allowed by conformal symmetry. We have derived dispersion relations for ideal, first order and second order MHD for the chiral plasma. We have also used our results to explain the observed pulsar kicks. | Relativistic hydrodynamics is useful in understanding several physical systems such as early Universe, astrophysical systems, quark gluon plasma etc. The evolution equations for the variables of the theory viz. local velocity $u^{\mu}(x)$, temperature $T(x)$ and chemical potential $\mu(x)$ associated with the conserved charges are derivable from conservation of the energy-momentum tensor. It is well known from quantum field theories that the conservation of chiral current is spoiled by parity violating quantum effect known as the chiral anomaly \cite{vilenkin:1969, bell:1969}. Recently, kinetic and hydrodynamic theories have been modified to incorporate the parity odd effect appropriately \cite{Son:2012zy, Son:2009tf}. Example for a plausible system that can be studied using chiral hydrodynamics is the plasma in the early Universe, when there is asymmetry in the left and right handed particle number densities. In the presence of either an external gauge field or rotational flow of the fluid, the parity may be broken and there may be a current in the direction parallel to external magnetic field or in the direction parallel to the vorticity generated due to rotational flow in the chiral plasma. These two currents are known as ``Chiral Magnetic Current" (CMC) and ``Chiral Vortical Current" (CVC) respectively. The effect due to which CMC and CVC appears, are called as ``chiral magnetic effect (CME)" \cite{Tashiro:2012mf,Basar:2012gm, Fukushima:2012vr} and ``chiral vortical effect(CVE)" \cite{Vilenkin:1979ui} respectively. The transport coefficients associated with these currents can be parametrized in terms of chiral chemical potential $\mu_A=(\mu_R-\mu_L)$. These effects vanish in the absence of any net chiral imbalance within the system. These transport coefficients are calculated by several authors by imposing second law of thermodynamics $\partial_{\mu} s^{\mu} \geq 0$, where $s^{\mu}$ is the entropy four current \cite{Son:2009tf, Erdmenger:2009, Banerjee:2011}. There are many attempt to explain the chiral effects using modified kinetic theory \cite{Son:2012dy, Stephanov:2012my, chen:2013jp, Buividovich:2009wi, Buividovich:2010tn} and it has been shown that there exist collective excitations (different from usual density waves in the standard plasma), called chiral magnetic waves (CMW) \cite{Kharzeev:2011ey, Newman:2005hd} and chiral vortical wave (CVW) \cite{Jiang:2015cva}. Also, there can be gap-less excitations in the presence of dynamical electromagnetic (colour) fields called chiral plasma instability (CPI) \cite{Sadofyev:2011, Akamatsu:2014uu, Joyce:2012mm, Boyarsky:2012fr, Yamamoto:2015ns}. In a recent work \cite{Yamamoto:2015ns}, author has found a new type of gap-less collective excitation induced by chiral effects in an external magnetic field. This is a transverse wave known as chiral Alfv\'en wave and it exists even in the incompressible fluids. It is shown that, these transverse modes, get split when we take account the effect of first order viscous terms along with the ideal terms in the energy momentum tensor \cite{Abbasi:2015saa}. However a detailed study of first and second order conformal chiral viscous hydrodynamics has not been done. In the present work, we have derived dispersion relations using the first and second order conformal viscous hydrodynamics theory in presence of the external background magnetic fields for the chiral plasma. At this juncture its worth introducing the pulsar kicks, as later we use our results from normal mode analysis of chiral magnetohydrodynamics to put forward a novel mechanism to explain it. It was observed that neutron stars often does not move with the same velocity of its progenitor star \cite{lyne1982proper,gott1970runaway,iben1996origin,hansen1997pulsar}, but rather with a substantially greater speed. There are several attempts to explain these observations. Interested readers are directed to the Refs. \cite{iben1996origin,kusenko1999pulsar,kusenko2004pulsar,Kaminski:2014jda}. The exact reasons for the pulsar kick is not known. However, it is believed that it must be because of the way in which supernovae explode. A proper understanding of the cause for pulsar kick may give more insight into the supernova explosion mechanisms. A particular interest in this direction of investigation is to understand whether there is some correlation between the direction of kick velocity and angular momentum, alignment of the magnetic field etc. Though there is no clear idea about these topics yet, it is worth investigating for we believe that, later observations may shed more light onto these questions. In our discussion, we have adopted $(-,+,+,+)$ signature for the metric, generally used in cosmology and the conformal metric is given by \begin{equation} ds^2= g^*_{\mu\nu}dx^\mu d^\nu= a(\tau)^2(-d\tau^2 + g^{ij} \,dx_i d_j), \label{eq:FLRW-met} \end{equation} where $\tau$ denotes the conformal time and comoving proper $t$ time is given in terms of the conformal time as $\tau=\int dt/a(t)$. One of the important parameter is Hubble parameter $H(t)=\dot{a}/a$ (here $\dot{a}=da/dt$), which gives the rate of expansion of Universe. The metric given in equation (\ref{eq:FLRW-met}) is also known as conformally flat metric as it can be written in terms of flat space Minkowski metric $\eta_{\mu\nu}$ as $g^*_{\mu\nu}= \eta_{\mu\nu}=a^{-2}\,g_{\mu\nu}$. It has been shown that, under a conformal transformation, evolution equations of the fluid remain invariant and one can transform the evolution equations to a flat space evolution equation by redefining the variables, for example magnetic fields and electric fields as $a^{-2} {\bm B}$ and $a^{-2} {\bf E}$ respectively. Similarly, other thermodynamic variables are scaled with scale factor in expanding conformal flat space-time as: $\sigma\rightarrow a^{-1}\sigma$, $\mu\rightarrow a^{-1}\mu$ and $T\rightarrow a^{-1}T$ \cite{MacDonald:1982, Detmann:1993}. With the new variables, Maxwell's equation remain same in the conformally flat space-time. In the following discussions, we will work with the above defined comoving quantities. The rest of this paper is organized as follows: in section (\ref{sec-chMHD}), we have discussed conformal fluid hydrodynamics for the chiral plasma using a ideal and viscous hydrodynamics. In section (\ref{sec-Dis}), dispersion relation for the transverse and longitudinal modes in the case of ideal as well as viscous Hydrodynamics has been derived. In section (\ref{sec-pulsarkick}), we put forward a novel mechanism to explain the pulsar kick using results obtained in the previous section. Last section, is dedicated for discussion and results of the present work. | In this work, we have considered chiral hydrodynamics which may be relevant in treating plasma whose constituents particles are massless. We have done the linear analysis to study the behaviour of the modes allowed within such plasmas. We have shown within the ideal hydrodynamic limit that, the longitudinal modes behaves in the same way as in standard plasma and the propagates with $|v_g| = \sqrt{v_s^2 +v_A^2}$, however, the transverse mode, travel with different group velocities in the direction parallel and opposite to the background magnetic field. Since the group velocity depends on the anomaly coefficient $\xi \propto [\mu_R(T)-\mu_L(T))]$, this distinction vanishes only if the plasma has no chiral imbalances. Using this result, we have estimated pulsar kick and shown that the kick velocity $\Delta V_{NS} \text{ can be of the order of } 10^2-10^3$ km/s for a background field strength $B_0\sim (10^{12}-10^{13})$ Gauss (for strength of the background magnetic fields see \cite{Pandey:2017zpg}), which matches with the observations. Next we have considered chiral hydrodynamics with first and second order dissipative terms allowed by the conformal symmetry and done the linear analysis. We have shown that the collective modes of the chiral plasma get substantially modified in presence of the external magnetic fields due to the dissipative terms. For ${\bf k}\parallel {\bm B}_0$ and $\delta {\bm v}_{\omega, {\bf k}}\parallel {\bm B}_0$, in absence of the first order viscous term, we have sound waves propagating parallel and anti-parallel to the external magnetic field. However, in presence of dissipative terms, the modes damp due to viscosity. Furthermore, when ${\bf k}\parallel {\bm B}_0$ and $\delta {\bm v}_{\omega, {\bf k}}\perp {\bm B}_0$ the frequency $\omega$ get modifications from first order dissipative terms which in turn result in the damping of the modes. In the case of ${\bf k} \perp {\bm B}_0$, sound waves and Alf\'ven modes of the plasma get mixed up. However, they get damped at smaller scale due the the first order viscous corrections. It is to be noted here that, the chiral effects are seen only in the case of ${\bf k} \parallel {\bm B}_0$. The analysis done in the case of the second order hydrodynamics is quite completed than ideal chiral and first order hydrodynamics. We have considered that chiral potential and the temperature of the plasma is homogeneous (i. e. $\nabla \mu=0$ $\nabla T = 0$) and $\nabla\cdot \delta {\bm v}=0$. When ${\bf k}\cdot {\bm v}_A =0$ for ${\bf k}\parallel \delta {\bf v}$, modes of the plasma will only damps due to the viscosity. However, in the case of ${\bf k}\cdot {\bm v}_A \neq 0$, Alf\'ven modes modified due to the second order viscosity term. In equation (\ref{eq:secorder-kvneq0}), second term represent the chiral Alf\'ven term. Due to the second and third term, collective modes of the plasma grow. However, due to first and fourth term, these modes will be damped exponentially. This is one of the important result of our work. In the last part of the work, we have found a completed cubic dispersion equation. So, to conclude the work, we have shown using first and second order conformal hydrodynamics that our results are consistent with the previous results. In the case of second order conformal hydrodynamics, for the chiral plasma, we have shown that the transport coefficients related with the second order conformal hydrodynamics actually contributes into the dispersion relations. We have calculated pulsar kick and we have found that the pulsar kick can be explained by chiral effects of the plasma at very high temperature. | 16 | 9 | 1609.01848 |
1609 | 1609.08158_arXiv.txt | The Central Molecular Zone (CMZ, the central 500 pc of the Milky Way) contains the largest reservoir of high-density molecular gas in the Galaxy, but forms stars at a rate 10--100 times below commonly-used star formation relations. We discuss recent efforts in understanding how the nearest galactic nucleus forms its stars. The latest models of the gas inflow, star formation, and feedback duty cycle reproduce the main observable features of the CMZ, showing that star formation is episodic and that the CMZ currently resides at a star formation minimum. Using orbital modelling, we derive the three-dimensional geometry of the CMZ and show how the orbital dynamics and the star formation potential of the gas are closely coupled. We discuss how this coupling reveals the physics of star formation and feedback under the conditions seen in high-redshift galaxies, and promotes the formation of the densest stellar clusters in the Galaxy. | \label{sec:intro} The gas-star formation cycle near the Galactic Centre is inherently a multi-scale process. There exists a close interplay between large-scale gas flows, galactic dynamics, star formation, feedback, and the feeding of the central supermassive black hole, Sgr~A$^*$. The dominant mass reservoir containing the fuel for star formation near the Galactic Centre is the Central Molecular Zone (CMZ; i.e.~the central 500 pc of the Milky Way). This region contains the largest concentration of high-density molecular gas in the Galaxy ($M_{\rm gas}\sim5\times10^7~{\rm M}_\odot$, \citealt{ferriere07}) and obtaining an understanding of the gas-star formation cycle in the CMZ is not just valuable from a star formation perspective, but also has key implications for wider areas in astrophysics and Galactic Centre research. There are several examples of the wider implications of CMZ studies. For instance, the physics driving the accretion and activity of Sgr~A$^*$ govern a large range of spatial scales with several independent bottlenecks. How is the gas deposited into the CMZ from the Galactic disc? Which transport mechanisms drive it further inwards once it has passed the inner Lindblad resonance (ILR)? How does it reach the sphere of influence of the nuclear cluster? How does it eventually reach the accretion disc of Sgr~A$^*$? The large-scale flow plays a critical role in providing the material for the eventual activity of Sgr~A$^*$. A related, major example of the importance of the gas in the CMZ is its three-dimensional geometry. How does the distribution of absorbers along the line of sight affect the ongoing search for dark matter annihilation signals from the Galactic Centre \citep[e.g.][]{daylan16}? A three-dimensional model for the gas in the CMZ would also provide a detailed record of the recent ($<10^3$ years) accretion history of Sgr~A$^*$ from X-ray light echoes \citep[e.g.][and these proceedings]{clavel13,clavel14}. While the accretion history over much longer time-scales may be reconstructed with high-energy observations of the outflowing relics in the Galactic halo, there exists an important degeneracy with feedback from (possibly bursty) star formation \citep[e.g.][]{su10}. If we can achieve an understanding of where and how stars from in the CMZ, this may allow this degeneracy to be lifted. At the same time, such an understanding will yield insights in the growth and structural evolution of the central regions of the bulge, where the baryons dominate the gravitational potential by orders of magnitude. Finally, the densest stellar clusters in the Milky Way are situated within 100~pc of the Galactic Centre (\citealt{walker16}; including the nuclear cluster, e.g.~\citealt{genzel10b}). The close proximity of the CMZ provides a unique opportunity for studying how such extreme stellar populations are formed, as well as for constraining the formation rates and mechanisms of compact objects within these clusters. Below, we describe our first steps in synthesising the multi-scale structure of the gas-star formation cycle in the CMZ, from the inflow of fresh gas along the bar (of the order $1~{\rm M}_\odot~{\rm yr}^{-1}$) to the accretion onto the supermassive black hole in Sgr~A* (of the order $10^{-9}~{\rm M}_\odot~{\rm yr}^{-1}$). The end goal is to obtain a complete understanding of the structure and evolution of the CMZ, which will help answering many of the questions raised above. | 16 | 9 | 1609.08158 |
|
1609 | 1609.08472_arXiv.txt | {We present a study of a recurring jet observed on October 31, 2011 by SDO/AIA, Hinode/XRT and Hinode/EIS. We discuss the physical parameters of the jet such as density, differential emission measure, peak temperature, velocity and filling factor obtained using imaging and spectroscopic observations. A differential emission measure (DEM) analysis was performed at the region of the jet-spire and the footpoint using EIS observations and also by combining AIA and XRT observations. The DEM curves were used to create synthetic spectra with the CHIANTI atomic database. The plasma along the line-of-sight in the jet-spire and jet-footpoint was found to be peak at 2.0 MK. We calculated electron densities using the \mbox{Fe \textrm{XII}} ($\lambda$186/$\lambda$195) line ratio in the region of the spire (\mbox{N$_{\textrm{e}}$ = 7.6$\times$10$^{10}$ cm$^{-3}$}) and the footpoint (\mbox{1.1$\times$10$^{11}$ cm$^{-3}$}). The plane-of-sky velocity of the jet is found to be \mbox{524 km/s}. The resulting EIS DEM values are in good agreement with those obtained from AIA-XRT. There is no indication of high temperatures, such as emission from \mbox{Fe \textrm{XVII} ($\lambda$254.87)} \mbox{(log T [K] = 6.75)} seen in the jet-spire. In case of the jet-footpoint, synthetic spectra predict weak contributions from \mbox{Ca \textrm{XVII} ($\lambda$192.85)} and \mbox{Fe \textrm{XVII} ($\lambda$254.87)}. With further investigation, we confirmed emission from the \mbox{Fe \textrm{XVIII} ($\lambda$93.932~{\AA})} line in the AIA 94 {\AA} channel in the region of the footpoint. We also found good agreement between the estimated and predicted \mbox{Fe \textrm{XVIII}} count rates. A study of the temporal evolution of the jet-footpoint and the presence of high-temperature emission from the \mbox{Fe \textrm{XVIII}} (\mbox{log T [K] = 6.85}) line leads us to conclude that the hot component in the jet-footpoint was present initially that the jet had cooled down by the time EIS observed it. } | \label{section1} Solar jets are small-scale ubiquitous transients observed as collimated flows of plasma in and at the boundary of the coronal holes (coronal hole (CH) jets) and also at the edge of active regions (active region (AR) jets). Active region jets have been observed in H$\alpha$, extreme-ultraviolet (EUV) (c.f. \citeads{2011A&A...531L..13I}, \citeads{2014A&A...561A.134Z}, \citeads{2014A&A...567A..11Z}, \citeads{2016arXiv160200151M}) and X-ray wavelengths (c.f. \citeads{2008A&A...481L..57C}, \citeads{2008A&A...491..279C}) using ground-based and space-based instruments. It has been observed that, AR jets are often associated with nonthermal type III radio bursts (\citeads{1995ApJ...447L.135K}, \citeads{2011A&A...531L..13I}, \citeads{2015MNRAS.446.3741C}, \citeads{2016arXiv160200151M}). The energetic particles follow the field lines that are open to the heliosphere and can produce impulsive, electron/ $^{3}$He rich solar energetic particle (SEP) events in the interplanetary medium (\citeads{2015ApJ...806..235N}, \citeads{2016arXiv160303258I}). Therefore, AR jets and their associated phenomena are one of the important features involved in space-weather studies. Using imaging and spectroscopic observations at a number of wavelengths, we can probe different layers of the solar atmosphere and study the temperature structure of jets in detail. Until recently, it was difficult to carry out a detailed study of jets because of the limited spatial and temporal resolution of early instruments. The high spatial and temporal resolution of the \textit{Atmospheric Imaging Assembly} \citepads[AIA; ][]{2012SoPh..275...17L} on the Solar Dynamic Observatory (SDO) and the \textit{X-ray Telescope} (\citeads[XRT; ][]{2007SoPh..243...63G}) imaging instrument on Hinode, together with the spectral capabilities of \textit{EUV Imaging Spectrometer} (\citeads[EIS; ][]{2007SoPh..243...19C}) on Hinode have enabled us to carry out an in-depth analysis. A number of authors have studied the physical parameters such as velocities, density, size, location and direction of AR jets using EUV imaging observations (\citeads{2011A&A...531L..13I}, \citeads{2013ApJ...763...24K}, \citeads{2013ApJ...769...96C}, \citeads{2016arXiv160200151M}). There are also a few results available from spectroscopic observations (\citeads{2007PASJ...59S.763K}, \citeads{2008A&A...481L..57C}, \citeads{2011RAA....11.1229Y}, \citeads{2011A&A...526A..19M}, \citeads{2012ApJ...759...15M}, \citeads{2013ApJ...766....1L}). \citetads{2007PASJ...59S.763K}, \citetads{2008A&A...481L..57C} and \citetads{2011RAA....11.1229Y} studied AR jets using simultaneous EIS and XRT observations. They found that EUV and SXR jets had similar projected speeds, lifetimes and sizes and they also observed that EUV jets had the same location, direction and collimated shape as the SXR jets. Using spectroscopic observations from EIS, \citetads{2007PASJ...59S.763K} observed a jet-footpoint; \citetads{2012ApJ...759...15M} and \citetads{2013ApJ...766....1L} observed a jet for the temperature range from \mbox{log \textit{T} [K] = 4.9 to 6.3} in their individual study of AR jets. \citetads{2011RAA....11.1229Y} reported the jet plasma temperature ranges from \mbox{log \textit{T} [K] = 4.7 to 6.3} i.e. from 0.05 to 2.0 MK and maximum electron densities ranging from \mbox{\textit{N$_{e}$} = 6.6$\times$10$^{9}$} to \mbox{\textit{N$_{e}$} = 3.4$\times$10$^{10}$ cm$^{-3}$}; whereas \citetads{2008A&A...481L..57C} reported a jet temperature ranges from \mbox{log \textit{T} [K] = 5.4} to \mbox{log \textit{T} [K] = 6.4} and found density above \mbox{log \textit{N$_{e}$} = 11 cm$^{-3}$}. The temperature distribution of AR jets has been studied using Differential Emission Measure (DEM) methods assuming multi-thermal plasma along the line-of-sight using EUV imaging observations. \citetads{2013ApJ...763...24K} studied an AR surge using the DEM method of \citetads{2013SoPh..283....5A} and reported an average temperature of \mbox{2 MK} and a density of \mbox{4.1$\times$10$^{9}$ cm$^{-3}$}; whereas using the same DEM method, \citeads{2013ApJ...769...96C} studied another AR jet and reported a high temperature (7 MK) in the footpoint region. A recent study of twenty AR jets by \citetads{2016arXiv160200151M} using multiwavelength AIA observations reported the temperature of the jet-spire ranging from \mbox{log \textit{T} [K] = 6.2 to 6.3} and the electron density ranges from 8.6$\times$10$^{9}$ to 1.3$\times$10$^{10}$ cm$^{-3}$. They also investigated the temperature structure at the region of the footpoint, which was found to peak at \mbox{log \textit{T} [K] = 6.5} with electron number density ranging from \mbox{8.4$\times$10$^{9}$} to \mbox{1.1$\times$10$^{10}$ cm$^{-3}$}. All the above studies provided various physical parameters of AR jets, but a detailed investigation of the temperature structure in the region of the spire and the footpoint of AR jets using simultaneous imaging and spectroscopic observations has remained elusive. Even with existing instruments, it has been a challenge to find simultaneous imaging and spectroscopic observations of an active region jet. After a careful search through available datasets, we have found suitable observations of a recurrent jet originating from the periphery of an active region. To the best of our knowledge, this is the first comprehensive investigation of the temperature structure of the ‘jet-spire’ and the ‘jet-footpoint’ of an AR recurrent jet using simultaneous imaging and spectroscopic observations. In this study, we focus on two instances of a recurrent jet where we individually observed the ‘spire’ and the ‘footpoint’ of a jet. In \mbox{section \ref{section2}}, we present our observations and describe the instruments from which the data has been taken for this study. \mbox{Section \ref{section3}} describes the DEM analysis techniques used to investigate the temperature structure of the jet spire and the footpoint. We also discuss the temporal evolution of the footpoint region and the change in temperature during that period. In \mbox{section \ref{section4}}, we discuss and summarise our results. | \label{section4} In this paper, we present a comprehensive investigation of the temperature structure of the jet-spire and the jet-footpoint of a recurrent AR jet observed on October 31, 2011 using simultaneous imaging (from the AIA and XRT) and spectroscopic observations (from the EIS instrument). The jets originated from the western edge of AR NOAA 11330 \mbox{(N08 W49)}. The highly variable nature of the jet-spire and the footpoint was observed during the jet evolution (see figs. \ref{fig4} and \ref{fig5}). We also observed plasma-blobs moving along the jet-spire in the AIA channels (see online movie1.mp4). We studied the temperature structure of the jet-spire and the jet-footpoint by performing a DEM analysis (see section~\ref{section3.6}). The plasma along the line-of-sight in the jet-spire and jet-footpoint was found to be peak at 2.0 MK (\mbox{log \textit{T} [K] = 6.3}) and we obtained similar DEM values at the peak of DEM curves (see table~\ref{table5}). The EIS and \mbox{AIA-XRT} DEM curves in both regions appear to be in good agreement in the temperature interval from \mbox{log \textit{T} [K] = 5.9 - 6.3}. Substantial variations were found between solutions obtained from the MC iterations at lower temperatures. We note that the DEM curves are not well constrained below \mbox{log \textit{T} [K] = 5.8} and above \mbox{log \textit{T} [K] = 6.4}. There are various factors which can affect the DEM results such as the choice of elemental abundances, range of temperatures over which the DEM inversion is performed, uncertainties in the atomic data and cross-calibration of instruments. We investigated cross-calibration issues by performing a similar analysis shown in section~\ref{section3.6} on a moss region (shown as yellow box in fig. \ref{fig1}) for which there was very little variation of the intensity with time (see Appendix). Based on the results obtained from the moss, we have confidence in the calibration of EIS, AIA and XRT. These results also confirm that the method we used in section \ref{section3.6} for the DEM analysis combining AIA and XRT observation is reliable. The synthetic spectra for the spire do not predict any measurable contribution from the high temperature lines such as \mbox{Fe \textrm{XVII}} \mbox{($\lambda$254.87)} at \mbox{log \textit{T} [K] = 6.75} confirming that the high temperature part of the DEM is consistent with the observed EIS spectra. In the case of the jet-footpoint, both synthetic spectra predict weak contributions from \mbox{Ca \textrm{XVII}} ($\lambda$192.85) and \mbox{Fe \textrm{XVII}} \mbox{($\lambda$254.87)}. With further investigation, we confirmed that there was emission from the \mbox{Fe \textrm{XVIII} (93.932~{\AA})} lines in the region of the footpoint during the early stages of the jet. We also found a good agreement between the estimated and predicted \mbox{Fe \textrm{XVIII}} count rates. The consistency between the nature of the AIA light curves and changes in the DEM values with temperatures during the evolution of the footpoint and the emission from the \mbox{Fe \textrm{XVIII} (93.932~{\AA})} line leads us to conclude that the hot component in the footpoint region was present initially that the jet had cooled down by the time EIS observed it. It is important to note that the predicted lines in each AIA channels confirmed the multi-thermal emission contributing to the AIA channels in the region of the spire and the footpoint (see fig. \ref{fig11} and \ref{fig12}). This is the first such detailed investigation of this nature of AR jets. We calculated an electron density using \mbox{Fe \textrm{XII}} ($\lambda$186/$\lambda$195) line ratio density diagnostics. The electron density was found to be \mbox{\textit{N}$_\textrm{e}$ = 7.6$\times$10$^{10}$ cm$^{-3}$} at the region of the spire and \mbox{1.1$\times$10$^{11}$ cm$^{-3}$} at the region of the footpoint (see fig.\ref{fig7}) taking account of 20\% error, the density could be even higher. For the first time in AR jet studies, we observed a region (shown by white arrow in \mbox{fig. \ref{fig7} (b)}, bottom panel) which has \mbox{Fe \textrm{XII}} \mbox{$\lambda$186/$\lambda$195} ratio greater than 1.2. This indicates that the region has a high density (\mbox{log \textit{N}$_\textrm{e}$ $>$ 11.5}), which is above the range of sensitivity of \mbox{Fe \textrm{XII}} lines ratio diagnostics. We also calculated a plasma filling factor using equation~\ref{eq:phi}. It was found to be 0.02 in the region of the spire and also in the region of the footpoint. These values are in agreement to the values obtained by \citeads{2008A&A...481L..57C} and \citeads{2011RAA....11.1229Y} from their spectroscopic study of a recurrent active region jet. The peak DEM, EM and filling factor values obtained using coronal abundances were found to be a factor of four lower than the values obtained using the photospheric abundances (see Table \ref{table5}). The \mbox{AIA 131~{\AA}} image showed a similar structure and morphology of the jet to the EIS \mbox{Fe \textrm{VIII}} ($\lambda$186.605; \mbox{log \textit{T} [K] = 5.8}) observations (see fig.~\ref{fig6}). We confirm the emission observed in the spire and the footpoint in the AIA 131~{\AA} images has a main contribution from the lower temperature \mbox{Fe \textrm{VIII}} line. We obtained an initial velocity of \mbox{524 km/s} for the jet observed at \mbox{14:58 UT} from the time-distance analysis (see section~\ref{section3.5}). A recent multiwavelength study of twenty AR jets by \citetads{2016arXiv160200151M} showed that most of the AR jets originated at the western periphery of the active region in the vicinity of sunspots and that they were temporally associated with nonthermal \mbox{type-III} radio bursts. The energetic particles gyrating along the open magnetic field structures generally produce nonthermal \mbox{type-III} bursts in the radio dynamic spectrum. Using a Potential Field Source Surface (PFSS) technique, authors investigated the spatial co-relation between the AR jets and \mbox{type-III} radio bursts and confirmed the presence of open magnetic field lines at the same region of the jet-footpoint. The velocities and DEMs found in the current analysis are consistent with their results. There are very few simulations of jets which give actual quantitative values for the plasma properties that can be compared to observations. Most simulations tend to predict much higher temperatures and lower densities than we observed, however most of them related to coronal hole jets. Two studies addressed active region jets. \citetads{2009A&A...506L..45G} studied the interaction of an emerging bipole and small active region by performing 3D MHD numerical simulations. They reported a hot ($\sim$2 MK) and high velocity (V = $\sim$100 km/s) bidirectional flows as a result of reconnection. They also observed a change in the shape and direction of the jet during the process. They discussed two scenarios of the jet event : firstly, they observed a ‘L-shaped’ reconnection jet moving with speeds of about \mbox{100 km/s} and reached a temperature around \mbox{1 MK}. Later, the jet was found to be trapped in the ambient field and adopted an ‘arc-like’ shape. The jet started moving laterally and reached a temperature of about \mbox{2 MK}. The authors found good qualitative and quntitative agreement between observations and simulations. \citeads{2010A&A...512L...2A} studied the long-term evolution of a similar system (a recurrent active region jet) by solving the time-dependent, resistive MHD equations in 3D. The authors reported recurrent jets which occurred in direction perpendicular to each other as a result of repeated reconnection events. The recurrent jets appeared to have different physical properties and it changed over the period of time. During the evolution, the authors reported an enhancement of the temperature along the reconnection outflow and they also observed spikes along the leading edge of the jet which further moved along the parallel field lines. The successive reconnection events found to be less effective than the previous one and eventually the system attained an equilibrium. From our spectroscopic and imaging observations, we have seen an inverted-Y topology at the footpoint of the jet and an arc-shaped jet-spire (see online movie1.mp4). Our observations show good agreement with the geometric shape of the jet and temperatures ($\sim$2 MK) seen in the numerical simulations. However, the bi-directional flow was not observed during the recurrent phase of the jet. The measured densities (spire = 10$^{10}$ and footpoint = 10$^{11}$) and velocities (\mbox{$\sim$524 km/s}) are found to be higher than the values reported in both simulations. It remains to be seen with new numerical simulations (which will be the subject of a future paper) if such dynamic behaviour can be explained within the standard reconnection scenario associated with flux emergence. It is important to note that AR jets are relatively common, and the fact that there is strong evidence that they occur in regions that are open to the heliosphere (\citeads{2011A&A...531L..13I}, \citeads{2015MNRAS.446.3741C}, \citeads{2016arXiv160200151M}) makes them one of the best candidates for future detailed studies with the Solar Orbiter and Solar Probe plus suite of remote-sensing and in-situ instruments. Further detailed studies of these events are therefore very useful to prepare for future observations with these missions. | 16 | 9 | 1609.08472 |
1609 | 1609.01079_arXiv.txt | {With the application of advanced astronomical technologies, equipments and methods all over the world, astronomy covers from radio, infrared, visible light, ultraviolet, X-ray and gamma ray band, and enters into the era of full wavelength astronomy. How to effectively integrate data from different ground- and space-based observation equipments, different observers, different bands, different observation time, requires the data fusion technology. In this paper we introduce the cross-match tool that is developed by the Python language and based on the PostgreSQL database and uses Q3C as the core index, facilitating the cross-match work of massive astronomical data. It provides four different cross-match functions, namely: I) cross-match of custom error range; II) cross-match of catalog error; III) cross-match based on the elliptic error range; IV) cross-match of the nearest algorithm. The cross-match result set provides good foundation for subsequent data mining and statistics based on multiwavelength data. The most advantage of this tool is a user-oriented tool applied locally by users. By means of this tool, users may easily create their own databases, manage their own data and cross-match databases according to their requirements. In addition, this tool is also able to transfer data from one database into another database. More importantly, the tool is easy to get started and used by astronomers without writing any code. | In astronomy, the data fusion technology is the foundation of multiwavelength astronomical research. Through the catalog fusion, we can integrate multiple independent catalogs or images, databases or data sets by positions or object names and other information into a whole, so as to deepen the understanding of the celestial bodies and promote the discovery of new objects or new physical phenomena. For example, Metchev et~al. (2008) reported new L and T dwarfs in a cross-match of SDSS and 2MASS. Maselli et~al. (2015) found new blazars by cross-matching the recent multi-frequent catalogs. Multiwavelength data obtained are of great significance for further statistical analysis and data mining (e.g. Zhang \& Zhao, 2003, 2004; Gao et~al. 2009; Zhang et~al. 2013). However, for the catalog fusion technology, the most important step is the calculation of cross-match, which refers to finding the corresponding entry in a catalog to each source in another catalog by means of the source location as the center. In general, the observation has errors due to various factors, which causes difficulty for cross-match. Any source in different catalogs has one or more counterparts within a certain error radius. In recent years, there are many studies focusing on the development of cross-match tools. Thus cross-match tools are in bloom. VizieR (http://vizier.u-strasbg.fr/), operated at CDS, Strasbourg, France, provides access to the most complete library of published astronomical catalogs and data tables available on line organized in a self-documented database. Query tools allow the user to select relevant data tables and to extract and format records matching given criteria. But the cross-match work only supports a small number of records. SIMBAD (http://simbad.u-strasbg.fr/simbad/) is an astronomical database operated at CDS, Strasbourg, France, which provides basic data, cross-identifications, bibliography and measurements for astronomical objects outside the solar system (Wenger et~al. 2000). SIMBAD has many kinds of query modes, such as object name, coordinates and various criteria. SIMBAD also provides links to some other on-line services. Users may submit lists of objects and scripts to query. Similar to VizieR, the number of lists cannot be large. The NASA Extragalactic Database (NED, http://www.ned.ipac.caltech.edu/), managed by NASA, contains names, positions, and a variety of other data for extragalactic objects, as well as bibliographic references to published papers, and notes from catalogs and other publications. NED may be searched for objects in many ways, including by name, position, redshift, type, or by object classifications. NED also offers a number of other tools and services. If users want to query a large number of objects, users may submit a NED Batch Job, and retrieve the results at Pick Up Batch Job Results. NED provides another batch query, i.e. one RA and Dec position or object name per line, maximum 500 positions and/or object names per request. The Tool for OPerations on Catalogues And Tables (TOPCAT, http://www.star.bris.ac.\\uk/$\sim$mbt/topcat/) is an interactive graphical viewer and editor for tabular data (Taylor 2005). It offers a variety of ways to view and analyze tables, including a browser for the cell data themselves, viewers for information about table and column metadata, and facilities for sophisticated interactive 1-, 2-, 3- and higher-dimensional visualization, calculating statistics and joining tables using flexible matching algorithms. It is developed in Java language and limited by computer memory when running. When cross-matching very large tables or tables with lots of columns, the computer is inclined to be out of memory. TOPCAT's sister package is STILTS (The Starlink Tables Infrastructure Library Tool Set), which is based on STIL, the Starlink Tables Infrastructure Library. STILTS offers many of the same functions as TOPCAT and forms the command-line counterpart of the GUI table analysis tool TOPCAT. STILTS is robust, fully documented, and designed for efficiency, especially with very large datasets. The CDS cross-match service (http://cdsxmatch.u-strasbg.fr/xmatch/) is a new data fusion and data management tool, which is used to efficiently cross-identify sources between very large catalogs (all VizeR tables, SIMBAD) or between a user-uploaded list of positions and a large catalog (Boch et al. 2012). About the xMatch algorithm, please refers to Pineau et~al. (2011). Users interact with the CDS xMatch service through a Web application. Due to narrow network bandwidth, it has some limitations, for example, long jobs are aborted if computation exceeds 100 minutes while short jobs are aborted if computation exceeds 15 minutes; the search radius is maximized to 120 arcsec for a simple cross-match; the cone radius is no more than 15 degrees for a cone search; results are saved no more than 7 days following their submission. Moreover the total size of uploaded tables is limited to 100 MB for anonymous users, and 500 MB for registered users. 2MASS catalog server kit, developed by Yamauchi (2011), realizes a high-performance database server for the 2MASS Point Source Catalog and several all-sky catalogs. This kit uses the open-source PostgreSQL, adopts an orthogonal $xyz$ coordinate system as the database index and applies other techniques (table partitioning, composite expression index, and optimization in stored functions) to enable high-speed search and cross-match of huge catalogs. Pei (2011) and Pei et al. (2011) had developed a high-efficient large-scale catalogue oriented fusion toolset based on MySQL database and HTM index. Zhang et al. (2012) had developed the toolkit for automated database creation and cross-match task, with which users may create their own databases and easily cross-match catalogs. Although the cross-match speed is quick, it costs a long time to retrieve the cross-matched result. In other words, the second operation of matched result is necessary before application. TAPVizieR is a new way to access the VizieR database using the ADQL language and the TAP protocol (Landais et~al. 2013). The database is based on PostgreSQL and the sky indexation depends on HEALPix. TAPVizieR provides query and cross-match functions. The result access is only limited to the owner recognized by the IP address and saved no more than 5 days. The execution time of an ADQL query is limited to 5 hours. The Large Survey Database (LSD, http://research.majuric.org/trac/wiki/LargeSurvey\\Database) is a framework for storing, cross-matching, querying, and rapidly iterating through large survey datasets (catalogs of $>10^9$ rows, $>1$ TB) on multi-core machines. It is implemented in Python, written and maintained by Mario Juric. LSD applies nested butterfly HEALPix pixelization and the catalogs are partitioned into cells in space and time. LSD employs LSD/MapReduce as the high-performance programming model. To some extent, all cross identification tools strongly promote the study of multiwavelength astronomy and provide strong cross-match function. Nevertheless these tools are almost for large data managers; some are for astronomers; some are difficult to learn; some are accessed by network and limited by network bandwidth, so users can't upload too large catalogs. Considering all factors, we develop a user-oriented cross-match tool based on PostgreSQL database with the sky-indexing Q3C, and continuously improve the system efficiency of identification, making the amount of cross-match records increase to tens of millions of lines and even higher. At the same time, we also develop the auxiliary tool of data exchange between different databases, helping astronomers better manage data. | This paper is devoted to the development of efficient and easy-to-use catalog cross-match tool. According to the astronomical data characteristics of large-scale, multiband and distributiveness, we analyze the international existing cross-match tools and develop a simple and efficient data fusion tool according to the actual needs. It could be used for the tens of millions of lines of data, or even larger, and we adopt the method of process pool to fully use CPU, which ensures the efficiency of cross-match. Users can arbitrarily choose the cross-match functions to obtain the final multiband cross-match result according to their own needs. Given high identification speed and good accuracy, the tool is a booster to large scale catalog cross-match. Moreover it is easy to learn and use for astronomers. It has been of very important significance for the subsequent data mining and statistical analysis work. Nevertheless, there are still lots of functions needed to be improved in the future. For example, this tool is limited to system environment, only in the use of the environment based on PostgreSQL database system. For the matched result set, users may choose less than 10 columns of data in each table except the right ascension RA and declination Dec, or all columns are output when setting default. If users want to get more than 12 columns, they need adopt the default setting. In the following work, the cross-match services can be fully deployed on Web servers, letting users input data into our database server, using our platform to do the cross-match work, which will greatly reduce the workload of astronomical work. Meanwhile the user can give feedback to us through the network service in the use process, so our program will be more robust. In the program itself, we can further improve the high efficiency of program using the multiprocessing module to realize the parallel program. The benefit is that it does not produce potential errors but high efficiency, the direct operation of process usually will be more efficient than the use of a good package library. So we can consider using the Python subprocess module to initiate multiple processes, but in this case each process will get their own unique results set, then we still need secondary processing to get the final result set. Database performance improvements can directly improve the running efficiency of the program, when a tabular data quantity is large enough, the memory reaches a bottleneck, even if using the index, the query work can still be very slow. Here it is very necessary for us to do the table division operation, dividing the large table into a plurality of small tables to do the cross-match work, so that the efficiency will be improved a lot. Moreover, if the database is arranged by distributed cluster layout method, the program robustness will be much higher. So in the future, we will take many better ways (e.g. MapReduce, Spark) to improve the efficiency of the program and apply new data mining methods to perform not only spacial cross-match, but also physical matching. Altogether the development of new computer technologies, new types of databases and database index methods oriented to big data is of great importance for today's multiwavelength observations and the time domain science of the upcoming survey telescopes. \begin{center} \bf Acknowledgment\end{center} We are very grateful to the referee for his insightful comments. This paper is funded by National Key Basic Research Program of China 2014CB845700, National Natural Science Foundation of China under grants NO.61272272, No.11178021, No.11033001, NSFC-Texas A\&M University Joint Research Program No.11411120219. We acknowledgment SDSS, WISE and UKIDSS databases. | 16 | 9 | 1609.01079 |
1609 | 1609.08644_arXiv.txt | One alternative to the cold dark matter (CDM) paradigm is the scalar field dark matter (SFDM) model, which assumes dark matter is a spin-0 ultra-light scalar field (SF) with a typical mass $m\sim10^{-22}\mathrm{eV}/ c^2$ and positive self-interactions. Due to the ultra-light boson mass, the SFDM could form Bose-Einstein condensates (BEC) in the very early Universe, which are interpreted as the dark matter haloes. Although cosmologically the model behaves as CDM, they differ at small scales: SFDM naturally predicts fewer satellite haloes, cores in dwarf galaxies and the formation of massive galaxies at high redshifts. The ground state (or BEC) solution at zero temperature suffices to describe low-mass galaxies but fails for larger systems. A possible solution is adding finite-temperature corrections to the SF potential which allows combinations of excited states. In this work, we test the finite-temperature multistate SFDM solution at galaxy cluster scales and compare our results with the Navarro-Frenk-White (NFW) and BEC profiles. We achieve this by fitting the mass distribution of 13 \textit{Chandra} X-ray clusters of galaxies, excluding the region of the brightest cluster galaxy. We show that the SFDM model accurately describes the clusters' DM mass distributions offering an equivalent or better agreement than the NFW profile. The complete disagreement of the BEC model with the data is also shown. We conclude that the theoretically motivated multistate SFDM profile is an interesting alternative to empirical profiles and ad hoc fitting-functions that attempt to couple the asymptotic NFW decline with the inner core in SFDM. | \label{introduction} One of the biggest challenges of cosmology and astrophysics is to understand how galaxies and clusters of galaxies were formed and evolved. In the context of General Relativity, it is known that without the assumption of a cold dark matter (CDM) component it is difficult to explain the observed anisotropies in the cosmic microwave background (CMB) radiation, the large-scale structure formation in the Universe, the galactic formation processes and gravitational lenses of distant objects, among others. Moreover, adding a positive cosmological constant $\Lambda$ can account for the accelerated expansion of the Universe. These components, along with the baryonic matter, form the current paradigm explaining the dynamics of the Universe, known as the $\Lambda$CDM or standard model. Current observations from the {\it{Planck}} mission set the contribution of the baryonic matter to the total matter-energy density of the Universe to $\sim 5\%$, meanwhile the CDM is $\sim 26\%$ and $\Lambda$ or dark energy is $\sim 69\%$ \citep{Planck:2016}. From CDM $N$-body simulations of structure formation, we know that CDM clusters form haloes with the universal Navarro-Frenk-White (NFW) density profile \citep{nfw-1997}, which is proportional to $r^{-1}$ (a `cuspy' profile) for small radii $r$ and to $r^{-3}$ for large radii (cf. equation~\ref{rho-nfw}). Even though the CDM paradigm is very successful at reproducing the large-scale observations, recent DM-only simulations are consistent with a `cuspy' profile \citep{navarro10}, meanwhile high-resolution observations of dark matter dominated systems, such as low surface brightness (LSB) galaxies \citep{deblok:2001} and dwarf spheroidal (dSph) galaxies \citep{oh:2011, walker:2011, penarrubia:2012}, suggest a constant central density or `core' profile ($\rho \sim r^{-0.2}$). This discrepancy is known as the `cusp-core problem'. In addition to the cusp-core issue, the CDM paradigm faces other challenges on small scales: it predicts more massive satellite galaxies around Milky Way like galaxies that have not been observed \citep{boylan:2011,sawala:2012}; it fails to reproduce the phase-space distribution of satellites around the Milky Way and Andromeda galaxies \citep{pawlowski:2012,ibata:2013,ibata:2014} and the internal dynamics in tidal dwarf galaxies \citep{gentile:2007,kroupa:2012}. Another potential difficulty may lie in the early formation of large galaxies: large systems are formed hierarchically through mergers of small galaxies that collapsed earlier, but recent observations have found various massive galaxies at very high redshifts \citep{caputi:2015}; it remains to be seen whether such rapid formation could represent a problem for the CDM model. An active field of research to solve the above issues takes into account the baryonic physics \citep{Navarro:1996,governato:2010, deblok:2010,maccio:2012,stinson:2012,DiCintio:2014,Pontzen:2014, Onorbe:2015,Chan:2015}, so the NFW universal profile is not expected to hold exactly once the simulations include the baryonic matter. Those have shown that a core profile can be obtained in simulations of dwarf galaxies in CDM if they include a bursty and continuous star formation rate \citep{pontzen:2012,governato:2012,Teyssier:2013,Madau:2014, DiCintio:2014,Onorbe:2015}. However, it is difficult to explain flat density profiles with these mechanisms in galaxies with masses smaller than $\sim 10^{6.5} M_\odot$ \citep{penarrubia:2012, Garrison-Kimmel:2013,Pontzen:2014,Chan:2015} and, possibly, in some LSB galaxies \citep[see e.g.][]{kuzio:2011}. Very recent simulations have shown that baryons could explain the small abundance of low-mass galaxies \citep{FIRE:2017}; it remains therefore uncertain whether the baryonic processes (star formation, supernova explosions, active galactic nuclei, stellar winds, etc.) and their effect on the dark matter haloes are enough to account for the discrepancies. There are some empirical density profiles proposed in order to describe the density distribution after accounting for the baryonic component, for instance, the Burkert profile \citep{burkert:1995} or the generalized NFW profile \citep{Zhao:1996}. However, these parametrizations, albeit useful, lack of theoretical support; it is therefore interesting to explore alternative dark matter models from which we can derive a density profile that agrees with a broad range of observations. A different approach is to find models trying to replace the dark matter hypothesis with a modified gravity law to explain the observations at different scales \citep[see e.g.][]{defelice:2010, mendoza11, bernal11, Famaey:2012, joyce:2015}. There are some gravity models capable of reproducing the observations of galaxy clusters and consistent at the galactic level also \citep{khoury:2015,Bernal:2015}; more work is being developed in this direction. Some of the DM alternatives to the CDM paradigm are warm dark matter, self-interacting dark matter \citep{spergel:2000,yoshida:2000,dave:2001, zavala:2009,navarro10,kuzio:2011,Elbert:2015,Robles:2017}, and scalar field dark matter \citep[SFDM,][]{Sin:1992,Ji:1994,Lee:1995}. In this work we will focus our study on the SFDM alternative in the mass range of galaxy clusters. The scalar fields (SF) as dark matter were first elucidated by \citet{Ruffini:1983}; since then the idea was rediscovered using different names \citep[see e.g.][]{Membrado:1989,Spergel:1989,Sin:1992, Ji:1994,Lee:1995,guzman-matos:2000,Sahni:1999,Peebles:2000,Goodman:2000, Matos-Urena:2000,matos-urena01,hu:2000,Wetterich:2001,Arbey:2001a, harko07,Vazquez-Magana:2008,Woo:2009,Lundgren:2010,Bray:2010, Marsh-Ferreira:2010,Robles:2013,Schive:2014,Calabrese:2016}, among others, and more recently by \cite*{Ostriker:2016}. However, the first systematic study of the cosmological behaviour started by \citet{Guzman:1999,guzman-matos:2000,Matos:1999,Matos-Urena:2000}. Other systematic studies were performed by \citet{Arbey:2001a,Arbey:2001b} and more recently by \citet{Marsh-Ferreira:2010,Schive:2014,Marsh:2015b}. In the SFDM model, the DM is a SF of spin-0 interaction, motivated by the well-known fundamental interactions of spin-1 or -2, being the spin-0 the simplest one. The model considers a spin-0 SF of a very small mass (typically $\sim 10^{-22} \mathrm{eV}/ c^2$) as the dark matter, in such a way that it is possible to form Bose-Einstein Condensates (BEC) at cosmological scales, hence behaving as CDM at large scales. The model has been widely explored by many authors, named simply SFDM \citep{Matos-Urena:2000,matos-urena01,alcubierre:2002a,alcubierre:2002b, matos-urena07,Matos:2009,suarez:2011,Magana:2012,robles:2012,Robles:2013, Robles-lensing:2013,Martinez-Medina:2014hca,Suarez:2014,Martinez:2015, Robles:2015,Matos-Robles:2016}. As the SFDM model gained interest, several authors gave it different names in the literature; however, we emphasize that the core idea described above remains unchanged. Some of the names are: fuzzy \citep{hu:2000}, wave \citep{bray:2012,Schive:2014, Schive:2014hza}, BEC \citep{harko07} or ultra-light axion \citep{Marsh-Ferreira:2010,hlozek:2015} dark matter. Additionally, most of these works assume the SFDM is at zero temperature, implying the SFDM ultra-light bosons occupy the ground state only. Some authors have explored thoroughly the possibility that the axion from quantum chromodynamics \citep[see e.g.][]{Peccei-Quinn:1977,Frieman:1995,Fox:2004} and string theory \citep[see e.g.][]{Arvanitaki:2010} is the DM of the Universe \citep[see][for a review]{Marsh:2015b}. The axion is a spin-0 particle with small mass ($\sim 10^{-5} \mathrm{eV}/c^2$) and weak self-interaction, and it has been proposed that axion DM can form BECs during the radiation-dominated era \citep{Sikivie:2009,Erken:2012}. However, it has not been proved that such axion BECs can be the DM haloes of the galaxies and clusters of galaxies \citep[see e.g.][] {Chavanis:2016}. The mentioned works on SFDM have shown that the model can account for the CDM discrepancies for a typical mass of the SF of $m\sim10^{-22} \mathrm{eV}/c^2$. Moreover, it was found that for small galaxies, the ground state solution is sufficient to reproduce current observations \citep{harko07,robles:2012}. However, as the galaxies become larger, temperature corrections to the SFDM potential are needed in order to obtain a solution that can account for the contribution of excited states and agree with the observational data \citep{Robles:2013}. From finite-temperature quantum field theory it is possible to obtain one-loop temperature corrections for the SF potential \citep{kolb:1994}. Following this approach, \cite{Robles:2013} found an approximate analytic solution to the field equations and derived a density profile that allows combinations of excited states of the SF. That solutions correspond to self-gravitating systems of SFDM, which are interpreted as dark matter haloes; they are also called multistate haloes. Such finite-temperature analytic solution has successfully described galactic systems \citep{Robles:2013,Bernal:2017}. In this article, we explore the galaxy clusters regime; our goal is to assess the viability of the SFDM model in these systems. In particular, we test the finite-temperature solution and compare it with the results of applying the NFW density profile to the same observations. We do so by fitting the SFDM mass profile to the mass distribution of 13 galaxy clusters from \citet{Vikhlinin:2006} and obtain that the multistate solution, and hence the finite-temperature SFDM model, is successful at reproducing the clusters mass regime, offering an alternative profile to describe the massive systems but with theoretical support, compared to the usual approach of fitting empirical profiles to observational data. Additionally, we demonstrate that the solution of a self-gravitating configuration at zero temperature and in the Thomas-Fermi limit, where the SF self-interactions dominate the SFDM potential \citep{harko07}, is incapable of fitting the galaxy clusters at all radii, which strongly favours the usage of excited states. The paper is organized as follows: In Section~\ref{sfdm-model}, we briefly review the SFDM model, mentioning the BEC dark matter at zero temperature in the TF limit and the analytic multistate SFDM model. In Section~\ref{cluster-profiles}, we provide the analysis tools required to derive the cluster mass profiles from the X-ray observations and perform the fits to the DM component once baryons are subtracted. In Section~\ref{discussion}, we show and discuss the results of the comparison between the three DM profiles: the SFDM ground state at zero temperature (BEC), the multistate SFDM halo with temperature-corrections and the NFW profile, representative of the CDM model. Finally, in Section~\ref{summary} we summarize our results and include our conclusions. | \label{summary} One of the alternative models to CDM is the SFDM model. In this model, the DM is a spin-0 scalar field with a typical mass of $m \sim 10^{-22}\mathrm{eV}/c^2$ and a positive self-interaction. This ultra-light boson is thought to form a BEC which after the recombination epoch behaves cosmologically as `cold' (pressureless and non-relativistic) dark matter. The equations that describe the scalar field (SF) constitute the Einstein-Klein-Gordon system and, in the non-relativistic limit, the BEC can be described by the Gross-Pitaevskii and Poisson (GPP) equations. The gravitationally bound solutions of the GPP system of equations are interpreted as the dark matter haloes. Assuming spherical symmetry, the ground state (or BEC) solution obtained in the Thomas-Fermi (TF) limit \citep{harko07}, where the SF self-interactions dominate the SF potential ($V(\psi)\sim \psi^4$) in the GPP system, can describe low-mass galaxies but is unable to keep the flattening of the rotation curves for massive galaxies. However, it was found that when finite-temperature corrections to the SF are taken into account in the Klein-Gordon equation, there exist exact solutions of excited states or, more generally, a combination of them, that provide an accurate description of both small and large galaxies \citep{Robles:2013}. In this work we explore the viability of these multistate SFDM solutions at the galaxy clusters regime. We fit the mass profiles of 13 \textit{Chandra} X-ray clusters of galaxies from \citet{Vikhlinin:2006} using both the universal NFW profile predicted by CDM simulations and the multistate density profile of the SFDM model. Additionally, we compare it with the BEC solution in the TF limit. We conclude that the analytic spherically symmetric SF configurations obtained in the finite-temperature SFDM model \citep{Robles:2013} can provide an accurate description of the DM mass distribution in galaxy clusters on the range probed by the data. As our main intention was to test the overall consistency of the multistate SFDM profile and compare it with the NFW and BEC profiles, we have left for a future work a more detailed modelling of the region where the brightest cluster galaxy is located. This region is dominated by the baryonic component and requires a more in-depth analysis with numerical simulations addressing the non-linear impact that baryons have on the core-like SFDM matter distribution. Therefore, as a first approximation, we excluded the central region of each cluster in the present article. Our results suggest that the multistate SFDM profile agrees with the data equally well as other empirical profiles currently used in the literature \citep[see e.g.][for the soliton+NFW profile]{Schive:2014}, but with the important difference that it is derivable from an underlying theory and not just from an ad hoc profile. In fact, the good fits of the multistate haloes to the data at large radii suggest that the approach of some authors to invoke an ad hoc profile to parametrize the SFDM density profile obtained from numerical simulations is not necessary. The multistate SFDM profile can account for the oscillating profile seen in simulations at large radii and also has an overlap at intermediate radii with the NFW profile (Fig.~\ref{densities-sfdm-nfw}). Also, it predicts the core-like behaviour at the innermost radii in the clusters, in contrast to the cuspy NFW profile. \citet{Bernal:2017} discussed the overlap between the multistate SFDM model and the soliton+NFW profile obtained from the fits of high-resolution rotation curves of galaxies. We found that galaxy clusters have different combinations of excited states, reflecting their diverse formation history. The total profile follows the data at all radii and, in comparison to the NFW profile, in some cases the SFDM is in better agreement especially at large radii where the asymptotic decline of the profiles is different. From our comparison with the BEC profile at zero temperature (Fig.~\ref{plot-harko}), we conclude that this profile is incapable of fitting the entire mass distribution of the galaxy clusters at $3\sigma$ CL. We found similar results for other clusters. Our results complement the previously observed discrepancies at galactic scales showing that the ground state in the TF limit is also not a good description in the mass range of clusters, implying that a purely self-interacting halo in the ground state is not adequate to model very large systems. If the dark matter is indeed an ultra-light boson, our results imply that the DM haloes of galaxies and galaxy clusters may not be fully BEC systems. In contrast, agreement with observations at different mass scales is achievable for multistate SFDM configurations. Finally, the oscillations in the SFDM profiles are within the data uncertainties, making difficult their use to distinguish it from CDM. Individual galaxies, particularly those in isolated environments where tidal forces are smaller, are better candidates to look for these wiggles. Being originated by small DM overdensities, the oscillations could be seen either as low surface brightness gas overdensities in the outskirts of the galaxies, or if the gas is cold and dense enough to trigger star formation, they would create radial stellar gradients. Since they damp with increasing radius, the largest effect would be given by the first DM overdensity. These positive results from the multistate SFDM fits motivate us to pursue a more detailed study of the centre of clusters and obtain constraints on the model, especially by analysing galaxy clusters where a core could be present \citep{Massey:2015, Limousin:2016}. Such study would require the addition of the baryonic component to the total mass profile and likely in high-resolution cosmological simulations in both CDM and SFDM models. Currently, the studies of halo mergers in SFDM have been idealized due to intrinsic code limitations \citep{Schive:2014,Mocz:2015,Schwabe:2016}. Surprisingly, the analytic multistate solution indicates that it is an interesting alternative profile that can be used as a fitting-function for a large variety of gravitational systems and that the SFDM model deserves further exploration. | 16 | 9 | 1609.08644 |
1609 | 1609.01765_arXiv.txt | We present new SOFIA-FORCAST observations obtained in Feburary 2016 of the archetypal outbursting low mass young stellar object FU Orionis, and compare the continuum, solid state, and gas properties with mid-IR data obtained at the same wavelengths in 2004 with Spitzer-IRS. In this study, we conduct the first mid-IR spectroscopic comparison of an FUor over a long time period. Over a 12 year period, UBVR monitoring indicates that FU Orionis has continued its steady decrease in overall brightness by $\sim$ 14\%. We find that this decrease in luminosity occurs only at wavelengths $\lesssim$ 20 $\mu$m. In particular, the continuum short ward of the silicate emission complex at 10 $\mu$m exhibits a $\sim$ 12\% ($\sim$ 3$\sigma$) drop in flux density, but no apparent change in slope; both the Spitzer and SOFIA spectra are consistent with a 7200 K blackbody. Additionally, the detection of water absorption is consistent with the Spitzer spectrum. The silicate emission feature at 10 $\mu$m continues to be consistent with unprocessed grains, unchanged over 12 years. We conclude that either the accretion rate in FU Orionis has decreased by $\sim$ 12-14\% over this time baseline, or that the inner disk has cooled, but the accretion disk remains in a superheated state outside of the innermost region. | The low mass pre-main sequence star FU Orionis (hereafter, FU Ori) brightened by $\Delta B = 6$ mag in 1936 \citep{herbig77}, and subsequently has declined slowly ($\sim$ 0.013 mag/yr; \citealt{kenyon00}) to the present day (further examined in this work). This burst in brightness established a class of variable star (FU Orionis objects, or ``FUors''; \citealt{hartmann96a,hartmann98}) that $\sim$10 other stars have since mimicked. \citet{paczynski76} first proposed that FUors are the result of a sudden cataclysmic accretion of material from a reservoir that had built up in the circumstellar disk surrounding a young stellar object. In this model, the accretion rate rises from the typical rate for a T Tauri star ($\dot{M} \lesssim 10^{-7} M_{\odot}$ yr$^{-1}$) up to $\dot{M} \sim 10^{-4} M_{\odot}$ yr$^{-1}$, and then decays over an e-fold time of $\sim$ 10-100 yr \citep{lin85,hartmann85,bell94}. Over the entire outburst the star could accrete $\sim$ 0.01 M$_{\odot}$ of material, roughly the entire mass of the Minimum Mass Solar Nebula or a typical T Tauri disk \citep{andrews05}. On average, FUor outbursts should occur (or recur) $\sim$ 5 times per star formed in the local region of the Milky Way \citep{hartmann96a}; there have been $\sim$ 10 FUors observed within a distance of 1.5 kpc in the last 80 yr, compared with the star formation rate in the same volume ($\sim$ 3 per 50 yr). These bursts also modify the protoplanetary disk chemistry and require a very different model than simple magnetospheric accretion \citep[e.g.][]{green06, quanz07a, zhu07,romanova09,cieza16}, usually invoked for accreting young stars. If FUors represent a short-duration stage that all young stars undergo, then understanding their properties is vital to models of planet formation and the evolution of protoplanetary gas-rich disks. The luminosity outburst is due to a sudden increase in the rate at which material accretes from the disk onto the star. Models explain the rise in accretion rate with the development of instabilities in the disk, but they differ as to where the instabilities originate. ``Inside-out" models are those in which the instability develops at several AU, where the lower temperatures, and therefore lower ionization fraction, render the magneto rotational instability (MRI) as an inefficient accretion mechanism \citep[e.g.][]{zhu09b,martin12}. ``Outside-in'' models are those in which gravitationally bound fragments develop at large radii (tens of AU or more) due to infall from a protostellar envelope, then migrate inward through the disk, ultimately generating an outburst when they accrete onto the star \citep[e.g.][]{vorobyov15}. A third option that has been posited is an external perturber -- the interaction of the disk with an exterior massive object that alters the balance of accretion and triggers the cascading flow \citep{bonnell92}, although recent studies suggest the refill rate is too slow to occur on few co-orbit timescales \citep{green16b}. The wavelength dependence of any post-outburst variability can distinguish among these classes of models. Dust grain growth, processing, and sedimentation are tracked by mid-infrared (MIR) dust features. Processing and grain growth in the disk can begin as early as the protostellar stage, when the disk is heavily extinguished. Most silicate features around low mass young stars are consistent with both grain growth and high crystallinity fractions \citep[e.g.][]{watson09,olofsson09}. Because grains from the ISM enter the disk as amorphous, high crystalline fractions in young stars indicate that dust processing occurs early on. EX Lup, the archetype of a smaller magnitude burst from a T Tauri disk, exhibited crystalline grain production during outburst \citep{abraham09}, due to enhanced heating. However, these crystalline grains disappeared during quiescence, likely due to X-ray amorphitization of the grains, or dust transport either radially or vertically. In contrast, FUors show no evidence for processed grains during outburst, only grain growth \citep{quanz07a}. No pre-outburst mid-IR spectra of FUors exist to constrain their historical grain properties, and it may be that the silicate grains are modified during the outburst. For protoplanetary disks, the 10 and 20 $\mu$m silicate features probe optically thin dust at specific temperatures on the disk surface; as the disk heats and then cools, the radii probed by these features changes accordingly, and may evolve during the burst \citep[e.g.][]{hubbard14}. As the disk cools, we might expect additional changes to occur, as grains are recirculated, modified, merged, or destroyed. During an FUor, the temperature at 1 AU may approach 1000 K or even higher; this becomes comparable to the temperature to form crystalline silicates or remove volatiles, which can affect habitable zone planet formation \citep{hubbard14}. Further out in the envelope, episodic increases in temperature can cause irreversible chemical processes, such as the observed conversion of mixed CO-CO$_2$ ice into pure CO$_2$ \citep{kimhj12b,poteet13}. Mid-IR spectroscopic variability has been only sparsely examined, although mid-IR evolution during bursts has been modeled \citep[e.g.][]{bell94,zhu07,johnstone13}. The biggest difference between the mid-IR SED of FU Ori and that of more typical young stellar objects is contribution of the superheated inner disk. The innermost regions of disk are expected to reach temperatures of 6000-8000 K, comparable to the stellar surface but over vastly greater emitting area (the inner radius of the disk; \citealt{hartmann96a,hartmann98}). Therefore the innermost disk radii are no longer coupled to any dust, which would be destroyed or ejected out to a significant fraction of an AU, and would not be an opacity source. Thus FU Ori's SED is dominated at {\it all wavelengths} by disk emission, even in the optical/near-IR, and changes at optical/near-IR wavelengths would reflect changes in the superheated disk rather than the central protostar. FU Ori (D $=$ 450-500 pc; \citealt{hartmann96a}) is a wide (0$\farcs$5) binary system consisting of a outbursting young stellar object modeled as a 0.3 $M_{\odot}$ with a 0.04 $M_{\odot}$ circumstellar disk \citep{zhu07} at an A$_V$ of $\sim$ 1.8 \citep{zhu10}, and a more massive young companion (M$>$ 0.5 $M_{\odot}$; \citealt{wang04,reipurth04,hales15}). The companion (FU Ori S) is at 227 AU projected separation \citep{pueyo12}, at an A$_V$ of 10 $\pm$ 2 \citep{pueyo12}. In this work, we present new mid-IR photometry and spectroscopy of FU Ori obtained with the Stratospheric Observatory for Infrared Astronomy (SOFIA) in 2016, and compare with previous observations with the Spitzer Space Telescope in 2004. We find that the continuum flux density in at wavelengths shorter than 8 $\mu$m (arising from the hot inner disk) has decreased by 12-14\%, dominating the change in bolometric luminosity. The continuum at wavelengths greater than 10 $\mu$m has decreased only 7\% within uncertainties. Additionally, we find that the H$_2$O vapor absorption resulting from the superheated disk photosphere remains present. Finally, we note no significant changes in the 10 $\mu$m silicate emission feature, which shows no evidence of crystallinity. Taken together, these observations suggest that the decrease in viscous dissipation energy over this period has occurred predominantly in the innermost section of the disk, which is changing rapidly. | We have performed the first comparison of multi-epoch mid-IR spectra of an FUor, to examine the changes occurring in the system during outburst. We compared the ca. 2004 SED and IR spectrum of FU Orionis with newly acquired (2016) SOFIA-FORCAST spectrum and photometry to identify changes over the intervening 12 year period. After establishing cross-calibration between the various measurements, we find a 12\% ($\sim$ 3$\sigma$) decrease in the 5-14 $\mu$m continuum without significant change in shape. We find lesser changes ($\lesssim$ 7\%) to the SED beyond 10 $\mu$m, and no significant change to the silicate dust or the rovibrational water absorption from the disk photosphere. From this, we posit a decrease in gas at the highest temperatures, and therefore the innermost regions of the disk, either due to cooling or depletion via accretion processes. | 16 | 9 | 1609.01765 |
1609 | 1609.01286_arXiv.txt | Gravitational waves emitted by distorted black holes---such as those arising from the coalescence of two neutron stars or black holes---carry not only information about the corresponding spacetime but also about the underlying theory of gravity. Although general relativity remains the simplest, most elegant and viable theory of gravitation, there are generic and robust arguments indicating that it is not the ultimate description of the gravitational universe. Here, we focus on a particularly appealing extension of general relativity, which corrects Einstein's theory through the addition of terms which are second order in curvature: the topological Gauss-Bonnet invariant coupled to a dilaton. We study gravitational-wave emission from black holes in this theory and {\bf(i)} find strong evidence that black holes are linearly (mode) stable against both axial and polar perturbations, {\bf(ii)} discuss how the quasinormal modes of black holes can be excited during collisions involving black holes, and finally {\bf(iii)} show that future ringdown detections with a large signal-to-noise ratio would improve current constraints on the coupling parameter of the theory. | \label{sec:intro} The historical detection of gravitational waves (GWs) by the LIGO/Virgo Collaboration has marked the beginning of a new era in astrophysics and the birth of GW astronomy~\cite{Abbott:2016blz}. The next generation of detectors will routinely observe the coalescence of compact objects, such as black holes (BHs) and neutron stars. These observations will probe, for the first time, the highly dynamical regime of strong-field gravity and may provide the answer to long-standing issues~\cite{Cardoso:2016rao,Nakano:2016sgf,Yunes:2016jcc}. Is cosmic censorship preserved in violent gravitational interactions? Do GW observations carry incontrovertible evidence for the event horizon of BHs? Can we pinpoint, in gravitational waveforms, the signature of the light ring or of ergosurfaces? Simultaneously, the entire coalescence process can be used to constrain gravity theories in novel ways~\cite{Berti:2015itd,TheLIGOScientific:2016src,Yunes:2016jcc}. That general relativity (GR) is not the ultimate theory of gravity is a possibility that should be entertained in the light of several observations (such as those related to the dark-matter and the dark-energy problems), and of the difficulty to reconcile GR with quantum field theory~\cite{Berti:2015itd}. Although such an extension of GR is unknown---and a robust spacetime parametrization in strong-field gravity is lacking---GW observations will help us to exclude or to strongly constrain wide classes of alternative theories. The inspiral stage, for example, when the two objects are far apart, can teach us about possible extra radiation channels~\cite{TheLIGOScientific:2016src,Barausse:2016eii,Cardoso:2016olt,Yunes:2016jcc}, while the final ringdown stage---when the end-product is relaxing to its final state---provides for remarkable tests of GR, through the measurement of the characteristic quasinormal modes (QNMs)~\cite{Berti:2009kk}. In GR, as well as in essentially any relativistic theory of gravity, BHs are extremely simple objects described by only a handful of parameters. Accordingly, their QNMs are completely characterized by only a few parameters as well. For example, Kerr BHs in GR are characterized by their mass and angular momentum, and so are their QNMs. In a nutshell, measurement of one single QNM (i.e, a ringing frequency and a decay time scale~\cite{Berti:2005ys,Berti:2009kk}) allows for a determination of the BH mass and angular momentum. The measurement of a second QNM tests GR~\cite{Berti:2005ys,Berti:2007zu,Gossan:2011ha,Meidam:2014jpa}. In the context of modified theories of gravity, a second QNM can be used to measure possible extra coupling parameters, as was shown recently for a theory with an extra vector degree of freedom~\cite{Cardoso:2016olt}. Some of the most viable and appealing modifications of gravity are those obtained via the inclusion of extra scalar fields---such as scalar-tensor theories of gravity---or of higher-curvature terms in the action, or both. Higher-order gravity is generically motivated by UV corrections, which also arise naturally in some low-energy truncations of string theories. The paradigmatic case, and the one we focus on here, is Einstein-dilaton-Gauss-Bonnet (EDGB) gravity, described by the action~\cite{Kanti:1995vq,Berti:2015itd} \be S=\int d^4 x\frac{\sqrt{-g}}{16\pi}\op(R-\frac{1}{2}\pa_a\phi\pa^a\phi+\frac{\alpha}{4}e^{\phi}{\cal R}_{\rm GB}^2\cl)+S_{m}\,, \label{eq:action} \ee where \be {\cal R}_{\rm GB}^2={R_{abcd}} R^{abcd}-4 {R_{ab}} R^{ab}+R^2\,, \ee is the Gauss-Bonnet topological term, $S_m$ represents the matter sector and we use (throughout this work) units for which the Newton's constant and the speed of light are unity, $G=c=1$. Current best constraints on the coupling constant $\alpha$ are $\sqrt{\alpha}<10\,{\rm km}$~\cite{Yagi:2012gp,Berti:2015itd}\footnote{We note a typo in the review~\cite{Berti:2015itd}. In the notation used in the review, Eq.~(2.26) should read $\sqrt{|\alpha_{\rm GB}|}\lesssim 5\times10^5\,{\rm cm}$.}. We will close two important gaps in the literature concerning BHs in this theory: we first find strong evidence that static EDGB BHs are linearly stable, and then compute gravitational waveforms from plunging particles, which can be argued to be an indicator of how BH collisions proceed in this theory. Finally, we discuss the constraints on the coupling parameter $\alpha$ from current and future ringdown observations. | EDGB gravity is a simple and viable higher-curvature correction to GR which predicts BH solutions with scalar charge. Since strong-curvature corrections are suppressed at large distance, it is natural to expect that the most stringent constraints on this theory come from the strong-curvature, highly dynamical regime as the one involved in a BH coalescence. Furthermore, compact stars in this theory possess only a very small scalar charge~\cite{Yagi:2011xp,Kleihaus:2016dui} and therefore EDGB gravity evades the stringent constraints on the dipole radiation coming from current binary-pulsar systems~\cite{Berti:2015itd}. The estimate~\eqref{boundzeta} translates to the following upper bound on the dimensionful EDGB coupling\footnote{Since one of the parameters of our Fisher-matrix analysis is $\zeta=\alpha/M^2$, propagation of errors implies a relative uncertainty $\delta\alpha/\alpha=\delta\zeta/\zeta+2\delta M/M$. However, in the large-$\rho$ limit the term $\delta M/M$ is negligible because it scales as $1/\rho$, compared to the $1/\sqrt{\rho}$ behavior of the error on $\zeta$ [cf. Eq.~\eqref{boundzeta}]. Therefore, in this limit $\delta \alpha\lesssim \delta \zeta M^2$.}, \begin{equation} \alpha^{1/2}\lesssim 11 \left(\frac{50}{\rho}\right)^{1/4}\left(\frac{M}{10 M_\odot}\right)\,{\rm km}\,, \label{boundalpha} \end{equation} where the prefactor changes by less than $10\%$ depending on the final BH spin. This result is in agreement with the simple estimates derived in Ref.~\cite{Barausse:2014tra}. As a consequence, our analysis also confirms that in most cases modified-gravity effects can be distinguished from environmental effects~\cite{Barausse:2014tra}. Future GW detectors will greatly increase the signal-to-noise ratio, a large value of which is necessary to perform ringdown tests of the Kerr metric~\cite{Berti:2016lat}. The signal-to-noise ratio of a ringdown waveform scales approximately (among its dependence on other quantities not shown here) as $\rho\sim M^{3/2}/S_n(f)^{1/2}$~\cite{Berti:2005ys}, where $M$ is the final BH mass and $S_n(f)$ is the detector noise power spectral density at a given frequency $f$. The best sensitivity of the future Voyager~\cite{Voyager} and Einstein Telescope~\cite{ET} detectors will be, respectively, roughly a factor of $10$ and a factor of $100$ better than in the first aLIGO observing run at the same optimal frequency $f\sim 10^2\,{\rm Hz}$~\cite{Berti:2016lat}. Thus, the Einstein Telescope with an optimal design can achieve a signal-to-noise ratio of roughly $\rho\approx 100$ for the ringdown signal of a GW150914-like event. From Eqs.~\eqref{boundalpha} and~\eqref{boundzeta}, this would translate into the bound $\alpha^{1/2}\lesssim 8 \left(\frac{M}{10 M_\odot}\right)\,{\rm km}$ and $\zeta\lesssim 0.4$. As expected, lighter BHs would provide a significantly more stringent constraint on $\alpha$, although their ringdown frequency might not fall into the optimal frequency range for ground-based detectors. Due to the small exponent of $\rho$ in Eq.~\eqref{boundalpha}, even an increase of $\rho$ of 1 order of magnitude will not provide a significantly more stringent constraint on the EDGB coupling. A stronger constraint may be set if future observations detect a light BH with a very large signal-to-noise ratio. Given this scenario, electromagnetic observations of accreting BHs (like the one discussed in Ref.~\cite{Maselli:2014fca}) might provide more stringent constraints in the future, although the latter are affected by astrophysical systematics that are absent in the ringdown case. Our estimates in the case of spinning BHs rely on the geodesic analogy for QNMs, which we verified only for axial modes in the static case and for Kerr BHs with any spin~\cite{Cardoso:2016olt}. It would be interesting to compute the modes of slowly rotating EDGB BHs (e.g. by adapting the methods discussed in Ref.~\cite{Pani:2013pma}) and to check the geodesic approximation in the spinning case. This computation will be required to place precise constraints on the EDGB coupling through future detections of BH ringing with high signal-to-noise ratio. Another interesting extension of our work concerns the scalar waves emitted during the coalescence. Although the luminosity in scalar waves is significant, this radiation may be possibly detected only if the dilaton is coupled to matter. Such coupling is presumably small and would not give rise to any effects in the detectors. Nonetheless, if the dilaton-matter coupling is non-negligible, the scalar radiation might be investigated through the same techniques developed to study the scalar emission in scalar-tensor theories, e.g. by using a network of ground-based detectors~\cite{hayama}. | 16 | 9 | 1609.01286 |
1609 | 1609.02370_arXiv.txt | PKS 1510-089 is one of the most variable blazars. Very high energy gamma ray emission from this source was observed by H.E.S.S. during March-April 2009 and by MAGIC from February 3 to April 3, 2012 quasi-simultaneously with multi-wavelength flares. The spectral energy distributions of these flares have been modeled earlier with the external Compton mechanism which depends on our knowledge of the densities of the seed photons in the broad line region, the dusty infrared torus or a hypothetical slow sheath surrounding the jet around the radio core. Here we show that to explain the multi-wavelength data with synchrotron emission of electrons and protons the jet power should be of the order of $10^{48}$ ergs/sec. | With the successful operation of the high energy gamma ray detectors it has become possible to study blazar flares even at very high energies. Blazars have relativistic jets directed toward us where the radiation losses from the relativistic electrons and protons result in the emission of photons of radio to gamma ray frequencies. \par They are powerful sources of GeV-TeV gamma rays. Their spectral attenuations at very high energy with cosmological distances are widely used to study the absorption of high energy gamma rays by the extragalactic background light (EBL) \cite{DK}. \par Their spectral energy distributions (SEDs) have two broad peaks. The peak at low frequency originates from synchrotron radiations of accelerated electrons in the relativistic jet and the peak at higher frequency from the inverse Compton scattering of these electrons by the seed photons in the jet, and the external regions including the disc torus, the broad line region (BLR). \par The high energy hump may also originate from synchrotron emission of accelerated protons in the jet and hadronic interactions \cite{Bo09,Diltz}. Hadronic interactions could be between accelerated protons and cold matter or low energy photons. \par Flat Spectrum Radio Quasars (FSRQs) and BL Lacs are two different classes of blazars having different spectral features. FSRQs have bright optical and UV emission lines \cite{Massaro}, also they are more luminous in high energy photons than BL Lacs. External Compton (EC) mechanism successfully describes the high energy emission from FSRQs in most cases while synchrotron self Compton (SSC) emission is the most popular scenario for BL Lacs. \par PKS 1510-089, PKS 1222+21, and 3C 279 are the three FSRQs observed in gamma rays of energy more than 100 GeV. The flares from 3C 279 have been modeled earlier with the synchrotron emission from accelerated electrons and protons, also with the two zone SSC model \cite{Paliya}. \par PKS 1510-089 is a FSRQ located at a redshift of 0.361 with highly polarised radio and optical emission. Although many FSRQs have been found to have a spectral break in the frequency range of a few GeV \cite{Abdo11}, the SED of PKS 1510-089 shows no such distinctive feature. In fact the transition from the high energy (HE:100 MeV to 100 GeV) to VHE range is quite smooth for the observed data. \par It has a black hole of mass $5.6\times 10^8$ times the mass of sun estimated from its accretion disc temperature and UV flux \cite{Abdo10}. Fermi LAT and AGILE detectors have detected highly variable gamma ray emission from it. Detection of gamma rays of energy upto 300---400 GeV has been reported by the H.E.S.S. collaboration \cite{Abram} during March-April, 2009 and the MAGIC collaboration \cite{Alek} from February 3 to April 3, 2012. \par The quasi-simultaneous data from radio, optical, X-ray and gamma ray telescopes have been combined and modeled with EC mechanism in \cite{BK}. They showed that the H.E.S.S. data given in \cite{H.E.S.S.13} could be included in their single zone model if EC emission happens due to the seed photons in the BLR and the dusty torus of PKS 1510-089. They also included the effect of the internal absorption of the gamma rays due to pair production with the photons in the blazar environment. Their model is primarily based on the assumption that the emission region is located near the central core i.e., the near dissipation zone scenario \cite{Abdo11}. Moreover, the absorption of the gamma rays by the EBL further attenuates the gamma ray spectrum before detection. \par However according to the findings of \cite{Marscher} it is possible that the emission region is located at large distances (tens of parsecs) from the blazar core. This would mean that the BLR cloud and the IR dusty torus can no longer act as possible sources of seed photons. In order to overcome this complication it has been hypothesized that the jet may have components moving with different relative velocities which provide the necessary seed photons for IC scattering. The authors of \cite{Alek} have considered both the far and near dissipation zone scenarios while modeling the SED obtained from observations. For the near dissipation zone scenario the IR torus was considered as the source of seed photons. Whereas for the far dissipation zone scenario they have considered a slow moving sheath enveloping the faster moving spine of the jet as the source of seed photons. \par PKS 1510-089 was detected in flaring states by the HESS and MAGIC telescopes in 2009 and 2012 respectively. In the present work we have used a single zone lepto-hadronic model to explain the multi-wavelength data during these flares. The lower energy peak is attributed to electron synchrotron mechanism whereas we consider the proton synchrotron mechanism for explaining the higher energy bump. Unlike the previous models we do not need to consider external sources of photons to explain the observed spectra. The following sections describe our work in detail. | We have discussed about a single zone lepto-hadronic model to fit the SEDs of PKS 1510-089 during its high states in 2009 and 2012. As our choice of $\delta$ values is guided by the fact that $\theta_{obs}$ can lie within the range 1.4$^{\circ}$---3$^{\circ}$ (as mentioned earlier in section--(\ref{section_2})) we can safely conclude that a lepto-hadronic model based explanation for the flaring states of PKS 1510-089 is applicable for a very wide range $1.59^{\circ}\leqslant \theta_{obs} \leqslant 2.86^{\circ} $. Due to inefficient cooling of protons we need very high jet power in protons to explain the higher energy bumps in the SEDs of flares. Although the jet power in our model is of the order of $10^{48}$ ergs/sec (which corresponds to isotropic luminosity of the order of $10^{50}$--$10^{51}$ ergs/sec), such high luminosities might be attained during blazar flares [see \cite{Abdo10} $\&$ \cite{Foschini}]. Earlier studies also indicated the need of such high luminosities in lepto-hadronic model (see \cite{Bo13}). \par The dimension of the emission region in our model is consistent with the observed week scale variability in the HE and radio frequency range. The hour scale variability reported by \cite{Saito} and \cite{Foschini} may be attributed to smaller `cells' inside the larger emission region. As discussed in \cite{Marscher14} the progression of turbulent plasma at relativistic velocities may give rise to the shorter timescale variabilities. Fluctuations in magnetic field and particle density may also play a significant role behind the rapid variability or ``flickering". Although no variability in the VHE regime was observed during the flaring episodes under discussion in our paper, it is probable that owing to reasons stated above the source may exhibit rapid variability in the VHE regime as well. | 16 | 9 | 1609.02370 |
1609 | 1609.09581_arXiv.txt | {Binary star systems are important for understanding stellar structure and evolution, and are especially useful when oscillations can be detected and analysed with asteroseismology. However, only four systems are known in which solar-like oscillations are detected in both components. Here, we analyse the fifth such system, HD 176465, which was observed by {\it Kepler}. We carefully analysed the system's power spectrum to measure individual mode frequencies, adapting our methods where necessary to accommodate the fact that both stars oscillate in a similar frequency range. We also modelled the two stars independently by fitting stellar models to the frequencies and complementary parameters. We are able to cleanly separate the oscillation modes in both systems. The stellar models produce compatible ages and initial compositions for the stars, as is expected from their common and contemporaneous origin. Combining the individual ages, the system is about $3.0\pm0.5\,\mathrm{Gyr}$ old. The two components of HD 176465 are young physically-similar oscillating solar analogues, the first such system to be found, and provide important constraints for stellar evolution and asteroseismology.}% | Observations of binary stars have been critical in advancing our knowledge of stellar structure and evolution. The shared formation history of stars in these systems results in their having the same initial chemical composition and age. Additionally, the dynamics of the system can reveal the component masses, and their radii if they eclipse. Studies of binary stars can be further enhanced by asteroseismic measurements. Asteroseismology of solar-like stars is rapidly proving its effectiveness at characterising stars, driven by the successes of the CoRoT and {\it Kepler} space telescopes \citep{Michel08,Gilliland10,Chaplin11a}. However, few binary systems have solar-like oscillations detected in both components. Three systems exist in which the two components have been observed separately: $\alpha$~Cen~A \citep[e.g][]{Bouchy02,Bedding04,Fletcher06,Bazot07}, and~B \citep{Carrier03,Kjeldsen05}, 16~Cyg~A~and~B \citep[KIC\,12069424 and KIC\,12069449;][]{Metcalfe12,Metcalfe15,Davies15}, and HD\,176071 \citep[KIC\,9139151 and KIC\,9139163;][]{Appourchaux12}. Additionally, oscillations in both components of HD\,177412 (HIP\,93511) have been measured while observed as a single {\it Kepler} target, KIC\,7510397 \citep{Appourchaux2015}. More commonly, oscillations have been detected in one member of a binary system \citep[e.g.][]{Mathur13}, particularly amongst the many red giants that have been observed \citep[e.g.][]{Hekker10b,Frandsen13,Gaulme13,Gaulme14,Beck14,Rawls16}. In addition, KIC\,4471379 \citep{Murphy14} is a binary in which both components are $\delta$\,Scuti pulsators, while KIC\,10080943 \citep{Schmid15,Keen15} has two $\gamma$\,Doradus/$\delta$\,Scuti hybrids. {\it Kepler} has detected oscillations in hundreds of Sun-like stars \citep{Chaplin11a,Chaplin14}. With an estimated $60 \%$ of stars thought to be multiple systems, it might be expected that {\it Kepler} will have observed many unresolved binary systems, some of which should exhibit oscillations in both components. However, \citet{Miglio14} used population synthesis models to predict that such systems are rare due to the requirement that both stars have oscillations with similar amplitudes in order to be detected. For this, they must have similar luminosity-to-mass ratios \citep{Kjeldsen95}. Despite this, HD\,177412 contains unequal components. The primary star of this system is $\sim$2.25 times more luminous than the secondary, and the ranges in which their oscillation modes are excited are well-separated in frequency \citep{Appourchaux2015}. In this case, the system was sufficiently bright ($V\,=\,7.9\,$mag) that the oscillation modes of the secondary star could still be detected. In this paper we report on another asteroseismic binary showing solar-like oscillations in both components. It corresponds to the previously-known binary HD~176465, which has been observed as a single {\it Kepler} target, KIC\,10124866\footnote{Within the {\it Kepler} Asteroseismic Science Consortium (KASC), stars have attracted nicknames that have been used by those analysing them. HD\,176465\,A~and~B are referred to as ``Luke'' and ``Leia'', respectively.}. HD~176465 was identified as a visual binary from 1902 observations as part of the Astrographic Catalogue \citep{Urban98}, and has since been observed on multiple occasions \citep{Mason01}. With a Tycho visual magnitude of 8.537, the primary, HD~176465~A is only $\sim$1.2 times more luminous than HD~176465~B ($V_T\,=\,8.674\,$mag), in line with the expectations of \citet{Miglio14}. Due to the similarity of the stars, their oscillation modes are excited at similar frequencies, complicating their analysis. In this paper we present the determination of the oscillation mode parameters and detailed asteroseismic models of both HD~176465~A~and~B. | Situated at only $49.6 \pm 1.8$ pc, the HD\,176465 binary system is sufficiently bright to reveal solar-like oscillations in both components. Only four other systems, namely $\alpha$\,Cen, 16\,Cyg, HD\,177412, and HD\,176071, are known to share this property. With both stars having solar-like oscillations with $\nu_\mathrm{max}\approx3500\,\mu$Hz and $\Delta\nu\,\approx\,150\,\mu$Hz, and with an effective temperature of $\approx\,5700$\,K, the system is comprised of two similar solar analogues. Detailed modelling of the power spectrum has enabled us to extract the frequencies, linewidths and heights of 45 modes for HD\,176465\,A, and 25 modes for HD\,176465\,B, up to an angular degree of $l=2$ and with a statistical significance greater than $75\%$. The rotational splittings of the non-radial modes reveal both stars to have a similar rotation period of $\sim18\,$d and inclination of $\sim50^\circ$. This rotation period is in agreement with that determined from the rotational modulation caused by the presence of starspots. Gyrochronology relations imply an age of $\sim3\,$Gyr. Precise estimates for the fundamental stellar parameters have been derived through detailed modelling of both stars. The four methods used to model these stars agree on the stellar properties in almost all cases. The masses of the stars are $M_A\,=\,0.95\pm0.02\,$M$_\odot$ and $M_B\,=\,0.93\pm0.01\,$M$_\odot$, and their radii are $R_A\,=\,0.93\pm0.01\,$R$_\odot$ and $R_B\,=\,0.89\pm0.01\,$R$_\odot$. From the modelling, the ages of both stars are found to be $3.0\pm0.5$\,Gyrs, in agreement with the gyrochronological value, and consistent with a synchronous formation. While main-sequence systems such as this are rare, they provide important tests of stellar structure and evolution, and of asteroseismology. \citet{Miglio14} predicted there should be more such systems amongst the many red giants observed by {\it Kepler}. The absence in the literature of systems with clear oscillations in two red giants is possibly a consequence of the difficulty in recognising the typical pattern of solar-like oscillations when modes overlap in frequency. While the overlapping modes of HD\,176465 have presented a (thus far) unique challenge in determining mode parameters, overlapping modes of red giants, with their many mixed $l=1$ modes, will present a far greater challenge. Despite these challenges, such systems will provide further tests of stellar structure and evolution when they are found, just as systems with a single oscillating red giant have already \citep[e.g.][]{Hekker10b,Frandsen13,Gaulme13,Gaulme14,Beck14,Rawls16}. With the future missions {\it TESS} \citep{Ricker15,Campante16} and {\it PLATO} \citep{Rauer14} to provide asteroseismic data for many more systems, there will be good opportunities to find more such asteroseismic binary systems. | 16 | 9 | 1609.09581 |
1609 | 1609.07139_arXiv.txt | We present an updated optical and mechanical design of NEWS: the Near-infrared Echelle for Wide-band Spectroscopy (formerly called HiJaK: the High-resolution J, H and K spectrometer), a compact, high-resolution, near-infrared spectrometer for 5-meter class telescopes. NEWS provides a spectral resolution of 60,000 and covers the full 0.8--2.5 $\mu$m range in 5 modes. We adopt a compact, lightweight, monolithic design and developed NEWS to be mounted to the instrument cube at the Cassegrain focus of the the new 4.3-meter Discovery Channel Telescope. | \label{sec:intro} High-resolution, near-infrared (NIR) spectroscopy enables an enormously broad range of scientific studies (see Ref.~\citenum{Muirhead2014} and references therein). However, relatively few facility-class, high-resolution, NIR spectrometers currently exist. Most are only available on large, heavily subscribed 8-to-10 meter class telescopes, such as NIRSPEC on the 10-meter Keck II Telescope\cite{McLean1998}, CRIRES on the 8.2-meter VLT UT 1 Telescope\cite{Kaeufl2004}, and IRCS on the 8.2-meter Subaru Telescope\cite{Tokunaga1998,Kobayashi2000}. High-resolution, NIR spectrometers for 3--5-meter class telescopes like Lowell Observatory's new 4.3-meter Discovery Channel Telescope\cite{Levine2012} (DCT) in Happy Jack, Arizona would provide greater accessibility for this powerful yet under-utilized tool for astronomy. Offering continuous, wide-band coverage has been an obstacle for high-resolution, NIR spectrometers. The number of resolution elements ($\Delta\lambda$) within the free spectral range (FSR) of a single order of a grating-based spectrometer is given by \begin{equation} \frac{\mathrm{FSR}}{\Delta\lambda} = \frac{\lambda N}{\phi D}, \end{equation} where $\lambda$ is the wavelength at the center of the order, $N$ is the number of illuminated grooves, $\phi$ is the angular width of the slit, and $D$ is the diameter of the telescope. Traditionally, higher resolution is achieved by increasing $N$ by using a larger grating or a grating with more closely spaced grooves. In the IR, the number of resolution elements per order quickly becomes too large to fit a full order across a single detector with at least two pixels per resolution element to fully sample the spectrum. Immersion gratings provide one path to high resolution while maintaining small free spectral ranges. Spectral resolution increases linearly with the index of refraction of the medium the grating is immersed in. IGRINS\cite{Yuk2010} and iSHELL\cite{Rayner2012} both achieve high-resolution ($R >$ 40,000) across the NIR through the use of a silicon ($n=3.4$) immersion grating. However, silicon is not transmissive below 1.2 $\mu$m. At constant resolution, the 0.8 to 1.2 $\mu$m range accounts for over 35\% of the information content in the 0.8 to 2.5 $\mu$m range. As we discuss in Section~\ref{sec:science}, Y-band around 1 $\mu$m is a requirement for our primary science goal. Resolution also increases linearly with $\tan(\delta)$, the tangent of the blaze angle. With a high-blaze Echelle grating, high resolution can be achieved in a format that can be imaged by a single 2k$\times$2k detector. Here we present an optical design for a high-resolution NIR spectrograph called NEWS: the Near-infrared Echelle for Wide-band Spectroscopy. The design is based on a high-blaze R6 ($\tan(\delta) = 6$) Echelle grating and achieves a resolution of 60,000 over the full 0.8--2.5 $\mu$m range. The photometric z, Y, J, H, and K bands can be observed in their entirety without gaps. | We have designed a high-resolution NIR spectrograph for the 4.3-meter Discovery Channel Telescope. NEWS achieves a resolution of $R$ = 60,000 over the full 0.8--2.5 $\mu$m range. Our design offers continuous coverage within each of its five observing modes corresponding to the photometric z-, Y-, J-, H-, and K-bands. If built, NEWS will be uniquely capable of measuring the composition and ages of field M dwarfs, including those who host planets detected by \textit{TESS}. | 16 | 9 | 1609.07139 |
1609 | 1609.04410_arXiv.txt | The demonstration of efficient single-mode fiber (SMF) coupling is a key requirement for the development of a compact, ultra-precise radial velocity (RV) spectrograph. iLocater is a next generation instrument for the Large Binocular Telescope (LBT) that uses adaptive optics (AO) to inject starlight into a SMF. In preparation for commissioning iLocater, a prototype SMF injection system was installed and tested at the LBT in the Y-band (0.970-1.065 $\mu$m). This system was designed to verify the capability of the LBT AO system as well as characterize on-sky SMF coupling efficiencies. SMF coupling was measured on stars with variable airmasses, apparent magnitudes, and seeing conditions for six half-nights using the Large Binocular Telescope Interferometer. We present the overall optical and mechanical performance of the SMF injection system, including details of the installation and alignment procedure. A particular emphasis is placed on analyzing the instrument's performance as a function of telescope elevation to inform the final design of the fiber injection system for iLocater. | \label{intro} iLocater is a high resolution, fiber-fed radial velocity (RV) spectrograph under development for the Large Binocular Telescope (LBT). Single-mode fibers (SMFs) will be used for the instrument as they provide a unique illumination source which mitigates modal noise and are capable of increasing the precision of RV measurements beyond that typically achieved by using multi-mode fibers (MMFs) systems\cite{Jovanovic}. The instrument will use a fiber injection system to couple light from each 8.4 meter diameter telescope primary mirror into a SMF. The requirements for efficient SMF coupling are a stable optical beam with low residual wavefront errors that matches the mode field diameter (MFD)\footnote{The MFD is defined as the 1/$e^2$ diameter of a Gaussian profile} of the fiber. Due to atmospheric turbulence, large ground-based telescopes require the use of adaptive optics (AO) to provide the necessary wavefront correction for SMF coupling. To date, efficient SMF coupling using AO had never been demonstrated at the LBT. As part of iLocater's development, it was necessary to demonstrate the principle of SMF coupling using the telescope AO system prior to full instrument commissioning. In order to verify this capability, an inexpensive prototype fiber injection system was installed at the LBT to measure and characterize SMF coupling using the telescope AO system. The Large Binocular Telescope Interferometer (LBTI) wavefront sensor (WFS) and the DX adaptive secondary of the LBT were used to provide a corrected input to the system\cite{Hinz}. The prototype system was designed to demonstrate SMF coupling efficiency (fraction of starlight) in the Y-band (0.970-1.065$\mu$m) and measure characteristics of the AO corrected beam (stability, FWHM etc). By obtaining SMF coupling measurements in advance of iLocater's commissioning date, the principle technology development and estimated throughput required for iLocater were verified. It is important to note that the prototype system only operated in the Y-band while iLocater will work in the Y- and J-bands simultaneously. Thus, additional fiber coupling tests across full wavelength band ($\lambda$=0.97 - 1.30$\mu$m) are required to develop a complete understanding of the throughput. An informed estimate however, can be made by extrapolating the Y-band measurements into the J-band. For details about the full iLocater instrument, see Crepp at al. 2016\cite{Crepp2016}. In this paper we discuss the techniques used to couple the telescope beam to the SMF and present the optical and mechanical performance of the SMF injection system. Section \ref{instrument} provides an overview of the 2016 fiber injection system with an updated prescription from the previously published design in Bechter et al. 2015\cite{BechterA}. Section \ref{fiberalign} discusses methods used to align the fiber and the time taken to couple to a target star. Sections \ref{optical} and \ref{mechanical} present measurements of the optical and mechanical performance respectively, with a focus on the instrument's atmospheric dispersion corrector (ADC) performance and the effects of fiber stage flexure. Section \ref{conc} gives a summary of the on-sky results and plans for future work. | \label{conc} The prototype SMF coupling system successfully achieved its primary goal of demonstrating the feasibility of SMF coupling using the AO system at the LBT with fiber coupling efficiencies of $\sim$10-25$\%$. Due to the weather conditions, $\sim$50$\%$ of scheduled on-sky time was lost and thus the targets were limited to a range of V-magnitudes from V=1 to V=10. Fainter targets (V$\sim$16) will be tested during the next phase of SMF testing at the LBT. Improvements in fiber coupling efficiency are expected due to the scheduled LBT AO SOUL upgrade upgrade\cite{SOUL}. Optical beam stability may be improved due to a new instrument location below the fast steering mirrors in LBTI, near the location of the combined focal plane. The design of the final fiber coupling system to be used in iLocater will include a full set of custom lenses with high surface quality ($\lambda/20$ goal) and minimal chromatic focal shift to be within the tolerances for fiber coupling across iLocater's full wavelength band. Due to the slow F/41.2 beam at the combined focus, the lenses will benefit from a smaller collimated beam diameter with a similar focal length collimating optic to that used after the F/15 focus. A smaller collimated beam will reduce the filling fraction of 25mm diameter optics and allow for easier alignment. The ADC proved to be critical for improving fiber coupling efficiency, on average improving the fiber coupling efficiency by a factor of $\sim$25$\%$ for all observed targets. Angular deviations from the output of the ADC limited the ZD which could be tested to $\sim$35$^{\circ}$ before the steering mirror retaining ring vignetted the collimated beam. In addition, the COTS singlet prisms limited the wavelength range which could simultaneously be corrected. SMF coupling in the final iLocater instrument will be improved by implementing a zero beam deviation ADC to allow active correction with custom triplet prisms for correction over the full wavelength range ($\lambda$=0.97 - 1.30$\mu$m)\cite{Kopon}. Mechanical flexure is a measurable effect with $\sim$0.7 pixels/degree change. This effect is shown to reduce fiber coupling efficiency by $\sim$15-20$\%$ over 5$^{\circ}$ of elevation change. The problem of flexure can be addressed in iLocater's final fiber injection system by improving upon the mechanical design of the fiber stage (avoiding spring-loaded stages), by designing the orientation of the stage to be gravitationally invariant with changes in telescope elevation, or by using high resolution optical encoders to provide feedback to the stage actuators. The fiber stage could also be downsized to include only one fiber ferrule, as the MMFs were not required. In addition, the final system's SMF may include a fiber bundle in which additional fibers are closely packed around a central science fiber. This will allow the surrounding alignment fibers to potentially be back-illuminated simultaneously while taking fiber coupling data. Further investigation is required to determine if active measurement of the back-illuminated images can provide a method of real-time stage adjustment. Using single-mode fibers for an RV spectrograph offers a new method to facilitate increased resolution and single measurement precision. The successful demonstration of SMF coupling at the LBT marks a major step forward in developing the SMF fiber injection system for use with iLocater. With performance upgrades scheduled for the telescope AO system and the implementation of fiber injection system design improvements, SMF coupling performance at the LBT shows promise to routinely exceed the minimum throughput requirements for iLocater. | 16 | 9 | 1609.04410 |
1609 | 1609.06309_arXiv.txt | The recent discovery of an enriched metallicity for the Smith high-velocity \hicap\ cloud (SC) lends support to a Galactic origin for this system. We use a dynamical model of the galactic fountain to reproduce the observed properties of the SC. In our model, fountain clouds are ejected from the region of the disc spiral arms and move through the halo interacting with a pre-existing hot corona. We find that a simple model where cold gas outflows vertically from the Perseus spiral arm reproduces the kinematics and the distance of the SC, but is in disagreement with the cloud's cometary morphology, if this is produced by ram-pressure stripping by the ambient gas. To explain the cloud morphology we explore two scenarios: a) the outflow is inclined with respect to the vertical direction; b) the cloud is entrained by a fast wind that escapes an underlying superbubble. Solutions in agreement with all observational constraints can be found for both cases, the former requires outflow angles $\!>\!40\de$ while the latter requires $\gtrsim1000\kms$ winds. All scenarios predict that the SC is in the ascending phase of its trajectory and have large - but not implausible - energy requirements. | High-velocity clouds \citep[HVCs,][]{WakkervanWoerden97} are large complexes of multiphase gas whose position-velocity is incompatible with them being part of the Galaxy disc. Their origin has been debated since the moment of their discovery, with two alternative scenarios proposed. One possibility is that HVCs have an extragalactic origin, either as gas stripped from satellites \citep{Putman+03} or as pristine material inflowing from the intergalactic space \citep{Blitz+99}. In this scenario the HVCs are currently accreting onto the Galaxy, building-up the gas reservoir that is consumed by the process of star formation. The alternative is a Galactic origin, where HVCs participate to a galactic-scale gas cycle triggered by stellar feedback, the so-called galactic fountain \citep{Bregman80, Fraternali+15}. An accurate determination of distances and metallicities of the HVCs is the key to disentangle between the two scenarios. The Smith Cloud \citep[SC,][]{Smith63} is one of the best-studied HVCs. It is located around $l,b\simeq39\de,-13\de$ at $\vlsr$ of about $+100\kms$, has total \hi\ mass of $\sim10^6\msun$ distributed in a coherent structure of $1\times3\kpc^2$ \citep{Lockman+08}, and a similar \hii\ mass \citep{Hill+09}. Its distance from the Sun ($9.8-15.1\kpc$) has been determined by \citet{Wakker+08} via absorption line studies of background and foreground sources. The SC has a head-tail morphology, with the head closer to the midplane, which suggests an ongoing interaction with the ambient medium. Different origins have been proposed for this system, such as a magnetised \hi\ jet from the 4-\kpc\ molecular ring of the disc \citep{Sofue+04}, or as a gaseous remnant of a dwarf galaxy like the Sagittarius dwarf \citep{BlandHawthorn98}. Recently, \citet{Fox+16} estimated the metal abundance of the SC by studying the absorption line spectra from three active galactic nuclei lying in the background of the system. They found a mean metallicity of $0.53$ Solar, which strongly supports a Galactic origin for the SC. Of the three absorption features, only one overlaps clearly with the \hi\ emission of the SC and shows a metallicity of $\sim0.7$ Solar, while the others ($Z\sim0.8,0.3$ Solar) are quite distant and potentially not associated with the Cloud. For this reason, we speculate that the SC is more metal enriched that what determined by \citet{Fox+16}. \citet[][hereafter F15]{Fraternali+15} proposed a model of the galactic fountain to explain the properties of another well-known HVC, complex C. In their model, complex C has formed by a powerful gas ejection from the disc in the region of Cygnus spiral arm. The ejection triggered the condensation of a vast portion of metal-poor coronal gas that, mixing with the enriched material from the disc, lowered the metal abundance of the complex down to the observed sub-solar value \citep[$0.1\!-\!0.3\zsun$,][]{Collins+07}. In this Letter we show that this model is also applicable to the SC. | Inspired by the findings of \citet{Fox+16}, in this Letter we have investigated the possibility that the Smith high-velocity \hi\ Cloud has originated via a Galactic fountain from the regions of the spiral arms of the Milky Way. We used a dynamical model of the galactic fountain and focussed on those orbits that reproduce the main observational properties of the SC, such as its position, line-of-sight velocity, distance and head-tail morphology. We found that a simple model of vertical outflow from the Perseus Arm, from a Galactocentric distance of $\sim7.7\kpc$ at a speed of $\sim330\kms$, reproduces all these constraints except the morphology, if we interpret it as due to ram-pressure stripping by the corona. The same model can be refined by including a fast ($\gtrsim1000\kms$) wind that escapes the underlying superbubble and entrains the cloud, providing the ram pressure required. Alternatively, a model where the outflow is inclined by $\sim43\de$ can reproduce all the observational constraints. In all scenarios considered, the SC is in the ascending phase of its trajectory and has travelled for no more than $50\Myr$. Such a short orbital time implies that the coronal gas condensation is minimal - less than $4\%$ of the final cloud mass comes from the corona - thus the cloud maintains the same metallicity of the underlying disc, in line with the findings of \citet{Fox+16}. We have verified that, in all scenarios, increasing the corona condensation rate (i.e. $t_{\rm delay}$) systematically worsens the fit. In the models without wind the typical drag timescale is $\sim\!150\Myr$. This is much longer than $t_k$, thus drag has little impact on the cloud trajectories. Decreasing this timescale to values closer to $t_k$ drastically worsens the fit. In the wind model the drag plays a key role in accelerating the cloud, thus varying the drag parameters has some influence: for $M_{\rm cl}\!=\!10^4\msun$ ($10^6\msun$) the best-fit orbits have $v_w\!\sim\!1000\kms$ ($2000\kms$) and $h_s\!\sim\!2.2\kpc$ ($1.3\kpc$). A galactic fountain origin would exclude the presence of dark matter associated to the SC. The metallicity of the SC is incompatible with its being a `dark dwarf galaxy' (which would have a much lower metal content), unless the minihalo has accreted gas from the Galaxy's ISM during a previous passage through the disc as in the model of \citet{GalyardtShelton16}. \citet{Lockman+08} computed a trajectory for the SC and found that the system has crossed the Galactic plane from above to below $\sim\!70\Myr$ ago at $R\!=\!13\kpc$. It is not surprising that we do not recover this trajectory amongst our best-fit solutions, as a) we impose an origin from one of the spiral arms; b) unlike Lockman et al., we do not force the SC's motion to be along the system's major axis. One could wonder whether the models presented in this work are energetically plausible. While the \hi\ mass of the SC is well constrained \citep[$\sim10^6\msun$,][]{Lockman+08}, its ionised gas mass is more uncertain and may dominate the total mass budget \citep{Hill+09}. Assuming a total gas mass in the range $1-5\times10^6\msun$, the kinetic energy $E_k$ required to kick this material at a velocity of $200\kms$ is $0.4\!-\!2\times10^{54}\erg$, comparable to the estimate for Complex C (F15) and to the energy associated to the \hi\ holes observed in the ISM of nearby spirals \citep{Boomsma+08}. A lower limit for the kinetic energy associated to the wind $E_w$ can be estimated by assuming that the wind operates only in the region of the SC, i.e., it is confined to a cone or a cylinder with base equal to the SC size, for which we use $760\pc$ from the extent of its minor axis. Adopting $v_w\!=\!1200\kms$ and a Gaussian density distribution in $z$ with $n_w\!=\!0.01\cmmc$ and $\sigma_w\!=\!1.5\kpc$, we find $E_w\!=\!1\!-\!3\times10^{54}\erg$ (depending on the geometry), thus $E_w$ is compatible to $E_k$ found for the model without wind. The issue is that the time window by which this energy should be released is extremely narrow, as our datacube-fitting routine typically returns $\Delta t_k\!=\!5\Myr$. F15 found $\Delta t_k\!=\!50\Myr$ for complex C, and concluded that a star formation rate density (SFRD) of $\sim0.01\msunsqkpcyr$ is needed to lift the complex from the disc to its current location. For the SC, the SFRD would be of the order of $0.1\msunsqkpcyr$. This is sufficient to trigger a Galactic wind \citep{Heckman02}. SFRDs of this magnitude are occasionally measured in nearby galaxies on kpc scales, but they are typically - although not exclusively - associated to the region of the galaxy centre \citep{Leroy+08}. We conclude that the energy requirements for our galactic fountain models of the SC are improbable, but not impossible. It is certainly possible that a combination of a superbubble wind and a skewed outflow can provide a good fit to the data and lower the energy requirements at the same time. Unfortunately this scenario has too many free parameters to be addressed here. | 16 | 9 | 1609.06309 |
1609 | 1609.06765_arXiv.txt | Abell 2146 consists of two galaxy clusters that have recently collided close to the plane of the sky, and it is unique in showing two large shocks on {\it Chandra X-ray Observatory} images. With an early stage merger, shortly after first core passage, one would expect the cluster galaxies and the dark matter to be leading the X-ray emitting plasma. In this regard, the cluster Abell 2146-A is very unusual in that the X-ray cool core appears to lead, rather than lag, the Brightest Cluster Galaxy (BCG) in their trajectories. Here we present a strong lensing analysis of multiple image systems identified on {\it Hubble Space Telescope} images. In particular, we focus on the distribution of mass in Abell 2146-A in order to determine the centroid of the dark matter halo. We use object colours and morphologies to identify multiple image systems; very conservatively, four of these systems are used as constraints on a lens mass model. We find that the centroid of the dark matter halo, constrained using the strongly lensed features, is coincident with the BCG, with an offset of $\approx$ 2 kpc between the centres of the dark matter halo and the BCG. Thus from the strong lensing model, the X-ray cool core also leads the centroid of the dark matter in Abell 2146-A, with an offset of $\approx$ 30 kpc. | \begin{figure*} \includegraphics[width=\textwidth]{becky_bcg_A_FINAL.eps} \caption{A false colour view of a {\it Hubble Space Telescope} of the brightest cluster galaxy in cluster A. There are two prominent strong lensing features with distinct bilateral symmetry, the `mask' system and the `bra-ket' system. The mask system has two emission knots that look like eyes. The bra-ket system resemble the symbols $<$ and $>$. South East of the centre of BCG-A is jet of gas from the active galactic nuclei.} \label{figMaskAndBraKet} \end{figure*} The cluster system Abell 2146 was first discovered to consist of two massive clusters undergoing a major merger by \citet{russel2010abel2146}, with an appearance on {\it Chandra X-ray Observatory} images reminiscent of the Bullet Cluster \cite[e.g.][]{bullet3}. On X-ray images, the system is unique in presenting two large shocks of Mach number $\sim 2$ \citep{russel2010abel2146,russellxray1}, indicative of a relatively recent merger between two clusters more similar in mass than those in the Bullet Cluster. Estimates from X-ray analysis \citep{russel2010abel2146,russellxray1} and dynamical analysis \citep{white2146dynamics} are consistent with a merger observed about 0.1-0.2 Gyr after first core passage, recent on the dynamical time scales of clusters. Abell 2146 holds great promise for investigating the transport processes in the plasma in cluster environments \citep{russellxray1}. Dark matter accounts for about 85\% of the mass of galaxy clusters. Most of the baryonic mass, accounting for about 15\% of the total gravitating mass, is hot X-ray emitting plasma, and at most a few percent of the total mass resides in the stellar components of galaxies. Major mergers of galaxy clusters occurring close to the plane of the sky are very rare events, and their importance in cosmology has been highlighted by the findings from the first such system to be discovered, the Bullet Cluster (e.g. \citealt{bullet3, markevitch2007}). When clusters collide, the clouds of hot plasma are slowed down by ram pressure, whereas the galaxies are essentially collisionless and affected mainly by tidal interactions. Dark matter also does not have a large cross-section for interaction (e.g. \citealt{bullet4, randall2008,Harvey2015darkmattercrosssection}), so shortly after collision the major concentrations of galaxies and the dark matter are expected to lead the plasma clouds (e.g. \citealt{bullet3}). A major merger thus results in a dissociation between the plasma clouds, galaxies and dark matter, the specifics of which depends on the cluster properties and merger geometry. The X-ray cool core of the cluster component Abell 2146-A \citep{russel2010abel2146,russellxray1} is offset from the Brightest Cluster Galaxy (BCG) seen on {\it Hubble Space Telescope} images \citep{king2146weak,canning2012_a2146}, but it leads rather than lags the BCG in their trajectories. At a later stage in a merger, a gravitational slingshot that causes the plasma to overtake the dark matter and galaxies is possible \citep{hallman2004} but the merger would have to be seen a factor of several times later since first core passage for this explanation to be dynamically viable \citep{russellxray1}. Weak lensing mass reconstruction using the distorted shapes of background galaxies on {\it Hubble Space Telescope} images is consistent with the peak in the dark matter in Abell 2146-A being offset from the X-ray cool core, but the resolution of the mass map is too low to draw a statistically robust conclusion. The galaxies in Abell 2146-B are located ahead of the peak in the plasma density, with the BCG being almost coincident with one of the X-ray shocks. Here our aim is to determine the centroid of the dark matter in Abell 2146-A, in order to establish the spatial location with respect to the X-ray cool core, and hence whether it also lags behind the X-ray cool core in its trajectory. We concentrate on modelling the mass around Abell 2146-A using newly-identified multiple image systems to construct the first strong lensing mass model of the system. Strong lensing analysis offers a higher resolution view of the mass around the BCG than obtained with weak lensing. In order to construct the strong lensing mass model we identify new candidate multiple image systems on {\it HST} images, see Figures~\ref{figMaskAndBraKet} and \ref{figMultipeImages}, on the basis of colours and morphologies. Since we do not have spectroscopic or accurate photometric redshift estimates for the candidate multiple images, we adopt a very conservative approach in our threshold for using a candidate system as a constraint. \begin{figure*} \includegraphics[width=\textwidth]{becky_bcg_A_little_regions_images_FINAL.eps} \caption{Note the rotation; north is towards the bottom right and east is towards the top right. Multiple image systems used as constraints in the vicinity of \bcga{}. Identical objects have the same letter prefix, e.g. `a1,' `a2,' and `a3.' The colour grouping indicates the objects considered to be at the same redshift. Objects `a,' `c,' and `d' are in cyan. Objects `e' and `f' are in green. Object `j' is in magenta. Objects `g,' `h,' and `m' are in red. For a close-up view of the systems, see Figures~\ref{figSamuraiMask} and \ref{figBraket}. The set a, c, and d was statically assigned a redshift of z = 2.0. Other systems were assumed to have a flat prior for the redshift in the range $z = 0.3$ to $z = 3.0$. } \label{figMultipeImages} \end{figure*} In \S~\ref{SecObsDataReduction}, we discuss the observations and data reduction. In \S~\ref{SecLensModel}, we discuss the software used and the components of a lens model. In \S~\ref{SecProcedure} we discuss the procedure used to build the model, including a technique for determining multiple image systems, cluster member selection, model constraints, and computation. In \S~\ref{SecResults}, we discuss the results of the lens models. The flat cosmology assumed has $H_{\rmn{0}} = \rmn{70\,km\,s^{-1} Mpc^{-1}}$, $\Omega_{\Lambda} = \rmn{0.7}$, and $\Omega_{m} = \rmn{0.3}$. Magnitudes used throughout are in the AB system. At the redshift of z = 0.2323 \citep{white2146dynamics} and given this cosmology, $1$ arcsec = $3.702$ kpc. For an overview of strong gravitational lensing, see \citet*{Schneider1995book} and \citet{SchneiderSaasFee2006}. | \label{secConclusion} We have used {\it Hubble Space Telescope} images to identify strongly lensed multiple image systems near to the BCGs of the merging cluster, Abell 2146. This merging cluster is an important laboratory for studying the physics of cluster mergers because the collision has occurred near the plane of the sky, the two clusters in the system are of comparable mass and the system also has two well defined shock fronts. The BCG in Abell 2146-A has an X-ray cool core. By identifying multiple image systems in the centre of Abell 2146-A, we have made a strong gravitational lensing mass model. We have determined that the location of the dark matter halo is coincident with the BCG, and is offset from the X-ray cool core. In other words from this strong lensing analysis, the cool core is leading, rather than lagging, the dark matter post collision, contrary to expectations for a merger seen shortly after first core passage. In \citet{canning2012_a2146} it is proposed that there is a causal link between the X-ray cool core and a plume of gas extending from the BCG in its direction, which is spatially coincident with soft X-ray emission. Together with the disrupted nuclear structure of the BCG, an interaction between the BCG and another galaxy in the cluster (prior to or during the merger) is proposed as a possible explanation of the offset between the BCG and the X-ray cool core \citep{canning2012_a2146}. \citet{Hamer2012MNRASthreeclustersgascooling} describe three clusters with significant offsets between the BCG and X-ray peak with the conclusion that a transitory event is the source of decoupling. The largest separation distance in \citet{Hamer2012MNRASthreeclustersgascooling} is on the order of $10$\,kpc, however, whereas in Abell 2146 the offset is on the order of $30$\,kpc. However, in light of \citet{Sanderson2009}, Abell 2146-A seems to fall in the upper range of offsets for BCG with line emission \citep{Crawford1999}. In order to test these hypotheses and to better understand the distribution of the dark matter (and galaxies), and plasma in the aftermath of the collision, computer simulations are being undertaken. These simulations will be guided by the results of lensing, X-ray, SZ and additional data. Redshift information for the strongly lensed features is critical to obtaining a properly normalized strong lensing mass model for Abell 2146-A. This redshift information would in addition allow us to identify multiple image systems to use as constraints in mapping the distribution of mass in Abell 2146-B. For objects that are bright enough, spectroscopic redshifts would be ideal, and otherwise photometric redshifts can be obtained with the addition of near-infrared imaging data to complement our optical imaging data. More work needs to be done to constrain the dark matter near \bcgb{}. A combined weak and strong lensing analysis will help accomplish this. | 16 | 9 | 1609.06765 |
1609 | 1609.00097_arXiv.txt | The formation and evolution of giant molecular clouds (GMCs) in spiral galaxies have been investigated in the traditional framework of the combined quasi-stationary density wave and galactic shock model. In this study, we investigate the structure and evolution of GMCs in a dynamically evolving spiral arm using a three-dimensional $N$-body/hydrodynamic simulation of a barred spiral galaxy at parsec-scale resolution. This simulation incorporated self-gravity, molecular hydrogen formation, radiative cooling, heating due to interstellar far-ultraviolet radiation, and stellar feedback by both ${\rm H_{II}}$ regions and Type-II supernovae. In contrast to a simple expectation based on the traditional spiral model, the GMCs exhibited no systematic evolutionary sequence across the spiral arm. Our simulation showed that the GMCs behaved as highly dynamic objects with eventful lives involving collisional build-up, collision-induced star formation, and destruction via stellar feedback. The GMC lifetimes were predicted to be short, only a few tens of millions years. We also found that, at least at the resolutions and with the feedback models used in this study, most of the GMCs without ${\rm H_{II}}$ regions were collapsing, but half of the GMCs with ${\rm H_{II}}$ regions were expanding owing to the ${\rm H_{II}}$-region feedback from stars within them. Our results support the dynamic and feedback-regulated GMC evolution scenario. Although the simulated GMCs were converging rather than virial equilibrium, they followed the observed scaling relationship well. We also analysed the effects of galactic tides and external pressure on GMC evolution and suggested that GMCs cannot be regarded as isolated systems since their evolution in disc galaxies is complicated because of these environmental effects. | \label{sec:Introduction} Understanding star formation mechanisms within galaxies is one of the most fundamental issues regarding the evolution of galaxies. It is known that the majority of stars form in giant molecular clouds (GMCs), which have masses of about $10^{4}$--$10^7~\rm M_\odot$ and sizes of about 10--100 pc \citep[e.g.][]{Colombo+2014}. Recent observational studies have shown that star formation activity \citep[e.g.][]{Muraoka+2009,Momose+2010,Hirota+2014,HuangKauffmann2015}, as well as the properties of the interstellar medium (ISM) and GMCs \citep[e.g.][]{Koda+2009,Koda+2012,Rebolledo+2012, Schinnerer+2013,Hughes+2013,Colombo+2014,Muraoka+2016}, vary for different galactic structures such as spirals, inter-arms, and bars. Accordingly, understanding the formation and evolution of GMCs, as well as the relationships between these processes and galactic structures, is a key factor in building a complete picture of star formation in galaxies. In this paper, the first of this series, we focus on the formation, evolution, and dynamical state of GMCs in spiral arms. According to the traditional view of GMC evolution in spiral arm environments, GMC evolution is influenced by `galactic shock' \citep[][]{Fujimoto1968,Roberts1969,Shu+1973} owing to so-called `quasi-stationary density waves' \citep[][]{LinShu1964,BertinLin1996}: if gas flows {\it across} a spiral arm, it experiences a sudden compression due to the galactic shock and is followed by cloud formation in a phase transition \citep{Shu+1972,Kim+2008}, shock compression of incoming clouds \citep{Woodward1976}, and gravitational collapse \citep{Elmegreen1979,KimOstriker2002}, which triggers star formation. This scenario predicts that GMCs have evolutionary sequences across spiral arms in a wide radial range, which has been preferred by recent observations of GMCs in nearby spiral galaxies such as M51 \citep[e.g.][]{Egusa+2011} and IC 342 \citep{Hirota+2011}. Several galactic-scale hydrodynamic simulations have been performed to investigate the dynamical response of the ISM to a {\it rigidly rotating} spiral potential, which models quasi-stationary density waves. Such hydrodynamic simulations have highlighted the roles of spiral arms in the formation and evolution of GMCs; the spiral potentials would enhance cloud--cloud collisions, which occur every 8--10 Myr, and result in the formation of massive GMCs up to $10^6$--$10^7~\rm M_\odot$ \citep{Dobbs2008,Dobbs+2015}. \citet{Dobbs+2011a} showed that these GMCs are predominantly gravitationally unbound objects, because cloud-cloud collisions and stellar feedback generate internal random motions of the gas. In addition to GMC formation, hydrodynamic simulations in spiral potentials showed that when a GMC passes through a spiral arm, strong shear within the spiral arm contributes to the destruction of the GMC \citep{WadaKoda2004,DobbsBonnell2006}. In particular, \citet{DobbsPringle2013} suggested that smaller $(\sim 10^4~\rm M_\odot$) clouds are strongly affected by feedback, whereas larger ($\sim 10^6~\rm M_\odot$) clouds are more affected by shear. In contrast to the traditional quasi-stationary density wave theory, wherein stellar spiral arms slowly change during several galactic rotation periods \citep[i.e. $\gtrsim 1$ Gyr;][]{BertinLin1996}, an alternative spiral theory has been developed \citep[see][for a recent review]{DobbsBaba2014}. This so-called `dynamic' spiral theory predicts that stellar spiral arms are dynamic structures, with amplitudes that change on the galactic rotation time scale, or even more rapidly \citep[i.e. a few hundred million years;][]{SellwoodCarlberg1984,Fujii+2011,Sellwood2011, Grand+2012a,Baba+2013,D'Onghia+2013,Pettitt+2015}. Dynamic spirals are also observed in $N$-body barred spiral galaxies \citep{Baba+2009,Grand+2012b,Roca-Fabrega+2013,Baba2015c}. In contrast to quasi-stationary density waves, such dynamic spirals {\it co-rotate} with material at any given radius\footnote{ Co-rotational behabiour is not true for tidally induced spirals such as M51. Recent numerical simulations of tidally interacting systems suggested that the pattern speeds of tidally induced spirals clearly differ from the galactic angular speed but that they decrease with increasing radius \citep{Dobbs+2010,Pettitt+2016}. } \citep{Wada+2011,Grand+2012a,Baba+2013,Kawata+2014}. This co-rotational behaviour may occur because the swing amplification is most efficient near the co-rotation radius \citep[e.g.][]{Toomre1981} and non-linear interactions between the swing-amplified wakelets develop a global spiral arm \citep{KumamotoNoguchi2016}. Furthermore, \citet{Wada+2011} and \citet{DobbsBonnell2008} performed hydrodynamic simulations of dynamic multiple spirals and found that the gas effectively falls into the spiral potential minimum from {\it both sides} of the spiral arm (the so-called `large-scale colliding flows'), rather than passing through the spiral arms, as predicted by galactic shock theory. \citet{Baba+2016a} observed such large-scale colliding flow in a simulated barred galaxy with a dynamic grand-design spiral. This recent progress related to the dynamics of spiral arms suggests that a rigidly rotating spiral could not be a reasonable dynamical model for investigating the formation and evolution of GMCs. It is therefore necessary to investigate the differences between these processes in quasi-stationary density waves and dynamic spirals. \citet{Renaud+2013} and \citet{Hopkins+2012} investigated GMCs by using $N$-body/hydrodynamic simulations with sub-parsec-scale or parsec-scale resolutions, although they did not focus on the relationship between GMCs and spiral arms. Thus, the formation and evolution of GMCs, as well as the relationship between GMCs and spiral arms, have not yet been well explored in a dynamic spiral context. In this study, we performed a three-dimensional $N$-body/hydrodynamic simulation of a barred spiral galaxy at a parsec-scale resolution in order to investigate the structures, formation and evolution of GMCs in a galactic context. Our galaxy model has {\it dynamic} barred grand-design spirals, which develop spontaneously from an axisymmetric bulge-disk-halo system \citep{Baba2015c}. To study the effects of the dynamical behaviours of spiral arms, we also performed a hydrodynamic simulation of a {\it fixed} spiral potential with a single pattern speed, which mimics the traditional spiral model. This paper is structured as follows. In Section \ref{sec:Method}, we describe our simulation methods regarding self-gravity, radiative cooling, heating due to interstellar radiation, molecular hydrogen formation, star formation from cold dense gas, and stellar feedback from $\rm H_{II}$ regions/supernova (SN) explosions. We describe the differences between the molecular gas structures and GMCs around the two types of spiral arms in Section \ref{sec:Comparison}. We then present the results regarding the formation, evolution, and dynamical state of GMCs in the dynamic spirals in Section \ref{sec:DynamicSpiralResults}. In particular, we focus on one simulated GMC in the spiral region and describe its evolution in detail and then present the statistical dynamical properties of GMCs, as well as the effects of galactic tides and external pressures. The formation and evolution of GMCs in the fixed spiral model are presented in Section \ref{sec:FixedSpiralResults}. Finally, we summarize the results in Section \ref{sec:Summary}. | \label{sec:Summary} We performed a three-dimensional $N$-body/SPH simulation of a barred spiral galaxy at parsec-scale resolution and investigated the dynamical states, formation, and evolution of GMCs in `dynamic' spiral arms. Our main findings and suggestions are as follows. \begin{enumerate} \item The simulated GMCs did not show systematic evolutionary sequences (in their masses and star formation activities) across dynamic spiral arms, in contrast to the expectation from traditional quasi-stationary density wave plus galactic shock theory \citep[e.g.][]{Fujimoto1968,Roberts1969,Shu+1972}. Investigations of whether GMCs show evolutionary sequences across spiral arms in {\it a wide radial range} will be a possible means of discriminating the origins of spiral arms. These studies will require high spatial resolution and wide-field mapping of molecular gas in spiral galaxies with equipment such as the Atacama Large Millimeter/submillimeter Array (ALMA). \item The simulated GMCs were highly dynamic and exhibited eventful lives involving collisional build-up, collision-induced star formation, and destruction via stellar feedback before all of the gas within the GMCs were transformed into stars. These findings are consistent with recent galactic-scale hydrodynamic simulations \citep[e.g.][]{Dobbs+2011b,DobbsPringle2013,Hopkins+2011,Hopkins+2012} and observations \citep[e.g.][]{Kawamura+2009,Murray2011,Fukui+2014}. The collisional build-up was driven by large-scale colliding flows associated with the spiral arm formation \citep{Wada+2011,Baba+2016a}, as well as by nearby SN explosions. \item Although the simulated GMCs were observed to be {\it collapsing} rather than in virial equilibrium, they followed the observed scaling relationships well. Thus, our results support the dynamic picture of GMCs \citep[e.g.][]{GoldreichKwan1974} rather than the traditional equilibrium picture \citep[e.g.][]{ZuckermanEvans1974}. The global collapse of molecular clouds is supported by recent observations \citep[e.g.][]{Schneider+2010,Peretto+2013,Ragan+2015}. \item The scaling relationships of the GMCs did not originate from the equilibrium state; instead, these could be explained by considering the collapsing state. Furthermore, this finding implies that a virial parameter is not a good indicator of the equilibrium state of a GMC \citep{Ballesteros-Paredes2006}. In contrast, through hydrodynamic simulations, \citet{Dobbs+2011a} demonstrated that GMCs are predominantly gravitationally unbound objects, although their arguments were based on the virial parameter. In fact, even if GMCs have $\alpha_{\rm vid,BM} > 1$, the GMCs would indicate $\langle \nabla\cdot{\bf v} \rangle < 0$, suggesting that the GMCs are collapsing. \item The effects of galactic tides and external pressure on the self-gravitational energy of the simulated GMCs were found to be non-negligible. This result suggests that both galactic tides (in particular, the components toward the galactic plane) and external pressure contributes to GMC collapse. Thus, our model suggests that a part of star formation activity in spiral arms is induced through the combined effects of increased rates of cloud-cloud collisions and compressions by SN explosions. \end{enumerate} According to our numerical resolutions and feedback models, GMCs are likely destroyed by stellar feedback (in particular, $\rm H_{II}$-region feedback). Nevertheless, some previous studies suggested that $\rm H_{II}$-region feedback only weekly affects GMC destruction. \citet{Renaud+2013} implemented the $\rm H_{II}$-region feedback using a Stromgren volume approach, which is similar to ours (see Section \ref{sec:SF}), into adaptive-mesh refinement (AMR) simulations of a Milky Way-like galaxy. They argued that $\rm H_{II}$-region heating is not expected to destroy clumps but is likely to modify their inner structures and the ongoing star formation. More recently, \citet{MacLachlan+2015} applied the post-process calculation of radiative transfer to a time series of SPH simulations of a spiral galaxy, and then suggested that the $\rm H_{II}$-region feedback may play only a minor role in the regulation of star formation. One possible reason for the discrepancy between the results of our study and those of the previous studies is the different numerical resolutions. If the stellar feedback is input into the neighbouring particles or cells, the use of a coarse resolutions could cause a large amount of gas to be affected. However, local-scale hydrodynamic simulations of individual GMCs, which were based on a simple ray-tracing algorithm and a Stromgren volume technique, showed that GMCs with masses up to $\sim 10^5~\rm M_\odot$ could be readily destroyed by the $\rm H_{II}$-region feedback \citep{Dale+2012,Dale+2013}. Therefore, the effect of stellar feedback could depend on the numerical resolutions, hydrodynamic schemes (AMR or SPH), and how the $\rm H_{II}$-region feedback is introduced into the simulations \citep[see a review by][and the references therein]{Dale2015review}. To reach a conclusion, a more sophisticated treatment of stellar feedback within a GMC, as well as higher resolutions, are required. Overall, the findings of this study imply that {\it both} galactic structures and local stellar feedback are important factors in GMC formation and evolution. It is worth re-emphasizing that the dynamical effects of galactic tides and external pressure on GMCs are not negligible. Thus, to understand formation and evolution of GMCs, as well as star formation in galaxies, more sophisticated treatment of stellar feedback within GMCs should be coupled with galactic-scale simulations. To explore the dynamical interactions between the ISM and time-dependent stellar structures such as spiral arms and bars, along with their environmental dependence, we will present detailed studies of these subjects using self-consistent simulations (with parsec-scale resolution) of barred spiral galaxies in forthcoming papers (Baba et al. in preparation). | 16 | 9 | 1609.00097 |
1609 | 1609.09349_arXiv.txt | By observing gravitational radiation from a binary black hole merger, the LIGO collaboration has simultaneously opened a new window on the universe and achieved the first direct detection of gravitational waves. Here this discovery is analyzed using concepts from introductory physics. Drawing upon Newtonian mechanics, dimensional considerations, and analogies between gravitational and electromagnetic waves, we are able to explain the principal features of LIGO's data and make order of magnitude estimates of key parameters of the event by inspection of the data. Our estimates of the black hole masses, the distance to the event, the initial separation of the pair, and the stupendous total amount of energy radiated are all in good agreement with the best fit values of these parameters obtained by the LIGO-VIRGO collaboration. | On September 14, 2015 the LIGO collaboration detected gravitational radiation from the merger of a binary black hole a billion light years away.\cite{ligo} This discovery is a major scientific breakthrough that constitutes the first direct observation of gravitational radiation almost a hundred years after Einstein predicted it. It has also opened a new window on the Universe.\cite{viewpoints} Arguably the LIGO observation is the most sensitive measurement ever made in the history of science. The experiment has generated tremendous interest both amongst the general populace as well as amongst students taking physics. Thus it represents an exceptional pedagogical opportunity. The event observed by LIGO (designated GW150914) consisted of the merger of two black holes with masses equal to 29 and 36 solar masses, respectively. The process took approximately a tenth of a second. The energy released in the form of gravitational radiation was the energy equivalent of three solar masses. The merger took place at a distance of a billion light years and hence a billion years ago. The direction of the source was only partially determined by the two LIGO detectors. All of these facts were inferred from data summarized in figure 1 (reproduced from the discovery paper by the LIGO collaboration). \cite{ligo} The parameters quoted were extracted by fitting the data to templates generated by state of the art numerical relativity. The purpose of this article is to explain key features of the data in figure 1 in terms of introductory physics and to use figure 1 to make back of the envelope estimates of the parameters quoted in the preceding paragraph. We make simple arguments based on Newtonian gravity, dimensional analysis and a rudimentary acquaintance with electromagnetism and waves. Black holes and their merger are relativistic phenomena and the peak of the observed signal comes from the coalescence of the two black holes, which is highly relativistic. To fully understand the underlying physics of a binary black hole merger in general and figure 1 in particular requires both analytic and numerical general relativity. The Newtonian treatment given here can only provide an understanding at an order of magnitude level. Our treatment is aimed at students in introductory college level physics courses, as well as high school students taking AP or IB Physics, who do not have a preparation in general relativity but want to understand the LIGO result. \begin{figure*} \includegraphics[width=\textwidth]{MathurFig1.eps} \caption{Summary of LIGO data (reproduced from the discovery paper).$^{ \cite{ligo}}$ The top left panel shows the strain $h$ observed by the Hanford detector as a function of time; the top right panel shows the data for the Livingston detector with the Hanford data time-shifted, inverted and overlaid to show the excellent match between the two detectors. The data have been band pass filtered to lie in the 35-350 Hz band of maximum detector sensitivity; spectral line noise features in the detectors within this band have also been filtered. The second row shows a fit to the data using sine-Gaussian wavelets (light gray) and a different waveform reconstruction (dark gray). Also shown in color are the signals obtained from numerical relativity using the best fit parameters to the data. The third row shows for both detectors the residuals obtained by subtracting the numerical relativity curve from the filtered data in the first row. The fourth row gives a time-frequency representation of the data and shows the signal frequency increasing in time.} \end{figure*} Binary black hole mergers take place in three stages. Initially the black holes circle their common center of mass in essentially circular orbits. During this stage they lose orbital energy in the form of gravitational radiation and spiral inward. In the second stage the black holes coalesce to form a single black hole. In the third stage, called ring-down, the merged object relaxes into its equilibrium state called a Kerr black hole.\cite{kerr} Gravitational radiation is emitted copiously during merger and ring-down as well but it is the in-spiral stage that is conducive to simple analysis, and that is the basis of the back of the envelope estimates presented here. By contrast the merger and ring-down are decidedly less simple. The ring down process is not a standard component of introductory courses or textbooks on general relativity but it can be presented at that level.\cite{chandrasekhar} The merger presents a formidable problem in numerical relativity that had until recently resisted all attempts at solution.\cite{numericalreview} The remainder of this paper is organized as follows. In section II we use simple arguments based on introductory physics to elucidate the underlying physics, and we use the data shown in figure 1 to estimate the masses of the black holes, their distance from earth, their initial separation and the total gravitational energy radiated. Along the way we define the chirp mass of a binary black hole system and derive the only equation that appears in the discovery paper.\cite{ligo} We also present a lower bound on the total mass of the black hole pair. In our analysis we do not estimate the rotational angular momentum of the black holes either before or after the merger. In section III we discuss this and other limitations of our analysis as well as other matters of pedagogical interest. In order to make our article more useful for instructors as well as for self study we provide some problems in appendix \ref{sec:probs}. | The above Newtonian analysis gives surprisingly good agreement with the parameters obtained by the fully relativistic treatment used by LIGO. In addition to the numerous simplifications explicitly stated above, we also ignore polarization of the gravitational radiation and the spin of the black holes\footnote{The spin of the black holes leads to additional velocity-dependent forces between the black holes during in-spiral. Minute forces of this kind that act on satellites and gyroscopes in Earth orbit due to the rotation of the Earth have been experimentally measured. For binary black holes undergoing in-spiral these forces are much more significant due to the larger masses and relativistic velocities involved. For simplicity we have not included these refinements in our analysis.}. Incorporation of these effects and other refinements is certainly possible but is contrary to the spirit of the ballpark estimates that we wished to present. Because of the approximations made our estimates should be correct only to order of magnitude (although serendipitously in many instances our estimates are within a factor of two of the best fit obtained by LIGO). Prior to LIGO the best evidence for gravitational waves came from observations of binary pulsars.\cite{taylornobel, taylor} Whereas LIGO is able to detect the actual distortion of space caused by the passage of gravitational waves, binary pulsars only provide indirect evidence for gravitational waves. Furthermore it is estimated that the best studied Hulse-Taylor binary pulsar will take 300 million years to coalesce (see problem 8 in appendix B). Thus for the foreseeable future the binary pulsar provides access only to the in-spiral phase whereas LIGO's binary black hole has provided a view of the strong gravity physics of coalescence and ring-down. Finally we briefly discuss physics after the merger. During the ring-down phase the signal from the merged black hole resembles the transients of a under-damped harmonic oscillator familiar from introductory physics (see figure 1). This transient corresponds to the longest lived ``quasi-normal'' mode of the black hole space-time. The damping rate and ringing frequency of the quasi-normal mode are determined by the mass and spin of the quiescent black hole that forms after the quasi-normal modes have died away. Thus the spins of the initial black holes can be determined using the in-spiral data and the spin of the final merged object using the ring-down data. By verifying that the initial and final spins are consistent with each other using a numerical analysis of the merger the LIGO team were able for the first time to test General Relativity in the hitherto inaccessible strong field regime, another significant outcome of their discovery.\cite{viewpoints, ligogr} {\em Note added.} After completion of this work we learnt of a new e-print from the LIGO-VIRGO collaboration that covers some of the same ground as the present manuscript.\cite{ligoped} We thank Andrew Matas, Laleh Sadeghian and Madeleine Wade for bringing ref \cite{ligoped} to our attention and Ofek Birnholtz and Alex Nielsen for a helpful correspondence. \appendix | 16 | 9 | 1609.09349 |
1609 | 1609.05398_arXiv.txt | We present a detailed analysis of the bright Cepheid-type variable star V1154~Cygni using 4 years of continuous observations by the {\it Kepler} space telescope. We detected 28 frequencies using standard Fourier transform method. We identified modulation of the main pulsation frequency and its harmonics with a period of $\sim$159~d. This modulation is also present in the Fourier parameters of the light curve and the O--C diagram. We detected another modulation with a period of about 1160~d. The star also shows significant power in the low-frequency region that we identified as granulation noise. The effective timescale of the granulation agrees with the extrapolated scalings of red giant stars. Non-detection of solar-like oscillations indicates that the pulsation inhibits other oscillations. We obtained new radial velocity observations which are in a perfect agreement with previous years data, suggesting that there is no high mass star companion of V1154~Cygni. Finally, we discuss the possible origin of the detected frequency modulations. | There is only one genuine Cepheid variable in {\it Kepler} field: V1154~Cyg (KIC~7548061). It has a mean V brightness of $\sim$9.1~mag and a pulsation period of $\sim$4.925~d. Its brightness variation was discovered by \citet{str63}. Further multicolor photoelectric and CCD photometric observations were published by \citet{wac76,sza77,are98,ign00,ber08,pig09}, while radial velocity data were published by \citet{gor98,imb99}. Detailed spectroscopic analysis was performed by \citet{luc06} and \citet{mol08} who determined the basic atmospheric parameters. \citet{jer13} has derived the radius and distance using Baade-Wesselink technique as ${\rm 44.5 \pm 4.1~R_{\odot}}$ and ${\rm 2100 \pm 200~pc} $. Although V1154~Cyg was already observed from space by the {\it Hipparcos} satellite \citep{esa97} and OMC onboard {\it INTEGRAL}, the accuracy of these observations is behind compared to the {\it Kepler} photometry. The first results based on the first four quarters of {\it Kepler} data were published by \citet{sza11} who found V1154~Cyg to be single periodic. The frequency analysis did not reveal any additional pulsation frequency while the period remained stable during the last 40 years. \citet{der12} analysed 600 days of {\it Kepler} data. The data revealed cycle-to-cycle fluctuations in the pulsation period, indicating that classical Cepheids may not be as accurate astrophysical clocks as commonly believed. A very slight correlation between the individual Fourier parameters and the O--C values was found, suggesting that the O--C variations might be due to the instability of the light-curve shape. This period jitter in V1154~Cyg represents a serious limitation in the search for binary companions as the astrophysical noise can easily hide the signal of the light-time effect. \begin{figure*} \begin{center} \includegraphics[width=17cm]{fig1.eps} \end{center} \caption{\label{lc} {\it Left panel:} Detrended long cadence {\it Kepler} observations of V1154~Cyg. {\it Right panel:} Zoom in four cycles of long cadence data.} \end{figure*} Later, \citet{eva15} also studied the light curve stability of RT Aur, a fundamental mode and SZ~Tau, an overtone mode Cepheid based on {\it MOST} data. They found cycle-to-cycle light curve variation of SZ~Tau and argued that it is the instability in the pulsation cycle and also a characteristic of the O--C curves of overtone pulsators whose oscillation seems to be less stable than that of the fundamental mode pulsator at both long and short timescales. The latest study of V1154~Cyg was performed by \citet{kanev} using the 4 years of long cadence {\it Kepler} data and studied the light curve by using Fourier decomposition technique. They found that the Fourier parameters $R_{21}$ and $R_{31}$ (see in Sect.\ \ref{foupars}) show modulation with a period of 158.2~d. They concluded that this modulation of the light curve is very similar to the phenomenon of the Blazhko effect in RR~Lyrae stars. In this paper, we present the analysis of V1154~Cyg using the whole {\it Kepler} dataset spanning 1460 d of continuous observations. In Sect.\ \ref{data}, we briefly describe the data used and details of the pixel-level photometry. In Section\ \ref{lcsection} we present the results of the Fourier analysis and the Fourier decomposition of the light curve, while the construction of the O--C diagram is shown Section~\ref{oc}. We combined our new radial velocities (RVs) and previous RV data in Section~\ref{newrv}. In Section~\ref{discussion} we discuss the detection of granulation noise, its properties and the origin of the frequency modulation. In Sect.~\ref{summary} we summarize our results. | \label{discussion} \subsection{Any secondary component?} We checked whether the $\sim$159~d modulation is caused by the presence of a companion star. Assuming that the $\sim$159~d modulation seen in the O--C diagram is caused by the light-time effect, i.e. to orbital motion in a binary system, and circular orbit, we can calculate the RV amplitude of the Cepheid variable. The semi-amplitude of the O--C in Fig.\ \ref{ocfig} is $A_{\rm (O-C)}= 0.0038$~d, so the expected RV amplitude is $\sim$45~km ${\rm s^{-1}}$. This $\gamma$-velocity variation is clearly not seen in Fig.\ \ref{rv}, nor in Fig.~14 in \citet{sza11}, where all the RV data are collected from the literature. Therefore, we can conclude that the detected $\sim$159~d modulation is not due to the presence of a companion star. \subsection{Blazhko-like modulation(s) of V1154\,Cygni } As we mentioned previously, the $\sim$ 159-d modulation was detected both in the Fourier parameters and in the O--C variations. The variation of the Fourier parameters corroborates our previous finding of light curve shape variations in this Cepheid. We note that the existence of light curve shape variation resembles the one seen in RR~Lyrae stars caused by the Blazhko effect (e.g. {\it Kepler}: \citet{kol11}; {\it CoRoT}: \citet{gug11}), and the simultaneous, cyclic frequency variation and light curve shape deformation also points to a Blazhko-like mechanism. Although Blazhko-like variations are very rare among single-mode Cepheids, there are a few such objects that may display similar modulation. The most prominent example within the Milky Way is V473 Lyr \citep{mol13,mol14}, which pulsates in the second overtone and has also two distinct modulation periods, 1204 d and 14.5 yr. Another well-known example is Polaris ($\alpha$ UMi) that went through a low-amplitude phase during the last few decades \citep{bru08}. However, even if the variations in Polaris eventually turn out to be periodic, they would represent an extreme case of centuries-long modulation. Recently, a few more promising candidates have been found, such as SV Vul that shows a $\sim 30$ year cycle in its pulsation period and possibly in its amplitude too \citep{engle2015}. However, these stars have cycle lengths in the range of decades and will require further observations to determine the exact nature of period and amplitude changes. A slightly different candidate is $\ell$ Car where changes in the RV amplitude were observed over the span of only two years, suggesting a shorter timescale, similar to V1154~Cyg, although no cycle length was determined for the star itself \citep{anderson2014}. We also note that several single-mode Cepheids within the Magellanic Clouds display periodic amplitude variations. However, most of them show only a single frequency peak next to the pulsation frequency, instead of symmetrical triplets, suggesting that in those cases the modulation is likely caused just by the beating between two closely-spaced pulsation modes \citep{soszynski2008,moskalikkov2009}. Recently, \citet{soszynski2016} described three Cepheids in the Large Magellanic Cloud that appear to show proper Blazhko-effect akin to that of V473~Lyrae, with modulation periods in the 1000--5000 d range. Whether these stars are modulated by the same mechanism as RR~Lyrae stars is not known yet. It also remains open whether the strongly modulated, second-overtone star V473~Lyr, and V1154~Cyg, which pulsates in the fundamental radial mode, share the same physical explanation of their variation. Nevertheless, the phenomenological similarity points towards a common mechanism. \subsection{The granulation noise} After prewhitening with the pulsation and modulation peaks, we are left with a Fourier spectrum that still contains significant power distributed into a forest of peaks between 0.0 and about 1.0 d$^{-1}$ frequency interval, increasing towards zero frequency (Figures \ref{granulation} and \ref{lorentz}). Some part of this residual power likely comes from the inaccuracies of stitching the {\it Kepler} quarters together, but the experience with RR~Lyrae light curves suggests that instrumental signals mostly manifest as few discrete peaks related to the length of the quarters and the orbital period of \textit{Kepler}, especially if the light curve contains quarter-long gaps \citep{ben14}. In this case, however, we see a combination of a wider, red noise-like component ($\sim f^{-2}$) with additional increases around the positions of the $nf_1$ frequency peaks. In stars that show solar-like oscillations, red noise is usually attributed to granulation, the overall effect of many convective cells appearing and disappearing in the photosphere. For the smaller red giants, up to about 25 R$_\odot$, we are now able to disentangle solar-like oscillations and granulation on a regular basis with data from photometric space telescopes like \textit{Kepler} (see, e.g., \citealt{mathur2011,kallinger2014}). For the largest, nearby red supergiants, such as Betelgeuse ($\alpha$ Ori) we can obtain direct observations via disk-resolved imaging or interferometry that show actual hot spots on the surface, and compare those to model calculations \citep{chiavassa2010}. Cepheids also possess envelope convection zones, therefore it is reasonable to expect that some form of granulation can occur in them as well. Furthermore, they lie between the oscillating red giants and the red supergiants in terms of size and mass, so comparison with both groups may be of importance. Visible-light observations obtained with the \textit{WIRE} space telescope suggested a small low-frequency excess in Polaris that was presumed to originate from granulation \citep{bru08}. However, both the frequency resolution and the precision of those data were much lower than that of V1154 Cyg. We computed the power density spectrum of the star after removing the pulsation and modulation signals from the light curve. \citet{kallingermatthews2010} followed a similar procedure for $\delta$ Scuti stars: first they prewhitened the data with 10 strongest frequency components, and then showed that the residual frequency spectra can be adequately described as a sum of granulation noise and a moderate number of pulsation modes. In the case of V1154~Cyg, we removed 28 frequency components and continued the analysis of the residual light curve. We filled the gaps in the residual light curve with linear interpolations, following the recipe of \citet{kallinger2014} to avoid leaking excess amplitude into the high-frequency regime through the wing structures of the spectral window. In addition, we calculated similar power density spectra for a few RR Lyrae stars as comparison, after prewhitening with the main harmonics and the modulation triplet peaks ($f_n\pm f_m$). The power density spectra of the RR Lyrae stars turned out to be flat, lacking any signs of excess noise that may arise either from granulation or instrumental effects, indicating that the signal in V1154 Cyg is intrinsic to the star. The granulation noise was first modeled for the Sun by \citet{harvey1985}. He concluded that the autocovariance of the granulation velocity field follows an exponential decay function, leading to a Lorentzian profile in the power density spectrum of the measured variations (note that the original notation there uses $\nu$ for frequency instead of $f$): \begin{equation} P(f) \sim \frac{\zeta\,\sigma^2\tau_{\rm gran}}{1+(2\pi\, f\, \tau_{\rm gran})^\alpha} \end{equation} \noindent where $\tau_{\rm gran}$ is the characteristic time scale and $\sigma$ is the characteristic amplitude of the granulation. The numerator, $P_{\rm gran} = \zeta\,\sigma \tau_{\rm gran}^2$ is defined as the amplitude of granulation power, with $\zeta$ being a normalisation factor that depends on the value of $\alpha$ \citep{kallinger2014}. For $\alpha = 2$ and $\alpha=4$, $\zeta$ can be analytically calculated to be 4 and $4\sqrt{2}$, respectively. \citet{harvey1985} originally employed $\alpha = 2$, i.e., a true Lorentzian function. Since then, several methods have been developed to investigate the granulation background of other stars (e.g., CAN: \citealt{kallinger2010}; OCT: \citealt{hekker2010}; SYD: \citealt{huber2009}). An important modification is that nowadays most methods use different exponents in the denominator that are usually higher than 2, called `super-Lorentzian' functions. We tested various prescriptions based on the comparative study of \citet{mathur2011}. The results are summarised in Figure \ref{granulation}: as the bottom panel shows, the original, single-component, $\alpha=2$ function of \citet{harvey1985}, and the SYD method (a combination of $\alpha=2$ and 4 functions) does not fit the data well. If we use the OCT method and use $\alpha$ as a free parameter, we find a fairly good fit at $\alpha=2.70$. The CAN method (top panel) that combines three $\alpha=4$ functions fits the data well too. In all cases the region with excess amplitude, between 2--8 $\mu$Hz (0.17-0.69 d$^{-1}$) has been excluded from the fit. \begin{figure} \includegraphics[width=1.0\columnwidth]{fig9_1.eps} \caption{Top: the Fourier spectrum of the residual data after we prewhitened with 28 pulsation and modulation frequency components and filled the gaps. The positions of the $nf_1$ components are indicated with the orange lines. The full-resolution spectrum is shown in grey, a smoothed version in black. Middle: the same, converted to power density spectrum. The solid orange line shows the fitted granulation signal, comprising of three super-Lorentzian functions (dashed blue lines), plus a constant noise component (the dash-dotted line), following the CAN method. Bottom: the granulation signal, fitted with three other methods, with varying degrees of success. } \label{granulation} \end{figure} With the invention of different methods, the comparison of various $\tau$ values became problematic. In the case of the CAN method, for example, $\tau_2 = \tau_{\rm gran}$, but the other two $\tau$ parameters have less well defined physical meanings. To solve this issue, \citet{mathur2011} proposed to calculate an effective timescale ($\tau_{\rm eff}$) instead, the e-folding timescale of the autocorrelation function. In the case of V1154~Cyg, we found that $\tau_{\rm eff} = (3.0 \pm 0.4)\, 10^5$ s, or $3.5 \pm 0.5$ d, in agreement with the $\tau_2$ parameter of the CAN method. We calculated the granulation power, defined as $P_{\rm gran} = \sum \zeta\,\sigma_i^2\tau_i$, and the amplitude of the intensity fluctuation, $A_{\rm gran}^2 = C_{\rm bol}^2 \sum (\sigma_i^2 / \sqrt{2})$ (where $C_{\rm bol}^2$ is a bolometric correction factor, as defined by \citealt{ballot2011}), to be $P_{\rm gran} = (2.65\pm 0.37)\, 10^5$ ppm$^2/\mu$Hz, and $A_{\rm gran} = 256 \pm 34$ ppm, respectively \citep{mathur2011,kallinger2014}. The values are summarised in Table \ref{table:gran}. \subsection{Granulation properties} To investigate the derived granulation parameters, we compared them to the red giant sample presented by \citet{mathur2011} and the well-observed supergiant, Betelgeuse (Figure \ref{gran_comp}). For the latter star, we analyzed the visual light curve data from the AAVSO (American Association of Variable Star Observers) database. The power density spectrum of Betelgeuse exhibits an obvious slope that can be fitted with various granulation noise curves. The light variations of the star are complicated by the semiregular variations, so we did not attempt a detailed analysis in this paper, instead we estimated $\tau_{\rm eff}$ only. Different fits to the autocorrelation function resulted in values between 120 and 435 d. We settled for a value of $\tau_{\rm eff} \approx 280 \pm 160$ d. Despite the large uncertainty, this confirms that the granulation timescale in red supergiants is in the range of a year. It is also in agreement with the 400-day timescale of convective motions in Betelgeuse, derived from line bisector variations \citep{gray2008}. Mass, radius, and log\textit{g} data for Betelgeuse are from the studies of \citet{lobeldupree2000} and \citet{neilson2011}. \begin{table} \begin{center} \caption{Granulation parameters for V1154~Cyg.} \begin{tabular}{ccc} \hline $\tau_{\rm eff}$ & $P_{\rm gran} $ & $A_{\rm gran}$ \\ (sec) & (ppm$^2/\mu$Hz) & (ppm) \\ \noalign{\vskip 0.1cm} \hline $(3.0 \pm 0.4)\, 10^5$ & $(2.65\pm 0.37)\, 10^5$ & $256 \pm 34 $ \\ \hline \end{tabular} \label{table:gran} \end{center} \end{table} \begin{figure} \includegraphics[width=1.0\columnwidth]{fig10.eps} \caption{Comparison of the $\tau_{\rm eff}$ effective timescale granulation parameter of V1154~Cyg (red circle), Betelgeuse (black square) and the \textit{Kepler} red giant sample of \citet{mathur2011}. Values are plotted against the stellar radius, logarithm of surface gravity, mass and effective temperature, respectively. The blue line in the top plot is an extrapolation of the scaling based on the red giant data. } \label{gran_comp} \end{figure} Figure \ref{gran_comp} shows that the scaling between the derived effective granulation timescale, $\tau_{\rm eff}$ and log $g$ is acceptable for both stars: they fall close but somewhat above the extrapolated power law based on the red giant data. Similar, but less tight scaling can be observed with the radius and mass as well. The effective temperature plot, on the other hand, is dominated by stellar evolution and it reproduces the positions of the stars in the Hertzsprung-Russell diagram instead. For V1154~Cyg we have a reliable estimate for the granulation power ($P_{\rm gran}$) too. The ratio of the two quantities, $P_{\rm gran}/\tau_{\rm eff}$, is related to the variance of the intensity variations over the stellar surface. This ratio is $\approx 0.9$ for the Cepheid but it is $\sim 10$ for red giants with similar log $g$ values (see Figure 5 by \citealt{mathur2011}). The difference can be attributed to various factors, e.g. lower contrast between cool and dark regions, or smaller cell sizes, leading to stronger cancellation effect over the surface. \subsection{Non-detection of solar-like oscillations} The observations of \textit{Kepler} revealed that solar-like oscillations in red giant stars have larger amplitudes and lower characteristic frequencies as the mass and size of the stars increase \citep{huber2011}. At first we searched for regular frequency spacings, a characteristic feature of the stochastically-driven oscillations, in the residual spectrum, but we found no significant patterns. Then we calculated the approximate range of $f_{\rm max}$ (or $\nu_{\rm max}$, in the notation used for solar-like oscillations), the frequency and amplitude of maximum oscillation power for V1154~Cyg, assuming a mass range of 4--8 M$_\odot$, based on the scaling relations of \citet{huber2011}. For this Cepheid, $f_{\rm max}$ would be between 5--10 $\mu$Hz, with an associated amplitude increasing from a minimum of 80 ppm to roughly 500 ppm, as the assumed $f_{\rm max}$ decreases. However, after we removed the granulation noise from the residual Fourier spectrum of V1154~Cyg, the remaining signals are about a factor of 4--5 smaller than the expected oscillation amplitudes in the entire frequency range. The only discernible features between 5--10 $\mu$Hz are the small excesses around the positions of the 3$f_1$ and 4$f_1$ frequency peaks. This result suggests that large-amplitude, coherent stellar pulsation suppresses or completely blocks solar like oscillations in Cepheids. Inhibition of regular oscillations was also observed in compact triple-star systems where tidally induced oscillations are excited instead \citep{derekas2011,fuller2013}. The remaining signals in the Fourier-spectrum are the broad forests around the positions of the pulsation frequencies. Forests of peaks indicate a non-coherent signal, therefore we fitted the positions of the first four harmonics from $f_1$ to $3f_1$, with Lorentzian profiles added to the granulation noise (Figure~\ref{lorentz}). The full width at half maximum values of the profiles indicates that the lifetime is $\tau = 1/\pi\Gamma = 4.5 \pm 0.4$ d. The origin of these profiles is not completely clear: they could originate from the pulsation jitter, but the Eddington-Plakidis test conducted in the previous study of V1154~Cyg indicate that the fluctuations average out on a longer time scale of 15 d \citep{der12}. Another possibility is that the signal originates from the interaction between granulation (e.g., convective motions) and stellar pulsation. \begin{figure} \includegraphics[width=1.0\columnwidth]{fig11.eps} \caption{The residual Fourier spectrum of V1154~Cyg with two different fits: the orange dashed line is the granulation noise profile only, the blue line is granulation plus Lorentzian profiles at the broad excesses. } \label{lorentz} \end{figure} | 16 | 9 | 1609.05398 |
1609 | 1609.00929_arXiv.txt | Fast radio bursts (FRBs) are highly dispersed, sporadic radio pulses that are likely extragalactic in nature. Here we investigate the constraints on the source population from surveys carried out at frequencies $<1$~GHz. All but one FRB has so far been discovered in the 1--2~GHz band, but new and emerging instruments look set to become valuable probes of the FRB population at sub-GHz frequencies in the near future. In this paper, we consider the impacts of free-free absorption and multi-path scattering in our analysis via a number of different assumptions about the intervening medium. We consider previous low frequency surveys alongwith an ongoing survey with the University of Technology digital backend for the Molonglo Observatory Synthesis Telescope (UTMOST) as well as future observations with the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and the Hydrogen Intensity and Real-Time Analysis Experiment (HIRAX). We predict that CHIME and HIRAX will be able to observe $\sim$ 30 or more FRBs per day, even in the most extreme scenarios where free-free absorption and scattering can significantly impact the fluxes below 1~GHz. We also show that UTMOST will detect 1--2 FRBs per month of observations. For CHIME and HIRAX, the detection rates also depend greatly on the assumed FRB distance scale. Some of the models we investigated predict an increase in the FRB flux as a function of redshift at low frequencies. If FRBs are truly cosmological sources, this effect may impact future surveys in this band, particularly if the FRB population traces the cosmic star formation rate. | The origin of fast radio bursts (FRBs) remains an unanswered question since their discovery a decade ago \citep{Lo07}. FRBs are millisecond duration, highly sporadic and dispersed radio pulses which follow the same dispersion relation seen in radio pulses from neutron stars. Of the 20 FRBs known so far, 18 have been found at Parkes~\citep{Th13,Lo07,Pe15,Ke16,Ch16}, one at Arecibo \citep{Sp14,Sp16} and one at Green Bank \citep{Ma15}. With the exception of the latter, FRB~110523, which was detected at 800~MHz, all the other FRBs have so far been seen in the 1--2~GHz band. FRB dispersion measures (DMs) are substantially greater than that expected from free electrons in our Galaxy, suggesting that FRBs are extragalactic in origin. There have been arguments about local origin of FRBs but the models cannot explain all the observed characteristics~\citep[for a review, see][]{Ka16}. Broadly speaking, the FRB source models fall into two categories: those of a catastrophic nature which would only be seen once~\citep[e.g., prompt emission from a gamma-ray burst;][]{Ya16} or those with the possibility to repeat \citep[e.g., giant pulses from Crab-like pulsars;][]{Co16,Co04}. So far, the only source known to repeat is FRB~121102~\citep{Sp16}. In the light of these recent discoveries, and to try to shed light on the origins of FRBs a number of groups are carrying out extensive radio surveys at sub-GHz frequencies~\citep{Ka15,Ca16,De16}. To date, however, the 0.7--0.9~GHz detection of FRB~110523 remains the only source found below 1~GHz~\citep{Ma15}. \cite{Ly16} argues that a lack of detections could be due to absorption in an ionized medium along the line of sight. Recent discoveries suggest low scattering in all FRBs which precludes a local plasma in the vicinity of the progenitor to explain their high DMs~\citep{Ma15,Ma13}. \cite{Ku15} argue for a young magnetar model with circum-dense medium around the star which can explain the high DM and the non-detections at lower frequency due to free-free absorption. The non-detections can also be explained by young neutron star progenitor within an expanding supernova remnant shell with hot ionized filaments~\citep{Pi16}. In this paper, we present a detailed analysis of the aforementioned absorption and scattering models. We use the approach to investigate the significance of non-detections in three recently completed surveys to constrain the spectral index of the burst for each model. Based on these constraints we make predictions for FRB detections from CHIME, UTMOST and HIRAX.~\cite{Co16b} make optimistic predictions for these upcoming low frequency surveys based on single FRB detection in the 0.7--0.9 GHz band. Here, we present predictions on the FRB detection rates based on different models of flux mitigation in the ISM. The plan for this rest of this paper is as follows. We describe our analysis methods in \S 2. In \S 3, we describe our results and discuss their implications in \S 4. | Our results suggest that telescopes in the 0.4--1.0~GHz band will make vital contributions to our understanding of FRBs. Even with free-free absorption and scattering playing a vital role in flux mitigation of FRBs, CHIME will be able to detect these bursts on a daily basis by the virtue of its extensive bandwidth and vast instantaneous sky coverage. We also looked into the possible caveats in the analysis and the effects those would have on the predictions for CHIME. Our investigation suggests that with all the caveats considered, the lowest yield for a future CHIME survey is $\sim 30$ FRBs per day which is very optimistic compared to expected yield from other surveys. For example, the corresponding yield for future UTMOST observations is about 1--2 FRBs per month for future observations which makes it difficult to differentiate between the two models at the moment. We also discussed certain caveats in our analysis (\S \ref{sec:caveats}) and how these assumptions affect the results. We found that a distribution in luminosities for FRBs, rather than a standard candle model assumed here, results in weaker constraints for the spectral indices of the population. Future surveys, however, will be excellent at probing the FRB luminosities through the dependence of luminosity on survey yield. If the FRBs currently observed lie predominantly in the local Universe (i.e.~have characteristic distances of 100~Mpc), then the large DMs cannot be accounted for by the Milky Way, host and IGM contributions. This discrepancy suggests that a large contribution to the DM comes from the local plasma around the source which favours models C and F as the most plausible scenarios describing these events. Assuming the parameters in model C, we can estimate the linear size of the absorber around the source in order to produce the high DMs observed for FRBs. If we take the FRB with the highest known DM (FRB 121002) and place it at $z = 0.025$ then, assuming model C, we obtain a linear size of $\sim$ 1.4~pc. This is very similar to the parsec size high density filaments found in supernova remnants and magnetar ejecta~\citep{Le15, Ko07, Ku15}. Thus, if future observations establish this distance scale for the FRB population, it should be possible to better constrain the model of absorption and the progenitor. During the course of this work, we observed an interesting trend in the FRB flux as a function of redshift for observations in the $<1$~GHz band where models C and F predict an increase in flux density as a function of redshift (see, e.g., the left panel of Fig.~\ref{fig:spec}). This behaviour is due to the Doppler shifting of a spectrum with a turn-over in its rest frame, which is a natural feature of the free-free absorption models. For sources at higher redshifts, we sample a different region in the spectrum of the source (see the right panel of Fig.~\ref{fig:spec}). If the spectrum has a turnover, the peak flux increases as we sample the rising edge of the spectrum. At higher redshifts, the frequency band passes over the turnover resulting in a decrease in the peak flux as expected. As discussed in \S \ref{sec:caveats}, we have not included the potential increase in the FRB rate with redshift that is predicted in cosmological models invoking star formation~\citep{Ma14}. If these models prove to be relevant in future, the aforementioned effect will be even stronger than seen in Fig.~\ref{fig:spec}. The constraints given in Table~\ref{tab:params} can tell us about the nature of the FRB progenitors. The observed and predicted spectral indices suggest that FRB spectral indices are different from pulsar spectral indices which have a mean of -1.4~\citep{Ba14}. Observations have suggested that at least some FRB spectral indices are positive \citep{Sp16}. Assuming a synchrotron source, the spectral index and the flux together can give us order of magnitude estimates about the magnetic field and effective electron temperature of the source~\citep[see for e.g][]{Co16c}. For example, if FRBs truly have a positive spectral index at frequencies of 1~GHz, the results favour a compact source with large magnetic field that is perpendicular to the line of sight (e.g., as seen in magnetar bursts) since the frequency at which the source becomes optically thick is proportional to the magnitude of the magnetic field while a negative spectral index would suggest other synchrotron sources (e.g., giant pulses from neutron stars). A large sample size of these sources expected from CHIME and HIRAX will definitely help to alleviate the problem. In summary, we have carried out a detailed analysis of possible FRB source populations and the expected yield from ongoing and future radio surveys below 1~GHz, based on results from the previous surveys. The previous results help in constraining the spectral index of the burst although no inference on the emission model can be drawn currently. Even with the most stringent model, in which spectral turnovers are expected in the observing band, CHIME is expected to see FRBs very frequently. Similar results are expected to be seen by HIRAX. The yields of CHIME, HIRAX and UTMOST will undoubtedly lead to a large sample that will provide great insights into the nature of and emission mechanism of these enigmatic sources. | 16 | 9 | 1609.00929 |
1609 | 1609.04027_arXiv.txt | {} {We studied the well known circumstellar disk around the Herbig Ae/Be star HD\,97048 with high angular resolution to reveal undetected structures in the disk, which may be indicative of disk evolutionary processes such as planet formation.} {We used the IRDIS near-IR subsystem of the extreme adaptive optics imager SPHERE at the ESO/VLT to study the scattered light from the circumstellar disk via high resolution polarimetry and angular differential imaging.} {We imaged the disk in unprecedented detail and revealed four ring-like brightness enhancements and corresponding gaps in the scattered light from the disk surface with radii between 39\,au and 341\,au. We derived the inclination and position angle as well as the height of the scattering surface of the disk from our observational data. We found that the surface height profile can be described by a single power law up to a separation $\sim$270\,au. Using the surface height profile we measured the scattering phase function of the disk and found that it is well consistent with theoretical models of compact dust aggregates. We discuss the origin of the detected features and find that low mass ($\leq$1\,M$_{\mathrm{Jup}}$) nascent planets are a possible explanation.} {} | In the past two decades a large variety of planetary systems have been discovered by indirect observation techniques such as radial velocity surveys (see e.g. \citealt{2007ARA&A..45..397U}) and transit searches (see \citealt{2013ApJS..204...24B}). To understand the formation process of these planets we need to study the initial conditions and evolution of protoplanetary disks. Intermediate mass Herbig Ae/Be stars are prime targets for such studies due to the massive disks they are hosting. High resolution imaging observations have been performed for a number of these disks in the past few years, e.g. \cite{2012ApJ...748L..22M} and \cite{2015ApJ...813L...2W} showed resolved spiral arms in the disks around SAO\,206462 and HD\,100453, while \cite{1999A&A...350L..51A}, \cite{2015MNRAS.450.4446B}, \cite{2016ApJ...819L..26C} and \cite{2016A&A...590L...7P} found asymmetric rings and gaps with increasing detail in the transitional disk around HD\,141569\,A. These structures may be signposts of ongoing planet formation. Indeed signatures of massive accreting protoplanets were directly detected in recent years in the disks of LkCa\,15 (\citealt{2012ApJ...745....5K}, \citealt{2015Natur.527..342S}) and HD\,100546 (\citealt{2013ApJ...766L...1Q}, \citealt{2015ApJ...807...64Q}, \citealt{2015ApJ...814L..27C}). Furthermore, several prominent young, massive planets orbiting stars of early spectral type were found through direct imaging observations, such as $\beta$\,Pic\,b (\citealt{2009A&A...493L..21L}), HR\,8799\,b,c,d,e (\citealt{2008Sci...322.1348M}, \citealt{2010Natur.468.1080M}), HD\,95086\,b (\citealt{2013ApJ...772L..15R}), 51\,Eri\,b (\citealt{2015Sci...350...64M}) and most recently HD\,131399\,Ab (\citealt{2016Sci...353..673W}). Thus these stars enable us to study the beginning and the end of the planet formation process at scales that we can spatially resolve.\\ HD\,97048 is a young (2-3\,Myr, \citealt{1998A&A...330..145V}, \citealt{2006Sci...314..621L}), well studied Herbig Ae/Be star at a distance of 158$^{+16}_{-14}$pc (\citealt{2007A&A...474..653V}). The mass of the star is estimated to be 2.5$\pm$0.2\,M$_\odot$ (\citealt{1998A&A...330..145V}). The star is well known to harbor a large ($\geq$\,600\,au, \citealt{2007AJ....133.2122D}) circumstellar disk. The disk was first spatially resolved in spectroscopy by \cite{2004A&A...418..177V} using TIMMI2 in the mid-IR and in imaging by \cite{2006Sci...314..621L} and \cite{2007A&A...470..625D} using VLT/VISIR with filters sensitive to PAH emission features in the mid-IR. Follow-up studies revealed the extended disk (between 320\,au and 630\,au) in optical scattered light (\citealt{2007AJ....133.2122D}), as well as in near-IR polarized light (\citealt{2012A&A...538A..92Q}). However, no structures were directly detected in the disk. From SED fitting combined with resolved Q-band imaging, \cite{2013A&A...555A..64M} deduced the presence of a gap and a puffed up outer disk inner edge at 34$\pm$4\,au.\\ We used the SPHERE (Spectro-Polarimetric High-contrast Exoplanet REsearch, \citealt{2008SPIE.7014E..18B}) instrument at the ESO-VLT to observe HD\,97048 in polarized and integrated light. By applying the polarized differential imaging technique (PDI, \citealt{2001ApJ...553L.189K}, \citealt{2004IAUS..221..307A}) as well as the angular differential imaging technique (ADI, \citealt{2006ApJ...641..556M}) we were able to remove the flux from the central star to study the circumstellar disk in unprecedented detail. In addition, we re-analyzed archival polarimetric VLT/NACO (\citealt{2003SPIE.4841..944L}, \citealt{2003SPIE.4839..140R}) data to compare them to our new observations. We identified four ring-like brightness enhancements and associated brightness decreases that we discuss in the following sections. | We observed the large circumstellar disk around HD\,97048 with SPHERE/IRDIS in scattered light using polarimetric and angular differential imaging and uncovered for the first time directly 4 gaps and rings in the disk. Our observations show very well the complementary nature of DPI and ADI observations. DPI observations enabled us to study the disk at the smallest angular separations and without self-subtraction effects, while the ADI observations provide deeper detection limits further out from the star.\\ The inclination and position angle of the disk that we extract from our observational data are consistent with the measurements by \cite{2006Sci...314..621L} as well as very recent ALMA Cycle 0 observations by \cite{2016arXiv160902011W}. Our innermost gap at $\sim$248\,mas (39\,au) and the following bright ring at $\sim$294\,mas (46\,au) are identical with the gap and ring at 34$\pm$4\,au inferred by \cite{2013A&A...555A..64M} from unresolved photometry and resolved Q-band imaging.\\ Our measurements suggest that the disk is flaring (assuming an axisymmetric disk) and that the scattering surface height profile of the disk is not significantly influenced by the observed structures. Specifically we find that the surface height can be described by a single power law up to a separation of $\sim$270\,au. Using this power law we derive the polarized scattering phase function of the disk. Assuming a bell-shaped dependency of the degree of polarization of the scattering angle we find that the total intensity scattering phase function shows a turn-off at $\sim$70$^\circ$, consistent with 1.2 $\mu$m compact dust aggregates as calculated by \citet{min2016}.\\ We find that nascent planets are one possible explanation for the structures that we are observing. However, given the low planet masses needed to carve out the gaps that we detected, it is unlikely that the planet's thermal radiation is directly detectable by current generation planet search instruments such as SPHERE or GPI. This conclusion is strengthened by the fact that the gaps are most likely not completely devoid of material and thus any thermal radiation from a planet inside the gap would be attenuated by the remaining dust.\\ A detailed radiative transfer study, which includes both our scattered light observations and high-resolution ALMA observations, is required for a more complete understanding of the disk structure and distribution of small and large grains in particular. We note that high resolution ALMA observation by \cite{2016arXiv160902488V} have just become available at the time of publication of our observations, which will enable such a study. | 16 | 9 | 1609.04027 |
1609 | 1609.04816_arXiv.txt | Due to observational challenges our knowledge of low-level accretion flows around neutron stars is limited. We present \nustar, \swift\ and \chan\ observations of the low-mass X-ray binary \source, which has been persistently accreting at $\simeq$0.1 per cent of the Eddington limit since 2006. Our simultaneous \nustar/\swift\ observations show that the 0.5--79 keV spectrum can be described by a combination of a power law with a photon index of $\Gamma$$\simeq$2, a black body with a temperature of $kT_{\mathrm{bb}}$$\simeq$$0.5$~keV (presumably arising from the neutron star surface), and disk reflection. Modeling the reflection spectrum suggests that the inner accretion disk was located at $R_{\mathrm{in}}$$\gtrsim$$100~\gmc$ ($\gtrsim$225~km) from the neutron star. The apparent truncation may be due to evaporation of the inner disk into a radiatively-inefficient accretion flow, or due to the pressure of the neutron star magnetic field. Our \chan\ gratings data reveal possible narrow emission lines near 1~keV that can be modeled as reflection or collisionally-ionized gas, and possible low-energy absorption features that could point to the presence of an outflow. We consider a scenario in which this neutron star has been able to sustain its low accretion rate through magnetic inhibition of the accretion flow, which gives some constraints on its magnetic field strength and spin period. In this configuration, \source\ could exhibit a strong radio jet as well as a (propeller-driven) wind-like outflow. | \label{sec:introduction} Low-mass X-ray binaries (LMXBs) contain a neutron star or a black hole that accretes gas from a less massive companion star. These are excellent laboratories to study accretion in the strong gravity regime. In particular, LMXBs are observed over a wide range in X-ray luminosity, hence accretion rate, allowing the investigation of different accretion morphologies. LMXBs are most easily discovered and studied when their X-ray luminosity is a sizable fraction of the Eddington limit, $\lx$$\gtrsim$0.1$~\ledd$. However, a lot of accretion activity occurs at much lower $\lx$. Indeed, many LMXBs are transient and accrete at $\lx$$>$$0.1~\ledd$ for only a few weeks or months and then spend years in quiescence before a new outburst commences. Thermal-viscous instabilities in the accretion disk provide the general framework for understanding such outburst-quiescence cycles \citep[though it cannot explain details; e.g.][for a review]{lasota01}. Accretion does not necessarily switch off in quiescence and may persist down to very low $\lx$ \citep[e.g.][]{wagner1994,campana1997,rutledge2002_aqlX1,kuulkers2008,cackett2010_cenx4,cackett2013_cenx4,bernardini2013,chakrabarty2014_cenx4,dangelo2014,rana2016}. Furthermore, there is a growing population of LMXBs that exhibit outbursts with a peak luminosity of only $\lx$$\simeq$$10^{-4}-10^{-2}~\ledd$ \citep[e.g.][]{hands04,sakano05,muno05_apj622,wijnands06,degenaar09_gc,campana09,heinke2010,armas2011,armas2014,sidoli2011}. Understanding the properties of LMXBs at $\lx$$<$$10^{-2}~\ledd$ is thus an important part of forming a complete picture of accretion flows around neutron stars and stellar-mass black holes. At $\lx$$>$$10^{-2}~\ledd$, matter is typically transferred through a geometrically thin and optically thick accretion disk that extends close to the compact primary. When moving towards lower $\lx$, the inner disk is expected to evaporate into a hot, geometrically thick and radiatively inefficient accretion flow \citep[e.g.][]{narayan1994,blandford99,menou2000,dubus2001_dim}. The X-ray spectral softening observed as black hole LMXBs transition from outburst to quiescence seems to support the formation of a radiatively-inefficient accretion flow \citep[see e.g.][for discussions]{plotkin2013,reynolds2014_qbh,yang2015}. Neutron star LMXBs also show X-ray spectral softening at $\lx$$<$$10^{-2}~\ledd$ \citep[e.g.][]{armas2011,armas2013_2,degenaar2013_xtej1709,bahramian2014,allen2015,weng2015}, although the behavior is not the same as for black holes \citep[][]{wijnands2015}. The X-ray spectra are also different; high-quality data obtained for neutron stars at $\lx$$\simeq$$10^{-4}~\ledd$ have revealed the presence of a thermal component, likely from the accretion-heated neutron star surface, and a power-law spectral component that is harder than for black holes at similar $\lx$ \citep[e.g.][]{armas2013,armas2013_2,degenaar2013_xtej1709,wijnands2015}. The picture proposed for neutron star LMXBs is that the radiation from the accretion flow softens at $\lx$$<$$10^{-2}~\ledd$ like in black holes, but becomes overwhelmed by the emission released when matter impacts the neutron star surface (causing thermal emission and a hard tail) at $\lx$$<$$10^{-3}~\ledd$ \citep[][]{wijnands2015}. Deep observations of the nearby neutron star Cen X-4 at $\lx$$\simeq$$ 4\times10^{-6}~\ledd$ may support this idea; it appears that only thermal emission from the stellar surface and bremsstrahlung from a boundary layer (where the accretion flow meets the surface) are observed, whereas the accretion flow itself is not directly detected \citep[][]{chakrabarty2014_cenx4,dangelo2014}. The magnetic field of a neutron star may also have a discernible effect on the accretion flow. It can potentially truncate the inner disk and re-direct plasma along the magnetic field lines. X-ray pulsations from the heated magnetic poles may then be seen \citep[e.g.][]{pringle1972,rappaport1977,finger1996,wijnands1998}. X-ray spectral observations revealed truncated inner disks in several X-ray pulsars \citep[e.g.][]{miller2011,papitto2013_hete,degenaar2014_groj1744,king2016,pintore2016}, whereas the inner disk seems to extend further in for non-pulsating neutron star LMXBs \citep[e.g.][]{cackett2010_iron,miller2013_serx1,degenaar2015_4u1608,disalvo2015,ludlam2016}. Magnetic field effects can possibly gain importance when the accretion rate drops, allowing the magnetic pressure to increasingly compete with that exerted by the disk. Since transient LMXBs typically only spend a short time at $\lx$$\simeq$$10^{-4}$--$10^{-2}~\ledd$, this is a particularly challenging accretion regime to characterize and to capture with sensitive observations. Fortuitously, a handful of neutron star LMXBs accrete in this range for several years \citep[e.g.][]{chelovekov07_ascabron,delsanto07,jonker08,heinke09_vfxt,zand09_J1718,degenaar2010_burst,degenaar2011_asca,armas2013}. These very-faint X-ray binaries (VFXBs) are interesting targets to further our knowledge of low-level accretion flows. VFXBs are also intriguing because the disk instability model has trouble explaining how their low accretion rates can be sustained for many years \citep[e.g.][]{dubus99,lasota01}. One possibility is that these objects have small binary orbits that only fit small accretion disks \citep[e.g.][]{king_wijn06,zand07,hameury2016}. The very dim optical counterparts indeed suggests that some VFXBs may have short orbital periods \citep[e.g.][]{bassa08,zand09_J1718}. However, a few other VFXBs were found to harbor H-rich donors, which rules out very compact orbits \citep[e.g.][]{degenaar2010_burst,arnason2015}. An alternative explanation for the quasi-stable low accretion rate of VFXBs is that the neutron star's magnetic field inhibits the accretion flow \citep[e.g.][]{wijnands2008_MC,heinke09_vfxt,heinke2014_gc,patruno2010_vf,degenaar2014_xmmsource}. \subsection{The very-faint X-ray binary \source} \source\ was discovered with \inte\ in 2006 \citep[][]{churazov2007}, but it was not until 2012 that it was identified as a neutron star LMXB through the detection of an energetic thermonuclear X-ray burst \citep[][]{degenaar2012_igrburster}. The X-ray burst light curve showed wild intensity variations that were presumably caused by extreme expansion of the neutron star photosphere; this suggests a source distance of $D$$\simeq$5~kpc \citep[][]{degenaar2013_igrj1706}, assuming that the peak flux of the X-ray burst reached the empirical Eddington limit of $L_{\mathrm{Edd}}$$=$$3.8\times10^{38}~\lum$ \citep[][]{kuulkers2003}. The source has been persistently accreting at a low luminosity of $L_X$$\simeq$$4 \times 10^{35}~\dist~\lum$ for the past 10 yr, which roughly corresponds to $\simeq$$10^{-3} \ledd$ \citep[e.g.][]{ricci2008,remillard2008,degenaar2012_igrburster}. It was not detected by the \rosat/PSPC in 1990 (obsID rs932824n00), suggesting that its luminosity was likely a factor $\gtrsim$10 lower at that time. Due to its relative proximity and relatively low interstellar extinction compared to other VFXBs, \source\ is a particularly good target to further our understanding of low-level accretion flows and the nature of these peculiar LMXBs. In particular, the powerful X-ray burst seen in 2012 revealed the presence of Fe in the accreted matter \citep[][]{degenaar2013_igrj1706}, which provides the chance of detecting reflection features from the accretion disk. Disk reflection manifests itself most prominently as an Fe-K emission line at $\simeq$6.4--6.97~keV and a Compton hump at $\simeq$20--40 keV \citep[e.g.][]{george1991,matt1991}. The shape of these features is modified by Doppler and gravitational redshift effects as the gas in the disk moves in high-velocity Keplerian orbits inside the gravitational well of the compact accretor. The reflection spectrum thus encodes information about the accretion morphology \citep[e.g.][for a review]{fabian2010}. In particular, detecting and modeling disk reflection features allows for a measure of the inner radial extent of the accretion disk, $R_{\mathrm{in}}$. If a radiatively-inefficient accretion flow forms or if the stellar magnetic field is dynamically important in governing the accretion flow in VFXBs, the inner disk is expected to be truncated away from the neutron star. However, so far no observational constraints on the inner radial extent of the accretion disks in VFXBs have been obtained yet. Radiatively-inefficient accretion flows are likely associated with outflows \cite[e.g.][]{rees1982,narayan1994,blandford99,narayan2005}. Furthermore, the magnetic field of a neutron star may act as a propeller and could expel (some of) the in-falling gas \citep[e.g.][]{illarionov1975,lovelace1999,romanova2009,papitto2015_prop}. Neutron star LMXBs accreting at $\lx$$<$$10^{-2}~\ledd$ may therefore be expected to exhibit outflows. In the X-ray band, these may reveal itself through the detection of blue-shifted narrow spectral lines. In this work we present \nustar, \swift\ and \chan/HETG observations of \source\ to study the accretion regime of $\lx$$\simeq$$10^{-3} \ledd$ and to understand the puzzling nature of neutron star LMXBs that are able to accrete at such a low rate for years. In particular, the aim of these observations was to constrain the continuum spectral shape, to measure disk reflection features to gain insight into the accretion geometry, and to search for narrow X-ray spectral lines that may be indicative of an outflow. | \label{sec:discuss} In this work we presented \nustar, \swift\ and \chan\ observations of the neutron star LMXB \source, which has been persistently accreting at $\lx$$\simeq$$10^{-3} \ledd$ since 2006. The aim of this study was to gain more insight into the morphology of low-level accretion flows, and the nature of neutron star LMXBs that are able to accrete at these low rates for several years. The 0.5--79~keV \nustar/\swift\ spectrum of \source\ can be modeled as a combination of a $\Gamma$$\simeq$2 power-law component and a soft, thermal component that can be described by a $kT$$\simeq$0.5~keV black body. This continuum spectral shape is very similar to that inferred from \xmm\ data obtained for a few neutron star LMXBs at $\lx$$\simeq$$10^{-4}~\ledd$ \citep[e.g.][]{armas2011,armas2013,armas2013_2,degenaar2013_xtej1709}. The temperature of the black body component appears to be too high for the measured X-ray luminosity, and the inferred radius to small, to be from the accretion disk. The thermal emission is therefore more likely coming from (part of) the neutron star surface, which is expected to become visible when moving to low $\lx$. We do not seem to detect the hard emission tail that is thought to be associated with surface accretion \citep[e.g.][]{deufel2001,dangelo2014,wijnands2015}. Possibly, at $\lx$$\simeq$$10^{-3}~\ledd$ this component is difficult to disentangle from the emission of the accretion flow itself. The spectral data of \source\ show a broadened Fe-K line at $\simeq$6--7~keV. Such a feature has never been detected for a neutron star LMXB accreting at $\lx$$\lesssim$$10^{-2} \ledd$ before \citep[despite the availability of high-quality data; e.g.][]{armas2013,lotti2016}, but it is commonly seen in brighter LMXBs. Assuming that the line is due to relativistic disk reflection, we modeled the spectral data with \relx. This suggests that the inner disk radius was truncated away from the ISCO, at $R_{\mathrm{in}}$$\gtrsim$$20~\risco$ ($\gtrsim$$100~\gmc$ or $\gtrsim$225~km; 1$\sigma$ confidence). Due to the low flux of \source, however, the data quality is not good enough to rule out a location at the ISCO at $>$3$\sigma$ significance. Nevertheless, it would not be surprising to find a truncated disk at $\lx$$\lesssim$$10^{-2} \ledd$ and it is therefore interesting to further explore this (Section~\ref{subsec:innerdisk}). Our high-resolution \chan\ gratings data of \source\ reveal hints of discrete emission and absorption lines in the $\simeq$0.5--1.5~keV energy range. This includes what appears to be a collection of narrow emission lines near 12~\AA\ ($\simeq$1~keV) that can be modelled as disk reflection or a collisionally-ionized plasma. Unfortunately the significance of the narrow spectral features is low ($\lesssim$4.5$\sigma$) and depends on the underlying continuum/reflection spectrum. However, since this is the first gratings data of a neutron star LMXB accreting as low as $\lx$$\simeq$$10^{-3} \ledd$, it is interesting to explore plausible physical scenarios that could account for these lines (Section~\ref{subsec:outflow} and~\ref{subsec:emission}). The strongest and most robust feature found in our simple line search is a relatively broad feature near 16~\AA\ ($\simeq$0.77~keV), which has a significance of $\simeq$4$\sigma$ for all spectral models that we explored (not accounting for trials). If the absorption is real, it can can be modelled as an outflowing photo-ionized plasma with a line-of-sight velocity of $\simeq$2\,000--3\,500~$\kms$ ($\simeq$0.01$c$). An outflow might be expected if the inner disk in \source\ is truncated due to the formation of a radiatively-inefficient accretion flow \citep[e.g.][]{narayan1994,blandford99,narayan2005}, or if the magnetosphere of the neutron star is acting as a propeller \citep[e.g.][]{illarionov1975,romanova2009,papitto2015_prop}. \subsection{Disk truncation at the magnetospheric boundary?}\label{subsec:innerdisk} If the inner disk is indeed truncated at $R_{\mathrm{in}}$$\gtrsim$$100~\gmc$ in \source, this is a factor $\gtrsim$7 higher than typically found for non-pulsating neutron star LMXBs accreting at $\lx$$\gtrsim$$10^{-2}~\ledd$ \citep[$R_{\mathrm{in}}$$\simeq$5--15$~\gmc$; e.g.][]{cackett2010_iron,egron2013,miller2013_serx1,degenaar2015_4u1608,disalvo2015,ludlam2016,sleator2016}. It is also a factor $\gtrsim$3 higher than inferred for several (millisecond) X-ray pulsars that accrete at $\lx$$\gtrsim$$10^{-2}~\ledd$ \citep[$R_{\mathrm{in}}$$\simeq$15--30$~\gmc$; e.g.][]{miller2011,papitto2013_hete,king2016,pintore2016}. The black hole LMXB GX 339--4 shows a much narrower Fe-K line at $\simeq$$10^{-3} \ledd$ than at higher accretion luminosity. This can be interpreted as the inner disk receding from the ISCO to $R_{\mathrm{in}}$$\simeq$35~$\gmc$ as the mass-accretion rate drops, presumably due to disk evaporation \citep[][]{tomsick2009}. Our study suggests a larger truncation radius for \source\ at similar Eddington-scaled accretion rate. Disk evaporation should operate in neutron star LMXBs too, although it is expected to set in at lower $\lx$ than for black holes because soft photons emitted from the stellar surface cool the hot flow \citep[e.g.][]{narayan1995}. If the inner disk in \source\ is indeed further out than in GX 339--4, this might point to a different truncation mechanism. We note that there is degeneracy in inferring a truncated disk from reflection modeling \citep[e.g.][]{fabian2014}. In particular, in case of GX 339--4 it has been pointed out that the narrowing of the Fe-K line with decreasing $\lx$ could also be due to the illuminating X-ray source moving away, i.e. an increasing height of the corona in a ``lamp-post'' geometry \citep[][]{dauser2013}. It is, however, not obvious that in neutron star LMXBs the accretion disk is also illuminated by a corona (rather than e.g. the boundary layer) and hence that a lamp-post geometry would apply for \source. In neutron star LMXBs, it is also possible that the stellar magnetic field truncates the inner accretion disk. In fact, a magnetically-inhibited accretion flow has been proposed as a possible explanation for the sustained low accretion rate of some VFXBs like \source\ \citep[][]{heinke09_vfxt,heinke2014_gc,degenaar2014_xmmsource}. If the blue-shifted absorption in the \chan\ data is real, this could possibly form a consistent physical picture in which the accretion flow is stopped at the magnetospheric boundary that acts as a propeller. This is an interesting scenario because the inferred inner disk radius would then provide constraints on the magnetic field strength and spin period of the neutron star. \subsection{Estimates of the neutron star magnetic field strength}\label{subsec:Bfield} If the inner accretion disk in \source\ is truncated at the magnetospheric radius, we can estimate the magnetic field strength. To this end we use equation (1) from \citet{cackett2009_iron}, which is based on the derivations of \citet{ibragimov2009}, to write the following expression for the magnetic field strength: \begin{eqnarray*} B = 1.2\times10^{5} \, k_{\mathrm{A}}^{-7/4} \, \left(\frac{R_{\mathrm{in}}}{GM/c^2}\right)^{7/4} \, \left(\frac{M}{1.4~\mathrm{M_\odot}}\right)^2 \, \frac{D}{5~\mathrm{kpc}} \nonumber \\ \times \left(\frac{R}{10^6~\mathrm{cm}}\right)^{-3} \, \left( \frac{f_{\mathrm{ang}}}{\eta} \frac{F_{\mathrm{bol}}}{10^{-9}~\mathrm{erg~cm^{-2}~s^{-1}}} \right)^{1/2}~\mathrm{G}, \end{eqnarray*} \noindent where $f_{\mathrm{ang}}$ is an anisotropy correction factor \citep[which is close to unity;][]{ibragimov2009}, $k_{\mathrm{A}}$ a geometry coefficient \citep[expected to be $\simeq$0.5--1.1;][]{psaltis1999,long2005,kluzniak2007}, and $\eta$ the accretion efficiency. We use $D$$=$5~kpc, $M$$=$1.4$~\Msun$, $R$$=$10~km, $R_{\mathrm{in}}$$\gtrsim$100~$\gmc$, and conservatively assume that the bolometric flux is equal to the 0.5--79 keV flux determined from our joint \nustar/\swift\ fits (i.e. $F_{\mathrm{bol}}$$=$$F_{\mathrm{0.5-79}}$$\simeq$$1.2\times10^{-10}~\flux$). Furthermore, we assume $f_{\mathrm{ang}}$$=$1, $k_{\mathrm{A}}$$=$1, and $\eta$$=$0.1. We then obtain $B$$\gtrsim$$4\times10^{8}$~G for \source. This is a factor of a few higher than typical estimates for neutron stars in LMXBs, although within the maximum allowable range determined in a recent analysis of the coherent timing properties of several millisecond X-ray pulsars \citep[][]{mukherjee2015}. \subsection{A propeller-driven outflow?}\label{subsec:outflow} If the accretion disk in \source\ is indeed truncated {\it and} this is due to the magnetic field of the neutron star, the rotating magnetosphere may act as a propeller \citep[e.g.][]{illarionov1975,lovelace1999,romanova2009,papitto2015_prop}. Magnetohydrodynamic simulations show that an active propellor can cause a two-component outflow consisting of an axial jet and a conical wind \citep[e.g.][]{romanova2009}. The wind component has a high density, outflow velocity of $\simeq$0.03$c$--0.1$c$, and is shaped like a thin conical shell with a half-opening angle of $\simeq$30$\degr$--40$\degr$. The jet component has a lower density and a higher outflow velocity ($\simeq$0.4$c$--0.6$c$). If the blue-shifted absorption in our \chan\ data is real, a line-of-sight velocity of $\simeq$0.01$c$ could potentially be consistent with a wind driven by an active propeller. Interestingly, a small subgroup of neutron star LMXBs that appear to exhibit propeller stages, the transitional millisecond radio pulsars \citep[e.g.][]{archibald2009,papitto2014,papitto2015_prop}, seem to have more luminous radio jets than other neutron star LMXBs \citep[][]{deller2014}. If a propeller is operating in \source, it may thus be expected to exhibit a strong radio jet too. We note that even if the magnetic field is truncating the inner accretion disk, it is not necessary that a propeller is operating. Another possibility is a ``trapped disk'' morphology \citep[e.g.][]{dangelo2010,dangelo2012}. In the propellor scenario, strong outflows are formed and little matter accretes on to the neutron star so that the accretion flow may dominate the overall X-ray luminosity. For a trapped disk, however, only a weak outflow is expected and considerable amounts of gas can still accrete on to the neutron star magnetic poles, which may dominate the overall X-ray luminosity. \subsection{Estimates of the neutron star spin period}\label{subsec:spin} If the blue-shifted absorption in our \chan\ data is real {\it and} due to a propeller-driven outflow, the assumption that the inner accretion disk is truncated at the magnetospheric boundary allows to put some constraints on the neutron star spin period. A neutron star is thought to be in the propellor regime when the magnetospheric radius is larger than the co-rotation radius. At this radius the Keplerian orbital velocity of the matter equals the rotational velocity of the neutron star, i.e. $R_\mathrm{co}$$=$$(GMP_{\mathrm{s}}^2/4\pi^2)^{1/3}$, where $P_{\mathrm{s}}$ is the spin period of the neutron star. Assuming that the inner disk radius is truncated by the magnetosphere, i.e. $R_\mathrm{m}$$=$$R_\mathrm{in}$$\gtrsim$$100~\gmc$ ($\simeq$225~km), the requirement that $R_\mathrm{m}$$>$$R_\mathrm{co}$ suggests that \source\ is in the propellor regime if $P_{\mathrm{s}}$$\lesssim$19~ms. We seem to detect thermal emission from the stellar surface in our X-ray spectra and two thermonuclear X-ray bursts have been detected from \source\ \citep[][]{degenaar2013_igrj1706,iwakiri2015,negoro2015_igrj1706}. This implies that at least some matter must be able to accrete on to the neutron star. The accretion disk must therefore lie within the light cylinder radius, where the rotational velocity of the magnetic field lines reaches the speed of light, i.e. $R_\mathrm{lc}$$=$$c/\Omega$ with $\Omega$$=$$2\pi/P_{\mathrm{s}}$ being the angular velocity. If $R_\mathrm{in}$$\gtrsim$$100~\gmc$ ($\simeq$225~km), this would suggest that $P_{\mathrm{s}}$$\gtrsim$4.7~ms. If the accretion disk is truncated by the magnetic field and a propellor operates, that would require $P_{\mathrm{s}}$$\simeq$4.7--19~ms for \source. This is within the typical range of spin periods measured for neutron stars LMXBs from coherent X-ray pulsations or burst oscillations \citep[1.6--10~ms; e.g.][for a list]{patruno2010}. \subsection{Low-energy narrow X-ray emission lines}\label{subsec:emission} Binning the \chan/HETG data reveals an emission feature near 1~keV. A broad line around the same energy was detected in the \swift/XRT data obtained during the energetic X-ray burst of \source\ in 2012 \citep[$E_{\mathrm{l}}$$=$$1.018\pm 0.004$~keV, and EW$=105 \pm 3$~eV;][]{degenaar2013_igrj1706}. It was interpreted as Fe-L or Ne \textsc{x} emission arising from irradiation of relatively cold gas orbiting at a distance of $\simeq$$10^{3}$~km ($\simeq$$500~\gmc$) from the neutron star (by assuming that the line was rotationally-broadened by gas moving in Keplerian orbits). Broad emission lines near 1 keV have been detected in the accretion spectra of a number of other neutron star LMXBs \citep[e.g.][]{vrtilek1991,kuulkers1997,diaztrigo2006,cackett2010_iron,papitto2013_hete}. Exploiting the high spectral resolution of the HETG, we found that in \source\ the emission feature near 1~keV ($\simeq$12~\AA) may be resolved into a number of narrow lines. Narrow emission lines also appear to be present at other energies (e.g. near 9 and 10~\AA; $\simeq$1.38 and 1.24~keV). High-resolution observations of some other neutron star LMXBs revealed complexes of narrow emission lines at low energies, typically consistent with being at rest \citep[e.g.][]{cottam2001_exo,cottam2001,schulz2001,beri2015}. Proposed explanations include a pulsar-driven disk wind or photo-ionized emission from a thickened structure in the accretion disk (e.g. the impact point where the gas stream from the companion hits the outer accretion disk). In case of \source, the strongest narrow emission line is located at $\simeq$11.6~\AA\ ($\simeq$1.07~keV). If real, it could correspond to Fe-L at rest. This would render a collisionally-ionized plasma more likely; photo-ionized gas lines from lower-Z elements (e.g. O, Ne) should be stronger than Fe-L, which doesn't seem to be the case for our data. Perhaps shocks resulting from the accretion flow running into the magnetosphere or from matter impacting the magnetic poles could give rise to collisionally-ionized emission in this neutron star LMXB. Alternatively, this line could correspond to Ne\,{\sc x} blue-shifted by $\simeq$0.045$c$ ($\simeq$$13.5\times10^{3}~\kms$), which would be indicative of an outflow. A third, perhaps more likely, possibility is that the emission lines are due to reflection. However, a single reflection component that also fits the Fe-K line seems to leave excess emission near 1~keV. This could indicate that there are multiple reflection zones, or that different emission mechanisms are responsible for the different lines. | 16 | 9 | 1609.04816 |
1609 | 1609.06352_arXiv.txt | We present a technique for increasing the internal quality factor of kinetic inductance detectors (KIDs) by nulling ambient magnetic fields with a properly applied magnetic field. The KIDs used in this study are made from thin-film aluminum, they are mounted inside a light-tight package made from bulk aluminum, and they are operated near 150~mK. Since the thin-film aluminum has a slightly elevated critical temperature ($T_\critical = \SI{1.4}{K}$), it therefore transitions before the package ($T_\critical = \SI{1.2}{K}$), which also serves as a magnetic shield. On cooldown, ambient magnetic fields as small as approximately \SI{30}{\micro T} can produce vortices in the thin-film aluminum as it transitions because the bulk aluminum package has not yet transitioned and therefore is not yet shielding. These vortices become trapped inside the aluminum package below \SI{1.2}{K} and ultimately produce low internal quality factors in the thin-film superconducting resonators. We show that by controlling the strength of the magnetic field present when the thin film transitions, we can control the internal quality factor of the resonators. We also compare the noise performance with and without vortices present, and find no evidence for excess noise beyond the increase in amplifier noise, which is expected with increasing loss. | 16 | 9 | 1609.06352 |
||
1609 | 1609.08179_arXiv.txt | We use bootstrapping to estimate the bias of concentration estimates on N-body dark matter halos as a function of particle number. We find that algorithms based on the maximum radial velocity and radial particle binning tend to overestimate the concentration by $15\%-20\%$ for halos sampled with $200$ particles and by $7\%$-$10\%$ for halos sampled with $500$ particles. To control this bias at low particle numbers we propose a new algorithm that estimates halo concentrations based on the integrated mass profile. The method uses the full particle information without any binning, making it reliable in cases when low numerical resolution becomes a limitation for other methods. This method reduces the bias to $< 3\%$ for halos sampled with $200$-$500$ particles. The velocity and density methods have to use halos with at least $\sim 4000$ particles in order to keep the biases down to the same low level. We also show that the mass-concentration relationship could be shallower than expected once the biases of the different concentration measurements are taken into account. These results show that bootstrapping and the concentration estimates based on the integrated mass profile are valuable tools to probe the internal structure of dark matter halos in numerical simulations. | \label{sec:introduction} In the current structure formation paradigm the properties of galaxies are coupled to the evolution of their dark matter (DM) hosting halo. In this paradigm the sizes and dynamics of galaxies are driven by the halo internal DM distribution. The internal DM distribution in a halo is usually parameterized through the density profile. In a first approximation this profile is spherically symmetric; the density only depends on the radial coordinate. One of the most popular radial parameterizations is the Navarro-Frenk-White (NFW) profile \citep{NFW}. This profile can be considered as universal \citep{Navarro2010}, assuming that one is not interested in the very central region where galaxy formation takes place, and where the effects of baryon physics on the DM distribution are still unknown. This profile is a double power law in radius, where the transition break happens at the so-called scale radius, $r_s$. The ratio between the scale radius and the halo virial radius $R_v$ is known as the concentration $c=R_v/r_s$. The concentration of the NFW profile provides a conceptual framework to study simulated DM halos as a function of redshift and cosmological parameters. Numerical studies \citep{Neto2007,Maccio2008,Duffy2008,Munoz2011,Prada2012,Ludlow2014,Ludlow2016,Klypin2016} summarized their results through the mass-concentration relationship; that is, the distribution of concentration values at a fixed halo mass and redshift. The success of such numerical experiments rests on a reliable algorithm to estimate the concentration. Such an algorithm should provide unbiased results and must be robust when applied at varying numerical resolution. There are two established algorithms to estimate the concentration parameter. The first method takes the halo particles and bins them into logarithmic radii to estimate the density in each bin, then it proceeds to fit the density as a function of the radius. A second method uses an analytic property of the NFW profile that relates the maximum of the ratio of the circular velocity to the virial velocity, $V_{\rm circ}$/$V_{\rm vir}$. The concentration can be then found as the root of an algebraic equation dependent on this maximum value. The first method is straightforward to apply but presents two disadvantages. First, it requires a large number of particles in order to have a proper density estimate in each bin. This makes the method robust only for halos with at least $10^2$ particles. The second problem is that there is not a way to estimate the optimal radial bin size, different choices may produce different results for the concentration. The second method solves the two problems mentioned above. It works with low particle numbers and does not involve data binning. However, it effectively takes into account only a single data point and discards the rest of the data. Small fluctuations on the maximum can yield large perturbations on the estimated concentration parameter. In this letter we use bootstrapping to estimate the bias and standard deviation on the concentration estimates as a function of particle number. We show that the two standard methods to estimate concentrations have increasing biases for decreasing particle numbers. This motivates us to present a third alternative based on fitting the integrated mass profile. This approach has two advantages with respect to the above mentioned methods. It does not involve any data binning and does not throw away data points. This translates into a robust estimate even at low resolution/particle numbers. Furthermore, since the method does not require any binning, there is no need to tune numerical parameters. This is a new independent method to estimate the concentration parameter. | \label{sec:conclusions} In this letter we used bootstrapping to quantify the biases on concentration estimates. We found that methods commonly used in the literature can overestimate the concentrations by factors of $15\%$-$20\%$ for halos with $200$ particles, or $7\%$-$10\%$ for halos with $500$ particles. This procedure provides a robust technique to quantify the bias in concentration estimates with the advantage that it works without having to run new simulations. These results motivated us to introduce a new method based on the integrated mass profile that show a robust performance at low particle numbers. The new algorithm showed a bias of $< 3\%$ for halos with $200$ particles and less than $1\%$ for halos with $500$ particles or more. To keep the bias of the velocity and density methods below $2\%$ only halos with at least $\sim 4000$ particles should be considered. The three methods are in broad agreement, within the statistical uncertainties, concerning their estimates of the mass-concentration relationship. Some noticeable differences include a $15\%$ systematically higher concentrations in the density method compared to the velocity method. This systematic offset has been reported before with the same dataset \citep{Prada2012} and with different simulations \citep{Klypin2016} without any conclusive explanation for its origin. Another difference is that the velocity and integrated mass methods start to differ for masses below $10^{12}\hMsun$ ($\sim 4000$ particles). We found that correcting the mean concentration by the mean bias factor found through bootstrapping brings these two techniques into agreement. These results show that using the integrated mass profile to estimate the DM halo concentrations is a tool deserving deeper scrutiny. Further tests with larger simulated volumes, varying numerical resolution, higher redshifts, stacked data and different density profiles are the next natural step to explore the full potential of this new method. \vspace{0.1cm} We acknowledge financial support from Uniandes and Estrategia de Sostenibilidad 2014-2015 Universidad de Antioquia. We thank Tom\'as Verdugo, Stefan Gottloeber and Nelson Padilla for their feedback. We thank the anonymous referees for comments that improved the presentation of these results. | 16 | 9 | 1609.08179 |
1609 | 1609.01091_arXiv.txt | Stationary features are occasionally observed in AGN jets. A notable example is the HST-1 knot in M87. Such features are commonly interpreted as re-confinement shocks in hydrodynamic jets or focusing nozzles in Poynting jets. In this paper we compute the structure and Lorentz factor of a highly magnetized jet confined by external pressure having a profile that flattens abruptly at some radius. We find the development of strong oscillations upon transition from the steeper to the flatter pressure profile medium. Analytic formula is derived for the location of the nodes of these oscillations. We apply the model to the M87 jet and show that if the jet remains magnetically dominated up to sub-kpc scales, then focusing is expected. The location of the HST-1 knot can be reconciled with recent measurements of the pressure profile around the Bondi radius if the jet luminosity satisfies $L_j\simeq10^{43}$ erg/s. However, we find that magnetic domination at the collimation break implies a Lorentz factor in excess of $10^2$, atypical to FRI sources. A much lower value of the asymptotic Lorentz factor would require substantial loading close to the black hole. In that case HST-1 may be associated with a collimation nozzle of a hydrodynamic flow. | HST-1 is a stationary radio feature associated with the sub-kpc scale jet in M87 (Biretta et al. 1999). The knot is located at a projected distance of 60 pc (0.86$\arcsec$) from the central engine, and is known to be a region of violent activity. Subfeatures moving away from the main knot of the HST-1 complex at superluminal speeds have been detected (Biretta et al. 1999; Cheung et al. 2007, Giroletti et al. 2012), indicating that a highly relativistic flow is passing through this region. Moreover, the reported variability of the resolved X-ray and optical emission from HST-1 implies that the (beaming corrected) size of the emission region is much smaller than the distance between the HST-1 knot and the central black hole (e.g., Cheung et al. 2007), suggesting a strong focusing of the flow at this location. Stationary radio features, similar to HST-1, are quite common in radio loud AGNs (e.g., Coehn, et al. 2014) and may have the same origin. It has been proposed that the stationary knot in the HST-1 complex is associated with a recollimation shock that forms either, due to a change in the gradient of the external pressure (Stawarz et al. 2006; Bromberg \& Levinson 2009, hereafter ST06 and BL09), or by hoop stresses of a subrelativistic, magnetized wind surrounding the spine, as in the two-component MHD model of Garcia et al. (2009; see also Nakamura et al. 2010). The recollimation shock scenario is further supported by the sudden change in the collimation profile observed at the location of HST-1 (Nakamura \& Asada 2013). In this picture, the rapid variability of the HST-1 emission and the ejection of superluminal subknots from the HST-1 complex are associated with internal shocks produced by self-reflection of the converging flow at the axis, just downstream of the recollimation nozzle (Bogovalov \& Tsinganos 2005; Levinson \& Bromberg 2008; Nakamura et al. 2010, 2014). \begin{figure*} \includegraphics[width=14.5cm]{fig1.pdf} \caption{\label{f1} Jet profile (lef panel) and Lorentz factor (right panel) computed using a confining pressure of the form ${\cal P}_{ext} = A\, z^{-2}$ at $z<z_{tr}$ and ${\cal P}_{ext} = (A/z_{tr})\, z^{-1}$ at $z>z_{tr}$, for $z_{tr}=10^4$ (solid line) and $z_{tr}=5\times10^4$ (dashed line).} \end{figure*} A question of interest is whether the M87 jet is highly or weakly magnetized at the recollimation nozzle. ST06 considered a hydrodynamic jet, and proposed that HST-1 reflects the location at which the reconfinement shock reaches the jet axis. They did not attempt to reproduce the entire collimation profile, but merely to demonstrate that convergence of the shock occurs under the conditions inferred from observations. BL09 have shown that strong focusing of a hydrodynamic jet at the reflection point is anticipated if the plasma behind the oblique shock cools rapidly. Both, ST06 and BL09 attribute the location of the nozzle to a change in the external pressure profile. In the two-component MHD model (Bogovalov \& Tsinganos 2005, Garcia et al. 2009), on the other hand, the focusing of the jet is not related to the properties of the ambient medium, but rather to the dynamics of a magnetized spine-sheath structure. This model can reproduce the entire collimation profile upon appropriate choice of model parameters. However, it requires the existence of an extended MHD disk wind with a regular magnetic field which, in our view, is highly questionable. The observed collimation profile within the Bondi radius can also be reproduced if the inner, Poynting jet, is confined by a hydrodynamic (weakly magnetized) disk wind (Globus \& Levinson 2016, hereafter GL16). Whether it can also account for the change in structure across the Bondi radius is one of the issues addressed in this paper. A highly magnetized jet is expected to undergo strong oscillations when encountering a medium with a flat pressure profile, $p_{ext}(z)\propto z^{-\kappa}$, $\kappa<2$ (Lyubarsky 2009, Komissarov et al. 2015, Mizuno et al. 2015). These oscillations occur in cases where the jet is not in its equilibrium state when encountering the confining medium (Lyubarsky 2009), and can be ascribed to a standing magnetosonic wave. In reality, substantial focusing of the jet should lead to a rapid growth of current-driven internal kink modes, and the subsequent dissipation of the magnetic field (Bromberg \& Tchekhovskoy 2016, Singh et al. 2016). Thus, focusing of a Poynting jet can, in principle, produce stationary jet features with observational imprints similar to those observed in M87 and other AGNs. In this paper we address the following question: can HST-1 in M87 be produced by the focusing of a Poynting-flux dominated jet in a way that satifies all observational constraints? And if so, what are the implications for jet dynamics? | A Poynting-flux dominated jet undergoes strong focusing upon encountering a confining medium with a flat pressure profile, $p_{ext}\propto z^{-\kappa}$, $\kappa<2$. At the focusing nozzle, rapid growth of internal kink modes, followed by dissipation of the magnetic field is anticipated (Bromberg \& Tchekhovskoy 2016, Singh et al. 2016). This can lead to the appearance of stationary emission features, as occasionally seen in radio loud AGNs. In case of M87 we find that the entire collimation profile can be reproduced if the confining pressure profile changes from approximately $p_{ext}\propto z^{-2}$ to the profile observed on scales $0.1$-$10$ kpc, $p_{ext}\propto z^{-0.7}$. The location of the HST-1 knot can be reconciled with the measured pressure provided that the jet power on those scales is $L_j\simeq 10^{43}$ erg/s. This value is significantly lower than the power of the large scale jet estimated from various observations (Bicknell \& Begelman 1996; de Gasperin et al. 2012), but is consistent with values obtained in recent GRMHD simulations (Moscibrodzka et al. 2016). As pointed out in the later reference, the jet power may be intermittent on timescales much shorter than the age of the system, roughly 30 Myr, and so it is conceivable that it is currently in a low state, well below the average power estimated on large scales. It is also found that if the jet remains magnetically dominated up to the focusing nozzle, here associated with the stationary feature in the HST-1 complex, then its Lorentz factor should be in excess of several hundreds. Such a high Lorentz factor is atypical to FRI sources, as inferred from statistics of superluminal motions (e.g., Kellermann et al. 2007). A much lower value of the asymptotic Lorentz factor would require substantial loading close to the black hole. We do not expect significant alteration of the collimation profile of the loaded jet, but the nature of HST-1 may be different. The relative proximity of HST-1 to the black hole implies that the confining pressure around the Bondi radius, that produces the collimation break, is unlikely to be supported by the cocoon produced by the relativistic jet, as hinted by Tchekhovskoy \& Bromberg (2016). Whether the interaction of disk winds with the ambient medium can account for the observed pressure profile on those scales remains to be investigated. If the jet is indeed collimated by disk winds, as proposed recently (GL16), then one naively anticipates strong shocks to form by virtue of the interaction of the disk wind with the flat density galaxy core. \\ We thank Masanori Nakamura for enlightening discussions and useful comments. AL acknowledges the support of The Israel Science Foundation (grant 1277/13). NG acknowledges the support of the I-CORE Program of the Planning and Budgeting Committee and The Israel Science Foundation (grant 1829/12) and the Israel Space Agency (grant 3-10417). \appendix | 16 | 9 | 1609.01091 |
1609 | 1609.06487_arXiv.txt | {The source \object{\1702} (Ara X-1) is a low-mass X-ray binary system hosting a neutron star. Albeit the source is quite bright ($\sim10^ {37}$ erg s$^{-1}$) its broadband spectrum has never been studied. Neither dips nor eclipses have been observed in the light curve suggesting that its inclination angle is smaller than 60$^{\circ}$. } {We analysed the broadband spectrum of \1702 in the 0.3-60 keV energy range, using {\it XMM-Newton} and {\it INTEGRAL} data, to constrain its Compton reflection component if it is present. } {After excluding the three time intervals in which three type-I X-ray bursts occurred, we fitted the joint XMM-Newton and INTEGRAL spectra obtained from simultaneous observations.} { A broad emission line at 6.7 keV and two absorption edges at 0.87 and 8.82 keV were detected. We found that a self-consistent reflection model fits the 0.3-60 keV spectrum well. The broadband continuum is composed of an emission component originating from the inner region of the accretion disc, a Comptonised direct emission coming from a corona with an electron temperature of $2.63 \pm 0.06$ keV and an optical depth $\tau=13.6 \pm 0.2$, and, finally, a reflection component. The best-fit indicates that the broad emission line and the absorption edge at 8.82 keV, both associated with the presence of \ion{Fe}{xxv} ions, are produced by reflection in the region above the disc with a ionisation parameter of Log$(\xi) \simeq 2.7$. We have inferred that the inner radius, where the broad emission line originates, is $64^{+52}_{-15}$ km, and the inner radius of the accretion disc is $39^{+6}_{-8}$ km. The emissivity of the reflection component and the inclination angle of the system are $r^{-3.2^{+0.5}_{-5.1}}$ and $44^{+33}_{-6}$ degrees, respectively. The absorption edge at 0.87 keV is associated to the presence of \ion{O}{viii} ions and it is produced in a region above the disc with Log$(\xi) \simeq 1.9$}. {} | Low-mass X-ray binaries (LMXBs) usually show discrete features such as emission lines and absorption edges. The most prominent feature is an emission line at 6.4-6.97 keV, usually interpreted as a fluorescence line from iron at different ionisation states. In fact, iron is a relatively abundant element with the highest fluorescence yield among the most abundant atomic species. These features are powerful tools to investigate the structure of the accretion flow close to the central source; in particular, important information can be obtained from the detailed spectroscopy of the line profile, since it is determined by the ionisation state, geometry, and velocity field of the reprocessing plasma \citep[see][for a review]{cackett_2010}. These emission lines are usually broad with Gaussian $\sigma$ from 0.3 up to more than 1 keV. This broadness is incompatible with a simple thermal broadening caused by the plasma temperature, because of the large mass of iron atoms. It has been interpreted as being caused by Compton broadening in a Comptonising medium of moderate temperatures and optical depth \citep[see e.g.][]{ng_10} or Compton scattering caused by strong outflowing winds illuminated by the radiation from the innermost part of the system \citep{tita_09}. Similarities were found between the accretion flows and the overall spectral shapes in LMXBs hosting neutron stars (NSs) and black holes (BHs). In both systems, an accretion disc surrounds a Comptonising corona located around the compact objects. This has led to the conclusion that in both LMXB systems, these emission lines may be produced by reflection of the primary continuum over the inner accretion disc. In this scenario, the line profile is shaped by Doppler and relativistic effects caused by the fast (Keplerian) motion of the plasma in the inner regions of the accretion disc. As a consequence, the line shows a characteristic broad and asymmetric (red-skewed) profile, the detailed shape of which depends on the inclination of the system with respect to the line of sight, and on how deep the accretion disc extends into the NS gravitational potential \citep[see][]{fabian_89,matt_92}. If the origin of this line is from disc reprocessing, one would also expect the presence in the spectra of other discrete features (such as emission lines and absorption edges from the other abundant elements) and an excess of emission (Compton hump) caused by direct Compton scattering of the primary spectrum by the electrons in the disc. Indeed, broad emission lines from Silicon, Argon, and Calcium have been detected together with iron features in the spectra of bright NS LMXBs (such as 4U 1705-44, e.g. \citealt{disalvo_09}; GX 349+2, \citealt{iaria_09}; GX340+0, \citealt{dai_09}; GX 3+1, \citealt{piraino} and \citealt{pintore_15}), and in some cases, a broadened absorption edge at $8-8.5$ keV was also required. The ionisation states of these elements were compatible with similar values of the ionisation parameter $\xi$, and the ratios of the widths of these features with respect to the corresponding energy were compatible with being constant for each source, implying that all these features were produced in the same disc region. The Compton hump at 20-40 keV has also been detected in the hard spectral state of these sources with high statistical significance \citep[see e.g.][]{disalvo_15,miller_13,degenaar_15,piraino_16}, in combination with the presence of the iron line, and both these features have been modelled with self-consistent reflection models. The reflection model is able to simultaneously fit all these features (broad emission lines and absorption edges as well as the Compton hump) and is therefore the most promising explanation for their origin \citep[see e.g.][]{disalvo_15,dai_10,reis_09,cackett_2010}. The X-ray source 4U 1702-429 (Ara X-1) is a NS LMXB showing type-I X-ray bursts. The source was detected as a burster with \textit{OSO 8} \citep{swank_76}, whilst the persistent X-ray emission was detected by \cite{lewin_79}. \cite{Oo_91} classified 4U 1702-429 as an atoll source using EXOSAT data. Using Chandra HRC-I data, \cite{wachter_05} gave the accurate position of the X-ray source with an associated error of $0\arcsec\!.6$. \cite{galloway_08}, analysing the photospheric radius expansion during the observed type-I X-ray bursts, inferred a distance to the source of $4.19 \pm 0.15$ kpc and $5.46 \pm 0.19$ kpc for a pure hydrogen and pure helium companion star, respectively. Furthermore, these authors suggested that the companion star should have a mass fraction of hydrogen lower than 50\%. \cite{mark_99}, using the data of the proportional counter array (PCA) onboard the {\it Rossi-XTE} (RXTE) satellite, detected burst oscillations at 330 Hz that could be associated with the spin frequency of the NS. Up to now a few works reported the analysis of the persistent spectrum of 4U 1702-429. \cite{Cristian_97} analysed three observations taken by the {\it Einstein} satellite combining the data of the solid-state spectrometer (SSS; 0.5-4.5 keV) and of the monitor proportional counter (MPC; 1.2-20 keV). The authors fitted the spectrum of the source with an absorbed cut-off power-law obtaining an equivalent hydrogen column density $N_H$ of the interstellar medium between $1.1 \times 10^{22}$ and $1.7 \times 10^{22}$ cm$^{-2}$. The photon-index spanned the range between 1.3 and 1.5, and the cut-off temperature between 8 and 16 keV. \cite{mark_99} analysed three observations of 4U 1702-429 taken with RXTE/PCA. These authors fitted the persistent spectrum with a cut-off power-law inferring a cut-off-temperature between 3.5 and 4.6 keV. \begin{figure*} \centering \includegraphics[width=8.5cm]{f1a.eps}\hspace{0.3truecm} \includegraphics[width=8.5cm]{f1b.eps}\\ \includegraphics[width=8.5cm]{f1c.eps}\hspace{0.3truecm} \includegraphics[width=8.5cm]{f1d.eps} \caption{Top-left panel: EPIC-pn light curve of \1702 with a bin time of 1 s. Three type-I X-ray bursts occur during the observation: between 2860 and 2980 s, 20780 and 20900 s, and 36150 and 36300 s from the start time. Top-right panel: 0.3-10 keV EPIC-pn persistent light curve. The bin time is 100 s. Bottom-left panel: 0.3-2 keV EPIC-pn persistent light curve (upper panel), 2-10 keV EPIC-pn persistent light curve (middle panel) and the corresponding HR (lower panel). The bin time is 100 s. Bottom-right panel: HR vs. intensity (bin time of 400 s). } \label{pn_light} \end{figure*} In this work we show the spectral analysis of the persistent spectrum of 4U 1702-429 in the 0.3-60 keV energy range using both {\it XMM-Newton} and {\it INTEGRAL} observations. | In this work, we have shown the first broadband spectral analysis of the persistent spectrum of \1702 in the 0.3-60 keV energy range. We detect the presence of a prominent feature close to 6.7 keV and two absorption edges at 0.87 and 8.83 keV, respectively. The emission line at 6.7 keV is associated with the fluorescence emission of \ion{Fe}{xxv} ions and it can be modelled using a Gaussian component with $\sigma=0.46$ keV and an equivalent width of 36 eV. Alternatively, it can be described by a relativistic smeared line caused by Compton reflection originating from the inner disc. We have fitted the spectrum with a self-consistent model composed of a multicoloured disc black-body component plus a Comptonisation component and a reflection component. We find that the inclination angle of the system is $44^{\circ}\!$, the inner radius of the accretion disc is $39^{+6}_{-8}$ km, and its inner temperature is 0.34 keV. The inner radius of the reflecting region, where the \ion{Fe}{xxv} smeared relativistic line and the \ion{Fe}{xxv} absorption edge are produced, is $64^{+52}_{-15}$ km, and the corresponding ionisation parameter is Log$(\xi)=2.69$. The ionisation parameter of the reflecting region where the absorption edge associated with \ion{O}{viii} ions originates is Log$(\xi) \sim 1.9$. The electron temperature of the Comptonised component is 2.6 keV and the corresponding optical depth is $\tau \sim 13.6$. From the best-fit value of the equivalent hydrogen column density of the interstellar medium ($N_H \sim 2.5 \times 10^{22}$ cm$^{-2}$), we have estimated the infrared extinction $A_{K_{s}} = 0.70 \pm 0.06$ mag and inferred a distance to the source of $5.4^{+1.6}_{-1.1}$ kpc. This value is compatible with a previous estimation obtained from the analysis of the photospheric radius expansion of the type-I X-ray bursts observed for \1702. | 16 | 9 | 1609.06487 |
1609 | 1609.03577_arXiv.txt | With the steadily improving sensitivity afforded by current and future galaxy surveys, a robust extraction of two-point correlation function measurements may become increasingly hampered by the presence of astrophysical foregrounds or observational systematics. The concept of mode projection has been introduced as a means to remove contaminants for which it is possible to construct a spatial map reflecting the expected signal contribution. Owing to its computational efficiency compared to minimum-variance methods, the sub-optimal \pcl (PCL) power spectrum estimator is a popular tool for the analysis of high-resolution data sets. Here, we integrate mode projection into the framework of PCL power spectrum estimation. In contrast to results obtained with optimal estimators, we show that the uncorrected projection of template maps leads to biased power spectra. Based on analytical calculations, we find exact closed-form expressions for the expectation value of the bias and demonstrate that they can be recast in a form that allows a numerically efficient evaluation, preserving the favorable \order{\lmax^3} time complexity of PCL estimator algorithms. Using simulated data sets, we assess the scaling of the bias with various analysis parameters and demonstrate that it can be reliably removed. We conclude that in combination with mode projection, PCL estimators allow for a fast and robust computation of power spectra in the presence of systematic effects -- properties in high demand for the analysis of ongoing and future large scale structure surveys. | \label{sec:intro} In modern cosmology, measurements of the power spectrum (or its real-space counterpart, the angular correlation function) have proven a powerful summary statistic and are widely used to confront theoretical models with observational data, e.g., \citet{1992ApJ...396L...1S, 1994Natur.367..333H, 1995ApJ...443L..57G, 1997ApJ...474...47N, 2000ApJ...545L...5H, 2002ApJ...568...38H, 2002Natur.420..772K, 2003ApJS..148..135H, 2010ApJ...722.1148F, 2010ApJ...719.1045L, 2014A&A...571A..15P, 2014ApJ...794..171T, 2015PhRvL.114j1301B} for an arbitrary selection of measurements of the cosmic microwave background radiation (CMB) two-point correlation function, or, e.g., \citet{1969PASJ...21..221T, 1996MNRAS.283..709H, 2001MNRAS.328...64N, 2002MNRAS.329L..37B, 2002ApJ...571..172Z, 2004ApJ...606..702T, 2005MNRAS.356..415C, 2005ApJ...633..560E, 2008ApJ...672..153C, 2010MNRAS.404...60R, 2011MNRAS.416.3017B, 2014MNRAS.438..825K, 2016MNRAS.455.4301C} for constraints on galaxy clustering. A decrease in statistical errors resulting from the increasing coverage or sensitivity of ongoing and future experiments will impose stricter limits on the level of contamination of the targeted cosmological signal by secondary sources. Such contaminants may be of astrophysical origin (e.g., foreground emission or dust extinction, e.g., \citealt{2005ApJ...619..147M}) or the result of complications associated with the data collection and processing procedure (for example, survey depth fluctuations, varying seeing conditions, image calibration uncertainties, \citealt{2013MNRAS.432.2945H, 2016ApJ...829...50A}). To aid assessment of the possible impact of systematic effects that may have altered the observed signal, it has become standard for galaxy surveys to compile libraries of template maps that describe the spatial variation of survey properties \citep{2002ApJ...579...48S, 2011MNRAS.417.1350R, 2012MNRAS.424..564R, 2014MNRAS.444....2L, 2016ApJS..226...24L, 2016arXiv160703145R}. Several approaches have been proposed that make use of these maps to correct measurements of the two-point statistics for systematic effects (\citealt{1992ApJ...398..169R, 2012ApJ...761...14H, 2014MNRAS.444....2L}, see \citealt{2016MNRAS.456.2095E} for a comparison). In \citet{2016MNRAS.463..467K}, the authors derive a template cleaning procedure for the popular FKP estimator \citep{1994ApJ...426...23F}. In the following, we focus on the mode projection procedure of \citet{1992ApJ...398..169R}. Attributing infinite variance to modes described by a set of templates, specific signal patterns can be excluded from the analysis and the computed result hence becomes more robust with respect to systematics captured by them \citep[see, e.g.,][for applications]{1998ApJ...499..555T, 2004PhRvD..69l3003S, 2009JCAP...09..006S, 2013A&A...549A.111E, 2013MNRAS.435.1857L}. Unfortunately, mode projection can only be straightforwardly implemented in case the estimator makes use of inverse variance-weighted data. Within the field of power spectrum estimation, this is the case for the maximum likelihood estimator \citep{1998PhRvD..57.2117B} and the optimal quadratic estimator \citep{1997PhRvD..55.5895T}. Regrettably, both of them are very expensive to evaluate numerically, usually prohibitively so for state-of-the-art high-resolution data \citep{1999PhRvD..59b7302B}. Conversely, the much faster \pcl (PCL) estimator introduced by \citet{2002ApJ...567....2H} makes no attempt at exact inverse variance-weighting, trading optimality for computational speed, and can be applied in only \order{\lmax^3} time to a data set band-limited at multipole moment \lmax. The purpose of this paper is to demonstrate that the concept of mode projection can be successfully integrated into the framework of PCL estimators, combining the desirable properties of fast and robust power spectrum estimation. This article is organized as follows. In \sect{sec:theory}, we review the concept of mode projection and discuss how it can be implemented in PCL estimators. Then, we use numerical simulations to verify our results and systematically study the impact of mode projection for different analysis parameters (\sect{sec:verify}). We conclude by summarizing our findings in \sect{sec:conclusions}. | \label{sec:conclusions} In modern cosmology, two-point correlation function measurements play a fundamental role in constraining theoretical models with observational data. In practical application, however, extracting statistical information about cosmological signals is often hampered by the presence of contaminants. As a consequence, a number of strategies have been developed to mitigate their impact on the scientific analysis. Here, we focus on mode projection, an algorithm that allows one to marginalize over templates constructed to describe the spatial patterns of possible systematic effects \citep{1992ApJ...398..169R}. While it can be straightforwardly implemented into optimal methods, the application to the popular \pcl (PCL) estimator, so far, has remained elusive. In this paper, we have developed a framework to integrate mode projection into PCL estimation algorithms. We have shown that a naive projection of templates in general leads to biased power spectrum estimates. Based on a rigorous mathematical treatment, we then derived exact closed-form equations for the estimator bias. Recasting the analytical expressions allowed us to compute them efficiently, thereby preserving the overall \order{\lmax^3} time complexity of PCL algorithms. Applied to a large number of simulations with various input parameters, we have systematically studied the impact of mode projection on PCL power spectrum estimates. We identified a nontrivial dependence of the cleaning procedure on the shape of signal and template power spectra. We further studied the scaling of the bias with the band limit of the maps, number of templates projected, and sky fraction available to the analysis, and discussed the impact of mode projection on the covariance properties of the power spectrum estimates. In all cases, we found a good agreement between the bias observed in simulations and our analytical prediction. We conclude that the framework presented here allows for a reliable correction of power spectrum estimates to obtain unbiased results. Possible future extensions of the algorithm include the generalization to spin-2 fields to allow more robust measurements of, for example, the cosmic shear signal \citep[e.g.,][]{2000MNRAS.318..625B, 2000astro.ph..3338K, 2000Natur.405..143W, 2012ApJ...761...15L, 2013MNRAS.430.2200K, 2015MNRAS.454.3500K, 2016PhRvD..94b2002B}, or the CMB polarization power spectrum \citep[e.g.,][]{2002Natur.420..772K, 2014PhRvL.112x1101B, 2014JCAP...10..007N, 2014ApJ...794..171T, 2016A&A...594A..11P}. Effective strategies for systematics mitigation are instrumental to fully exploring the information content of ongoing and future large scale structure surveys like the Sloan Digital Sky Survey \citep{2000AJ....120.1579Y}, the Dark Energy Survey \citep{2013AAS...22133501F}, or observations planned with the Dark Energy Spectroscopic Instrument \citep{2013arXiv1308.0847L}, or the Large Synoptic Survey Telescope \citep{2009arXiv0912.0201L}. The results of our studies indicate that the combination of mode projection and \pcl power spectrum estimation offers an attractive means to robustly measure the two-point correlation function in the presence of contaminants, an important milestone on the way to reliable clustering estimates. | 16 | 9 | 1609.03577 |
1609 | 1609.05092_arXiv.txt | Since the L$\alpha$ rocket observations of (Gabriel, {\it Solar Phys.} {\bf 21}, 392, 1971), it has been realized that the hydrogen (H) lines could be observed in the corona and offer an interesting diagnostic for the temperature, density, and radial velocity of the coronal plasma. Moreover, various space missions have been proposed to measure the coronal magnetic and velocity fields through polarimetry in H lines. A necessary condition for such measurements is to benefit from a sufficient signal-to-noise ratio. The aim of this article is to evaluate the emission in three representative lines of H for three different coronal structures. The computations have been performed with a full non-local thermodynamic-equilibrium (non-LTE) code and its simplified version without radiative transfer. Since all collisionnal and radiative quantities (including incident ionizing and exciting radiation) are taken into account, the ionization is treated exactly. Profiles are presented at two heights (1.05 and 1.9 solar radii, from Sun center) in the corona, and the integrated intensities are computed at heights up to five solar radii. We compare our results with previous computations and observations ({\it e.g.} L$\alpha$ from UVCS) and find a rough (model-dependent) agreement. Since the H$\alpha$ line is a possible candidate for ground-based polarimetry, we show that in order to detect its emission in various coronal structures, it is necessary to use a very narrow (less than 2~\AA~wide) bandpass filter. | It came as a surprise to discover that a hot and diluted medium such as the corona was emitting the ``cool'' L$\alpha$ line \citep{1971SoPh...21..392G}. Since this rocket observation (eclipse), many more L$\alpha$ observations have been performed ({\it e.g.} \citet{1994ESASP.373..363H} and \citet{1995SSRv...72...29K} by the \textit{Ultraviolet Coronal Spectrometer} (UVCS) on board \textit{Spartan}, and later on by the \textit{Ultraviolet Coronal Spectrometer} (UVCS) on board the \textit{Solar and Heliospheric Observatory} (SOHO) (\citet{1999A&A...342..592Z} and \citet{1999SSRv...87..265M})) with the help of a coronagraph. The emission was quickly identified as the resonance scattering of the chromospheric L$\alpha$ radiation by ``trace'' neutral hydrogen (usually taken as about $10^{-6}$ electron density). Because L$\alpha$ is the strong resonance line of the most abundant element (hydrogen) and because the emitted chromospheric profile is about as wide as the absorption profile of coronal neutral hydrogen, in the absence of velocity field, the emission is rather strong (about $10^{-6}$ the disk value at 1.5 R$_{\odot}$) and even stronger (a few $10^{-5}$) in a streamer \citep[\textit{e.g.}][]{1999ESASP.448.1193M}. This is why a major future mission, {\it Solar Orbiter}, includes the L$\alpha$ coronograph called \textit{Multi Element Telescope for Imaging and Spectroscopy} (METIS) \citep{2012SPIE.8443E..09A}. Moreover, it has been shown as early as 1982 \citep{1982SoPh...78..157B} that the line was sensitive to the Hanle effect (generally effective in weak magnetic fields). Consequently, many (space) projects have proposed polarimetric measurements in this line ({\it e.g.} the \textit{Small Explorer for Solar Eruptions} (SMESE) mission \citep{2007AdSpR..40.1787V} and more recently the \textit{Coronal UV spectro-polarimeter} (CUSP) on board the \textit{Solar magnetism eXplorer} (SolmeX) \citep{2012ExA....33..271P}, the \textit{MAGnetic Imaging Coronagraph} (MAGIC) on board the \textit{INvestigation of Solar-Terrestrial Activity aNd Transients} (INSTANT) mission (Lavraud {\it{et al.}} (2015), proposal to ESA), the \textit{MAGnetic Imaging Coronagraph} (MAGIC) on board the \textit{Magnetic Activity of the Solar Corona} (MASC) mission (Auch\`ere {\it{et al.}} (2015), proposal to ESA). It has also been proposed to use the L$\beta$ line for performing polarimetric measurements in the faint corona \citep{2012ExA....33..271P}.\\ However, until now, these projects are still at the proposal level for various reasons including the (relative) complexity of the instrumentation and the fact that polarimetry is ``photon-hungry'' and requires large apertures in the ultra-violet (UV). Apart from radio observations above active regions, another path towards coronal polarimetry has been pursued with ground-based infrared (IR) observations measuring the Zeeman effect \citep{2000ApJ...541L..83L,2008SoPh..247..411T}.\\ Another possibility has been opened with eclipse polarization measurements in red and green channels by \citet{2013Ge&Ae..53..901K} from which these authors concluded that ``the polarization excess (green-red) can be explained by the presence of neutral hydrogen in the corona'' \citep[see also][]{2014A&A...567A...9D}. As mentioned by \citet{2013Ge&Ae..53..901K}, \citet{1976ApJ...209..927P} and \citet{2011A&A...530L...1M} had already concluded that H$\alpha$ contributed to coronagraphic images of transients and coronal mass ejections (CMEs), respectively. Actually this was demonstrated with eclipse measurements made at the Canada-France-Hawa\"{\i} Telescope (CFHT) in 1991 where \citet{1992ESASP.344...87V} detected a plasmoid in the solar corona that \citet{1994A&A...281..249K} interpreted as emitting essentially in the H$\alpha$ line, a claim discussed later on by \citet{2000A&A...353..786Z} who proposed an upper limit of the emission of about 2 \% of the background corona. Moreover, the Hanle effect has been successfully used in the H$\alpha$ line, in spite of its optical thickness, in magnetic-field measurements in prominences \citep[\textit{e.g.}][]{1981SoPh...71..285L,1981A&A...100..231B}.\\ In order to derive the plasma properties (including magnetic field) it is imperative to take into account all processes involved and first of all the proper ionization degree. The aim of this work is to compute most observable parameters (line profile, intensity) for the main H lines exactly emitted by (three) typical regions of the solar corona and at various heights above the limb. \\ In Section \ref{section2}, we present the full non-LTE computations derived from 1D non-LTE codes which are adapted to the geometry of the corona. In Section \ref{section3}, we focus on profiles obtained in the L$\alpha$, L$\beta$ and H$\alpha$ lines at various heights. In Section \ref{comparaison_Ly_obs}, we also compare with other computational and observational results in the L$\alpha$ and L$\beta$ lines. In Section \ref{section4}, we provide the variation with altitude of the ionization degree for the three models. In Section \ref{section5}, we discuss all our results, and we pay some attention to the possibility of observing the H$\alpha$ line in the corona. In Section \ref{section6}, we conclude on further improvements in the computations. \\ We also present in the Appendix an approximation to obtain the H$\alpha$ intensity from the (measured) L$\alpha$ emission. \\ | \label{section5} Let us note that since we have a five-level atom, we actually treat more transitions [L$\gamma$, H$\beta$, P$\alpha$, H$\gamma$, P$\beta$, H$\delta$, H$\epsilon$] than the three presented above. Half-profiles and integrated intensities of all these lines are available on the \textit{Multi Experiment Data and Operation Center} (MEDOC) site \\ \textsf{https://idoc.ias.u-psud.fr/MEDOC/Radiative transfer codes/PROMCOR}\\ We now raise the issue of the visibility of the hydrogen lines in the corona and in particular the polarimetry, since, as mentioned in many proposals and road maps \citep[see, {\it e.g.},][]{2015AdSpR..55.2745S} the measurement of the coronal magnetic field, is now a major objective in solar physics.\\ First, as shown in Section 4, we are not surprised as far as the L$\alpha$ line is concerned since the UVCS measurements (Figure \ref{fig8}) at a distance as low as 1.5 R$_{\odot}$ are close to our computations for our streamer model (see Figure \ref{fig5-2}). The L$\alpha$ variation of Figure \ref{fig5-2} shows that at 2.5 R$_{\odot}$ (1.5 R$_{\odot}$ above the surface) the L$\alpha$ intensity is about $1.4\times 10^{-5}$ the disk intensity. This altitude is the maximum altitude where linear polarization measurements can provide useful information about the coronal magnetic field through the Hanle effect \citep{2010A&A...511A...7D}. This value seems to be compatible with the scattering performances of the proposed instrumentation \citep[\textit{e.g.}][]{2007AdSpR..40.1787V}. However, it is clear that the coronal intensity is about a magnitude lower in a quiet corona and still lower in coronal holes (Figure \ref{fig5-1}) which means that measurements will be challenging at those locations.\\ Second, as for L$\beta$, in our streamer model the intensity variation with distance compares relatively well to the results of \citet{2006A&A...455..719L} in terms of number of photons. According to \citet{2013JGRA..118..967G}, the L$\beta$ intensity is 0.03 erg~s$^{-1}$cm$^{-2}$sr$^{-1}$ at 1.9 R$_{\odot}$ where we find 0.09 (note that the L$\alpha$ values are closer: 8 for our computations and 6.4 for \citet{2013JGRA..118..967G} at 1.9 R$_{\odot}$). The ratio L$\beta$/L$\alpha$ is about $10^{-3}$ as in \citet{2006A&A...455..719L} at 3 R$_{\odot}$ but it is about $10^{-1}$ instead of $10^{-2}$ in \citet{2006A&A...455..719L} for 1 R$_{\odot}$. With the quiet-Sun (Allen) model, the L$\beta$/L$\alpha$ ratio is lower than $10^{-1}$ at 1 R$_{\odot}$ and $2\times 10^{-3}$ at 2.5 R$_{\odot}$, which means that polarization measurements in the L$\beta$ line \citep{2012ExA....33..271P} will face serious difficulties because of the low signal-to-noise ratio. \\ Third, as far as the H$\alpha$ intensity is concerned, Figures \ref{fig5-1} and \ref{fig5-2} provide a useful information on the proper line emission (lower than the L$\beta$ line by a factor eight). But in order to evaluate the feasibility of H$\alpha$ measurements in the corona and even possibly polarimetric ones, one definitely needs to take into account the continuum (Thomson) absorption and scattering. From Figures \ref{fig6-1}, \ref{fig6-2} and \ref{fig6-3}, one can compute the variation of the integrated intensity with the width of the integration band (or bandpass). \\ At 1.05 R$_{\odot}$, over a 2~\AA~bandpass, we find 8.6 erg~s$^{-1}$cm$^{-2}$sr$^{-1}$ for the streamer model and 0.16 erg~s$^{-1}$cm$^{-2}$sr$^{-1}$ at 1.9 R$_{\odot}$. For the quiet Sun, the values are still much lower (1.3 and 0.02 erg~s$^{-1}$cm$^{-2}$sr$^{-1}$, respectively, see Table \ref{tab1}). \\ Although these values are very low, the contrast of intensities between the streamer and the equatorial quiet-Sun is of the order of seven. This means that with the technique of background subtraction currently used in coronagraphic data, it is possible to access H$\alpha$ in the coronal extension of active regions, provided that the bandpass is equal or less than 2~\AA. \\ As far as coronal holes are concerned, the H$\alpha$ intensity (slightly dependent on the temperature) is 0.8 at 1.05 R$_{\odot}$ and $3.7\times 10^{-3}$ erg~s$^{-1}$cm$^{-2}$sr$^{-1}$ at 1.9 R$_{\odot}$. The contrast of the H$\alpha$ coronal hole (ratio to the quiet Sun) is 0.6 at 1.05 R$_{\odot}$ and 0.19 at 1.9 R$_{\odot}$. These numbers will actually be higher because of the LOS contamination; this leaves a small hope for detection in H$\alpha$ of out-of-the limb coronal holes.\\ The possibility of performing polarimetric measurements in H$\alpha$ has been discussed by \citet{2013SoPh..288..651K} who included the effect of instrumental stray light. Our computations show that the H$\alpha$ polarimetry in the corona could be envisaged above active regions with an instrumentation with a large aperture. However, the complexity of the line and its separation between polarizable and non-polarizable states (Dubau, 2015, private communication) make the interpretation complex, as noted by \citet{2012ApJ...749..136L} for the chromosphere. \\ Finally the H$_\alpha$ results are summarized in Table \ref{tab1}. \\ \begin{table}[H] \begin{tabular}{lllllll} \hline Band- & Quiet & Quiet & Coronal & Coronal & Streamer & Streamer \\ pass & Sun & Sun & hole & hole & & \\ \AA & 1.05R$_{\odot}$ & 1.9R$_{\odot}$ & 1.05R$_{\odot}$ & 1.9R$_{\odot}$ & 1.05R$_{\odot}$ & 1.9R$_{\odot}$ \\ \hline 1 & $3.97~10^{-1}$ & $6.7~10^{-3}$ & $2.31~10^{-1}$ & $1.06~10^{-3}$ & 2.91 & $4.72~10^{-2}$ \\ 1.5 & $7.87~10^{-1}$ & $1.37~10^{-2}$ & $4.61~10^{-1}$ & $2.19~10^{-3}$ & 5.43 & $9.65~10^{-2}$ \\ 2 & 1.29 & $2.3~10^{-2}$ & $7.60~10^{-1}$ & $3.67~10^{-3}$ & 8.57 & $1.61~10^{-1}$ \\ 3 & 2.42 & $4.4~10^{-2}$ & 1.43 & $7.01~10^{-3}$ & 15.5 & $3.07~10^{-1}$ \\ 4 & 3.61 & $6.65~10^{-2}$ & 2.14 & $1.06~10^{-2}$ & 22.7 & $4.63~10^{-1}$ \\ 5 & 4.86 & $9.03~10^{-2}$ & 2.89 & $1.44~10^{-2}$ & 30.1 & $6.27~10^{-1}$ \\ \hline \end{tabular} \caption{Integrated intensity [erg~s$^{-1}$cm$^{-2}$sr$^{-1}$] of the H$\alpha$ line as a function of the bandpass~\AA,~for the quiet-Sun, coronal-hole, and streamer models at positions 1.05 and 1.9 R$_{\odot}$ of the LOS.}\label{tab1} \end{table} | 16 | 9 | 1609.05092 |
1609 | 1609.09275_arXiv.txt | {We apply the new constraints from atom-interferometry searches for screening mechanisms to the symmetron model, finding that these experiments exclude a previously unexplored region of parameter space. We discuss the possibility of networks of domain walls forming in the vacuum chamber, and how this could be used to discriminate between models of screening.} \begin{document} | Theories of dark energy that introduce new, light scalar fields coupled to matter have inspired the study of screening mechanisms to explain why the associated fifth forces have not yet been detected \cite{Joyce:2014kja,Clifton:2011jh}. Screening mechanisms allow the scalar field theory to have non-trivial self-interactions, and so the properties of the scalar, and the resulting fifth force, can vary with the environment. Whilst screening mechanisms were introduced in order to explain the absence of an observation of a fifth force to date, that does not mean that such fifth forces are intrinsically unobservable. Experimental searches need only to be carefully designed to take advantage of the non-linear screening behaviour. Given a background field profile, the self interactions of the screened scalar field can have three possible consequences on the properties of scalar fluctuations on top of that background \cite{Joyce:2014kja}: \begin{enumerate} \item The mass of the fluctuations becomes dependent on the background. If the field becomes heavy in dense environments and light in diffuse ones, this can explain why the scalar force would not be detected around the macroscopic dense sources used in current fifth force experiments. This is known as the chameleon mechanism after the archetypal chameleon model \cite{Khoury:2003rn,Khoury:2003aq}. \item The strength of the coupling to matter becomes dependent on the background. If the field becomes weakly coupled in experimental environments it is clear that it will be harder to detect. Examples of models that employ this mechanism include the symmetron \cite{Hinterbichler:2010es,Hinterbichler:2011ca} and density dependent dilaton \cite{Damour:1994zq,Brax:2010gi}. \item The coefficient of the scalar kinetic term becomes dependent on the background. If the coefficient becomes large in experimental searches it becomes difficult for the scalar to propagate, and so the force is suppressed. This effect occurs in any model which has gradient self interactions, including Galileon \cite{Nicolis:2008in} and k-essence models \cite{Babichev:2009ee,Brax:2012jr,Burrage:2014uwa}, and is called the Vainshtein mechanism \cite{Vainshtein:1972sx}. \end{enumerate} It has recently been demonstrated that atomic nuclei inside a high quality vacuum chamber are very sensitive probes of chameleon screening, this is because the nucleus is so small that the screening cannot work efficiently. Forces on individual atoms can now be measured to a very high precision using atom interferometry, and as a result new constraints on chameleon models have been derived. Further improvements to these experiments are cureently underway. It remains to be determined whether the power of atom interferometry can be extended to constrain theories which screen through other means. Vainshtein screening will not be accessible, because the gradient self-interactions mean that the screening takes place over much longer distance scales than are achievable in a terrestrial laboratory. In contrast, however, theories which screen by varying their coupling constant with the environment are phenomenologically similar to chameleon models, and so it is expected that atom interferometry could also provide useful constraints. In this work we will focus on the symmetron model, as an example of a theory which screens by varying its coupling constant. This model is chosen because it has been shown that the model can be constructed in such a way that it is radiatively stable and quantum corrections remain under control \cite{Burrage:2016xzz}. Earlier work studied a similar model but with a different motivation~\cite{Pietroni:2005pv,Olive:2007aj}, and string-inspired models with similar phenomenology have also been proposed~\cite{Damour:1994zq,Brax:2011ja}. In Section \ref{sec:symm} we will review the symmetron model, and how the force between two extended objects can be screened. In Section \ref{sec:atom} we apply the results of existing atom interferometry experiments to find new constraints on the symmetron model which are presented in Figure \ref{fig:constraints}. In Section \ref{sec:domain} we discuss the possibility that domain walls could form inside the vacuum chamber, leading to the possibility that atoms could experience a symmetron force, even in the absence of a source inside the vacuum chamber. We conclude in Section \ref{sec:conclusions}. | \label{sec:conclusions} We have shown that symmetron fifth forces, inspired by theories of dark energy, can be constrained by terrestrial experiments using cold atoms. The constraints we have found in Figure \ref{fig:constraints}, are particularly interesting as they fill a previously empty region of parameter space between the constraints coming from E\"{o}t-Wash experiments, and those coming from observations of exo-planets. We have also discussed the possibility that symmetron domain walls may form in the vacuum chamber, leading to the atoms experiencing a fifth force without the need to place a source mass inside the vacuum chamber. Whilst we find that the accelerations experienced by the atoms are smaller than the sensitivity of current experiments, they are not so small that it would be impossible to detect them in the future. Additionally, as the domain walls only form for symmetron models, if a screened fifth force is ever detected in a terrestrial experiment the presence or absence of these domain walls would provide a way to discriminate between different models of screening. \subsection*{} In the final stages of writing this article it has come to our attention that Brax and Davis have derived the same constraints on the symmetron model using the tomographic model of screening \cite{A&P}. | 16 | 9 | 1609.09275 |
1609 | 1609.07742_arXiv.txt | Most viable models of Type Ia supernovae (SN~Ia) require the thermonuclear explosion of a carbon/oxygen white dwarf that has evolved in a binary system. Rotation could be an important aspect of any model for SN~Ia, whether single or double degenerate, with the white dwarf mass at, below, or above the Chandrasekhar limit. {\sl Differential rotation} is specifically invoked in attempts to account for the apparent excess mass in the super--Chandrasekhar events. Some earlier work has suggested that only uniform rotation is consistent with the expected mechanisms of angular momentum transport in white dwarfs, while others have found pronounced differential rotation. We show that if the baroclinic instability is active in degenerate matter and the effects of magnetic fields are neglected, both nearly-uniform and strongly-differential rotation are possible. We classify rotation regimes in terms of the Richardson number, Ri. At small values of Ri $\leq$ 0.1, we find both the low-viscosity Zahn regime with a non-monotonic angular velocity profile and a new differential rotation regime for which the viscosity is high and scales linearly with the shear, $\sigma$. Employment of Kelvin-Helmholtz viscosity alone yields differential rotation. Large values of Ri $\gg$ 1 produce a regime of nearly-uniform rotation for which the baroclinic viscosity is of intermediate value and scales as $\sigma^3$. We discuss the gap in understanding of the behavior at intermediate values of Ri and how observations may constrain the rotation regimes attained by nature. | \label{intro} Although the basic explosion mechanism of supernovae of Type Ia (henceforth SN~Ia) has been established to be the thermonuclear combustion of degenerate C/O white dwarfs (henceforth WD), many aspects of the progenitor systems of remain to be understood. Nearly all viable progenitor models involve mass transfer in binary systems (Howell 2011; Wang \& Han 2102; Maoz, Mannucci \& Nelemans 2014; but see Chiosi et al. 2014). One idea is the initiation of carbon ignition as the mass approaches the classical Chandrasekhar limit of stability, $\MCh \approx 1.44\Msun$, for non--rotating WDs by means of accretion in a binary system. This classic model is most closely associated with mass transfer from a non--degenerate companion, the single--degenerate (SD) scenario. Variations on this theme allow for explosions with less than \MCh\ when accretion of helium from a companion leads to the accumulation of an explosive degenerate layer of helium on top of the C/O core that generates compression waves that can trigger a central carbon detonation (Fink et al. 2010; Woosley \& Kasen 2011; Shen \& Moore 2014). This might occur by accretion from a non--degenerate companion, or from a degenerate companion in one variety of the double--degenerate (DD) scenario. Other DD models involve the tidal disruption of one WD, thus adding mass to the other, resulting in explosion (Dan et al. 2014), or the violent merger or collision of two WDs (Pakmor et al. 2012; Kushnir et al. 2013). The DD scenarios typically invoke WDs with mass less than \MCh, but the total mass might exceed this amount. Other scenarios manifested in either the SD or DD context involve spinning up a WD until it is rotationally supported, with a mass exceeding \MCh, the explosion being postponed until sufficient angular momentum is lost from the star. These are loosely called {\sl spin--up/spin--down} models (Yoon \& Langer 2005; Di Stefano et al. 2011; Justham 2011; Tornambe \& Piersante 2013). In these models, the central density rises to the point of carbon ignition because angular momentum is lost, not because mass is gained. Yet another variation invokes the merger of a WD with a stellar core in the context of common--envelope evolution (Livio \& Riess 2003; Ilkov \& Soker 2013). In the violent merger models, the explosion occurs so quickly that an issue of the quasi--static rotational state of the WD does not arise, but in most models the physical context requires the accumulation of mass and angular momentum, and hence that the WD should rotate. The rotational state is ignored in many models of the progenitor evolution and explosion, including many computationally--demanding multi--dimensional models; however, it is obvious that, in the absence of a specific mechanism to lose angular momentum, it must accumulate. A generic question that persists throughout the various SN~Ia progenitor models is how the internal rotation profile of the accreting WD influences the essential dynamical and secular processes that operate in SN~Ia progenitor environments. One basic influence of the internal rotation has been known now for four to five decades, \viz, that (a) uniform rotation can increase the maximum mass of stable WDs above the Chandra limit by only about 3 to 4 percent, and (b) differential rotation can increase this maximum mass substantially, exceeding the Chandra limit by factors of up to $\sim 2-3$, and so resulting in maximum WD masses up to $\sim (3-4)\Msun$ (see Ostriker \& Bodenheimer 1968 and references therein). We shall henceforth refer to \MCh\ as the ``Chandra limit,'' and WDs with masses above this limit as ``Super--Chandra.'' Most typical SN~Ia are consistent with explosion at \MCh\ (but see Scalzo et al. 2014). Polarization observations suggest that most typical SN~Ia may not rotate significantly, but that subluminous events (SN~1991bg--like) may do so (Patat et al. 2012). Observations of some very bright SN~Ia have led to inferred values of the ejecta mass and hence the mass of the pre--SN WD in the range (2.1 -- 2.8) \Msun. Examples are SN~2003fg, SN~2006gz, SN~2007if, SN~2009dc \citep{howetal,hicketal,yametal,scaletal,silveretal,taubetal}. These masses are much in excess of \MCh, and possible implications for the internal rotation of the pre--SN WD have been widely discussed. In this context, one may ask what evolutionary pathway would lead to a WD in a slowly--rotating state, and so in a slightly Super--Chandra condition, as opposed to a pathway that would lead to a rapidly and differentially rotating WD in a substantially Super--Chandra condition. If the WD rotates rapidly, then issues also arise about the onset of bar--mode instabilities that might affect the onset of the explosion and the subsequent dynamics. In this paper, we focus on clarifying the origins of the different regimes of internal rotation that can exist inside accreting WDs. We consider WDs without strong, permanent magnetic fields. Accordingly, all angular-momentum transport processes considered here are necessarily described by viscosities generated only by non--magnetic mechanisms, \eg, hydrodynamic mechanisms such as Kelvin--Helmholtz and baroclinic instabilities, and secular mechanisms such as the Zahn instability (Zahn 1992). We formulate these viscosities with the aid of well--known prescriptions given in the literature. We thus describe angular-momentum transport inside accreting WDs in terms of the standard angular--momentum transport equation applied in a background WD model, which is pre-specified (\S \ref{elltransport}, \S \ref{angmomtransport}). We apply boundary conditions at the WD surface to describe the deposition of angular momentum by accreting matter. For low--viscosity (Zahn) transport (\S \ref{rothydro}), we recover the differential rotation profile found earlier \citep{sainom}. For high--viscosity transport, which includes viscosities due to both Kelvin-Helmholtz and baroclinic instabilities, we find both (a) the nearly-uniform rotation profile found earlier \citep{sainom,piro}, and, (b) a new, differential rotation profile, which is qualitatively similar to the inner parts of the differential rotation profile found earlier for viscosity due to Kelvin-Helmholtz instability alone \citep{yl04}, but different in detail. All of the above regimes of rotation appear to be self-consistent, corresponding to different viscosities and different regimes of operation in terms of the Richardson number. All regimes described have profiles of specific angular momentum (henceforth $\ell$--profile) that increase monotonically outward, as they must to be Rayleigh--stable, but the profile of the angular velocity, $\Omega$, (henceforth the $\Omega$--profile) can have a maximum inside the WD, from which it decreases both outward to the surface and inward to the center. A general and comparative discussion of these rotation profiles are given in \S \ref{rotzahn}, \S \ref{rotyl} and \S \ref{discussregime}. A discussion, our conclusions and the prospects for future work are given \S \ref{discuss}. | \label{discuss} We have attempted to clarify the nature of the different regimes of internal rotation that can exist inside accreting WDs. We consider WDs without strong, permanent magnetic fields and hence consider angular-momentum transport processes described by viscosities generated by hydrodynamic mechanisms such as Kelvin--Helmholtz and baroclinic instabilities, and secular mechanisms such as the Zahn instability. We formulated these viscosities with the aid of prescriptions given in the literature. We elucidate that the BC viscosity as adopted here implies two asymptotic regimes depending on the Richardson number, Ri. The BC viscosity, \viscBC, scales as ${\rm Ri}^{-1/2} \propto \sigma$ in the regime of small Ri. This yields a regime of high viscosity that nevertheless corresponds to differential rotation, a solution presented here for the first time. The BC viscosity scales as ${\rm Ri}^{-3/2} \propto \sigma^3$ in the regime of large Ri, yielding an intermediate level of viscosity and solid-body rotation. We thus classify the collection of rotation regimes explored here in terms of the Richardson number, Ri, in the following way. At small values of Ri $\lta$ 0.1, we have both the low-viscosity Zahn regime and the new, high-viscosity regime found in this work. Near the critical value of Ri $\approx$ 1/4, we have the inner, intermediate-viscosity region of the YL regime, its outer, low-viscosity region being at a higher value of Ri. Employment of KH viscosity alone yields differential rotation. Finally, at large values of Ri $\gg$ 1, we have the intermediate-viscosity nearly-uniform rotation regime. The two regimes of the BC viscosity correspond to a viscosity that scales with the shear as $\sigma$ in the small Ri regime and as $\sigma^3$ in the large Ri regime (\S\ref{BCI}). This implies, in turn, that the viscous stress, $\tau = \nu \sigma$, scales with the shear as $\sigma^2$ in the small Ri regime, but as $\sigma^4$ in the large Ri regime. The form of nonlinearity is a power-law with an index $n>1$, $n$ being 2 in the small Ri regime, and 4 in the large Ri regime. It is interesting to consider what the situation would be in a more complete theory of BC viscosity. Instead of the knowledge of \viscBC\ only in the two limits ${\rm Ri} < {\rm Ri}_{\rm BC}$ and ${\rm Ri} \gg {\rm Ri}_{\rm BC}$, we would then have a complete prescription over the whole range of Ri, which would reduce to the above limits appropriately. The non-linearity in the viscous stress will change from a power-law with $n=2$ to one with $n=4$ as Ri increases, and the rotation regime will change from a strongly differential to nearly-uniform. Accordingly, the two limiting regimes will have a \emph{transition region} between them, as illustrated schematically in Figure \ref{Ri_nu}. An insight that is particularly useful for our problem in the regimes of power-law viscosities is available from the literature on the p-Laplacian nonlinear diffusion equation \citep{KaVa,lpv,B-V,AkMa}, whose form, $\partial u/\partial t = {\bf\nabla}\cdot (\vert{\bf\nabla} u\vert^{p-2}{\bf\nabla} u)$, is very similar to that of Equation (\ref{transport2}) in the limit where viscous transport dominates over advective transport, as is the case for the large hydrodynamic viscosities. This similarity becomes clear if the advective term in Equation (\ref{transport2}) is neglected and the equation is rewritten back in terms of the angular velocity $\Omega$ to read $\partial\Omega/\partial t = (1/\rho r^4) (\partial/\partial r)(\rho r^4\nu(\partial\Omega/\partial r))$. The power-law index $n$ for the viscous stress $\nu \sigma$ is related to the index $p$ by $n=p-1$, so that that the two asymptotic regimes correspond to $p=3$ and $p=5$, respectively. The non-trivial asymptotic solution of the p-Laplacian PDE for a \emph{given} value of $p$ can be shown to be unique, but the solutions for \emph{different} values of $p$ are quite different \citep{KaVa,lpv}. This is consistent with the two viscosity regimes found here. The implication is that when $p$ changes from one value to another through the transition region, the solution will undergo a corresponding transition. The specific issue of the behavior of the BC viscosity at such intermediate $p$- or $n$-values (or, equivalently, the corresponding values of Ri) are beyond the scope of this paper, but of definite interest. There has been discussion in the literature about the applicability of BCI in the electron-degenerate matter inside WDs since completely degenerate matter is barotropic, pressure is only a function of density and their gradients cannot be skew to one another (Kippenhahn \& M\"olenhoff 1974; Tassoul 1984; Yoon \& Langer 2004). Realistic WDs have finite temperature so the issue of baroclinicity is a quantitative one. The key point is that buoyancy may become very small in degenerate matter, with consequences for Ri and other parameters of the problem, in which case the standard BCI formulation, including the Fujimoto prescription, may not apply. A first-principles reformulation of the problem may be necessary. While our immediate goal in this work has been to better understand the physics that drives the differential rotation regimes of accreting white dwarfs, our larger, long--term goal is to elucidate the progenitor evolution of SN~Ia. Currently viable models of SN~Ia involve either accretion onto a WD from a non--degenerate star (the SD scenario), from a degenerate companion (the DD scenario), or the violent impact of two degenerate stars (Maoz, Mannucci \& Nelemans 2014). All these possibilities demand that the WD progenitor of the SN~Ia be rotating. It is an interesting task to use the physics of angular momentum transport described here to elucidate and guide our understanding of the possible rotation state of the progenitors of SN~Ia. A major challenge remains to determine what rotational states nature accommodates, under what circumstances, and to what effect on the subsequent explosion. The reverse problem, \viz, using observations of SN~Ia to constrain the physics of the progenitor evolution, is equally interesting and perhaps even more challenging. While acknowledging the definite variety among typical SN~Ia, we must recognize that the majority of these events display a remarkable degree of homogeneity. The fact that most SN~Ia are consistent with values of ejecta mass not remarkably different from \MCh\ suggests that most SN~Ia cannot be in a regime of strong differential rotation, neither that of low Ri we have presented here nor in the regime propounded by Yoon \& Langer (2004). Thus, it is important to understand the conditions that prevent regimes of differential rotation from occurring in common circumstances. The answer cannot be so simple as saying that the viscosity, even magnetic viscosity, is large, because we have shown here that there can be differential rotation in a high-viscosity regime. Likewise, some SN~Ia fall in the Super-Chandrasekhar regime that would seem to demand differential rotation, implying that the nearly solid-body rotation solutions of Saio \& Nomoto (2004) and of Piro (2008) do not pertain. If many SN~Ia involve sub-Chandra masses, as suggested by Scalzo et al. (2014) and others, then the state of rotation is currently unconstrained. The nature of internal rotational profiles in all these circumstances requires deeper understanding. | 16 | 9 | 1609.07742 |
1609 | 1609.07268_arXiv.txt | {The B-W method is used to determine the distance of Cepheids and consists in combining the angular size variations of the star, as derived from infrared surface-brightness relations or interferometry, with its linear size variation, as deduced from visible spectroscopy using the projection factor. The underlying assumption is that the photospheres probed in the infrared and in the visible are located at the same layer in the star whatever the pulsation phase. While many Cepheids have been intensively observed by infrared beam combiners, only a few have been observed in the visible.} {This paper is part of a project to observe Cepheids in the visible with interferometry as a counterpart to infrared observations already in hand.} { Observations of $\delta$~Cep itself were secured with the VEGA/CHARA instrument over the full pulsation cycle of the star.} {These visible interferometric data are consistent in first approximation with a quasi-hydrostatic model of pulsation surrounded by a static circumstellar environment (CSE) with a size of $\theta_\mathrm{CSE}=8.9\pm3.0$ mas and a relative flux contribution of $f_\mathrm{CSE}=0.07\pm0.01$. A model of visible nebula (a background source filling the field of view of the interferometer) with the same relative flux contribution is also consistent with our data at small spatial frequencies. However, in both cases, we find discrepancies in the squared visibilities at high spatial frequencies (maximum 2$\sigma$) with two different regimes over the pulsation cycle of the star, $\phi=0.0-0.8$ and $\phi=0.8-1.0$. We provide several hypotheses to explain these discrepancies, but more observations and theoretical investigations are necessary before a firm conclusion can be drawn.} {For the first time we have been able to detect in the visible domain a resolved structure around $\delta$~Cep. We have also shown that a simple model cannot explain the observations, and more work will be necessary in the future, both on observations and modelling.} | The Baade-Wesselink (BW) method for the distance determination of Cepheids is, in its first version, purely spectro-photometric \citep{lindermann18,baade26, wesselink46}. Results by \citet{fouque07} and \citet{storm11a, storm11b} illustrate the central and current role of this method in the distance scale calibration, even if recent calibrations of the Hubble constant rely exclusively on the trigonometric parallaxes of a few Galactic Cepheids \citep{riess11, benedict07}. The first interferometric version of the BW method was attempted in the visible by \citet{mourard97}, and soon afterward in the infrared by \citet{kervella99, kervella01} and \citet{lane00}. Since then, the infrared interferometric BW method has been applied to a significant number of Cepheids, twelve in total (see Table~\ref{Tab.hra}), while among these stars only four have been observed by visible interferometers, and the pulsation could actually be resolved for only one of them, $\ell$~Car \citep{davis09}. % The principle of the interferometric version of the BW method is simple. Interferometric measurements lead to angular diameter estimations over the whole pulsation period, while the stellar radius variations can be deduced from the integration of the pulsation velocity. The latter is linked to the observational velocity deduced from spectral line profiles by the projection factor $p$ \citep{nardetto04,merand05, nardetto07, nardetto09}. There are several underlying assumptions to the BW method. First, the limb-darkening of the star is assumed to be constant during the pulsation cycle. This has no impact on the interferometric analysis, at least in the infrared \citep{kervella04a}, while in the visible \citet{davis09} reported the need to take into account a limb-darkening variation from Sydney University Stellar Interferometer (SUSI) observations. On the theoretical side, \citet{nardetto06b} found via hydrodynamical simulation that considering a constant limb darkening in the visible leads to a systematic shift of about 0.02 in phase on the angular diameter curve, which basically means that there is no impact on the derived distance (because the amplitude of the angular diameter curve is unchanged). Second, the projection-factor, mostly dominated by the limb-darkening calculated in the visible domain, is also assumed to be constant, which seems reasonable, at least in theory \citep{nardetto04}. Third, when applying the BW method, visible spectroscopy (e.g. \citealt{nardetto06a}) is often combined with infrared interferometric data, or even -- in the recent photometric version of the BW method -- with various photometric bands \citep{breitfelder15}. In the distance determination, we implicitly assume that the angular and linear diameters correspond to the same physical layer in the star. In this context, testing these hypotheses using visible interferometric observations seems to be of prime importance. This can be done first by simply verifying the internal consistency of the BW distances derived from visible and infrared interferometry, and then comparing them with available precise parallaxes \citep{benedict07, majaess12}. This paper is the first in a series which investigates Cepheids with the Visible spEctroGraph and polArimeter (VEGA) beam combiner \citep{mourard09} operating at the focus of the Center for High Angular Resolution Astronomy (CHARA) array \citep{ten05} located at the Mount Wilson Observatory (California, USA). The study focuses on the prototype $\delta$~Cep star. The VEGA data are first reduced (Sect.~\ref{s_vega}) and then analysed in terms of uniform disk angular diameters (Sect.~\ref{s_UD}). In Sect.~\ref{s_CSE}, we show that $\delta$~Cep is clearly surrounded by a resolved structure, while some evidence in our interferometric data point toward an additional physical effect. We explore two hypotheses: a circumstellar reverberation and a strong limb-darkening variation. We draw our conclusions in Sect.~\ref{s_C}. \begin{table*} \caption{\label{Tab.hra} Cepheids for which an interferometric BW method has been applied. For some studies corresponding to the first attempts (indicated by asterisks) the pulsation could not be clearly resolved angularly leading to a mean value of the angular diameter of the Cepheid. In the visible domain, the BW method was applied successfully to only one Cepheid, $\ell$~Car, while in the infrared, among the eleven Cepheids the pulsation could be resolved for all stars, even X~Sgr, which is known to be atypical likely owing to shockwaves travelling within the atmosphere \citep{mathias06}.} \begin{center} \setlength{\doublerulesep}{\arrayrulewidth} \begin{tabular}{ll} \hline \hline Cepheids & reference \\ \hline \multicolumn{2}{c}{visible} \\ $\delta$~Cep$^{\star}$ & \citet{mourard97} \\ $\alpha$~UMi$^{\star}$, $\zeta$~Gem$^{\star}$, $\delta$~Cep$^{\star}$, $\eta$~Aql$^{\star}$ & \citet{nordgren00} \\ $\delta$~Cep$^{\star}$, $\eta$~Aql$^{\star}$ & \citet{armstrong01} \\ $\ell$~Car & \citet{davis09} \\ \hline \multicolumn{2}{c}{H band} \\ $\zeta$~Gem & \citet{lane00} \\ $\zeta$~Gem, $\eta$~Aql & \citet{lane02} \\ $\kappa$~Pav & \citet{breitfelder15} \\ $\ell$~Car & \citet{anderson16} \\ X~Sgr, W~Sgr, $\zeta$~Gem, $\beta$~Dor, $\ell$~Car & \citet{breitfelder16} \\ \hline \multicolumn{2}{c}{K band} \\ $\zeta$~Gem$^{\star}$ & \citet{kervella01} \\ X~Sgr$^{\star}$, $\eta$~Aql, W Sgr, $\zeta$~Gem$^{\star}$, $\beta$~Dor, Y Oph$^{\star}$, $\ell$~Car &\citet{kervella04a} \\ $\delta$~Cep & \citet{merand05} \\ Y Oph & \citet{merand07} \\ FF Aql, T Vul & \citet{gallenne12} \\ $\delta$~Cep, $\eta$~Aql & \citet{merand15} \\ \hline \end{tabular} \end{center} \end{table*} \begin{table*} \caption{\label{Tab.cals} List and properties of calibration stars selected with the {\it SearchCal} software provided by the Jean-Marie Mariotti Center (JMMC) \citep{bonneau06, bonneau11}. T$_\mathrm{eff}$ is the effective temperature, $g$ the gravitation acceleration, R the magnitude of the calibrator in the Johnson R filter, $\theta_\mathrm{UD}$ the uniform disk angular diameter for the R filter of the Johnson photometric system. These parameters were adopted from \citet{lafrasse10} for all calibrators, except HD~195725 (C3) for which we used the SearchCal tool itself. C1 and C2 were used in this study to calibrate the $\delta$~Cep VEGA/CHARA data (see Fig.~\ref{Fig.ft}), while C3 to C8 were used to test the robustness of the C1 and C2 calibrators (see Fig.~\ref{Fig.cals}).} \begin{center} \begin{tabular}{lcccccc} \hline \hline Calibrator HD & number & Spectral type & T$_\mathrm{eff}$ & $\log$ g & R & $\theta_\mathrm{UD}$ (R band) \\ & & & K & [cgs] & & [mas] \\ \hline HD 214734 & C1 & A3IV & 8600 & 4.2 & 5.073 & 0.327 $\pm$ 0.023 \\ HD 213558 & C2 & A1V & 9500 & 4.1 & 3.770 & 0.458 $\pm$ 0.033 \\ \hline HD 195725 & C3 & A7III & 8000 & 3.3 & 4.050 & 0.617 $\pm$ 0.044 \\ HD 182564 & C4 & A2IIIs & 9380 & 3.4 & 4.550 & 0.377 $\pm$ 0.027 \\ HD 211336 & C5 & F0IV & 7300 & 4.3 & 3.920 & 0.714 $\pm$ 0.051 \\ HD 214454 & C6 & A8IV & 7500 & 4.3 & 4.410 & 0.581 $\pm$ 0.042 \\ HD 3360 & C7 & B2IV & 20900 & 3.9 & 3.740 & 0.284 $\pm$ 0.020 \\ HD 192907 & C8 & B9III & 10500 & 3.4 & 4.410 & 0.346 $\pm$ 0.025 \\ \hline \end{tabular} \end{center} \end{table*} | \label{s_C} We observed $\delta$~Cep intensively on twenty nights. The initial purpose of these observations was to apply the BW method, but instead we detected for the very first time a static resolved structure around $\delta$~Cep contributing to about 7\% of the total flux in the visible. This is not totally surprising as envelopes around Cepheids have already been discovered by long-baseline interferometry in the K band with VLTI and CHARA \citep{kervella06a, merand06}. In addition, four Cepheids have also been observed in the N band with VISIR and MIDI \citep{kervella09,gallenne13b} and one with NACO \citep{gallenne11,gallenne12}. Some evidence has also been found using high-resolution spectroscopy \citep{nardetto08b}. From these observations, the typical size of the envelope of Cepheids seems to be around 3 stellar radii and the flux contribution from 2\% to 10\% of the continuum in the K band for medium- and long-period Cepheids, respectively, while it is around 10\% or more in the N band. However, \citet{merand05} do not mention any contribution from a CSE in the case of $\delta$~Cep in their infrared FLUOR data, while \citet{merand06} found an improved agreement with a larger set of data when considering a model with a CSE. They used a ring model $3.54$ mas in size, 0.5 mas in width, and with a relative brightness of 1.5\%, which is confirmed in \citet{merand15}. The processes at work in infrared and in the visible regarding the CSE are different. We expect thermal emission in the infrared and scattering in the visible. It is also worth mentioning that the mid-infrared flux in excess is not necessarily the evidence for mass loss (see e.g. \citealt{schmidt15}) and that the resolved structure we observe around $\delta$~Cep, instead of a CSE, could be simply a visible nebulae (also contributing to 7\% of the total flux), as reported in the infrared by \citet{marengo10} and in the radio domain by \citet{matthews12}. Our second result is the presence of an additional second-order discrepancy between the observations and the models (pulsating disk + CSE or pulsating disk + background) at high spatial frequencies, which is not clearly understood. One possibility could be that the star is lighting up its environment differently at minimum ($\phi \simeq 0.8-1.0$) and maximum ($\phi \simeq 0.0-0.8$) radius. This reverberation effect would then be more important in the visible than in the infrared since the contribution in flux of the CSE (or the background) in the visible band is about 7\% compared to 1.5\% in the infrared. Interestingly, the phase interval from 0.8 to 1.0 is usually disregarded in the infrared surface brightness version of the BW method owing to general poor agreement between spectroscopic and photometric angular diameters \citep{storm11a,storm11b}. The other possibility is to consider a {\it static} environment with a constant brightness in time, but with an additional dynamical effect. However, from the hydrodynamical simulations and observations of Cepheids in eclipsing binary systems, it seems that the limb-darkening effect in the visible band does not vary strongly enough to reproduce the second-order discrepancy found in our interferometric observations. Also possible is a strong compression or shockwave occurring near the photosphere at the minimum radius, which is indeed the layer probed by photometry and interferometry. However, such a shock is not seen in the hydrodynamical code \citep{nardetto04} or in the spectroscopic data, conversely to X~Sgr, an atypical Cepheid in which a shockwave has indeed been reported \citep{mathias06}. Why this dynamical effect is seen in the visible band and not in the infrared is another pending question in this hypothesis. We also exclude non-radial pulsation, since very accurate space photometry does not support the detection of such modes in Galactic classical Cepheids (e.g. \citealt{poretti15}), and the previous spectroscopic campaigns would have shown up quite easily. Furthermore, \citet{anderson15a} found the signature of a companion in recent spectroscopic data of $\delta$~Cep. The expected flux contribution is supposed to be lower than 1\% in the visible, clearly not detectable by VEGA/CHARA. Finally, reverberation seems to be the more plausible hypothesis. More interferometric data on Cepheids in the visible might shed light on it. In particular, covering the spatial frequencies properly ($x$ from 0.2 to 3) at a unique pulsating phase (maximum and minimum radii) is probably required to go further in the analysis. | 16 | 9 | 1609.07268 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.