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1403 | 1403.3401_arXiv.txt | Coy Dark Matter removes the tension between the traditional WIMP paradigm of Dark Matter and the latest exclusion bounds from direct detection experiments. In this paper we present a leptophilic Coy Dark Matter model that, on top of explaining the spatially extended 1-5~GeV $\gamma$-ray excess detected at the Galactic Center, reconciles the measured anomalous magnetic moment of muon with the corresponding Standard Model prediction. The annihilation channel of DM is $\chi\chi \to \tau\bar\tau$ with the DM mass $m_\chi = 9.43\,(^{+.063}_{-0.52}\,{\rm stat.})\,(\pm 1.2 \,{\rm sys.})$~GeV given by best-fit of the $\gamma$-ray excess. Fitting the measured anomalous magnetic moment of the muon requires instead a pseudoscalar mediator with a minimal mass $m_a = 12^{+7}_{-3}$~GeV. | According to the present understanding, the matter content of the Universe is dominated by a very weakly interacting component: the Dark Matter (DM). In the most promising scenarios, DM consists of a thermal relic density of stable and weakly interacting massive particles (WIMPs). In fact, miraculously, particles with masses and annihilation cross sections set by the electroweak scale automatically yield the observed value for DM density, through the freeze-out mechanism (for a review, see~\cite{Jungman:1995df,Bertone:2004pz}). On the experimental side, the WIMP paradigm motivates the efforts aimed to the detection of three types of DM signature: elastic scattering between DM and SM particles, production of DM particles at colliders and annihilation of DM particles in the Universe. In particular, for the latter case, it is essential to search for direct annihilation signals from dense DM regions, as well as studying the implied indirect large scale effects that, for example, would affect CMB. In this regard, the center of our Galactic DM halo at the Galactic Center (GC) should provide the strongest annihilation signal. Unfortunately, GC also harbours an extremely dense environment filled with stars, stellar relics and related cosmic rays, dust and gas. As a consequence the possible annihilation signals can easily be disguised as result of active astrophysical processes. In spite of that, different hints of DM annihilation have been reported in literature in recent years pointing towards the DM annihilation cross sections at the order of the thermal freeze-out one, $\cs_{\rm th}$. In 2008, the PAMELA satellite mission measured an excess of cosmic positrons above the energy of 20~GeV, later confirmed by Fermi LAT and AMS-02 \cite{Adriani:2008zr,Abdo:2009zk,Aguilar:2013qda}. In 2009, instead, the public data of Fermi LAT~\cite{Atwood:2009ez} showed a spatially extended $\gamma$-ray excess at 1-5~GeV at GC~\cite{Goodenough:2009gk,Hooper:2010mq,Abazajian:2010zy,Boyarsky:2010dr,Hooper:2011ti,Abazajian: 2012pn,Gordon:2013vta,Macias:2013vya,Abazajian:2014fta,Daylan:2014rsa,Lacroix:2014eea}. In 2012, a hint of a $\gamma$-ray line(s) at 130~GeV was found \cite{Bringmann:2012vr,Weniger:2012tx,Tempel:2012ey,Su:2012ft}. On the other hand, strong constraints from XENON100 [8] and LUX [9] direct detection experiments recently excluded scattering cross sections near the typical weak-scale value. Hence, with the new exclusion bounds approaching the predicted region, both the above claims and the WIMP paradigm itself have started to tremble. Fortunately, it is still possible to construct rather natural particle physical models that possess an annihilation cross section large enough to explain the detected signal, but, at the same time, present a suppressed DM-nucleon scattering cross section. A minimal and elegant example is provided by the so-called ``Coy Dark Matter'' (CDM), recently proposed by Boehm~et~al~\cite{Boehm:2014hva}. In this model, the DM particle is a Dirac fermion which interacts with the Standard Model (SM) particles by the exchange of a relatively light pseudoscalar mediator. The new couplings to the SM particles are assumed to be proportional to the corresponding Higgs Yukawa couplings, as motivated by minimal flavor violation [42]. Hence, if the mass of the DM particle $\chi$ is below the mass of top quark, the dominant annihilation channel is $\chi\chi \to \bar{b}b$. With the choice $m_\chi \simeq 30$~GeV the spatially extended $\gamma$-ray excess at 1-5~GeV at GC can be fitted for a natural value of the DM annihilation cross section $\sim\cs_{\rm th}$~\cite{Gordon:2013vta,Macias:2013vya,Abazajian:2014fta,Daylan:2014rsa}. Alternatively, the $\chi\chi \to \bar{\tau}\tau$ channel can fit the signal, provided a lower mass for $\chi$ is adopted: $m_\chi \simeq 10$~GeV. In this case the SM Yukawa structure adopted for the SM-pseudoscalar couplings in the CDM model is also to be modified. For instance, a viable model is achieved by assuming leptophilic SM-pseudoscalar couplings, i.e. by maintaining the Yukawa structure only for the SM leptons and by neglecting the coupling of the pseudoscalar mediator to quarks. Intriguingly, a light pseudoscalar coupled to muons, as proposed by CDM, results in a new contribution to the anomalous magnetic moment of this particle, $a_\mu$~\cite{Chang:2000ii}. To this regard, among DM, neutrino masses and baryon asymmetry, the $\sim 3.4\sigma$ deviation of $a_\mu$ from the SM value is a compelling experimental evidence that points to physics beyond SM (for a review see~\cite{Beringer:1900zz} and references therein). In this study, we calculate the anomalous magnetic moment of electron, muon and tau in the framework of CDM, aiming to constrain and fit both the measured value of $a_\mu^{\rm obs}$ and the $\gamma$-ray excess at 1-5~GeV from GC. We will show that the pseudoscalar-muon coupling has to be enhanced by a factor ${\cal O}(100)$ to fit $a_\mu^{\rm obs}$. Within the CDM framework this if forbidden by the studies on the $\Upsilon$ resonance decays, which constrain the pseudoscalar-muon coupling below the required value \cite{Aaltonen:2009rq,Aubert:2009cka,Schmidt-Hoberg:2013hba}. However, this constraint is trivially avoided in case of leptophilic CDM, where the $\chi\chi \to \bar{\tau}\tau$ channel is responsible for fitting the 1-5~GeV $\gamma$-ray excess at GC. We will therefore show that the leptophilic CDM scenario allows to explain $a_\mu^{\rm obs}$, to fit the $\gamma$-ray excess at 1-5~GeV from GC and to avoid the remaining well known constraints. The paper is structured as follows: in Sec. II we calculate the anomalous magnetic moment of muon, electron and tau within the CDM framework. In Sec. III discuss the constraints on CDM from $a_{e,\mu,\tau}$ and the resulting scenario. Finally, in Sec. IV we draw our conclusions. | The CDM model removes the tension between the traditional WIMP paradigm of Dark Matter and the latest exclusion bounds from direct detection experiments~\cite{Boehm:2014hva}. We presented a leptophilic Coy Dark Matter model that, on top of explaining the spatially extended 1-5~GeV $\gamma$-ray excess detected at the Galactic Center, reconciles the measured anomalous magnetic moment of muon. Our results can be summarized as follows. \begin{itemize} \item The $\gamma$-ray excess measured at GC is due to DM annihilation via the $\chi\chi \to \tau\bar\tau$ channel, with the resulting best-fit mass $m_\chi \simeq 10$~GeV. \item Within our model, the measured value of the anomalous magnetic moment of the muon is due to the contribution of a light pseudoscalar mediator with mass $m_a = 12^{+7}_{-3}$~GeV. At this minimal mass, the pseudoscalar-muon coupling must be a factor $\sim 50$ larger than the muon Yukawa coupling. \item The leptophilic Coy Dark Matter scenario (which explains the measured anomalous magnetic moment of the muon) is compatible with the constraints from CMB, dwarf galaxies, solar neutrinos, accelerator and direct detection experiments. The CMB and dwarf galaxy constraints are approaching the predicted best-fit value ${\cs}_{\tau\bar\tau}^{\rm GC}$ and might potentially rule out the model in near future. \end{itemize} ~ | 14 | 3 | 1403.3401 |
1403 | 1403.1297_arXiv.txt | {} {We introduce a new algorithm for the calculation of multidimensional optical depths in approximate radiative transport schemes, equally applicable to neutrinos and photons. Motivated by (but not limited to) neutrino transport in three-dimensional simulations of core-collapse supernovae and neutron star mergers, our method makes no assumptions about the geometry of the matter distribution, apart from expecting optically transparent boundaries.} {Based on local information about opacities, the algorithm figures out an escape route that tends to minimize the optical depth without assuming any pre-defined paths for radiation. Its adaptivity makes it suitable for a variety of astrophysical settings with complicated geometry (e.g., core-collapse supernovae, compact binary mergers, tidal disruptions, star formation, etc.). We implement the MODA algorithm into both a Eulerian hydrodynamics code with a fixed, uniform grid and into an SPH code where we make use a tree structure that is otherwise used for searching neighbours and calculating gravity.} {In a series of numerical experiments, we compare the MODA results with analytically known solutions. We also use snapshots from actual 3D simulations and compare the results of MODA with those obtained with other methods such as the global and local ray-by-ray method. It turns out that MODA achieves excellent accuracy at a moderate computational cost. In an appendix we also discuss implementation details and parallelization strategies.} {} | \label{sec:intro} Recent years have seen an enormous increase in the physical complexity of multi-dimensional, astrophysical simulations. This is particularly true for three-dimensional radiation-hydrodynamic simulations as exemplified by recent advances in, say, star formation \citep[e.g.,][]{bate12} and core-collapse supernovae \citep[e.g.,][and references therein]{Janka2012,Burrows2013,ott13}. In the context of radiative transfer problems, the optical depth ($\tau$) is of central importance. When it is calculated from the radiation production site up to the transparent edges of the system, it counts the average number of interactions experienced by a radiation particle before it can finally escape. The optical depth allows the distinction between diffusive ($\tau \gg 1$), semi-transparent ($\tau \sim 1$), and transparent ($\tau \ll 1$) regimes. The surface where $\tau = 2/3$ represents the last interaction surface and is often called \textit{neutrinosphere} in the case of neutrino radiation (or \textit{photosphere} in the case of photons). Codes that solve the Boltzmann equations, through either finite difference (e.g., the discrete ordinate method, see \citealt{liebendoerfer04} in 1D, \citealt{ott08} in 2D), or spectral methods (e.g., the spherical harmonic method, see \citealt{peres13b}), Monte-Carlo codes \citep[e.g.,][]{abdikamalov12}, and most approximative schemes such as flux-limited diffusion \citep[e.g.,][]{whitehouse05,swesty09} or M1 schemes \citep[e.g.,][]{shibata2011,OConnor2013}, do not need to compute $\tau$ separately, since it is a physical quantity that results from the algorithm itself. Other codes, such as that of \cite{kuroda12}, which also employs the M1 closure of the transport equations using a variable Eddington factor, calculate $\tau$ assuming that radiation moves along radial paths. Some approximated radiation transport schemes, like the Isotropic Diffusion Source Approximation \citep{Liebendorfer2009}, require the calculation of $\tau$ to determine the location of the neutrinospheres. Also, light-bulb methods \citep[e.g.][]{Nordhaus2010,Hanke2012,Couch2013a} and ray-tracing methods \citep[e.g.,][]{kotake03,Caballero2009,Surman2013}, in which the neutrino flux intensity in the free streaming region is computed from the inner boundary luminosities or by assuming black body emission at the neutrino decoupling surface, often demand the computation of $\tau$, at least where $\tau \lesssim 1$. Codes that treat radiation with leakage schemes \citep[going back to][]{vanriper81,bludman1982,cooperstein1986} need to calculate the optical depth explicitly everywhere inside the computational domain, since it is directly related to the diffusion time scale. In grid-based codes, this is traditionally achieved using either a global or a local ray-by-ray (RbR) approach, while in meshless codes like SPH one often interpolates the mean free path to a grid, calculates $\tau$ just like in the grid-based approach, and then interpolates it back to the SPH particles. The global RbR method employs a number of pre-defined radial rays, centered in one element of the domain, to calculate the optical depth, and is most effective in geometries with spherical symmetry, such as core-collapse supernovae \citep[CCSNe;][]{peres13,ott13} and isolated (relativistic) stars \citep{galeazzi13}. The local RbR method, on the other hand, integrates the optical depth equation along pre-defined rays starting at each point of the grid. This approach is computationally more expensive, but it is able to handle more complex geometries, and has been used for instance in Newtonian neutron star mergers \citep{ruffert96,rosswog03} and neutron star--black hole mergers \citep{deaton13}. More recently, neutrino leakage schemes have been adapted to the formalism of general relativity \citep{sekiguchi10,galeazzi13} and used in simulations of neutron star mergers \citep{sekiguchi11}. Our work is motivated by questions related to core-collapse supernovae and neutron star mergers, but our algorithm makes no assumption about the geometry, radiation path or the astrophysical scenario, and could therefore be readily used in other contexts (e.g., photons in stellar atmospheres).\\ \noindent This paper is organised as follows. \sec{sec:method} is devoted to a brief review of the concept of optical depth and an outline of our main hypotheses (\sec{sec:method definitions assumptions}), together with a general description of our new algorithm (\sec{sec:method algorithm}). In \sec{sec:implem} we describe its implementation in grid-based (\sec{sec:implem grid}) and SPH schemes (\sec{sec:implem SPH}). \sec{sec:tests analytic} presents a number of tests with analytically known solutions, while \sec{sec:tests astroph} compares the results of various numerical methods applied to snapshots from grid-based (\sec{sec:tests astroph grid}) and SPH (\sec{sec:tests astroph SPH}) simulations. Performance and scaling of MODA are discussed in \sec{sec:performance}. Finally, our results are summarized in \sec{sec:discussion}, while technical details about the implementation and the parallelization are presented in \seca{sec:app technical}, and in \seca{sec:app parallelization}. | \label{sec:discussion} In this paper we presented a new, efficient algorithm for the calculation of optical depths $\tau$ from any given profile of the mean free path $\lambda$. There are no restrictions related to the symmetry or the configuration of the computational domain. All that is needed is that $\lambda$ be globally increasing towards the edges of the domain, which is normally a fair assumption. The algorithm was implemented both in a grid-based and a tree-based code, and proved to be suitable for both Eulerian and Lagrangian methods. The three-dimensional tests we presented, starting with analytic, spherically-symmetric configurations and ending with highly anisotropic and heavily shocked configurations, proved that the algorithm provides excellent accuracy in multi-dimensional calculations, while being less computationally expensive than more traditional ray-by-ray methods. | 14 | 3 | 1403.1297 |
1403 | 1403.4960_arXiv.txt | { We study the dark matter from an inert doublet and a complex scalar singlet stabilized by $\Z_{N}$ symmetries. This field content is the minimal one that allows dimensionless semi-annihilation couplings for $N > 2$. We consider explicitly the $\Z_3$ and $\Z_4$ cases and take into account constraints from perturbativity, unitarity, vacuum stability, necessity for the electroweak $\Z_{N}$ preserving vacuum to be the global minimum, electroweak precision tests, upper limits from direct detection and properties of the Higgs boson. Co-annihilation and semi-annihilation of dark sector particles as well as dark matter conversion significantly modify the cosmic abundance and direct detection phenomenology. } \arxivnumber{14xx.xxxx} \begin{document} | \label{sec:intro} The $\Lambda$CDM model that explains 22\% of the Universe's energy density with non-baryonic collisionless cold dark matter (DM) has turned out to give an excellent description of the Universe at large scales~\cite{Ade:2013zuv}. The most popular candidates for the DM are weakly interacting massive particles (WIMPs) \cite{Jungman:1995df,Bertone:2004pz,Bergstrom:2000pn} that are stable due to an imposed discrete symmetry. A large class of models beyond the standard model (SM), such as supersymmetric models~\cite{Nilles:1983ge,Haber:1984rc}, correctly predict the observed DM abundance as a thermal relic density of WIMPs. At the same time, there is an increasing number of experimental and observational hints that the WIMP paradigm may not be realised in Nature in its simplest form. The negative results in searches for DM direct~\cite{Aprile:2011hi,Aprile:2012nq,Akerib2013111} and indirect detection~\cite{Cirelli:2010xx} severely constrain the simplest DM models. The not yet conclusive cosmological observations (see \cite{Weinberg:2013aya} for a review) suggest that the DM density profiles in the centres of galaxies and in dwarf galaxies, and the masses of the biggest satellite halos, may significantly deviate from the results of $N$-body simulations. Those hints may suggest that the DM freeze-out processes are non-standard, and the DM interactions with baryons and with other DM particles may be more complicated than the simplest models predict. In addition, the dark sector may have complicated dynamics with more than one DM component. In light of those results studies of non-standard DM dynamics in non-minimal models are well motivated. The discovery of the Higgs boson at the Large Hadron Collider (LHC) \cite{Aad:2012tfa,Chatrchyan:2012ufa} has proven that scalar particles play an important r\^{o}le in fundamental physics. Since the nature of DM is yet unknown, scalar DM models are among the best motivated DM scenarios~\cite{McDonald:1993ex,Barger:2007im,Barger:2008jx,Burgess:2000yq,Gonderinger:2009jp,Cai:2011kb,Deshpande:1977rw,Ma:2006km,Barbieri:2006dq,LopezHonorez:2006gr,Belanger:2012zr,Belanger:2012vp}. The latest studies show that the SM scalar potential is very close to the critical bound \cite{Bezrukov:2012sa,Degrassi:2012ry,Buttazzo:2013uya,Masina:2012tz}. Scalar DM couplings to the Higgs boson, the so-called Higgs portal~\cite{Patt:2006fw,Chu:2011be,Djouadi:2011aa,Djouadi:2012zc}, can stabilise the SM Higgs potential via its contribution to the running of Higgs quartic self-coupling~\cite{Gonderinger:2009jp,Kadastik:2011aa,Chen:2012faa,Cheung:2012nb,Gonderinger:2012rd,Chao:2012mx,Gabrielli:2013hma} or via singlet threshold effects~\cite{Lebedev:2012zw,EliasMiro:2012ay,Hambye:2013dgv}. The scalar DM framework is also suitable for constructing DM models based on Abelian $\Z_N$ or non-Abelian (discrete) symmetries \cite{Batell:2010bp,DeMontigny:1993gy,Agashe:2010gt,DEramo:2010ep,Martin:1992mq,Agashe:2010tu,Belanger:2012vp,Ma:2007gq,Belanger:2012zr,Ivanov:2012hc,Lovrekovic:2012bz,DEramo:2012rr,Ko:2014nha} that have non-standard freeze-out processes, such as semi-annihilations~\cite{Hambye:2009fg,Hambye:2008bq,Arina:2009uq,DEramo:2010ep}, that modify the predictions for the DM abundance and for its interactions with matter. Due to the new type of processes the relations between DM annihilation cross sections and spin-independent scattering cross section with nuclei are modified, explaining the present negative results. The aim of this work is to perform a comprehensive study of $\Z_3$ and $\Z_4$ scalar DM models with semi-annihilation by scanning systematically over their full parameter space. We consider models presented in~\cite{Belanger:2012vp} with scalar sectors that comprise, in addition to the Higgs doublet, gauge singlet and doublet scalars. The $\Z_{4}$ model may have more than one species of stable DM. The $\Z_{3}$ singlet model~\cite{Ma:2007gq,Belanger:2012zr} and the inert doublet model \cite{Deshpande:1977rw,Ma:2006km,Barbieri:2006dq,LopezHonorez:2006gr} with a $Z_2$ symmetry are just limiting cases of this general framework. Since the new semi-annihilation modes, $\mathrm{DM}+\mathrm{DM} \to \mathrm{DM} + \mathrm{SM}$, modify the DM freeze-out, our aim is to study the impact of the non-standard physics on DM direct detection and on the LHC Higgs phenomenology in those models. In particular, we study the possible deviations of the Higgs boson decay mode to two photons, $h\to \gamma\gamma,$ from the SM prediction. As for the singlet model we found that the main constraint from Higgs physics comes from the upper bound on the invisible width that rules out the light DM scenarios. We also discuss the possibility of having direct signals from two different DM candidates. The layout of our paper is the following. We formulate $\Z_N$ symmetric models and study their field content in Section~\ref{sec:ZN}. The scalar potentials that give rise to semi-annihilations are presented in Section~\ref{sec:z:3:4:semiannih}. We list the various experimental and theoretical constraints on those models in Section~\ref{sec:constraints}. The results of our study for $\Z_3$ models are presented in Section~\ref{sec:Z:3} and for $\Z_4$ models in Section~\ref{sec:Z:4}. We conclude in Section~\ref{sec:concl}. One loop $\beta$-functions for renormalisation of our models are presented in Appendix~\ref{se:z3:z4:1-loop:beta:functions}. | \label{sec:concl} We have explored the phenomenology of an inert doublet and complex scalar dark matter model stabilized by $\Z_N$ symmetries, with explicit investigation of the $\Z_3$ and $\Z_4$ cases. The new feature of these models as compared to the $\Z_2$ case is the possibility of semi-annihilation and dark matter conversion. This has important consequences for all dark matter observables. In the $\Z_3$ model, semi-annihilation processes, e.g. $x_1 x_1\to x_1 h$, can give the dominant contribution to the relic abundance through the cubic ($\mu''_{S} S^3$) or quartic ($\lambda_{S12} S^2 H_1^\dagger H_2$) terms in the scalar potential. This means that the $\lambda_{S1}$ parameter which sets the coupling of DM to the Higgs and thus the direct detection cross section is not uniquely determined by the relic density constraint as occurs in the $\Z_2$ model. Large semi-annihilation is therefore associated with suppressed direct detection rate. While the bulk of the points will be testable by ton-scale detectors, it is possible to satisfy the constraints from vacuum stability and globality of the minimum of the potential with very small values of $\lambda_{S1}$ -- hence to escape all future searches, in particular when the DM is near the TeV range. The direct detection limits from LUX almost completely rule out the region where dark matter masses are below 120 GeV since for kinematic reasons the semi-annihilation does not play an important r\^{o}le (the Higgs cannot be produced in the final state). In this model, because there can be resonance enhancement of the annihilation cross section in the Galaxy when the mass of the DM is tuned to be half the mass of the doublet Higgs, the indirect detection cross section can be much enhanced as compared to the canonical value. The semi-annihilation processes will however lead to softer spectra since the DM particle in the final state drains part of the energy of the reaction. Furthermore we have shown that the model can be perturbative up to the GUT scale even with a large fraction of semi-annihilation. Enlarging the symmetry to $\Z_4$ entails two dark sectors, hence two dark matter candidates: a singlet and a doublet. In this case both semi-annihilation and dark matter conversion significantly affects the dark matter phenomenology of the model. While this model shares many characteristics of the inert doublet model especially when interactions between the two dark sectors can be ignored, the presence of the singlet dark matter candidate means that the doublet DM could only contribute to a fraction of the relic density (and vice versa). This means in particular that the doublet DM can have any mass instead of being confined to be at the electroweak scale or heavier than 500 GeV as in the inert doublet model. We found that for the sub-dominant dark matter component, it is possible to have a detectable signal in future direct detection experiments even after taking into account the fraction of each component in the DM density. This occurs in particular when the sub-dominant component is the doublet since it typically has a large direct detection rate. Furthermore in some cases a detectable signal in future ton-scale experiments is predicted for each DM component, opening up the exciting possibility of discovering two DM particles. \newpage \appendix | 14 | 3 | 1403.4960 |
1403 | 1403.8149_arXiv.txt | Turbulent motion driven by the magnetorotational instability (MRI) is believed to provide an anomalous viscosity strong enough to account for observed accretion rates in protostellar accretion disks. In the first of two papers, we perform large-scale, three fluid simulations of a weakly ionised accretion disk and examine the linear and non-linear development of the MRI in the net-flux and zero net-flux cases. This numerical study is carried out using the multifluid MHD code HYDRA. We examine the role of non-ideal effects, including ambipolar diffusion, the Hall effect, and parallel resistivity, on the non-linear evolution of the MRI in weakly ionised protostellar disks in the region where the Hall effect is believed to dominate. We find that angular momentum transport, parametrised by the $\alpha$-parameter, is enhanced by inclusion of non-ideal effects in the parameter space of the disk model. The case where $\Omega \cdot \mathbfit{B}$ is negative is explored and the Hall effect is shown to have a stabilizing influence on the disk in this case. | In protostellar accretion disks mass accretes onto the central object with accretion rates in the range of 10$^{-7}$ - 10$^{-9}$ M$_{\odot}$\,yr$^{-1}$ \citep{Gullbring:1998}. For mass to accrete inwards radially, it is necessary for angular momentum to be transported outwards radially. A key question in accretion disk physics is what process or combination of processes is responsible for the efficient transport of angular momentum to obtain accretion rates in the observed range? The magnetorotational instability \citep{Balbus:1991} is the most promising transport mechanism proposed thus far. The magnetorotational instability (MRI) has been studied extensively in the ideal MHD regime using local shearing-box \citep{Hawley:1995, Stone:1996, Sano:2002a, Sano:2002b, Bai:2013a} and global \citep{Armitage:1998, Arlt:2001, Lyra:2008} numerical simulations. Results obtained from these simulations have shown that the MRI process can lead to efficient transport of angular momentum and may produce a rate of accretion similar to those obtained from observations. However, protostellar accretion disks are weakly ionised and so the ideal MHD regime may not be sufficient in describing the physics involved. Ionisation sources such as X-ray radiation from the protostar only ionize the surface of the disk, and accretion disks are typically too cold to provide effective thermal ionisation in the body of the disk. As a result, large regions adjacent to the mid-plane of the disk are not thought to be susceptible to the MRI \citep{Gammie:1996}, whereas the MRI is active closer to the surface of the disk. In weakly ionised accretion disks, the plasma is largely made up from neutral fluid with a small fraction of the bulk fluid consisting of a number of ionised species of differing properties. Three non-ideal processes are introduced by the interaction of the various species, namely Ohmic dissipation, ambipolar diffusion and the Hall effect. In protostellar accretion disks, Ohmic dissipation is believed to dominate in high density regions with a low ionisation fraction such as the midplane and inner disk, ambipolar diffusion dominates in the opposite regime and the Hall effect is important in between \citep{Bai:2011b}. A number of studies have been performed where Ohmic dissipation is the dominant non-ideal process. When Ohmic dissipation is important the MRI can be heavily suppressed. The importance of Ohmic dissipation can be measured by the magnetic Reynolds number, which determines the relative importance advection and diffusion and is given by $R_M = c_s^2/ \eta \Omega$ where $\eta$ is the magnetic diffusivity. A study by \citet{Fleming:2000} determined that the MRI cannot be self-sustained when $R_M \ge 10^4$. Ambipolar diffusion arises from the imperfect coupling of the neutral and ionised fluids in a weakly ionised plasma such as that typically found in accretion disks. The importance of ambipolar diffusion is determined by the value of the parameter $Am=\gamma \rho_i/\Omega$ where $\rho_i$ is the density of the ionised fluid, $\gamma$ is the ion-neutral collisional coefficient, and $\Omega$ is the orbital frequency. It was determined in the linear analysis of \citet{Blaes:1994} that once the ion-neutral collision frequency dropped below the orbital frequency, the MRI is suppressed. This result was confirmed by \citet{Hawley:1998} using numerical simulations. In this case when $Am < 0.01$ the neutrals behave independently from the ions. In the opposite case, when $Am > 100$ ideal MHD behaviour is obtained. In the paper of \citet{Bai:2011a}, the above results were again confirmed using local simulations, but it was seen that in the case of a net field it was possible for MHD turbulence to be maintained when $Am$ is small. The effect of ambipolar diffusion is dependent on the field geometry. In local simulations such as the above, field geometry is arbitrarily applied to the computational domain. The field geometry has important implications for the non-linear evolution of the MRI and so to gain a deep understanding what effect ambipolar diffusion has on the saturation state of the MRI it is necessary to use global simulations \citep{Bai:2011b}. The Hall effect is very interesting as it can have a stabilising or destabilising effect depending upon the orientation of the magnetic field because of the handedness introduced by the effect. We refer the reader to \citet{Wardle:2012} for details of the destabilisation mechanism. The linear analysis of \citet{Salmeron:2003} suggests that the Hall effect in this regime may have important consequences for the growth and saturation of the MRI. In the study of \citet{Sano:2002a, Sano:2002b}, the Hall-Ohm regime was investigated where Ohmic dissipation is large enough to have a damping effect on the MRI. Although the Hall effect was believed to allow the MRI to grow in situations where Ohmic and ambipolar diffusion would normally suppress the MRI entirely \citep{Wardle:1999}, the simulations presented in this study did not investigate this specific point. However the parameter space investigated was narrow and did not include the Hall dominated case which would be common in protostellar disks where a large extent of the disk may be in this regime. In this regime it is believed that estimates of the depth of magnetically active layers in accretion disks may be inaccurate because of disk destabilisation due to the Hall effect and protostellar disks may be turbulent much closer to the mid-plane of the disk \citep{Wardle:2012}. The scenario where the Hall effect dominates over the other non-ideal processes has only recently begun to be explored. In the paper of \citet{Kunz:2013}, the saturation of the MRI in a weakly ionised protostellar disk, dominated by the Hall effect, is studied using the shearing box approximation. The authors describe "large scale" axisymmetric effects (insofar as local simulations can make predictions about large scale effects) forming in the magnetic and velocity fields. The structures described by the authors are very long-lived and have the net effect of reducing the amount of MRI driven turbulent transport present. These results suggest that the Hall effect, may not be as effective in allowing the MRI to develop in regions which should be inactive to MRI driven turbulence as suggested by \citet{Wardle:2012}. Their results also appear to be in contradiction to those of \citet{Bai:2013a} and \citet{Salmeron:2003,Salmeron:2005}, although the authors acknowledge that the inclusion of a stratification may be important. The model of \citet{Kunz:2013} occupies a similar parameter space to the global multifluid model presented here. In this paper, we present the first fully multifluid MHD, global numerical simulations of accretion disks in a region of the disk where the Hall effect is believed to dominate over other non-ideal effects. In the presence of purely diffusive non-ideal effects, angular momentum transport would be expected to be damped compared to the ideal MHD case. This work investigates the destabilising nature of the Hall effect and illustrates the importance of a net magnetic field and its orientation relative to the net angular momentum vector in determining the non-linear evolution of the disk in the presence of the Hall effect, confirming the results of \citep{Sano:2002a, Sano:2002b}. The structure of this paper is as follows. In section 2 we present the numerical set-up and explain the model and boundary conditions used. In section 3, the analysis techniques used to produce the results are explained. Section 4 contains a validation of the model. In section 5, a resolution study is performed and the results of a direct comparison between the ideal MHD and fully multifluid models are presented. Finally, we conclude and discuss the implications of the results in section 6. \section[]{Numerical Approach} The numerical simulations described in this paper are performed using the multifluid magnetohydrodynamic code HYDRA which models weakly ionised plasmas \citep{OSullivan:2006, OSullivan:2007}. The multifluid simulations include three fluids, consisting of a neutral species, an electron and an ion species. \subsection{Multifluid equations} The following set of equations model the evolution of a neutral fluid and $N-1$ charged fluids in the presence of a magnetic field. These equations govern a weakly ionised plasma. In the case of a weakly ionised plasma, the pressure and inertial terms of the evolution equations for the ionised species (subscripted by $i$) may be ignored. This is because the mass density of the plasma is dominated by the neutral component \citep[e.g.][]{Falle:2003, Ciolek:2002}. An isothermal closure relation is used, therefore allowing the energy equations for the neutrals and ionised species to be ignored. \begin{equation} \frac{\partial \rho_{i}}{\partial t} + \nabla \cdot (\rho_{i} \mathbfit{v}_{i}) = 0 \end{equation} \begin{equation} \frac{\partial \rho_{1} \mathbfit{v}_{1}}{\partial t} + \nabla \cdot (\rho_{1} \mathbfit{v}_{1}\mathbfit{v}_{1} + p_{1} \mathbfss{I} ) = \mathbfit{J} \times \mathbfit{B} \end{equation} \begin{equation} \frac{\partial \mathbfit{B}}{\partial t} + \nabla \cdot (\mathbfit{v}_{1} \mathbfit{B} - \mathbfit{B} \mathbfit{v}_{1} ) = - \nabla \times \mathbfit{E}^{'} \end{equation} \begin{equation} \alpha_{i} \rho_{i}(\mathbfit{E} + \mathbfit{v}_{i} \times \mathbfit{B}) + \rho_{i} \rho_{1} K_{i1} (\mathbfit{v}_{1} - \mathbfit{v}_{i}) = 0 \: ; \: (2 \leq i \leq N) \end{equation} \begin{equation} \nabla \cdot \mathbfit{B} = 0 \end{equation} \begin{equation} \nabla \times \mathbfit{B} = \mathbfit{J} \end{equation} \begin{equation} \displaystyle\sum_{i=2}^{N} \alpha_{i} \rho_{i} = 0 \end{equation} \begin{equation} \displaystyle\sum_{i=2}^{N} \alpha_{i} \rho_{i} \mathbfit{v}_{i} = \mathbfit{J} \end{equation} The subscripts in the above equations denote the species in question. The neutral component is represented by a subscript of 1, and the charged species are denoted by subscript 2 to $N$. The variables $\rho_{i}$, $\mathbfit{v}_{i}$, $p_{i}$ represent the mass density, pressure and velocity of species $i$ respectively. The collisional coefficient $K_{i1}$ represents the collisional interaction between species $i$ and the neutral fluid. The charge to mass ratio of the $i^{\rm th}$ species is represented by $\alpha_{i}$. The identity matrix, current density, and magnetic flux density are represented by \textbfss{I}, \textbfit{J} and \textbfit{B} respectively and finally the full electric field is given by $\mathbfit{E}=-\mathbfit{v}_{1} \times \mathbfit{B} + \mathbfit{E}^{'}$. One more equation is needed to close the set. An equation of state may be used. In this case the isothermal relation $c_{s}^{2}=p_{1}/\rho_{1}$ is added to the set. This set of equations leads to an expression for the electric field in the frame of the fluid, $\mathbfit{E}^{'}$, given by the generalised Ohm's law \begin{equation} \mathbfit{E}^{'} = \mathbfit{E}_O + \mathbfit{E}_H + \mathbfit{E}_A \end{equation} \noindent where the electric field components are given by \begin{equation} \mathbfit{E}_O = (\mathbfit{J} \cdot \mathbfit{a}_O)\mathbfit{a}_O \end{equation} \begin{equation} \mathbfit{E}_H = \mathbfit{J} \times \mathbfit{a}_H \end{equation} \begin{equation} \mathbfit{E}_A = -(\mathbfit{J} \times \mathbfit{a}_H) \times \mathbfit{a}_H \end{equation} \noindent using the definitions $\mathbfit{a}_O \equiv f_O \mathbfit{B}$, $\mathbfit{a}_H \equiv f_H \mathbfit{B}$ and $\mathbfit{a}_A \equiv f_A \mathbfit{B}$ where $f_O \equiv \sqrt{r_O}/B$, $f_H \equiv r_H/B$ and $f_A \equiv \sqrt{r_A}/B$. The resistivities are given by \begin{equation} r_{o} \equiv \frac{1}{\sigma_o} \end{equation} \begin{equation} r_{H} \equiv \frac{\sigma_{H}}{\sigma_{H}^{2} + \sigma_{A}^{2}} \end{equation} \begin{equation} r_{A} \equiv \frac{\sigma_{A}}{\sigma_{H}^{2} + \sigma_{A}^{2}} \end{equation} \noindent where the conductivities are defined for each charged species $i$ by \begin{equation} \sigma_{o} = \frac{1}{B} \displaystyle\sum_{i=2}^{n} \alpha_{i} \rho_{i} \beta_{i} \end{equation} \begin{equation} \sigma_{H} = \frac{1}{B} \displaystyle\sum_{i=2}^{n} \frac{\alpha_{i} \rho_{i}} {1 + \beta_{i}^{2}} \end{equation} \begin{equation} \sigma_{A} = \frac{1}{B} \displaystyle\sum_{i=2}^{n} \frac{\alpha_{i} \rho_{i} \beta_{i}} {1 + \beta_{i}^{2}} \end{equation} where ($\beta_{i}$) is the Hall parameter for the charged species and is a measure of how well tied to the magnetic field the charged species ($i$). This is given by \begin{equation} \beta_{i} = \frac{\alpha_{i} B}{K_{i1} \rho_{1}} \end{equation} To solve these equations numerically, the time integration of these equations is multiplicatively operator split into 3 separate operations which may be summarised as follows: \begin{enumerate} \item {The neutral fluid is advanced. Equations (1), (2) and (3), with index $i=1$ for equation (1) are solved using a standard finite volume integration method to 2nd order temporal and spatial accuracy. The diffusive term on the RHS of equation (3) is not evaluated until a later step. The restriction described by equation (5) is also maintained using the method of \citet{Dedner:2002}.} \item{The diffusive term in equation (3) is now evaluated. By using standard discretisation, a restriction is imposed by the potentially vanishing timestep associated with very high values of Hall resistivity \citep{Falle:2003}. To overcome this problem, the induction equation is integrated by multiplicatively operator splitting the Hall and ambipolar terms. Special techniques, known as super-timestepping and the Hall diffusion scheme are then used to advance the Hall and ambipolar terms efficiently while simultaneously relaxing the timestep restriction and maintaining 2nd order accuracy.} \item{Finally, the densities and velocities of the various charged species are evaluated. The densities are evaluated using the mass conservation equation (1) for $2 \leq i \leq N$, where $N$ is the number of fluids.} \end{enumerate} For further details on the numerical code HYDRA, including discussions of stability and accuracy of the results, we refer the reader to \citet{OSullivan:2006,OSullivan:2007}. \subsection{The model} The computational model used in this study is similar to that found in \citet{Lyra:2008}. A Cartesian grid is used in this model. This approach has been used for accretion disk studies before with success \citep{Peplinski:2008,Zhang:2008}. It has been shown rigorously by \citet{Valborro:2006} that codes based on Cartesian grids produce results that are not significantly different to those produced with other grid types. To save computational expenditure, we only simulate one quadrant of the accretion disk \citep{OKeeffe:2013}. This approach has been used in the accretion tori study of \citet{Stone:2000} where it was found that using a $\pi/2$ domain does not significantly change the quantitative results at saturation. It is possible to further reduce the azimuthal domain \citep{Dzyurkevich:2010}, however as the domain is reduced the results will begin to diverge from those obtained using a complete azimuthal domain \citep{Flock:2012}. This occurs because the larger azimuthal modes of the MRI no longer fit within the domain. The use of a $\pi/2$ domain is convenient when using a Cartesian coordinate system where a smaller azimuthal domain would be non-trivial to set-up. \subsection{Boundary conditions} Implementing a global accretion disk model on a Cartesian grid presents problems with how to deal with the boundaries. The boundary conditions can be categorised as box-face and interior boundaries. The box-face boundaries are applied to the sides of the computational box in which the disk is situated. The interior boundaries are placed inside this box to take into account the cylindrical nature of the disk. Outside of the cylindrical disk, the fluid variables are not allowed to evolve and are essentially frozen. The fluid is allowed to flow in and out of these interior boundaries and so some mass and magnetic energy is expected to flow through these boundaries and the disk is not a closed system. These two types of boundaries will now be described in turn. \begin{figure} \includegraphics[width=84mm]{Fig1.eps} \caption{Illustration of computational domain and boundary conditions. The upper right hand quadrant is the extent of the Cartesian grid. The thickened edges of this quadrant represent the azimuthal boundaries. Material which leaves through the low-$x1$ boundary will re-enter through the low-$x2$ boundary and vice-versa. The arrows illustrate this. The shaded region in the upper right hand quadrant is the active computational domain and the white regions are the frozen zones. The line between the active and frozen domain is the wavekilling interior boundary. } \end{figure} \subsubsection{Box-face boundaries} The box-face boundaries are applied to the sides of the computational box. The upper and lower $z$ boundaries are simply periodic as we assume there is no vertical gravity gradient. This ensures that no mass or energy is lost through the vertical boundaries. The upper $x$ and $y$ boundaries are unimportant as they are directly adjacent to the frozen zone. No fluid crosses these boundaries and they can simply be ignored. The lower $x$ and $y$ boundaries are periodic with each other. Fluid that flows out of one boundary is transported across the other. This allows and is consistent with the use of the quarter disk approximation mentioned at the beginning of this section. \subsubsection{Interior boundaries} The accretion disk itself is a quarter cylinder which is placed in a flattened square prism. This sets a limit to the radial extent of the disk i.e. $r\leq L_{x}$. This condition makes it necessary to introduce an interior radial boundary. As mentioned previously, a frozen region is introduced for $r \leq r_{\rm{int}}$ and $r \geq r_{\rm{ext}}$ where the dynamical equations are not evolved for the fluids or the magnetic field. In the models presented here $r_{\rm{int}} = 0.5$, $r_{\rm{ext}} = 2.58$ and $L_x = L_y = 2.6$ and $L_z=0.075 \times L_x$ . The inner bufferzone is positioned just outside the inner frozen zone at $0.5 < r < 0.6$, similarly the outer bufferzone is positioned at $2.48 < r < 2.58$. Fig.2 shows the position of these zones relative to the box boundaries. The purpose of the radial buffer zone is to smoothly transition the fluid parameters so that any numerical instabilities associated with the abrupt jump from free to frozen regions may be avoided \citep{Lyra:2008}. There is a dual purpose to this type of inner boundary. It allows an escape route for undesirable waves at the beginning of the simulation. In the models presented here, transient waves are seen to originate from the frozen region at the beginning of the simulations. If the wavekilling boundaries were not present these waves could reflect back and forth throughout the computational domain. It is important to note that the bufferzones are not fixed in nature and allow accretion through them. \begin{figure} \includegraphics[width=84mm]{Fig2.eps} \caption{Schematic showing the x,y plane of the computational domain. The dark shaded area is the active computational domain. The white areas bounded by the black curves and the sides of the box are the frozen regions. The light shaded regions are the wavekilling interior boundaries. Refer to section 2.3.2 and Fig.1 for a detailed description. } \end{figure} The inner buffer zone must kill waves faster as the fluid evolves dynamically on shorter time-scales here and hence the risk of instabilities arising at this boundary is higher. It is worth noting that \citet{Lyra:2008} performed some simulations without this inner boundary and models with and without inner radial boundaries behave similarly with little quantitative difference. A smaller timestep results as the fluid will be rotating at a much higher rate closer to the origin than at the inner radial edge of the bufferzone. Following \citet{Lyra:2008}, the bufferzone drives the fluid parameter $X$ gradually and smoothly to its initial condition such that \begin{equation} \frac{dX}{dt}= -\frac{X-X_0}{\tau }S(r) \end{equation} \noindent where $S(r)$ is the driving function which has a range of [0,1.0], and $\tau$ is the orbital period at the boundary in question. Linear and non-linear functions were evaluated for the driving function. It was decided to use a linear driving function as no quantitative difference was found between the linear and non-linear functions. The driving function is defined by the following piecewise linear function: \[S(r) = \left\{ \begin{array}{ll} 1.0 & \textrm{if } r \leq 0.5\\ 10(0.6-r) & \textrm{if } 0.5 < r < 0.6\\ 0 & \textrm{if } 0.6 \leq r \leq 2.48\\ 10(r-2.48) & \textrm{if } 2.48 < r < 2.58\\ 1.0 & \textrm{if } r \ge 2.58 \end{array} \right. \] \subsection{Gravity} A Newtonian gravitational potential is applied to the fluid within the computational domain \begin{equation} \Phi = - \frac{GM}{\sqrt{x^2 + y^2}+c} \end{equation} \noindent where $G$ is the universal constant of gravitation, $M$ is the mass of the central object, and c is a softening parameter. Notice that this gives a cylindrical potential, where the fluid is attracted to a pole whose centre is located at $x=y=0$ rather than a single point. Whereas normally a radial and vertical stratification would exist, in this case vertical stratification is omitted. The vertical extent of the disk model is small compared to the radial domain size but large enough that vertical structure in the densities and magnetic field may develop without influence from the vertical boundaries. \subsection{Initial conditions} For the ideal MHD model the following initial conditions are used. The neutral density is uniform initially and is set to 1.17$\times$10$^{-11}$g/cm$^3$. The average mass of the neutral particles is taken to be $m_{\rm{n}} = 2.33 m_{\rm{p}}$ , where m$_{\rm{p}}$ is the mass of a proton. This corresponds to a fluid of 90\% molecular hydrogen and 10\% atomic helium by number, which is representative of molecular clouds. There is no pressure gradient initially. All models presented are isothermal and the neutral pressure is found using the isothermal relation $a=\sqrt{P/\rho}$. The choice of an appropriate model for the study of the MRI is not trivial. From linear analysis \citep{Balbus:1991} of the MRI it is found that only a weak magnetic field, and differential rotation is required for the MRI to be present. In numerical simulations, it is necessary that the processes involved in an instability be adequately resolved by the computational grid. In the case of the MRI, it is found from linear analysis that a critical vertical wavelength must be resolved \citep{Balbus:1991, Balbus:1998}: \begin{equation} \lambda_{c}=\frac{2\pi}{\sqrt{3}} \frac{v_{A}}{\Omega} \end{equation} \noindent where $v_{A}$ is the Alfv\'{e}n speed which is given by \begin{equation} v_{Az}=\frac{B_z}{\sqrt{\mu_{0} \rho}} \end{equation} The critical wavelength of the MRI is approximately the distance an Alfv\'{e}n wave would travel vertically in a single orbital period. The model must be constructed while considering the requirement that this critical wavelength be resolved either initially or become resolved though the use of perturbation at an appropriate time. An initial magnetic flux of 50mG is chosen. Magnetic fields are known to reach a strength of an order of a 1G in the region of interest in this work \citep{Konigl:1993}. The critical wavelength of the MRI using this initial value of magnetic flux is resolved by 12 cells at the $r=2.0$ when using the finest resolution. At $r=1.0$ the critical wavelength is marginally resolved by approximately 4 zones but becomes resolved soon after the fluid perturbation is applied. Using the criterion of \citet{Hawley:2013}, the critical wavelength is sufficiently resolved at the outer radii, however after the fluid perturbation is applied, the inner radii begin to succumb to MRI driven turbulence and the MRI slowly becomes better resolved. At saturation, the $\lambda_z$ is resolved by 12-15 cells and $\lambda_\phi$ is resolved by 25-30 cells at $r=1.0$. The densities for the charged species are much smaller than the neutral species as the plasma is weakly ionised. The ion fluid represents an average of ions produced from a number of metal atoms, including Na, Mg, Al, Ca, Fe and Ni. These metals have sufficiently similar ionisation and recombination rates, and so can be modelled collectively as ions of a single positive charge \citep{Umebayashi:1990}. The molecular ions, of which HCO$^+$ is the most numerous, are significantly less abundant than the metal ions, allowing us to neglect them. An average mass of $m_{\rm{ion}} = 24 m_{\rm{p}}$ is assigned to the particles of the ion fluid, approximately equal to that of a magnesium ion. An ionisation fraction of approximately 4$\times 10^{-11}$ is expected in the radial range studied in this work. The number density of the neutral fluid is expected to be approximately 7$\times 10^{12}$cm$^{-3}$ \citep{Salmeron:2003}. The ionisation fraction ($\zeta$) is given by $\zeta=n_{\rm{e}}/n_{\rm{H}}$ leading to a number density for the electron fluid of approximately 300 cm$^{-3}$. The charge to mass ratios are calculated as follows, \begin{equation} \alpha_{\mathrm{ion}} = \frac{+e}{m_{\mathrm{ion}}}=\frac{1.6 \times 10^{-19}\mathrm{C}}{24m_{\mathrm{p}}}=4.0\times 10^{3} \mathrm{g}^{-1}=1.2\times 10^{13} \mathrm{stat C \, g}^{-1} \end{equation} \begin{equation} \alpha_{\mathrm{e}} = \frac{-{e}}{m_{\mathrm{e}}}=\frac{1.6 \times 10^{-19}\mathrm{C}}{m_{\mathrm{e}}}=-5.27 \times 10^{17} \mathrm{stat C \, g}^{-1} \end{equation} The number density of the ion fluid is then found using the charge neutrality condition \begin{equation} \alpha_{\mathrm{ion}} \rho_{\mathrm{ion}} + \alpha_{\mathrm{e}} \rho_{\mathrm{e}} = 0 \end{equation} \noindent The ion density, $\rho_{\rm{ion}}$, is then found to be 1.2$\times10^{-20}$ g cm$^{-3}$. The importance of the multifluid effects are set through the collision coefficients. Collisions between the charged fluids are not considered as their respective densities are low and so such collisions are rare in comparison to the collisions between charged particles and neutrals. The rate coefficient for the ion fluid may be found in \citet{Wardle:1999}. The collisional coefficients are found thus \begin{equation} K_{\mathrm{ion,n}} = \frac{<\sigma \nu>_{\mathrm{ion}}}{m_{\mathrm{ion}}+m_n} = \frac{1.6 \times 10^{-19} \mathrm{cm}^3 \mathrm{s}^{-1}} {24m_{\mathrm{p}}+2.33m_{\mathrm{p}}} = 3.64 \times 10^{13} \mathrm{cm}^3 \mathrm{g}^{-1} \mathrm{s}^{-1} \end{equation} \begin{equation} K_{\mathrm{e,n}} = \frac{<\sigma \nu>_{\mathrm{e}}}{m_{\mathrm{e}}+m_{\mathrm{n}}} = \frac{1.15\times^{-15}\left( \frac{128 K_{\mathrm{B}} T_{\mathrm{e}}}{9\pi m_{\mathrm{e}}} \right)}{m_{\mathrm{e}} + 2.33m_{\mathrm{p}}}=2.88 \times 10^{15} \mathrm{cm}^3 \mathrm{g}^{-1} \mathrm{s}^{-1} \end{equation} | In this, the first of two papers, we have presented the results of a series of simulations designed to examine whether non-ideal effects manifested by the multifluid regime affect the long term dynamics of accretion in disks around protostars. A weakly ionised disk model is implemented in a region of the disk where the Hall effect is believed to dominate over ambipolar diffusion. The results of this study show, that angular momentum transport, parametrised by the $\alpha$-parameter, is significantly enhanced by inclusion of all the non-ideal effects in this parameter space. The most surprising result is that in the multifluid regime such an accretion disk, active to the MRI, produces an unbounded exponential growth in the total magnetic energy. It is not clear if saturation would occur at a later time, though it may be assumed that once the magnetic energy reaches high enough levels the MRI would cease to be active as the disk would effectively lock up. The case where $\Omega \cdot \mathbfit{B}$ is negative leads to a suppression of the MRI and much slower rates of angular momentum transport. Likewise for the zero net field case, but for different reasons. These results confirm similar results found in the literature. Our results strongly suggest that the Hall effect is responsible for enhancement of the MRI where a net field (with appropriate orientation) is present. In a forthcoming paper the individual effects of ambipolar diffusion and the Hall effect on the dynamics of a protoplanetary disk will be studied. | 14 | 3 | 1403.8149 |
1403 | 1403.7128_arXiv.txt | The dynamically new comet, C/2013 A1 (Siding Spring), is to make a close approach to Mars on 2014 October 19 at 18:30~UT at a distance of $40\pm1$ Martian radius. Such extremely rare event offers a precious opportunity for the spacecrafts on Mars to closely study a dynamically new comet itself as well as the planet-comet interaction. Meanwhile, the high speed meteoroids released from C/Siding Spring also pose a threat to physically damage the spacecrafts. Here we present our observations and modeling results of C/Siding Spring to characterize the comet and assess the risk posed to the spacecrafts on Mars. We find that the optical tail of C/Siding Spring is dominated by larger particles at the time of the observation. Synchrone simulation suggests that the comet was already active in late 2012 when it was more than 7~AU from the Sun. By parameterizing the dust activity with a semi-analytic model, we find that the ejection speed of C/Siding Spring is comparable to comets such as the target of the Rosetta mission, 67P/Churyumov-Gerasimenko. Under nominal situation, the simulated dust cone will miss the planet by about 20 Martian radius. At the extreme ends of uncertainties, the simulated dust cone will engulf Mars, but the meteoric influx at Mars is still comparable to the nominal sporadic influx, seemly indicating that intense and enduring meteoroid bombardment due to C/Siding Spring is unlikely. Further simulation also suggests that gravitational disruption of the dust tail may be significant enough to be observable at Earth. | Near-Earth Objects (NEOs) play an important role in shaping the geological histories of terrestrial planets. Recent studies have shown NEO impacts are common in inner solar system \citep[c.f.][]{str05}. For other terrestrial planets, it has been suggested that the impact flux is comparable to the near-Earth environment \citep{feu11}. Although over 99\% of the impactors are asteroids \citep{yeo13}, comets are generally of special interests, as they carry significant amount of volatile and organic material, which is life-essential. On Earth, kilometer-sized cometary impacts occur every $\sim10^{8}$~yr \citep{sto03}. On the other hand, close comet-planet approach is also significant in terms of the accretion of water and organic materials on the planet: comets eject a large amount of material into the vicinity of their nuclei, and they may still influence the planet without a direct impact. Although approaches are more common than impacts, it is still too rare for us to observe and study a real case: the closest cometary approach to the Earth since the establishment of modern science was D/1770 L1 (Lexell), which missed the Earth by $\sim 356$ Earth radius. From the impact rates, we estimate that close approach within 25 Earth radius with kilometer-sized comets occurs once every $\sim10^5$~yr. This is equivalent to the frequency of cometary approach within 50 Martian radius to Mars assuming that the cometary impact flux (like the total impact flux) is comparable between Earth and Mars. Yet this is what would happen later this year: a dynamically new comet, C/2013 A1 (Siding Spring), is to miss Mars by $\sim 40$ Martian radius at 2014 Oct. 19.8 (UT) (Figure~\ref{fig-a1orb} and \ref{fig-dist}). C/Siding Spring was discovered on 2013 Jan. 3 at a heliocentric distance of 7.2~AU; subsequent follow-up observations revealed a 10'' coma which indicated distinct cometary activity at such a large heliocentric distance \citep{mcn13}. As of 2014 Feb. 1, the comet is determined to be in a hyperbolic orbit, with $e=1.0006$; the current estimated miss distance between C/Siding Spring and Mars is about $40\pm1$ Martian radii or $135600\pm6000$~km\footnote{Update numbers can be found at \url{http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2013 A1}.}. Dynamically new comets are constrained on loosely bounded or unbounded orbits, and are thought to originate from the outer region of solar system, namely the Oort cloud. Due to the fact that they have had nil access to the inner solar system, they preserve valuable and unique information about the pre-solar nebula. However, comparing to the periodical comets, which usually return to the inner solar system on a frequent and predictable basis, the dynamically new comets are difficult to investigate due to their small number and limited opportunity to study individual objects (generally only once). The most productive method to study comets -- in-situ exploration -- is currently very difficult to be used on dynamically new comets, due to very short lead-time available for preparing and operating such missions. As such, the close approach offers an unprecedented and extremely rare opportunity to directly study how material may be transferred from comets to terrestrial planets as well as the dynamically new comet itself. Currently there are three operational orbiters (Mars Reconnaissance Orbiter, Mars Odyssey and Mars Express) and two operational rovers (Opportunity and Curiosity) on Mars; in addition, two orbiters (Mars Atmosphere and Volatile Evolution or MAVEN, and Mars Orbiter Mission or MOM) will arrive $\sim 1$ month before C/Siding Spring's closest approach. The fleet will have front seats for this event; however, the small miss distance of the encounter also means that they may pass inside the dust coma/tail of C/Siding Spring. While the Martian atmosphere will shield incoming dust particles (meteoroids) for the two rovers, the five orbiters will be at risk of bombardment of dust particles originated from the comet. Cometary dusts pose a significant threat of causing physical damage to the spacecrafts \citep[c.f.][]{ahe08}. Additionally, meteoroids originated from C/Siding Spring have higher kinetic energy than nominal sporadic (background) meteoroids, as the relative speed between the comet and Mars is twice as high as the latter. Early studies of C/Siding Spring before its close visit to Mars will be essential in the sense of monitoring the evolution of the comet and helping assess the risk posed to the spacecrafts. Here we present our observations and modeling effort of C/Siding Spring in the hope to characterize the physical properties of the comet. We will first discuss our observations and their significance for constraining the particle size distribution (PSD) of the comet, then we will present the semi-analytic model that will be used to match the observation and parameterize the cometary dust activity. Eventually, we will use the best-matched parameters to investigate the fluency of cometary dust particles experienced by Mars (and anything in the proximity) during the close encounter. | We reported the observations and modeling works of C/Siding Spring, a dynamically new comet that will make a close approach to Mars on 2014 Oct. 19. By fitting the observations with syndyne simulations, we found that the tail of C/Siding Spring was dominated by larger particles at the time of observation. Synchrone simulation suggested that the particles dominate the optical tail was released by the comet as early as late 2012, when the comet was more than $\sim7$~AU from the Sun. We then developed a semi-analytic model to simulate the cometary dust activity. The modeling result suggested a modest ejection velocity of C/Siding Spring that is comparable to a few other comets, including P/Churyumov-Gerasimenko, target of the Rosetta mission. The same model was then used to study the meteoroid influence to Mars during the encounter, fed with the constraints found in the previous steps. We found that the planet will miss the dust cone by some 20 Martian radius (67,800~km) under nominal situation. Although the planet may be engulfed by the cometary dust tail if we made an educative guess about the uncertainties and pushed the parameters to the extreme cases, the simulation suggested that the meteoroids reach the vicinity of Mars are dominated by non-spacecraft-threatening meteoroids, and the meteoric influx is not significantly higher than the sporadic background influx; the duration of the event is at the order of 1~hr. From our simulation, it seems that intense and enduring meteoroid bombardment at Mars and its vicinity region is unlikely during the flyby of C/Siding Spring. We also study the potential gravitational disruption of the cometary dust tail. A simple numerical integration suggested that the dust ``clump'' created by the gravitational drag would be at the order of tens of arcsecs at $T+20$~days as seen from the Earth which may be detectable by ground-based facilities. At the time of the writing, C/Siding Spring is about 4~AU from the Sun. As the comet travels into the inner solar system and enters the water-ice sublimation line, the story could evolve dramatically. We encourage observers to closely monitor C/Siding Spring as it helps on creating a full picture of this unprecedented cosmic event. \textit{Note:} at the reviewing stage of this paper, J. Vaubaillon et al. also reported their modeling result of the same event \citep[see][]{vau14}. Our initial check using their input values suggested an order-of-magnitude agreement between the two results, which indicated that the difference between the two results is primary due to input parameters. | 14 | 3 | 1403.7128 |
1403 | 1403.2820_arXiv.txt | We present new deep, high-resolution radio images of the diffuse minihalo in the cool core of the galaxy cluster RX\,J1720.1+2638. The images have been obtained with the Giant Metrewave Radio Telescope at 317, 617 and 1280 MHz and with the Very Large Array at 1.5, 4.9 and 8.4 GHz, with angular resolutions ranging from $1^{\prime\prime}$ to $10^{\prime\prime}$. This represents the best radio spectral and imaging dataset for any minihalo. Most of the radio flux of the minihalo arises from a bright central component with a maximum radius of $\sim 80$ kpc. A fainter tail of emission extends out from the central component to form a spiral-shaped structure with a length of $\sim 230$ kpc, seen at frequencies 1.5 GHz and below. We find indication of a possible steepening of the total radio spectrum of the minihalo at high frequencies. Furthermore, a spectral index image shows that the spectrum of the diffuse emission steepens with the increasing distance along the tail. A striking spatial correlation is observed between the minihalo emission and two cold fronts visible in the {\em Chandra}\/ X-ray image of this cool core. These cold fronts confine the minihalo, as also seen in numerical simulations of minihalo formation by sloshing-induced turbulence. All these observations favor the hypothesis that the radio emitting electrons in cluster cool cores are produced by turbulent reacceleration. | \label{sec:intro} The high-resolution X-ray imaging capabilities of \chandra\ and {\em XMM-Newton} have provided an unprecedent view of galaxy clusters, revealing a wealth of substructure in their cores and surrounding Mpc-scale gaseous atmospheres. In particular, {\em Chandra} showed that the low-entropy gas in many, if not most, relaxed cool-core clusters is ``sloshing'' in the central potential well, generating the ubiquitous sharp, arc-like gas density discontinuities, or ``cold fronts,'' that are concentric with the cluster center and often form a spiral pattern \citep[e.g.,][see, for instance, Ghizzardi et al.\ 2010 for examples of cold fronts detected with {\em XMM-Newton}]{2001ApJ...562L.153M,2001ApJ...555..205M,2003ApJ...596..190M, 2003ApJ...583L..13D,2007PhR...443....1M, 2009ApJ...704.1349O, 2013A&A...555A..93E}. Such sloshing motions are believed to result from a recent gravitational perturbation of the cluster central potential in response to collisions with small subclusters, which do not cause significant visible X-ray disturbance outside the core \citep[e.g.,][]{2005ApJ...618..227T,2006ApJ...650..102A,2011ApJ...743...16Z, 2011MNRAS.413.2057R}. Active galactic nucleus (AGN) explosions in the cluster central galaxy, occurring in an asymmetric gas distribution, may also create a disturbance and set off sloshing of the core gas \citep{2001ApJ...562L.153M,2011MNRAS.415.3520H}. A number of relaxed, cool-core clusters are hosts to radio ``minihalos'', diffuse steep-spectrum\footnote{spectral index $\alpha >1$, for $S_{\nu} \propto \nu^{-\alpha}$, where $S_{\nu}$ is the flux density at the frequency $\nu$.} and low surface brightness radio sources, which enclose -- albeit they are not obviously connected to -- the radio source associated with the central elliptical galaxy \citep[e.g.,][and references therein]{2014ApJ...781....9G}. Their emission typically fills the cooling region ($r\sim 50-300$ kpc) and often appears to be bounded by sloshing cold fronts, suggesting a casual connection between minihalos and gas sloshing \citep[S. Giacintucci et al. in preparation, M. Markevitch et al. in preparation]{2008ApJ...675L...9M,2013ApJ...777..163H,2014ApJ...781....9G}. The origin of minihalos in cool-core clusters and their possible connection with the giant radio halos found in merging clusters is still unclear \citep[e.g.,][for a review]{2014IJMPD..2330007B}. One possibility is that sloshing may amplify the magnetic fields and induce turbulence in the cluster cool cores \citep[hereafter Z13]{2004ApJ...612L...9F,2010ApJ...719L..74K,2011ApJ...743...16Z, 2012A&A...544A.103V,2013ApJ...762...78Z}. Numerical simulations show that such turbulence is generated mainly in the region enclosed by the cold fronts, with velocities up to $\sim 200$ km s$^{-1}$ on scales of tens of kpc, whereas negligible turbulence is driven outside the sloshing region (Z13). Turbulence in the cool core, in turn, may re-accelerate pre-existing, aged relativistic electrons in the intracluster medium (ICM) and, coupled with the amplification of the local magnetic field, generate diffuse radio emission within the cold front envelope with properties similar to the observed minihalos \citep[turbulent reacceleration models,][Z13]{2002A&A...386..456G}. As an alternative to turbulent reacceleration models, hadronic (or secondary) models posit that the radio-emitting electrons in minihalos are continuously injected by interactions between relativistic cosmic ray protons with the cluster thermal proton population \citep{2004A&A...413...17P,2007ApJ...663L..61F,2010ApJ...722..737K,2010arXiv1011.0729K,2012ApJ...746...53F,2013MNRAS.428..599F,2014MNRAS.438..124Z}. Recent numerical simulations of gas sloshing, modeling the formation of a minihalo from secondary electrons emitting in the sloshing-amplified magnetic field, have shown that, in these models, the radio emission is expected to be less confined within the sloshing region, due to the amplification of the magnetic field in regions outside the cold fronts (ZuHone et al. 2014). On average, the radio emission is found to be more extended than in the turbulent reacceleration simulations, where the turbulence, and thus the minihalo, are entirely confined to the region bounded by the cold fronts (Z13). \\ \\ In this paper, we present a radio/X-ray analysis of the cool-core cluster RX\,J1720.1+2638 (hereafter RX\,J1720.1) at $z=0.16$, which is host to a radio minihalo in its center. This cluster was the first relaxed system in which sloshing cold fronts have been revealed by {\em Chandra} \citep{2001ApJ...555..205M} as well as one of the first two clusters in which a correlation between minihalo and cold fronts has been reported \citep{2008ApJ...675L...9M}. Here, we use multi-frequency radio observations from the Giant Metrewave Radio Telescope (\gmrt) and Very Large Array (\vla) to study the spectral properties of the minihalo, which provide important information on the origin of the radio-emitting electrons, and investigate its connection with the sloshing cold fronts seen in the {\em Chandra} image. In Table 1, we summarize the general properties of RX\,J1720.1. We adopt $\Lambda$CDM cosmology with H$_0$=70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_m=0.3$ and $\Omega_{\Lambda}=0.7$. \begin{table}[t] \caption[]{Properties of the galaxy cluster RX\,J1720.1+2638} \begin{center} \begin{tabular}{lc} \hline\noalign{\smallskip} \hline\noalign{\smallskip} Parameter & Value \\ \hline\noalign{\smallskip} $^{\rm a}$ R.A.$_{\rm J2000}$ (h m s) & 17 20 09.3 \\ $^{\rm a}$ Decl.$_{\rm J2000}$ ($^{\circ}$ $^{\prime}$ $^{\prime\prime}$) & +26 37 38 \\ \phantom{0}$z$ & 0.16 \\ \phantom{0}$D_L$ (Mpc) & 765.4 \\ \phantom{0}Linear scale (kpc/$^{\prime \prime}$) & 2.758 \\ $^{\rm b}$ $L_{\rm X,\,500 \, [0.1-2.4 \, keV]}$ ($10^{44}$ erg s$^{-1}$) & $7.1$ \\ $^{\rm c}$ $kT$ (keV) & $6.3$ \\ $^{\rm d}$ $M_{\rm 500}$ ($10^{14}$ $M_{\odot}$) & $6.3$ \\ \noalign{\smallskip} \hline\noalign{\smallskip} \end{tabular} \end{center} \label{tab:sources} {\bf Notes.} $^{\rm a}$ J2000 X-ray coordinates from \cite{2011A&A...534A.109P}. $^{\rm b}$ $[0.1-2.4]$ keV X-ray luminosity within $R_{\rm 500}$ from \cite{2011A&A...534A.109P}, where $R_{\rm 500}$ is the radius corresponding to a total density contrast $500\rho_c(z)$, $\rho_c(z)$ being the critical density of the Universe at the cluster redshift. $^{\rm c}$ Global cluster temperature from \cite{2009ApJS..182...12C}. $^{\rm d}$ Cluster mass within $R_{500}$ from Planck collaboration et al. (2013). \end{table} \begin{table*} \caption[]{Radio observations of RX\,J1720.1+2638} \begin{center} \begin{tabular}{lccccccccc} \hline\noalign{\smallskip} \hline\noalign{\smallskip} Array & Project & Frequency & Bandwidth & Observation & Time & FWHM, p.a. & rms & $u-v$ range & $\theta_{\rm LAS}$ \\ & & (GHz) & (MHz) & date & (min) & ($^{\prime \prime} \times^{\prime \prime}$, $^{\circ}$)\phantom{00} & ($\mu$Jy b$^{-1}$) & (k$\lambda$) & ($^{\prime}$) \\ \noalign{\smallskip} \hline\noalign{\smallskip} {\em GMRT} & 11MOA01 & 0.317 & \phantom{0}12$^{\rm a}$ & 2007 Mar 8 & 220 & $9.1\times8.0$, 4 & 210 & 0.15-25.2 & 14 \\ {\em GMRT} & 11MOA01 & 0.617 & \phantom{0}11$^{\rm b}$ & 2007 Mar 10 & 250 & $5.0\times4.3$, $-71$ & 28 & 0.22-53.5 & 9\\ {\em GMRT} & 11MOA01 & 1.28 & 21 & 2007 Mar 8 & 320 & $2.5\times2.2$, 87 & 45 & 0.41-112 & 5 \\ {\em VLA}--BnA & AH988$^{\rm c}$ & 1.42 & 25 & 2009 Jan 26 & 60 & $3.8\times2.1$, 87 & 40 & 1.1-80 & 2\\ {\em VLA}--A & AE117 & 1.42 & 50 & 1998 Apr 12 & 20 & $1.5\times1.3$, 68 & 20 & 3.3-166 & 0.6 \\ {\em VLA}--B & AH190 & 1.48 & 25 & 1985 Apr 25 & 70 & $4.6\times3.7$, 68 & 30 & 0.5-52.5 & 4 \\ {\em VLA}--A & AF233 & 4.86 & 50 & 1992 Oct 20 & 1 & $0.8\times0.4$, 66 & 70 & 16-550 & $\sim 0.05^{\rm d}$\\ {\em VLA}--B & AH190 & 4.86 & 50 & 1985 Apr 25 & 30 & $1.4\times1.2$, 64 & 30 & 2.1-181 & 1 \\ {\em VLA}-C & AE125 & 4.86 & 50 & 1999 Jan 16 & 4 & $4.1\times3.6$, $-13$ & 40 & 0.7-53 & $\sim 2.5^{\rm d}$\\ {\em VLA}-DnC & AH0355 & 8.44 & 50 & 1989 Jun 2 & 3 & $6.1\times2.6$, 78 & 35 & 1.2-62 & $\sim1.5^{\rm d}$\\ \hline{\smallskip} \end{tabular} \end{center} \label{tab:obs} {\bf Notes.} Column 1: radio telescope. Column 2: project code. Columns 3--5: frequency, usable bandwidth after bandpass calibration, and observation date. Column 6: useful time on source after flagging. Columns 7 and 8: full width at half-maximum (FWHM) and position angle (PA) of the synthesized beam and rms noise level ($1\sigma$) in images made using a uniform weighting scheme ($ROBUST=-5$). Columns 9: effective $u-v$ range of the observation. Column 10: largest angular scale detectable by the array. \\ $^{\rm a}$ The observation was made using both USB (central frequency 333 MHz) and LSB (central frequency 317 MHz) with an observing bandwidth of 16 MHz each (before bandpass calibration), but only the LSB dataset was used for the analysis presented in this paper (see \S \ref{sec:gmrt} for details). \\ $^{\rm b}$ The observation was made using both USB (central frequency 617 MHz) and LSB (central frequency 602 MHz) with an observing bandwidth of 16 MHz each (before bandpass calibration), but only the USB dataset was used for the analysis presented in this paper (see \S \ref{sec:gmrt} for details). \\ $^{\rm c}$ An image from this observation has been presented by \cite{2012AJ....144...48H}. \\ $^{\rm d}$ Due to the short duration of this observation, the angular scale that can be imaged reasonably is much smaller than the nominal $\theta_{\rm LAS}$ of full-synthesis observations in the same array configuration ($0.15^{\prime}$ for {\em VLA}--A at 4.9 GHz, $5^{\prime}$ for {\em VLA}--C at 4.9 GHz and $3^{\prime}$ for {\em VLA}--DnC at 8.4 GHz; http://science.nrao.edu/facilities/vla/proposing/oss/ossjan09.pdf). \end{table*} \begin{table*} \caption[]{Properties of the Radio Galaxies} \begin{center} \begin{tabular}{lccccccccc} \hline\noalign{\smallskip} \hline\noalign{\smallskip} Radio Source & $S_{\rm 317 \, MHz}$ & $S_{\rm 617 \, MHz}$ & $S_{\rm 1.28 \, GHz}$ & $S_{\rm 1.48 \, GHz}$ & $S_{\rm 4.86 \, GHz}$ & $S_{\rm 8.44 \, GHz}$ & $\alpha_{\rm tot}$ & $P_{\rm 1.48 \, GHz}$ & Size \\ & (mJy) & (mJy) & (mJy) & (mJy) & (mJy) & (mJy) & & ($10^{24}$ W Hz$^{-1}$) & (kpc) \\ \noalign{\smallskip} \hline\noalign{\smallskip} point source (BCG) & \phantom{0}$24\pm2^{\rm a}$ & \phantom{0}$11\pm1^{\rm a}$ & $6.9\pm0.4$ & $6.7\pm0.3$ & \phantom{0}$2.3\pm0.1^{\rm b}$ & $1.4\pm0.1$ & $0.87\pm0.03$ & $0.47\pm0.02$ & $<1.4^{\rm c}$\\ head tail & $31\pm3$ & $12\pm1$ & $5.4\pm0.3$ & $5.5\pm0.3$ & $1.9\pm0.1$ & $1.0\pm0.1$ & $1.05\pm0.04$ & $0.39\pm0.02$ & \phantom{0}$140^{\rm d}$ \\ wide-angle tail & $72\pm6$ & $44\pm2$ & $30\pm2$ & $27\pm1$ & $-$ & $-$ & $0.64\pm0.06$ & $1.89\pm0.09$ & \phantom{0}$500^{\rm d}$ \\ \hline{\smallskip} \end{tabular} \end{center} \label{tab:flux} {\bf Notes.} Column 1: radio source. Columns 2--7: radio flux densities measured at full resolution (uniform weighting; Table \ref{tab:obs}). Column 8: total spectral index. Column 9: radio power at 1.48 GHz. Column 10: largest linear size. \\ $^{\rm a}$ Measured on images obtained using only baselines $>15$ k$\lambda$. \\ $^{\rm b}$ From the {\em VLA} B-configuration image (Fig.~\ref{fig:mh_center}b). \\ $^{\rm c}$ Beam-deconvolved size from a Gaussian fit to the source in the {\em VLA} A-configuration image at 4.9 GHz (Fig.~\ref{fig:mh_center}a). \\ $^{\rm d}$ Measured on the 617 MHz image (Fig.~\ref{fig:field}). \end{table*} \begin{figure*} \centering \includegraphics[width=0.89\textwidth,bb=40 70 450 397, clip]{fig1.pdf} \smallskip \caption{Radio and X-ray emissions in RX\,J1720.1. The size of the field is $18^{\prime}\times15^{\prime}$ (3 Mpc $\times$ 2.5 Mpc). The GMRT 617 MHz image at a resolution of $5.6^{\prime\prime}\times4.7^{\prime\prime}$, in p.a. $-74^{\circ}$ is shown as black and yellow contours, spaced by a factor of 2 starting from 0.2 mJy beam$^{-1}$. The extended radio sources are labelled. The X-ray image (color and white contours) is a wavelet reconstruction of the \xmm\ point source-subtracted image in the 0.5-2.5 keV band. The X-ray contours are spaced by a factor of $\sqrt2$.} \label{fig:field} \end{figure*} \begin{figure*} \centering \hspace{-0.5cm} \includegraphics[width=17cm]{fig2.pdf} \smallskip \caption{(a) \gmrt\ 617 MHz contours of the central minihalo in RX\,J1720.1 and nearby head-tail radio source, associated with a cluster member galaxy at $\sim 1^{\prime}.3$ from the BCG (see \S~\ref{sec:ps}). The radio image has been obtained using natural weighting and is overlaid on the optical r-band SDSS image. The restoring beam (black ellipse) is $7^{\prime\prime}.8\times6^{\prime\prime}.1$, in p.a. $-83^{\circ}$ and r.m.s. noise level is $1\sigma=30$ $\mu$Jy beam$^{-1}$. Contour levels are spaced by a factor of 2 starting from $+3\sigma$. Contours at $-3\sigma$ are shown as dashed. (b) Grayscale image at 617 MHz (same as (a)) with contours at 0.09 (black) and 1.4 (white) mJy beam$^{-1}$. The minihalo is composed by a bright central part (magenta region) and a much fainter tail to the south-east (blue region; \S~\ref{sec:mh}). The yellow circle marks the position of the radio point source associated with the BCG.} \label{fig:scheme} \end{figure*} \begin{figure*} \centering \includegraphics[width=17cm]{fig3.pdf} \smallskip \caption{(a) \vla\ A-configuration contours at 4.86 GHz, overlaid on the {\em HST} WFPC2 image of the BCG (grayscale). The restoring beam (black ellipse) is $0^{\prime\prime}.8\times0^{\prime\prime}.4$ , in p.a. $66^{\circ}$ and r.m.s. noise level is $1\sigma=70$ $\mu$Jy beam$^{-1}$. Contours are 0.2, 0.4, 0.6 mJy beam$^{-1}$. (b) \vla\ B-configuration image at 4.86 GHz (grayscale and contours) and (c) \vla\ A-configuration image at 1.42 GHz (grayscale and contours) of the point source at the BCG (white contours) and innermost region of the diffuse minihalo (black contours). The restoring beam is $2^{\prime\prime}$ (black circle) and $1^{\prime\prime}.9\times1^{\prime\prime}.5$, in p.a. $63^{\circ}$ (black ellipse), respectiveley. The r.m.s. noise levels are $1\sigma=30$ $\mu$Jy beam$^{-1}$ and $1\sigma=15$ $\mu$Jy beam$^{-1}$. Contours are spaced by a factor of 2 from $+3\sigma$. Contours at $-3\sigma$ are shown as dashed. The central box indicates the region covered by the image in panel (a).} \label{fig:mh_center} \end{figure*} | \label{sec:summ} We presented multi-frequency GMRT and VLA observations of the radio minihalo in the cool core of RX\,J1720.1, which constitute the most detailed radio dataset for this class of objects to date. The RXJ1720.1 minihalo consists of a bright central region that contains most of its flux density, and a $\sim 230$ kpc-long, arc-shaped tail of lower surface brightness. Based on our flux density measurements at six frequencies between 317 MHz and 8.44 GHz, we studied the integrated radio spectrum of the minihalo and its components. We found indication of a possible steepening of the spectrum above 5 GHz. This steepening is seen separately in the spectrum of the central region of the minihalo and possibly in the spectrum of the tail. Deeper, high-frequency observations are necessary to confirm this steepening and quantify the change of the spectral slope. If confirmed, the presence of a break has important implications for the physical mechanism responsible for the radio-emitting relativistic electrons. The map of the spectral index between 617 MHz and 1.48 GHz shows that the spectrum steepens systematically with increasing distance from the center, in particular, along the tail of the minihalo. We have shown that interpretations of this steepening that involve diffusion or advection of electrons produced in the central region and their aging along the way require extreme microphysical conditions or implausible gas velocities. The proposed mechanisms for the origin of minihalos are turbulent reacceleration and continuous injection of secondary electrons due to inelastic collisions between relativistic and thermal protons. The presence of a possible spectral break and strong spatial variations of the spectral index challenge the ``secondary'' origin of the minihalo and favors reacceleration by turbulence. As shown in MHD simulations (Z13), the required turbulence can be generated by sloshing of the low-entropy gas in the cluster cool core. Sloshing also amplifies the magnetic field in the core, increasing the radio emission from the cosmic-ray electrons. The turbulence should be limited to the volume enclosed by cold fronts visible in the X-ray. This scenario produces a radio minihalo entirely contained within the sharp boundaries at the positions of cold fronts --- exactly as we observe in RXJ1720.1. \\ \\ {\it Acknowledgements.} The authors thank the anonymous referee, whose comments and suggestions improved the paper. SG thanks Tracy Clarke for useful discussions. SG acknowledges the support of NASA through Einstein Postdoctoral Fellowship PF0-110071 awarded by the Chandra X-ray Center (CXC), which is operated by SAO. JAZ is supported under the NASA Postdoctoral Program. GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The scientific results reported in this article are based on observations made by the {\em Chandra} X-ray Observatory. | 14 | 3 | 1403.2820 |
1403 | 1403.5631_arXiv.txt | Bolometers are most often biased by Alternative Current (AC) in order to get rid of low frequency noises that plague Direct Current (DC) amplification systems. When stray capacitance is present, the responsivity of the bolometer differs significantly from the expectations of the classical theories. We develop an analytical model which facilitates the optimization of the AC readout electronics design and tuning. This model is applied to cases not far from the bolometers in the Planck space mission. We study how the responsivity and the NEP (Noise Equivalent Power) of an AC biased bolometer depend on the essential parameters: bias current, heat sink temperature and background power, modulation frequency of the bias, and stray capacitance. We show that the optimal AC bias current in the bolometer is significantly different from that of the DC case as soon as a stray capacitance is present due to the difference in the electro-thermal feedback. We also compare the performance of square and sine bias currents and show a slight theoretical advantage for the last one. This work resulted from the need to be able to predict the real behaviour of AC biased bolometers in an extended range of working parameters. It proved to be applicable to optimize the tuning of the Planck High Frequency Instrument (HFI) bolometers. | Bolometers are now the most sensitive receivers for astrophysical observations in the submillimetre spectral range. After decades of improvement, they are able to operate with a sensitivity limited by the photon noise of the observed source when operated outside of the atmosphere \cite{Bock2009}. The principle of a bolometer is that the heat deposited by the incoming radiation is measured by a thermometer. The theory of bolometers has been developed in founding papers \cite{Jones1953} and refined later \cite{Mather1982,Mather1984a,Mather1984b}. They have shown that their photometric responsivity strongly depends on its interaction with the readout electronics, through the variation of the electrical power deposited in the thermometer (the electro-thermal feedback). These theories have been developed for a semiconductor thermometer element biased by a Direct Current (DC) voltage through a load resistor. The readout electronics for bolometers experienced a radical change more than a decade ago. Most of them are now using a modulated bias current in order to get rid of low frequency noises that plague amplification systems \cite{Rieke1989,Wilbanks1990,Delvin1993,Gaertner1997,Kreysa2003}. The theory developed for a DC bias must be altered for Alternative Current (AC) biased bolometers in the presence of stray capacitance in the circuit. This was evidenced in the Planck-HFI instrument \cite{Lamarre2010} in spite of the fact that the readout electronics had been designed \cite{Gaertner1997} to mimic, as far as possible, the operation of a DC bias. Very significant differences were found in absolute responsivity and even in value of the optimal bias current for the Planck bolometers. This was shown to be mostly due to the effect of parasitic capacitances in the wiring, which cannot be neglected in many practical experimental setups. This effects have been studied in several papers dedicated to the characterization of bolometers and calorimeters by measuring their effective impedance (e.g. \cite{Vaillancourt2005}), but we are here essentially interested in effective tools able to predict the responsivity and optimise the tuning of bolometers in specific configurations. Brute force modelling based on numerical integration of thermal and electrical equations of the bolometers proved to be feasible but computationally too heavy to be applied on wide ranges of the many parameters of the models. To facilitate the computation, we have developed an analytical model of the responsivity of AC biased semiconductor bolometers. This model was used as an aid to predict the behaviour of the bolometer of Planck-HFI and to optimize their tuning. Its numerical application proved to be flexible and fast enough to study the effects of all variable parameters. This paper describes this analytical model and its application with a set of parameters not too far from the realistic cases encountered in Planck-HFI. The next section is dedicated to the differential equations driving the thermal and the electrical behaviour of the electro-thermal system comprising the bolometer and its readout electronics. It focuses on the derivation of an analytical solution giving the responsivity for both the DC and AC biased cases. Section three addresses the various noises encountered and shows that the optimal bias currents are different in the two cases. In the fourth section the model is applied to analyze the effects of some essential parameters (cold stage temperature, modulation frequency, value of the stray capacitance, optical background). Section five deals with the shape of the periodic bias wave to cover the case of square bias current used in Planck-HFI. | \begin{table}[t!] \centering \begin{tabular}{lcccccc} \hline & wavelength & $R_{*} [Ohm]$ & $G_{so} [pW/K]$ & $T_g [K]$ & $n$&$\beta$ \\ \hline Bolo \#1 & 3 mm & 100 & 52 & 16 & 0.5 & 1.3\\ Bolo \#2 & 1 mm & 94 & 70 & 16 & 0.5 & 1.3 \\ Bolo \#3 & 0.3 mm & 105 & 703 & 16.5 & 0.5 & 1.1\\ \hline \end{tabular} \caption{\emph{Parameters of the test bolometers used to illustrate the results of the analytical model.}}\label{tab:tab} \end{table} The analytical model presented in this paper has been developed for the HFI on board Planck satellite. It allowed us to predict the responsivity and the noise of semi-conductor bolometers cooled at 100 mK and biased by AC currents in a realistic environment. It sheds some light on the differences between AC and DC biased bolometer and on the different optimal bias currents for these two cases. Three test bolometers rather similar to Planck's ones were used to illustrate our results. Our main conclusions are: \begin{itemize} \item The AC responsivity is always lower than the DC responsivity. This is due to a more effective electro-thermal feedback. The resulting excess of NEP depends on the relative part of the preamplifier noise in the total NEP. In our test cases the excess NEP ranges from 4 \% to 10 \%, which is more than compensated for by shifting of the low frequency noises out of the range of useful frequencies. Frequencies down to 1 mHz are measurable with a well designed AC readout electronics. \item The AC bias RMS current providing to the maximum of the responsivity is about twice larger than that obtained for a DC bias. This concerns the current through the bolometer and results from the different electro-thermal feedback. \item For a stray capacitance of $\sim$ 150 pF we obtain an excess NEP of 10 \% in the worst case (3~mm bolometer) and 4\% in the best case (0.3 mm bolometer). \item Around a modulation frequency of 90 Hz, the excess NEP ranges between 0.2 \% and 0.5 \% per Hz. \item The sensitivity of NEP to background is dlog(NEP)/dlog(Wbg) = 0.22 to 0.42 \item The sensitivity of NEP to the plate temperature is dlog(NEP)/dlog(Tplate) = 0.3 to 0.8 around 100 mK, but is rather non-linear. \item The performances of a sine bias are better than the square bias. In our test cases, this result is more obvious in the responsivity (better by about 10 \%) than in the total NEP (better by about 4 \%). But non-linear effects may show up in the sine case for bolometers fast enough to respond to the modulation frequency. \end{itemize} | 14 | 3 | 1403.5631 |
1403 | 1403.0708_arXiv.txt | We study the influence of the large-scale interplanetary magnetic field configuration on the solar energetic particles (SEPs) as detected at different satellites near Earth and on the correlation of their peak intensities with the pa\-rent solar activity. We selected SEP events associated with X and M-class flares at western longitudes, in order to ensure good magnetic connection to Earth. These events were classified into two categories according to the global interplanetary magnetic field (IMF) configuration present during the SEP pro\-pagation to 1~AU: standard solar wind or interplanetary coronal mass ejections (ICMEs). Our analy\-sis shows that around 20\% of all particle events are detected when the spacecraft is immersed in an ICME. The correlation of the peak particle intensity with the projected speed of the SEP-associated coronal mass ejection is similar in the two IMF categories of proton and electron events, $\approx 0.6$. The SEP events within ICMEs show stronger correlation between the peak proton intensity and the soft X-ray flux of the associated solar flare, with correlation coefficient $r=\,$0.67$\pm$0.13, compared to the SEP events propagating in the standard solar wind, $r=\,$0.36$\pm$0.13. The difference is more pronounced for near-relativistic electrons. The main reason for the different correlation behavior seems to be the larger spread of the flare longitude in the SEP sample detected in the solar wind as compared to SEP events within ICMEs. We discuss to which extent observational bias, different physical processes (particle injection, transport, etc.), and the IMF configuration can influence the relationship between SEPs and coronal activity. | % \label{S-Introduction} Solar energetic particles (SEPs) are transient enhancements of the intensities of energetic protons, ions, and electrons observed in the interplanetary (IP) space. They are known to follow in time eruptive phenomena in the solar corona, such as flares and coronal mass ejections (CMEs). Both small scale processes during flares and CME-driven shock waves are used to explain the particle acceleration (see, {\it e.g.}, the review of \opencite{2006SSRv..123..217K}). The question how flares and CMEs affect SEPs is, however, largely unresolved, because particle measurements near 1~AU are related to the coronal accelerator through a poorly understood chain of processes of acceleration, access to, and propagation in the dynamic interplanetary medium. One approach to identify physical relationships between SEPs and the parent solar activity is statistical. Numerous studies have shown that SEP events are associated both with flares, as manifested, {\it e.g.}, by their soft X-ray \cite{2004SpWea...2.6003G} or radio (\opencite{1982ApJ...261..710K}, \citeyear{1982JGR....87.3439K}) emission, and with fast and broad coronal mass ejections \cite{1992ARA&A..30..113K,1999SSRv...90..413R}. The recent global study of SEP events in the 23rd solar cycle by \inlinecite{2010JGRA..11508101C} confirmed this. Pure cases of SEP events in association with fast CMEs lacking evidence of other, flare-like, acceleration processes in the corona are rare \cite{1986ApJ...302..504K} or non existent \cite{2006ApJ...642.1222M}. On the other hand, strong flares that are not accompanied by CMEs are not associated with SEP events (detectable by GOES) either, mostly because the flare-accelerated particles remain confined in coronal magnetic fields \cite{2010SoPh..263..185K,2011SoPh..269..309K}. More detailed statistical studies tried to relate the peak intensity of SEP events to parameters of the flare or the CME. \inlinecite{1990AN....311..379C} showed a close correlation between peak proton intensities measured in space and gamma-ray line fluxes, but others concluded that the ratio between the numbers of deka-MeV protons emitting gamma-ray lines and detected in situ varied considerably from event to event \cite{1989ApJ...343..953C,1993AdSpR..13..275R}. There are also indications for some statistical correlations between SEP intensities and microwave burst parameters \cite{1982JGR....87.3439K}. \inlinecite{2004SpWea...2.6003G} developed a very detailed empirical analysis relating the proton intensity at energies above 10~MeV to a combination of parameters of the soft X-ray (SXR) burst (peak flux, duration, and emission measure). Correlations between SEP peak intensities and CME parameters were also found, especially with the plane-of-the-sky speed of CMEs \cite{2001JGR...10620947K}. The reported correlation coefficients range between 0.6 and 0.7. Since the significance of correlation coefficients was either not assessed, or only confidence levels were given, it is hard to see if any difference in the correlation coefficients is statistically significant. The large scatter in most correlations was considered as an argument that other factors contribute to the efficiency of SEP acceleration. \inlinecite{2001JGR...10620947K} showed that correlations also exist between the SEP peak intensity and the pre-event intensity, and interpreted this as evidence that a pre-accelerated seed population increases the acceleration efficiency of a CME shock. \inlinecite{2004JGRA..10912105G} argued that CME interaction enhances SEP intensities. The main and inevitable limitation of such statistical studies is that SEP intensities are generally measured at only one point. Its magnetic connection to the accelerator in the corona is not well known. It is often approximated by a Parker spiral. But this may not be true, as has been shown by event studies where SEPs reach the detector in transient interplanetary magnetic field (IMF) structures, {\it i.e.} interplanetary coronal mass ejections or ICMEs \cite{1987JGR....92....6T,2004ApJ...600L..83T,2005JGRA..11009S06M,2011JGRA..11601104K}. \inlinecite{2012A&A...538A..32M} showed recently that the majority of relativistic SEP events of solar cycle 23 were detected within or in the vicinity of ICMEs. These ICMEs stem from solar activity that occurred one or several days before the SEP event, so that the magnetic configuration had the time to expand and reach the Earth. This paper presents a re-assessment of statistical relationships between the peak intensities (and fluences) of particle events ({\it i.e.}, near-relati\-vistic electrons of tens to hundreds of keV and deka-MeV protons), and the parameters of the associated coronal activity ({\it i.e.}, the peak SXR flux of the flare and the speed and width of the CME). Two categories of IMF configuration guiding the particles through the IP space are distinguished: standard solar wind and ICMEs. All SEP events of solar cycle 23 (1997$-$2006) that occurred with flares of classes M and X\footnote{GOES X-ray classification in the 1$-$8 \AA $\,$channel: M class flares have peak flux that exceeds $10^{-5}\,$W$\,$m$^{-2}$, whereas the X class flares are 10 times more intense.} in the western solar hemisphere are considered. The data sets and analysis technique are described in Section~\ref{S-Data}. Section~\ref{S-Observations} presents the observational findings: the identification of SEP events within ICMEs and within the standard solar wind, together with the distributions of peak particle intensities (Section~\ref{S-IP_field}), rise times (Section~\ref{S-Rise_time}), and connection distances to the parent flare (Section~\ref{S-Conn_dist}). In se\-parate subsections we address the following statistical relationships: between the flares and CMEs (Section~\ref{S-correlfc}), between the SEP intensity (Section~\ref{S-correlations}), and rise-to-peak fluence (Section~\ref{S-Fluence}), on one hand, and the parameters of the associated solar activity, on the other. The ICME category is discussed in more details in Section~\ref{S-ICME-category} and the effect of the connection distance on the correlations in Section~\ref{S-Corr_conn_dist}. Section~\ref{S-disc} addresses the influence of observational bias and physical effects on the correlation between the intensity of deka-MeV protons and near-relativistic electrons and the parameters of the parent coronal activity. | \label{S-disc} \subsection{Summary of Observational Findings} The results of the statistical study of SEP events of solar cycle 23 associated with flares of class M or X in the western solar hemisphere are summarized as follows: \begin{enumerate} \item A significant number of SEP events (about 20\% $-$ 17/81 GOES proton events and 18/96 ACE/EPAM electron events) were detected while the Earth was immersed in an interplanetary coronal mass ejection. This means that these deka-MeV protons and near-relativistic (tens to hundreds of keV) electrons were guided along transient interplanetary field lines, instead of the Parker spiral of the nominal solar wind. \item SEP events are relatively more often detected within ICMEs when the associated flare is of class X (10/35, 29\%) than of class M (7/46, 15\%). \item The peak intensities of electrons and protons cover a similar range for SEP events detected within ICMEs and in the standard solar wind. Indications of different peak intensity distributions in the two event categories are seen for protons, but they are not statistically significant. No such indication is seen for electrons. \item The proton profiles have a median rise time shorter (by a factor of 3) within ICMEs than in the solar wind. \item Contrary to protons, electrons have similar distributions of rise times in ICMEs and in the solar wind. \item The longitudes of the parent active regions of the SEP events cluster around the nominal Parker spiral with some scatter for the ICME events, but have a very broad distribution for the events detected in the solar wind. There is no evident dependence of the peak intensity of protons or electrons on the connection distance. \item The underlying relationship between flares and CMEs ({\it i.e.}, between peak SXR flux and CME speed) is stronger for ICME events ($r\,$=$\,$0.61$-$0.70) and weaker for SoWi events ($r\,$=$\,$0.23$-$0.28). The weak correlation is ascribed to the randomization of the projected CME speed in the SoWi category. We conclude that there is a stronger intrinsic correlation between SXR peak flux and CME speed in the two IMF categories. The correlation for the entire event sample ($r\,$=$\,$0.39$-$0.47) is comparable to previous reports. \item The correlation of SEP peak intensities $J_{\rm max}$ with the peak flux of the associated soft X-ray burst, $I_{\rm SXR}$, and the speed of the associated CME, $V_{\rm CME}$, depends on the IMF configuration: \begin{itemize} \item On average over all events, the correlation coefficients of $\log J_{\rm max}$$-$$\log I_{\rm SXR}$ and $\log J_{\rm max}$$-$$\log V_{\rm CME}$ are comparable, with values in the range 0.6$-$0.7 for the protons and 0.4$-$0.6 for the electrons. \item The correlation $\log J_{\rm p}$$-$$\log I_{\rm SXR}$ is twice as high in SEP events detected within ICMEs as for SEP events in the solar wind. The difference disappears when the sample is restricted to limb events. \item The correlation $\log J_{\rm e}$$-$$\log I_{\rm SXR}$ is about six times higher for the entire ICME sample and also for limb events as for SoWi sample. \item The correlation $\log J_{\rm max}$$-$$\log V_{\rm CME}$ is similar in both event categories and particle species. \end{itemize} \end{enumerate} \subsection{The IMF Configuration of SEP Events} The occasional detection of SEP events within ICMEs is a well-known phenomenon. ICMEs provide an evident explanation why fast rising SEP events are occasionally observed in association with activity in the eastern solar hemisphere \cite{1991JGR....96.7853R}. These authors estimated that about 15\% of SEP events from the eastern solar hemisphere have a rapidly rising intensity profile and showed that this may be due to propagation within an ICME. The percentage found in the present study for the SEP events from the western solar hemisphere ({\it i.e.}, 20\% arrive within ICMEs) is similar. The fraction of GOES SEP events detected within ICMEs increases with the flare size. Such trend is also found by a relativistic proton event study. \inlinecite{2012A&A...538A..32M} showed that 7/10 relativistic SEP events of solar cycle 23 occurred within or in the vicinity of ICMEs. The associated flares ranged from X5.7 to X14 (with the exception of one behind-the-limb event). The numbers are not directly comparable, because the events in the neighborhood of ICMEs are excluded from the ICME events in the present study. Nonetheless there appears to be a trend that the more energetic the flare associated with a particle event, the greater the likelihood to detect the SEP within or in the vicinity of an ICME. This probably reflects the fact that on the one hand the ICME rate is enhanced in periods of high activity \cite{2010SoPh..264..189R}, and that on the other hand strong flares \cite{1987ApJ...314..795B,2000ApJ...540..583S} and fast CMEs \cite{2008ApJ...680.1516W} preferentially occur in a small number of highly active regions. We found no significant evidence that the SEP intensity distributions differ between ICME events and SoWi events. However, ICME events display on average faster rises in the proton profiles than SoWi events. This is consistent with the reported long scattering mean free paths of energetic protons in ICMEs \cite{1987JGR....92....6T,2004ApJ...600L..83T}. No such effect is seen for the electrons. This is the first time, to our knowledge, that such a comparison is carried out. \subsection{IMF Configuration and the Correlation between SEP Parameters and Solar Activity} A number of studies in the literature report overall, but noisy, correlations between the logarithms of SEP proton ($J_{\rm p}$) intensity and the logarithms of SXR peak flux and/or CME speed. The correlation coefficients between $\log I_{\rm SXR}$ and $\log J_{\rm p}$ at deka-MeV energies were found near 0.5 (36 events in 1973$-$1979) from \inlinecite{1982ApJ...261..710K} or 0.4 (25 events in 1996$-$2001) from \inlinecite{2003GeoRL..30lSEP3G}. Higher correlation coefficients were reported with $\log V_{\rm CME}$: 0.7 (71 events in 1986$-$2000) from \inlinecite{2001JGR...10620947K} or 0.6 from \inlinecite{2003GeoRL..30lSEP3G}. \inlinecite{2010JGRA..11508101C} report the same value of 0.6 for the correlation with $\log I_{\rm SXR}$ and $\log V_{\rm CME}$ ($\approx$100 events in 1997$-$2006). No estimate of the uncertainty of these correlation coefficients was given. The overall correlations found in the present study between the logarithms of peak SEP intensity and SXR peak flux on the one hand, CME speed on the other, are comparable, with correlation coefficients in the range of 0.4$-$0.7 for both electrons and protons and a statistical uncertainty of about $\pm 0.07$. The entire event sample does not support the claim \cite{2003GeoRL..30lSEP3G} of a higher correlation coefficient of SEP peak intensities with CME speed than with soft X-ray flux. Our result agrees in this respect with that of \inlinecite{2010JGRA..11508101C} who reported a value of 0.6. A finer distinction between the two IMF categories $-$ the standard solar wind and ICMEs $-$ is subject to caution, because the solar wind sample is more strongly affected by projection effects on CME speeds (due to larger variety in longitudes of the associated flare) and variable connections between the parent solar activity and the Earth-connected IMF line. We find no difference between the correlation coefficients $\log J_{\rm max}$$-$$\log V_{\rm CME}$ in the two IMF categories, but a marked difference for the correlation $\log J_{\rm max}$$-$$\log I_{\rm SXR}$. This is true for both protons and electrons. For electron events propagating in the solar wind there is virtually no correlation between $\log J_{\rm e}$ and $\log I_{\rm SXR}$, while it is significant in ICME events. The behavior of protons is less clear: They show low correlation between $\log J_{\rm p}$ or peak fluence and $\log I_{\rm SXR}$ for the entire SoWi sample (as the electrons), but the difference disappears when the sample is restricted to limb events. However, it is uncertain if the latter relationship points to a real physical effect due to the small event sample involved and large error bars on the correlation coefficients. We conclude that the IMF structure likely affects the correlation between peak particle intensity and peak SXR flux, and that this difference comes mostly from the fact that the ICME events covers a narrower range of flare longitudes and connection distances than the SoWi events. \subsection{A Tentative Interpretation} The correlation between $\log J_{\rm max}$ on the one hand, and $\log V_{\rm CME}$ or $\log I_{\rm SXR}$ on the other, is not suited to discriminate clearly between CME-related and flare-related SEP acceleration processes. Statistical relationships do exist, but they appear to be strongly dependent on the location of the parent activity in the corona and the observer. Furthermore, the statistical relationship between SXR peak flux and CME speed is rather strong itself. This agrees with the recent findings of close relationships between CME kinematics and energy release in flares \cite{Zha:al-01,Bei:al-12}. Irrespective of the acceleration agent and mechanism, particles are released from the acceleration region in a direction that can cover a range of angular orientations and also be event-dependent. If it scatters around the normal to the photosphere, the direction of maximum particle intensity will be in some range around the longitude and latitude of the flare, and may well vary during the event ({\it cf.} \opencite{2012SoPh..276..199M}). Since they are detected at the Earth, the particles reach the magnetically well-connected IMF line, which is likely a Parker spiral on average, but again with a broad scatter ({\it e.g.}, \opencite{Smi-08book}). During their interplanetary travel the particles are also subject to pitch-angle scattering due to the magnetic inhomogeneities. All these effects will introduce additional blurring in the correlation between the particle intensity and the parameters of the parent activity. We consider in more details the IP transport and the connection distance. The estimation of rise time in the present study is used as a proxy for the IP transport. We find the rise times of proton profiles scatter over a much broader range in SoWi events than in ICME events. This suggests a broader variation of mean free paths with respect to pitch angle scattering in the SoWi events. One then expects that a given peak intensity at injection will be smeared out into a range of peak intensities at 1~AU, depending on the scattering conditions encountered. The much lesser dispersion of rise times in the ICME events is consistent with the long mean free paths found in some earlier studies. Then, any existing correlation between the peak SEP intensity and the flare strength will be better preserved in ICME events than in SoWi events. But while this argument works for protons, it does not for electrons: Electrons, like protons, show stronger correlation with SXR flux in ICME events than in SoWi events, but have similar (median values for the) rise times in the two IMF categories. So the interplanetary propagation of the SEP cannot be the only reason for the different correlations with peak SXR flux. The other difference between the ICME and SoWi samples is in the connection distance. We found that both electrons and protons tend to come from activity that is closer to the optimal magnetic connection with the Earth in ICME events than in SoWi events. Flare-related particle acceleration occurs in small volumes within or around an active region. The coronal magnetic field guiding the particles from the acceleration site to the magnetically well connected field lines is essential for the detection of flare-related particles. The broad scattering of connection distances observed in SoWi events then suggests a stronger blurring than in ICME events, and an ensuing loss of correlation between $J_{\rm max}$ and $I_{\rm SXR}$. The broad range in connection distances combined with a spread in injection angles of the SEPs may also be responsible for the flat distribution of the particle intensity with connection distances (see Figure~\ref{F-histo_cd}). A CME shock is a rather extended accelerator and is expected $-$ at least in simple scenarios $-$ to inject particles into a broad cone of interplanetary field lines. This makes the correlation of the peak SEP intensity with the CME speed less sensitive to the connection distance than the correlation with the SXR peak flux. At the present time such interpretation is speculative. Irrespective of the physical relationships, the usefulness of either the CME speed or the SXR peak flux in empirical schemes of SEP prediction is confirmed by the present study, with a greater sensitivity to the angular connection if the peak SXR flux is used. \begin{acks} The authors acknowledge D.~Boscher (ONERA Toulouse) for making the IPODE database of GOES particle measurements available to us. We also thank T. Dudok de Wit, M. Temmer, G. Trottet, H. Reid, and A. Veronig for helpful discussions and the referee for her/his comments. RM acknowledges a post-doctoral fellowship by Paris Observatory. The CME catalog is generated and maintained at the CDAW Data Center by NASA and The Catholic University of America in cooperation with the Naval Research Laboratory. SOHO is a project of international cooperation between ESA and NASA. \end{acks} \appendix \label{Appendix} Tables~\ref{T-ICME_events}$-$\ref{T-Other_events} summarize all data used in the paper, organized in different IMF categories, namely ICME, SoWi and SEP events in the vicinity of an ICME (Section~\ref{S-IP_field}). The events in each table are listed chronologically: The event date is given in column~(1). The proton and electron peak intensities (with their onset time) follow in columns (2)$-$(5). The next four columns give the SXR peak flux (with the onset time), the flare position on the western (W) hemisphere, the projected CME speed and the angular width (AW), as reported in catalogs or from previous works. The data sources are explained in detail in the footnotes under each Table. In column~(10) we give the temporal offset between the GOES SEP start (or at {\it Wind} at 1~AU) and the nearest-in-time boundary of the ICME (shifted at GOES orbit or as observed at 1~AU). This value is used as a confidence check for the identification of the IMF category. Although we used exclusively the timings of the ICME boundaries as reported in \inlinecite{2010SoPh..264..189R}, differences might exist with other ICME lists due to different definition used for an ICME, variation in the IMF data from different satellites and also due to the subjectivity of the observer. In the ICME category (Table~\ref{T-ICME_events}) two events are relatively close (about 2 h) to the reported ICME onset and may change category after a detailed analysis. All other events in this category are well within the body of the ICME. Similarly for the last SEP category (Table~\ref{T-Other_events}), some SEP events might be propagating in quiet solar wind conditions, although many are in the sheath region of the ICME or occur only several hours before or after the ICME boundary. Rise times are given in column~(11) in Tables~\ref{T-ICME_events} and \ref{T-SoWi_events}. Finally, in the last two columns in each table the solar wind speed (averaged values) and the connection distance are given. \begin{sidewaystable}[h] \caption[]{ICME solar energetic particle events.\\} \label{T-ICME_events} \tiny \vspace{0.5cm} \begin{tabular}{crrrr|rrrr|rrrr} \hline Event &\multicolumn{4}{c|}{Particle intensity$\quad$ (cm$^2$ s sr MeV)$^{-1}$} &\multicolumn{2}{c}{$\quad$Flare} & \multicolumn{2}{c|}{$\quad$CME} & \multicolumn{2}{c}{$\quad$SEP} & & \\ date & GOES & {\it Wind}/EPACT & \multicolumn{2}{c|}{ACE/EPAM ($\times 10^4$)} & Peak SXR & Long. & & & & Rise time & SoWi & Conn.\\ yymmdd& 15$-$40 & 19$-$28 & 38$-$53 & 175$-$135 & flux & W & speed & AW & offset & (2)/(3)/(4)/(5) & speed & dist.\\ & [MeV] & [MeV] & [keV] & [keV] & [W$\,$m$^{-2}$] & [deg] & [km/s] & [deg] & [hrs] & [min] & [km/s] & [deg] \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) & (12) & (13) \\ \hline 98 05 02 & 5.2 (14:00) & 1.5 (14:00) & 22 (13:55) & 1 & X1.1 (13:31) & 15 & 938 & 130 & $-$8.2 & 8/18/19/5 & 619 & $-$23\\ 98 05 06 & 8.7 (08:30) & 5.7 (08:30) & 140 (08:10) & 4.1 & X2.7 (07:58) & 65 & 1099 & 90 & +39.2 & 9/11/4/$-$ & 506 & ~18\\ 99 12 28 & $-$ & 0.006$^w$ (02:00) & 3.6 (01:45) & 0.11 & M4.5 (00:39) & 56 & 672 & 60 & +2 & $-$/$-$/62/18 & 465 & 5\\ 00 06 25 & 0.04 (12:30)$^{d}$& 0.03 (12:00)$^{d}$& 0.45 (08:00) &0.0032& M1.9 (07:17) & 55 & 1617 & 70 & +20.3 & $u$ & 508 & 9\\ 00 07 14 & 312 (10:30) & 88 (10:40) & 72 (10:40) & 12 & X5.7 (10:03) & 7 & 1674 & 360 & +5.2 & 11/6/5/6 & 579 & $-$34\\ 00 08 12 & 0.06 (11:00) & 0.05$^{u}$ (11:00) & 0.47 (10:55) &0.0046& M1.1 (09:45) &(79)& 662 & 60 & $-$5.3 & $u$ & 617 &(41)\\ 00 09 09 & $-$ & 0.02 (10:00) & 0.21 (10:00) &0.0077& M1.6 (08:28) & 67 & 554 & 70 & $-$22 & $-$/$-$/25/58 & 468 & 17 \\ 00 09 19 & 0.03 (14:00)$^{d}$& 0.02 (13:00)$^{d}$& 2.3 (09:15) & 0.019& M5.1 (08:06) & 46 & 766 &60 & +34.7 & $u$/$u$/81/65 & 672 & 11 \\ 00 11 08 & 377 (23:30) & 179$^{u}$ (23:00) & 240 (23:00) & 32 & M7.4 (22:42) &[78]& 1738 &120 & $-$9.6 & 6/4/4/2 & 460 &[27]\\ 01 03 29 & 0.9 (12:30) & 0.66 (12:00) & 7.9 (10:37) & 0.35 & X1.7 (09:57) & 19 & 942 & 360 & $-$18.7& 69/45/74/20 & 566 & $-$23\\ 01 04 02 & 0.09 (12:00) & 0.08 (13:00) & $-$ & $-$ & X1.1 (10:58) &(62)& 992 & 50 & +28.8 & 119/6$^u$/$-$/$-$ & 585 & (22)\\ 01 04 02 & 43 (23:00) & 36$^m$ (23:00) & 46 (22:05) & 2.2 & X20 (21:32) &[70]& 2505 & 100 & +16.7 & 18/4/14/9 & 543 & [27]\\ 01 04 12 & 1$^{m}$ (11:30) & 0.75$^{m}$ (12:00) & $-$ & $-$ & X2.0 (09:39) & 43 & 1184 & 120 & $-$12.9& $u$/$-$ & 633 & 6\\ 01 10 22 & 0.5 (16:40)$^{d}$ & 0.4 (17:00)$^{d}$ & 0.92 (01:13) & 0.0076& M1.0 (00:22)& 57 & 772 & 20 & $-$8 & 53/$u$/186/196 & 553 & 14 \\ 02 04 21 & 81.5 (01:30) & 81 (01:30) & 84 (01:40) & 3.5 & X1.5 (00:43) & 84 & 2393 & 120 & +17.3 & 15/11/3/2 & 485 & 35\\ 02 08 03 & $-$ & 0.007$^{w}$ (00:00)$^{nd}$& 0.9 (20:05)& 0.01 & X1.0 (18:59) & 76 & 1150 & 30 & +2.4 & $-$/$u$ & 497 & 29\\ 02 08 20 & 0.07 (09:00) & 0.37 (09:00) & 40 (08:52) & 1.3 & M3.4 (08:22) & 38 & 1099 & 40 & $-$20.1& 54/37/14/13 & 466 & $-$13 \\ 02 12 22 & $-$ & 0.02$^w$ (14:00)$^{d}$ & $-$ & $-$ & M1.1 (02:14) & 42 & 1071 & 80 & +5 & $-$ & 454 & $-$10 \\ 03 05 31 & 0.73 (03:00) & 0.57 (03:00) & 14 (02:55) & 0.65 & M9.3 (02:13) & 65 &1835 & 150 & $-$4.4 & 20/15/19/9 & 702 & 31 \\ 03 08 19 & $-$ & 0.007 (10:00) & 2.9$^{w}$ (08:30)& 0.045& M2.0 (07:38)& 63 & 412 & 40 & +5.9 & $-$/$-$/16/15 & 467 & 12 \\ 03 10 29 & 57$^m$ (21:30) & 94$^m$ (21:30) & 150 (22:05) & 12 & X10 (20:37) & 2 & 2029 & 360 & +5.8 & $u$ & 812$^{s}$ & $-$27\\ 04 11 10 & 1.5$^m$ (03:00)& 5.5$^m$ (06:00) & $-$ & $-$ & X2.5 (01:59) & 49 & 3387 & 120 & $-$6.4 & 14/37/$-$/$-$ & 758 & 18\\ \hline \end{tabular} \footnotetext{Column (7) lists the heliographic west longitude of the flare according to: the preliminary listings of the GOES solar X-ray flares in the {\it Solar Geophysical Data} (SGD), the corresponding H$\alpha$ flare longitude in the comprehensive reports in the SGD (in the parentheses), or the daily flare active region longitude reported in \url{SolarMonitor.org} (in square brackets). In column (9), the angular width \cite{2010JGRA..11508101C} of the corresponding CME is given. Column (10) lists the temporal offset in hours between the SEP start at GOES data (or {\it Wind}/EPACT when no event in GOES is observed) and the nearest ICME boundary, {\it i.e.}, a positive value denotes the time from the SEP onset to the end of the ICME and a negative value $-$ to the start of the ICME. \\ {\it C}: proton intensity from \inlinecite{2010JGRA..11508101C}; {\it d}: delayed SEP onset; {\it m}: multiple SEP intensity peaks; {\it nd}: next day; {\it s}: strong increase in the solar wind speed (1-h average data) during the 6-h period before the SEP onset; {\it w}: weak SEP intensity; {\it u}: uncertain.} \end{sidewaystable} \begin{sidewaystable}[h] \caption[]{SoWi solar energetic particle events.\\} \label{T-SoWi_events} \tiny \vspace{0.5cm} \begin{tabular}{crrrr|rrrr|rrrr} \hline Event &\multicolumn{4}{c|}{Particle intensity$\quad$ (cm$^2$ s sr MeV)$^{-1}$} &\multicolumn{2}{c}{$\quad$Flare} & \multicolumn{2}{c|}{$\quad$CME} & \multicolumn{2}{c}{$\quad$SEP} & & \\ date & GOES & {\it Wind}/EPACT & \multicolumn{2}{c|}{ACE/EPAM ($\times 10^4$)} & Peak SXR & Long. & & & & Rise time & SoWi & Conn.\\ yymmdd& 15$-$40 & 19$-$28 & 38$-$53 & 175$-$135 & flux & W & speed & AW & offset & (2)/(3)/(4)/(5) & speed & dist.\\ & [MeV] & [MeV] & [keV] & [keV] & [W$\,$m$^{-2}$] & [deg] & [km/s] & [deg] & [days] & [min] & [km/s] & [deg] \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) & (12) & (13) \\ \hline 97 05 21 & $-$ & 0.006$^w$ (21:00) & $-$ & $-$ & M1.3 (20:08) & 12 & 296 & 30 & +4.8 & $-$ & 311 & $-$64 \\ 97 11 03 & $-$ & 0.005$^u$ (12:00) & 0.23 (10:50) & 0.0059 & M4.2 (10:18) &(22)& 352 & 100& +3.7 & $-$ & 317 & ($-$52) \\ 97 11 04 & 2$^m$ (06:30)& 1 (07:00) & 12 (06:24) & 0.46 & X2.1 (05:52) & 33 & 785 & 110& +2.9 & 22/38/$-$/$-$ & 307 & $-$44 \\ 98 11 05 & \multicolumn{2}{c}{{\it 0.0006 ($<$22:00)}$^C$}& $-$& $-$& M8.4 (19:00) & 18 & 1118 &60& +2 & $-$ & 433 & $-$36 \\ 98 12 17 & \multicolumn{2}{c}{{\it 0.0003 (11:00)}$^C$} & 0.4 (08:20) & 0.0086 & M3.2 (07:40) & 46 & 302 & $-$& +12.3 & $-$/$-$/13/60 & 382 & $-$16 \\ 99 08 28 & \multicolumn{2}{c}{{\it 0.0005 (20:00)}$^C$} & $-$ & $-$ & X1.1 (17:52) & 14 & 462 & 110 & $-$5.4 & $-$ & 642 & $-$23 \\ 00 03 03 & $-$ & 0.01$^w$ (03:00) & 1 (02:30) & 0.029 & M3.8 (02:08) & 60 & 841 & 80 & $-$1 & $-$/$u$/24/$<$5 & 423 & 4 \\ 00 03 22 & 0.03 (19:00) & 0.02 (19:00) & $-$ & $-$ & X1.1 (18:34) & 57 & 478 & 80 & $-$3.25 & $u$/$-$ & 473 & 7\\ 00 04 04 & 0.62 (16:30) & 0.57 (18:00) & 17.5 (15:33) & 0.0946 & C9.7 (15:12) & 66 & 1188 & 60& +2.7 & 29/53/4/$<$5 & 380 & 4 \\ 00 05 01 & 0.04 (10:30) & 0.007$^{u}$ (11:00) & 74 (10:23) & 1.3 & M1.1 (10:16) & 54$^c$&1360 & 20& +1.4 & $u$/$u$/$<$5/$<$5 & 436 & 0 \\ 00 06 15 & \multicolumn{2}{c}{{\it 0.001 (21:00)}$^C$} & 7.3 (19:52) & 0.025 & M1.8 (19:38) & 65 & 1081 & 70 & $-$1.6 & $-$/$-$/$<$5/$<$5 & 606 & 26 \\ 00 06 17 & 0.03 (05:00) & 0.01 (05:00) & 16 (03:20) & 0.086 & M3.5 (02:25) & 72 & 857 & 60 & +1.2 & $u$/$u$/12/20 & 472 & 22 \\ 00 07 22 & 0.52 (12:00) & 0.34$^m$ (12:00) & $-$ & $-$ & M3.7 (11:17) & 56 & 1230 & 80 & +1.1 & 22/32/$-$/$-$ & 449 & 3 \\ 00 09 12 & 5.5 (14:30) & 3.4 (14:00) & 4.5 (12:47) & 0.26 & M1.0 (11:31) & 9 & 1550 & 100& $-$2.1 & 36/53/13/14 & 468 & $-$41 \\ 00 11 24 & 0.23 (06:30) & 0.15 (06:00) & 2.3 (05:50) & 0.078 & X2.0 (04:55) & (5)& 1289 & 360& +3.1 & 45/80/63/59 & 318 & ($-$69)\\ 00 11 24 & 2.2$^m$ (15:30) & 1.8$^m$ (15:30) & 14 (15:43) & 0.51 & X2.3 (14:51) & 7 & 1245 & 360& +2.7 & 64/79/28/29 & 410 & $-$50\\ 01 01 28 & 0.73 (16:30) & 0.63$^m$ (16:30) & 5.1 (16:35) & 0.2 & M1.5 (15:40) & 59 & 916 & 120& $-$2.4 & 24/68/30/15 & 326 & $-$13 \\ 01 03 10 & \multicolumn{2}{c}{{\it 0.002 (08:00)}$^C$} & 0.73 (05:40) & 0.028 & M6.7 (04:00) & 42 & 819 & 20& $-$5.3 & $-$/$-$/33/57 & 419 & $-$14 \\ 01 04 10 & 2.7 (08:00) & 2.6 (08:00) & 5.8 (05:55) & 0.21 & X2.3 (05:06) & 9 & 2411 & 360& $-$1.1 & 76/123/162/130 & 535& $-$35 \\ 01 04 26 & \multicolumn{2}{c}{{\it 0.0003 ($<$22:00)}$^C$} & 0.7 (13:30) & 0.0051 & M7.8 (11:26) & 31 & 1006 & 360& +1.7 & $-$/$-$/19/$w$ & 433 & $-$25 \\ 01 07 19 & \multicolumn{2}{c}{{\it 0.0003 (11:00)}$^C$} & 0.88 (10:20) & 0.018 & M1.8 (09:52) & 62 & 1668 & 40& $-$5.4 & $-$/$-$/70$^u$/77 & 601 & 23 \\ 01 10 19 & 0.18 (02:00) & 0.14 (02:30) & 1.1 (02:20) & 0.036 & X1.6 (00:47) & 18 & 558 & 180 & +2.8 & 34/81/32/51 & 309& $-$58 \\ 01 10 19 & 0.18 (17:30) & 0.22$^m$ (17:30) & 1.9 (17:10) & 0.039 & X1.6 (16:13) & 29 & 901 & 160 & +2.1 & 81/139/27/35 & 326 & $-$43 \\ 01 11 04 & 39$^m$ (16:30)& 284 (16:30) & 88 (16:45) & 5.7 & X1.0 (16:03) & 18 & 1810 & 130 & +1.1 & 101/19/8/4 & 310 & $-$58 \\ 01 11 22 & 177 (21:00) & 103 (21:00) & 64 (21:00) & 3.1 & M3.8 (20:18) & 67 & 1443 & 120 & $-$1.3 & 16/35/19/7 & 433 & 13 \\ 01 12 26 & 23 (05:30) & 22 (06:00) & 80 (05:40) & 2.5 & M7.1 (04:32) & 54 & 1446 & 90 & +1.8 & 11/16/6/6 & 384 & $-$7 \\ \hline \end{tabular} \footnotetext{Here, column (10) lists the temporal offset in days between the SEP start from GOES data (or {\it Wind}/EPACT when no event in GOES is observed) and the nearest ICME boundary: Positive (negative) values denote the time from the SEP onset to the start (end) of the ICME following (preceeding) the SEP event, respectively.} \footnotetext{{\it c}: flare longitude as reported by \inlinecite{2010JGRA..11508101C}; {\it m}: multiple SEP intensity peaks; {\it w}: weak SEP intensity; {\it u}: uncertain.} \end{sidewaystable} \begin{sidewaystable}[h] \addtocounter{table}{-1} \caption[]{SoWi solar energetic particle events (cont'd).\\} \label{T-SoWi_events1} \tiny \vspace{0.5cm} \begin{tabular}{crrrr|rrrr|rrrr} \hline Event &\multicolumn{4}{c|}{Particle intensity$\quad$ (cm$^2$ s sr MeV)$^{-1}$} &\multicolumn{2}{c}{$\quad$Flare} & \multicolumn{2}{c|}{$\quad$CME} & \multicolumn{2}{c}{$\quad$SEP} & & \\ date & GOES & {\it Wind}/EPACT & \multicolumn{2}{c|}{ACE/EPAM ($\times 10^4$)} & Peak SXR & Long. & & & & Rise time & SoWi & Conn.\\ yymmdd& 15$-$40 & 19$-$28 & 38$-$53 & 175$-$135 & flux & W & speed & AW & offset & (2)/(3)/(4)/(5) & speed & dist.\\ & [MeV] & [MeV] & [keV] & [keV] & [W$\,$m$^{-2}$] & [deg] & [km/s] & [deg] & [days] & [min] & [km/s] & [deg] \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) & (12) & (13) \\ \hline 02 02 20 & 0.55 (06:30) & 0.24 (06:30) & 43 (06:05) & 0.9 & M5.1 (05:52) & 72 & 952 & 50 & +8.5 & 13/6/3/5 & 404 & 14 \\ 02 03 15 & 0.05 (02:00)$^{nd}$& 0.01$^{u}$ (01:00)$^{nd}$& 0.9 (00:30)$^{nd}$& 0.027& M2.2 (22:09) & 3 & 957 & 360 & +3.2 & 350/485/39/35 & 345 & $-$65 \\ 02 04 15 & \multicolumn{2}{c}{{\it... (03:00)}$^C$}& 4.8 (03:00) & 0.029 & C9.8 (02:46) & 79 & 674 & 45 & $-$1.6 & $-$/$-$/$<$5/$<$5 & 373 & 16 \\ 02 07 15 & 1.3 (11:00)$^{nd}$& 1$^m$ (09:00)$^{nd}$& $-$& $-$ & X3.0 (19:59) & 1 & 1151 & 100& +2.1 & 91/120/$-$/$-$ & 344 & $-$68\\ 02 08 14 & 0.29$^m$ (02:30) & 0.32$^m$ (02:30) & 78 (02:00) & 0.48 & M2.3 (01:47) & 54 & 1309 & 60 & +5.45 & $u$/$u$/3/6 & 444 & 1\\ 02 08 16 & 0.02 (07:00) & 0.01$^w$ (08:00) & 19 (06:30) & 0.054 & M2.4 (05:46) & 83 & 1378 & 70 & +3.3 & $u$/$u$/3/5 & 597 & 44 \\ 02 08 24 & 10$^m$ (01:30) & 10$^m$ (01:30) & 19 (01:30) & 1.1 & X3.1 (00:49) & 81 & 1913 & 150& $-$2.4& 13/7/5/5 & 384 & 20\\ 02 11 09 & 9.2 (15:00) & 8.3 (15:30) & 1.9 (14:00) & 0.055 & M4.6 (13:08) & 29 & 1838 & 90 & +7.8 & 31/31/23/26 & 365 & $-$36 \\ 03 03 17 & 0.02 (20:00) & 0.01 (19:30) & 2.9 (19:14) & 0.052 & X1.5 (18:50) & 39 & 1020 & 50 & $-$1.9& $u$/$u$/8/$<$5 & 722 & 6\\ 03 03 18 & 0.03 (14:00) & 0.01 (14:00) & 49 (12:30) & 0.32 & X1.5 (11:51) & 46 & 1042 & 80 & $-$1.1& $u$/$u$/5/8 & 762 & 15 \\ 03 04 23 & $w$ & 0.01 (02:00) & 0.15 (01:15)& 0.0076& M5.1 (00:39) & 25 & 916 & 70 & +16.2 & $u$/$u$/$u$/15 & 518 & $-$21 \\ 03 04 24 & 0.04 (13:30) & 0.02 (13:00) & 0.91 (13:10)& 0.0093& M3.3 (12:45) & 39 & 609 & 45 & +14.75& 60/$u$/8/$<$5 & 459 & $-$12 \\ 03 05 27 & \multicolumn{2}{c}{{\it 0.0003 (22:00)}$^C$} & $-$ & $-$ & X1.3 (22:56) & 17 & 964 & 360 & +1.6 & $-$ & 468 & $-$30 \\ 03 11 04 & 11.7 (21:30) & 10.5 (21:25) & 6 (20:25) & 0.38 &X28 (19:29) & 83 & 2657 & 130& $-$2.9& 123/100/$u$/187 & 637 & 46\\ 04 02 04 & $-$ & 0.006$^w$ (12:00) & 0.5 (11:26) & 0.0097 & C9.9 (11:12)& 48 & 764 & 20 & $-$10.3& $-$/$-$/243/42 & 568 & 6 \\ 04 04 11 & 0.64 (06:00) & 0.5 (06:00) & 2.9 (04:36) & 0.14 & C9.6 (03:54) & 47 & 1645 & 90 & $-$5.5& 39/37/$<$5/10 & 441 & $-$6 \\ 04 07 13 & 0.04 (01:00) & 0.03 (01:30) & 0.17 (00:40)& 0.0063& M6.7 (00:09)&[60] & 607 & 60 & +9.7 & 71/327/122/74 & 506 & [13]\\ 04 10 30 & 0.06 (07:00) & 0.03$^m$ (07:30) & 5.4$^u$ (06:25) & 0.062$^u$ & M4.2 (06:08)& 21 & 422 & 90& +8.65 & 110/251/14/21 & 387 & $-$40 \\ 05 05 06 & 0.05 (07:30) & 0.03 (05:00) & 8.4 (03:47) & 0.078 & C9.3 (03:05)& (74) & 1120 & 20& +9 & 380/202/52/62 & 338$^{s}$ & (4)\\ 05 05 06 & 0.03 (16:30) & 0.03 (15:00) & 30 (12:00) & 0.046 & M1.3 (11:11)&(80)& 1144 & 30 & +8.5 & $u$/$u$/86/82 & 357 &(14)\\ 05 05 11 & 0.03$^{nd}$ (21:30) & 0.01 (21:00) & 0.8 (20:00) & 0.0074& M1.1 (19:22)&(47)& 550 & 70 & +3.4 & $u$/$u$/38/79 & 461 &($-$4) \\ 05 07 13 & \multicolumn{2}{c}{{\it 0.0003 (05:00)}$^C$} & 4.7 (04:10) & 0.013 & M1.1 (02:35) &[79]& 759 & 40 & $-$1.04 & $-$/$-$/16/30 & 525 & [34] \\ 05 07 13 & 0.34 (16:30) & 0.22 (16:00) & 23 (14:40) & 0.22 & M5.0 (14:01) & (80) & 1423 & 70 & $-$1.5 & 133/168/26/16 & 580 & (39) \\ 05 08 22 & 0.22 (02:00) & 0.2 (02:00) & 11 (01:17) & 0.15 & M2.6 (00:44) & (48) & 1194 & 160 & +1.95 & 47/42/5/13 & 537 & (4) \\ 05 08 22 & 10.7 (19:00) & 8.5 (19:00) & 58 (17:40) & 1.2 & M5.6 (16:46) & [62] & 2378 & 100 & +1.25 & 47/66/16/15 & 545 & [19] \\ 06 07 06 & 0.08 (09:00) & 0.07 (10:00) & 0.24 (09:05)& 0.0057& M2.5 (08:13) & (32) & 911 & 160 & +4.5 & 65/22823$^u$/69$^u$ & 576 & ($-$9) \\ 06 12 13 & 25 (02:30) & 20.4 (03:00) & 120 (02:41) & 5.4 & X3.4 (02:14) & (24) & 1774 & 180 & +1.8 & 17/23/$<$5/$<$5& 665$^W$ & ($-$13)\\ \hline \end{tabular} \footnotetext{{\it d}: delayed SEP onset; {\it m}: multiple SEP intensity peaks; {\it nd}: next day; {\it s}: strong increase in the solar wind speed (1-h average data) during the 6-h period before the SEP onset; {\it w}: weak SEP intensity; {\it W}: solar wind data from {\it Wind}/SWE; {\it u}: uncertain.} \end{sidewaystable} \begin{sidewaystable}[h] \caption[]{Solar energetic particle events in the vicinity of an ICME.\\} \label{T-Other_events} \tiny \vspace{0.5cm} \begin{tabular}{crrrr|rrrr|rrr} \hline Event &\multicolumn{4}{c|}{Particle intensity$\quad$ (cm$^2$ s sr MeV)$^{-1}$} &\multicolumn{2}{c}{$\quad$Flare} & \multicolumn{2}{c|}{$\quad$CME} & & & \\ date & GOES & {\it Wind}/EPACT & \multicolumn{2}{c|}{ACE/EPAM ($\times 10^4$)} & Peak SXR & Long. & & & SEP & SoWi & Conn.\\ yymmdd& 15$-$40 & 19$-$28 & 38$-$53 & 175$-$135 & flux & W & speed & AW & offset & speed & dist.\\ & [MeV] & [MeV] & [keV] & [keV] & [W$\,$m$^{-2}$] & [deg] & [km/s] & [deg] & [hrs] & [km/s] & [deg] \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) & (12) \\ \hline 97 11 06 & 14.6 (12:30) & 13.2 (12:30) & 47 (12:35) & 3.4 & X9.4 (11:49) & 63 & 1556 & 115 & +16.5 & 359 & $-$3 \\ 99 06 04 & 1.4 (08:15) & 1$^m$ (08:00)& 16 (07:22) & 0.53 & M3.9 (06:52) & 69 & 2230 & 80 & $-$9.3 & 428 & 14 \\ 99 06 27 & $-$ & 0.01 (10:00) & 1.1 (09:00) & 0.0164 & M1.0 (08:34) & 25 & 903 & 40 & +10 & 479 & $-$24 \\ 00 02 12 & 0.05 (05:20) & 0.05 (06:00) & 1.1 (04:50) & 0.013 & M1.7 (03:51) & 23 & 1107 & 110 & sheath & 573 & $-$18 \\ 00 03 02 & 0.03 (09:00) & 0.02 (10:00) & 0.51 (08:46) & 0.025 & X1.1 (08:20) &(52)& 776 & 60 & $-$5.15 & 437 & ($-$2) \\ 00 05 23 & \multicolumn{2}{c}{{\it 0.002 (22:00)} Cane {\it et al.} (2010)} & 4.7 ($-$) & 0.031 & C9.5 (20:48) & 43 & 475 & 50 & sheath & 591 & 3 \\ 00 06 10 & 1.4 (17:30) & 1.7 (17:30) & 60 (17:09) & 0.53 & M5.2 (16:40) & 38 & 1108 & 120 & $-$0.01 & 512 & $-$8 \\ 00 06 18 & 0.07 (02:30) & 0.05$^m$ (03:00) & 3.2 (02:22) & 0.067 & X1.0 (01:52) & 85 & 629 & 70 & +7.6 & 432 & $-$30 \\ 00 06 23 & 0.05 (15:45) & 0.02 (15:30) & 23 (14:45) & 0.16 & M3.0 (14:18) & 72 & 847 & 60 & sheath & 494 & 24 \\ 01 04 09 & 0.16 (16:35) & 0.1 (17:00) & 1.7 (16:34) & 0.081 & M7.9 (15:20) & 4 & 1194 & 360 & $-$12.6 & 521 & $-$41 \\ 01 04 14 & $-$ & 0.02$^{u}$ (18:00) & 51 (17:35) & 0.43& M1.0 (17:15) & 71 & 830 & 50 & $-$6 & 655 & 35 \\ 01 04 15 & 30.4 (14:00) & 30.5 (14:00) & 62 (14:05) & 5.5 & X14.4 (13:19)& 85 &1129 & 110 & +2.8 & 499 & 38 \\ 01 09 12 & $-$ & 0.01$^{u}$ (22:30) & $-$ & $-$ & C9.6 (21:05) & 62$^c$& 668 & 30& +19.5 & 356 & $-$4 \\ 01 09 15 & 0.33 (12:10) & 0.19 (12:30) & 2.3 (12:07) & 0.028 & M1.5 (11:04) & 49 & 478 & 80 & $-$13.2 & 526 & 4 \\ 02 04 11 & 0.03 (17:30) & 0.08 (17:00) & 6.1 (16:40) & 0.0155 & C9.2 (16:16) & 33 & 540 & 50 & +8 & 475 & $-$17 \\ 02 04 14 & $-$ & 0.01 (13:00)$^d$ & 0.8 (09:00) & $-$ & C9.6 (07:28) & 57 & 757 & 50 & $-$23.9 & 386 & $-$4 \\ 02 04 17 & 0.47 (11:20)$^d$ & 0.46 (11:00)$^d$ & 84 ($-$) & 0.67 & M2.6 (07:46) & 34 & 1240 & 70 & +5.5 & 333 & $-$37 \\ 02 08 18 & 0.05 (22:35) & 0.06 (23:00) & 12 (21:41) & 0.11 & M2.2 (21:12) & 19 & 682 & 100 & sheath & 472$^s$& $-$31 \\ 02 08 19 & \multicolumn{2}{c}{{\it 0.017 (10:00)}$^C$} & 55 (10:55) & 0.47 & M2.0 (10:28) & 25 & 549 & 80 & sheath & 532 & $-$19 \\ 02 08 22 & 1.1 (02:50) & 0.5$^m$ (03:00) & 10 (02:21)& 0.15 & M5.4 (01:47) & 62 & 998 & 80 & $-$12.1 & 416 & 5 \\ 02 12 19 & 0.06 (00:55)$^{nd}$ & 0.11 (22:30) & 6.6 (22:00) & 0.16 & M2.7 (21:34) &(9) & 1092 & 120 & $-$12 & 478 &($-$40) \\ 03 10 26 & 14.5$^m$ (18:00) & 9.4$^m$ (18:00) & 34 (17:53) & 0.16 & X1.2 (17:21) & 38 & 1537 & 130 & +4.9 & 468 & $-$10 \\ 03 11 02 & 60 (17:30) & 52.6 (18:00) & 40 (17:42) & 4.1 & X8.3 (17:03) & 56 & 2598 & 130 & $-$17 & 533 & $-$12 \\ 03 11 20 & 0.14 (08:40) & 0.08 (08:00) & 14.2 (08:18)& 0.266 & M9.6 (07:35) & 8 & 669 & 90 & sheath & 503$^{s}$ & $-$39 \\ 04 07 25 & 1.6 (16:30) & 1.4$^m$ (16:00) & 13 (15:27) & 0.35 & M1.1 (14:19) & 33 & 1333 & 130 & sheath & 590 & $-$7 \\ 04 11 07 & 14.2$^m$ (17:30) & 11.8$^m$ (18:00) & 17 (17:00) & 0.08 & X2.0 (15:42) & 17$^c$& 1759 & 150& +3.15 & 436 & $-$37 \\ 04 11 09 & 1.7 (19:40) & 1.1$^m$ (19:30) & 46 (18:05) & 0.46 & M8.9 (16:59) & 51 & 2000 & 130 & sheath & 690 & 17 \\ 05 01 15 & 11.2 (00:00)$^{nd}$ & 0.2 (07:00)$^{nd}$ & 92 (23:15) & 1.3 & X2.6 (22:25) &(3) & 2861 & 130 & +14.8 & 567$^W$ &($-$37)\\ 05 01 17 & 181$^m$ (13:30)$^d$ & 205$^m$ (13:00)$^d$ & 280 (10:00) & 19 & X3.8 (06:59) &(24) & 2094 & 110 & $-$5.7 & 577 &($-$16) \\ 05 01 20 & 53 (07:00) & 66.3 (07:00) & 110 (06:46) & 12 & X7.1 (06:36) & 58 & 882 & 80 & $-$3.5 & 822$^s$& 32 \\ 05 07 09 & 0.08 (02:30)$^{nd}$&0.1$^m$ (01:00)$^{nd}$ & 2.3 (23:15) & 0.038 & M2.8 (21:47) &(27) & 1540 & 65 & +8.5 & 345 &($-$41) \\ 05 07 12 & $-$ & 0.007$^{u}$ (18:00) & 1.2 (17:13) & 0.012 & M1.5 (15:47) &(64) & 523 & 80 & $-$14 & 502 &(17) \\ 06 12 14 & 8.1 (22:30) & 0.6$^m$ (00:40)$^{nd}$ & 6 (22:50) & 0.23 & X1.5 (21:07) &(46) & 1042 & 70 & $-$0.05& 936 & (21)\\ \hline \end{tabular} \footnotetext{In column (10) positive (negative) values denote the time from the SEP (GOES) onset to the start (end) of the following (preceding) ICME, respectively. \\ {\it c}: flare longitude as reported by \inlinecite{2010JGRA..11508101C}; {\it d}: delayed SEP onset; {\it m}: multiple SEP intensity peaks; {\it nd}: next day; {\it s}: strong increase in the solar wind speed (1-h average data) during the 6-h period before the SEP onset; {\it w}: weak SEP intensity; {\it W}: solar wind data from {\it Wind}/SWE; {\it u}: uncertain.} \end{sidewaystable} \begin{table}[t!] \caption{Linear correlation coefficients (with standard deviations) between $J_{\rm max}$ and $\log I_{\rm SXR}$ or $\log V_{\rm CME}$ for GOES proton and ACE/EPAM low energy electron data, for the entire event sample ({\it i.e.} no event restriction) and for different sub-samples. The number of events in each group is given in brackets.} \label{T-J-SXR-CME} \begin{tabular}{lccc} \hline SEP event & \multicolumn{3}{c}{IMF categories of SEP events}\\ sub-samples & ICME & SoWi & All SEPs \\ \hline \hline Protons & \multicolumn{3}{c}{ GOES 15$-$40 MeV} \\ $\log J_{\rm p}$$-$$\log V_{\rm CME}$ & & & \\ No event restriction & 0.57$\pm 0.15$ (17) & 0.66$\pm 0.07$ (38) & 0.63$\pm 0.05$ (81)\\ $\,$ Flares $ > {\rm W} 30^{\circ}$ & 0.59$\pm 0.16$ (13) & 0.61$\pm 0.11$ (26) & 0.59$\pm 0.08$ (56) \\ $\,$ Flares $ > {\rm W} 50^{\circ}$ & 0.63$\pm 0.20$ (9) & 0.60$\pm 0.12$ (17) & 0.58$\pm 0.11$ (36) \\ $\,$ Flares $ > {\rm W} 60^{\circ}$ & 0.76$\pm 0.22$ (7) & 0.65$\pm 0.14$ (11) & 0.64$\pm 0.09$ (24) \\ $\log J_{\rm p}$$-$$\log I_{\rm SXR}$ & & & \\ No event restriction & 0.67$\pm 0.13$ (17) & 0.36$\pm 0.13$ (38) & 0.59$\pm 0.07$ (81)\\ $\,$ Flares $ > {\rm W} 30^{\circ}$ & 0.58$\pm 0.16$ (13) & 0.36$\pm 0.18$ (26) & 0.56$\pm 0.09$ (56) \\ $\,$ Flares $ > {\rm W} 50^{\circ}$ & 0.61$\pm 0.17$ (9) & 0.52$\pm 0.14$ (17) & 0.62$\pm 0.09$ (36) \\ $\,$ Flares $ > {\rm W} 60^{\circ}$ & 0.51$\pm 0.34$ (7) & 0.54$\pm 0.17$ (11) & 0.60$\pm 0.11$ (24) \\ \hline \hline Electrons & \multicolumn{3}{c}{ ACE/EPAM 38$-$53 keV} \\ $\log J_{\rm e}$$-$$\log V_{\rm CME}$ & & & \\ No event restriction & 0.64$\pm 0.14$ (18) & 0.55$\pm 0.09$ (46) & 0.53$\pm 0.07$ (96) \\ $\,$ Flares $ > {\rm W} 30^{\circ}$ & 0.60$\pm 0.16$ (14) & 0.57$\pm 0.11$ (33) & 0.56$\pm 0.07$ (68) \\ $\,$ Flares $ > {\rm W} 50^{\circ}$ & 0.62$\pm 0.17$ (11) & 0.45$\pm 0.22$ (21) & 0.53$\pm 0.10$ (45) \\ $\,$ Flares $ > {\rm W} 60^{\circ}$ & 0.72$\pm 0.16$ (9) & 0.14$\pm 0.28$ (15) & 0.52$\pm 0.13$ (32) \\ $\log J_{\rm e}$$-$$\log I_{\rm SXR}$ & & & \\ No event restriction & 0.73$\pm 0.10$ (18) & 0.12$\pm 0.11$ (46) & 0.40$\pm 0.08$ (96) \\ $\,$ Flares $ > {\rm W} 30^{\circ}$ & 0.67$\pm 0.12$ (14) & 0.08$\pm 0.12$ (33) & 0.35$\pm 0.08$ (68) \\ $\,$ Flares $ > {\rm W} 50^{\circ}$ & 0.72$\pm 0.12$ (11) &$-$0.02$\pm 0.17$ (21)& 0.35$\pm 0.11$ (45) \\ $\,$ Flares $ > {\rm W} 60^{\circ}$ & 0.67$\pm 0.18$ (9) & 0.11$\pm 0.28$ (15) & 0.38$\pm 0.13$ (32)\\ \hline \end{tabular} \end{table} \mbox{}~\\ | 14 | 3 | 1403.0708 |
1403 | 1403.6068_arXiv.txt | We study the cosmological consequences of a recently proposed nonlocal modification of general relativity, obtained by adding a term $m^2R\,\Box^{-2}R$ to the Einstein-Hilbert action. The model has the same number of parameters as $\Lambda$CDM, with $m$ replacing $\Omega_{\Lambda}$, and is very predictive. At the background level, after fixing $m$ so as to reproduce the observed value of $\Omega_M$, we get a pure prediction for the equation of state of dark energy as a function of redshift, $w_{\rm DE}(z)$, with $w_{\rm DE}(0)$ in the range $[-1.165,-1.135]$ as $\Omega_M$ varies over the broad range $\Omega_M\in [0.20,0.36]$. We find that the cosmological perturbations are well-behaved, and the model fully fixes the dark energy perturbations as a function of redshift $z$ and wavenumber $k$. The nonlocal model provides a good fit to supernova data and predicts deviations from General Relativity in structure formation and in weak lensing at the level of 3-4\%, therefore consistent with existing data but readily detectable by future surveys. For the logarithmic growth factor we obtain $\gamma\simeq 0.53$, to be compared with $\gamma\simeq 0.55$ in $\Lambda$CDM. For the Newtonian potential on subhorizon scales our results are well fitted by $\Psi(a;k)=[1+\mu_s a^s]\Psi_{\rm GR}(a;k)$ with a scale-independent $\mu_s\simeq 0.09$ and $s\simeq 2$, while the anisotropic stress is negligibly small. | The problem of understanding the origin of dark energy (DE) has stimulated in recent years a very active search for modifications of General Relativity (GR). The challenge is to construct a theoretically consistent theory that modifies GR in the far infrared, i.e. at cosmological scales, while retaining its successes at the scale of the solar system and of terrestrial laboratories. The first example of an infrared modification of GR was provided by the DGP model \cite{Dvali:2000hr}, which indeed has a self-accelerated solution \cite{Deffayet:2000uy,Deffayet:2001pu}. This solution is however plagued by a ghost instability~\cite{Luty:2003vm,Nicolis:2004qq,Gorbunov:2005zk,Charmousis:2006pn,Izumi:2006ca} and is therefore not viable. Significant advances have then been done toward the construction of a consistent theory of massive gravity with the dRGT theory \cite{deRham:2010ik,deRham:2010kj} (see also \cite{deRham:2010gu,deRham:2011rn,deRham:2011qq,Hassan:2011hr,Hassan:2011vm,Hassan:2011tf,Hassan:2011ea,Hassan:2012qv,Comelli:2012vz,Comelli:2013txa,Jaccard:2012ut}), although at present a number of open conceptual issues still persist, and it is also unclear whether acceptable cosmological solutions emerge (see \cite{Hinterbichler:2011tt,deRham:2014zqa} for reviews). In a recent series of papers \cite{Jaccard:2013gla,Maggiore:2013mea,Foffa:2013sma,Foffa:2013vma,Kehagias:2014sda,Maggiore:2014sia} an alternative approach has been proposed in which a mass parameter enters the theory as the coefficient of a nonlocal term. Different implementations of the idea have been explored. The one which is probably closest in spirit to the original degravitation idea~\cite{ArkaniHamed:2002fu,Dvali:2006su} consists in writing a modified Einstein equation of the form \be\label{modelGmnT} \Gmn -m^2\(\iBox_g\Gmn\)^{\rm T}=8\pi G\,\Tmn\, , \ee where the superscript T denotes the operation of taking the transverse part (which is itself a nonlocal operation), $\Box_g$ is the d'Alembertian computed with the curved-space metric $\gmn$, and its inverse $\iBox_g$ is defined using the retarded Green function. The extraction of the transverse part ensures that energy-momentum conservation is still automatically satisfied (see also \cite{Porrati:2002cp}), while the use of a retarded Green's function ensures causality. It was then realized in \cite{Maggiore:2013mea,Foffa:2013vma,Modesto:2013jea} that such tensor nonlocalities generate instabilities in the cosmological evolution (see also \cite{Ferreira:2013tqn} for similar conclusions in a different nonlocal model). The attention then shifted to theories where the nonlocal operator $\iBox$ is applied to the Ricci scalar. Basically, two possibilities come to mind. One possibility, which was proposed in \cite{Maggiore:2013mea}, is to add a term $m^2(\gmn\iBox_g R)^ {\rm T} $ to the Einstein equations, writing \be\label{modelRT} \Gmn -(1/3)m^2\(\gmn\iBox_g R\)^{\rm T}=8\pi G\,\Tmn\, , \ee (where the factor $1/3$ is a convenient normalization of the parameter $m^2$ in $d=3$ spatial dimensions). We will refer to this as the ``$\gmn\iBox R$ model". It was found in \cite{Maggiore:2013mea} that this model generates a dynamical dark energy. Its value today can be matched to the observed value $\ode\simeq 0.68$ by tuning the mass $m$ (which is obtained setting $m\simeq 0.67 H_0$). The fact that a DE is dynamically generated and that the observed value can be reproduced is already quite significant. Furthermore, having fixed $m$, we have fixed the only free parameter of the theory and we then obtain a pure prediction for the EOS parameter of dark energy. For this model, writing in the recent epoch $w_{\rm DE}(a)=w_0+(1-a) w_a$, one finds $w_0\simeq-1.04$ and $w_a\simeq -0.02$ \cite{Maggiore:2013mea}, which is consistent with the {\it Planck} data, and on the phantom side. In an interesting recent paper, Nesseris and Tsujikawa \cite{Nesseris:2014mea} have studied the cosmological perturbations of this model and have compared them to CMB, BAO, SNIa and growth rate data. They find that, if one uses a prior on $H_0$ derived from local measurements of the Hubble parameter \cite{Riess:2011yx}, $h_0\,\gsim\, 0.70$, the data strongly support this nonlocal model over $\Lambda$CDM, while using a lower prior, $0.67\lsim\, h_0\,\lsim\, 0.70$, as suggested by the {\it Planck} data \cite{Ade:2013zuv}, the two models are statistically comparable. It should be observed that the nonlocal gravity model has the same number of free parameters as $\Lambda$CDM, with the mass $m$ replacing $\ola$. A second possibility, recently put forward in \cite{Maggiore:2014sia}, is to add a term involving $R\,\Box_g^{-2} R$ directly to the action, writing \be\label{S1} S_{\rm NL}=\frac{1}{16\pi G}\int d^{4}x \sqrt{-g}\, \[R-\frac{1}{6} m^2R\frac{1}{\Box_g^2} R\]\, . \ee Observe that, upon integration by parts, we can equivalently write $R\,\Box^{-2}R=(\iBox R)^2$. We will refer to it as the ``$R\,\Box^{-2}R$ model". As discussed in \cite{Maggiore:2014sia}, when linearizing the equations of motion derived from the action (\ref{S1}) around flat space, one finds the same equations of motion as those obtained by linearizing \eq{modelRT}. However, at the full non-linear level, the two theories are different. In the $R\,\Box^{-2}R$ model there is again a dynamically generated dark energy, which can be made to agree with the presently observed value by choosing $m\simeq 0.28H_0$. The prediction for the DE equation of state is then $w_0\simeq -1.14$, $w_a=0.08$ (with a mild dependence on the value of $\Omega_M$ today, that will be discussed in more detail below). These values are compatible with existing limits, but will be easily distinguished from the predictions of $\Lambda$CDM with forthcoming data. In particular, in the next few years the DES survey should measure $w_0$ to an accuracy of about $\Delta w_0\simeq 0.03-0.04$ and later {\sc Euclid} should measure it to an accuracy $\Delta w_0\simeq 0.01$ \cite{Amendola:2012ys}. The above models are therefore highly testable. In this paper we focus in particular in the $R\,\Box^{-2}R$ model. Since its predictions, at the level of background evolution (and, as we will see in this paper, also at the level of perturbations), differ from $\Lambda$CDM more than the predictions of the $\gmn\iBox R$ model, it is presumably the first of the two that will be ruled out (or possibly confirmed) by future data. At the conceptual level, one might be worried by the presence of nonlocal terms in the equations of motion. However, it is important to observe that nonlocal classical equations, constructed with a retarded Green function, appear in a number of different situations. As discussed in detail in \cite{Maggiore:2013mea,Foffa:2013sma} (and as recognized in similar contexts also in \cite{Tsamis:1997rk,Deser:2007jk,Barvinsky:2011rk,Deser:2013uya}), such nonlocal equations should not be thought of as the classical equations of motion of a fundamental nonlocal quantum field theory. Rather, they can emerge, already in a purely classical context, from some form of smoothing or iterative procedure in an underlying local fundamental theory. Probably the simplest example is provided by the formalism for gravitational-wave production in GR beyond lowest order. In linearized theory the gravitational wave (GW) amplitude $\hmn$ is determined by $\Box\bhmn=-16\pi G\Tmn$, where $\bhmn=\hmn-(1/2)h\emn$. In such a classical radiation problem, this equation is solved with the retarded Green's function, $\bhmn=-16\pi G\iBox_{\rm ret}\Tmn$. When the non-linearities of GR are included, the GWs generated at some perturbative order become themselves sources for the GW generation at the next order. In the far-wave zone, this iteration gives rise to effective nonlocal equations involving $\iBox_{\rm ret}$, and is at the basis of both the Blanchet-Damour and the Will-Wiseman-Pati formalisms (see e.g. \cite{Blanchet:2006zz} or chapter~5 of \cite{Maggiore:1900zz} for reviews). A nonlocal action can be seen as a compact way of summarizing such effective nonlocal equations of motion.\footnote{However, the use of a nonlocal action implies a (rather revealing) subtlety~\cite{Deser:2007jk,Barvinsky:2011rk,Jaccard:2013gla,Foffa:2013sma}. The variation of a nonlocal action involving $\iBox$, where $\iBox$ is defined with some Green's function $G(x;x')$, produces equations of motion where appears $\iBox$ constructed with the symmetrized Green's function $(1/2)[G(x;x')+G(x';x)]$. It is therefore impossible to obtain in this way a retarded Green's function in the equations of motion. We can still take the formal variation of the action and at the end replace by hand all factors $\iBox$ by $\iBox_{\rm ret}$ in the equation of motion. In this way, the nonlocal action is seen just as a convenient ``device" that allows us to compactly summarize the equations of motion. However, any connection to a corresponding nonlocal quantum field theory is then lost. Indeed, also the action (\ref{S1}) should be understood in this sense. In other words, the nonlocal classical theory that we consider is {\em defined} by the equations of motion derived from a formal variation of \eq{S1}, in which $\iBox\ra\iBox_{\rm ret}$. The use of an action is however convenient because it ensures automatically the covariance of the equations of motions.} Another example of this type is the effective action describing the interaction between two compact bodies in GR, which at fourth post-Newtonian order develops a term nonlocal in time \cite{Damour:2014jta}. Such a term reflects the existence of the so-called ``tail terms", i.e. nonlocal terms that represent radiation emitted earlier and that come back to the particle after performing multiple scattering on the background curvature. Such terms therefore depend on the whole past history (see also \cite{Poisson:2011nh}). One more recent example of this type is the effective field theory of cosmological perturbations, which is an effective classical theory for the long-wavelength modes obtained by integrating out the short-wavelength modes~\cite{Baumann:2010tm} and again has terms that are nonlocal in time, expressed through a retarded Green function~\cite{Carrasco:2012cv,Carroll:2013oxa}. The above examples are purely classical. Nonlocal effective classical equations can also appear by performing a quantum averaging. Nonlocal field equations govern the effective dynamics of the vacuum expectation values of quantum fields. In particular, the in-in matrix elements of operators satisfy nonlocal but causal equations, involving only retarded propagators \cite{Jordan:1986ug,Calzetta:1986ey}. The bottom-line of this discussion is that nonlocality often appears in physics, but is always derived from some averaging process in a fundamental local theory. Issues of quantum consistency, such as the possible existence of ghosts in the spectrum of the quantum theory, cannot be addressed in the effective nonlocal classical theory, but can only be studied in the underlying fundamental quantum theory. The approach that we are proposing, based on the addition of nonlocal terms to the Einstein equations, therefore has two natural directions of development: (1) to understand whether such nonlocal effective classical equations can be embedded in a consistent quantum theory, and (2): to understand whether such models have interesting and viable cosmological consequences. At least in a first approximation these two problems are decoupled.\footnote{Of course, one must keep in mind the possibility that the necessity of embedding the classical equations in a consistent quantum theory will require a different nonlocal structure. In any case, the study of the cosmological consequences of models such as (\ref{S1}) will provide a first step for further refinements. Also, in principle the fundamental quantum theory could have degrees of freedom that modify, e.g., the spectrum of quantum fluctuations at inflation that seed the subsequent cosmological evolution. This would affect the prediction of a fundamental inflationary model for the spectral index $n_s$ and the amplitude of the gravitational potential $\d_H$, that appear in the initial conditions, see \eqst{initcond1}{initcond4}. In any case, in a full analysis obtained evolving the perturbations with a Boltzmann code and comparing with the data, $n_s$ and $\d_H$ will be taken as free parameters to be fitted, just as one does in $\Lambda$CDM.} In this paper we study the cosmological perturbations of these nonlocal cosmological models, focusing in particular on the $R\,\Box^{-2}R$ model as our reference model. The first issue that we wish to understand is whether the perturbations are well-behaved. This is already a non-trivial point. Indeed, infrared extensions of GR such as DGP have been ruled out by the lack of well-behaved perturbations over the cosmologically interesting solutions, and similar problems can appear in massive gravity theories such as dRGT \cite{Gumrukcuoglu:2011ew,Gumrukcuoglu:2011zh,Koyama:2011wx}. We will see that, in our nonlocal model, cosmological perturbations are indeed well behaved. This opens the way for a more detailed comparison with CMB, BAO, SNIa and structure formation, and we will see that the model performs quite well when compared to observations. Finally, we observe that our model differs from the nonlocal model proposed by Deser and Woodard \cite{Deser:2007jk,Deser:2013uya,Woodard:2014iga} and studied in many subsequent papers (see e.g. \cite{Nojiri:2007uq,Jhingan:2008ym,Koivisto:2008xfa,Koivisto:2008dh,Capozziello:2008gu,Elizalde:2011su,Zhang:2011uv,Elizalde:2012ja,Bamba:2012ky,Park:2012cp,Dodelson:2013sma}, and also \cite{Barvinsky:2003kg,Barvinsky:2011hd,Barvinsky:2011rk} for a related approach). The Deser-Woodard model does not involve a mass scale $m$, and is instead constructed adding to the Einstein-Hilbert action a term of the form $Rf(\iBox R)$. The function $f(\iBox R)$ is then tuned so that, at the level of background evolution, this model reproduces $\Lambda$CDM, which turns out to require that $f(X)=a_1[\tanh (a_2Y+a_3Y^2+a_4Y^3)-1]$ with $Y=X+a_5$, and $a_1,\ldots a_5$ suitably chosen coefficients. The action of this model is therefore significantly more involved, compared to the nonlocal action (\ref{S1}) where, in terms of $X=\iBox R$, the nonlocal term is simply $m^2 X^2$, and is also not predictive as far as the background evolution is concerned. More importantly, after fixing $f(\iBox R)$ so to reproduce the background evolution of $\Lambda$CDM, one can study its cosmological perturbations, and it has been found in \cite{Dodelson:2013sma} that the Deser-Woodard model is ruled out by comparison with structure formation (with the model being disfavored, with respect to GR, at the 7.8~$\sigma$ level from redshift space distortion, and at the 5.9~$\s$ level from weak lensing). This shows the power of structure formation data for testing nonlocal modifications of GR, and it is therefore natural to ask how our nonlocal models perform in this respect. We will see that the model (\ref{S1}) (and also the model (\ref{modelRT}), as recently shown in \cite{Nesseris:2014mea}) passes these tests with flying colors, giving predictions for structure formation that are sufficiently close to $\Lambda$CDM to be consistent with existing data, yet sufficiently different to be distinguishable by near-future surveys. We also observe that a phantom equation of state has also been obtained recently in \cite{Konnig:2014dna} for a bimetric gravity model. In this case, $w_{\rm DE}(0)\simeq -1.22$ and again structure formation is consistent with existing data, with a growth index $\gamma\simeq 0.47$. The organization of the paper is as follows. In sects.~\ref{sect:model} and \ref{sect:back} we recall the properties of the model and we study its background evolution, expanding on the results already presented in \cite{Maggiore:2014sia}. Since supernova (SN) data are mostly sensitive to the background evolution, the results found in these sections already allow us to test the nonlocal model against SN data, and we find that it performs as well as $\Lambda$CDM, although the fit to SN data suggests a higher value of $\oma$, compared to $\Lambda$CDM. The equations governing the cosmological perturbations for the $R\,\Box^{-2}R$ model are presented in sect.~\ref{sect:pert}. In sect.~\ref{sect:analytic} we derive analytic results in the sub-horizon limit, and we show that the predictions of this model are well compatible with the data on structure formation. We confirm this discussion in sect.~\ref{sect:numeric} by numerically integrating the perturbation equations, and we also show the full evolution on all scales. Sect.~\ref{sect:concl} contains our conclusions. In App.~\ref{app:gmnR} we collect similar results for the perturbations of the $\gmn\iBox R$ model, that partially overlap with those recently presented in \cite{Nesseris:2014mea}. | \label{sect:concl} The introduction of nonlocal models such as those given in \eq{modelRT} and in \eq{S1} raises a number of interesting questions, both of conceptual nature, and on their viability as cosmological models. At the conceptual level, as extensively discussed in \cite{Maggiore:2013mea,Foffa:2013sma,Kehagias:2014sda} and as we have mentioned in the Introduction, the crucial point is that such nonlocal equations of motion, involving a retarded propagator (which is necessary in order to ensure causality), cannot be taken as the equations of motion of a fundamental nonlocal quantum field theory. Rather, they must be understood as effective classical theories. In this direction, the main open problem is to understand if and how such nonlocal theories can be obtained with some form of classical or quantum smoothing from a more fundamental (and local) quantum theory, see the discussion in the Introduction and in \cite{Maggiore:2013mea}. Another important set of questions, which was the focus of the present paper, concerns the phenomenological viability of such theories. As shown in \cite{Kehagias:2014sda}, the nonlocal models (\ref{modelRT}) and (\ref{S1}) recover all successes of GR at solar system and lab scales. In this paper we have worked out the cosmological perturbations of the nonlocal model (\ref{S1}) (as well as of the model (\ref{modelRT}), see the Appendix). The main results that we have obtained can be summarized as follows. \begin{itemize} \item The cosmological perturbations are well-behaved. Of course, cosmological perturbations are always unstable, even in $\Lambda$CDM. For instance, the dark matter perturbation $\d_M$ on sub-horizon scales in MD grows as $a$ and eventually become non-linear already in $\Lambda$CDM. The issue is therefore whether the growth of the perturbation in the nonlocal model is sufficiently close to that of $\Lambda$CDM to be consistent with the observations, which is indeed the case in both the nonlocal models that we have studied. \item A nonlocal model such as the $R\,\Box^{-2}R$ model defined in \eq{S1} is remarkably predictive. In terms of a single parameter $m$ (that replaces the cosmological constant in $\Lambda$CDM), it predicts a whole set of functions of the redshift. At the background level, it gives a pure prediction for the dark energy equation of state parameter $w_{\rm DE}$ as a function of $z$. The result is shown in Fig.~\ref{fig:wDE}. Equivalently, it predicts the time evolution of the dark energy density, see Fig.~\ref{fig:rhoDE}. In particular, the EOS turns out to be phantom. With the usual parametrization (\ref{ChevLind}) near the recent epoch, we get $w_0 \simeq -1.14$ and $w_a = 0.08$, with exact values depending on $\oma$, see Fig.~\ref{fig:wvsOM}, but still ranging over a relatively narrow set of values. Varying $\oma$ over the rather broad range $\oma\in [0.20,0.36]$, $w_0$ remains within the relatively narrow interval $[-1.165,-1.135]$, while $w_a\in [0.07,0.11]$. Similar considerations hold for the model defined in \eq{modelRT}, see the appendix. \item At the perturbation level, the model fully predicts the energy density perturbations, pressure perturbations, anisotropic stress and velocity divergence, all as a function of redshift and of momentum, that fully characterize the DE perturbations as an effective fluid. From these, we can derive other quantities more readily comparable to the observation. In particular, structure formation is mostly affected by the function $\mu(a;k)$ defined by \eq{defmu} while lensing is affected by the function $\Sigma(a;k)$ defined in \eq{defSigma}. We find that, for the modes relevant to observations, these function are to a very good approximation scale-invariant, i.e. independent of $k$. Our prediction for $\mu$ and $\Sigma$ as a function of redshift are given in Figs.~\ref{fig:N3N3b} and \ref{fig:N4N5}. We find that the widely used parametrization $\mu(a)=\mu_s a^s$ fits well our numerical results, and we predict $\mu_s=0.094 $ and $s=2$. For the growth rate index $\gamma(z;k)$, we find again that, for the relevant modes, it is scale-independent, and the result is given in Fig.~\ref{fig:G4G5}. As in $\Lambda$CDM, it is in a first approximation independent also of $z$, and has the value $\gamma\simeq 0.53$, to be compared with 0.55 in $\Lambda$CDM. \item Comparison with structure formation shows that the difference between this model and $\Lambda$CDM is small with respect to the present observational errors. The model therefore fits structure formation at a level that at present is statistically indistinguishable from $\Lambda$CDM. This is a non-trivial result. For instance, the non-local model proposed in \cite{Deser:2007jk} has been ruled out at the $8\sigma$ level by the comparison with structure formation~\cite{Dodelson:2013sma}. We have also verified that the nonlocal models fit the SNa~Ia data from the JLA set, again with an accuracy which is statistically indistinguishable from $\Lambda$CDM, see Table~\ref{tab:bgfit}. It is particularly interesting the fact that the deviations from $\Lambda$CDM are sufficiently small, so that the model passes these tests, but still sufficiently large to allow a clear distinction to be made with near-future surveys. \end{itemize} We believe that these nonlocal models can provide a new and interesting line of attack to the dark energy problem and, to the least, they can be a useful benchmark against which we can compare $\Lambda$CDM. \vspace{5mm} \noindent {\bf Acknowledgments.} We thank Michele Mancarella and Ermis Mitsou for useful discussions. The work of YD, SF, MK and MM is supported by the Fonds National Suisse. NK thanks the D\'epartement de Physique Th\'eorique of Geneva University for the hospitality during part of this work. \appendix | 14 | 3 | 1403.6068 |
1403 | 1403.6859_arXiv.txt | We perform a study on the optical and infrared photometric properties of known luminous blue variables (LBVs) in M31 using the sample of LBV candidates from the Local Group Galaxy Survey \citep{2007AJ....134.2474M}. We find that M31 LBV candidates show photometric variability ranging from 0.375 to 1.576 magnitudes in $\rps$ during a three year time-span observed by the Pan-STARRS 1 Andromeda survey (PAndromeda). Their near-infrared colors also follow the distribution of Galactic LBVs as shown by \cite{2013A&A...558A..17O}. We use these features as selection criteria to search for unknown LBV candidates in M31. We thus devise a method to search for candidate LBVs using both optical color from the Local Group Galaxy Survey and infrared color from Two Micron All Sky Survey, as well as photometric variations observed by PAndromeda. We find four sources exhibiting common properties of known LBVs. These sources also exhibit UV emission as seen from \textit{GALEX}, which is one of the previously adopted method to search for LBV candidates. The locations of the LBVs are well aligned with M31 spiral arms as seen in the UV light, suggesting they are evolved stars at young age given their high-mass nature. We compare these candidates with the latest Geneva evolutionary tracks, which show that our new M31 LBV candidates are massive evolved stars with an age of 10 to 100 million years. | Luminous blue variables are hot massive stars which undergo sporadic eruptions on timescales of years and decades \citep{1994PASP..106.1025H}. The prototype is S Doradus, as well as Hubble-Sandage variables in M31 and M33 \citep{1953ApJ...118..353H}, which shows eruptions of 1-2 magnitude level in a time-span of several decades. Other examples are $\eta$ Carina and P Cygni, which show giant eruptions ($>$ 2 mag) at a frequency of several centuries. \cite{1984IAUS..105..233C} is the first to coin the name Luminous Blue Variables for this type of stars, and separates them from other type of bright blue stars like Wolf-Rayet stars. LBVs play an important role at the very late stage of massive star evolution. They are considered as a transition phase where O stars evolve toward Wolf-Rayet Stars \citep{2011A&A...525L..11M}. LBVs were originally regarded only as supernova impostors because they often show giant eruptions mimicking the explosion of supernovae, but the central star remains after the ejecta have been expelled. However, a link between LBVs and supernova progenitors was suggested by \cite{2006A&A...460L...5K} when interpreting the radio lightcurves of supernovae. The radio emission seen after the supernova explosion is induced by the interaction between supernova ejecta and the progenitor's circumstellar medium, thus radio lightcurves bear information on the mass-loss history of the progenitor. \cite{2006A&A...460L...5K} suggested that radio lightcurves of SNe indicate high mass-loss histories of the progenitors which matches well with LBVs. Pre-eruption images of several SNe also suggest LBVs as their progenitor. For example, the progenitor of SN 1987A was recognized as a blue supergiant \citep{1987ApJ...321L..41W} and \cite{2007AJ....133.1034S} suggested that it could be classified as a low-luminosity LBV. \cite{2009Natur.458..865G} identified the progenitor of SN 2005gl using \textit{HST} and attributed it to be a LBV. Recently a previously known LBV - SN 2009ip - has undergone its third eruption and has been linked to a true supernova \citep{2013MNRAS.430.1801M}. The nature of the recent eruption of SN 2009ip is under debate; subsequent follow-up has been carried out to verify or reject it as a core-collapse SN \citep{2013MNRAS.433.1312F}. Yet there are only a few known LBVs, either in our Galaxy or in M31 and M33. Thus, increasing the number of known LBVs is essential toward understanding their nature and evolution. In addition to the pioneering decades-long photometric monitoring campaign conducted by Hubble and Sandage \citep{1953ApJ...118..353H}, there are several methods to uncover LBVs. For example, LBVs are strong UV and H-alpha emitters \citep[see][ and reference therein]{2007AJ....134.2474M} and can be revealed e.g. with observations of the \textit{GALEX} satellite or H-alpha surveys. \cite{2007AJ....134.2474M} conducted a H-alpha survey of M31 and M33 and followed-up a selected sample of strong H-alpha emitters spectroscopically. By comparing the spectra of their H-alpha emitter sample with known LBVs, they were able to identify candidate LBVs, which saved a substantial amount of time required to uncover LBVs photometrically. Because they have uncovered more than 2,500 H-alpha emitting stellar objects, they can only follow-up dozens of them, yet there are much more to be explored. \cite{2013ApJ...773...46H} are currently exploring other H-alpha emitting sources in this list, in combination with infrared photometry including 2MASS, \textit{Spitzer} and \textit{WISE} to search for luminous and variable stars. Since LBVs undergo several eruptions and exhibit high mass-loss rates, they accumulate vast amounts of material in their circumstellar environment which could be detectable in the infrared \citep[e.g.][]{2012MNRAS.421.3325G}. \cite{2013ApJ...767...52K} have made use of \textit{Spitzer} IRAC photometry and searched for $\eta$ Carina analogs in nearby galaxies including M33 (but not M31). They estimate that 6$\pm$6 of their candidates are true $\eta$ Carina-like sources. Here we outlined a novel approach utilizing mid-term photometric variation, as well as optical and infrared color to search for LBVs using the LGGS optical and 2MASS infrared photometry, with the combination of the photometric variability from PAndromeda monitoring campaign. Our paper is organized as follows: in \textsection~2 we describe the optical and infrared data we use. In \textsection~3 we outline our method. A discussion of our candidates is presented in \textsection~4, followed by an outlook in \textsection~5. \\ | In this section we examine the properties of our LBV candidates, investigate whether they are UV emitters, derive their ages from the massive star evolutionary model, and examine their \textit{HST} images (if available). \subsection{\textit{GALEX} UV detection} It has been suggested that LBVs can be revealed in the UV channel \citep{1996ApJ...469..629M}. We have plotted the positions of our candidates on the \textit{GALEX} near-UV images \citep[\textit{GALEX} nearby galaxy atlas,][]{2007ApJS..173..185G}. As shown in Fig. \ref{fig.UVstamp}, all LBV candidates are aligned with bright UV sources, and they are located in the spiral arms of M31 (see Fig. \ref{fig.spat}). For comparison we also show zoom-ins of the known LBV and LBV candidates listed in \cite{2007AJ....134.2474M} in the appendix. \subsection{Comparison with isochrones} \begin{figure*}[!h] \centering \includegraphics[scale=1.0]{isochrone.eps} \caption{ Location of our LBV candidates in the B-V v.s. V CMD, over-plotted with the Geneva massive star isochrones. We adopt the distance modulus of 24.4 mag from \cite{1990ApJ...365..186F}. We apply a correction for the extinction effect on B-V color using the extinction map by \cite{2009A&A...507..283M}. By assuming A$_V$/E(B-V) = 3.1, we also correct the extinction effect on the V-band magnitude. The positions on the CMD before and after extinction correction are linked with black lines. The extinction corrected value are marked with error-bars. The four candidates are indicated in black color. Evolutionary tracks of metallicity \textit{Z} = 0.014 with different age, log(t) = 6.6, 6.8, 7.0 ... 7.6 are shown with different colors from top to bottom. The errors on the magnitude are not photometric errors, but are taken from the variability seen during the time-span of PAndrome da, as shown in Table \ref{tab.cphot}.} \label{fig.isochrone} \end{figure*} In order to see whether our candidates are consistent with the evolutionary model of massive stars, we compare the B-V color and the V band magnitude of these four candidates with the latest Geneva evolutionary tracks \citep{2012A&A...537A.146E}. As shown in Fig. \ref{fig.isochrone}, our candidates are in good agreement with the Geneva models. In addition, from the evolutionary tracks, we are able to estimate their ages. As indicated by the models, their age are of the order of 10$^7$ years. In Fig. \ref{fig.isochrone} we also indicate the possible variabilities of LBVs by drawing the photometric variations $\Delta$mag$_{\rps}$ seen from PAndromeda as an error-bar. LBVs can also suffer from dust extinction from their circumstellar material. To take this into account, we apply a correction for the extinction effect on B-V color using the extinction map by \cite{2009A&A...507..283M}. By assuming A$_V$/E(B-V) = 3.1, we also correct the extinction effect on the V-band magnitude. Taking the extinction effect into consideration, the true B-V value of our LBV candidates would be smaller. In this case, our LBV candidates would be blue-ward on the color-magnitude plot in Fig. \ref{fig.isochrone}, which is still consistent with the evolutionary model of a age in the order of 10 million years. \subsection{HST observations} To confirm that our LBV candidates are stellar objects, we thus request the M31 HST images from the Panchromatic Hubble Andromeda Treasury project \citep[PHAT,][]{2012ApJS..200...18D}. Since the PHAT survey only covers the northern disk of M31, we only find images for two of our LBV candidates, PSO J11.0457+41.5548 and PSOJ11.2574+42.0498. We show the HST ACS images of them in Fig. \ref{fig.pstamphst}. With the exquisite spatial resolution of HST, we can see that the shape of PSO J11.0457+41.5548 and PSOJ11.2574+42.0498 traces the typical point-spread function in the field. In addition to the PHAT archived images, we also found PSO J10.1165+40.7082 covered by the ``Treasury Imaging of Star Forming Regions in the Local Group'' program \citep{2012AJ....144..142B}. The HST images of this candidate, astrometrically aligned to the PAndromeda data using our own pipeline (Kodric et al. in prep.), is shown in Fig. \ref{fig.pstamphst} as well. HST resolved two sources within 1 arcsec of PSO J10.1165+40.7082. To distinguish which is the varying source, we examine the difference image from PAndromeda during maximum flux (at MJD=55816.38 and 56218.38) and found that the brighter source in the F814W band is the varying source. \begin{figure} \centering \includegraphics[scale=0.7]{hst-PSOJ101165.eps} \includegraphics[scale=0.7]{hst-PSOJ110457.eps} \includegraphics[scale=0.7]{hst-PSOJ112574.eps} \caption{Postage stamps from HST archive. Upper panel: HST images of PSOJ10.1165+40.7082 from the ``Treasury Imaging of Star Forming Regions in the Local Group'' program \citep{2012AJ....144..142B}. Middle and lower panels: HST images of PSOJ11.0457+41.5548 and PSOJ11.2574+42.0498 from the ``Panchromatic Hubble Andromeda Treasury'' program \citep{2012ApJS..200...18D}. The LBV candidates are indicated by the cyan circles, which have a radius of 1 arcsec. The observed passbands (F160W, F336W, F475W, F555W, and F814W) are also indicated in the lower corner of each stamp. All HST images are astrometrically aligned to the PAndromeda image using our own pipeline (Kodric et al. in prep.). The median positional difference between the LGGS catalog and the PAndromeda catalog is 0.36 arcsec.} \label{fig.pstamphst} \end{figure} \subsection{A further look at the variability criterion} \label{sec.det_eff} In Fig. \ref{fig.det_eff}, we plot the number of sources which pass our optical and infrared photometric criteria against the photometric variability from PS1 $\rps$-band lightcurves. There are in total seven sources showing $\Delta$mag$_{\rps}$ $>$ 0.4 mag out of which we selected four as possible LBV candidates. Among the remaining three, they are all known LBVs (AF And, M31 Var 15, and M31 Var A-1). In Fig. \ref{fig.det_eff}, there are three more sources that varying at 0.3 mag level, which are AE And with $\Delta$mag$_{\rps}$ = 0.375 and other variables with $\Delta$mag$_{\rps}$ = 0.339 and 0.307. Even if we lowered the $\Delta$mag$_{\rps}$ criterion to the lowerest value of known LBVs (0.375), we would only select AE And, but no additional new LBV candidates. For comparison, we also show the $\rps$ lightcurves of the four known LBVs listed in \cite{2007AJ....134.2474M} in the appendix. \begin{figure*}[!h] \centering \includegraphics[scale=1.0]{10_sigma_histo.eps} \caption{$\Delta$mag$_{\rps}$ distribution of variable sources passing our optical and infrared color criteria: we show the number of lightcurves which fulfill both the H-K$<$0.5,V$<$20, and B-V $<$ 0.5 criteria. Seven lightcurves pass these criteria, and four of them are previously unknown. The rest of them are known LBVs. The vertical lines indicate the variability of known LBVs from \cite{2006AJ....131.2478M}.} \label{fig.det_eff} \end{figure*} | 14 | 3 | 1403.6859 |
1403 | 1403.7521_arXiv.txt | Motivated by the recent observation of the $B$-mode signal in the cosmic microwave background by BICEP2, we study the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model is promoted to a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial conditions. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the $B$-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial conditions. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity. | 14 | 3 | 1403.7521 |
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1403 | 1403.0071_arXiv.txt | {The source GX 13+1 is a persistent, bright Galactic X-ray binary hosting an accreting neutron star. It shows highly ionized absorption features, with a blueshift of $\sim$ 400 km s$^{-1}$ and an outflow-mass rate similar to the accretion rate. Many other X-ray sources exhibit warm absorption features, and they all show periodic dipping behavior at the same time. Recently, a dipping periodicity has also been determined for GX 13+1 using long-term X-ray folded light-curves, leading to a clear identification of one of such periodic dips in an archival $Chandra$ observation.} {We give the first spectral characterization of the periodic dip of GX 13+1 found in this archival \textit{Chandra} observation performed in 2010.} {We used \textit{Chandra}/HETGS data (1.0--10 keV band) and contemporaneous \textit{RXTE}/PCA data (3.5--25 keV) to analyze the broad-band X-ray spectrum. We adopted different spectral models to describe the continuum emission and used the XSTAR-derived warm absorber component to constrain the highly ionized absorption features.} {The 1.0--25 keV continuum emission is consistent with a model of soft accretion-disk emission and an optically thick, harder Comptonized component. The dip event, lasting $\sim$ 450 s, is spectrally resolved with an increase in the column density of the neutral absorber, while we do not find significant variations in the column density and ionization parameter of the warm absorber with respect to the out-of-dip spectrum.} {We argue that the very low dipping duty-cycle with respect to other sources of the same class can be ascribed to its long orbital period and the mostly neutral bulge, that is relatively small compared with the dimensions of the outer disk radius.} | Low-mass X-ray binary (LMXB) dipping sources are characterized by periodic (or quasi-periodic) dips in their light-curves that are evidence for a fixed structure in the reference frame of the binary system. These dips may also be related to super-orbital periodicities, which are more difficult to constrain when their appearance is transient \citep{grise13}. To date, 13 LMXBs hosting a neutron star (NS) and 6 LMXBs hosting a black hole have shown clear dips in their light curves. In Table~\ref{table_sources}, we show an updated list of these sources with some basic data and references to the literature. \begin{table*} \caption{\label{table_sources} LMXB dipping sources} \centering \begin{tabular}{l ccccc} \hline \hline \multicolumn{6}{c}{NEUTRON STAR LMXBs}\\ \hline Source & P$_{\textrm{orb}}$ & M$_2$ & D & Ref. (dips) & Ref. (WA) \\ & hr & M$_{\textrm {sun}}$ & kpc & \\ \hline EXO 0748-676 & 3.82 & 0.1? & 7.1$\pm$1.2 & 1a & 1b\\ 4U 1254-690 & 3.88 & 0.4? & 10? & 2a & 2b\\ % GX 13+1 & 588 & $>$1.1 & 7$\pm$1 & 3a & 3b \\ 4U 1323-62 & 2.94 & 0.3? & 10? & 4a & 4b \\ X1624-490 & 20.9 & 2.3? & 15? & 5a & 5b \\ X1658-298 & 7.12 & 0.8? & 15? & 6a & 6b \\ XTE J1710-281 & 3.28 & 0.4? & 16? & \multicolumn{2}{c}{7} \\ AX J1745.6–2901 & 8.35 & 0.9? & 10? & \multicolumn{2}{c}{8} \\ 1A 1744-361 & 0.87? & 0.1? & 9? & 9a & 9b \\ XB 1746-371 & 5.73 & 0.6? & 9? & 10a & 10b \\ GRS J1747-312 & 12.4 & 4.5$\pm$3.5 & 6.8$\pm$0.5 & 11 & $\cdots$\\ XB 1916-053 & 0.83 & 0.1? & 9? & 12a & 12b \\ Cir X-1 & 400.32 & 10? & 6? & 13a & 13b \\ \hline \multicolumn{6}{c}{BLACK-HOLE LMXBs} \\ \hline GRO J1655-40\tablefootmark{a} & 62.92 & 2.34$\pm$0.12 & 3.2$\pm$0.2 & 14a & 14b \\ H 1743-322 & $>$10? & $\cdots$ & 8.5? & 15a & 15b \\ GRS 1915+105\tablefootmark{b} & 739.2 & 0.8$\pm$0.5 & 9.4$\pm$0.2 & 16a & 16b\\ 4U 1630-47 & $\cdots$& $\cdots$ & 10? & 17a & $\cdots$ \\ MAXI J1659-152 & 2.414 & 0.20$\pm$0.05& 8.6$\pm$3.7 & 18a & $\cdots$\\ MAXI J1305-704 & 9.74 & $<$ 1? & 6? & \multicolumn{2}{c}{19}\\ \hline \hline \end{tabular} \tablefoot{ The question mark indicates very uncertain values. Columns list the most often used source name, orbital period, companion star mass, distance, reference to most recent works related to absorption dips and X-ray spectroscopy of warm absorption features. Companion star masses are estimated assuming that the companion belongs to the lower main sequence. \tablefoottext{a}{M$_{\textrm{BH}}$ = 7.0$\pm$0.2} \tablefoottext{b}{M$_{\textrm{BH}}$ = 12.9$\pm$2.4} } \tablebib{ (1a) \citet{parmar86}; (1b) \citet{vanpeet09}; (2a) \citet{smale02}; (2b) \citet{diaztrigo09}; (3a) \citet{iaria14}; (3b) \citet{diaztrigo12}; (4a) \citet{parmar89}; (4b) \citet{boirin05}; (5a) \citet{smale01}; (5b) \citet{iaria07}; (6a) \citet{oosterbroek01}; (6b) \citet{sidoli01}; (7) \citet{younes09}; (8) \citet{hyodo09}; (9a) \citet{bhattacharyya06}; (9b) \citet{gavriil12}; (10a) \citet{balucinska04}; (10b) \citet{diaztrigo06}; (11) \citet{intzand03}; (12a) \citet{white82}; (12b) \citet{boirin04}; (13a) \citet{shirey99}; (13b) \citet{dai07a}; (14a) \citet{kuulkers98}; (14b) \citet{ueda98}; (15a) \citet{homan05}; (15b) \citet{miller06}; (16a) \citet{naik01}; (16b) \citet{lee02}; (17) \citet{kuulkers98}; (18)\citet{kuulkers13}; (19)\citet{shidatsu13}. } \end{table*} Two main physical models are widely discussed in the literature to explain the occurrence of dips: \citet{white82} proposed a variable, azimuthal-dependent height of the accretion disk's outer rim and a large system-inclination angle. According to the orbital phase, our line-of-sight partially or totally intercepts the rim that causes local absorption of X-rays produced in the innermost parts of the system. The rim geometry was empirically adjusted by matching synthesized geometries and the regular patterns observed in the light curves \citep[both at X-rays and in the optical-UV, e.g. for 4U 1822-371,][]{mason86}. Some dippers also show periods without dips, which points to a strong variability of the occulting regions \citep{smale99}. Alternatively, another explanation was proposed by \citet{frank87}: if matter from the companion star is able to skim across the thickness of the outer accretion disk, part of the incoming stream may impact the disk at a much closer radius \citep{lubow89}; when part of this stream collides with the disk, it is quickly dynamically and thermally virialized; but a fraction of it (which is a tunable parameter of the model) receives energy from the impact shock and splits into a two-zone medium, forming blobs of cold, condensed gas, surrounded by a lower density hotter plasma at large scale-heights above the disk \citep{krolik81}. This scenario is able to partially account for many empirical facts such as the dip's periodic occurrence, the dependence on orbital phase, and the duration and time scales of the single dips. Both scenarios involve the common ingredient of a high inclination angle. For low-mass companion stars with short orbital periods ($<$ 1 day), the inferred inclination angle, $i$, is constrained between 65$^{\circ}$ and 85$^{\circ}$, while for higher inclinations eclipses are also expected. In these eclipsing binaries, direct emission from the NS is blocked by the disk thickness and only scattered emission from an accretion-disk corona (ADC) may be observed \citep{iaria13}. Together with these physical scenarios, many studies have been focused on deriving geometrical and physical constraints by spectrally resolving the dip events. Spectra from dipping sources have been fitted using a two-component spectral decomposition consisting of a thermal black-body emission from the surface of the NS and a Comptonized emission (usually fitted with a cut-off power-law). Seed photons of the Comptonized spectrum come from the accretion disk and the Comptonization is thought to occur at large disk radii in an extended corona, whose radius is $>>$ 10$^{9}$ cm. Using the ingress and egress times of the deep dips (where emission is totally blocked at the dip bottom), it has been shown that the corona emission is gradually covered (\textit{progressive covering} approach) and therefore extended, with a disk-like geometry, while the black-body emission is point-like and attributed to the NS emission \citep{church04}. The main assumption in deriving the estimates for the ADC radius is that the dip is caused by the bulge located at the outer accretion disk \citep[as described by the geometry envisaged by][]{white82}, whose main effect is a progressive photoelectric absorption of the primary incident source flux. Detection in the past decade of resonant absorption features of highly ionized elements in the X-ray spectrum (see Table~\ref{table_sources}) has provided new clues for separating the spectral formation. Local absorption features often appear to be blue-shifted, which points to a disk-wind or generally out-flowing, photoionized plasma. The ionization state of the optically thick absorbing plasma is variable and the time scales can be as short as a few ks \citep{ueda04}, with a wind velocity of thousands of km/s. In all cases, the most clearly resolved lines are from H-like and He-like transitions of iron, which implies that the ionization parameter, $\xi$, of the warm absorber is $>$ 100 \citep{kallman04}. \citet{boirin05} first advanced the hypothesis that during dipping there might be a \textit{tight} relation between cold and warm absorption because the overall X-ray variability during dipping would be driven by fast changes in the column density and ionization state of the warm absorbing medium along our line of sight. In this scenario, there is no more need for a partial covering of an extended continuum corona because the soft excess observed during dipping is naturally accounted for by a combination of strong increase in the column density of the warm medium and a decrease of its ionization parameter. Outside dips, a warm absorber has been always observed, which implies that the medium has a cylindrical distribution and is not confined to the locus of the bulge. In light of these findings, the continuum decomposition has also been questioned, because an extended corona was felt to be less necessary \citep{diaztrigo12}. \subsection*{The source GX13+1} The source GX 13+1 is a persistent X-ray binary system belonging to the so-called class of GX bright bulge sources, with an estimated distance of 7 $\pm$ 1 kpc. The compact object is an accreting NS that has sporadically shown type-I X-ray bursts \citep{matsuba95}, orbiting an evolved mass-donor giant star of spectral class KIII V \citep{bandyopadhyay99}. The system has peculiar characteristics, being in between the classification of low-mass and high-mass systems; this is also testified by the long orbital period of $\sim$ 24 days \citep{corbet10,iaria14}, which makes it the LMXB with the second-longest orbital period after GRS 1915+105 (30.8 d period; it has a black hole as accreting compact object). The 3--20 keV \textit{Rossi-XTE} (\textit{RXTE}) spectrum of GX 13+1 has been investigated by \citet{homan04}, in connection with its radio emission. The spectrum was deconvolved according to the \textit{Eastern} interpretation, that is the sum of a softer multicolored accretion-disk emission and a thermal Comptonized, harder optically thick emission in the boundary layer. The low-resolution \textit{RXTE}/PCA spectrum also needed some local features (broad iron Gaussian line and a 9 keV absorption edge) to obtain a satisfactory fit. More recently, emission of higher than 20 keV has been observed with \textit{INTEGRAL}/ISGRI data \citep{paizis06}, and was subsequently analyzed according to a thermal plus bulk Comptonization model \citep{mainardi10}. Using narrower bands such as the 1--10 keV CCD typical range, the general continuum adopted was found to be well approximated with the sum of soft disk emission and black-body harder emission \citep{ueda01,sidoli02,ueda04,diaztrigo12}. The black-body emission approximates an optically thick Comptonized emission, which we deduce from the difficulty in constraining both the optical depth and the electron temperature with a limited energy range and the high optical depths characteristics of the very soft spectra of bright accreting NS LMXBs. Analysis of K-$\alpha$ edge depths has also shown that in the direction of the source the ISM composition (or absorbing, circumbinary cold matter) is significantly overabundant in elements heavier than oxygen \citep[e.g. silicon and sulphur]{ueda05}, with X-ray fine-structure absorption features (XAFS) around the Si and S K-$\alpha$ edges. High-resolution spectroscopy with the \textit{Chandra} HETGS revealed a radiatively/thermally driven disk wind with an outflow velocity of $\sim$ 400 km s$^{-1}$ and multiple absorption features from highly ionized elements \citep{ueda04}. The wind probably carries a significant fraction of the total mass-accretion rate, up to 10$^{18}$ g s$^{-1}$. Observations with \textit{XMM-Newton} also revealed a broad (equivalent width $\gg$ 100 eV) iron emission line, whose origin is associated to a disk-reflection component, and the broad width is ascribed to Compton broadening in the warm corona. A global spectral account of the total variability has also been proposed, where the main drivers for the spectral variability are neutral cold absorption and variability associated with a reflection component \citep{diaztrigo12}. Periodic dipping in the LMXB GX 13+1 was suspected for a long time, on the basis of an energy-dependent modulation observed in long-term light curves \citep{corbet10,diaztrigo12}. \citet{iaria14} systematically searched in archived X-ray observations for clear signatures of periodic dips. Applying timing techniques to long-term folded X-ray light curves provided a successful method that led to a refined orbital-period estimate (24.5274(2) d) and to the first ephemeris for the dip passage times. The only periodic dip that could be assigned on the basis of this ephemeris for a pointed X-ray observation was in an archival \textit{Chandra} observation performed in 2010. This corroborates that inclination is a key factor to spot warm absorbing winds in LMXBs and that they are optically thick to radiation only close to the plane of the accretion disk. This relation has recently also been pointed out by \citet{ponti12} for Galactic LXMBs hosting black-holes. We present in this article the results of the spectroscopic analysis of the $Chandra$ dip event, showing that the main driver of the dipping in this source is an increase in cold photoelectric absorption. | We have reported the first spectroscopic time-resolved investigation of the periodic dip of GX 13+1. The broad-band spectrum derived by a combined fit of \textit{Chandra}/HEG and \textit{RXTE}/PCA allowed us to consistently determine the continuum and discrete emission features of the source. \textit{Chandra} data confirm an out-flowing optically thick warm absorber. Because of the short duration of the dip, we were unable to firmly constrain possible changes in the properties of the absorbing wind. The observed spectral hardening during the dip is mostly due to an increase in the column density of a neutral absorber, while the warm-absorber component is not modified with respect to the out-of-dip spectrum. Simple estimates on the dimensions of the structure that cause the dip indicate a very small occulting region when compared with the expected scale-heights at the outer radius, while simple geometric considerations on the system point to a possible inclination of $\lesssim$ 70\degr. | 14 | 3 | 1403.0071 |
1403 | 1403.0247_arXiv.txt | We describe a search for submillimeter emission in the vicinity of one of the most distant, luminous galaxies known, HerMES FLS3 at $z=6.34$, exploiting it as a signpost to a potentially biased region of the early Universe, as might be expected in hierarchical structure formation models. Imaging to the confusion limit with the innovative, wide-field submillimeter bolometer camera, SCUBA-2, we are sensitive to colder and/or less luminous galaxies in the surroundings of HFLS3. We use the Millennium Simulation to illustrate that HFLS3 may be expected to have companions if it is as massive as claimed, but find no significant evidence from the surface density of SCUBA-2 galaxies in its vicinity, or their colors, that HFLS3 marks an over-density of dusty, star-forming galaxies. We cannot rule out the presence of dusty neighbours with confidence, but deeper 450-$\mu$m imaging has the potential to more tightly constrain the redshifts of nearby galaxies, at least one of which likely lies at $z\gs5$. If associations with HFLS3 can be ruled out, this could be taken as evidence that HFLS3 is less biased than a simple extrapolation of the Millennium Simulation may imply. This could suggest either that it represents a rare short-lived, but highly luminous, phase in the evolution of an otherwise typical galaxy, or that this system has suffered amplification due to a foreground gravitational lens and so is not as intrinsically luminous as claimed. | \label{intro} \begin{figure*} \centerline{\psfig{file=fls3-scuba2.eps,width=3.4in,angle=0} \psfig{file=fls3-spire-rgb.eps,width=3.4in,angle=0}} \caption{{\it Left:} SCUBA-2 imaging at 850\,$\mu$m, with 450- and 850-$\mu$m sources marked by red squares and white circles, respectively, for the 67.2\,arcmin$^2$ where $\sigma_{850}\le 1.5$\,mJy\,beam$^{-1}$. The negative bowl around HFLS3 is a typical artifact of the filtering procedures employed here. The FWHM of the SCUBA-2 beams are shown as solid ellipses. {\it Right:} Three-color representation of the data obtained using SPIRE at 250, 350 and 500\,$\mu$m for the same field around HFLS3, superimposed with blue PACS 160-$\mu$m contours. Several of the SCUBA-2 850-$\mu$m sources are associated with green SPIRE sources -- those with SEDs peaking at 350\,$\mu$m, consistent with $z\approx 2$; others have no obvious SPIRE counterparts and may lie at considerably higher redshifts. The region over which PACS sensitivity is better than half the best is outlined in blue. Positions of faint 1.4-GHz sources from the $\sim1.3''$-resolution, $\sigma\sim11\,\mu$Jy\,beam$^{-1}$ Karl G.\ Jansky Very Large Array imaging described in \citet{riechers13} are marked `+' (the radio catalog covers only $\approx$25\% of the region shown, hence the detection rate is unremarkable). N is up; E is left; offsets from $\alpha_{2000}=17$:06:47.8, $\delta_{2000}=+58$:46:23 are marked. } \label{fig:imaging} \end{figure*} Dust extinction and a profusion of less luminous foreground galaxies makes it difficult to select high-redshift ultraluminous star-forming galaxies ($L_{\rm IR}\geq 10^{12}$\,L$_\odot$) at rest-frame ultraviolet/optical wavelengths. Although extinction is not an issue at radio wavelengths, an unfavourable $K$-correction works against detecting the highest redshift examples, $z\gg 3$. Since the advent of large-format submillimeter (submm) cameras such as the Submillimeter Common-User Bolometer Array \citep[SCUBA --][]{holland99}, however, it has been possible to exploit the {\it negative} $K$-correction in the submm waveband to select dusty, star-forming galaxies (submm-selected galaxies, or SMGs) almost independently of their redshift \citep[e.g.][]{fran91, blainlongair93}. The scope of this field has been substantially expanded by {\it Herschel} \citep{pilbratt10} which has surveyed approximately a hundred square degrees of extragalactic sky to the confusion limit at 500\,$\mu$m \citep[as defined by][]{nguyen10}, with simultaneous imaging at 250 and 350\,$\mu$m, using the SPIRE instrument \citep{griffin10}. A SPIRE image of the {\it Spitzer} First Look Survey (FLS) field, obtained as part of the {\it Herschel} Multi-Tiered Extragalactic Survey \citep[HerMES\footnote{hermes.sussex.ac.uk} --][]{oliver12}, led to the discovery of 1HERMES\,S350\,J170647.8+584623 \citep[hereafter HFLS3 --][]{riechers13, dowell14} as an unusually red SPIRE source with $S_{250}<S_{350}<S_{500}$, i.e.\ with its thermal dust peak within or beyond the 500-$\mu$m band \citep[see also][]{cox11, combes12, rawle14}. Some of these ``500-$\mu$m risers'' are in fact due to synchrotron emission from bright, flat-spectrum radio quasars \citep[e.g.][]{jenness10}, but HFLS3 does not exhibit such powerful AGN-driven radio emission. Panchromatic spectral-line observations place HFLS3 at $z=6.34$ via the detection of H$_2$O, CO, OH, OH$^+$, NH$_3$, [C\,{\sc i}] and [C\,{\sc ii}] emission and absorption lines. Its continuum spectral energy distribution (SED) is consistent with a characteristic dust temperature, \Td\ = 56\,\kelvin, and a dust mass of $1.1\times 10^9$\,M$_\odot$. Its infrared luminosity, \lir\ = $2.9\times 10^{13}$\,L$_\odot$, suggests a star-formation rate (SFR) of $2900\,\mu_{\rm L}^{-1}$\,M$_\odot$\,yr$^{-1}$ for a \citet{chabrier03} initial mass function, where the lensing magnification suffered by HFLS3 due to a foreground galaxy less than 2$''$ away has been estimated to be in the range $\mu_{\rm L}=1.2$--1.5 \citep[][although \citealt{cooray14} estimate $\mu_{\rm L}=2.2\pm 0.3$]{riechers13}. It is expected that the most massive galaxies found at very high redshifts grew in (and thus signpost) the densest peaks in the early Universe, making them useful tracers of distant proto-clusters. Above $z \sim 6$, such sources may also contribute to the rapid evolution of the neutral fraction of the Universe, during the so-called `era of reionisation', and to the earliest phase of enrichment of the interstellar medium in galaxies, less than 1\,Gyr after the Big Bang. They may also host the highest redshift quasars. In the submm regime, to explore distant galaxies and their environments we have observed radio galaxies and quasars, typically detecting factor $\sim2$--4$\times$ over-densities of submm companions around these signposts \citep[e.g.][]{ivison00, stevens03, stevens10, robson04, priddey08}. Here, we continue this tradition, targeting the most distant known submm galaxy, HFLS3 at $z= 6.34$, with the 10,000-pixel SCUBA-2 bolometer camera \citep{holland13}, which is more sensitive than {\it Herschel} to cold dust in high-redshift galaxies. In \S\ref{observations} we describe our SCUBA-2 observations of the field surrounding HFLS3, after its discovery with SPIRE aboard {\it Herschel}, and our reduction of those data. In \S\ref{results} we analyze the surface density of SCUBA-2 galaxies in the field, and their color, and discuss whether there is any evidence that HFLS3 inhabits an over-dense region of the Universe, as might be expected in hierarchical structure-formation models \citep[e.g.][]{kaufman99, springel05}. We finish with our conclusions in \S\ref{conclusions}. Throughout, we adopt a cosmology with $H_0 = 71$\,km\,s$^{-1}$\,Mpc$^{-1}$, $\Omega_{\rm m}=0.27$ and $\Omega_\Lambda = 0.73$, so 1$''$ equates to 5.7\,kpc at $z=6.34$. | \label{conclusions} We have detected the most distant, dusty starburst galaxy, HFLS3, at high significance with SCUBA-2. We detect another 29 dusty galaxies within an area of 67.2\,arcmin$^2$ surrounding HFLS3, most of them likely at lower redshift. We find no compelling evidence, from surface density or color, for an over-density of SMGs around HFLS3, although applying similar selection criteria to theoretical models suggests that a modest excess could be expected, as is found for some other high-redshift SMGs \citep[e.g.\ GN\,20 --][]{daddi09}. We can therefore draw no strong conclusions regarding the likely gravitational amplification suffered by HFLS3, or for the likely fraction of its luminosity provided by a buried AGN. | 14 | 3 | 1403.0247 |
1403 | 1403.6657_arXiv.txt | {Although the Milky Way nuclear star cluster (MWNSC) was discovered more than four decades ago, several of its key properties have not been determined unambiguously up to now because of the strong and spatially highly variable interstellar extinction toward the Galactic centre.} {In this paper we aim at determining the shape, size, and luminosity/mass of the MWNSC.} {To investigate the properties of the MWNSC, we used Spitzer/IRAC images at $3.6$ and $4.5\,\mu$m, where interstellar extinction is at a minimum but the overall emission is still dominated by stars. We corrected the $4.5\,\mu$m image for PAH emission with the help of the IRAC $8.0\,\mu$m map and for extinction with the help of a $[3.6-4.5]$ colour map. Finally, we investigated the symmetry of the nuclear cluster and fit it with S\'ersic, Moffat, and King models. } {We present an extinction map for the central $\sim300\times200$\,pc$^{2}$ of the Milky Way\thanks{The extinction map and the corresponding uncertainty map shown in Fig.\,\ref{Fig:ext} are made available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/566/A47}, as well as a PAH-emission- and extinction-corrected image of the stellar emission, with a resolution of about $0.20$\,pc. We find that the MWNSC appears in projection to be intrinsically point-symmetric, that it is significantly flattened, with its major axis aligned along the Galactic plane, and that it is centred on the black hole, Sagittarius\,A*. Its density follows the well known approximate $\rho\propto r^{-2}$-law at distances of a few parsecs from Sagittarius\,A*, but becomes as steep as $\rho\propto r^{-3}$ at projected radii around 5\,pc. We derive a half light radius of $4.2\pm0.4$\,pc, a total luminosity of $L_{MWNSC,4.5\,\mu{m}}=4.1\pm0.4\times10^{7}\,L_{\odot}$, and a mass of $M_{MWNSC}=2.5\pm0.4\times10^{7}$\,M$_{\odot}$.} {The overall properties of the MWNSC agree well with the ones of its extragalactic counterparts, which underlines its role as a template for these objects. Its flattening agrees well with its previously established rotation parallel to Galactic rotation and suggests that it was formed by accretion of material that tended to fall in along the Galactic plane. Our findings support the in situ growth scenario for nuclear clusters and emphasise the need to increase the complexity of theoretical models for their formation and for the interaction between their stars and the central black hole in order to include rotation, axisymmetry, and growth in recurrent episodes.} | Nuclear star clusters (NSCs) have been detected in $\sim$75\% of all galaxies and appear as compact clusters at the photometric and dynamical centres of their host galaxies \citep[e.g.,][]{Boker:2002kx,Carollo:1998fk,Cote:2006eu,Neumayer:2011uq}. They have luminosities in the range of $10^{5}-10^{8}$\,L$_{\odot}$, effective radii of a few pc, and masses of $10^{6}-10^{8}$\,M$_{\odot}$. They are typically one to two orders of magnitude brighter and more massive than globular clusters \citep{Boker:2004oq,Walcher:2005ys}, which places NSCs among the most massive known clusters in the Universe \citep[for a brief review, see][]{Boker:2010ys}. Star formation in NSCs appears to be a recurrent process. The majority of NSCs have mixed old and young stellar populations and frequently show signs of star formation within the past 100\,Ma \citep[e.g.,][]{Rossa:2006zr,Seth:2006uq,Walcher:2006ve}. NSCs show complex morphologies and can coexist with massive black holes \citep[MBHs; ][]{Seth:2008kx,Graham:2009lh,Neumayer:2012fk}. The study of NSCs can serve to make progress in a variety of astrophysical fields, such as (1) the accretion history of galactic nuclei. While MBHs are the final product of accretion, with only their mass (and perhaps angular momentum) as measurable parameters, NSCs provide a record of the accretion {\it history} through their multiple stellar populations. (2) Since NSCs are, on average, the densest observable stellar systems \citep{Walcher:2005ys,Misgeld:2011kx} and may frequently contain MBHs, they play a key role in the study of stellar dynamics, for example in tests of fundamental ideas such as the formation of stellar cusps around MBHs. Also, phenomena such as tidal disruption events or extreme mass-ratio infall events (so-called EMRIs), which are considered to be important potential sources for gravitational wave emission, are thought to occur in NSCs containing MBHs. (3) Star formation in NSCs probably proceeds under extreme conditions, at least if we consider the centre of our own Galaxy as representative, which is characterised by a strong Galactic tidal field \citep[e.g.,][]{Portegies-Zwart:2002fk}, high stellar densities \citep[e.g.,][]{Schodel:2007tw}, an intense magnetic field \citep{Crocker:2010fk}, strong UV radiation \citep{Launhardt:2002nx}, and high turbulence and temperature of the interstellar medium \citep[ISM; e.g.,][]{Morris:1996vn}. NSCs can thus help us explore the limits of our understanding of star formation. \begin{figure*}[!htb] \includegraphics[width=\textwidth,angle=0]{NSC_Ks_45.pdf} \caption{\label{Fig:NSC_Ks_4.5} Left: Nuclear cluster of the Milky Way at $2.15\,\mu$m seen with VIRCAM/VISTA. Right: The same field at $4.5\,\mu$m, seen with IRAC/Spitzer. Galactic north is up and Galactic east is to the left, so that the Galactic Plane runs horizontally across the middle of the images. Offsets are given in parsecs relative to Sgr\,A*. The colour scale is logarithmic and both images have been scaled in an identical way. } \end{figure*} Two basic scenarios are considered for the formation of NSCs, that is, inspiral and mergers of massive star clusters, such as globular clusters, and in situ formation \citep[e.g.,][]{Boker:2010ys,Hartmann:2011uq,Antonini:2013ys,Gnedin:2013vn}. It is probable that both mechanisms contribute to the growth of NSCs. The study by \citet{Seth:2006uq} of NSCs in edge-on spiral galaxies has shed light on this issue. They have found that most of the clusters in their sample are significantly flattened and closely aligned with the plane of their host galaxy. In addition, they have identified discs or rings superposed onto some of the NSCs. These additional components have a bluer colour than the actual NSCs, which suggests that the stars in the discs/rings have formed $<1$\,Ga ago. In a more detailed, integral field spectroscopy study of one of their targets, the NSC in NGC\,4244, they confirm the existence of an older, flattened spheroidal component and a younger, disc-like component. In addition, they find that the entire NSC rotates parallel to the rotation of its host galaxy \citep{Seth:2008kx}. These findings lead them to strongly favour a scenario where most of the NSC mass is formed through the infall of gas from the galaxy disc, followed by in situ star formation or by the infall of young star clusters, which are formed near the nuclear cluster, along the galaxy plane. The biggest obstacle for studying NSCs, and galactic nuclei in general, is their great distance, which limits us to the study of the integrated light, averaged on scales of several parsecs to tens of parsecs, that is dominated by the brightest stars. Even with the next generation 30-40\,m class telescopes this situation will remain fundamentally unchanged. The centre of the Milky Way is, however, located at only $\sim$8 kpc from Earth, about a hundred times closer than the Andromeda galaxy, and five hundred times closer than the next active galactic nucleus. The Galactic centre (GC) contains the nearest NSC and MBH and is the only galaxy nucleus in which we can actually resolve the stellar population observationally and examine its properties and dynamics on scales of milli-parsecs. It is thus a crucial laboratory for studying galactic nuclei \citep{Ghez:2009kx,Genzel:2010fk,Schodel:2011ab}. In this work we assume a GC distance of $8.0$\,kpc \citep[][]{Malkin:2012uq}. An important aspect in the study of the GC is that it presents one of the best cases for the existence of a MBH. The mass of the Galaxy's MBH, Sagittarius\,A* (Sgr\,A*), has been measured with high accuracy through the observation of the orbits of individual stars \citep[e.g.,][]{Ghez:2008fk,Gillessen:2009qe}. The $\sim4\times10^{6}$\,M$_{\odot}$ MBH Sgr\,A* is surrounded by the Milky Way's NSC (MWNSC), the mass of which has been estimated to $(3\pm1.5)\times10^{7}$\,M$_\odot$ \citep{Launhardt:2002nx} and its half light radius to 3-5\,pc \citep[][]{Graham:2009lh,Schodel:2011ab}. The MWNSC has been found to rotate parallel to Galactic rotation \citep{Trippe:2008it,Schodel:2009zr} and to contain multiple stellar populations \citep[e.g.,][]{Krabbe:1995fk,Paumard:2006xd,Pfuhl:2011uq}. Of particular interest is that at least 50\% of the stars that formed in the most recent star formation event \citep[between $2-6$\,Ma ago, ][]{Lu:2013fk} appear to have formed in situ in a disc around Sgr\,A* \citep{Levin:2003kx,Paumard:2006xd,Lu:2009bl}. We note that this disc, with a radius $\lesssim0.5$\,pc, is, however, much smaller than the discs or rings of young stars found in extragalactic systems \citep{Seth:2006uq,Seth:2008kx}. This may be a selection effect from the lack of linear resolution in other galaxies, where it would be extremely hard to resolve stellar populations on scales below 0.5\,pc. On the other hand, the discs or rings observed by \citet{Seth:2006uq,Seth:2008kx} may be more like the nuclear stellar disc (NSD) of $\sim$200\,pc radius in which the MWNSC is embedded \citep{Launhardt:2002nx}. Our current knowledge of the MWNSC shows that it is probably a close cousin to its extragalactic counterparts and can thus serve as a benchmark for these far-away and therefore observationally unresolved systems. There are, however, significant uncertainties in our knowledge of the intrinsic properties of the MWNSC because the strong and spatially highly variable extinction across the GC region \citep[$A_{K}\approx2-5$, e.g.,][]{Scoville:2003la,Schodel:2010fk} subjects our observations, even at near-infrared (NIR) wavelengths, to potentially significant bias. Although the apparent elongation of the MWNSC along the Galactic plane has already been pointed out by \citet{Becklin:1968nx}, up to now almost all observational and theoretical work has implicitly assumed a spherical shape of the cluster. This assumption was influenced in part by early work on extragalactic NSCs, which suggested that they were spherical. More recent work, however, shows that many NSCs may indeed by flattened and aligned with the disc of their host galaxies \citep[e.g.,][]{Seth:2008rr,Seth:2010fk}. Azimuthal averaging can obviously affect the estimated density law and half-light radius. In addition, most existing work has not taken the contribution from the NSD into which the MWNSC is embedded into account, which may also have biased some of the measured quantities \citep[see discussion in][]{Graham:2009lh}. The size, shape, and total mass of the MWNSC are fundamental quantities that must be accurately known if we want to study the formation history of the GC and the interaction between the central BH and the surrounding stellar cluster. A flattened NSC, for example, would suggest formation from material that fell in predominantly along the Galactic plane. The question of a spherical or axisymmetric shape of the MWNSC can also affect our understanding of the interaction between the MBH and the surrounding stars. For example, cusp growth has so far almost exclusively been studied in spherical, isotropic systems. Intriguingly, the stellar distribution within $0.5$\,pc of Sgr\,A* is far flatter than what has been predicted by theoretical work \citep[see, e.g.,][]{Buchholz:2009fk,Do:2009tg,Bartko:2010fk}. Can this be related to erroneous assumptions about the overall properties of the MWNSC? Finally, the rate of events such as EMRIs or stellar disruptions will also depend on the overall size and shape of the MWNSC. Fortunately, interstellar extinction is a strongly decreasing function of wavelength. Towards the GC it reaches minimum levels at mid-infrared (MIR) wavelengths of $3-5\,\mu$m \citep{Nishiyama:2009oj,Fritz:2011fk}. To illustrate this point, we show a comparison between an image of the MWNSC at $2.15\,\mu$m and at $4.5\,\mu$m in Fig.\,\ref{Fig:NSC_Ks_4.5}. It can be easily seen that the interstellar clouds near the GC, in particular towards (Galactic) south of the NSC, are almost opaque in the NIR, while they become partially transparent in the MIR. The aim of our paper is therefore to use MIR images from the Spitzer Space Telescope from the IRAC survey of the GC \citep{Stolovy:2006fk,Arendt:2008fk,Ramirez:2008fk} to infer the intrinsic large-scale structure of the MWNSC and address the following questions: Is it spherically symmetric or flattened? In the latter case, is it aligned with the Galactic plane? What is its size and overall luminosity? \begin{figure}[!tb] \includegraphics[width=\columnwidth,angle=0]{CMD.pdf} \caption{\label{Fig:CMD} CMD resulting from our work (left) compared to the results of \citet{Ramirez:2008fk}. The green line connects the mean colours in given magnitude intervals and the red line shows the unreddened giant sequence. The red arrow indicates the reddening law used in this work. The blue dashed lines indicate magnitude and colour cuts applied to the detected stars.} \end{figure} | } Previous measurements of the overall properties of the MWNSC suffered from the strong differential extinction in the Galactic Centre region that exceeds several magnitudes even at wavelengths of $\lambda\sim2\,\mu$m. Those NIR studies could therefore not provide unambiguous answers to questions such as the extent and symmetry of the cluster, even when they tried to compensate for the differential extinction \citep[e.g.,][]{Catchpole:1990rz,Philipp:1999nx}. In addition, many studies, in particular those at high angular resolution, were limited to regions far inside the half-light radius of the NSC \citep[e.g.,][]{Scoville:2003la,Eckart:1993zr,Genzel:2003it,Schodel:2007tw}. In this work, we provide a new description of the NSC, based on extinction-corrected MIR data from the Spitzer IRAC survey that overcomes some of the major difficulties and provides an overall view of the NSC at the centre of the Milky Way. In this section we summarise and discuss our main results. \subsection{Properties of the MWNSC} Strong, differential extinction has so far impeded an accurate assessment of one of the most basic properties of the MWNSC, which is whether it is intrinsically spherically symmetric or not. By using MIR images, where interstellar extinction is at a minimum, combined with extinction correction, we minimise the influence of extinction on the observed shape of the cluster. The resulting light profiles of the MWNSC are clearly different in directions perpendicular and parallel to the Galactic plane. We further provide evidence for the intrinsic (projected) shape of the MWNSC by a comparison between the original (PAH and extinction corrected) image and a symmetrised image of the GC at $4.5\,\mu$m. We do not find any significant differences between the two images, except for what can be attributed to the influence of a large-scale IR-dark cloud. We therefore feel that the evidence supports clearly the notion of a flattened MWNSC, symmetric with respect to the Galactic plane and a perpendicular axis through its centre. Such a projected form is in agreement with an intrinsically flattened, axisymmetric cluster. While it had been shown previously that stellar number counts in the central parsec peak within $1"/0.04\,$pc of the black hole \citep{Genzel:2003it,Schodel:2007tw}, it was not clear whether the {\it entire} NSC would be centred on Sgr\,A* on {\it large} scales. Our analysis shows that the cluster centre lies within $\lesssim0.20$\,pc of Sgr\,A*, not more than one pixel of the rebinned images used here. Considering the low-angular resolution of the images used and the possible systematic uncertainties in the central parsec owing to the presence of strong PAH and /or warm dust emission and a small number of very bright MIR sources, we consider that, on large scales, there is no evidence of any offset between the centre of the NSC and Sgr\,A*. This agrees with the centring of the cluster on scales of a few 10 mpc that has been found in high angular resolution studies \citep[e.g.,]{Eckart:1993zr,Ghez:1998ad,Genzel:2003it,Schodel:2007tw}. The alignment of the MWNSC with the Galactic plane appears to be almost perfect. In combination with its flattening, this is consistent with its rotation parallel to overall Galactic rotation. We find a well constrained value of the ratio of minor to major axis of $q=0.71\pm0.02$, corresponding to an ellipticity $\epsilon=1-q=0.29\pm0.02$. In this point we disagree with the recent work of \citet{Fritz:2013hc}, who claim a spherical shape for the MWNSC and interpret the flattened density contours as being caused by overlap with the NSD. In our work, the flattening of the MWNSC already becomes apparent in the light profiles at $\gtrsim1$\,pc projected distance from Sgr\,A* (see Figs.\,\ref{Fig:profiles}, \ref{Fig:diffuse} and \ref{fig:profile_mge}). Our simultaneous fits of2D models of the MWNSC and the NSD to the data also result in a clearly flattened MWNSC. We interpret our findings as evidence that the flattening of the MWNSC is {\it intrinsic} and not just an apparent effect because of a superposition with the NSD. The main difference between our work and the work of \citet{Fritz:2013hc} is that we use MIR imaging while they base their analysis on NIR imaging. The NIR image in the left-hand panel of Fig.\,\ref{Fig:NSC_Ks_4.5}, the $3.6\,\mu$m images in Figs.\,\ref{Fig:maps} and \ref{Fig:colorcheck} and the extinction map in Fig.\,\ref{Fig:ext} show that there is considerable extinction present at offsets $\pm10$\,pc running parallel to the GP toward the north and south, with typical values of $A_{4.5}\approx1$ and thus $A_{1.7}\approx4.4$ \bibpunct[ ]{(}{)}{,}{a}{}{;} \citep[using the extinction law of][ for the wavelength conversion]{Nishiyama:2009oj}. \bibpunct[ ]{(}{)}{,}{a}{}{;} At such high values there is the danger of strong systematic uncertainties in the NIR because there will be little signal in the highly extincted regions. Few stars will be detected in star counts and those will lie preferably in front of the dark clouds. It appears therefore plausible that, in the NIR, extinction correction, masking and symmetrising may suffer from significant systematic effects. Thus, extinction would naturally lead to finding a more flattened NSD around the MWNSC. This, in turn, would make the MWNSC appear less flattened in a double-component fit. The difference between our results and those presented by \citet{Fritz:2013hc} demonstrate that the GC is once more a challenging target and that caution is required when interpreting the data. It is possible that there are still significant systematic effects also present in the analysis presented in this work. For example, the small uncertainty of the estimated flattening of the MWNSC quoted in this work may underestimate the true uncertainty. In any case, it would be surprising to find a spherical nuclear star cluster embedded in a strongly flattened NSD, and the rotation of the MWNSC would also be difficult to reconcile with a spherical system. As for the density function of the MWNSC, it appears to be described well overall by the $\rho\propto r^{-1.8}$ density law that has been established by many studies in the past decades \citep[see, e.g., discussion in][]{Schodel:2007tw}. Here we note that this density law is an approximation for a spherical cluster and only valid within a few parsecs of Sgr\,A*. In fact, the density law is steeper in the direction perpendicular to the GP and flatter along the GP. At distances beyond $p\approx5$\,pc, the cluster profile appears to be significantly steeper \citep[see also][]{Launhardt:2002nx}. There has been much discussion about the existence or not of a stellar cusp around Sgr\,A* in the past years, triggered by the finding of a flat core of old stars within about $0.5$\,pc of the MBH (see Sect.\,\ref{sec:dynamics}). Here we add two minor remarks to the discussion: (1) The stellar cusp will form within the influence radius of the MBH, which contains roughly the stellar mass corresponding to the mass of the BH. The radius of influence lies between 1\,pc and 3\,pc in case of the GC \citep[e.g.,][]{Trippe:2008it,Schodel:2009zr,Merritt:2010ve}. The observed $\sim$$r^{-1.8}$ density law at these distances from Sgr\,A* agrees well with the canonical density law of a stellar cusp \citep[$\rho\propto r^{-1.75}$, e.g.,][]{Bahcall:1977ys,Lightman:1977ly,Murphy:1991zr,Preto:2010kx}. The ``missing cusp'' problem at the GC only refers to the region within $\sim$0.5\,pc of Sgr\,A*. (2) It would be of interest to investigate the density law of a stellar cusp in a {\it rotating} stellar system. We derive a total luminosity for the MWNSC of $L_{NSC,4.5\,\mu{m}}=(4.1\pm0.4)\times10^{7}\,L_{\odot}$. Lower bounds to this value are provided from the innermost five components of the MGE fitting ($L_{NSC,4.5\,\mu{m}}=3.6\times10^{7}\,L_{\odot}$). Recent research into the stellar mass-to-luminosity ratio in the MIR has come to the result that it is largely constant, i.e.\ independent of the properties and history of the stellar population. \citet{Meidt:2014fk} find $\Upsilon_{\ast}^{3.6\mu{m}}=0.6\pm0.1$. According to the modelling of MIR mass-to-light ratios by \citet{Oh:2008fk} we can use the same value at $4.5\,\mu$m because the uncertainty of the simple wavelength conversion from $3.6\,\mu$m to $4.5\,\mu$m will be significantly smaller than the uncertainty of $\Upsilon_{\ast}^{3.6\mu{m}}$. We assume $\Upsilon_{\ast}^{4.5\mu{m}}=0.6\pm0.1$, therefore, which also agrees with the value $\Upsilon_{\ast}^{4.5\mu{m}}=0.6\pm0.2$ determined from modelling of spectroscopic data of the MWNSC by Feldmeier et al. (submitted to A\&A). We thus derive a mass of $M_{MWNSC}=(2.5\pm0.2_{stat}\pm0.4_{syst})\times10^{7}$\,M$_{\odot}$, where the systematic uncertainty reflects the uncertainty of $\Upsilon_{\ast}^{4.5\mu{m}}$. This value lies between the $M_{NSC}=3.0\pm1.5\times10^{7}$\,M$_{\odot}$ derived by \citet{Launhardt:2002nx} and the $(1.3\pm0.3)\times10^{7}$\,M$_{\odot}$ estimated by \citet{Fritz:2013hc} based on isotropical spherical Jeans modelling (for a GC distance of 8\,kpc) and agrees with both on the $1\,\sigma$ level. We note that our measurements are based on a completely different data set and at a different wavelength than the work of \citet{Launhardt:2002nx}, who used the K-band measurements of \citet{Philipp:1999nx}. In particular, our measurements are significantly less affected by extinction, take the non-spherical shape of the NSC into account, and profit from the low uncertainty of the stellar mass-to-light ratio in the MIR. The complementarity of the data and the reduced uncertainty in our work give us confidence in the accuracy of the mass measurement of the NSC, which thus contains about five times as much mass as the central black hole, Sgr\,A*. We note that the models fitted to the MWNSC images in this work are optimised to describe its overall properties on large scales and at relatively low linear resolution and would like to remind the reader that it is well established that the MWNSC has a core radius of $\sim$$0.25-0.4$\,pc \citep[e.g.,][]{Schodel:2007tw,Buchholz:2009fk}. This corresponds roughly to the central $2\times2$ pixels in our rebinned map. Care should therefore be taken when using our results for modelling the inner parsecs of the MWNSC. A different approach, e.g., with a broken power law, should then be chosen \citep[see][]{Do:2009tg,Schodel:2009zr}. On the other hand, the overall properties of the MWNSC do not seem to be affected significantly by the exact choice of the model. This is demonstrated by the agreement of the best-fit angles, half light radii, flattening parameters, and total luminosities between the King and S\'ersic models. Overall, the main characteristics of the MWNSC, i.e.\ its half light radius and luminosity/mass agree well with the properties of extragalactic NSCs. The luminosity/mass of the MWNSC lies at the higher end of the observed values, but is not unusual considering that the Milky Way is a relatively massive galaxy \citep[see, e.g., Fig.\,14 in ][]{Rossa:2006zr}. \subsection{Implications for NSC formation} The strong flattening of the MWNSC, as well as its alignment with and rotation parallel to the Galactic disc, agrees with the findings of \citet{Seth:2006uq} for extragalactic NSCs in edge-on spirals and supports their model of repeated in situ formation of stars in accreted gas discs. In fact, a disc of young stars is observed in the GC right now \citep[e.g.,][]{Levin:2003kx,Paumard:2006xd,Lu:2009bl}. One of the problems of the model discussed by \citet{Seth:2006uq} is how subsequent star formation in disc components from gas infalling from the galaxy plane can form an ellipsoid/spherical system. The case of the Milky Way shows that discs of recently formed stars must not necessarily be aligned with the galaxy plane. In fact, the clockwise system of stars in the central parsec lies at an angle of roughly 60\,degrees with the Galactic plane \citep{Paumard:2006xd}. As a result, while infalling gas will be aligned with the galaxy disc {\it on average}, this must not be true for an individual event. This is not surprising, given that the vertical extent of the NSC is orders of magnitude smaller than the scale height of the Galactic disc. About 50\% of the few million-year-old stars in the central parsec of the GC do not form part of the clockwise disc and appear to be distributed in a more isotropic way - or form part of a less-well defined disc/streamer \citep{Bartko:2009fq,Lu:2009bl}. This provides further evidence that in situ star formation from infalling gas may be able to create spheroidal systems. The flattening and rotation of the MWNSC support the notion that infall of material occurs, on average, along the GP. This means that a certain connection exists between the Galactic disc and the MWNSC. \citet{Antonini:2012fk} have studied the formation of the MWNSC by the repeated infall and merger of globular clusters. Their simulations can result in a flattened cluster with an axis ratio close to the one measured in this work. However, this result only holds for the inner 10\,pc of their simulated cluster, which, in addition, has a half-mass radius about twice as large as the one measured here for the MWNSC (assuming a constant mass-to-light ratio). Also, they find a low degree of rotation, which may contradict observations that indicate that the rotation of the NSC at radii of a few parsecs is of the same order of magnitude as its velocity dispersion \citep{Trippe:2008it,Schodel:2009zr}. It must be pointed out that models are usually fine-tuned to reproduce the current state-of-the art of observational knowledge. It is therefore possible that the infall of globular clusters may have provided a significant contribution to the stellar population of the MWNSC. No observational evidence still exists for the globular cluster infall scenario. The in situ formation scenario, however, is clearly supported by observations. Finally, \citet{Hartmann:2011uq} have compared integral-field spectroscopic observations of nuclear clusters with dynamical models and conclude that purely stellar dynamical mergers cannot reproduce the observations. On the other hand, they also exclude a formation scenario based on gas infall and only in situ formation. It is therefore likely that both processes contribute to the formation of NSCs. \subsection{Implications for stellar dynamics \label{sec:dynamics}} Our improved knowledge of the overall properties of the MWNSC are fundamental to understanding its formation and future evolution, as well as to interpreting observations of external systems that suffer from linear resolutions orders of magnitude smaller than in the Milky Way. A question of stellar dynamics that has attracted considerable attention in the past years is the problem of the formation of a stellar cusp around the central black hole. While cusp formation is a firm prediction of theoretical dynamics \citep[e.g.,][]{Alexander:2006fk,Merritt:2013uq,Preto:2010kx}, the distribution of the old -- and therefore dynamically relaxed -- stars within $0.5\,$pc of Sgr\,A* is significantly flatter than predicted by theory \citep{Buchholz:2009fk,Do:2009tg,Bartko:2010fk,Do:2013fk}. Several ideas have been forwarded to explain this discrepancy between theory and observations, among them that collisions may destroy the envelopes of giant stars and thus render the cusp invisible \citep[e.g.,][]{Dale:2009ca,Amaro-Seoane:2014fk} or that the cluster formed with a large core and has not yet reached equilibrium \citep{Merritt:2010ve}. What are the implications of the axisymmetry that we find here for the MWNSC? Deviation from sphericity has been addressed in the context of triaxial bulges, bars, or stellar discs on scales of 100\,--\,1000~pc, but also a number of theoretical studies have investigated non-spherical structures of the nucleus itself \citep{Holley-Bockelmann:2001fk,Holley-Bockelmann:2002uq,Berczik:2006kx,Merritt:2011cr,Vasiliev:2013ys,Khan:2013zr}. The origin of the non-sphericity in these studies can be the merger with another nucleus \citep{Milosavljevic:2001ly} or dissipative interactions between the stars and a dense accretion disc \citep{Rauch:1995ve}. Deviations from spherical symmetry are important in the study of galactic nuclei for two reasons. (i) One is the potential \emph{temporary} boost in disruption rates of extended stars or in the capture via gravitational radiation of compact ones \citep{Poon:2001qf,Holley-Bockelmann:2001fk,Holley-Bockelmann:2002uq,Merritt:2004bh,Poon:2004dq,Merritt:2011cr}. As discussed in \citet{Amaro-Seoane:2012nx}, deviations from non-sphericity lead to orbits that can get very close to the centre, the so-called ``centrophilic'' orbits. At distances within the sphere of influence, a significant percentage of stars might be on centrophilic orbits. The reason we call them temporary is that this would lead to a consequent depletion of stars in the loss cone, with the implication that current rates would drop, although this depends on the lifetime of the deviation from sphericity. The problem is not an easy one to model, so we usually have to resort to large simplifications. In particular, we must explore the behaviour of the potential \emph{very} close to the MBH because, by definition, the potential is completely dominated by the MBH at some point and, thus, spherically symmetric. The implications are still debated. Recently, \citet{Vasiliev:2013oq} have performed statistical models calibrated with direct $N-$body simulations for different values of the capture radius and the amount of flattening and found that the rates are only slightly enhanced, by a factor of a few. (ii) The second reason is the driving of massive binaries of black holes to distances below one parsec, the so-called ''last parsec problem'', in nuclei without gas. It has been claimed with direct-summation $N-$body integrations of galactic nuclei with an initial amount of rotation that triaxiality or axisymmetry alone drives the binary efficiently to coalescence in less than a Hubble time \citep{Berczik:2006kx}. However, \citet{Vasiliev:2013kl} have recently shown, also with direct-summation simulations, that the shrinkage of the binary does depend on the number of particles used in the simulations. They find a mild enhancement between their spherical and non-spherical models, of less than two, which translates into a warning in the extrapolation of numerical simulations to real galaxies \citep{Vasiliev:2013kl}. While it is true that it is very unlikely that the MW has recently had a major merger, a minor merger is not ruled out. Indeed, as we can see, for example, in Figure\,21 of \citet{Genzel:2010fk}, there is a significant part of the parameter space that still allows the existence of intermediate-mass MBHs in the GC (although there is a lack of evidence of any such object). In a broader context, if the MWNSC deviates from spherical symmetry, the same can be true for other nuclei, which might be harbouring binaries of SMBHs. From a theoretical standpoint, both tidal disruption or gravitational capture event rates and the last parsec problem in gas-poor galaxies remain open, and the input from observational data is crucial in our understanding of these scenarios. | 14 | 3 | 1403.6657 |
1403 | 1403.1594_arXiv.txt | Observations have revealed cold gas with large velocity dispersions ($\approx300$ km/s) within the hot outflows of ultra-luminous infrared galaxies (ULIRGs). This gas may trace its origin to the Rayleigh-Taylor (RT) fragmentation of a super-bubble or may arise on smaller scales. We model a ULIRG outflow at two scales to recreate this gas in three-dimensional hydrodynamic simulations using FLASH. Although resolution is limited, these models successfully produce cold gas in outflows with large velocity dispersions. Our small-scale models produce this cold gas through RT fragmentation of the super-bubble wall, but the large-scale models produce the cold gas after hot bubbles fragment the disc's gas into cold clouds which are then accelerated by thermal pressure, and supplemented by cooling within the outflow. We produce simple mock spectra to compare these simulations to observed absorption spectra and find line-widths of $\approx 250$ km/s, agreeing with the lower end of observations. | Nuclear and galactic scale outflows are common in ultra-luminous infrared galaxies (ULIRGs), and have been detected in X-Ray \citep{1996ApJ...457..616H,2003ApJ...591..154M,2003ApJ...592..782P,2009ApJ...691..261T} and H$\alpha$ \citep{2004ApJ...602..181C} emission as hot lobes extending $10-15$ kpc beyond the infrared-luminous portion of the galaxy. These ``super-winds'' are primarily driven by supernovae, with outflow rates comparable to the host's star formation rate ($\approx10-1000 M_\odot$/yr), and correspondingly high luminosities ($10^{41}-10^{44}$ erg/s) and projected velocities ($300-400$ km/s). Several observations \citep[e.g.][]{1993AJ....105..486P,2000ApJS..129..493H,2005ApJ...621..227M,2006ApJ...647..222M} have detected cold gas with large velocity dispersions in these outflows. The presence of this gas provides a challenge to theoretical models, which must explain how such a cold component \citep[i.e. NaI and KI absorption lines, with ionization potentials of 5.1 eV and 4.3 eV,][]{2005ApJ...621..227M} can exist within a flow of very hot ($T\sim10^6$ K) gas. These models must also explain the large velocity dispersion of this gas --- i.e. the large non-thermal broadening of the NaI lines. A number of works have investigated explanations for the cold component, often supported by numerical calculations \citep{1986PASJ...38..697T,2005ApJ...618..569M,2009ApJ...698..693F,2010ApJ...713..592E} and simulated spectra \citep{2009ApJ...698..693F,2011ApJ...734...24P}. In these models, cold gas is either produced in the disc and then advected by ram-pressure, or produced by gas rapidly cooling within the wind through radiative processes. In the simulations of \citet{2009ApJ...698..693F}, cold gas is produced by turbulence in the wind, which leads to dense condensations that rapidly cool. Specifically, these condensations trace their origin to a super-bubble, which is inflated by the outflow, driving a ``snowplough'' that builds up a dense bubble wall. The density of this wall allows it to cool efficiently, due to the $\rho^2$ dependency in radiative cooling, and the wall is supported against gravity by the pressure of the hot low-density gas within it. This situation is extremely susceptible to Rayleigh-Taylor (RT) \citep{1950RSPSA.201..192T,1984PhyD...12....3S} and Richtmyer-Meshkov (RM) \citep{CPA:CPA3160130207,meshkovref} instabilities, which cause the bubble wall to fragment into clouds that become a cold high velocity-dispersion component of the wind. This situation is difficult to analyze numerically, because the RT and RM instabilities can be strong at a wide range of wavelengths, and so simulations that strongly depend on the RT and RM instabilities will not converge until a fine enough resolution is used to resolve the full turbulent cascade. Alternatively, a sub-grid model for turbulent evolution can be considered, as we do in part II of this series. To better resolve the scales relevant to turbulent formation and destruction of clouds, the simulations of \citet{2009ApJ...698..693F} were performed in two dimensions with cylindrical symmetry. While this allows a resolution of as fine as $0.1$ pc in a $100$ pc by $200$ pc box, it suppresses modes of instability and gas flow that may be present in three dimensions. Furthermore, even at this high resolution, \citet{2009ApJ...698..693F} note a significant resolution dependence in the scale of these clouds, which suggests that the turbulence is still not fully-resolved. There is thus motivation to reexamine this scenario with a fully three-dimensional hydrodynamic model. However, even using adaptive methods, we are not able to attain an equivalent resolution in 3D models on currently available computer resources. Instead we develop 3D models with two scales of size --- one with the same scale as \citet{2009ApJ...698..693F} but lower resolution, and a full-scale galaxy model to examine large-scale effects. We also vary the initial conditions and mass loading rates, and thus produce a suite of models to investigate numerical effects. To facilitate a more direct comparison with observations, we have also produced a raytracing code for calculating mock NaI absorption spectra of the models. The layout of the paper is as follows: in section~\ref{simmodel} we give a summary of the simulation method for both the full galaxy and galaxy centre models. In section~\ref{raytracespectra} we present the raytracing and mock spectra algorithms. In section~\ref{cloudfind} we summarise the cloud tracking technique. In section~\ref{resultscoldflows} we present our results for the full galaxy models (section~\ref{fullgalaxyresults}) and galaxy centre models (section~\ref{galaxycentreresults}). We present our conclusions in section~\ref{coldflowsconc}. | \label{coldflowsconc} We performed three-dimensional simulations to explain the source of cold high velocity-dispersion gas in ULIRG outflows \citep[as observed by][in particular]{2005ApJ...621..227M}. Our initial conditions were set up to produce a scenario where clouds are produced by the fragmentation of the wall of a galactic super-bubble, induced by the Rayleigh-Taylor instability \citep[as in][]{2009ApJ...698..693F}. This was done in two scenarios, one focusing on the central $200$ pc of the galaxy, and another where the entire galaxy is included in the simulation domain. We produced spectra of the simulations with a raytracing algorithm to facilitate comparison with observation. Our models succeeded at producing cold outflowing gas with large velocity dispersions, but only at the higher resolutions. The velocity dispersions were $220-260$ km/s in our galaxy centre models, and $200-300$ km/s in our full galaxy models. These results are similar, and both agree with the lower end of the observations ($330\pm100$ km/s). Our two scales of simulation produce this cold outflowing gas through different means. In the highest resolution full galaxy models the cold disc gas is fragmented by the large number of hot bubbles produced in the disc. This gas is then pushed into the outflow by the intense pressure of the feedback beneath it, and is supplemented by cooling within the hot wind. In the lower resolution full-galaxy models, cold gas is only produced by cooling within the hot wind, or at very low resolutions, is not produced at all. In the galaxy centre models, the cold gas is instead produced by the Rayleigh-Taylor fragmentation of the wall of a feedback-inflated bubble. Precise determination of the most important process will require larger-scale and higher resolution simulations, perhaps with improvements to the physical model such as the inclusion of self-gravity and a more self-consistent feedback algorithm. In paper II, we will perform simulations with a sub-grid turbulence model to better model feedback and alleviate resolution issues. Nevertheless, in this paper we have demonstrated that cold gas with high velocity-dispersions can indeed be present in simulations of ULIRG outflows. | 14 | 3 | 1403.1594 |
1403 | 1403.6461_arXiv.txt | {The existence of lithium-rich low-mass red giant stars still represents a challenge for stellar evolution models. Stellar clusters are privileged environments for this kind of investigation.} {To investigate the chemical abundance pattern of the old open cluster Trumpler\,5, we observed a sample of four red-clump stars with high-resolution optical spectrographs. One of them (\#3416) reveals extremely strong lithium lines in its spectrum.} {One-dimensional, local thermodynamic equilibrium analysis was performed on the spectra of the observed stars. A 3D-NLTE analysis was performed to derive the lithium abundance of star \#3416.} {Star \#3416 is super Li-rich with A(Li)=3.75\,dex. The lack of $^6$Li enrichment ($^6$Li/$^7$Li$<$2\%), the low carbon isotopic ratio ($^{12}$C/$^{13}$C=14$\pm$3), and the lack of evidence for radial velocity variation or enhanced rotational velocity ($v\sin i = 2.8\,$\kms) all suggest that lithium production has occurred in this star through the Cameron \& Fowler mechanism.} {We identified a super Li-rich core helium-burning, red-clump star in an open cluster. Internal production is the most likely cause of the observed enrichment. Given the expected short duration of a star's Li-rich phase, enrichment is likely to have occurred at the red clump or in the immediately preceding phases, namely during the He-flash at the tip of the red giant branch (RGB) or while ascending the brightest portion of the RGB.} | Lithium is a fragile element that is destroyed at temperatures higher than 2.5$\times$10$^6$K, which may already be reached during the contraction of a protostellar cloud (pre-main sequence phase) that leads to a central hydrogen-burning star. Some depletion is known to take place in the atmosphere of stars similar to the Sun, whose lithium abundance is less than a hundredth the level we observe in meteorites and the interstellar medium (ISM, Population I value). In low-mass stars, additional depletion occurs once the star's atmosphere expands as the star evolves toward the red giant phase. At this stage, the convection in the stellar envelope brings material to the surface from the inner parts. This material was exposed to relatively high temperatures and is, therefore, depleted in lithium. Observations firmly confirm the scenario depicted above \citep[][]{gratton04}, and yet the existence of low-mass stars having lithium abundances in their atmosphere that exceed the prediction of standard stellar models (lithium-rich giants) and even the ISM level (super Li-rich giants) indicates that these stars must synthesize lithium in their interior. Planet engulfment can be advocated to explain lithium-rich giants, and some suggestive cases have been presented \citep[see, e.g.,][]{adamow12}. However, accretion of a planet or a brown dwarf in the stellar envelope would not be able to increase the surface abundance above the Population I value. Additionally, Li-rich giants do not show enhanced $^9$Be abundances, which would be expected if lithium enrichment is due to planet accretion \citep[][]{melo05}. Coupled with adequately modeled mixing in the stellar atmosphere, the \citet[][hereafter CF71]{cameron71} mechanism is considered a viable way to produce fresh lithium in intermediate-mass asymptotic red giants and low-mass red giants. The stellar convective envelope is first enriched in $^3$He after the first dredge up. The latter can be burned into $^7$Be if it is transported to regions with high enough temperature, like the hydrogen-burning shell. $^7$Be then decays into $^7$Li, which should be brought to the stellar surface on a fast enough timescale to escape destruction. Lithium will then be depleted again. The lithium-rich phase would, therefore, be a short-lived one, which would explain the low frequency ($\sim$1\%) of these kinds of stars \citep[][]{delareza12}. The identification of the sites responsible for this production is, however, challenging. Early indications supported the red giant branch luminosity bump for low-mass stars and the asymptotic giant branch clump for intermediate-mass stars, as the preferred evolutionary stages for lithium production \citep[][]{charbonnel00}. There are suggestions of possible clustering of Li-rich objects among central He-burning stars \citep[][]{kumar11}, while indications that there are lithium-rich stars all along the red giant branch (RGB) sequence have also emerged \citep[][]{monaco11}. Most of these studies were, however, limited by the lack of a proper evolutionary status determination. For these kinds of investigations, stellar clusters are, therefore, privileged environments, since they are single stellar populations, whose stars share a common distance, age, and metallicity. The evolutionary stages of cluster's stars are also readily identified. We present here our identification of a super Li-rich, core-helium-burning red-clump star in the old, massive open cluster Trumpler\,5 \citep[][]{kaluzny98}. | \label{disc} Stellar clusters provide easy access to a wealth of information about the basic parameters of stars in the underlying stellar population (evolutionary stage, age, mass, and metallicity) and are, in principle, ideal environments for investigating the phenomenon of lithium enrichment in giant stars. Unfortunately, specifically devised investigations \citep[][]{pilachowski00} have provided negative results. A few lithium-rich giants have been, however, identified in clusters, both open and globular \citep[][]{carney98,hill99,kraft99,ruchti11,twarog13}. They are generally found along the RGB, apart for the Population\,II Cepheid V42 discovered by \citet[][]{carney98} in the globular cluster M\,5. Here we have presented the detection of a super-lithium-rich star (A(Li)=3.75\,dex), among core He-burning red-clump stars in the open cluster Trumpler\,5. Traditionally, three possible causes of lithium enrichment beyond the level allowed by standard stellar evolution theory models have been suggested: preservation of the original lithium content, pollution by an external source, for instance, the engulfment of a planet or a brown dwarf and, finally, internal production through the CF71 mechanism. In the present case, the first possibility is excluded by the abundance higher than the ISM level in Star \#3416. Additionally, Trumpler 5 is very similar to the open cluster NGC2243 in terms of age and metallicity. Unevolved main sequence stars in this cluster have lithium abundances well below the Population\,I value \citep[A(Li)=2.70$\pm$0.20,][]{francois13}, in agreement with the abundance measured at similar metallicity in the Small Magellanic Cloud ISM \citep[][]{howk12}. It is, therefore, reasonable to think that Trumpler\,5 has a similar original lithium abundance. Furthermore, the low measured $^{12}$C/$^{13}$C ratio (14$\pm$3) indicates that this star underwent the internal mixing episodes associated with the first dredge-up and the RGB-bump level \citep[see][]{gratton04}. This is common for Li-rich giants, which do present evidence of the mixing they have experienced \citep[][]{charbonnel00}. In a similar vein, lithium enrichment due to a planet engulfment episode would not be able to raise the star's atmospheric abundance above the ISM value. This should also be recognizable by the presence of a large fraction of $^6$Li, which we rule out for Star \#3416. Increase in $^6$Li is also foreseen for lithium enrichment due to stellar flares \citep{tati}, which can also be ruled out as a cause of enrichment. Additionally, Star \#3416 presents a slow rotational velocity (2.8\,\kms), and we did not find any indication of binarity -- the radial velocities measured on the two UVES epochs and the MIKE observations are compatible with no variation ($\Delta v_{\rm helio}<$1\,\kms), given the errors in the measurements. A significant lithium production must then have occurred in the stellar interior of Star \#3416. For the three other stars in Trumpler 5, we measure lithium abundances A(Li)$<$1.3\,dex (see Table\,\ref{PA}). Star \#3416 thus shows a factor $\sim$280 increase in its surface lithium abundance, compared to other red-clump stars in Trumpler\,5. At which evolutionary phase was the lithium produced? Given the expected short lifetime of the Li-rich phase of a star and its high abundance, we may consider that enrichment in \#3416 appeared either during the current red-clump phase or just before, i.e. at the tip of the RGB and its connected core He-flash or on the brightest portion of the RGB. Trumpler\,5 red-clump stars have, in fact, a current mass range of $\sim$1--1.4\,M$_\odot$ (see Fig.\ref{cmd}), as derived by the comparison with isochrones from the \citet[][]{girardi02} collection and adopting the K98 parameters in terms of distance, reddening and age (4 Gyr). Other cases of lithium-rich giants associated with the red-clump phase have been suggested \citep[][]{ruchti11,kumar11,adamow12b,martell13}, but, being field stars, they lacked any firm determination of their evolutionary status. A preferred association of low-mass lithium-rich giants with the RGB-bump was proposed by \citet[][]{charbonnel00}. They argue that removing the mean molecular weight discontinuity left over by the first dredge-up occurring at the RGB-bump led to the onset of the extra mixing between the hydrogen-burning shell (HBS) and the envelope, allowing the CF71 mechanism to become an effective route for producing lithium-rich giants. Indeed, it is now accepted that the onset of thermohaline mixing at the RGB-bump will induce extra mixing between the convective envelope and the stellar interior \citep[see][and references therein]{eggleton08,charbonnel10}. The more robust sample studied by \citet[][hereafter KRL11]{kumar11}, on the other hand, supports an association with the red-clump region and lithium production associated with the He-flash at the RGB tip. We notice that a number of lithium-rich and super lithium-rich giants have been identified in the brightest portions of the RGB \citep[][]{kraft99,monaco08,monaco11,ruchti11,martell13}, therefore the \citet[][]{charbonnel00} or the KRL11 proposals are unable to embrace the whole complex phenomenology of lithium-rich giants, nor do they try to account for it \citep[see][]{charbonnel00}. Nevertheless, the existence of such a preferred association would be an important feature. That extensive surveys for Li-rich giants \citep[][]{monaco11,ruchti11,martell13} have failed to detect it calls for an explanation. This is, however, beyond the scope of the present paper. Suffice it to say here that the different studies may be covering different parameter spaces. As an example, the bulk of lithium-rich giants in the KRL11 work have \teff between $\sim$4500 and 5000\,K and log\,g between 1.3 and 2 (see their Fig.2, bottom panel), which is a region poorly sampled by the \citet[][]{martell13} survey (see their Fig.\,1). It is unclear at present if current stellar models are capable of producing a significant amount of lithium during the He-flash. We remark here that our stars very likely have lower masses than the KRL11 ones, and a lower amount of $^3$He might remain in the stellar envelope to allow for the CF71 mechanism to operate, after the depletion operated by thermohaline mixing \citep[][]{eggleton08}. Therefore, different mechanisms may have operated to produce the lithium abundances observed in KRL11 stars and in Star \#3416 in Trumpler\,5. Indeed, the \citet[][hereafter D12]{denissenkov12} models do not allow for lithium production during the He-flash \citep[see their discussion but also][for a possible alternative scenario]{mocak11a,mocak11b}. D12 proposes, alternatively, that lithium-rich stars identified as belonging to the red clump in the KRL11 sample may, in fact, be close to the RGB bump. but that some internal extra-mixing, perhaps related to fast internal rotation, may cause the stars to perform an excursion in the HR diagram towards redder and fainter magnitudes, compatible with the expected location of red-clump stars with masses of $\sim$2\,M$_\odot$. This scenario may apply to all the lithium-rich giants tentatively identified in the field as red-clump stars. It fails, however, to explain the Trumpler\,5 case. Stars compatible with the D12 hypothesis would be found at redder colors than the red clump and at fainter magnitudes, but this location is incompatible with Star \#3416. While the present paper was in the refereeing stage, the detection in the {\it Kepler} field of a core-helium-burning lithium-rich giant (A(Li)$_{NLTE}$=2.71) confirmed by asteroseismic analysis was reported \citep[][]{silva14}. As for Star \#3416, this giant is not carbon rich, and it presents a low carbon isotopic ratio ($^{12}$C/$^{13}$C$<$20). These two stars, then provide definitive confirmations of the existence of low-mass lithium-rich and super-lithium-rich stars among red-clump stars. The D12 model may, nevertheless, be at work in other cases. In this respect, it is important to notice the detection of a lithium-rich giant at a level below the RGB-bump in the open cluster NGC6819. This location may indeed be explained by the D12 model \citep[][]{twarog13}. | 14 | 3 | 1403.6461 |
1403 | 1403.3591_arXiv.txt | { A new method for analyzing the returns of the custom-made 'micro'-LIDAR system, which is operated along with the two MAGIC telescopes, allows to apply atmospheric corrections in the MAGIC data analysis chain. Such corrections make it possible to extend the effective observation time of MAGIC under adverse atmospheric conditions and reduce the systematic errors of energy and flux in the data analysis.\\ LIDAR provides a range-resolved atmospheric backscatter profile from which the extinction of Cherenkov light from air shower events can be estimated. Knowledge of the extinction can allow to reconstruct the true image parameters, including energy and flux. Our final goal is to recover the source-intrinsic energy spectrum also for data affected by atmospheric extinction from aerosol layers, such as clouds. } | Using the optimized atmospheric calibration technique in the MAGIC data analysis chain should enable a reliable use of data taken during moderate cloudy conditions. This way, the effective duty cycle of the telescopes will be extended by up to 15$\%$. Some low energy events close to the threshold will be lost, because they do not trigger any more. But for the higher energies, MAGIC will gain significantly in observation time. | 14 | 3 | 1403.3591 |
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1403 | 1403.3072_arXiv.txt | We study the capture and crossing probabilities into the 3:1 mean motion resonance with Jupiter for a small asteroid that migrates from the inner to the middle Main Belt under the action of the Yarkovsky effect. We use an algebraic mapping of the averaged planar restricted three-body problem based on the symplectic mapping of \citet{1993CeMDA..56..563H}, adding the secular variations of the orbit of Jupiter and non-symplectic terms to simulate the migration. We found that, for fast migration rates, the captures occur at discrete windows of initial eccentricities whose specific locations depend on the initial resonant angles, indicating that the capture phenomenon is not probabilistic. For slow migration rates, these windows become narrower and start to accumulate at low eccentricities, generating a region of mutual overlap where the capture probability tends to 100\%, in agreement with the theoretical predictions for the adiabatic regime. Our simulations allow to predict the capture probabilities in both the adiabatic and non-adiabatic cases, in good agreement with results of \citet{1995CeMDA..61...97G} and \citet{2006MNRAS.365.1367Q}. We apply our model to the case of the Vesta asteroid family in the same context as \citet{2008Icar..194..125R}, and found results indicating that the high capture probability of Vesta family members into the 3:1 mean motion resonance is basically governed by the eccentricity of Jupiter and its secular variations. | } Asteroid taxonomy classify the asteroids in different types according to the characteristics of their reflectance colors and/or spectra (e.g. \citealt{1984PhDT.........3T}; \citealt{2002Icar..158..146B}; \citealt{2009Icar..202..160D}). V-type asteroids are a particular class whose reflectance spectra have been recognized to be compatible with the spectra of the basaltic achondritic meteorites (e.g. \citealt{1993Sci...260..186B}; \citealt{1998AMR....11..163H}; \citealt{2001M&PS...36..761B}). Currently, the only known source for these asteroids is the Vesta family (e.g. \citealt{1997M&PS...32..903M}; \citealt{2005Icar..174...54M}) a group of asteroids in the inner Main Belt ($2.1<a<2.5$ AU) which constitute the outcome of a collision that excavated the basaltic surface of asteroid (4) Vesta more than 1 Gyr ago (e.g. \citealt{1970Sci...168.1445M}; \citealt{1997Sci...277.1492T}; \citealt{1997M&PS...32..965A}). Although most of the V-type asteroids, the so called vestoids, are found within the limits of the Vesta family ($2.22<a<2.47$ AU), several V-type bodies are also found far away from the family outskirts (e.g. \citealt{1991Icar...89....1C}; \citealt{2000Sci...288.2033L}; \citealt{2008Icar..194..125R}; \citealt{2008ApJ...682L..57M}; \citealt{2009P&SS...57..229D}), which raises the question of how these asteroids get to their current locations. Among the suggested mechanisms, \citet{2008Icar..194..125R} show that some V-type asteroids initially in the Vesta family would be able to cross the 3:1 mean motion resonance (MMR) with Jupiter (hereafter J3:1) at 2.5 AU to get to the middle Main Belt ($2.5<a<2.8$ AU). The crossing would be driven by a slow migration of the orbital semimajor axis induced by the thermal emission forces on the asteroid's surface, the so called Yarkovsky effect (e.g. \citealt{2002aste.conf..395B}). Inspired by this result, we address here the problem of resonance crossing/capture in the case of the J3:1 MMR from a wider perspective, aiming to investigate how this phenomenon happens and how the results of \citet{2008Icar..194..125R} can be interpreted in the light of the general resonance crossing/capture mechanism. Different authors have proposed different dynamical mechanisms to explain, at least partially, the presence of V-type asteroid in the inner Main Belt beyond the domains of the Vesta family. \citet{2005A&A...441..819C} showed that some V-type asteroids could have migrated from the Vesta family to their current orbits due to the interplay between the Yarkovsky effect and non-linear secular resonances. \citet{2008Icar..193...85N} addressed a similar interplay, but with two-body and three-body MMRs. Even the role close encounter with massive asteroids has also been proposed as a mechanism (\citealt{2007A&A...465..315C}; \citealt{2012A&A...540A.118D}). However, these mechanisms are not sufficient to account for all the V-type asteroids found in the inner Main Belt. To add to the puzzle, several V-type candidates have been recently discovered in the middle Main Belt (e.g. \citealt{2006Icar..183..411R}; \citealt{2008Icar..198...77M}), and although most of them still lack spectroscopic confirmation, they are strong photometric candidates. Some of these bodies have moderate sizes, with diameters between 2-5 km, and their origin is still a matter of debate. For the time being, the only reliable source of these asteroids should be the Vesta family. However, in order to reach their present locations, these asteroids should have crossed the J3:1 MMR which, at first hand, appears a near impossible task due to the strong chaotic behavior that a small asteroid temporarily trapped in this MMR would experiment. Actually, it is well known that even in the simplest models, the J3:1 resonant motion drives asteroids to high- and very high-eccentricity orbits in less than a few tens of million years (\citealt{1982AJ.....87..577W}; \citealt{1991pscn.proc..177F}; \citealt{1996CeMDA..64...93F}). This behavior allows the asteroids to cross the orbits of Mars and of the Earth, thus being removed by close encounters with these planets. \citet{2008Icar..194..125R}, used full N-body simulations, including the perturbations of all the planets from Venus to Neptune, to find that for asteroids with diameter of the order of 0.1-1.0 km there is a small probability ($\sim3\%$) of crossing this resonance going from the inner to the middle Main Belt. For larger bodies, the probability would be even lower. In principle, the results of \citet{2008Icar..194..125R} could only explain very few cases of V-type candidates in the middle Main Belt. The above scenario raises some questions like: Is the interaction with the J3:1 MMR enough to explain other V-type candidates? How does the resulting evolution depend on the asteroid's size? What dynamical effects are relevant to the crossing/capture probability? Would other planetary configurations lead to different results? These questions shift the spotlight from the origin of the V-type asteroids to a more fundamental issue: What is the capture/crossing probability in the J3:1 MMR? And how does this vary in different dynamical models and migration regimes? The problem of resonance trapping has been approached by many authors. \citet{1975PriMM..39R.621N} presented one of the first studies of passages through a resonance separatrix with a slowly-varying parameter (i.e. adiabatic regime). \citet{1979CeMec..19....3Y} calculated the capture probability in the case of a simple pendulum, while \citet{1982CeMec..27....3H} extended the study to the second fundamental model for first-order resonances. The case of higher-order commensurabilities was undertaken by \citet{1984CeMec..32..109L} and by \citet{1984CeMec..32..127B}. Finally, \citet{1990Icar...87..249M} analyzed the capture in secondary resonances including mutual inclination between the asteroid and the perturbing planet. All these works, however, deal with the adiabatic case in which the migration timescale towards the resonance is much longer than the libration period. For very small asteroids, however, the Yarkovsky effect may lead to a non-adiabatic migration (e.g. \citealt{1998Icar..132..378F}; \citealt{2000Natur.407..606V}), and many of the classical predictions by the above authors may not be valid. The problem of resonance capture/crossing under a non-adiabatic regime is still little understood. \citet{1995CeMDA..61...97G} studied the evolution of small particles migrating due to the Poynting-Robertson drag. He found that the capture probability decreases for increasing migration rates, especially for almost circular orbits. A similar result was also found by \citet{2006MNRAS.365.1367Q}, who addressed the case where the migrating body is the perturber. In particular, this author introduces a simple semi-analytical model which allows her to study the capture probability in a single MMR of any order and also in the occurrence of a secondary resonance. Recently, \citet{2011MNRAS.413..554M} used a Hamiltonian model to investigate the capture probabilities in first and second order resonances considering different scenarios like planet migration through a gas disk, through a debris disk, and also dust migration under the Poynting-Robertson drag. These authors found that resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. They also found that more massive planets can capture particles at higher eccentricities and migration rates. In this work we focus on the behavior of convergent migration towards the J3:1 MMR due to the Yarkovsky effect, both in the adiabatic and non-adiabatic regimes. We are particularly interested in three key issues: (i) how the capture probability changes with the migration rate, (ii) the effects of different dynamical models, and (iii) an application of these results to the Vesta family. We are also interested in the behavior of the dynamical system for a wide range of migration rates, and consequently will also discuss drifts that correspond to meteoroid-size bodies. Since the orbital evolution of such small particles is also influenced by other physical processes (e.g. YORP, spin reorientations, etc), our results for this high non-adiabatic regime should not be considered as accurate predictions, but solely for theoretical completeness. The paper is organized as follows. In Sect. \ref{model}, we present our dynamical model and equations of motion. In Sect. \ref{mapping}, we introduce an algebraic mapping that allows us to follow the evolution of a huge number of sets of initial conditions with less computational cost. The probability of resonance capture in the adiabatic and non-adiabatic cases is discussed in Sect. \ref{capture}. Numerical simulations with our mapping in both adiabatic and non-adiabatic regimes are presented in Sect. \ref{simula}. An application of our results to the present-day distribution of V-type asteroids is given in Sect. \ref{compa}. Finally, conclusions close the paper in Sect. \ref{conclu}. | } In this work, we have studied the capture vs. crossing probability into the 3:1 mean motion resonance with Jupiter for an asteroid that migrates from the inner to the middle Main Belt under the action of a force that produces a secular change on its orbital semimajor axis. We were specially interested in the behavior of asteroids belonging to the Vesta family, that can migrate due to the thermal emission forces producing the so called Yarkovsky effect. In order to perform a statistically significant analysis, we developed an algebraic mapping of the restricted three body problem, averaged over the synodic angle. The mapping is based on the symplectic approach developed by \citet{1993CeMDA..56..563H}, but we add the secular variations on the orbit of the perturber, as well as non-symplectic terms to simulate the migration. The mapping has the advantage of being much faster than a full three-body high-order integration, but keeping the basic features of the behavior of the full model. This allowed us to perform a huge set of simulations with less computational cost. Moreover, the mapping model has the advantage that different parts of the model (eccentricity of Jupiter, secular variations, etc.) can be switched on and off, thus allowing us to analyze the relevance of these parts on the actual dynamics. To simplify our study, we concentrated on three planar models (although the mapping could be easily extended to take into account the orbital inclinations of the bodies), according to the behavior of Jupiter's eccentricity: (i) circular model, (ii) elliptic model, and (iii) elliptic model with secular variations due to the other Jovian planets. The mapping results have been compared to numerical simulations of the full equations of motion for the circular and elliptic models, obtaining a very good agreement. At very fast migration rates, most of the asteroids cross the resonance, while the few that are captured have initial eccentricities within a given range or ``window''. As the migration rate slows down, this window shifts to smaller eccentricities and becomes narrower, while new, even narrower, windows start to appear at higher eccentricities. At very slow migration rates, the shift of the windows to smaller eccentricities produces and accumulation of them, and their mutual overlap generates a region of very low $e$ where the capture probability is 100 \%, in agreement with the theoretical predictions. Using the mapping, we have performed simulations of initial conditions distributed over a line in the $a-e$ plane close to the left branch of the resonance separatrix. For each initial condition, the initial angles $\theta=2\sigma$ and $\Delta\varpi$ were distributed between 0 and 2$\pi$. Testing different values of the migration rate, we arrive to the following results: \begin{itemize} \item For the fastest migration rates (i.e. highly non-adiabatic regime) almost all the asteroids are able to cross the resonance without being captured. The first captured orbits appear in the elliptic and secular elliptic models for values of $\dot{a}_{Y}=5.0\times10^{-4}$ AU/yr ($D=0.05$ cm) and slower ones. For the circular model, captures start at $\dot{a}_{Y}=2.5\times10^{-4}$ AU/yr ($D=0.1$ cm). \item For the non-adiabatic case, we obtained similar results to those of \citet{1995CeMDA..61...97G}. The capture probability increases for increasing eccentricity until it reaches a maximum value (always less than 1) at an eccentricity $e_{max}$. From this value on, the probability decreases for increasing eccentricity, tending asymptotically to zero. Nevertheless, we observe several fluctuations along the probability curve due to the presence of the above mentioned capture windows. These fluctuation tend to disappear as we approach the adiabatic case. \item The limit between the non-adiabatic and adiabatic regimes occurs for $\dot{a}_{Y}=2.5\times10^{-7}$ AU/yr ($D=1$ m) in the circular model, and for $\dot{a}_{Y}=5.0\times10^{-6}$ AU/yr ($D=5$ cm) in the elliptic and secular elliptic models. \item For both the adiabatic and non-adiabatic regimes, our capture probabilities show a behavior similar to that described by \citet{2006MNRAS.365.1367Q}, even though her model significantly differs from ours. \end{itemize} We computed the total capture probability as a function of the migration rate, by integrating over a range of eccentricities. Along the range $0\leq e\leq0.4$, we obtained that, in the adiabatic limit, the probability tends to 40$\%$ in the circular model and to 30$\%$ in the other models. Restricting the integral to the range $0\le e\leq0.04$, we found that the total capture probability is 100$\%$ for a migration rate of $\dot{a}_{Y}=5.0\times10^{-7}$ AU/yr ($D=50$ cm) in the circular model, and for $\dot{a}_{Y}=5.0\times10^{-6}$ AU/yr ($D=5$ cm) in the elliptic models. It is worth noting that these rates are compatible with the rates at which the transition between the non-adiabatic and adiabatic regimes actually occur. On the other hand, integrating over the interval $0.04\leq e\leq0.4$, the capture probability tend to 30 \% in the adiabatic limit, independently of the model. All these percentages are approximate, and have been estimated from the outcome of a series of simulations for each system. A complete error estimation is beyond the scope of this paper, and not necessary for the current discussion. Finally, integrating over the range of eccentricities typical of the Vesta family, $0.07\leq e\leq0.14$, we found that in the circular model the capture probability tend to 50 \% for $\dot{a}_{Y}\leq5.0\times10^{-6}$ AU/yr (i.e., $D>5$ cm). However, in the elliptic models the probability is at least 87 \% and 96 \%, respectively, for $\dot{a}_{Y}\leq1.0\times10^{-9}$ AU/yr (corresponding to $D>250$ m). This result is in agreement with those of \citet{2008Icar..194..125R}, who found that the capture probability of real asteroids under the perturbation of a full Solar System model is about 97 \%. We conclude that the high capture probability of Vesta family members into the J3:1 MMR is basically governed by the eccentricity of Jupiter and its secular variations. The direct perturbations of other planets over the asteroids can be disregarded in the description of this phenomenon. | 14 | 3 | 1403.3072 |
1403 | 1403.0717_arXiv.txt | { We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of orbital elements, we use the phase-space coordinates the object would have at a given point in its (Keplerian) orbit if the perturbing forces were removed. This formulation is suitable for almost any numerical integrator; thus, multistep schemes are easy to build, stepsize can be adjusted, and dissipative forces are allowed. Compared with traditional non-symplectic N-body integrators, the approach often offers increase in speed or accuracy if perturbations are small. | Objects in sparsely populated systems dominated by a single massive body spend most of their time in the perturbed two-body state. Since Euler and Lagrange, dynamicists have constructed integration methods that can explicitly take into account this near-integrable character of problems in celestial mechanics. In principle, any scheme that returns the exact Kepler orbit of a two-body problem when perturbations are removed describes the system much better than a `blind' conventional N-body method (such as one of Gauss-Jackson or other multistep and double-integration type), the foremost advantage being a longer timestep. No single integration method is automatically superior to others, owing to the fact that different problems usually require somewhat different approaches. However, traditional schemes modelled in cumbersome forms and variables have lately been replaced by symplectic integrators (SIs): in addition to allowing the representation of near-integrability, they exhibit no secular growth of energy error. Development in this field has been rapid in recent years, and some of the disadvantages of early SIs have been alleviated by, e.g., symplectic correctors, (limited) adjustability of stepsize, and the possibility to accommodate weak dissipative forces (see, e.g., Levison \& Duncan \cite{Le94}; Saha \& Tremaine \cite{Sa94}; Wisdom, Holman \& Touma \cite{Wi96}; Mikkola \cite{Mi97}, \cite{Mi98}). Symplectic integrators that allow close encounters have also been constructed (Duncan, Levison \& Lee \cite{Du98}; Chambers \cite{Ch99}; Mikkola \& Tanikawa \cite{Mi99}; Preto \& Tremaine \cite{Pr99}; Levison \& Duncan \cite{Le00}). However, SIs cannot by definition tackle general non-Hamiltonian forces, and there is as yet no proper way of using multistep information to build inexpensive high-order schemes. The principal manifestation of traditional methods is analytical perturbation theory (often referred to as `general perturbations'). In the numerical domain (`special perturbations') most of the traditional schemes have now little more than historical interest: they were developed for pen and paper, not for modern computing machines. However, the method known as `variation of parameters' or `variation of arbitrary constants', used in different forms by Euler, Lagrange, Poisson and many others after them (see, e.g., Herrick \cite{He72}; Danby \cite{Da87}), is quite useful in its basic principle. The main question is the choice of parameters, which we discuss in this paper. The geometric Keplerian elements (and their variants) have usually been the first choice for variational formulation; however, they are not the best option for modern purposes. We describe an approach that uses the phase-space coordinates the object would have at a given point in its (Keplerian) orbit if the perturbing forces were removed. This results in a simple near-integrable formulation that is suitable for almost any numerical integrator; one is thus free to build multistep or hybrid schemes, vary the stepsize, and add dissipative forces. This scheme is, in a way, complementary to SIs, offering an increase in speed or accuracy in problems of celestial mechanics where SIs cannot be employed. The basic principles and concepts are presented in Sect.\ 2. In Sect.\ 3 we describe a choice of frame in which low-order methods are especially simple to integrate. In Sect.\ 4 we define another frame; in this case, any high-order multistep scheme can be efficiently applied. In Sect.\ 5 we discuss numerical results, and Sect.\ 6 sums up. | The primary motivation for our study was to find out whether there is a way of formulating a near-integrable non-symplectic scheme more efficient than the direct N-body computation. The traditional perturbative methods are now {\it pass\'e}, but some of their basic principles can still be used for efficient numerical computation. Since the straightforward formulation presented here is based on the choice of the integrated variables, the actual integration method can be chosen quite freely. The simplest frame is the one with $t_0=t$, best used with low-order extrapolation methods such as Bulirsch-Stoer; the longest integration steps are allowed by high-order multistep schemes in a spatially fixed frame. The error in integration depends on the specific method chosen; not much can be said about the error elements introduced by the generic principle. Various numerical experiments indicate that (e.g., in the case of our solar system) the stepsize can be sizably larger in this approach than in a non-perturbative one to cause similar error magnitudes in the two methods. The main limitation is, of course, the strength of the perturbation: roughly speaking, its maximum value for efficient use is of the order of one percent of the dominating force. Integrators based on near-integrability are somewhat more efficient than direct ones, but this advantage is not as clear as that provided by symplectic integrators especially in long-term integrations. The special characteristics exhibited by SIs in symplectic systems are, indeed, quite remarkable, and due to a `deeper' connection with the dynamics of the system than mere near-integrability and conservation of energy. However, when SIs cannot be used, the next best thing to do to maintain some knowledge about the nature of the system may often be to use the near-integrable formulation. In some cases (especially in dissipative systems) the advantage gained can be considerable. | 14 | 3 | 1403.0717 |
1403 | 1403.0651_arXiv.txt | The recurrent nova (RN) V745 Scorpii underwent its third known outburst on 2014 February 6. Infrared monitoring of the eruption on an almost daily basis, starting from 1.3d after discovery, shows the emergence of a powerful blast wave generated by the high velocity nova ejecta exceeding 4000 kms$^{-1}$ plowing into its surrounding environment. The temperature of the shocked gas is raised to a high value exceeding 10$^{8}$K immediately after outburst commencement. The energetics of the outburst clearly surpass those of similar symbiotic systems like RS Oph and V407 Cyg which have giant secondaries. The shock does not show a free-expansion stage but rather shows a decelerative Sedov-Taylor phase from the beginning. Such strong shockfronts are known to be sites for $\gamma$ ray generation. V745 Sco is the latest nova, apart from five other known novae, to show $\gamma$ ray emission. It may be an important testbed to resolve the crucial question whether all novae are generically $\gamma$ ray emitters by virtue of having a circumbinary reservoir of material that is shocked by the ejecta rather than $\gamma$ ray generation being restricted to only symbiotic systems with a shocked red giant (RG) wind. The lack of a free-expansion stage favors V745 Sco to have a density enhancement around the white dwarf (WD), above that contributed by a RG wind. Our analysis also suggests that the WD in V745 Sco is very massive and a potential progenitor for a future SN Ia explosion. | The symbiotic recurrent nova V745 Scorpii experienced its third known outburst recently on 2014 February 6.694 UT (Stubbings 2006) with two earlier eruptions being recorded in 1937 and 1989. It is a relatively less well studied nova amongst the 10 currently known RNe (viz., T Pyx, IM Nor, CI Aql, V2487 Oph, U Sco, V394 CrA, T CrB, RS Oph and V3890 Sgr) and belongs to the sub-class of RNe which have giant secondaries (viz., RS Oph, T CrB and V3890 Sgr). The secondary has been classified to be a giant of spectral type M6 III $\pm$ 2 sub classes (Harrison et al. 1993; Anupama $\&$ Mikolajewska 1999; Duerbeck et al. 1989; Sekiguchi et al. 1990; Williams et al. 1991) with an orbital period of 510 $\pm$ 20 days (Schaefer 2009). V745 Sco is a very fast nova with $t_{2}$ and $t_{3}$ of 6.2 and 9 days respectively which is estimated to lie at a distance of 7.8 $\pm$ 1.8 kpc in the middle of the galactic bulge (Schaefer 2010). Optical studies of the 1989 eruption are documented in Sekuguchi et al. (1990) and Duerbeck et al. (1989). The latter work shows the early spectroscopic evolution through a montage of 8 spectra covering the period between $\sim$ 10 to 40d after outburst. Other spectroscopic studies include those by Williams (2003) and Wagner (1989). In the infrared, Sekiguchi et al. (1990) recorded the lightcurves in the $JHKL$ bands while a near-IR spectrum at $\sim$ 70d after outburst was recorded by Harrison, Johnson $\&$ Spyromilio (1993). The observational coverage of this RN is sparse and there are notably no early time IR spectra which record its evolution in the infrared. This work, and another in preparation, should contribute to filling this gap. We have been obtaining multi-epoch, photometric and spectroscopic NIR observations in the 0.85 to 2.4 $\mu$m region starting from 1.3d after discovery. During the course of analysis it was noticed that the emission lines were rapidly narrowing with time. This phenomenon is rarely seen and is indicative of decelarating matter associated with a shock which in turn can be associated with $\gamma$ ray generation (see below). The other similar instances where such a phenomenon was witnessed earlier was in RS Oph (Das et al. 2006) and V407 Cyg (Munari et al. 2010). Since the development of a strong shock in V745 Sco is a rare and significant phenomenon, we use part of our data covering only the {\it I} and {\it J} bands to analyse and study the implications of the event. In a follow-up paper, we will present a more detailed analysis using our complete $JHK$ spectroscopy and photometry as in RS Oph (Banerjee et al. 2010). The present 2014 outburst is being observed at all wavelengths from radio to the $\gamma$ ray regime (Rupen et al. 2014, Banerjee et al. 2014, Anupama et al. 2014, Page et al. 2014, Mukai et al. 2014, Luna et al. 2014, Rana et al. 2014, Cheung et al. 2014). Among the notable early results is the reported detection of $\gamma$ rays from the object (Cheung et al. 2014). This has important ramifications for the present study. $\gamma$ ray detections from nova are recent and few in number and V745 Sco is only the sixth nova to be detected in $\gamma$ rays after V407 Cyg, Nova Sco 2012, Nova Mon 2012, Nova Del 2013 and Nova Cen 2013. All detections have been made by the Fermi LAT starting with the first detection in V407 Cyg in 2010 (Abdo et al. 2010). As per present understanding, $\gamma$ rays from novae are generated by a diffusive acceleration mechanism as particles rebound back and forth across a shockfront created by the nova's ejecta plowing into a pre-existing dense surrounding medium. Generically it is the same principle that leads to creation of high energy cosmic rays. A shock is thus an essential prerequisite for $\gamma$ ray generation and it is hence very necessary to establish its presence unambiguously. V407 Cyg was the first $\gamma$-ray nova where the decelerating shock front was clearly detected (Munari et al. 2010). Unfortunately during the 2006 RS Oph outburst no $\gamma$-ray observing facility, with comparable sensitivity as the Fermi telescope, was available. The generation mechanism of the $\gamma$ ray emission in novae is also under debate. For the shock to develop it is necessary to have a dense ambient medium into which the nova ejecta propagates and decelerates. In the case of V407 Cyg and RS oph the pre-existing dense ambient medium is provided by the high mass-loss from the secondary late-type giant star (the companion in V407 Cyg is a Mira variable). In contrast, for instance in the case of Nova Mon 2012 - another $\gamma$ ray nova - it is fairly certain that the companion is not a late-type giant (Munari et al. 2013) and hence cannot provide the dense ambient medium through copious mass loss. Thus there is uncertainty as to how $\gamma$ rays are indeed generated in novae systems. In this context, recent calculations show that a late-type giant's wind, solely by itself, may not be enough to create the requisite density enhancements necessary to explain the observed behavior of the $\gamma$ ray light curve. Additional sources of density enhancement in the form of a reservoir of circum-binary material around the WD is perhaps needed (Martin $\&$ Dubus 2013). This is a new point of departure from earlier thinking and interestingly enough, similar arguments for pre-existing circum-binary material were already proposed by Williams (2013) from totally different considerations. In such a context, the eruption of V745 Sco is thus an important testbed for understanding unexplained aspects of $\gamma$ ray generation in novae. | We present in Figure 1 the complete set of spectra in the $\it IJ$ band between 0.85 to 1.35 $\mu$ms obtained from Mount Abu. The major lines are marked and it may be seen that most of the lines are of H and He with HeI 1.0830 $\mu$m overwhelming all other lines in strength. The NIR spectra are typical of the He/N class of novae (Banerjee \& Ashok 2012) and are fairly similar to those observed in RS Oph except that the strength of Lyman beta fluoresced OI 1.1287 $\mu$m line develops relatively much slower in V745 Sco. Unlike Duerbeck et al. (1989), who detected coronal lines $\sim$ 10d after outburst, we do not see any coronal lines during the span of our observations. The highest excitation lines seen here are due to HeII. The spectrum obtained from FIRE is showed in Figure 2. All the emission lines of Figure 1 are clearly seen here too but at higher resolution. The sequence of Brackett lines in the H band between Br 10 at 1.7362 $\mu$m to Br 25 at 1.4967 $\mu$m is rather striking. A magnified view shows that mild first overtone CO emission at 2.29 $\mu$m and beyond, arising from the secondary, had already begun to appear in the FIRE spectrum. The CO features became more pronounced with time as emission from the secondary becomes dominant. This is demonstrated in the bottom panel of Figure 1 which shows two $\it K$ band spectra; one on 1.3d and the other 12.3d after outburst-- in the latter the CO bands are clearly seen. Figure 3 well illustrates the evolution of the profile of the Pa$\beta$ 1.2818 $\mu$m line which was chosen since it is both a strong line and also unblended with other lines. Profile width measurements are therefore reliable. The observed profiles are composed of a broad component which is attributed to the nova ejecta on which is superposed a sharp and narrow component. The profiles are very similar to those seen in V407 Cyg in which the sharp component was attributed to the sudden ionization of a large fraction of the secondary's wind by the flash of energetic radiation produced by the thermonuclear event (Munari et al. 2010). A similar origin is proposed here too. What is striking is the rapid narrowing of the profiles with time. We decomposed each profile into two gaussians representing the broad and narrow components respectively and measured the evolution of their FWHM (full width at half-maximum) values. A representative two gaussian fit to one of the profiles is shown in Figure 3 with the variation of the FWHM's with time is shown in the bottom panel. The right panel shows a similar evolution for the 2010 outburst of V407 Cyg from unpublished material not included in Munari et al (2010). The shape and evolution of the profiles of both objects share a good similarity. For V745 Sco, the narrow component from the Mira wind does not show much variation. During the early stages it is kinematically perturbed to some extent but its FWHM gradually tends to evolve towards its value observed at quiescence. We consider the FWHM of the H lines in quiescence to be adequately represented by the FWHM of the H$\beta$ line whose intrinsic width (corrected for instrumental broadening) is $\sim$ 450 $\pm$ 15 kms$^{-1}$ (Munari, private communication) as presented in the high-resolution atlas of symbiotic stars by Munari \& Zwitter (2002). We discuss the evolution of the broad component in V745 Sco below. The behavior of the shockwave as it propagates into the dense ambient medium surrounding the WD is usually divided into the following stages (e.g. Bode \& Kahn 1985). First is a free expansion or ejecta-dominated stage, where the ejecta expands freely and the shock moves at a constant speed without being impeded by the surrounding medium. This phase generally extends to the time it takes for the swept-up mass to equal the ejecta mass. The second phase is a Sedov-Taylor stage, where the majority of the ejecta kinetic energy has been transferred to the swept-up ambient gas. This is an adiabatic phase since the shocked material is so hot that there is negligible cooling by radiation losses. During this phase a deceleration is seen in the shock whose velocity {\it v} versus time {\it t} is expected to behave as {\it v} $\propto$ $t^{-1/3}$, assuming a $r^{-2}$ dependence for the decrease in density of the wind. In phase 3, the shocked material has cooled by radiation, and here the expected dependence of the shock velocity is {\it v} $\propto$ $t^{-1/2}$. One may mention that the strong X-ray blast wave, seen during the 2006 outburst of RS Oph, largely conformed to the above behavior (Sokolski et al. 2006; Bode et al. 2006). The free expansion stage was not seen in V745 Sco whose implications need to be understood. The intrinsic colors of the late M type giant in V745 Sco are estimated to be $(J-H)$$_{0}$ $\sim$0.95 and $(H-K)$$_{0}$ $\sim$0.41 using 2MASS magnitudes of $JHK$ = 10.04, 8.85 $\&$ 8.3 respectively as quiescent values and correcting them using an adopted reddening value of $E(B-V)$ = 0.70 (Schlafly \& Finkbeiner 2011). A value of $E(B-V)$ $>$ 0.6, for the estimated distance of 7.8 kpc to V745 Sco, is also supported from modelling of the galactic interstellar extinction by Marshall et al. (2006). On an IR color-color diagram (see Figs 6 \& 4 of Whitelock \& Munari, 1992) this places it among galactic bulge giants, a conclusion that was also reached by Sekiguchi et al. (1990). A comparison by Whitelock \& Munari (1992) of the IR characteristics of neighborhood M giants, bulge M giants and the M giants of S type symbiotic systems shows that the M giant secondaries in symbiotic systems are very similar to those in the bulge and are thus low mass ($<$ 1 M$_{\odot}$) objects. We adopt this as an upper limit for the mass of the secondary in V745 Sco. It is also likely that a significant fraction of all the symbiotic M stars are actually asymptotic giant branch (AGB) stars rather than giant branch stars (Kniazev et al. 2009). This suggestion that symbiotics have AGB stars as mass donors would support the view that additional mass could be transferred through the stellar winds, above that transferred via Roche lobe overflow, since the winds from AGB stars are stronger than from normal giants. We thus adopt a mass loss rate of around 10$^{-7}$ M$_{\odot}$yr$^{-1}$. This is a reasonable value for an AGB star and also in line with that chosen for V407 Cyg (Martin $\&$ Dubus; 2013). Assuming a high-mass for the WD (in the range 1.2 to 1.4 M$_{\odot}$), M$_{sec}$ $\sim$ 1M$_{\odot}$ and orbital period of 520d, the separation between the binary components in V745 Sco is tightly constrained in the range 1.4 to 1.5 AU. In the elapsed time of 1.3d between onset of outburst and our first observation, the blast wave traveling at at over 4000 kms$^{-1}$ will sweep up material within a radius of 3 AU from the WD. The mass of this material is estimated to be M$_{swept}$ = 0.7$\times$10$^{-7}$M$_{\odot}$ assuming (d$\dot{\textrm{M}}$/dt)$_{secondary}$ = 10$^{-7}$ M$_{\odot}$yr$^{-1}$, a geometric 1/r$^{2}$ dilution in the density profile of the RG wind and a velocity of the RG wind of 10 km/s. Increasing the wind velocity will reduce M$_{swept}$ while increasing (dM/dt)$_{secondary}$ will linearly increase it. But for a reasonable physical choice of parameters M$_{swept}$ appears constrained between 10$^{-7}$ to 10$^{-6}$ M$_{\odot}$. M$_{swept}$ is estimated assuming the material between WD and secondary has no additional enhancements beyond that due to spherically symmetric wind from the secondary (see Figure 1 of Martin $\&$ Dubus, 2013). The free expansion stage, if it ever occurred, had commenced and completed before our first observation made 1.3d after discovery. The small value of matter swept out during these 1.3d indicates one of two possibilities. First, the mass of the ejected matter M$_{ej}$ in the outburst is small and of the order of M$_{swept}$. The small value of M$_{ej}$ in turn would imply that the central WD is massive since the critical mass of the accreted envelope required to trigger a thermonuclear runaway is inversely proportional to the mass of the WD ($M_{acc}=\frac{4\pi{R_{WD}}^4P_{crit}}{GM_{WD}}$ where $P_{crit}$=1020 dyne cm$^{-2}$ for $M_{WD}$ = 1.4 $M_{\odot}$; Truran $\&$ Livio 1986). The second conclusion that can be drawn from a free expansion stage that is either very short-lived (< 1.3 d) or absent is that the ejecta was very quickly impeded by additional material apart from the giant's wind. That is, the Martin \& Dubus (2013) hypothesis positing additional material enhancement, as applicable to V407 Cyg, is valid here too. Preliminary results from the $\gamma$ ray detection by Fermi-LAT data indicates the detections with largest observed significances were on 2014 February 6 and 7 with no significant emission (within stipulated detection limits given) was detected in the subsequent days through the end of 2014 February 10. The fact that the $\gamma$ rays peaked early, coincident with the optical outburst, strongly points at a dense circumbinary reservoir around the WD. The greatest difficulty that Martin \& Dubus (2013) faced while reproducing the $\gamma$ ray lightcurve of of V407 Cyg was in simulating the early peaking of the $\gamma$ ray emission using just a RG wind. To overcome this they were forced to invoke the presence of dense additional matter close to the WD. It may be noted that the above argument does not rule out the possibility of a small ejecta mass (or equivalently a massive WD). Independent support for a high mass WD is found in the extremely early turn-on of the super-soft X-ray phase at $\sim$3d after discovery (Page et al. 2014). This, coupled with the very high ejecta velocities observed, imply the presence of very low mass ejecta and thereby a massive WD (Figure 6 of Schwarz et al., 2011). V745 Sco thus could be a potential progenitor candidate for a SN Ia explosion by virtue of having a high mass WD whose mass additionally, as in other similar symbiotic systems like RS Oph, T CrB and V3890 Sgr, is suggested to be increasing after each outburst (Hachisu $\&$ Kato 2001; Hachisu, Kato $\&$ Luna 2007). The adiabatic (decelerative) phase in Figure 2 deviates significantly from the $t^{-1/3}$ dependency indicating that the shock is propagating into a wind which is not spherically symmetric. The reasons for this are two fold. The nova shell is expected to be slowed down more effectively in the parts moving in the direction of the RG due to the increasing density in that direction. In addition, as discussed above, there is additional material, most likely distributed over the equatorial plane. The combined effect of these is to make matter distribution around the WD's position anisotropic and the shockfront should thus rapidly becomes aspherical. Good support for this is offered by the detailed radio monitoring and modeling of the V407 Cyg outburst by Chomiuk et al. (2012; refer their Figure 6). V745 Sco was observed 10d after the optical discovery on February 16 with NuSTAR showing a luminous hard X-ray source whose spectrum could be modeled by a plasma in collisional ionization equilibrium at kT = 2.6 keV or equivalently 3.02$\times$10$^{7}$K (Rana et al. 2014). This is consistent with what we observe. For a strong shock, the post-shock temperature $T_{s}$ is given by $T_{s}= \frac{3\bar{m}v^{2}}{16k}$ where k is the Boltzmann constant and $\bar{m}=10^{-24}$g is the mean particle mass including electrons (Bode et al. 2006). On day 10.3 we measure $v$ = 1930 kms$^{-1}$ equivalent to a temperature of 5.05$\times$10$^{7}$K which agrees satisfactorily with the X ray result. Extending the calculations, the gas must have been heated to extremely high temperatures exceeding 1$\times$10$^{8}$K at 1.3d when the FWHM was 4825 kms$^{-1}$. In comparison, in RS Oph whose evolution was very well documented, a Pa$\beta$ FWHM of 3066 kms$^{-1}$ on 1.16d was measured (Das et al. 2006) and for the same line in V407 Cyg we obtained a value 1862 kms$^{-1}$ on 2010 March 13 (3.2d after outburst; Munari et al. 2010 measured a FWHM of 2760 kms$^{-1}$ on day +2.3 from the H $\alpha$ profile). Clearly the outburst of V745 Sco is extremely powerful, an aspect that needs to be emphasized and which was not established from its earlier outbursts. Its energetics overshadow even those of RS Oph and V407 Cyg. Research at PRL is supported by the Department of Space, Government of India. GHM thanks D. Osip, P. Palunas, Y. Beletsky and the engineering group at the Las Campanas Observatory for their support of observations. The CfA Supernova Program is supported by NSF grant AST-1211196 to the Harvard College Observatory. We thank the reviewer Prof Ulisse Munari for helpful comments. | 14 | 3 | 1403.0651 |
1403 | 1403.4244_arXiv.txt | An instability can potentially operate in highly irradiated disks where the disk sharply transitions from being radially transparent to opaque (the ''transition region''). Such conditions may exist at the inner edges of transitional disks around T Tauri stars and accretion disks around AGNs. We derive the criterion for this instability, which we term the ''irradiation instability'', or IRI. We also present the linear growth rate as a function of $\Bo$, the ratio between radiation force and gravity, and $\cs$, the sound speed of the disk, obtained using two methods: a semi-analytic analysis of the linearized equations and a numerical simulation using the GPU-accelerated hydrodynamical code \texttt{PEnGUIn}. In particular, we find that IRI occurs at $\Bo \sim 0.1$ if the transition region extends as wide as $\sim 0.05r$, and at higher $\Bo$ values if it is wider. This threshold value applies to $\cs$ ranging from $3\%$ of the Keplerian orbital speed to $5\%$, and becomes higher if $\cs$ is lower. Furthermore, in the nonlinear evolution of the instability, disks with a large $\Bo$ and small $\cs$ exhibit ''clumping'', extreme local surface density enhancements that can reach over ten times the initial disk surface density. | \label{sec:intro} Accretion disks are susceptible to a wide range of instabilities, including the magnetorotational instability (MRI) \citep{MRI}, gravitational instability \citep{GI2,GI}, Papaloizou-Pringle instability \citep{PP84,PP85,PP87,GGN86}, and Rossby wave instability (RWI) \citep{RWI1}. The list goes on as non-ideal MHD and vertical shearing \citep{VShear} are considered. These instabilities drive the evolution of disks by generating turbulence and creating complex, sometimes extreme, structures, such as the formation of planets in protoplanetary disks. Radiation pressure is a force generally present in all types of accretion disks. Its effect on accretion disks has been studied in many different aspects, including driving disk winds in active galactic nuclei (AGN) \citep[e.g.][]{Higginbottom2014}, shaping particle size distributions in debris disks \citep{Thebault2014}, and influencing the motions of the inner rims of transitional disks \citep{CM07,DD11}. We demonstrate in this paper that radiation pressure can also cause a disk instability of its own kind. In the following, we give a brief introduction to this instability before launching into the formal theoretical work. The strength of radiation pressure compared to gravity is measured by the number $\Bo$: \begin{equation} \label{eq:beta0} \Bo = \frac{\kappa_{\rm opa} L}{4 \pi cGM} ~, \end{equation} where $L$ is the central object's luminosity, $M$ is its mass, and $\kappa_{\rm opa}$ is the opacity of the disk material; $c$ and $G$ are the speed of light and gravitational constant respectively. The key to this instability is shadowing. As the front part of the disk gets pushed by radiation pressure, it also casts a shadow that reduces the amount of radiation pressure on the material further out in the disk. In a 1D, radial picture, since radiation pressure always diminishes outward, the inner part of a disk always feels a stronger push than the outer part, and the net effect is therefore radial compression. In other words, any two concentric disk annuli would feel an attraction between them due to the combined effects of radiation pressure and shadowing. This 1D scenario does not easily extend to a 2D disk however, because radiation pressure from a central source does not exert any azimuthal force. By the conservation of angular momentum, when a disk element is perturbed radially, it will oscillate at some epicyclic frequency. \figref{fig:iri} illustrates what effect this oscillating element has on the disk. One can see that disk material near the orbit of the perturbed element will experience a variation in shadowing along the azimuth. This variation creates a forcing that induces the unperturbed material to follow the motion of the perturbed element. The result is a global collective motion that is capable of growing on its own. We term this phenomenon the ''irradiation instability'' (IRI), since it relies on irradiation by the central object. Because a larger $\Bo$ allows for a more rapid radial motion, its value is crucial for the survival of this collective motion against disk shear. In most systems, dust grains provide the largest contribution to $\Bo$. In circumstellar disks, micron-size grains can have $\Bo>1$ for F-type stars, and up to $\Bo\sim10^1$ for A-type stars (e.g., Equation 10 of \citet{KW2013}). Given that the gas-to-dust ratio is typically $\sim10^2$, $\Bo$ of a perfectly coupled gas+dust mixture may be of the order of a few percent. Additionally, dust settling can enhance $\Bo$ in the midplane by reducing the local gas-to-dust ratio, while the radial migration of dust results in size segregation \citep{Thebault2014}, which can also enhance $\Bo$ at local radii. In other systems where radiation pressure can drive significant mass loss, such as AGN accretion disks, one would even expect $\Bo$ to exceed unity. This paper aims to provide a basic understanding of IRI, of both the conditions that trigger it, and its consequences. In \secref{sec:theory}, we present a theoretical foundation for IRI and derive its instability criterion. \secref{sec:disk} contains our disk model. \secref{sec:two} describes our semi-analytic and numerical methods. \secref{sec:result} reports the modal growth rate as a function of $\Bo$ and the sound speed $\cs$ of the disk, and gives a discussion on the nonlinear evolution of IRI. \secref{sec:disc} concludes with an outlook for future work. \begin{figure}[] \includegraphics[width=0.99\columnwidth]{iri} \caption{Simple illustration describing IRI. The blue curve denotes the orbit of a perturbed disk element oscillating around its guiding center, denoted by the dashed black line at $r_0$. The shaded area is where the disk sees the shadow cast by the perturbed element. The red arrows show the directions of radial forcing on the background disk relative to the average amount of radiation pressure received along $r_0$. These arrows are inward when they are in the shadow of the element, and outward when they are not. One can see that the background disk near $r_0$ is forced in the direction of amplifying the initial perturbation.} \label{fig:iri} \end{figure} | \label{sec:disc} We demonstrated that IRI can operate at an inner disk edge where there is a transition from being radially transparent to opaque. A local criterion for axisymmetric instability was derived (\eqnref{eq:crit2}). For our given disk model we computed the linear modal growth rates for $\Bo$ varying from $0$ to $0.3$, and $\cs$ from $0.02$ to $0.06$. We found growth rates ranging from $10^{-2}$ to $10^0~t_{\rm dyn}^{-1}$ (\figref{fig:para}). The fastest rates were found for the largest $\Bo$ and smallest $\cs$. We empirically determined that the threshold for IRI is $\Bo\sim0.1$ when $\Delta r=0.05$, with a weak dependence on $\cs$. For a wider edge, $\Delta r=0.1$, this threshold rises to $\Bo\sim0.25$. We note that this implies the threshold can be lowered by reducing $\Delta r$; however, at the same time $\cs$ must also be lowered for IRI to dominate over other forms of instability that may be triggered by the sharpness of the edge, such as RWI and Rayleigh instability. We employed two independent approaches to obtain the growth rates of the linear modes: simulating the disks numerically using \texttt{PEnGUIn}, and solving the linearized equations semi-analytically. Their excellent agreement lends confidence in our results. Moreover, we discovered a parameter space, labeled region I in \figref{fig:para}, where ''clumping'' occurs. There one can find over 10 times the local surface density enhancements in the nonlinear evolution of IRI. \subsection{Connection to Physical Disks} Our disk model is inspired by transitional disks \citep[e.g.][]{Calvet05,Espaillat07,OB1a, ResolvedImages}. The inner edges of these disks are currently unresolved by observation, but theoretical work has shown that the sharpness of disk edges created by X-ray photoevaporation \citep[e.g.][]{Owen2010} is similar to that described by our \eqnref{eq:sden} with $\Delta r=0.05$ (compare our \figref{fig:sden} to Figure 2 of \cite{Owen2013}). If a transitional disk undergoes IRI, the asymmetric structure at the inner edge will create an azimuthal variation in shadowing. \citet{Warps} showed that this can lead to a significant variation in disk emission. Indeed, some variability in the infrared emission of transitional disks has been reported by \citet{LRLL31Vari1}, \citet{LRLL31Vari2}, and \citet{SpitzerDisks}. On the other hand, IRI is by no means limited to circumstellar disks. AGN accretion disks, for example, can be subjected to IRI if there are any sharp jumps in density and/or opacity, such as the inner edges of the board-line regions. IRI can potentially generate the stochastic asymmetry, which is used to explain the variability in the double-peaked Balmer emission lines in radio-loud AGNs \citep{AGN08}. We note that the dynamics in AGN accretion disks are considerably more complicated since they do not have a point-like light source. \subsection{Implications of ''Clumping''} The ''clumping'' found in a part of our parameter space (\figref{fig:para}) opens new possibilities for IRI. For instance, very high density regions in protoplanetary disks may be favorable environments for the formation of planetary cores. The density of individual clumps may even become high enough to trigger gravitational instability at the inner edges of massive disks. One should be cautious to interpret the enhancement factors reported as realistic, however, since it is only one disk model that we have studied. The clumping also leads to a possibility of preventing inward dust migration. \citet{DD11} demonstrated that while radiation pressure can initially push dust outward and form a dust wall, the wall eventually succumbs to the global accretion flow and migrates inward. If this wall becomes unstable due to IRI, clumping can occur, effectively creating ''leakage'' within the wall, allowing radiation to push dust further back. The true behavior of these dust walls is important to understand disks where inner clearings have been observed, such as transitional disks. Dynamical interactions between radiation, dust, and gas must be considered for this kind of study. \subsection{Outlook} There are three main aspects of our model that we feel would benefit greatly from a more realistic treatment. First, our model ignores the vertical dimension. A notable difference from 2D to 3D is that the location of the inner edge of a disk, defined as the $\tau=1$ point, would become a function of height, spreading over a distance of $\sim h$. One possible consequence is that IRI would generate a vertical circulation at the inner edge, which would dilute the opacity in the midplane and allow radiation pressure to penetrate further into the disk. Additionally, in a flared disk, radiation pressure is exerted on the photosphere of the entire disk rather than just the inner edge. On the other hand, because of dust settling, we expect the value of $\Bo$ in the photosphere to be smaller than the midplane, making it even more difficult to reach the $\Bo\approx0.1$ threshold. Nonetheless, for disks around exceptionally luminous stars, IRI can potentially operate at all radii. Second, we assume a perfect coupling between gas and dust. In a more realistic approach, dust should be allowed to migrate with respect to gas. One expects dust to gather near the initial $\tau=1$ point, because where it is optically thin, dust migrates outward due to the effect of radiation pressure, and in the optically thick disk, dust migrates inward due to gas drag. This behavior of dust is described in Section 3 of \citet{TA2001}. The buildup of a dust wall is almost certain to trigger IRI due to its large $\Bo$ gradient. Lastly, we lack a realistic treatment for radiative transfer. As the disk crosses from being radially transparent to opaque, the midplane of the disk also transitions from being heated directly by irradiation, to passively by the irradiated atmosphere. Consequently the midplane temperature should be decreasing across the disk edge. This is not captured by our globally isothermal assumption. Additionally, the clumps we find in some of our nonlinear results are sufficiently dense that they are optically thick. With our isothermal treatment, they remain the same temperature as their surroundings, while in truth these clumps should be capable of shielding themselves from irradiation and creating a non-trivial internal temperature structure. Whether this is an effect that aids or inhibits their formation and survival requires future investigation. | 14 | 3 | 1403.4244 |
1403 | 1403.4591_arXiv.txt | We carry out a comprehensive analysis of the simplest curvaton model, which is based on two non-interacting massive fields. Our analysis encompasses cases where the inflaton and curvaton both contribute to observable perturbations, and where the curvaton itself drives a second period of inflation. We consider both power spectrum and non-Gaussianity observables, and focus on presenting constraints in model parameter space. The fully curvaton-dominated regime is in some tension with observational data, while an admixture of inflaton-generated perturbations improves the fit. The inflating curvaton regime mimics the predictions of Nflation. Some parts of parameter space permitted by power spectrum data are excluded by non-Gaussianity constraints. The recent BICEP2 results [1] require that the inflaton perturbations provide a significant fraction of the total perturbation, ruling out the usual curvaton scenario in which the inflaton perturbations are negligible, though not the admixture regime where both inflaton and curvaton contribute to the spectrum. | While observational results, including recent ones from the {\it Planck} mission \cite{planckI,planckXXII} and from BICEP2 \cite{bicep2}, continue to strongly support inflation as the origin of cosmic structure, it remains an open issue whether the observed perturbations arise from fluctuations in the field driving inflation or from a different degree of freedom. A particular example of the latter class is the curvaton model \cite{seminal}, and there have been several reports on the status of those models in the light of {\it Planck} satellite results \cite{Enq-Tak,kobayashi,ellis,higgs,tarrant}. In this work we carry out an analysis of the simplest curvaton model \cite{BL}, aiming at an exhaustive study of parameter space while minimizing the set of usual assumptions. Our analysis is principally analytical. We consider wide regimes of relative inflaton/curvaton contribution to the curvature perturbation and energy densities. We extend the existing literature in several directions. We impose simultaneous constraints from the full set of observables in the model parameter space. We provide a detailed modelling of the number of $e$-foldings corresponding to observable scales --- the so-called `pivot' scale \cite{CLM} --- and allow it to respond to the change in inflationary energy scale in different parts of parameter space. We include the effect of the curvaton mass on perturbations generated via the curvaton, and we consider the region of parameter space where the curvaton may itself drive a second period of inflation. After ensuring that the accurately-observed perturbation amplitude is reproduced, and once a reheating model is selected, the model reduces to three parameters which can be taken as the masses of the inflaton and curvaton and the value of the curvaton when the pivot scale crosses the horizon. Each observable depends on at most two of these, but in different combinations. Allowing for arbitrary decay times of the both fields extends the parameter space, which we parametrize by the number of matter-like $e$-foldings. This is due to the pressureless equation of state while a field oscillates in a quadratic potential. We do not make assumptions for the time of curvaton decay, nor the relative size of field masses. Extending the analysis of Ref.~\cite{Enq-Tak}, we show that the curvaton mass can be comparable but not significantly greater than the inflaton mass. | In Fig.~\ref{ns-r} we show the locations occupied by curvaton models in the $n_{\rm S}$--$r$ plane in all the regimes we have explored. The simplest curvaton model is in some tension with the {\it Planck} data for all parameter values, primarily due to the observed redness of the spectral index. However the model is not ruled out by this data, and the observational statistical errors are now small enough that any systematic shifts in the spectral index constraints are now important, see e.g.~Ref.~\cite{Spergel:2013rxa}. Despite the stringent constraint on local non-Gaussianity that the deviations from Gaussianity of curvature perturbation must be less than one part in a thousand, this does not strongly constrain the curvaton scenario. In the curvaton limit, which maximises $\fnl$, the constraint requires that the fraction of the curvaton's energy density at the decay time must satisfy $r_{\rm dec}>0.15$ at $95\%$ confidence \cite{Ade:2013ydc}. This constraint is weakened if the inflaton perturbations are not negligible, $m_{\phi}\simeq m_{\rm single}$. \begin{figure}[t!] \includegraphics[width=0.5 \textwidth]{Combined-Planck-ns-r.pdf} \caption{Region occupied by curvaton models, allowing $N_*$ to vary between 50 and 60 in all cases. The area between the red lines is the region covered by the usual curvaton scenario when $m_\sigma\ll m_\phi$. The blue lines set $m_\sigma=m_\phi/2$ to show the effect of a massive curvaton. The horizontal green lines are the inflating curvaton regime, which mimics the predictions of Nflation.} \label{ns-r} \end{figure} By contrast, the new BICEP2 results indicating \mbox{$r \gtrsim 0.1$} will, if confirmed, convincingly rule out the pure curvaton limit. They require that the energy scale of inflation is similar to that of quadratic inflation, which requires $m_\phi\sim m_{\rm single}$ and hence that the inflaton perturbations must be comparable to or dominant over the curvaton perturbations. A significant suppression of $r$ in the curvaton limit is generic for all curvaton models, suggesting that this result has ruled out the curvaton limit (i.e.~the original curvaton scenario assumption \ref{curvaton-limit}) regardless of the choice of inflaton and curvaton potentials. | 14 | 3 | 1403.4591 |
1403 | 1403.1711_arXiv.txt | The extreme flatness of stellar discs in superthin galaxies is puzzling and the apparent dearth of these objects in cosmological simulation poses challenging problem to the standard cold dark matter paradigm. Irrespective of mergers or accretion that a galaxy might be going through, stars are heated as they get older while they interact with the spirals and bars which are ubiquitous in disc galaxies -- leading to a puffed up stellar disc. It remains unclear how superthin galaxies maintain their thinness through the cosmic evolution. We follow the internal evolution of a sample of 16 initially extremely thin stellar discs using collisionless N-body simulation. All of these discs eventually form a bar in their central region. Depending on the initial condition, some of these stellar discs readily form strong bars while others grow weak bars over secular evolution time scale. We show that galaxies with strong bars heat the stars very efficiently, eventually making their stellar discs thicker. On the other hand, stars are heated very slowly by weak bars -- as a result, galaxies hosting weak bars are able to maintain their thinness over several billion years, if left isolated. We suggest that some of the superthin galaxies might as well be forming weak bars and thereby prevent any strong vertical heating which in turn helps maintaining their thinness during the course of secular evolution. | \label{sec:intro} Galaxy formation under the $\Lambda$CDM cosmology produces too few thin, disc-dominated late-type galaxies with little or essentially no bulge \citep{MoMaoWhite1998,DOnghiaBur2004, Mayeretal2008}. On the other hand, up-to-date observational surveys show abundance of flat galaxies \citep{Karachentsevetal1999, Matthews2000b, kautschetal2006} in the local universe. The apparent dearth of very thin disc galaxies in cosmological simulation has put up a challenge against the standard theory of CDM cosmology. Superthin galaxies (hereafter SGs) are the extreme case of these flat edge-on galaxies with their axial ratios (defined as the ratio of scale height to the scale length) generally below $0.1$. Due to the lack of strong morphological features SGs belong to the late-type in the Hubble classification scheme. In few cases, the thin discs of SGs are seen to be warped e.g., UGC 7170, UGC 3697 (in which case, the axial ratios are $\sim 0.1$) \citep{Karachentsevetal1999} which could be considered as the limiting case of a superthin galaxy. SGs do have other unique properties of the late-type galaxies e.g., low surface brightness (LSB), high atomic hydrogen gas fractions, low metallicities \citep{vanderHulstetal1993}. The extreme thinness of the stellar discs suggest that SGs somehow prevent strong heating in the vertical direction. It is puzzling how SGs maintain their superthinness over several billion years since they are formed. Observations point out that SGs, like many LSB galaxies, lack environmental influences \citep{Rosenbaumetal2009,Galazetal2011} which could give rise to tidal heating, heating due to satellite infall or mergers. The discs of superthin galaxies e.g., UGC 7321, IC2233 appear to be featureless, smooth with no visible signs of interactions such as tidal streams or other irregularities \citep{Matthewsetal1999, Matthews2008}. In contrast, the resulting stellar discs of CDM simulations are often smaller and thicker \citep{Kazantzidisetal2008}. This indicates that the heating of stellar discs of SGs are unlikely due to satellite infall, merger or due to massive subhalos (as it is in the CDM simulations). Since external mechanisms appear to be unimportant in heating stars of SGs, one must rely upon various internal sources. Indeed, as a galaxy evolves, internal heating of stars in the disc is unavoidable. In the case of our Milky Way, it is evident from the Hipparcos data \citep{Binneyetal2000}. Recently, it has been shown by \cite{Sahaetal2010} that a strong bar could efficiently heat stars in the vertical direction through physical processes like chaotic diffusion suggested by \cite{Pfenniger1985}. In fact, the possibility that superthin galaxies might be harbouring thin bars e.g., in UGC 7321 \citep{ Uson2003, Pohlenetal2003} could not be ruled out unambiguously. Bars are ubiquitous in disc galaxies \citep{Eskridgeetal2000,Barazzaetal2008} suggesting that they are formed spontaneously and perhaps survive through the cosmic evolution \citep[see][for a recent review]{Sellwood2013}. However, depending on the initial physical condition of a stellar disc and the distribution of dark matter, bars could grow to be stronger over a few rotation time scales or remain weak over several billion years \citep{Sahaetal2010}. The analysis of \cite{Sahaetal2010} further indicates that weak bars are not efficient in vertical heating of stars -- implying that if an initially superthin galaxy were to prevent strong vertical heating, it could possibly do so by growing a weak bar at the most during the course of secular evolution. The main focus of the current paper is to follow the evolution of such superthin galaxies embedded in various dark matter halo configuration and find out how many of these initial superthin galaxies are able to maintain their thinness such that they are still classified as superthin. We use collisionless N-body simulations to study the evolution of $16$ initially superthin galaxies in isolation. Our study suggest that weak bars are perhaps the maximal non-axisymmetric features that a self-consistent superthin galaxy might be able to support in order to maintain their thinness over several Gyr. The paper is organized in the following way. Section~\ref{sec:model} describes the models of superthin galaxies and N-body simulation. Section~\ref{sec:heating} summarizes plausible sources of heating relevant for superthin galaxies. The detailed evolution of superthin galaxies is presented in section~\ref{sec:evolution}. Section~\ref{sec:discuss} contains the discussion and primary conclusions from this work. | \label{sec:discuss} The very presence of smooth, featureless superthin galaxies in our local universe suggest that they are not subject to strong minor mergers or significant accretion events, as otherwise they would either be destroyed or converted to thicker disc galaxies \citep{Toth1992, Purcelletal2009}. And if they are isolated as observation indicates, they should be subject to disc heating arising due to the internal sources mentioned in section~\ref{sec:heating}. Obviously, if we could switch off some of these heating sources, the issue of maintainance of superthinness could be resolved. Our simulations suggest that this is unlikely as stellar discs, with diverse initial condition, form either strong or weak bars both of which heat stars but of course, with varying efficiency. On the other hand, the apparently smooth, flat stellar discs also indicate that SGs are unlikely to host strong bars as otherwise such discs eventually would have to face a buckling instability \citep[see][for coherent review]{Sellwood2013}. The other possibility, which can not be ruled out unambiguously, is that SGs do form weak bars over a longer time scale (as shown by our simulations). The question arises on the validity of the initial condition that we assume. Were progenitors of present day superthin galaxies really radially hot? If yes, how those progenitors achieved such a radially hot discs? The answer, of course, remains unknown as it depends on how these galaxies were actually formed. We speculate that during the early phase of galaxy formation, an extremely thin disc would have gone through strong spiral instabilities and the amount of preferential radial heating produced by it, would have self-destroyed the spiral arms leaving a red-hot dead disc. The low star formation rates as suggested by \cite{Matthewsetal1999}, indicates that the present day superthin galaxies are radially hot preventing them from forming further strong non-axisymmetric instabilities. Then our study shows that during the course of secular evolution such radially hot stellar discs when embedded in a massive live dark matter halo form only weak bars. {\it In other words, our simulations suggest that weak bars are perhaps the maximal non-axisymmetric features that a self-consistent superthin galaxy might be able to support if left isolated for several billion years.} Our main conclusions from the present work are the following: 1. We show that an initially thin stellar disc is able to maintain its thinness over several billion years if it hosts a weak bar. Such weak bars heat the stars very slowly and can increase the stellar scale-height roughly by a factor of $2$ in about $5 - 6$~ billion years. 2. Our simulations suggest that superthin discs with strong bars are unlikely as well as weak bars making thicker discs. There seems to be a good correlation between the thickness of a stellar disc and the amplitude of the bar it hosts. 3. Our results show that there is no strong preference for smaller halo core radii amongst superthin galaxies. Thicker discs could also reside in halos with smaller core radii. However, our study do not cover a wide range of halo core radius to disc scale length ratios. 4. We show that during the course of evolution, the underlying nature of the vertical density profile in a model hosting a weak bar remains unchanged except fattening by a small amount. | 14 | 3 | 1403.1711 |
1403 | 1403.4905_arXiv.txt | We report the detection of vertically extended far-ultraviolet (FUV) and near-UV emissions in an edge-on spiral galaxy NGC 891, which we interpret as being due to dust-scattered starlight. Three-dimensional radiative transfer models are used to investigate the content of the extraplanar dust that is required to explain the UV emission. The UV halos are well reproduced by a radiative transfer model with two exponential dust disks, one with a scaleheight of $\approx0.2-0.25$ kpc and the other with a scaleheight of $\approx1.2-2.0$ kpc. The central face-on optical depth of the geometrically thick disk is found to be $\tau_{B}^{{\rm thick}}\approx0.3-0.5$ at B-band. The results indicate that the dust mass at $|z|>2$ kpc is $\approx3-5$\% of the total dust mass, which accord well with the recent Herschel sub-millimeter observation. Our results, together with the recent discovery of the UV halos in other edge-on galaxies, suggest the widespread existence of the geometrically thick dust layer above the galactic plane in spirals. | The three-dimensional structure and the amount of dust in galaxies are of great importance in understanding galaxy evolution processes such as star formation. The dust content has been inferred from the radiative transfer models of the dust attenuation in optical/near-infrared (NIR) images of edge-on galaxies \citep{KylafisBahcall,Byun1994,Kuchinski1998,Xilouris1997,Xilouris1998,Xilouris1999,DeLooze2012}. The absorbed energy by dust is re-emitted in far-IR (FIR)/sub-millimeter (submm) wavelengths, and thus FIR/submm observations provide another way to derive the dust content. However, it has been revealed that the spectral energy distribution (SED) in FIR/submm requires at least a dust mass twice as large as estimated from the radiative transfer model of optical/NIR images \citep{Popescu2000,Misiriotis2001,Bianchi2008,Bae2010,DeLooze2012}. To resolve the discrepancy, an extra dust mass in the form of a secondary thin disk + clumpy dust clouds associated with molecular clouds that was supposed to be hidden in optical images was introduced \citep{Popescu2000,Tuffs2004,Misiriotis2004,Bianchi2008,Popescu2011}. We note that the previous radiative models assumed the geometrically thin dust disk that is concentrated in the galactic midplane ($z=0$). It may therefore be worthwhile to examine an additional dust component that is existing in a form different from the thin disk. In fact, there have been various attempts to investigate the existence of dust residing outside the galactic plane. Filamentary dust structures above the galactic plane have been observed up to $|z|\lesssim2$ kpc in nearby edge-on spiral galaxies using high-resolution optical images \citep{Howk1997,Alton2000,Rossa2004,Thompson2004}. The extraplanar dust filaments were found to contain too small an amount of dust ($\sim1-2$\% of the total dust mass) to be considered as the additional dust component \citep{Popescu2000}. The filamentary features, however, were traced in absorption against the background starlight, thereby implying preferentially ``dense'' dust features visible only to heights limited by the vertical extent of the background starlight. Therefore, ``diffuse'' dust component above the galactic plane was not traceable in the studies. We searched the diffuse extraplanar dust based on the fact that the dust should appear as a faint extended reflection nebula illuminated by starlight. The scattered light would not be easily distinguished from direct starlight when the scaleheight of the light source is greater than or comparable to that of the extraplanar dust. Therefore, far-ultraviolet (FUV) and/or near-UV (NUV) observation of edge-on galaxies can provide the best method for detecting the scattered light from the diffuse extraplanar dust, because OB stars, the main source of the UV continuum, have a scaleheight $<0.2$ kpc and have no bulge or halo component. We thus examined the UV data of the edge-on galaxies obtained from the\emph{ Galaxy Evolution Explorer (GALEX)} mission. The discovery of the UV halos due to the diffuse dust existing above the galactic plane of NGC 891 was first reported in \citet{SeonWitt2012}. \citet{Hodges-Kluck2014} describe the discovery of the UV halos around many galaxies, including NGC 891. In this Letter, we use a radiative transfer model to study the content of the extended UV emission in NGC 891. | Two exponential (geometrically thin + thick) dust disks were needed to represent the vertically extended UV emissions of NGC 891. The optical depth of the thick dust disk was found to be $\tau_{{\rm B}}^{{\rm thick}}\approx0.3-0.5$, corresponding to about half of the value inferred in the optical/NIR observations. We note that about half of the dust amount in the thick disk is located near the central plane ($z\lesssim1$ kpc). Therefore, the thick disk can hide completely from the radiative transfer models of optical/NIR images when only a single dust disk is assumed. The brightness of the UV scattered light depends not only on the amount of dust in the halo, but also on the flux of UV light coming from the galactic plane incident onto the halo. Our models adjust the stellar luminosity such that the edge-on surface brightness of the model matches the observed surface brightness. As the optical depth of the thin disk was increased, the fraction of the UV flux incident onto the halo was decreased while the stellar luminosity was increased. Moreover, the scaleheight of the thick disk was increased, as shown in Figures \ref{model_results} and \ref{model_results-NUV}. This resulted in a well constrained range of the optical depth of the thick disk regardless of the model type. We also note that the SFR estimated from the FUV data in the third model type is $\approx3-4$ $M_{\odot}$yr$^{-1}$, which is consistent with the results of \citet{Popescu2000} and \citet{Bianchi2008}. However, the SFRs obtained with the NUV data are about twice higher. Better understanding on the UV halo would be obtained through radiation transfer modeling that simultaneously considers the full UV-to-submm emission from all geometrical components of dust and stellar emissivity. The possibility of the diffuse extraplanar dust was also investigated by searching the vertically extended submm emissions in SCUBA images of NGC 891 \citep{Alton2000,Alton2000b}. Recently, \citet{BianchiXilouris2011} analyzed \emph{Herschel}/SPIRE images of NGC 891 and placed an upper limit of $\sim1$ MJy/sr on the excess emission above the galactic plane beyond that of the thin, unresolved, disk. The integrated excess emission over the effective solid angle of the halo ($\sim4.6\times10^{-6}$ sr) is then $\sim4.6$ Jy, which is about 3\% of the total emission of 169 Jy at 250 $\mu$m. In our best-fit models with $\tau_{{\rm B}}^{{\rm tot}}=4.0$, about $3-5$\% of the total dust mass is found in the halo above $|z|>2$ kpc. Therefore, the present results are consistent with the submm observation. \citet{Hodges-Kluck2014} investigated the possibility that the UV halos in late-type galaxies are caused by stellar populations in the halos. However, they conclude that the dust scattering nebula model is most consistent with the observations of the UV halo emission. The scaleheight of the optical polarization pattern in NGC 891 was a few kpc \citep{Fendt1996}. If only a thin dust layer is assumed, the polarization arising from scattering or dichroic extinction should be very low at high altitudes, and hence the extended polarization pattern cannot be explained \citep{Wood1997}. Therefore, the extended optical-polarization most likely indicates the existence of a thick dust disk. We assumed the dust properties of Milky Way dust \citep{Draine03}. On the other hand, \citet{Hodges-Kluck2014} claimed that the the halo colors and luminosities are consistent with the SMC-type dust (lacking a 2175\AA\ UV ``absorption'' bump), using a simple reflection nebula model. However, the SED of the scattered flux in an optically thin environment depends only on the wavelength dependence of the scattering efficiency of the grains. Spectrophotometric studies \citep{Andriesse1997,Calzetti1995} of the scattered light in reflection nebulae with normal to strong 2175\AA\ features in their extinction curves have demonstrated that the 2175\AA\ bump is a pure absorption feature, having no signature in the wavelength dependence of the scattering efficiency. Therefore, the determination of dust type in the halos does not appear possible with only the UV scattered light data. Panchromatic observations including the mid-IR (MIR) observations, together with a self-consistent radiative transfer model, may be required to determine the dust type in the halos. In fact, the vertically extended MIR continuum and PAHs emissions were also observed in the halos of NGC 891 \citep{Burgdorf2007} and other galaxies \citep{McCormick2013}, implying the presence of the carrier of the UV absorption bump at high altitudes. One of the promising scenarios for the origin of the extraplanar dust would be expulsion of dust in the galactic plane via stellar radiation pressure and/or (magneto)hydrodynamic flows such as galactic fountains and chimneys \citep{Howk1997,Greenberg1987,Ferrara1990}. \citet{Hodges-Kluck2014} found a correlation between the UV halo luminosity and the star formation rate. A nearly linear correlation between the extraplanar PAH flux and the star formation activity in the disk was also found \citep{McCormick2013}. A large amount of dust in the intergalactic medium (IGM) was inferred from studies of dust reddening of background quasars by foreground galaxies and associated large scale structure \citep{Ostriker1984,Zaritsky1994,Aguirre2001,Menard2010}. \citet{Hodges-Kluck2014} reported the discovery of the vertical UV halos in many spiral galaxies. The results, together with ours, suggest that the geometrically thick dust disk may be common to disk galaxies. The geometrically thick dust disk found in our study would then be an interface from which dust is ejected from spiral galaxies to the IGM. | 14 | 3 | 1403.4905 |
1403 | 1403.6131_arXiv.txt | { The EPOCH (EROS-2 periodic variable star classification using machine learning) project aims to detect periodic variable stars in the EROS-2 light curve database. In this paper, we present the first result of the classification of periodic variable stars in the EROS-2 LMC database. To classify these variables, we first built a training set by compiling known variables in the Large Magellanic Cloud area from the OGLE and MACHO surveys. We crossmatched these variables with the EROS-2 sources and extracted 22 variability features from 28\,392 light curves of the corresponding EROS-2 sources. We then used the random forest method to classify the EROS-2 sources in the training set. We designed the model to separate not only $\delta$ Scuti stars, RR Lyraes, Cepheids, eclipsing binaries, and long-period variables, the superclasses, but also their subclasses, such as RRab, RRc, RRd, and RRe for RR Lyraes, and similarly for the other variable types. The model trained using only the superclasses shows 99\% recall and precision, while the model trained on all subclasses shows 87\% recall and precision. We applied the trained model to the entire EROS-2 LMC database, which contains about 29 million sources, and found 117\,234 periodic variable candidates. Out of these 117\,234 periodic variables, 55\,285 have not been discovered by either OGLE or MACHO variability studies. This set comprises 1906 $\delta$ Scuti stars, 6\,607 RR Lyraes, 638 Cepheids, 178 Type II Cepheids, 34\,562 eclipsing binaries, and 11\,394 long-period variables. A catalog of these EROS-2 LMC periodic variable stars will be available online at \href{http://stardb.yonsei.ac.kr}{http://stardb.yonsei.ac.kr} and at the CDS website (\href{http://vizier.u-strasbg.fr/viz-bin/VizieR}{http://vizier.u-strasbg.fr/viz-bin/VizieR}).} | Studying periodic variable stars has improved our understanding of the Universe for many decades. For instance, Cepheid variables are one of the most important variable types as a standard candle for measuring extra-galactic distances \citep{Freedman2001ApJ, Riess2011ApJ} because of their well-established period-luminosity relation \citep{Feast1997MNRAS, Storm2011AA}, which provided evidence for the expanding Universe \citep{Lemaitre1927ASSB, Hubble1931ApJ}. RR Lyrae stars are useful for tracing the Galaxy formation history (e.g. see \citealt{Catelan2009ApSS} and references therein) and for studying globular clusters \citep{Carretta2000ApJ} and the Galactic structure \citep{Oort1975AA, Vivas2001ApJ}. In addition, long-period variables such as Mira variables show a period-luminosity relation that can be used for measuring distances to some objects in the Galaxy, such as globular clusters \citep{Feast1989MNRAS, Knapp2003AA}. In brief, periodic variable stars are crucial for studying and understanding the Galaxy and the Universe. The Exp$\acute{\text{e}}$rience pour la Recherche d'Objets Sombres (EROS) is a wide-field sky survey for probing dark matter in the Galactic halo by detecting microlensing events (see \citealt{Tisserand2007AA} and references therein). EROS monitored the Large/Small Magellanic Cloud (LMC/SMC), the Galactic bulge and spiral arms for about seven years, and was a major microlensing survey together with the MACHO \citep{Alcock2000ApJ} and OGLE \citep{Udalski1997AcA} microlensing surveys. In addition to microlensing detections, the EROS database is also useful for detecting periodic variable stars because of its well-sampled light curves over a long period of observation, relatively faint limiting magnitude of $\sim$20 in the EROS B band\footnote{EROS B and R bands (i.e., $B_E$ and $R_E$) are not a standard astronomical B and R bands. See Section \ref{sec:eros_database} for details.}, its wide field of view, and two simultaneous passbands. Previous studies have found several types of variable stars in the EROS-2 database. \citet{Beaulieu2001AA} discovered two variable stars resembling Herbig Ae/Be or classical Be stars, \citet{Tisserand2004AA} detected five R Coronae Borealis stars, \citet{Marquette2009AA} discovered 185 new beat Cepheid variables, \citet{Spano2011AA} reported forty-three thousand long-period variable candidates, and \citet{Dubath2012IAUS} found about 300 variable candidates from a subset of EROS-2 database but without identifying their variable types. Although these works produced some variable star candidates of various types, no study has searched the entire EROS-2 light curve database to classify different types of variable stars including $\delta$ Scuti stars, RR Lyraes, Cepheids, eclipsing binaries, and long-period variables. For instance, \citet{Dubath2012IAUS} used a supervised machine-learning method and multiple variability features to train a classification model, but their training set is incomplete because it consists of visually classified variables sorted into four classes including periodic, small-amplitude, semi-regular, and nonperiodic variables. Thus the model cannot distinguish conventional types of astronomical variable stars such as the types of variable stars listed above. We initiated the {\bf{E}}ROS-2 {\bf{P}}eri{\bf{O}}dic variable star {\bf{C}}lassification using mac{\bf{H}}ine learning (EPOCH) project\footnote{\href{http://stardb.yonsei.ac.kr}{http://stardb.yonsei.ac.kr}} that aims to detect periodic variables in the EROS-2 light curve database to significantly increase the total number of known variable stars in the EROS-2 survey fields. The EPOCH project is different from the previous studies because we used 1) the richest possible training set including multiple types of variable stars, 2) a few tens of variability features to separate variable stars from others, and 3) one of the most powerful supervised classification methods, random forest \citep{Breiman2001}. Random forest combines a large number of decision trees to build a classification model and has successfully solved many astronomical classification problems (e.g. \citealt{Dubath2011MNRAS, Pichara2012MNRAS}). Even though some of the above conditions were fulfilled by previous work, none of the works has fulfilled all of these conditions simultaneously. In this paper, we present the first results of the EPOCH project. We also present periodic variable star candidates detected from the EROS-2 LMC light curve database. The EROS-2 database is briefly introduced in Section \ref{sec:eros_database}. Section \ref{sec:classifcation_for_periodic} presents a classification method including 1) the training set we used to build a classification model, 2) multiple variability features, 3) parameter optimization for the random forest model training, and 4) performance of a trained model. We then show detection results of periodic variable stars from the entire EROS-2 LMC database in Section \ref{sec:variable_candidate_selection}. Section \ref{sec:summary} is a summary. | \label{sec:summary} We presented the first result of the EPOCH project: the classification of periodic variable stars in the EROS-2 LMC light-curve database. We first compiled the richest possible training set based mainly on the previously known OGLE variable stars. We chose 22 variability features based on the variable importance estimated by the random forest algorithm and then calculated the features using the visually examined training set. We then trained a random forest classification model using these variability features. We applied the model to the 29 million EROS-2 LMC sources and detected 117\,234 variable candidates. The catalog of the variable candidates containing EROS IDs, RA, Dec, colors (i.e., $B_E - R_E$), magnitudes (i.e., $B_E$), periods, period S/N, probabilities and crossmatched OGLE/MACHO information is available at \href{http://stardb.yonsei.ac.kr}{http://stardb.yonsei.ac.kr} and at the \href{http://vizier.u-strasbg.fr/viz-bin/VizieR}{CDS}. Note that the catalog contains all 150\,115 variable candidates without removal of the faint sources or low-period S/N sources mentioned in Section \ref{sec:variable_candidate_selection}. The classification quality of any supervised machine-learning methods depends on the richness of the training set and informativeness of the features on which a classification model is trained. In this work, we used previously known OGLE variable sources to build a training set. Thus a classification model would not be feasible for selecting and classifying variable types that do not exist in the OGLE variable source catalogs. In future works, we will consider adding more variable sources of different types to increase the completeness of the training set. In addition, we visually removed sources without variability while building the training set, which might result in an incomplete training set because of unintended removal of weak-variability sources. Although we showed that the trained model was able to classify both strong and weak variability sources, additional investigation on an enhanced training set would be useful to increase classification quality. We used 22 variability features of the highest variable importance estimated with the random forest method. We did not see any noticeable improvements by using more or fewer features. Nevertheless, it would be interesting to perform a comprehensive feature selection based on a variety of methods (e.g. see \citealt{Guyon2003} and references therein) to find irrelevant and/or highly correlated features that could be removed without detriment to the classification quality. In future works, we will apply a similar classification approach to the one presented for the EROS-2 SMC, Galactic bulge, and spiral arm databases to select and classify variable candidates. | 14 | 3 | 1403.6131 |
1403 | 1403.3008_arXiv.txt | Infrared continuum observations provide a means of investigating the physical composition of the dust in the ejecta and swept up medium of the Cas A supernova remnant. Using low resolution {\it Spitzer} IRS spectra (5--35~$\micron$), and broad-band {\it Herschel} PACS imaging (70, 100, and 160~$\micron$), we identify characteristic dust spectra, associated with ejecta layers that underwent distinct nuclear burning histories. The most luminous spectrum exhibits strong emission features at $\sim9$ and 21 $\micron$ and is closely associated with ejecta knots with strong Ar emission lines. The dust features can be reproduced by magnesium silicate grains with relatively low Mg to Si ratios. Another dust spectrum is associated with ejecta having strong Ne emission lines. It has no indication of any silicate features, and is best fit by Al$_2$O$_3$ dust. A third characteristic dust spectrum shows features that are best matched by magnesium silicates with a relatively high Mg to Si ratio. This dust is primarily associated with the X-ray emitting shocked ejecta, but it is also evident in regions where shocked interstellar or circumstellar material is expected. However, the identification of dust composition is not unique, and each spectrum includes an additional featureless dust component of unknown composition. Colder dust of indeterminate composition is associated with emission from the interior of the SNR, where the reverse shock has not yet swept up and heated the ejecta. Most of the dust mass in Cas A is associated with this unidentified cold component, which is $\lesssim0.1$ $M_{\sun}$. The mass of warmer dust is only $\sim 0.04$~$M_{\sun}$. | Interstellar dust models that fit the average interstellar extinction curve, the diffuse infrared emission and scattering, polarization, and abundance constraints employ a very limited variety of dust compositions, consisting primarily of polycyclic aromatic hydrocarbons (PAHs), graphite or amorphous carbon, and astronomical silicates \citep{Li:2001,Zubko:2004,Brandt:2012,Siebenmorgen:2014}. Yet observations of the primary sources of interstellar medium (ISM) dust (or at least the metals therein), asymptotic giant branch (AGB) stars and supernovae (SNe), reveal a significantly richer variety of dust compositions. For example, magnesium sulfide (MgS) is inferred from spectral features of pre-planetary nebulae \citep{Omont:1995} with similar features in carbon-rich AGB stars and PNe \citep{Forrest:1981, Hony:2002}. \cite{Cherchneff:2012} contains a detailed model of the formation of a wide variety of molecules and dust in an AGB star. More directly, presolar grains of supernova or stellar origin, such as silicate carbide (SiC), silicon nitride (Si$_3$N$_4$), and aluminum-, calcium- and titanium-oxides are found as meteoritic inclusions \citep[e.g.][] {Zinner:2008}. The absence of a wide variety of specific compositions in interstellar dust models indicates that these compositions are not required for fitting various manifestations of dust in the general ISM, either because of their low abundance relative to silicates and carbonaceous dust, or due to the fact that they may have been processed in the ISM. Supernovae can be important sources of interstellar dust. They produce all the refractory elements needed for the formation of dust, and their ejecta largely retain the compositional inhomogeneity of the progenitor star. They may therefore be sources of dust with unusual chemical and isotopic compositions. Furthermore, SNe are drivers of the chemical evolution in galaxies, and therefore potentially the most important sources of interstellar dust. In young populations before low mass stars have evolved off the main sequence, e.g. high redshift galaxies, SNe are the dominant source of thermally-condensed dust, though additional grain growth by cold accretion within dense clouds may be required to explain the inferred dust mass in these systems \citep{Dwek:2011, Valiante:2011}. Determining the mass and composition of SN condensed dust is therefore key for understanding the origin, evolution, and processing of dust in galaxies. The Cas~A remnant is an ideal object for studying the composition and abundance of dust that formed in the ejecta of a core collapse SN. The SN was not definitively recorded at the time that it occurred. Studies of the expansion of the supernova remnant (SNR) estimate that the explosion was in the year 1681$\pm$19 \citep{Fesen:2006}. Yet fortunately, light echoes of the Cas~A SN have allowed studies of this old event with modern instruments. Such observations have revealed that Cas~A was a Type IIb SN \citep{Krause:2008} with distinct asymmetry in its explosion \citep{Rest:2011}. Dynamical and compositional asymmetries are still imprinted on the Cas~A SNR today, but the dominant structure of the Cas A SNR is characterized by a clear distinction between the forward shock sweeping up the interstellar (and/or circumstellar) medium, and the reverse shock through which the SN ejecta is expanding. The ejecta consists of three main components: the first, containing most of the mass, is a low density phase that is heated by the reverse shock to X-ray emitting temperatures ($\gtrsim 10^6$ K). The second component consists of dense fast-moving knots (FMKs) that have gone through the reverse shock, and are radiatively cooling by line emission at optical and infrared (IR) wavelengths. A third component comprises ejecta that has not yet encountered the reverse shock, and is primarily heated by the ambient radiation within the SNR interior. In this paper we revisit the analysis of the mid- to far-IR spectra of the dust in Cas~A. IR emission can arise from dust in each of the ejecta components discussed above, as well as the circumstellar medium (CSM) or ISM that is shocked by the advancing SN blast wave, i.e. the forward shock. Our main goal is to separate and identify different types of dust that associated with different ejecta (and ISM or CSM) components and to determine the spatial distribution of the different types of dust. Our approach will provide important information on the physical processes that facilitate or inhibit the nucleation of dust in the different layers of the ejecta, the resulting dust composition, and the dust heating mechanisms that give rise to the IR emission. Our approach is different from previous ones \citep{Ennis:2006,Rho:2008} which only grouped the IR emission into distinct spectral components, with no relation to the nature of the ejecta from which they originated. The outline of our analysis is: \\ (1) We identify a set of {\it spatial templates} that are used as the initial indicators of regions of different ejecta composition and/or physical conditions around the SNR. These are illustrated in Figure \ref{fig:spatial_templates}, with the details of their derivation in the Appendix.\\ (2) For each spatial template, we identify {\it zones} (subregions) where that template is most prominent with respect to the other templates. These are described in Section 3.1 and shown in Figure \ref{fig:zones}.\\ (3) Within each of the zones and at each wavelength, we use the spatial correlation between the data and the template (see Eq. 1) to derive the {\it characteristic spectra} associated with each spatial template. These are presented in Section 3.1 and Figure \ref{fig:spectral_distributions}. Analysis of these characteristic spectra provides indications of the dust composition and temperature(s).\\ (4) Finally, at each spatial location across the entire SNR, the spectrum is decomposed as a linear combination of the characteristic spectra. The coefficients of these decompositions are mapped out to reveal images of the {\it spatial distributions} of the dust that gives rise to each characteristic spectrum. This is described in Section 3.2 and illustrated in Figure~\ref{fig:spatial_distributions}. Section 2 of this paper describes the preparation of the {\it Spitzer} IRS data to create a spectral cube of the dust continuum emission of Cas A. Section 3 explains the data analysis steps described above, with the details and results of modeling the characteristic spectra presented in Section 4. In Section 5 we discuss the results, including what conclusions can and cannot be drawn concerning the dust composition and mass. The work is summarized in section 6. | \subsection{Dust Compositions} The identifications of possible dust compositions in the different environments in Cas A are summarized in Table \ref{tab:families}. A single dust composition can never provide a good fit to the observed spectra, except for the \ion{Si}{2} spectrum which has only upper limits at $<70$ $\micron$. In general, 2 compositions are sufficient to get acceptable fits to the spectra. The \ion{Ar}{2} and \ion{Ar}{3} spectra are the only ones that show significant (though small) benefit for the addition of a third composition. Among the 7 characteristic dust spectra examined, the results can be grouped into 3 different families of dust. The first family is found in association with the \ion{Ar}{2} and \ion{Ar}{3} emitting ejecta, which are distributed widely across the SNR. This family consists of the Mg silicate with the lowest Mg/Si ratio in combination with one or more other compositions that have featureless spectra. The Mg$_{0.7}$SiO$_{2.7}$ is a good fit to the 9 and 21 $\micron$ peaks in the observed spectrum, but only if a featureless dust composition is also present to reduce the apparent strength of these features. However, the Ar dust spectra also contain a weaker 12 $\micron$ feature which is not accounted for by any Mg silicate. Nonstoichiometric spinel with low Mg/Al ratios can provide a feature at approximately the correct wavelength, but only when the dust grains are extremely hot, such that longer wavelength spinel features are relatively faint. A better explanation for the 12 $\micron$ feature may be provided by SiO$_2$. The spectrum of SiO$_2$ exhibits all three peaks seen in \ion{Ar}{2} and \ion{Ar}{3} spectra, although they are significantly sharper and slightly bluer than the observed ones, and even in combination with other materials the fits are not very good. However, this is when Mie theory is used to calculate the absorption cross sections assuming small spherical grains. Using a continuous distribution of ellipsoids (CDE) approximation instead broadens and shifts the SiO$_2$ features to be a better match as a third component. \cite{Jager:2003} point out that the 12 $\micron$ SiO$_2$ feature disappears in Mg silicates when Mg/Si $> 0.5$. Therefore, it seems likely that the dust associated with the Ar emission is a mixture of silica and Mg silicate (with Mg/Si $\lesssim 0.5$) in combination with a separate featureless dust component. SiC can also provide the 12 $\micron$ feature, but again only if CDE calculations are applied to this component. If SiC is present, this would be the only direct evidence of carbon-bearing dust. Table \ref{tab:12um} lists the possible origins for the 12 $\micron$ feature of the Ar dust. The strong 21 $\micron$ peak in this family has been the hallmark of Cas A IR spectra since it was first observed using the Kuiper Airborne Observatory (KAO) and the {\it Infrared Space Observatory (ISO)}. On the basis of those data, the peak was suggested to arise from Mg protosilicate \citep{Arendt:1999}. Subsequent analysis by \cite{Douvion:2001} modeled an {\it ISO} spectrum as MgSiO$_3$, SiO$_2$ and Al$_2$O$_3$ with the weak 12 $\micron$ feature largely produced by the Al$_2$O$_3$ as proposed for the feature in ``Spectrum 2'' of \cite{Douvion:1999}. \cite{Ennis:2006} using {\it Spitzer} IRS data noted the distinction of several different dust spectra in different parts of Cas A and referred to this as the ``Strong 21 $\micron$'' spectrum, and calling it ``21 $\micron$ peak dust'' \cite{Rho:2008} modeled it as Mg protosilicate and MgSiO$_3$ with secondary components of SiO$_2$, FeO, FeS, Si, and Al$_2$O$_3$ and/or Fe. Later work indicated that the 21 $\micron$ feature may be fit primarily by SiO$_2$ grains if CDE calculations rather than spherical grain approximations are used \citep{Rho:2009}. The second dust family is associated with the \ion{Ne}{2} emission, which is especially prominent in two opposing ``Ne crescents'' \citep{Ennis:2006,Smith:2009} in the N and S parts of the SNR. These morphological features are evident in the derived spatial distribution of the \ion{Ne}{2} dust shown in Figure \ref{fig:spatial_distributions}. This dust has a very smooth spectrum that does not suggest any silicate material. The best fits to the spectrum are found with Al$_2$O$_3$ in combination with other featureless dust. Featureless dust alone can provide moderately good fits, but a broad asymmetric feature in the 10 -- 20 $\micron$ portion of the Al$_2$O$_3$ absorption cross section seems to match the observed spectrum especially well. Alternately, nonstoichiometric spinel can provide the needed emission at 10 -- 20 $\micron$, although the spinel absorption efficiency has more detailed substructure that is not evident in the observed spectrum. This second family corresponds to the ``weak 21 $\micron$'' components noted by \citep{Ennis:2006} and \cite{Rho:2008}, which they also associate with relatively strong Ne emission. However, the fact that they see even a weak 21 $\micron$ peak in their spectrum suggests that it is a mixture of what we identify as very distinct Ar and Ne dust families. As in our fitting, \citep{Rho:2008} fit this spectrum with hot and cool featureless dust (C glass) and with an intermediate temperature Al$_2$O$_3$ components. They included other components to add the weak 21 $\micron$ peak that appears in their spectrum. \cite{Douvion:1999} had also noted an anti-correlation between the 9 $\micron$ silicate emission and \ion{Ne}{2} and \ion{Ne}{3} emission. The third dust family is associated with the X-ray Fe emission and the South Spot. This family also seems to match the dust associated with the radio emission, which is expected to be dust that has been swept up from the interstellar or circumstellar medium by the forward shock. The primary component in this family is one of the Mg silicates with high Mg/Si ratios or MgFe silicate: Mg$_2$SiO$_4$, Mg$_{2.4}$SiO$_{4.4}$, MgFeSiO$_4$. Other Mg silicates with Mg/Si $\geq 1$ can provide acceptable fits, but the silicates with lower ratios that were needed for the Ar dust are not suitable here because of the changing placement and shape of the 9 and 21 $\micron$ features. This dust family is matched by the ``Broad'' component identified by \cite{Ennis:2006} and the ``Featureless'' component modeled by \cite{Rho:2008}. In both cases this component is {\it not} associated with Ar or Ne emission lines, just as we also find. \cite{Rho:2008} modeled this component as MgSiO$_3$, FeS, and Si combined with Al$_2$O$_3$, Mg$_2$SiO$_4$ and/or Fe. Using 5--17 $\micron$ ISO data, \cite{Douvion:1999} extracted a spectrum (``Spectrum 3'') from a region that should match our Radio spectrum. Despite the limited wavelength coverage, they also found that the spectrum could be fit with astronomical silicate \citep{Draine:1984} at $T \sim 105$ K, as we confirm (in Fig. \ref{fig:radiodust}). The \ion{Si}{2} dust has no significant emission across the 5-40 $\micron$ wavelength range of the IRS. The three {\it Herschel} PACS measurements at 70, 100, and 160 are insufficient to constrain the composition of the associated dust. The \ion{Si}{2} dust may belong to one of the above families, or it may be an entirely different composition. \subsection{Dust Masses} The modeled dust temperatures and compositions allow the determination of the dust mass in each of the components. The dust mass, $M_d$, is calculated as: \begin{equation} M_d = {D^2 S_\nu(\lambda)\over{\kappa_\nu(\lambda) B_\nu(\lambda,T_d)}} \end{equation} where $D = 3.4$ kpc is the distance to Cas A \citep{Reed:1995}, $S_\nu(\lambda)$ is the total flux density of the component in question, $\kappa_\nu(\lambda)$ is the mass absorption coefficient appropriate for the derived composition of the dust, and $B_\nu(\lambda,T_d)$ is the Planck function evaluated at the derived temperature. For each of the models fit to the characteristic spectra, the total mass was calculated by summing Eq. 4 over all temperature components of each of the compositions used in the fit. Generally the total dust mass is dominated by a warm component (60 - 130K) that also produces the bulk of the luminosity. However the X-ray Fe spectrum is an exception where an additional cold component dominates the mass, because the {\it Herschel} PACS data at 70--160 $\micron$ are elevated relative to the shorter wavelength emission. The composition of this cold component is uncertain because absorption efficiencies are smooth and the spectral resolution is poor at the long wavelengths. This situation is worse for the \ion{Si}{2} dust which is only detected at $\geq$ 70 $\micron$. Its temperature is relatively well constrained, but its composition, and therefore its mass, is not. If the dust is composed of Mg silicates, then the total mass of the \ion{Si}{2} dust is $\lesssim 0.1$ M$_{\sun}$, but this value can be much lower if other compositions are appropriate. Much higher masses are ruled out by the expected nucleosynthetic yields of various elements, and would imply very high condensation efficiencies given that the mass of the unshocked gas is only $\sim0.4$ M$_{\sun}$ \citep{DeLaney:2014}. The derived dust masses averaged over all models that fit within a factor of 2 of the minimum $\chi^2$ and are dominated by Mg silicates (or Al$_2$O$_3$ for the \ion{Ne}{2} spectrum) are listed in Table \ref{tab:families}. Figure \ref{fig:arii_mass} plots the total dust mass for {\it all} 2--component models of the \ion{Ar}{2} dust spectrum as a function of $\chi^2$ with color coding to indicate compositions and temperatures. The ``good'' models are within a factor of 2 of the minimum $\chi^2$ (to the left of the dashed line). The figure shows that although there are correlations between composition and temperatures, the derived mass is more strongly dependent on the composition than the temperature. % The total mass of warm and hot dust for all components that contribute to the $<35$ $\micron$ spectrum is found to be $0.04\pm0.01\ M_\sun$ (see Table 3). This is consistent with other measurements from {\it IRAS} \citep{Braun:1987, Arendt:1989,Saken:1992} and other analysis of the {\it Spitzer} IRS data \citep{Rho:2008} because the mid-IR (12--100 $\micron$) flux density $S_\nu(\lambda)$ remains basically the unchanged since the {\it IRAS} measurements. This is the primary observable factor in determining the mass. When corrected for the same distance, previously published mass estimates contain modest differences (factors of $\sim2$) due to different assumptions of the mass absorption coefficients, $\kappa_\nu(\lambda)$, and dust temperature, $T_d$. {\it ISO}, {\it Akari}, BLAST, and {\it Herschel} have revealed an additional cool dust component in Cas A which contains $\sim 0.08\ M_\sun$ of dust \citep[e.g.][]{Tuffs:1999, Tuffs:2005, Sibthorpe:2010, Barlow:2010}. This cool component is what we associated with the \ion{Si}{2}. Our mass estimate of this component is consistent, but is very uncertain due to the unknown composition of the dust, and the difficulty in distinguishing the SNR dust from the heavy confusion of the line of sight ISM at these wavelengths. | 14 | 3 | 1403.3008 |
1403 | 1403.8138_arXiv.txt | {A class of supersymmetric grand unified theories is introduced that has a single scale below the cutoff, that of the supersymmetry breaking masses $\tilde{m}$. For a wide range of the dimensionless parameters, agreement with the observed mass of the Higgs boson determines $\tilde{m} \sim 10^9\mbox{--}10^{13}~{\rm GeV}$, yielding Intermediate Scale Supersymmetry. We show that within this framework it is possible for seesaw neutrino masses, axions, and inflation to be described by the scale $\tilde{m}$, offering the possibility of a unified origin of disparate phenomena. Neutrino masses allowing for thermal leptogenesis can be obtained, and the axion decay constant lies naturally in the range $f_a \sim 10^9\mbox{--}10^{11}~{\rm GeV}$, consistent with a recent observational suggestion of high scale inflation. A minimal $SU(5)$ model is presented that illustrates these features. In this model, the only states at the grand unified scale are those of the heavy gauge supermultiplet. The grand unified partners of the Higgs doublets have a mass of order $\tilde{m}$, leading to the dominant proton decay mode $p \rightarrow \bar{\nu} K^+$, which may be probed in upcoming experiments. Dark matter may be winos, with mass environmentally selected to the TeV scale, and/or axions. Gauge coupling unification is found to be successful, especially if the wino is at the TeV scale.} \end{center} \end{titlepage} | \label{sec:intro} The key discovery from the first run of the Large Hadron Collider (LHC) is a highly perturbative Higgs boson coupled with no sign of any new physics that would allow a natural electroweak scale. Remarkably, the value of the Higgs mass implies that the Standard Model (SM) remains perturbative to very high energy scales. Although this ``Lonely Higgs'' picture could easily be overturned by discoveries at the next run of the LHC, at present we are confronted with a very surprising situation. A variety of new physics possibilities was introduced in the 1970s and 1980s yielding a standard paradigm of a natural weak scale that was almost universally accepted. While the absence of new physics at LEP and elsewhere led to doubts about naturalness, the Lonely Higgs discovery at LHC warrants new thinking on the naturalness of the weak scale and the likely mass scale of new physics. An intriguing feature of the Lonely Higgs discovery is that the Higgs quartic coupling, on evolution to high energies, passes through zero and then remains close to zero up to unified scales, providing evidence for a highly perturbative Higgs sector at high energies. This closeness to zero of the quartic coupling cannot be explained by the SM, and hence is a guide in seeking new physics at very high scales. The Higgs boson mass was predicted to be in the range $\approx (128-141)~{\rm GeV}$ from a supersymmetric boundary condition at unified energies~\cite{Hall:2009nd}. Furthermore, it was pointed out that in such theories $\tan\beta$ near unity can result naturally, leading to a Higgs mass prediction of $(128 \pm 3)~{\rm GeV}$, with the central value gradually decreasing as the scale of supersymmetry is lowered below the unified scale. After the Higgs boson discovery, the connection between supersymmetry at a high scale and the Higgs mass was investigated further~\cite{Hebecker:2012qp,Ibanez:2012zg}. In a previous paper~\cite{Hall:2013eko}, two of us introduced {\it Intermediate Scale Supersymmetry} (ISS) to explain two key observations \begin{itemize} \item The SM quartic coupling, when evolved to large scales, passes through zero at $\mu_c$. This can be accounted for by taking the SM superpartner mass scale $\tilde{m} \sim \mu_c$. From Fig.~\ref{fig:scale_lambda}, $\mu_c \sim 10^9~\mbox{--}10^{13}~{\rm GeV}$ at 1-$\sigma$ (allowing for the possibility of a TeV-scale wino for dark matter). \item States of a minimal supersymmetric grand unified theory at $\tilde{m}$ can account for precision gauge coupling unification. \end{itemize} In addition to these, in this paper we study ISS models that have a third key feature \begin{itemize} \item Below the cutoff scale of the theory $\Lambda$, which is likely close to the Planck mass, the theory possesses only a single mass scale, $\tilde{m}$. \end{itemize} In this paper we study two different aspects of ISS. In Section~\ref{sec:model}, we pursue a class of ISS models that lead more cleanly to the vanishing of the quartic coupling near $\tilde{m}$, have a new proton decay signal and are more elegant. In Section~\ref{sec:scales}, we argue that in ISS the mass scale $\tilde{m}$ may be identified with one or more key mass scales of new physics:\ the axion decay constant, the energy scale of inflation, and the seesaw scale for neutrino masses. ISS provides a unifying theme to the diverse physics that we discuss, since it is all triggered by the same underlying mass scale. The scale $\tilde{m}$ directly gives the superpartner masses and can also be the origin of the axion decay constant, inflation, and right-handed neutrino masses. Within this framework, the scale of weak interactions and of the Grand Unified Theory (GUT) need some explanation. \begin{figure}[t!] \begin{center} \subfigure[Higgs quartic coupling $\lambda$] {\includegraphics[clip, width = 0.48 \textwidth]{lambda.pdf} \label{fig:scale_lambda}} \subfigure[1-$\sigma$ band of $\tan\beta$] {\includegraphics[clip, width = 0.48 \textwidth]{tanb.pdf} \label{fig:scale_tanb}} \caption{(a) The renormalization group running of the Higgs quartic coupling $\lambda$ for the SM (solid black line, with 1-$\sigma$ and 2-$\sigma$ regions from uncertainties of the experimental input parameters indicated by dark and light shades, respectively) and for the $1~{\rm TeV}$ wino (solid blue) and gluino (dashed green) in addition to the SM particles. (b) The value of $\tan\beta$ required to reproduce the observed Higgs boson mass as a function of the superpartner mass scale $\tilde{m}$ in the case that the theory below $\tilde{m}$ is the SM (red region bounded by solid lines), the SM with $1~{\rm TeV}$ wino (blue region bounded by dashed lines), and the SM with $1~{\rm TeV}$ gluino (dashed green line). The regions for the first two cases correspond to the 1-$\sigma$ uncertainties for the input experimental parameters.} \label{fig:scale} \end{center} \end{figure} In ISS the weak scale is highly fine-tuned, for example by twenty orders of magnitude for $\tilde{m} = 10^{12}~{\rm GeV}$, and can be understood in the multiverse, which provides a coherent framework for understanding both the fine-tuning of the weak scale and the cosmological constant~\cite{Weinberg:1987dv,Agrawal:1997gf}. In the $SU(5)$ unified model introduced in this paper, the fields responsible for weak breaking, $H, \bar{H}$, and $SU(5)$ breaking, $\Sigma$, do not have supersymmetric mass terms and are massless in the supersymmetric flat-space limit. Once supersymmetry is broken and the cosmological constant is fine-tuned, supergravity interactions induce an effective superpotential \begin{equation} W_{\rm eff} \sim \tilde{m} \times \left( \Sigma^2, \; H \bar{H}, \; \frac{1}{\Lambda} \Sigma^3, \; \frac{1}{\Lambda} H \Sigma \bar{H}, \; ... \right). \label{eq:W_effintro} \end{equation} This yields an $SU(5)$ breaking vacuum $\langle \Sigma \rangle \sim O(\Lambda)$, and we choose order unity coefficients so that this vacuum expectation value (VEV) is somewhat less than $\Lambda$. The heavy $XY$ gauge supermultiplet lies just below $\Lambda$, while all other states in $H, \bar{H}, \Sigma$ have masses of order $\tilde{m}$. These states make a significant contribution to gauge coupling unification, and the color triplet states in $H, \bar{H}$ yield an interesting proton decay signal. The $H \Sigma \bar{H}$ coupling is of order $\tilde{m}/\Lambda$, and hence leads to a negligible contribution to the Higgs quartic, which is dominated by the electroweak gauge contribution:\ $\lambda(\tilde{m}) \simeq 0.03\, (\tan^2\!\beta -1)^2$ for $|\tan^2\!\beta - 1| \ll 1$, where $\lambda$ is normalized such that $V(h) \supset (\lambda/2) (h^\dagger h)^2$, and the angle $\beta$ defines the combination of Higgs doublets that is fine-tuned light to become the SM Higgs. A value of $\tan^2\!\beta$ in the range of about $0.5$ to $2$ is sufficient to understand a small value of $\lambda(\tilde{m})$; however, in the limit that the Higgs mixing parameter (the Higgsino mass) $\mu$ becomes larger than $\tilde{m}$, $\tan^2\!\beta - 1 \sim O(\tilde{m}^2/\mu^2)$, so that $\lambda(\tilde{m})$ rapidly drops below $0.01$.% \footnote{If $\mu$ is too large ($\mu/m_{\tilde{t}} \gtrsim 4$), however, there can be sizable threshold corrections to $\lambda$ which affect the relation between $\tilde{m}$ and $\tan\beta$ in Fig.~\ref{fig:scale_tanb}.} The organization of the rest of the paper is as follows. In Section~\ref{sec:ISS} we closely examine the running of the Higgs quartic coupling in the SM, and with the addition of a TeV-scale wino, to determine the range of $\mu_c$. In Section~\ref{sec:model} we introduce and study a specific simple $SU(5)$ GUT that is representative of a class of grand unified theories that have just a single mass scale, $\tilde{m}$. We study the spectrum, dark matter, gauge coupling unification and proton decay in this model. In Section~\ref{sec:scales} we argue that in ISS other fundamental physics may be linked to the scale $\tilde{m}$, in particular, neutrino masses, axions, and inflation. Finally we summarize in Section~\ref{sec:summary}. | \label{sec:summary} We have explored supersymmetric grand unified theories that have a single scale, that of supersymmetry breaking, determined by the value of the Higgs boson mass to be in the intermediate range of $\tilde{m} \sim 10^9\mbox{--}10^{13}~{\rm GeV}$. Mass terms for the $SU(5)$ Higgs multiplets, $\Sigma, H, \bar{H}$ are generated at $\tilde{m}$ in the same way that in minimal supersymmetric models the Higgs mass parameter $\mu$ can arise at the supersymmetry breaking scale. However, unlike electroweak breaking in these minimal models, the breaking of the unified symmetry by $\Sigma$ occurs at a scale parametrically higher than $\tilde{m}$, close to the cutoff scale of the theory. A variety of diverse physics can be described by such GUTs with ISS, as illustrated in Fig.~\ref{fig:summ}. For a wide range of parameters, the SM Higgs quartic coupling is constrained to be small at $\tilde{m}$; indeed we determine the allowed range of $\tilde{m}$ by using the Higgs mass as input as shown in Fig.~\ref{fig:scale}. The result is illustrated by the upper horizontal green bar in Fig.~\ref{fig:summ}, showing the range of the scale $\mu_c$ where the quartic coupling vanishes in the SM (possibly augmented by a TeV wino for dark matter). \begin{figure}[t!] \begin{center} {\includegraphics[clip]{box.pdf}} \caption{The experimentally allowed ranges of four key mass scales:\ $\mu_c$ (the scale at which the SM Higgs quartic coupling vanishes); $M_{H_C,\Sigma}$ (the masses of the $H_c$ and $\Sigma$ states in the ISS model of Section~\ref{sec:model}); $M_L$ (the scale of lepton number violation for seesaw neutrino masses and leptogenesis); and $f_a$ (the axion decay constant in minimal models that solve the strong $CP$ problem). All are consistent with ISS, with supersymmetry breaking centered around the shaded region.} \label{fig:summ} \end{center} \end{figure} In the minimal ISS model, introduced and studied in depth in Section~\ref{sec:model}, proton decay is induced by both the tree-level exchange of the colored triplet $SU(5)$ partner of the Higgs boson $H_C$, of mass $M_{H_C}$, and by the exchange of the GUT gauge bosons $X$. The mass of $H_C$ is expected to be comparable to the mass of the uneaten states in $\Sigma$, $M_\Sigma$, and the experimental constraint on these masses is shown in the second horizontal green bar of Fig.~\ref{fig:summ}. The lower end of the range results from the limit on $p \rightarrow \bar{\nu} K^+$ from $H_C$ exchange, while the upper end of the range arises from the limit on $p \rightarrow e^+ \pi^0$ from $X$ exchange; the mass of $X$ being sensitive to $M_\Sigma$ via gauge coupling unification. Even though there are order unity couplings that lead to differences between $\mu_c$ and $M_{H_C, \Sigma}$, it is important for the consistency of the theory that the ranges of the top two green bars overlap. While the presence of $\Sigma$ states at $\tilde{m}$ solves the proton decay problem of non-supersymmetric $SU(5)$, having $H_C$ states at $\tilde{m}$ does not introduce a new proton decay problem, but offers the possibility of a signal. The precision of gauge coupling unification is further enhanced if dark matter is environmentally selected by fine-tuning the wino mass to the TeV region. The basic model of Section~\ref{sec:model} leaves open two key questions, the origin of neutrino masses and inflation. Seesaw neutrino masses occur very naturally in our framework as the lepton number violating mass for the right-handed neutrinos, $M_L$, can arise from the same mechanism that generates the masses for $\Sigma, H, \bar{H}$. The experimentally allowed range for $M_L$ is shown by the third horizontal bar in Fig.~\ref{fig:summ}. The upper end of the range arises from the need to explain the size of the atmospheric neutrino oscillation, and is shown for neutrino Yukawa couplings of order unity, while the lower end arises from the requirement of a leptogenesis origin for the cosmological baryon asymmetry. Note that leptogenesis also requires that $M_L$ be less than the reheat temperature after inflation, so that the upper bound on $M_L$ may be lower than shown. Recent data from BICEP2 indicates that the scale of the vacuum energy that drives inflation is $\simeq 2 \times 10^{16}~{\rm GeV}$. However, this need not be a Lagrangian mass scale; for example, for an inflation potential $m_\phi^2 \phi^2/2$ the required inflaton mass is $m_\phi \simeq 10^{13}~{\rm GeV}$. We do not show this in Fig.~\ref{fig:summ} because it is specific to this particular potential. However, it is certainly consistent with the masses $\mu_c, M_{H_c,\Sigma}, M_L$, so we may expect that this also arises from $\tilde{m}$. Finally, the axion is the most promising solution to the strong $CP$ problem, and may also account for dark matter. The large value of the Hubble parameter during inflation indicated by the BICEP2 data, implies that the simplest axion models having PQ symmetry broken during inflation are excluded. In Fig.~\ref{fig:summ} we therefore show the experimentally allowed range of the axion decay constant in theories having a PQ phase transition after inflation. The upper limit arises from overclosure by axions, and the lower limit from axion emission from supernovae and white dwarfs. Again, from Fig.~\ref{fig:summ} we notice a remarkable consistency between the mass scales required for very different physics; in ISS these masses are not precisely equal, but may all arise from $\tilde{m}$, the scale of supersymmetry breaking. | 14 | 3 | 1403.8138 |
1403 | 1403.6125_arXiv.txt | The cosmological 21cm signal is a physics-rich probe of the early Universe, encoding information about both the ionization and the thermal history of the intergalactic medium (IGM). The latter is likely governed by X-rays from star-formation processes inside very high redshift ($z \gsim 15$) galaxies. Due to the strong dependence of the mean free path on the photon energy, the X-ray SED can have a significant impact on the interferometric signal from the cosmic dawn. Recent \textit{Chandra} observations of nearby, star-forming galaxies show that their SEDs are more complicated than is usually assumed in 21cm studies. In particular, these galaxies have ubiquitous, sub-keV thermal emission from the hot interstellar medium (ISM), which generally dominates the soft X-ray luminosity (with energies $\lsim$ 1 keV, sufficiently low to significantly interact with the IGM). Using illustrative soft and hard SEDs, we show that the IGM temperature fluctuations in the early Universe would be substantially increased if the X-ray spectra of the first galaxies were dominated by the hot ISM, compared with X-ray binaries with harder spectra. The associated large-scale power of the 21cm signal would be higher by a factor of $\sim$ three. More generally, we show that the peak in the redshift evolution of the large-scale ($k \sim 0.2$ $\mathrm{Mpc}^{-1}$) 21cm power is a robust probe of the soft-band SED of the first galaxies, and importantly, is not degenerate with their bolometric luminosities. On the other hand, the redshift of the peak constrains the X-ray luminosity and halo masses which host the first galaxies. | \label{sec:intro} The redshifted 21cm line is sensitive to the thermal and ionization state of the cosmic gas, making it a powerful probe of the early Universe. As it is a line transition, it has the potential to map out the three dimensional structure of cosmic gas and its evolution. First generation interferometers, including the Low Frequency Array (LOFAR; \citealt{vanHaarlem13})\footnote{http://www.lofar.org/}, Murchison Wide Field Array (MWA; \citealt{Tingay12})\footnote{http://www.mwatelescope.org/}, and the Precision Array for Probing the Epoch of Reionization (PAPER; \citealt{Parsons10})\footnote{http://eor.berkeley.edu}, are already taking data. Their focus is on a statistical detection of reionization, though even earlier epochs of heating (when the cosmic gas was heated to temperatures above the CMB) could be detectable \citep{ME-WH14}. Second generation instruments, like the Square Kilometre Array (SKA; \citealt{SKA12})\footnote{http://www.skatelescope.org/} will be coming on-line soon, with high sensitivity and wide frequency coverage, allowing us to witness the birth of the very first galaxies through their imprint on the intergalactic medium (IGM). X-rays play a very important role during these epochs. Reionization with a significant X-ray contribution proceeds more uniformly, complicating the interpretation of 21cm fluctuations on large-scales \citep{MFS13}. More importantly, X-rays are thought to be responsible for heating the IGM to temperatures above the CMB, before reionization gets well-underway (e.g. \citealt{Furlanetto06, MO12}). In fiducial models, the large-scale temperature fluctuations during this heating epoch are responsible for the strongest 21cm interferometric signal, an order of magnitude greater than the signal during reionization. Understanding the timing and homogeneity of X-ray heating is critical in interpreting 21cm observations of the pre-reionization and reionization epochs (e.g. \citealt{PF07, ME-WH14}). A common approach is to parameterize our uncertainty of the early X-ray background by fixing the galactic X-ray spectral energy distribution (SED), and varying its normalization, i.e. bolometric luminosity (e.g. \citealt{Furlanetto06, Santos11, CL13, ME-WH14}; though see also exploratory work in \citealt{PF07, Baek10, MFS13}). The X-ray luminosity of the first galaxies\footnote{For convenience, we use the adjective ``first'' somewhat imprecisely, referring to the galaxies responsible for heating the IGM, which likely occurs at $z\sim$10--20 (see below). The very first galaxies could appear even earlier ($z\sim30$), though star formation inside these rare mini-halos is likely insufficient to significantly heat the IGM (e.g. \citealt{MO12}). Nevertheless, our qualitative conclusions are not affected by the precise redshift at which the relevant galaxies appear (see below).} regulates the timing of the heating epoch. However, the actual X-ray SED should also be important in setting the signal, as the mean free path of X-rays through the IGM, $\lambda_{\rm X}$, has a very strong dependence on the photon energy (e.g. \citealt{FOB06, McQuinn12}): \begin{equation} \label{eq:mfp} \lambda_{\rm X} \approx 34 ~ \avenf^{-1} \left( \frac{E_{\rm X}}{\rm 0.5 ~ keV} \right)^{2.6} \left( \frac{1+z}{15} \right)^{-2} ~ {\rm comoving ~ Mpc} ~, \end{equation} where $\avenf$ is the mean neutral fraction of the IGM. Soft photons are much more likely to be absorbed closer to the galaxies, while high energy photons heat (or ionize) the IGM more uniformly. Indeed, \citet{MFS13} showed that if X-ray heating is dominated by high-energy photons, the redshift evolution of the amplitude of the large-scale 21cm power spectrum does not show an associated pronounced peak. It is important to also note that because of this strong energy dependence of $\lambda_{\rm X}$, photons with energies $\gsim$ 2 keV effectively free-steam, barely interacting with the IGM; this makes the soft X-ray SED much more relevant for the 21cm signal. Observations show that the SED of local galaxies is more complicated than is usually assumed in 21cm studies. Locally, the hot ISM contributes significantly to the galaxy's soft X-ray emission (e.g. \citealt{Strickland_2000, Grimes05, Owen09, Strickland_2004, Li_Wang_2013}; see the review in \S 7.1 of \citealt{Mineo_ISM}). As an example, we note that using \textit{Chandra}, \citet{Mineo_ISM} recently studied the diffuse emission in a local sample of 21 star-forming galaxies, finding sub-keV thermal emission from the hot ISM in {\it every} galaxy in the sample. The stacked, bolometric soft-band (0.5--2 keV) luminosity per star formation rate (SFR) of the thermal emission is comparable to that from resolved sources, dominated by high mass X-ray binaries (HMXBs) with much harder spectra (e.g. \citealt{GGS04, Mineo_HMXB}). In this paper we illustrate the impact of the X-ray SED of the first galaxies on the 21cm power spectrum. We use simple models representative of dominant populations of either soft (corresponding to the hot ISM) or hard (corresponding to HMXBs) X-ray sources. To show the robustness of our results, we also vary the X-ray luminosity per SFR (SED normalization) and the halo mass which hosts the dominant galaxy population. As this work was nearing completion, a related study was published by \citet{FBV14}. The most important distinction between the two works is that our analysis is motivated by {\it Chandra} observations of nearby star-forming galaxies, rather then a theoretical model of HMXBs. Furthermore, our proof-of-concept focuses on predicting qualitative trends which are robust to the many astrophysical uncertainties. This paper is organized as follows. In \S \ref{sec:SED} we discuss possible contributions to the X-ray SED of high$-z$ galaxies, placing them in the context of recent \textit{Chandra} observations. In \S \ref{sec:21cm} we present our simulations of the cosmological 21cm signal. In \S \ref{sec:results} we discuss our main results, showing how the SED has a robust imprint in the 21cm signal. Finally, we conclude in \S \ref{sec:conc}. Unless stated otherwise, we quote all quantities in comoving units. Throughout, we adopt recent Planck cosmological parameters \citep{Planck_Parameters}: $(\Omega_m, \Omega_{\Lambda}, \Omega_b, h, n_s, \sigma_8)= (0.32, 0.68, 0.049, 0.67, 0.96, 0.83)$. | \label{sec:conc} In this proof-of-concept, we investigated if the X-ray SED of the first galaxies could have a robust imprint in the 21cm signal. We were motivated by {\it Chandra} observations of local star-forming galaxies, in which the relevant soft-band luminosity has two main contributors: (i) the hot, diffuse ISM and (ii) HMXBs. Using simple SEDs corresponding to these two populations, we studied their imprint on the 21cm signal, focusing on the epoch when the first galaxies began heating the IGM with their X-rays. Understandably a soft SED, representative of the hot ISM, results in larger fluctuations of the IGM temperature, as the absorption cross-section for X-rays has a strong dependence on the photon energy. Low energy photons are much more likely to be absorbed closer to the galaxies. These stronger temperature fluctuations drive up the amplitude of the large-scale ($k\sim0.2$ Mpc$^{-1}$) 21cm power by a factor of $\sim$ 3, compared with models dominated by hard SEDs representative of HMXBs. More generally, we show that the X-ray SED determines the amplitude of the peak 21cm power, for a wide range of X-ray luminosities ($10^{-1.5}\lsim f_X\lsim 10^{1.5}$) and host halo virial temperatures ($10^4$ K $\lsim \Tvir\lsim$ 10$^5$ K). The reverse is true for the redshift at which the large-scale power peaks: it is insensitive to the SED, and instead determined by the X-ray luminosity and host halo mass of the first galaxies. Thus, upcoming interferometers can determine the X-ray luminosities and host halo mass of the first galaxies from the redshift of the peak 21cm power, while the amplitude of the peak power will constrain the SED. The absorption intrinsic to the host galaxies remains a significant source of uncertainty, and could substantially impact the emerging soft-band SED. In this work, our fiducial models assume a sharp cut below $E_0 = 0.3$ keV, corresponding to photons whose mean free path is greater than unity given the same column densities observed in local galaxies, {\it but} assuming a low metallicity such that the ISM absorption is dominated by hydrogen and helium. If on the other hand the emerging X-ray SED of the first galaxies is {\it exactly} as observed in local ones, the 21cm signal should be as predicted in our hard, $\alpha=0.8$ models. This is because in observed composite spectra (see Fig. \ref{fig:spectrum}), the additional absorption of the HMXB template at $\lsim1$ keV provided by the metals is almost exactly compensated for by the additional contribution from the absorbed, hot ISM. This makes the total spectrum (absorbed hot ISM + absorbed HMXBs) look like an unabsorbed, $\alpha\sim0.8$ power law down to low energies ($\lsim 0.5$ keV), which is effectively our hard SED for the first galaxies. Subsequent work will focus on constructing more complete and detailed models of the X-ray SEDs emerging from the first galaxies, guided by hydrodynamic simulations including metal pollution. Combined with upcoming 21cm interferometric observations, we will be able to robustly study high energy processes inside the first galaxies. \vspace{+1cm} We thank Bret Lehmer for stimulating conversations which contributed to motivating this work. SM acknowledges support from the NASA's Astrophysics Data Analysis Program (ADAP) grant NNH13CH56C. | 14 | 3 | 1403.6125 |
1403 | 1403.1705_arXiv.txt | We present integral field spectroscopy of 10 early-type galaxies in the nearby, low-mass, Fornax cluster, from which we derive spatially resolved stellar kinematics. Based on the morphologies of their stellar velocity maps we classify 2/10 galaxies as slow rotators, with the remaining 8 galaxies fast rotators. Supplementing our integral field observations with morphological and kinematic data from the literature, we analyse the `kinematic' type of all 30 galaxies in the Fornax cluster brighter than M$_K = -21.5$ mag (M$_* \sim 6 \times 10^9$ M$_\odot$). Our sample's slow rotator fraction within one virial radius is $7^{+4}_{-6}$ per cent. $13^{+8}_{-6}$ per cent of the early-type galaxies are slow rotators, consistent with the observed fraction in other galaxy aggregates. The fraction of slow rotators in Fornax varies with cluster-centric radius, rising to 16$^{+11}_{-8}$ per cent of all kinematic types within the central 0.2 virial radii, from 0 per cent in the cluster outskirts. We find that, even in mass-matched samples of slow and fast rotators, slow rotators are found preferentially at higher projected environmental density than fast rotators. This demonstrates that dynamical friction alone cannot be responsible for the differing distributions of slow and fast rotators. For dynamical friction to play a significant role, slow rotators must reside in higher mass sub-halos than fast rotators and/or form in the centres of groups before being accreted on to the cluster. | \label{sec:intro} The population of galaxies that reside in clusters shows significant differences to that in the field and other lower-density environments. Cluster galaxies are more likely to be red \citep{Butcher:1978a} and have a higher fraction of early-type morphologies \citep{Oemler:1974,Dressler:1980} than similar populations in low density environments. Cluster galaxies also typically have lower specific star formation rates than group and field galaxies. At higher redshifts the difference between cluster and field galaxies is less pronounced, with the red fraction of cluster galaxies increasing significantly since z\ $=0.5$ \citep{Butcher:1978b}. A number of authors \citep{Stanford:1998,vanDokkum:2000,Smith:2005,Postman:2005,Cooper:2006,Capak:2007,Poggianti:2008} have more recently confirmed this picture, showing that in the highest density regions the early-type fraction is already high at z\ $\sim 1$ (though increases still further up to the present day), but in low and intermediate density regions significant morphological evolution is only seen between z\ $=0.5$ and today. Despite these long-recognised differences the precise effects of environment on galaxy evolution are poorly understood. Much of this uncertainty is due to the difficulty of disentangling the effects of galaxy mass from environment. Many of the differences between cluster and non-cluster galaxy populations are similar to differences between high and low-mass galaxy populations. It has been suggested that the observed effects of environment are simply due to a differing mass function between low- and high-density environments \citep{Treu:2005}, although recent studies involving large samples do find a statistically significant variation in e.g. specific star formation rate beyond that which would be expected from a differing mass function alone \citep{Bamford:2009,Peng:2010}. While large samples are effective in quantifying the difference between cluster and non-cluster galaxy populations they are less effective at revealing the physical mechanisms responsible for those differences. Many such mechanisms have been proposed, including: ram pressure stripping \citep{Gunn:1972}, strangulation \citep{Larson:1980}, galaxy-galaxy mergers, pre-processing in infalling groups, harassment \citep{Moore:1996} and tidal interactions \citep[see][for an overview]{Boselli:2006}. Individual examples of many of these processes in action have been observed \citep[e.g.][who identified galaxies undergoing ram-pressure stripping in the Virgo cluster and Shapley supercluster respectively]{Chung:2007,Chung:2009,Abramson:2011,Merluzzi:2013}. What is missing is an understanding of how frequently these processes occur and which are significant in driving the observed differences between cluster and non-cluster galaxies. A fruitful compromise between detailed studies of individual objects and large surveys that lack high-quality data are integral field spectrograph (IFS) surveys of nearby clusters. By combining the new insights derived from two-dimensional spectroscopic information with the statistical power of large samples we can shed new light on the detailed role of environment in shaping the way galaxies evolve. \citet{Emsellem:2007} and \citet{Cappellari:2007} proposed a kinematic classification for early-type galaxies (E and S0) based on the morphology of their velocity maps, dividing early-type galaxies into two kinematic classes. These classes are slow rotators (SRs), systems with low specific angular momentum, and fast rotators (FRs), systems with significant, ordered, disk-like rotation. This classification is less affected by the inclination affects that trouble visual morphology classification schemes and seems likely related to the formation history of each galaxy. It is also complementary to structural morphology classifications obtained from quantitative bulge-disc decompositions. \citet{Cappellari:2011b} applied this classification scheme \citep[as updated by][]{Krajnovic:2011,Emsellem:2011} to revisit the morphology-density relation, presenting the kinematic morphology-density relation for the ATLAS$^\mathrm{3D}$ survey --- a large sample of early-type galaxies brighter than M$_K = -21.5$ mag covering a range of environments from the Virgo cluster to galaxy groups and the field \citep{Cappellari:2011a}. They found that spirals are transformed into FRs at a rate that increases linearly (with log environment) across all environments, whereas the ratio of SRs to FRs seems nearly insensitive to environment. Only in the Virgo cluster was a clear difference observed. There, all SRs are found within the dense core of the Virgo cluster. The Coma cluster was studied by \citet{Scott:2012} and \citet{Houghton:2013}, and the Abell~1689 cluster by \citet{DEugenio:2013} using a range of integral-field spectrographs. Both clusters are significantly more massive than the Virgo cluster. They again found that, within a cluster, the SR fraction increases significantly in the densest regions, however the local environmental density that this increase occurs at varies widely from cluster to cluster. \citet{DEugenio:2013} and \citet{Houghton:2013} argued that SRs make up a constant proportion, $\sim 15$ per cent, of early-type galaxies brighter than M$_{K} = -21.5$ mag, independent of the environment explored. Past studies have focused predominantly on massive clusters or the field, with the low-mass cluster and group environment largely unexplored. In this paper we present an integral field study of early-type galaxies in the Fornax cluster. Fornax is a relatively low-mass cluster \citep[M$_* \sim 7 \times 10^{13}$ M$_\odot$][approximately 1/10$^{th}$ the mass of the Virgo cluster]{Drinkwater:2001}, lying close to the boundary between cluster and group environments. Adding the Fornax cluster to the previously mentioned IFS studies of cluster early-type galaxies extends coverage of the broad range of cluster environments found in the nearby Universe. Several works have already examined the spatially-resolved kinematics of bright galaxies in the Fornax cluster, though these have been limited to long-slit spectroscopy observations. Of these, \citet{DOnofrio:1995} and \citet{Graham:1998} present the largest number of galaxies (15 and 12 respectively). \citet{DOnofrio:1995} discovered that 6 of their 9 galaxies classified as elliptical harbour a disc-like component. Building on this, \citet{Graham:1998} reported that only 3 of their 12 brightest (M$_B \le 14.7$ mag, $M_K \le 11.8$ mag) elliptically-classified galaxies in the Fornax cluster are actually pressure supported systems. Long-slit studies can accurately identify FRs and SRs when the galaxy is significantly flattened, or when either the rotation or dispersion is highly dominant. In intermediate cases the spatial information contained in IFS data is critical in accurately classifying the kinematic morphology of a galaxy. The classic case of this is identifying face-on discs, which traditional classification schemes often but mistakenly class as ellipticals \citep{Emsellem:2011}. The key advance of this study over past long-slit work is in using IFS data to accurately separate disc-like systems from true SRs, and then applying this robust kinematic classification to the morphology--density relation in the low-mass cluster environment of Fornax. In Section \ref{sec:sample} we describe our sample of Fornax galaxies. In Sections \ref{sec:spec} and \ref{sec:phot} we describe the integral field observations, reduction and kinematic analysis, as well as supplementary information derived from imaging. In Section \ref{sec:results} we present the kinematic morphology-density relation for the Fornax cluster. In Section \ref{sec:disc} we place our Fornax cluster results into context with other IFS surveys of nearby clusters and discuss the implications for the impact of cluster environments on the evolution of early-type galaxies. | In this work we have presented integral-field data on a sample of 10 early-type galaxies brighter than M$_K = -21.5$ mag in the Fornax cluster. We derived spatially-resolved maps of the velocity and velocity dispersion for each galaxy, classifying them as either fast or slow rotators based on i) the morphology of their velocity maps and ii) their specific stellar angular momentum, $\lambda_R$. The remaining 10 early-type galaxies in the Fornax cluster that satisfy our selection criteria, but for which we were unable to obtain integral-field data, are highly likely to be FRs based on their apparent flattenings and previous long-slit spectroscopy. From our kinematic classification we determine that 2/30 (7$^{+}_{-}$ per cent) galaxies in the Fornax cluster are slow rotators, 18/30 (60$^{+}_{-}$ per cent) are fast rotators and the remaining 10/30 (33$^{+}_{-}$ per cent) are spirals. Using the binomial distribution, we infer the fraction of early-type galaxies in the Fornax cluster that are slow rotators is $13^{+8}_{-6}$ per cent, consistent with the findings of \citet{Emsellem:2011} and \citet{Houghton:2013}. This fraction, observed for early-type galaxies brighter than M$_K = -21.5$, appears constant across all environments explored to date, though may only be a coincidence given the variation in cluster-centric radius probed by the different samples currently available. As with previous studies of more massive clusters, we find that the slow rotators are strongly concentrated towards the cluster centre. Unlike in the Virgo, Coma and Abell~1689 clusters, the Fornax slow rotators are not strongly concentrated in the highest local-density region of the cluster --- although one of the two SRs is near the peak density, the other is offset. This difference is not very significant given the small number of galaxies in the cluster. Future studies involving statistically significant numbers of galaxies in low-mass clusters and groups will be required to identify whether the trends in slow rotator fraction described above are present in lower mass halos. Such studies will be able to constrain the relative importance of different environmental transformation mechanisms that produce slow rotators as a function of a galaxy's local and global environment. | 14 | 3 | 1403.1705 |
1403 | 1403.4585_arXiv.txt | We locally reconstruct the inflationary potential by using the current constraints on $r$ and $n_{\rm s}$ from BICEP2 data. Assuming small and negligible $\alpha_{\rm s}$, the inflationary potential is approximately linear in $\Delta\phi\sim \Mp$ range but becomes non-linear in $\Delta\phi\sim 10 \Mp$ range. However if we vary the value of $\alpha_{\rm s}$ within the range given by constraints from {\it Planck} measurement, the local reconstruction is only valid in the range of $\Delta\phi\sim 0.4 \Mp$, which challenges the inflationary background from the point of view of effective field theory. We show that, within the range of $\Delta \phi \sim 0.4 \Mp$, the inflation potential can be precisely reconstructed. With the current reconstruction, we show that $V(\phi) \sim \phi^{2}$ and $\phi^{3}$ are consistent, while $\phi$ model is ruled out by $95\%$ confidence level of the reconstructed range of potential. This sets up a strong limit of large-field inflation models. | \label{sec:intro} The Inflation paradigm \cite{Guth81,Linde82} is successful in explaining the horizon problem, flatness problem and the homogeneity problem in the standard hot-big-bang cosmology. The generic inflation model predicts a nearly scale-invariant primordial scalar power spectrum which has been measured accurately by the observations of the cosmic microwave background radiation (CMB) such as {\it Wilkinson Microwave Anisotropy Probe} (hereafter {\it WMAP}) \cite{Hinshaw13} and {\it Planck} \cite{Planck16} satellites. However, even with precise constraints from CMB temperature fluctuations, there are still many models that predict the values of spectral index $n_{\rm s}$ and its running $\der n_{\rm s}/\der \ln k$ which are allowed by the constraints from current data. Recently, the ground-based ``Background Imaging of Cosmic Extragalactic Polarization'' experiment just completed its second phase experiment (hereafter BICEP2), which observed the CMB B-mode polarization (divergence-free mode of polarization) on angular scales of a few degrees \cite{BICEP2} (For cosmological implications, see also \cite{cosmoa,cosmob,cosmoc,cosmod}). The CMB B-mode polarization can only be sourced by primordial gravitational waves, which is a very clean test of the primordial tensor fluctuations. Results from BICEP2~\cite{BICEP2} show that the power spectrum of B-mode polarization $C^{BB}_{\ell}$ on a few degree angular scales is detected at $\sim 7\sigma$ confidence level (CL), which clearly indicates a signature of primordial gravitational waves. If this is true, it becomes a strong observational support of the scenario in which the Universe started from the inflationary exponential expansion, when the primordial tensor fluctuations are produced and stretched to super-Hubble length, and later entered into the Hubble horizon and decayed at small scales. Indeed, this field of CMB observation has been developing very fast over the past decades and many on-going experiments are seeking such a CMB B-mode polarization signal. For instance, the {\it Planck} satellite with its nine frequency channels may achieve higher signal-to-noise ratio and probe even larger angular scales than BICEP2. Ground-based SPTPol \cite{Austermann12}, ACTPol \cite{Niemack10}, PolarBear \cite{PolarBear} and CLASS \cite{Eimer12} experiments are also completing with each other to make more precise measurement on the CMB B-mode polarization signals. Therefore further experiments may precisely determine not only the amplitude but also the shape of the primordial tensor power spectrum, therefore constitutes a direct test of the inflation mechanism. Therefore it is important to connect the predictions from inflation models with the current observational results from BICEP2 and {\it Planck}. In pervious {\it WMAP} and {\it Planck} analysis papers \cite{Hinshaw13,Planck22}, the authors plot the predictions of spectral index of scalar power spectrum $n_{\rm s}$ and tensor-to-scalar ratio $r$ of various inflation models with the constraints from CMB data (fig.~7 in \cite{Hinshaw13} and fig.~1 in \cite{Planck22}). While making the prediction of $n_{\rm s}$--$r$ relation for a given potential, the variation of the inflaton field is calculated by integrating the equation of motion from the end of inflation to some early epoch. This duration of inflation is assumed by to around $50$--$60$ number of e-folds ($N=\log(a/a_{\rm i})$). Although the $n_{\rm s}$-$r$ relation works well, it is worth noticing the underlying assumption that during inflation, the inflaton potential (which is typically taken as a monomial, for example, $V\propto \phi^2$) is the same as that during the first 10 e-folds of observable inflation. With the recent measurement of tensor-to-scalar ratio $r$, this assumption become problematic. It becomes much more challenging than before to build an inflation model, in which a simple potential describes the total $60$ e-folds of inflation without changing its shape and parameters. To see this, remember that the inflationary potential can be perturbatively expanded near a value of $\phi_*$ as \begin{eqnarray}\label{eq:eft} V(\phi) = V(\phi_*) + \partial_\phi V \Delta\phi + \cdots \frac{1}{4!} \partial_\phi^4 V \Delta\phi^4 + \cdots ~, \end{eqnarray} where $\Delta \phi =\phi- \phi_{\ast}$ is the change of $\phi$ value during inflation. From the effective field theory point of view, the potential derivatives up to $\partial_\phi^4 V$ are relevant and marginal operators. Those operators can be naturally turned on without suppression. On the other hand, the $\partial_\phi^4 V$ and higher derivatives are irrelevant operators, which are suppressed with an energy scale defined by the UV physics (at most the Planck scale). For the expansion \eqref{eq:eft} to converge we need $\Delta\phi$ to be smaller than the UV completion scale of inflation. However, Lyth bound \cite{Lyth:1996im} suggests that, the change of the field with respect to the number of e-folds is related to the value of $r$ \begin{eqnarray} \left|\frac{\der \phi}{\der N}\right| = \frac{\Mp}{4}\sqrt{2r}, \label{eq:Lyth} \end{eqnarray} where $\Mp=(8 \pi G)^{-1/2}$ is the reduced Planck mass. By substituting the current measurement of $r$ from BICEP2 \cite{BICEP2} \begin{equation} r = 0.20 ^{+0.07}_{-0.05} \text{ } (1\sigma{\rm CL}). \label{eq:r-val} \end{equation} Thus per e-fold, $\Delta\phi = 0.16 \Mp$. By assuming $N \simeq 60$, we find that the inflaton field moves at least at a distance \footnote{Here we do not take the time variation of $\epsilon$ into account, to avoid model dependence. Otherwise the number in \eqref{eq:phi60} could change, while keep within the same order of magnitude. Also note that it is also possible that $\epsilon$ is not varying monotonically, to avoid large field inflation \cite{Hotchkiss:2011gz,Ben-Dayan10}.} \begin{align} \label{eq:phi60} \Delta\phi \simeq 9.6 \Mp ~, \end{align} in its field space. If this is true, $\Delta\phi$ at 60 e-folds is much greater than $\Mp$. Thus the expansion \eqref{eq:eft} is no-longer valid since all the high derivatives of $V$ could in principle contribute along the 60 e-folds of the inflationary trajectory. The effective field theory of inflationary background is therefore non-perturbative, and becomes out of control for higher order derivatives. The UV completion of inflation becomes a sharper problem then ever before. However, the leading UV completion paradigm, string theory, actually makes the problem worse. On the one hand, most string inflation models predict much smaller $r$ and thus not consistent with the BICEP2 data. On the other hand, the characteristic energy scale of string theory is the string scale. For string theory to be perturbatively solvable, strong coupling had better to be small and the string scale should be lower than the Planck scale (say, 0.1 $M_\mathrm{pl}$ or lower). The size of extra dimension may further lower the string scale. With such a lower scale as the cutoff, the effective field becomes a greater challenge than that with the Planck scale cutoff. Before BICEP2, the major challenge for building stringy inflation models is the $\eta$-problem \cite{Copeland:1994vg}, with the observational $\eta$ smaller than theoretical expectations. Now, a more serious $\epsilon$-problem emerges, leaving the observed large $\epsilon$ for the string theorists to explain. In the effective field theory point of view, given the current constraint on $r$, we may not be able to trust the inflaton potential along the whole 60 number of e-folds. This motivates us not to integrate the potential throughout $60$ number of e-folds, but to reconstruct the potential \cite{Copeland:1993jj, Lidsey:1995np,Ben-Dayan10} locally. Therefore we focus on a local range of field values, along the first a few e-folds window. In this range, $\Delta \phi \sim \Mp$ thus the inflationary potential expanded by Eq.~(\ref{eq:eft}) is in better control. We will show that, assuming small running, with current data it is possible to accurately reconstruct the amplitude and shape of the inflaton potential within the CMB observation window of about 10 e-folds. However, in the case of large running, the uncertainty of the reconstruction becomes large when $\Delta\phi$ is comparable with $0.4\Mp$, which corresponds to a field range of about 3 e-folds. This paper is organized as follows: in Sec.~\ref{sec:slow-roll}, we explain our notations of slow-roll parameters, and show the connection with $n_{\rm s}$ and $r$. In Sec.~\ref{sec:recon-slow} we directly constrain the slow-roll parameters with current data from BICEP2. In Sec.~\ref{sec:recon-poten}, we sample the inflationary potential and compare its amplitude and shape with the large-field inflation models. The conclusion and discussions are presented in the last section. | \label{sec:conclude} We have reconstructed the inflationary potential locally around a value $\phi_*$, which corresponds to the time when the $\ell \simeq 50 \sim 100$ modes exits the horizon. The distribution of the inflationary slow-roll parameters (which are defined through the expansion) are calculated, and converted to derivatives of the inflationary potential. Two different assumptions have been tested against the reconstruction -- a (theoretically) small and negligible running of the spectral index $\alpha_{\rm s}$, and an observationally allowed $\alpha_{\rm s}$ from current constraints. For the case of small and negligible $\alpha_{\rm s}$, the reconstructed potential is highly linear over $\Delta\phi \sim \Mp$ range. The effective field theory is practically fine (although still theoretically challenged). However, for the large $\alpha_{\rm s}$ case, higher derivative corrections to the potential quickly dominates while $\phi$ rolls, which implies the inflaton keeps switching between different effective field theories, or there is a need of a tuned inflaton field theory. With the new observational window as shown by BICEP2 data \cite{BICEP2}, much works are left to be done to accurately reconstruct the amplitude and shape of the inflation potential. Here we fit the ($n_{\rm s}$, $r$) diagram with the multi-variant Gaussian distribution. We find that with current constraints from {\it Planck}+WP+highL+BICEP2 data, the $V(\phi) \sim \phi^{2}$ and $\phi^{3}$ models are consistent within $95.4\%$ CL, while $\phi$ potential is ruled out at around $99.7\%$ CL, and $\phi^{4}$ model is consistent within $95.4\%$ CL if the number of e-folds is around $60$. This is of-course, not a global fitting of the inflationary prediction, but constitutes a quick examination of the consistency between models and data. It is also important to examine the theoretical assumption of the shape of gravitational wave spectra. For example, if parity is violated, which results in different amplitudes for the two tensor modes. Another example would be non-Gaussianly distributed tensor modes. It remains interesting to see whether the different theoretical models can fit the new data of CMB polarization. Theoretically, the super-Planckian range of $\phi$ motion poses serious challenge to the field theory of inflation. It is very important to see how to obtain theoretical naturalness for large field inflation. Alternatively, it remains an open question that if other sources of gravitational waves, instead of the tensor fluctuation from the vacuum, could change the predictions. | 14 | 3 | 1403.4585 |
1403 | 1403.4250_arXiv.txt | We constrain the properties of the progenitor system of the highly reddened Type Ia supernova (SN) 2014J in Messier 82 (M82; $d \approx 3.5$~Mpc). We determine the SN location using Keck-II {\it K}-band adaptive optics images, and we find no evidence for flux from a progenitor system in pre-explosion near-ultraviolet through near-infrared {\it Hubble Space Telescope (HST)} images. Our upper limits exclude systems having a bright red giant companion, including symbiotic novae with luminosities comparable to that of RS~Ophiuchi. While the flux constraints are also inconsistent with predictions for comparatively cool He-donor systems ($T \lesssim$ 35,000~K), we cannot preclude a system similar to V445 Puppis. The progenitor constraints are robust across a wide range of $R_V$ and $A_V$ values, but significantly greater values than those inferred from the SN light curve and spectrum would yield proportionally brighter luminosity limits. The comparatively faint flux expected from a binary progenitor system consisting of white dwarf stars would not have been detected in the pre-explosion {\it HST} imaging. Infrared {\it HST} exposures yield more stringent constraints on the luminosities of very cool ($T < 3000$~K) companion stars than was possible in the case of SN~Ia~2011fe. | The exceptional luminosity of Type Ia supernovae (SN~Ia), and the tight empirical relationships among the decline rate, color, and peak luminosity of their light curves \citep{ph93,ri96}, make SN~Ia useful probes of the cosmic expansion history \citep{riess98,perlmutter99}. SN~Ia spectra and inferred $^{56}$Ni masses (e.g., \citealt{mazzali07}) show reasonable agreement with models of the thermonuclear explosions of carbon-oxygen white dwarfs (\citealt{hill00}; \citealt{kas05}; \citealt{kas07}; \citealt{kas09}). Additional evidence for a comparatively old progenitor population comes from the presence of SN~Ia in passive galaxies, and the observation that they show no preference for the brightest regions of their hosts, in contrast to core-collapse explosions that also exhibit H- and He-deficient spectra (\citealt{kel08}; see also \citealt{ras09}). For sufficiently nearby SN~Ia ($d \lesssim 10$~Mpc), pre-explosion {\it HST} imaging has the sensitivity to detect several classes of candidate progenitor systems. Current constraints suggest that SN~Ia progenitor systems consist primarily of either binary white dwarfs \citep{ibe84,web84,shenbildsten14}, or binaries where a single white dwarf accretes matter from a stellar companion (\citealt{whe73}; \citealt{hanpodsiadlowski04}). For the latter, single-degenerate channel, the white dwarf gains matter from a companion star up to a point where its mass is close to the Chandrasekhar limit (1.4~M$_{\odot}$), precipitating eventual thermonuclear runaway. Accretion onto a white dwarf primary can occur through Roche-lobe overflow (RLOF) from a secondary with a H envelope \citep{vandenheuvelbhattacharya92} or from a He star \citep{nomoto82,yoonlanger03,wangmeng09,liuchen10,geiermarsh13}. Alternatively, in the case of the symbiotic channel, the white dwarf accretes mass from the wind generated by the secondary \citep{munarirenzini92,patatchugai11}. Characterizing the diversity of SN~Ia progenitor systems may be useful for explaining evidence that the luminosities of SN~Ia have a $\sim0.1$ mag dependence on the properties of the host galaxy, after correcting for light-curve shape and color \citep{kel10, sullivan10, lampeitl10, childressaldering13}. While earlier analyses have found useful nondetections at SN~Ia explosion sites (e.g., \citealt{maozmannucci08}; \citealt{nelemansvoss08}), \citet{libloom11} were able to place significantly fainter limits on the luminosity at the explosion site of SN~Ia~2011fe in M101 ($d \approx 6.4$~Mpc; \citealt{shappeestanek11}). Their nondetection excludes a bright red giant companion, specifically both model Galactic progenitor symbiotic systems RS~Ophiuchi (RS~Oph) and T~Coronae Borealis (T~CrB), as well as the He-star system V445 Puppis (V445~Pup). Here we report constraints on the progenitor system of SN~2014J using pre-explosion near-ultraviolet (UV) through near-infrared (IR) {\it HST} imaging of the explosion site whose coordinates we measure using Keck-II adaptive optics (AO) imaging. Section~\ref{sec:discovan} provides a brief summary of the discovery and early analysis of the spectra and light curve of SN~2014J. In \S \ref{sec:data}, we describe the Keck AO and {\it HST} pre-explosion images that we analyze in this paper. The methods we use to extract upper luminosity limits for the progenitor system are explained in \S \ref{sec:methods}, while \S \ref{sec:results} presents constraints on possible progenitor systems. Section~\ref{sec:conclusions} provides a summary of our conclusions. \begin{figure*}[t] \centering \subfigure{\includegraphics[angle=0,width=3.3in]{Keck_AO.pdf}} \subfigure{\includegraphics[angle=0,width=3.3in]{F160W_AO.pdf}} \caption{Coadded Keck-II {\it K}-band NIRC2 AO (left) and {\it HST} pre-explosion F160W (right) exposures of the location of SN~2014J. We use only the central \aodim~of the distortion-corrected AO image to perform astrometric registration. The \keckstarmatches~sources used for registration are identified with white circles, while the position of SN~2014J is marked by a black circle with radius corresponding to the uncertainty in that position estimate. } \label{fig:AO} \end{figure*} \begin{figure*}[t] \centering \subfigure{\includegraphics[angle=0,width=3.25in]{Coadded.png}} \subfigure{\includegraphics[angle=0,width=3.25in]{F435W.png}} \subfigure{\includegraphics[angle=0,width=3.25in]{F814W.png}} \subfigure{\includegraphics[angle=0,width=3.25in]{F160W.png}} \caption{AO position of SN~2014J in a coadded image of all pre-explosion {\it HST} exposures, as well as in coadded F435W, F814W, and F160W {\it HST} images. The center of the solid white circle shows the position that we measure from our AO data, while the center of the dashed yellow circle corresponds to the position published by Tendulkar et al. (\citeyear{tendulkarliu14}; also \citealt{goobarjohansson14}) from separate AO observations. The root-mean square (RMS) scatter of the astrometric fit between our NIRC2 AO image and the HLA F160W image is \keckrarms~in RA and \keckdecrms~in Dec, and that reported by \citet{tendulkarliu14} relative to the HLA F814W image is \eightfourteenonesixtyrarms~in RA and \eightfourteenonesixtydecrms~in Dec. The radii of the circles shown in each image correspond to the positional uncertainty of the SN in either the F160W or F814W image, respectively, convolved when appropriate with the RMS astrometric scatter between images in different bands (e.g., F160W and F435W). Our position is farther from a source considered as a possible progenitor candidate by \citet{goobarjohansson14} and is coincident with a region having strong extinction from dust. } \label{fig:hstimages} \end{figure*} | \label{sec:conclusions} We have used archival, pre-explosion {\it HST} images of M82 in the near-UV through near-IR to place constraints on the progenitor system of the Type~Ia SN~2014J. Assuming that the extinction and selective extinction along the line of sight to the SN estimated from the SN light curve and optical spectra are approximately correct (e.g., \citealt{goobarjohansson14}; \citealt{patattaubenberger14}), we can exclude a progenitor system with a bright red giant mass-donor companion, including recurrent novae with luminosities comparable to the Galactic prototype symbiotic system RS~Oph. Our limits are fainter than the predicted luminosity of He-star-channel progenitors with comparatively low effective temperature. The available near-IR M82 data provide a fainter limit for mass donors with very low effective temperatures ($T < 3000$~K) than was possible at the explosion site of SN~2011fe in M101. A hypothetical progenitor system consisting of two white dwarf stars that does not experience a long-lived merger phase \citep{shenbildsten12} would have a luminosity significantly fainter than the upper limits we estimate. \begin{deluxetable*}{cccccccc} \tablecaption{{\it HST} Datasets and Upper Absolute Magnitude Limits on Point-Source Flux at Explosion Site} \tablecolumns{8} \tablehead{ \colhead{Instrument}&\colhead{Aperture}& \colhead{Filter}&\colhead{UT Date Obs.}&\colhead{Exp. Time (s)}&\colhead{Prop. No.}& \colhead{Visual Limit}& \colhead{3$\sigma$ Background Limit} } \startdata WFC3&UVIS&F225W&2010-01-01&1665.0&11360&26.50&26.80\\ WFC3&UVIS&F336W&2010-01-01&1620.0&11360&26.71&27.23\\ ACS&WFC&F435W&2006-09-29&1800.0&10766&26.30&27.05\\ WFC3&UVIS&F487N&2009-11-17&2455.0&11360&26.01&25.94\\ WFC3&UVIS&F502N&2009-11-17&2465.0&11360&25.93&26.28\\ WFPC2&WF&F502N&1998-08-28&3600.0&6826&21.76&22.70\\ WFC3&UVIS&F547M&2010-01-01&1070.0&11360&26.14&25.94\\ WFPC2&WF&F547M&1998-08-28&100.0&6826&21.63&22.12\\ ACS&WFC&F555W&2006-03-29&1360.0&10766&26.42&26.52\\ WFPC2&WF&F631N&1998-08-28&1200.0&6826&21.43&22.17\\ ACS&WFC&F658N&2004-02-09&700.0&9788&24.63&24.76\\ ACS&WFC&F658N&2006-03-29&4440.0&10766&25.06&25.17\\ WFPC2&WF&F658N&1997-03-16&1200.0&6826&21.31&21.86\\ WFC3&UVIS&F673N&2009-11-15&2760.0&11360&24.53&25.62\\ ACS&WFC&F814W&2006-03-29&700.0&10766&24.83&25.09\\ WFC3&IR&F110W&2010-01-01&1195.39&11360&23.54&23.51\\ WFC3&IR&F128N&2009-11-17&1197.69&11360&22.90&22.85\\ WFC3&IR&F160W&2010-01-01&2395.39&11360&22.43&22.48\\ WFC3&IR&F164N&2009-11-17&2397.7&11360&21.98&22.17 \enddata \tablecomments{ Limiting magnitudes in the Vega system for point sources near the explosion coordinates in the {\it HST} images. Visual limiting magnitudes are estimated by injecting a point source of increasing brightness in close proximity to the AO explosion coordinates, and identifying when a source is clearly detected. The 3$\sigma$ background detections are computed using the RMS of the background measured in a region without point sources or pronounced background gradients. } \label{tab:datasets} \end{deluxetable*} \begin{deluxetable*}{cccccc} \tablecaption{Stellar and Blackbody Upper Magnitude Limits} \tablecolumns{6} \tablehead{ &\multicolumn{2}{c}{$M_V$ (2$\sigma$)} & \multicolumn{2}{c}{$M_J$ (2$\sigma$)} & \colhead{Most Constraining} \\ \colhead{Star} & \colhead{``1-Frame''}& \colhead{Combined} & \colhead{`1'-Frame}& \colhead{Combined}&\colhead{`1'-Frame Bandpass}} \startdata O5 V&-3.25&-2.53&-2.51&-1.79&F555W\\ B0 V&-3.25&-2.55&-2.55&-1.85&F555W\\ A0 V&-3.26&-2.54&-3.26&-2.54&F555W\\ A5 V&-3.26&-2.48&-3.54&-2.76&F555W\\ F0 V&-3.08&-2.37&-3.61&-2.90&F814W\\ F5 V&-2.94&-2.26&-3.76&-3.08&F814W\\ G0 V&-2.76&-2.15&-3.77&-3.16&F814W\\ G5 V&-2.69&-2.08&-3.87&-3.26&F814W\\ K0 V&-2.55&-1.95&-3.93&-3.33&F814W\\ K5 V&-2.04&-1.40&-4.21&-3.57&F814W\\ M0 V&-1.63&-0.86&-4.49&-3.72&F110W\\ M4 V&-0.09&0.57&-4.52&-3.86&F110W\\ M5 V&0.71&1.43&-4.55&-3.83&F160W\\ B5 III&-3.25&-2.54&-2.92&-2.21&F555W\\ G0 III&-2.69&-2.03&-4.00&-3.34&F814W\\ G5 III&-2.55&-1.90&-4.09&-3.44&F814W\\ K0 III&-2.44&-1.79&-4.12&-3.47&F814W\\ K5 III&-1.81&-1.03&-4.48&-3.70&F110W\\ M0 III&-1.67&-0.86&-4.48&-3.67&F110W\\ M5 III&0.18&0.90&-4.48&-3.76&F160W\\ M10 III&3.84&4.42&-4.51&-3.93&F128N\\ B5 I&-3.26&-2.51&-3.09&-2.34&F555W\\ F0 I&-3.11&-2.38&-3.55&-2.82&F814W\\ F5 I&-3.04&-2.33&-3.70&-2.99&F814W\\ G0 I&-2.76&-2.13&-3.80&-3.17&F814W\\ G5 I&-2.60&-1.99&-3.91&-3.30&F814W\\ M2 I&-1.10&-0.42&-4.40&-3.72&F814W\\ BB1&-3.25&-2.53&-2.62&-1.90&F555W\\ BB2&-3.25&-2.53&-2.50&-1.78&F555W\\ BB3&-3.25&-2.53&-2.45&-1.73&F555W \enddata \tablecomments{Limiting magnitudes in $V$ and $J$ bands in the Vega system for a point source at the explosion site. The BB1, BB2, and BB3 blackbody spectra have 35,000, 65,000, and 95,000 K temperatures, respectively. Stellar classifications are those of the \citet{pickles98} spectra used as models of the potential companion. The bandpass in right column is the most constraining observation for the ``1-frame'' upper magnitude limits. } \label{tab:hrlimits} \end{deluxetable*} | 14 | 3 | 1403.4250 |
1403 | 1403.5898_arXiv.txt | When measuring the one-dimensional power spectrum of the \lya\ forest, it is common to measure the power spectrum in the flux fluctuations red-ward of the \lya\ emission of quasars and subtract this power from the measurements of the \lya\ flux power spectrum. This removes the excess power present in the \lya\ forest which is believed to be dominated by the metal absorption by the low-redshift metals uncorrelated with the neutral hydrogen absorbing in \lya. In this brief report we note that, assuming the contaminants are additive in the optical depth, the correction contains a second order term. We estimate the magnitude of this term for two currently published measurements of the 1D \lya\ flux power spectrum and show that it is negligible for the current generation of measurements. However, future measurements will have to take this effect into account when the errorbars improve by a factor of two or more. | The Lyman-$\alpha$ forest measurements are becoming increasingly more accurate and to that end careful investigation of possible systematic effects is required. In this brief report we study the effect of the background power fluctuations which contaminate the signal in the \lya\ forest region. Fluctuations in the \lya\ forest region in the spectra of distant quasars, that is region between the rest \lya\ and \lyb\ emission lines (with some buffer to immunize against proximity effects) is dominated by the \lya\ absorption. However, metals in the inter-galactic medium will contaminate this signal coming from neutral hydrogen. There are several techniques to attack this important systematics. For metal transitions which occur at wavelengths similar to the \lya\ emission wavelength ($\lambda_\alpha = 1215.67$\AA) we can rely on the fact that the contaminant metals are closely tracing the dominant absorption by neutral hydrogen producing detectable ``beating'' in the power spectrum measurements. This has been demonstrated in \cite{2006ApJS..163...80M,2013A&A...559A..85P} for Si III and \cite{2013JCAP...09..016I} for O VI. On the other hand it is relatively easy to remove contribution to absorption by metals whose transitions $\lambda$ are sufficiently larger than $\lambda_\alpha$. The most common way to do this is to measure the power spectrum of fluctuations redward of the \lya\ emission in the spectra of quasars. Since gas behind a given quasar cannot absorb quasar light, this power is often termed the background power -- the power spectrum in absence of signal -- and subtracted from the measured flux power spectrum. Note that for a given observed wavelength $\lambda_o$, there are quasars at somewhat larger redshift $1+z>\lambda_o/\lambda_\alpha$ for which the wavelength is subject to both \lya\ and contaminant absorptions and \emph{other} quasars at somewhat lower redshifts $1+z<\lambda_o/\lambda_\alpha$ for which the same wavelength is absorbed only by the contaminant. Therefore, we are correcting the observed \lya\ forest flux power spectrum by subtracting contaminant flux power measured in the lower redshift quasars, but corresponding to the same observed wavelength range and thus to the statistically the same component. It is believed that majority of the contaminant signal is coming from a mixture of metal absorptions by a lower redshift ($z<1.5$) intergalactic medium. However, this simple subtraction will remove all absorption associated with metal lines with rest-frame wavelength falling red-ward of the region in which contaminant power is estimated. It is most common to use the region $1270<\lambda<1380$\AA, which also removes significant absorption due to both Si IV (a doublet at rest wavelengths 1393.75\AA and 1402.77\AA) and C IV (another doublet absorbing at 1548.20\AA and 1550.78\AA). Since the gas casing contaminant absorption is physically very far from the gas causing primary \lya\ forest, the fluctuations in the two are uncorrelated. However, the contaminant signal adds to the total optical depth experienced by the quasar's photons, which leads to a second order effect, which we discuss in this work. We will show that this effect is negligible for the present generation of the one-dimensional flux power spectra measurements, but that it will likely become important for the final BOSS (\cite{2013AJ....145...10D,2012AJ....144..144B}) analysis, eBOSS (\cite{eBOSS}) and DESI (\cite{2013arXiv1308.0847L}) experiments. | In this brief report we have shown that the multiplicative contaminations in the Lyman-$\alpha$ forest, such as those arising by the intervening low redshift metals cannot be simply subtracted by measuring them outside the forest region, but instead produce higher-order corrections. These corrections are typically small and we have demonstrated that they do not matter for the current generation of the 1D power spectrum measurements. The measurement of \cite{2013A&A...559A..85P} has used approximately 14 thousands high signal-to-noise BOSS quasars, producing an effect of $\Delta \chi^2\sim2$. The full survey will contain approximately 160 thousand quasars and eBOSS and DESI experiments will likely increase the number of quasars to well over 600 thousand. This signal to noise is hence likely to increase by a factor of at least a few, bringing the expected size of the effect well into the realm where correction will have to be applied. Finally, we note that the correction mixes up small scales and large scales. This can have important consequences, when continuum fluctuations are taken into account. Traditionally, analyses have relied on the fact that the continuum fluctuations, that is excess fluctuations associated with the fact that un-absorbed continua vary from quasar to quasar, are both slowly-varying with wavelength and uncorrelated with the cosmic structure. Hence, the existing 1D power spectrum measurements have limited their analyses to sufficiently large wave-vectors (e.g. $k>10^{-3}$s/km) and the 3D analysis have relied on cross-power. Note, that we cannot simply subtract continuum fluctuations from the red-side, because these are now in a wrong part of the rest-frame spectrum: continuum fluctuations at 1100\AA\ are not necessarily the same as continuum fluctuations at 1300\AA\ rest-frame. For standard correction, this does not matter, as we can simply discard large scales. But the convolution in the second-order correction discussed in this report in principle requires knowledge of power at \emph{all} scales. This might set a fundamental limitation on how well one can perform this correction, since the power on very large and very small scales will most likely have to be estimated using some form of extrapolation. We do not deal with this question in this brief report, but undoubtedly new techniques will arrive that will attack these issues. | 14 | 3 | 1403.5898 |
1403 | 1403.7854_arXiv.txt | We present a comparative study of three infrared asteroid surveys based on the size and albedo data from the Infrared Astronomical Satellite (IRAS), the Japanese infrared satellite AKARI, and the Wide-field Infrared Survey Explorer (WISE). Our study showed that: (i) the total number of asteroids detected with diameter and albedo information with these three surveyors is 138,285, which is largely contributed by WISE; (ii) the diameters and albedos measured by the three surveyors for 1,993 commonly detected asteroids are in good agreement, and within $\pm$10\% in diameter and $\pm$22\% in albedo at 1$\sigma$ deviation level. It is true that WISE offers size and albedo of a large fraction ($>20$\%) of known asteroids down to a few km bodies, but we would suggest that the IRAS and AKARI catalogs compensate for larger asteroids up to several hundred km, especially in the main belt region. We discuss the complementarity of these three catalogs in order to facilitate the use of these data sets for characterizing the physical properties of minor planets. | Presently, the number of asteroids is known to be more than 620,000. Most asteroids are, however, known only from their orbital data and their other properties are poorly constrained. In particular, size of asteroid, which is one of the most basic physical quantities, has been unknown for most asteroids. Several techniques have been developed to determine the size of asteroid. One of the most effective methods for measuring asteroidal size and albedo indirectly is through the use of radiometry, where a combination of the thermal infrared flux and the absolute magnitude as the reflected sunlight. This radiometric method can provide unique data for asteroidal size and albedo. Observations in mid-infrared wavelengths are suitable for studying asteroids with this method, particularly in the inner solar system inside the orbit of Jupiter. Using radiometric measurements, a large number of objects can be observed in a short period of time, providing coherent data for large populations of asteroids within the asteroid belt. Infrared observations can be made still better under ideal circumstances, from space. The first space-borne infrared telescope is the Infrared Astronomical Satellite (IRAS; ~\cite{Neugebauer1984}), launched in 1983 and performed a survey of the entire sky. To date, there are two other infrared astronomical satellites dedicated to all-sky surveys: the Japanese infrared satellite AKARI~\citep{Murakami2007}, and the Wide-field Infrared Survey Explorer (WISE; ~\cite{Wright2010}). Other space-borne infrared telescopes, e.g., the Midcourse Space Experiment (MSX; \cite{Mill94}), the Infrared Space Observatory (ISO; \cite{Kessler96}), the Spitzer Space Telescope~\citep{Werner2004}, and the Herschel Space Observatory~\citep{Pilbratt2010} have conducted a series of observations with imaging and/or spectroscopy of asteroids. Based on the all-sky survey data obtained by IRAS, AKARI, and WISE (hereafter I--A--W), the largest asteroid catalogs containing the size and albedo data were constructed. However, at present little is known about the consistency of these three catalogs of asteroidal data. Performance of the on-board detectors and the survey strategies are different, the time and season of the observations and the duration of surveys are different, and the thermal model of asteroids adopted for determining size and albedo are different, between I--A--W. The relationship between these three catalogs should be checked in order to facilitate the use of these data sets for scientific purposes. In this paper, we compare the asteroidal catalog data obtained by I--A--W to investigate the consistency and characteristics of these data sets and reveal some benefits of the usage of synthesized these three data for studying the physical properties of minor planets. We have reviewed each surveyor and its data set, and have compiled these data into a single data set. Subsequently, we compare the number and distribution of the asteroids detected by these satellites, and discuss the completeness of the data sets obtained from each of the three satellites. | \label{discussion} \subsection{Survey period of the infrared satellites} The survey period is one of the important factors for asteroid surveys in the infrared (see table~\ref{3 satellites}). At least one year is required to survey all of the solar system bodies beyond a semimajor axis of 2~AU with the surveyor in a fixed solar elongation of 90$^\circ$, while the inertial sky can be covered in half a year. The IRAS mission, which lasted ten~months, surveyed approximately 96\% of the sky covered with two or more hours-confirming scans~\citep{Neugebauer1984, Beichman1988}. The All-Sky Survey conducted for 16 months by AKARI fully covered the main belt region, using a combination of 170 litres of super-fluid liquid helium and two sets of two-stage Stirling cycle mechanical coolers~\citep{Nakagawa2007}. Thus, the AKARI asteroid catalog provides a 100\% complete data set of asteroids with $H < 9$, as mentioned above. The WISE mission conducted a seven-month-long full cryogenic survey and a six-month-long post-cryogenic survey (after depleting its cryogenic tanks). In the post-cryogenic phase, only the near-infrared channels (3.4 and 4.6~\micron~bands) were used. At these shorter wavelengths, asteroid fluxes are a mix of reflected sunlight and thermal emissions. Nevertheless, \citet{Mainzer2012}, \citet{Masiero2012}, and \citet{Grav2012a} produced reasonable estimates of the sizes and albedos of asteroids, assuming a relationship between visual albedo and infrared albedo, which are calibrated with data obtained in the full cryogenic phase. \subsection{Factors causing discrepancies among IRAS, AKARI, and WISE} The differences between the mean sizes and albedos obtained by I--A--W are generally within $\sim$10\% and $\sim$22\% of each other, respectively (at the 1$\sigma$ standard deviation). These values are mostly larger than the uncertainties within each data set (typically, 5--13\% for diameter and 10--33\% for albedo). Several possible reasons may explain the I--A--W differences. First, the different types of measurements do not fully include system uncertainties. Also, several factors which may cause discrepancies originate from the physical properties of asteroids, such as their shape, thermal inertia, surface roughness, rotation rate, and pole orientation. Asteroids are often elongated and irregularly shaped, and sometimes form binary systems, which generate lightcurve variance as they rotate. The Asteroid Lightcurve Database\footnote{http://www.minorplanet.info/lightcurvedatabase.html} \citep{Warner2009} indicates that, as of September 2013, the mean value of the maximum amplitude of the lightcurve for the 5,730 available asteroids is $0.344 \pm 0.296$~mag. Asteroids with larger amplitude lightcurves are likely to add to the uncertainty in establishing their size and albedo, especially for estimations based on single or a few sightings. In addition, uncertainties in the treatment of scattered sunlight in the visible wavelengths limit the accuracy of radiometric measurements. Usually, simultaneous observations in visible and infrared wavelengths are not achieved. Instead, the $H$--$G$ system~\citep{Bowell1989} is adopted to represent photometric values in visible wavelengths. Uncertainties in the absolute magnitudes mainly impact the accuracy of the resulting albedo values~\citep{Harris1997}. \citet{Pravec2012} found that a discrepancy exists between absolute magnitudes listed in the MPC orbit database and those measured by dedicated photometric observations over 30 years. They found that the MPC values are mostly too small for the 583 observed asteroids; the mean offset of $H$ is $-0.4$ to $-0.5$ at $H \sim 14$. The slope parameter given in \citet{Pravec2012} varies from $-0.15$ to 0.55 (mean, $0.21 \pm 0.09$), while this value is often assumed to be $0.15$. These discrepancies can account for the uncertainties in the estimated albedo, especially for $H > 10$. Once improved measurements of $H$ become available, the values for the sizes and albedos can be revised. For example, \citet{Harris1997} devised a simple and convenient approximation for recalculating the size and albedo from improved $H$ values that does not require detailed thermal model calculations. Saturation of the observed flux leads to another severe problem for larger asteroids. \citet{Lebofsky1989} found that the IRAS observations of (1)~Ceres and (2)~Pallas showed unusual behaviors (systematic wavelength variations) as compared with the results of ground-based observations, perhaps due to saturation in 25 and 60~\micron~bands. While these point sources may be saturated, properly corrected values do not affect estimates of the sizes of other objects using the IRAS data~\citep{Tedesco2002}. \citet{Cutri2013} reported that point sources detected with WISE brighter than 0.88~Jy in 12~\micron~band or 12.0~Jy in 22~\micron~band show larger uncertainties owing to the onset of detector saturation. The former saturation level corresponds to the thermal emission from $\sim$30--70~km sized main belt asteroids. In contrast, no sign of saturation is apparent in the AKARI observations~\citep{Ishihara2010}; in 18~\micron~band, recorded flux densities for (1)~Ceres were in the range of 500--800~Jy, and those for (4)~Vesta were in the range of 470--600~Jy, both of which are below the saturation limit (D. Ishihara, 2014, private communication). \subsection{The thermal model and the beaming parameter} The STM (with some modification) or the NEATM can be used to characterize the physical properties of asteroids, although care should be exercised when applying these simple models to various types of asteroids. The STM produces good results if the asteroid has a small thermal inertia, rotates slowly, is observed at small solar phase angles, and is not heavily cratered or irregularly shaped (i.e., typical larger main belt asteroids). However, many asteroids are small irregular bodies with predominantly regolith-free rocky surfaces and relatively high thermal inertias~\citep{Delbo2007}. Most studies support the assumption that asteroid surfaces are generally heavily cratered and rough at all scales (e.g., \cite{Ivanov2002}). In combination with the lack of an atmosphere and small thermal skin depths, surface roughness gives rise to substantial temperature contrasts, even at small scales, and produces a {\it beaming effect} in which thermal emission is enhanced in the solar direction. A beaming parameter was introduced to adjust the surface temperature by compensating for the angular distribution of the thermal emission (e.g., \cite{Lebofsky1986}). The beaming parameter physically correlates with the surface roughness and thermal inertia of an asteroid, and in practice, it can be considered as a normalization or calibration factor. For the IRAS catalog, the STM was adopted as the thermal model, using a beaming parameter of $\eta = 0.756$, which was derived from observations of (1)~Ceres and (2)~Pallas using a ground-based telescope~\citep{Lebofsky1986}. It should be noted that the size and albedo estimations of 60\% of asteroids (and $> 80$\% of asteroids larger than 40~km) detected by IRAS have been revised by a more robust estimation using the NEATM, with $\eta$ values ranging from 0.75 to 2.75~\citep{Ryan2010}. The AKARI asteroid catalog was processed using the ``modified'' STM, in which $\eta$ was determined separately for two observed mid-infrared bands ($\eta$~=~0.87 for 9~\micron~band and 0.77 for 18~\micron~band), by comparing existing data from several different types of measurements for 55 asteroids ranging in diameter from 90 to 960~km (see \cite{Usui2011}, table 11). The WISE results used the NEATM with independently varying $\eta$ values, which were determined by fitting multiple observations using the WISE data alone; the results were then examined by comparisons with 49 unique objects with diameters ranging from 0.4 to 312~km (data from several sources; see \cite{Mainzer2011b}, table 1). The distribution of $\eta$ in the WISE thermal model is shown for main belt asteroids in, for example, figure 6 of \citet{Masiero2011} (the mean value of their beaming parameters is $\eta~=~0.962~\pm~0.153$, for asteroid diameters of $>10$~km). Here, we consider the dependency of the size estimation on the value of the beaming parameter, under the conditions of the thermal model calculation. We assume an asteroid with given visible and thermal fluxes at given distances from the Sun and an observer. Once an incident solar flux is assumed, an absorbed flux is determined (although it depends weakly on albedo). A larger $\eta$ causes lower surface temperatures of the thermal flux to balance the absorbed flux and the thermal emission. This can be easily found from the formulation of the temperature of the subsolar point ($T_{\rm SS}$) on the surface of the asteroid (e.g., \cite{Harris1998}), as follows: \begin{eqnarray} T_{\rm SS} &=& \left\{\frac{(1-A_{\rm B})S_{\rm s}}{\eta \epsilon \sigma R_{\rm h}^{~2}}\right\}^{1/4}~ , \label{eq:max temperature} \end{eqnarray} where $A_{\rm B}$ is the Bond albedo, $S_{\rm s}$ is the solar flux at 1~AU (i.e., the solar constant), $\eta$ is the beaming parameter, $\epsilon$ is the infrared emissivity, $\sigma$ is the Stefan--Boltzmann constant, and $R_{\rm h}$ is the heliocentric distance in units of AU. A lower temperature implies a lower thermal flux per unit area. To provide the observed thermal flux, a larger asteroid is needed, and a larger size is equivalent to a smaller albedo under a given flux in visible wavelengths. Thus, larger $\eta$ values reflect larger sizes of asteroids. It should also be noted that there is a phase angle (Sun--target--observer angle; $\alpha$) dependency of the beaming parameter. In the STM, the temperature on the nightside of an asteroid is assumed to be zero, which is a reasonable assumption at small phase angles, where the dayside flux dominates; i.e., in the case of the main belt asteroids. However, \citet{Harris2002} pointed out that care must be exercised when applying simple thermal models to the near-Earth asteroids because thermal model calculations based on observations made at larger solar phase angles are subject to relatively large uncertainties; it was because of this that the NEATM was developed~\citep{Harris1998}. As compared with main belt asteroids, the near-Earth asteroids tend to have irregular shapes, and they are often observed at moderate to large solar phase angles ($\alpha > 30^{\circ}$), which is out of the valid range of the STM. If the nightside temperature is treated as non-zero, then the relationship between $\eta$ and $\alpha$ can vary depending on the temperature distribution. Based on the WISE data obtained using the NEATM, the average relationship between $\eta$ and $\alpha$ is given as $\eta~=~0.00963^{\pm 0.00015} \alpha~+~0.761^{\pm 0.009}$~\citep{Mainzer2011d}, or $\eta~=~0.011^{\pm 0.001} \alpha~+~0.79^{\pm 0.01}$~\citep{Masiero2011}, although the spread around this value is large for $0.3 \leq \eta \leq \pi$. Note that due to the constraints of the attitude control of infrared surveyors, the solar elongation angle of the WISE observations is fixed at approximately $90^{\circ}$, which means that the observing phase angle, heliocentric distance, and geocentric distance are strongly correlated. The thermophysical model (TPM, \cite{Lagerros1996, Lagerros1997, Lagerros1998}), which is a sophisticated approach for asteroid modeling, assuming a spherical body, is developed to derive the size, albedo, thermal inertia, and sense of rotation without assuming a value of the beaming parameter. \citet{Mueller2014} discussed the validity of the TPM for a selected target by using only this simple spherical shape model. \subsection{Comparisons with the other measurements} Importantly, none of the I--A--W catalogs consider the irregular shapes of asteroids. While a non-rotating spherical body is assumed for asteroids in both the STM and NEATM, the actual shapes of asteroids are generally elongated, especially in the cases of smaller asteroids. Figure~\ref{fig:relative difference} shows the relative differences between the diameters measured by I--A--W and the effective (volume-equivalent) diameters ($D_{\rm ref}$) derived from the shape models determined by several methods: direct imaging with the Hubble Space Telescope~\citep{Tanga2003}, with the adaptive optics system on the W.M. Keck II telescope \citep{Hanus2013, Marchis2006, Drummond2009, Conrad2007}, or by spacecraft observations\footnote{Although more than ten asteroids have been explored by spacecraft % flyby/rendezvous/landing/sample return, only (243) Ida ($d \sim 30$~km) % has also been observed by all three infrared surveyors.}% \citep{Thomas1996}, stellar occultation combined with lightcurve inversion techniques~\citep{Durech2011}, speckle interferometry~\citep{Cellino2003, Drummond1985}, and radar observations~\citep{Ostro2000}. In total, 88 main belt asteroids ranging in size from 30 to 540~km are included. The relative difference is defined as $\left(D_{i} - D_{\rm ref}\right) / D_{\rm ref}$, where $i$ refers to IRAS, AKARI, or WISE. The mean values of the relative differences are 2.8\%, 1.7\%, and 7.5\% for IRAS, AKARI, and WISE, respectively, and the standard deviations for each are 12--13~\%. We found that the size derived by AKARI is closer to that derived by IRAS or WISE. This is not a surprising result, as the beaming parameter adopted in the thermal model calculation in the AKARI catalog is calibrated with well-studied main belt asteroids larger than 90~km, whose size, shape, rotational properties, and albedo are known from different measurements, as mentioned above. In this respect, the diameters obtained by radiometric measurements based on I--A--W are reliable in a statistical sense, which are smoothed out and averaged over a limited number of observations, even though the sizes obtained by radiometric and other measurements can be discrepant by up to 30\%. | 14 | 3 | 1403.7854 |
1403 | 1403.5583_arXiv.txt | Quantum scale invariance in the UV has been recently advocated as an attractive way of solving the gauge hierarchy problem arising in the Standard Model. We explore the cosmological signatures at the electroweak scale when the breaking of scale invariance originates from a hidden sector and is mediated to the Standard Model by gauge interactions (Gauge Mediation). These scenarios, while being hard to distinguish from the Standard Model at LHC, can give rise to a strong electroweak phase transition leading to the generation of a large stochastic gravitational wave background in possible reach of future space-based detectors such as eLISA and BBO. This relic would be the cosmological imprint of the breaking of scale invariance in Nature. | 14 | 3 | 1403.5583 |
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1403 | 1403.7912_arXiv.txt | \noindent Recent work by Aplin and Lockwood \cite{AL} was interpreted by them as showing that there is a multiplying ratio of order 10$^{12}$ for the infra-red energy absorbed in the ionization produced by cosmic rays in the atmosphere to the energy content of the cosmic rays themselves. We argue here that the interpretation of the result in terms of infra-red absorption by ionization is incorrect and that the result is therefore most likely due to a technical artefact | Atmospheric molecular cluster ions (MCI) are bipolar charged species formed by ionization in the atmosphere. The absorption of infra-red radiation (IR) by such clusters is interesting since it could have an effect on the Earth's radiation budget and thereby allow the ionization from cosmic rays (CR) to affect the climate. Recently, an experiment has been described by Aplin and Lockwood (AL) in which they claim to observe a large absorption of IR by MCI produced by CR in the atmosphere \cite{AL}. In the AL experiment infra-red (IR) detectors are operated close to a small CR telescope. The IR band studied is 9.15$\pm$0.45 $\mu$m, a region of reduced absorption by atmospheric greenhouse gases \cite{PandO}. They observe an average decrease of $\sim$2.5 mW/m$^2$ in intensity over this wavelength range in a time duration of order 800 seconds following counts in the telescope. They assume that the decrease is caused by the absorption of IR radiation by MCI produced by CR showers, one particle of which gives the detected count (usually a muon). They claim that the ratio of the total IR energy absorbed by these showers to the energy in the CR itself is of order of 10$^{12}$. This quite remarkable result needs careful independent analysis and this is what we propose to do. We will show that the interpretation of result as absorption of IR by MCI leads to impossible consequences and we conclude that this interpretation is wrong. | We have demonstrated that the results of the AL measurements, as interpreted by AL, lead to impossible consequences. What then could be the reason for the result? It might be thought that an explanation is that it is due to some new unknown process. This seems highly unlikely since the contributing processes involve rather low energy electromagnetism. Furthermore, there would still be the inconsistency with their own laboratory measurements. A more likely explanation is that the result is due to a bias or 'cross-talk' between the CR and IR detectors. Averaging noisy signals to produce a small observed deviation from zero such as is done in the AL experiment is very sensitive either to the presence of an apparatus bias or to such cross talk. It is evident that an independent analysis of IR signals associated with CR is needed before the dramatic results of AL are considered further. Such analysis should include the careful monitoring of atmospheric conditions and searches for apparatus biases eg by an equal study of random triggers and CR triggers. | 14 | 3 | 1403.7912 |
1403 | 1403.7409_arXiv.txt | Motivated by the properties of matter quantum fields in curved space-times, we work out a gravity theory that combines the Born-Infeld gravity Lagrangian with an $f(R)$ piece. To avoid ghost-like instabilities, the theory is formulated within the Palatini approach. This construction provides more freedom to address a number of important questions such as the dynamics of the early universe and the cosmic accelerated expansion, among others. In particular, we consider the effect that adding an $f(R)=a R^2$ term has on the early-time cosmology. We find that bouncing solutions are robust against these modifications of the Lagrangian whereas the solutions with {\it loitering} behavior of the original Born-Infeld theory are very sensitive to the $R^2$ term. In fact, these solutions are modified in such a way that a plateau in the $H^2$ function may arise yielding a period of (approximately) de Sitter inflationary expansion. This inflationary behavior may be found even in a radiation dominated universe. | Extensions of General Relativity (GR) have been considered in the literature following different approaches and motivated by a variety of reasons. Theoretical arguments support that GR is just an effective theory that fits well the behavior of gravitational systems at relatively low energies. At ultrahigh and at very low energies or, equivalently, at ultrashort and very large length scales, corrections to the GR Lagrangian are expected. The form of these corrections is difficult to guess from first principles and probably results from complicated processes related to the fundamental constituents and/or structure of space-time and how their symmetries are broken. Moreover, there is no experimental evidence whatsoever about what is the most reasonable or favourable formulation of classical GR that should be used to consider its high-energy and low-energy extensions. What should be the classical starting point? Should we stick to the traditional metric (or Riemannian) approach or should we consider a Palatini (or metric-affine) formulation? Whatever the choice, the potential extensions offered by each starting point can lead to significantly different gravitational physics. In this sense, it is well-known that high-curvature extensions of GR in the usual metric formalism generically lead to higher-order derivative equations and/or to the emergence of new dynamical degrees of freedom. This is the case, for instance, of $f(R)$ theories \cite{review0,review1,review2,review3,review4,Sotiriou:2008rp}, quadratic gravity, and the Born-Infeld type gravity action considered by Deser and Gibbons \cite{Deser:1998rj}, to name just a few. If a Palatini formulation of those theories is chosen, however, one finds completely different physics \cite{Banados}. In fact, it is well established that in the Palatini approach those theories lead to second-order metric field equations which in vacuum exactly recover the dynamics of GR \cite{olmo11}. It turns out that, in the above mentioned Palatini theories, despite the fact of allowing the connection to vary independently of the metric, the number of dynamical fields ends up being the same as in standard GR. One finds that the connection can be solved in terms of the metric and the matter sources via a set of algebraic (not differential) equations. Leaving aside the dependence on the matter, this is exactly what happens in the Palatini formulation of GR, where the connection becomes a constrained object algebraically related with the first derivatives of the metric, thus defining the Levi-Civita connection. Therefore, even though one might {\it a priori} expect many new additional degrees of freedom in the metric-affine formulation due to the independence of the connection, the resulting equations yield a different answer, namely, that the connection is not a dynamical object and that the metric satisfies second-order equations. Moreover, in general, one finds that in the absence of matter fields the metric field equations exactly boil down to those of GR with an effective cosmological constant (see \cite{olmo11} for further details and discussions). The modified dynamics of these theories, therefore, is not generated by new dynamical degrees of freedom, which has motivated recent related research on theories with non-dynamical fields \cite{Bazeia:2014rea,Pani:2013qfa}. A closer inspection of the Palatini models puts forward that the modified dynamics is due to nonlinearities induced by the matter sources and by higher-order spatial derivatives of the fields \cite{Olmo:2011fh,Harko:2014zma}. \\ The fact of having second-order equations so closely related to GR is of great importance \cite{Fiorini} because it minimizes the number of extra inputs necessary to characterize a given solution simply because higher-order equations require more boundary/initial conditions. In the Palatini version of the Born-Infeld gravity model, for instance, there is no more freedom than in GR to get rid of cosmic singularities starting from a solution which asymptotes to our current accelerated expansion phase. If the big bang singularity is avoided in this model, it is because the theory is doing something robust and relevant on the dynamics, not because we have extra freedom to select a subset of solutions in an {\it ad hoc} manner, as it happens in theories with higher-order derivatives. This type of theories, therefore, must be explored in more detail, as the modified dynamics they generate is enough to successfully avoid important problems without any further external or {\it ad hoc} input. Quadratic gravity is also able to avoid the big bang singularity \cite{Barragan:2010qb,Barragan:2009sq}. When the Palatini version is considered, this occurs in a purely dynamical way with exactly the same number of initial conditions (at late times) as in GR. In the metric version of the theory \cite{Anderson, Novello}, however, additional restrictions on the parameters that characterize the asymptotically FRW solutions are necessary. The Born-Infeld (BI) gravity model is a very interesting starting point to consider high-energy extensions of GR because BI-like Lagrangians naturally arise in different scenarios in a very fundamental way. For instance, the original Born-Infeld theory replaced the classical Maxwell Lagrangian $L_M=-\frac{1}{16\pi}F_{\mu\nu}F^{\mu\nu}$ by a new version \begin{equation} \LL_{BI}= \frac{\beta^2}{8\pi}\left(\sqrt{-\vert \eta_{\mu\nu} + \beta^{-1} F_{\mu\nu} \vert} - 1 \right) \label{eq:BIem0} \ , \end{equation} which for a pure electric field can also be written as \begin{equation} \LL_{BI}= \frac{\beta^2}{8\pi}\left(\sqrt{1+\frac{F_{\mu\nu}F^{\mu\nu}}{\beta^2}} - 1 \right) \label{eq:BIem1} \ . \end{equation} This new theory sets an upper bound for the electric field strength and regularizes the energy of a point particle, which is divergent in the standard Maxwell theory. On the other hand, the modification needed in the Lagrangian of a free point-particle to go from a non-relativistic, $L_{nr}=\frac{1}{2}mv^2$, to a relativistic description is also of the BI type \cite{Ferraro:2009zk}: $L_{rel}=mc^2(1-\sqrt{1-\frac{mv^2}{mc^2}})$. In analogy with (\ref{eq:BIem0}), Deser and Gibbons \cite{Deser:1998rj} proposed a Born-Infeld like theory of gravity which has been recently reconsidered by Ba\~{n}ados and Ferreira \cite{Banados} in the Palatini formulation, \begin{equation}\label{eq:A0} S_{BI}=\frac{1}{\kappa^2\epsilon}\int d^4x \left[\sqrt{-|g_{\mu\nu}+\epsilon R_{\mu\nu}(\Gamma)|}-\lambda \sqrt{-|g_{\mu\nu}|}\right]+S_m \ , \end{equation} as it yields second-order equations and avoids ghost-like instabilities. Here $g_{\mu\nu}$ represents the (non-flat) space-time metric and $R_{\mu\nu}(\Gamma)$ the Ricci tensor of the independent connection (further notational details later). It is worth noting that the Born-Infeld electromagnetic Lagrangian is consistent with the one-loop version of supersymmetric QED \cite{susyQED}. Additionally, the Lagrangians describing the electromagnetic field of certain D-branes are also of the Born-Infeld determinantal type \cite{Gibbons:2001gy}. Therefore, this type of Lagrangians appear in a very fundamental way in different scenarios of interest. The possibility of regularizing curvature scalars in gravity via this type of Lagrangians has motivated a burst of activity in the context of Born-Infeld gravity in cosmological scenarios, where the growth of perturbations, the effects on the angular power spectrum of the cosmic microwave background, and other aspects of scalar and tensorial linear perturbations and inflation have been investigated \cite{Du:2014jka, Kim:2013noa,Kruglov:2013qaa, Yang:2013hsa,Avelino:2012ue, DeFelice:2012hq, EscamillaRivera:2012vz, Cho:2012vg, Scargill:2012kg, EscamillaRivera:2013hv}. Other relevant questions dealing with astrophysics \cite{Harko:2013xma,Avelino:2012ge}, stellar structure \cite{Sham:2013cya,Kim:2013nna,Harko:2013wka,Sham:2013sya, Avelino:2012qe, Sham:2012qi,Pani:2012qd, Pani:2011mg}, the problem of cosmic singularities \cite{Bouhmadi-Lopez:2013lha, Ferraro:2010at}, black holes \cite{Olmo:2013gqa}, and wormhole physics \cite{Lobo:2014fma,Harko:2013aya} have also been considered in the literature. From an observational perspective, we note that BI theory recovers GR with an effective cosmological constant at the zeroth order in a series expansion in the parameter $\epsilon$. For this reason the theory can be made to agree with all current observations by just suitably tuning this parameter. Since we are mainly interested in theoretical aspects concerning the avoidance of singularities and alternative mechanisms for inflation, we will always assume that $\epsilon$ is sufficiently small so as not to enter in conflict with observations. \\ Despite the appealing properties of the BI gravity Lagrangian, our ignorance on the behavior of gravity at the highest energies motivates the exploration of departures from that basic structure to check the robustness of its predictions. In fact, if quantum effects in curved space-time are considered \cite{Parker-Toms}, in general one finds curvature corrections that are necessary to account for the renormalizability of matter fields in such backgrounds. These corrections are known to be quadratic in the Ricci and Riemann tensors at high energies, but other types of $R-$dependent corrections may arise in the infrared, thus having a relevant impact on the late-time cosmic expansion \cite{PARKER1,PARKER2}. This fact has also motivated recent studies of hybrid scenarios in which the Einstein-Hilbert Lagrangian is supplemented with $f(R)$ corrections of the Palatini type \cite{Harko:2011nh,Capozziello:2012ny,Capozziello:2012hr,Capozziello:2012qt,Capozziello:2013uya, Capozziello:2013yha,Capozziello:2013gza}. The quantum properties of matter fields in curved space-times, therefore, naturally justify the interest in exploring high-energy and low-energy modifications of the classical BI theory via $f(R)$-type terms. In this sense, as advanced above, the BI gravity Lagrangian yields a low-energy perturbative expansion with GR as the lowest order followed by quadratic and higher-order curvature corrections with specific coefficients, which is in consonance with the expected quantum field theory corrections at high energies. Theories of this type, with up to quadratic curvature corrections, have been investigated within the Palatini approach in the literature \cite{or12a,or13d,PLB13,lor,Olmo:2013mla,Lobo:2014zla,Lobo:2014fma}, and specific methods to deal with the resulting field equations have been developed \cite{OSAT}. However, higher-order curvature corrections involving cubic powers or higher of the Ricci tensor (such as $R_{\mu\alpha}R_{\beta\gamma}R_{\delta\nu}g^{\alpha\beta}g^{\gamma\delta}g^{\mu\nu}$, for instance) have not been explored yet and are likely to require new methods. By contrast, though the BI theory contains terms of that kind in a perturbative expansion, in its exact determinantal form the methods required to deal with the field equations are much simpler even than for the quadratic theory. It is thus far from clear how a theory with a similar perturbative expansion as the BI theory but with different coefficients multiplying the higher-order curvature terms or including low-curvature corrections, like in the case of $f(R)$ theories, could be put in a form amenable to calculations. In other words, slight modifications of the action possibly generated by the quantum properties of the matter fields can lead to non-trivial changes in the structure of the field equations, which may substantially difficult the analysis. In particular, if an $f(R)$ piece is added to the BI action (\ref{eq:A0}), one finds that the connection equation cannot be solved by just using the tensor $q_{\mu\nu}=g_{\mu\nu}+\epsilon R_{\mu\nu}$ as an auxiliary metric, and more elaborate manipulations are necessary in general. In this work we consider this problem in detail and extend the existing methods to deal with $f(R)$-like modifications of the field equations. This will allow us to explore, in particular, if the high-energy behavior of the BI theory itself is robust against small changes in the coefficients that define its perturbative series expansion. Recall, in this sense, that in curved space-times \cite{Parker-Toms,Anderson} the coefficients of the high-curvature corrections depend on the number and spin of the matter fields. \\ Taking a cosmological scenario with perfect fluids, we provide an algorithm that allows to efficiently study $f(R)$ departures from the original BI gravity theory in a fully non-perturbative way. This aspect, namely, the exact (non-perturbative) treatment of the field equations, is very important because the field equations of Palatini theories usually involve algebraic relations which must be handled with care in order not to miss important physical information (see, for instance, the discussion in the introduction of \cite{Ashtekar} regarding the properties of nonperturbative systems). In fact, the replacement of the big bang singularity by a cosmic bounce and of black hole singularities by wormholes \cite{Lobo:2014fma,Olmo:2013gqa} in Palatini theories are non-perturbative properties that need not respond linearly to small modifications in the parameters of the theory. With the technical aspects of these BI-$f(R)$ theories under control, as an illustration, we study the robustness of the nonsingular cosmic solutions against modifications of the quadratic curvature terms. We confirm that the bouncing solutions of the original BI theory persist even for large variations in the coefficients of the perturbative expansion and find that the other kind of non-singular solutions, which represent a minimum volume in unstable equilibrium, may develop a big bang singularity followed by a period of approximately de Sitter expansion due to a plateau in the Hubble function. Unstable equilibrium configurations also arise for certain values of the equation of state. \\ The content is organized as follows. In section \ref{sec:field_eqs} we introduce the BI-$f(R)$ theory, derive the field equations, and put them in a form amenable to calculations. In section \ref{sec:fluids} we discuss the procedure to deal with perfect fluids, which will be used in a cosmological scenario in section \ref{sec:cosmology}, where the main physical results are obtained. We conclude in section \ref{sec:summary} with a summary of the work and a discussion of the results. | } In this work we have considered a gravity theory formulated within the Palatini formalism consisting on a Born-Infeld-like gravitational Lagrangian plus an $f(R)$ term. This form of the gravity Lagrangian provides more flexibility to the original Born-Infeld theory, which possesses very interesting properties in scenarios involving cosmic as well as black hole singularities, and allows to explore modifications of its dynamics at high and low energies. We have provided a formal solution for the connection equation and a compact representation of the metric field equations. An algorithm that facilitates the analysis of perfect fluid cosmologies has also been worked out in detail and has been used to study some aspects of the high-energy dynamics of a specific model. Our interest has focused on an $f(R)$ term of the form $f(R)\propto R^2$ which allows to tune at will the coefficient multiplying the $R^2$ term that arises in the low-energy series expansion of the Born-Infeld theory. This type of quadratic corrections are expected to arise due to the quantum properties of the matter fields in curved backgrounds. Depending on the number and types of matter fields \cite{Parker-Toms,Anderson}, the coefficient of the $R^2$ term may change, which justifies our study of this particular term. The methods developed in this work are not restricted to the $R^2$ term and can also be applied to other $f(R)$ Lagrangians. \\ \begin{figure}[h] \begin{center} \includegraphics[width=0.75\textwidth]{Inflation_radiation.eps} \caption{Representation of the (dimensionless) Hubble function $\epsilon H^2$ as a function of the (dimensionless) energy density $\epsilon \kappa^2\rho$ for a radiation universe ($\omega=1/3$) in the cases $a=0$ (solid blue), $a=1/10$ (dashed brown), $a=1/3$ (dashed green), $a=1/2$ (dashed orange), and $a=1$ (dashed red). Note the long plateau following the local maximum around $\epsilon \kappa^2\rho\approx 0.6$ in the case $a=1/3$, which could support a period of inflation generated by the radiation fluid. \label{Fig:Inflation}} \end{center} \end{figure} We have found that the solutions with $\epsilon<0$, which yield a cosmic bounce, are robust against modifications of the $R^2$ coefficient, whereas those with $\epsilon>0$ undergo significant changes as compared to the original Born-Infeld theory. For equations of state $\omega>0$, the $\epsilon>0$ branch of Born-Infeld theory yields cosmologies with a stationary point characterized by $H^2=0$ and $dH^2/d\rho=0$. These solutions do not represent a bounce, but a state of minimum volume and maximum density that evolves into a standard FRW cosmology at late times. From Fig.\ref{Fig:Inflation} we see that any modification of the $R^2$ term in a radiation universe destroys the regularity of the original solution. However, the modifications experienced by these solutions may lead to a period of inflationary (de Sitter-like) expansion shortly after the big bang singularity, as is evident from the plateau of the curve $a=1/3$ in Fig.\ref{Fig:Inflation} and of the lower left curve with $a=1/2$ in Fig. \ref{Fig:Positive_Branch}. These results put forward that with slight modifications of the Born-Infeld theory one may get the conditions for an inflationary stage without the need for new dynamical degrees of freedom. Additional effects could be obtained by including higher-order powers of $R$ with free coefficients without altering the number of dynamical degrees of freedom of the theory. \\ The possibility of combining the Born-Infeld Lagrangian with an $f(R)$ term also offers new avenues to address a number of relevant questions of the gravitational dynamics at lower energies. In particular, one may look for $f(R)$ terms designed to modify the high-energy dynamics which combined with the Born-Infeld Lagrangian could leave a low-energy remnant in the form of an effective cosmological constant able to justify the late-time cosmic accelerated expansion. Another application could be the identification of $f(R)$ terms able to yield fully satisfactory models of stellar structure without the need to reconsider the convenient perfect fluid approximation \cite{Kim:2013nna,Olmo:2013gqa, Avelino:2012qe}, a currently open question that has attracted much attention from different perspectives. These and other questions will be considered elsewhere. \\ | 14 | 3 | 1403.7409 |
1403 | 1403.6533_arXiv.txt | The chemistry in the diffuse interstellar medium initiates the gradual increase of molecular complexity during the life cycle of matter. A key molecule that enables build-up of new molecular bonds and new molecules via proton-donation is H$_3^+$. Its evolution is tightly related to molecular hydrogen and thought to be well understood. However, recent observations of \textit{ortho} and \textit{para} lines of H$_2$ and H$_3^+$ in the diffuse ISM showed a puzzling discrepancy in nuclear spin excitation temperatures and populations between these two key species. H$_3^+$, unlike H$_2$, seems to be out of thermal equilibrium, contrary to the predictions of modern astrochemical models. We conduct the first time-dependent modeling of the \textit{para}-fractions of H$_2$ and H$_3^+$ in the diffuse ISM and compare our results to a set of line-of-sight observations, including new measurements presented in this study. We isolate a set of key reactions for H$_3^+$ and find that the destruction of the lowest rotational states of H$_3^+$ by dissociative recombination largely control its \textit{ortho}/\textit{para} ratio. A plausible agreement with observations cannot be achieved unless {a ratio larger than 1:5 for} the destruction of $(1,1)-$ and $(1,0)-$states of H$_3^+$ is assumed. Additionally, {an increased CR ionization rate to $10^{-15}$ s$^{-1}$ further improves the fit whereas} variations of other individual physical parameters, such as density and chemical age, have only a minor effect on the predicted \textit{ortho}/\textit{para} ratios. Thus our study calls for new laboratory measurements of the dissociative recombination rate and branching ratio of the key ion H$_{3}^{+}$ under interstellar conditions. | H\dthree\jon~plays a pivotal role in the gas-phase chemistry of the interstellar medium due to its very low proton affinity, allowing it to transfer a proton to many neutral atoms and molecules (exception being N and O\dtwo). The chemistry of H\dthree\jon~is straightforward. The formation process via the ion-molecule reaction H$_{2}^{+}$ + H$_{2}$ -> H$_{3}^{+}$ + H is well-established \citep[e.g.][]{2006RSPTA.364.3049L}. The destruction of H$_{3}^{+}$ can occur via ion-molecule reactions or dissociative recombination (DR) with free electrons. {Under typical conditions of different ISM environments H$_{3}^{+}$ was long believed to exist below observable limits. Still,} H\dthree\jon~was observed in the interstellar medium by \citet{1996Natur.384..334G} for the first time, followed by other detections \citep[e.g. ][]{1998Sci...279.1910M, 1999ApJ...510..251G, 2002ApJ...567..391M,2008ApJ...688..306G, 2007ApJ...671.1736I, 2012ApJ...745...91I}. These observations have also revealed several unexpected results, which are summarized below. In the simple gas-phase chemistry of H\dthree\jon~only three parameters can strongly affect its {steady-state} abundance: the dissociative recombination rate coefficients, the electron abundance, and the cosmic-ray (CR) ionization rate \citep{2003Natur.422..500M}. The former two parameters are thought to be well constrained in diffuse interstellar clouds \citep{1996ApJ...467..334C, 2003Natur.422..500M}, which leaves the CR ionization rate as the only controlling parameter. \citet{2003Natur.422..500M}, \citet{2007ApJ...671.1736I} and \citet{2012ApJ...745...91I} observed absorption lines of H\dthree\jon~toward several diffuse cloud sight lines, and inferred CR ionization ratios on the order of $\sim 10^{-16}$ s$^{-1}$, about an order of magnitude higher than the value inferred for dark prestellar cores \citep[$\sim 10^{-17}$ s$^{-1}$, see e.g.][]{1998ApJ...506..329W, 2000A&A...358L..79V, 2003Ap&SS.285..619C, 2006RSPTA.364.3101V}. {If one relaxes the steady-state approximation, the density starts to play an important role in the H$_3^+$ evolution \citep[see e.g.][]{2009ApJ...706.1429C, 2013IAUS..292..223F}. } {Furthermore}, observations of the average excitation temperature derived from the two lowest rotational states of H\dthree\jon, $T($H$_3^+$) $\approx 30$ K \citep{2007ApJ...671.1736I, 2012ApJ...745...91I}. It differs significantly from that of the two lowest rotational states of H\dtwo, $T_{01} \approx 70$ K \citep{2002ApJ...577..221R, 2009ApJS..180..125R}. Because the conversion between the two lowest nuclear spin states of H$_{2}$ in collisions with free protons is very efficient, the H$_{2}$ \textit{ortho}$-$\textit{para} ratio is expected to be thermalized with the gas kinetic temperature. Hence, the excitation temperature derived from the relative intensities of H\dtwo~\textit{ortho} and \textit{para} levels are also expected to be an accurate measure of the gas kinetic temperature in the diffuse ISM ($\approx 70$ K). Assuming that collisional thermalization between H$_{3}^{+}$ and H$_{2}$ is also efficient, in previous studies by \citet{2003Natur.422..500M} and \citet{2010ApJ...715..757G} the nuclear spin states of H$_{3}^{+}$ were assumed to be in thermal equilibrium with the kinetic cloud temperature. However, in later studies the excitation temperatures of H\dtwo~and H\dthree\jon directly derived from observations did not agree with each other, indicating that a large population of H$_3^+$ is not thermalized with the diffuse ISM gas. \citet{2011ApJ...729...15C} have investigated this discrepancy by comparing observations of the nuclear spin temperature of H\dthree\jon~\citep[subsequently refined by][]{2012ApJ...745...91I} to that of H\dtwo~for a sample of diffuse interstellar clouds. Their results confirmed that the excitation temperature of H\dthree\jon~and H\dtwo~do not agree. \citet{2011ApJ...729...15C} concluded that the H\dthree\jon~\textit{ortho}/\textit{para} ratio is likely governed by a competition between the collisionally-driven thermalization of H\dthree\jon~and the DR reactions with electrons. The thermalization reaction \textit{ortho}/\textit{para}$-$H$_{3}^{+}$ + H$_{2}$ $\rightarrow$ \textit{ortho}$/$\textit{para} H$_{3}^{+}$ + H$_{2}$ has recently been studied experimentally by \citet{2012ApJ...759...21G}. It was found that the reaction has indeed the expected thermal outcome. From a theoretical point of view, there are more unknown factors related to the chemistry of H\dthree\jon. Theoretical calculations have shown that the photodissociation of H\dthree\jon~is not efficient in the diffuse interstellar medium \citep[see e.g.][]{1987IAUS..120...51V}. In the absence of other abundant molecules like CO and H$_2$O, this leaves DR as the only major destruction pathway for H\dthree\jon. Recent theoretical calculations by \citet{santos:124309} predict the DR rate coefficient for \textit{para}$-$H$_{3}^{+}$ at low temperature to be an order of magnitude higher than that for \textit{ortho}$-$H$_{3}^{+}$. This claim has later been backed up by the plasma experiments of \citet{2011PhRvL.106t3201V}. Meanwhile, other laboratory groups have observed a different dependence, with similar dissociation rates between the two nuclear spin states of H$_{3}^{+}$ \citep[see e.g.][]{kreckel05,tom09, kreckel10}. In this paper we conduct the first time-dependent study of the \textit{ortho}$-$\textit{para} chemistry of H$_{3}^{+}$ in the diffuse interstellar medium. We isolate a set of key processes for the evolution of the \textit{ortho}- and \textit{para}-states of H$_3^+$, and we present new observational measurements to better test our model predictions. The paper is structured as follows. In Section~\ref{sec:obs} we discuss the new observations. In Section~\ref{sec:model} we describe the chemical and physical models utilized in the analysis of the observations. Our results and the underlying chemistry is presented and discussed in Section~\ref{sec:results}, followed by conclusions given in Section~\ref{sec:conclusions}. | \label{sec:conclusions} {We present the results of three new sight lines towards diffuse clouds, where both H$_{3}^{+}$ and H$_{2}$ have been observed in their \textit{ortho} and \textit{para} forms. The new observations follow the same trend as found by \citet{2011ApJ...729...15C}, lying between the nascent and thermalized distribution. We come to the conclusion that H$_{3}^{+}$ is not fully thermalized as the thermalization by collisions with H$_{2}$ is competing with destruction of H$_{3}^{+}$ by dissociative recombination.} To study this, we conducted the first time-dependent modeling of the nuclear spin-states of H\dtwo~and H\dthree\jon~in the diffuse interstellar medium, and compared our results to the observed values, including the new measurements. We found that the DR of H$_3^+$ is a key process that governs the \pHtre~values. Our model indicates that a branching ratio of $\sim 1$ between the $(1,1)$- and $(1,0)$- H$_3^+$ dissociation is needed to achieve an agreement with the observations. {An increased CR ionization rate to 10$^{-15}$ s$^{-1}$ also has a significant effect on the $p_3$ values and brings the calculated values much closer to the observed values.} The remaining studied parameters, initial H$_2$ \textit{ortho}/\textit{para} ratio, $n_{H}$, chemical age and total DR rates will increase the pace at which the \pHtre~values approach the nascent distribution by a smaller, but significant amount. {However, increasing the CR ionization rate to $10^{-15}$ s$^{-1}$ causes difficulties with reproducing observed abundances of other molecules, whereas many molecules are underproduced by our models. This is the same problem that has been raised before in the discussion of H$_3^+$ in diffuse clouds, but here we can also show that the high CR ionization rate is an essential ingredient in order to achieve an agreement with the \textit{para}-fractions of H$_3^+$. } We conclude that the best fit to observations is achieved {for the ``2X+C15'' model with} a density of 10 cm$^{-3}$, CR ionization rate {10$^{-15}$ s$^{-1}$}, a 1:1 DR branching ratio, a time scale of {$10^6$} years and a total DR rate a factor of 2 larger than that derived by \citep{2004PhRvA..70e2716M}, or an equivalent reduction of thermalization rates \citep[see Figure 6 of][]{2011ApJ...729...15C}. With this model, we find that our predicted H$_{3}^{+}$\,/\,H$_{2}$ values match that derived from the observed column densities within an order of magnitude (where the largest impact is due to the adopted density and CR ionization rate). {These results warrant a more detailed study with a better treatment of the clumpy structure of diffuse clouds. Furthermore, better understanding of the CR ionization rate, and its possible variation within the diffuse cloud, and chemical ages need to be better constrained for future studies \citep[e.g.][]{2012A&A...537A...7R}.} It is {also} evident that the H$_3^+$ DR process is vital in order to better understand the \textit{ortho}$-$\textit{para} hydrogen chemistry in the diffuse ISM. For that, one has to bring in agreement the laboratory results on the DR of H$_3^+$ obtained with various experimental setups, such as the storage ring experiments \citep{kreckel05, tom09, kreckel10}, and the afterglow experiments \citep[e.g.][]{1995IJMSI.149..131G, 1998JPhB...31.2111L, 2002IJMSp.218..105P, glosik09}. Therefore, we highly recommend new accurate studies of the H$_{3}^{+}$ DR reactions, in order to both determine the absolute DR rate as well as the nuclear spin dependence for the lowest rotational states. | 14 | 3 | 1403.6533 |
1403 | 1403.3120_arXiv.txt | We present two new late-type brown dwarf candidate members of the TW~Hydrae association (TWA)~: 2MASS~J12074836-3900043 and 2MASS~J12474428-3816464, which were found as part of the BANYAN all-sky survey (BASS) for brown dwarf members to nearby young associations. We obtained near-infrared (NIR) spectroscopy for both objects (NIR spectral types are respectively L1 and M9), as well as optical spectroscopy for J1207-3900 (optical spectral type is L0$\gamma$), and show that both display clear signs of low-gravity, and thus youth. We use the BANYAN~II Bayesian inference tool to show that both objects are candidate members to TWA with a very low probability of being field contaminants, although the kinematics of J1247-3816 seem slightly at odds with that of other TWA members. J1207-3900 is currently the latest-type and the only isolated L-type candidate member of TWA. Measuring the distance and radial velocity of both objects is still required to claim them as bona fide members. Such late-type objects are predicted to have masses down to 11~\textendash~15~\Mjup at the age of TWA, which makes them compelling targets to study atmospheric properties in a regime similar to that of currently known imaged extrasolar planets. | The known population of brown dwarfs (BDs) has significantly increased in the last decades due to all-sky near-infrared (NIR) surveys such as 2MASS and \emph{WISE} (\citealp{2006AJ....131.1163S}, \citealp{2010AJ....140.1868W}). The acumulation of a large number of BDs allowed for a better understanding of the underlying physics in their atmospheres, which went along with the development of increasingly more realistic atmosphere models (\citealp{2003A&A...402..701B}, \citealp{2008ApJ...689.1327S}, \citealp{2012ApJ...756..172M}, \citealp{2013MSAIS..24..128A}) and empirical spectral classification schemes (\citealp{1991ApJS...77..417K}, \citealp{2005ApJ...623.1115C}, \citealp{2006ApJ...637.1067B}, \citealp{2009AJ....137.3345C}, \citealp{2013ApJ...772...79A}). These tools allowed in turn the identification of peculiar BDs, most of which are now recognized as having atypical metallicity or surface gravity. \\ Low surface gravity BDs are thought to be younger than several hundred million years since they have not yet reached their equilibrium radii \citep{2001RvMP...73..719B}. The youngest and latest-type of these objects are believed to have cool, low-pressure atmospheres similar to those of currently known imaged gaseous giant exoplanets, but only a few of those are known in the solar neighborhood (e.g. 2MASS~J03552337+1133437; \citealp{2013AJ....145....2F}; PSO J318.5338-22.8603; \citealp{2013ApJ...777L..20L}; CFBDSIR 2149-0403; \citealp{2012A&A...548A..26D}). Hence, atmosphere models for such physical conditions are still subject to poor empirical constraints (e.g. the behavior of dust in these low-pressure environments). While the luminosity, equivalent width of atomic lines, and shape of the continuum can be used to identify young brown dwarfs, there is no evidence yet that those can be used to narrowly constrain ages \citep{2013ApJ...772...79A}. Therefore, assembling an an age-calibrated sample identified by kinematics could potentially help addressing this in an empirical way. Given their relative proximity, nearby, young associations (NYAs) such as TW Hydrae (TWA; \citealp{2004ARA&A..42..685Z}) are perfect test benches for such empirical calibrations. The search for late-type objects in NYAs has been the subject of many efforts (\citealp{2004ARA&A..42..685Z}; \citealp{2007ApJ...669L..97L}; \citealp{2008hsf2.book..757T}; \citealp{2013ApJ...762...88M}), however their late-type ($>$ M5) population is poorly constrained. To address this further, \citeauthor{2014ApJ...783..121G} (\citeyear{2014ApJ...783..121G}; called G2014 hereafter) developed Bayesian Analysis for Nearby Young AssociatioNs II (BANYAN~II), a tool based on \cite{2013ApJ...762...88M} that uses naive Bayesian inference to identify late-type candidate members to such NYAs from their sky position, proper motion and photometry. Using this new tool, our team has initiated the BANYAN all-sky survey (BASS) that generated hundreds of $>$ M5 candidate members to NYAs from the 2MASS and \emph{WISE} surveys, using both catalogues as a baseline for a proper motion measurement. The current status of this project is described in more detail in \cite{2013arXiv1307.1127G}. \\ Here, we present two of the potential latest-type and lowest-mass objects that were identified as candidate members to TWA from this all-sky survey : 2MASS~J12474428-3816464 (M9; called J1247-3816 hereafter) and 2MASS~J12074836-3900043 (L1; called J1207-3900 hereafter), with NIR spectral types M9 and L1, respectively. We present NIR SpeX spectroscopy for the two objects, as well as optical MAGE spectroscopy for J1207-3900 in Section~\ref{sec:spt}. In Section~,\ref{sec:lowg}, we show evidence that both have a low surface gravity, and we use the BANYAN~II tool in Section~\ref{sec:bayes} to show that both objects are likely members of TWA with a small probability of being young field contaminants, but that J1247-3816 seems to display slightly discrepant kinematics. | \label{sec:Ldwarf} The two new candidates to TWA presented here were discovered as part of BASS, an all-sky survey for late-type low-mass stars (LMSs) and BDs in NYAs based on the 2MASS and \emph{WISE} catalogs. This survey has already identified other young objects such as 2MASS~J01033563-5515561 ABb (see \citealp{2013A&A...553L...5D}), and several hundreds of $>$ M5 candidates identified in the same way are currently being followed and results will be published in an upcoming paper (see \citealp{2013arXiv1307.1127G} for more information). | 14 | 3 | 1403.3120 |
1403 | 1403.6828_arXiv.txt | We investigate how different cosmological parameters, such as those delivered by the \textit{WMAP} and \textit{Planck} missions, affect the nature and evolution of dark matter halo substructure. We use a series of flat $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological $N$-body simulations of structure formation, each with a different power spectrum but the same initial white noise field. Our fiducial simulation is based on parameters from the \textit{WMAP} 7th year cosmology. We then systematically vary the spectral index, $n_s$, matter density, $\Omega_M$, and normalization of the power spectrum, $\sigma_8$, for 7 unique simulations. Across these, we study variations in the subhalo mass function, mass fraction, maximum circular velocity function, spatial distribution, concentration, formation times, accretion times, and peak mass. We eliminate dependence of subhalo properties on host halo mass and average over many hosts to reduce variance. While the ``same'' subhalos from identical initial overdensity peaks in higher $\sigma_8, n_s$, and $\Omega_m$ simulations accrete earlier and end up less massive and closer to the halo center at $z=0$, the process of continuous subhalo accretion and destruction leads to a steady state distribution of these properties across all subhalos in a given host. This steady state mechanism eliminates cosmological dependence on all properties listed above except subhalo concentration and $V_{max}$, which remain greater for higher $\sigma_8, n_s$ and $\Omega_m$ simulations, and subhalo formation time, which remains earlier. We also find that the numerical technique for computing scale radius and the halo finder used can significantly affect the concentration-mass relationship computed for a simulation. | 14 | 3 | 1403.6828 |
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1403 | 1403.4536_arXiv.txt | The measurement of a large tensor-to-scalar ratio by the BICEP2 experiment, $r = 0.20_{-0.05}^{+0.07}$, severely restricts the landscape of viable inflationary models and shifts attention once more towards models featuring large inflaton field values. In this context, chaotic inflation based on a fractional power-law potential that is dynamically generated by the dynamics of a strongly coupled supersymmetric gauge theory appears to be particularly attractive. We revisit this class of inflation models and find that, in the light of the BICEP2 measurement, models with a non-minimal gauge group behind the dynamical model seem to be disfavored, while the model with the simplest group, i.e.\ $SU(2)$, is consistent with all results. We also discuss how the dynamical model can be distinguished from the standard chaotic inflation model based on a quadratic inflaton potential. | Cosmic inflation\,\cite{Guth:1980zm} is an enormously successful paradigm of modern cosmology, which not only explains why the universe is almost homogeneous and spatially flat but which also accounts for the origin of the anisotropies in the Cosmic Microwave Background (CMB) radiation as well as for the origin of the Large Scale Structure of the Universe\,\cite{Mukhanov:1981xt,Lyth:1998xn}. Among the various models of inflation, chaotic inflation\,\cite{Linde:1983gd} is particularly attractive since it is free from the initial condition problem at the Planck time. Moreover, the large field values typically encountered in models of chaotic inflation predict a large contribution from gravitational waves to the CMB power spectrum\,\cite{Starobinsky:1985ww}, which can be tested by measuring the so-called B-mode of the CMB polarization spectrum. Interestingly, the BICEP2 collaboration recently announced the first measurement of just such a B-mode signal, corresponding to a tensor-to-scalar ratio of $r=0.20^{+0.07}_{-0.05}$ at $1\,\sigma$\,\cite{BICEP2}, which strongly suggests the presence of primordial B-mode polarization in the CMB.% \footnote{As pointed out in\,\cite{BICEP2}, the observed ratio, $r=0.20^{+0.07}_{-0.05}$, is in tension with the upper limit on this ratio, $r<0.11$ (at 95\%C.L.)\cite{Ade:2013zuv}, which is deduced from a combination of Planck, SPT and ACT data with polarization data from WMAP. In the following discussion, we shall keep this tension in mind when applying the BICEP2 result to our dynamical model of chaotic inflation.\smallskip} This recent progress motivates us to revisit \textit{dynamical chaotic inflation}, which was proposed in\,\cite{Harigaya:2012pg} and in which the inflaton potential is generated by the dynamics of a simple strongly coupled supersymmetric gauge theory. One prominent feature of this class of models is that it predicts a fractional power-law potential for the inflaton with the fractional power being $1$ or smaller.% \footnote{Such potentials can also be realized by introducing a running kinetic term for the inflaton\,\cite{Takahashi:2010ky}. In string theory, fractional power-law potentials have been derived in \cite{Silverstein:2008sg}. For dynamical chaotic inflation featuring fractional powers larger than 1, cf.\,\cite{Harigaya:2014zz}.} Chaotic inflation of this type can be distinguished from the simplest versions of chaotic inflation, i.e.\ models with a quadratic or quartic potential, by precise measurements of the inflationary CMB observables. Furthermore, dynamical chaotic inflation is also attractive since it entails that the energy scale of inflation is generated via dimensional transmutation due to the strong gauge dynamics. This provides an explanation for why inflation takes place at energies much below the Planck scale.% \footnote{For other examples of models in which the scale of inflation is generated dynamically, cf.\ Refs.\,\cite{Dimopoulos:1997fv}.\smallskip} The organization of the paper is as follows. First, we review chaotic inflation emerging from a strongly coupled supersymmetric gauge theory, which eventually leads us to an inflaton potential proportional to some fractional power of the inflaton field. Then, we discuss how the value of the tensor-to-scalar ratio observed by BICEP2 can be explained in this class of models. | 14 | 3 | 1403.4536 |
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1403 | 1403.1063_arXiv.txt | {We present an algorithm using Principal Component Analysis (PCA) to subtract galaxies from imaging data, and also two algorithms to find strong, galaxy-scale gravitational lenses in the resulting residual image. The combined method is optimized to find full or partial Einstein rings. Starting from a pre-selection of potential massive galaxies, we first perform a PCA to build a set of basis vectors. The galaxy images are reconstructed using the PCA basis and subtracted from the data. We then filter the residual image with two different methods. The first uses a curvelet (curved wavelets) filter of the residual images to enhance any curved/ring feature. The resulting image is transformed in polar coordinates, centered on the lens galaxy center. In these coordinates, a ring is turned into a line, allowing us to detect very faint rings by taking advantage of the integrated signal-to-noise in the ring (a line in polar coordinates). The second way of analysing the PCA-subtracted images identifies structures in the residual images and assesses whether they are lensed images according to their orientation, multiplicity and elongation. We apply the two methods to a sample of simulated Einstein rings, as they would be observed with the ESA Euclid satellite in the VIS band. The polar coordinates transform allows us to reach a completeness of 90\% and a purity of 86\%, as soon as the signal-to-noise integrated in the ring is higher than 30, and almost independent of the size of the Einstein ring. Finally, we show with real data that our PCA-based galaxy subtraction scheme performs better than traditional subtraction based on model fitting to the data. Our algorithm can be developed and improved further using machine learning and dictionary learning methods, which would extend the capabilities of the method to more complex and diverse galaxy shapes.} | With the many ongoing or planned sky surveys taking place in the optical and near-IR, gravitational lensing has become a major scientific tool to study the properties of massive structures at all spatial scales. On the largest scales, in the weak regime, gravitational lensing constitutes a crucial cosmological probe \citep[e.g.][]{Heymans2013, Frieman2008}. On smaller scales, weak galaxy-galaxy lensing allows us to study the extended halo of individual galaxies or of groups of galaxies \citep[e.g.][]{Simon2012} and to constrain cosmology \citep[e.g.][]{Mandelbaum2013, Parker2007}. In the strong regime, when multiple images of a lensed source are seen, gravitational lensing offers an accurate way to weigh galaxy clusters \citep[][for reviews]{Bartelmann2013, Hoekstra2013, Meneghetti2013, Kneib2011}, galaxy groups \citep[e.g.][]{Foex2013, Limousin2009} and individual galaxies \citep[e.g.][]{Brownstein2012, Treu2011, Bolton2006}. However, all strongly lensed systems known today, combined together, represent only hundreds of objects. Wide field surveys have the potential to produce samples three orders of magnitude larger, allowing us to study statistically dark matter and its evolution in galaxies as a function, e.g. of morphological type, mass, stellar and gas contents \citep[see][]{Gavazzi2012, Ruff2011, Sonnenfeld2013, SonnenfeldGavazzi2013}. For example, \citet{Pawase2012} predicts that a survey like Euclid will find at least 60000 galaxy-scale strong lenses. To find and to use them efficiently, it is vital to devise automated finders that can produce samples of lenses with high completeness and purity and with a well defined selection function. Note that the lenses of \citet{Pawase2012} are source selected. There is no volume-limited sample of lens-selected systems, so the number 60000 systems is given here only to give an order of magnitude of the number of objects that future wide-field surveys will have to deal with. \begin{figure*}[t!] \begin{center} {\includegraphics[width=4.0cm, height=4.0cm]{Figures/base0}} {\includegraphics[width=4.0cm, height=4.0cm]{Figures/base1}} {\includegraphics[width=4.0cm, height=4.0cm]{Figures/base2}} {\includegraphics[width=4.0cm, height=4.0cm]{Figures/base16}} \caption{Examples of PCA components obtained using 1000 simulated galaxies from the Bologna Lens Factory (see Sect.~\ref{Euclid}).\label{fig:PCA_coefs}} \end{center} \end{figure*} Several automated robots exist to find strong lenses. Among the best ones are {\tt Arcfinder} \citep{Seidel2007}, which was primarily developed to find large arcs behind clusters and groups, and the algorithm by \citet{Alard2006} used by \citet{Cabanac2007} and \citet{More2012}, to look for arcs produced by individual galaxies and groups in the CFHT Strong Lensing Legacy Survey. Other automated robots consider any galaxy as a potential lens and predict where lensed images of a background source should be before trying to identify them on the real data \citep{Marshall2009}. In order to detect lenses with small Einstein radii or with faint rings, most of these algorithms rely on foreground lens subtraction \citep[e.g.][]{Gavazzi2012}. So far, this subtraction has been performed through model fitting. An example of a ring detector is given in \citet{Sygnet2010} which selects objects with possible lensing configuration according to their lensing convergence, estimated from the Tully-Fisher relation. This algorithm relies on photometric information but requires a visual check of a large number of candidates. In the present paper, we propose a "lens finder" which uses single-band images to find full and partial Einstein rings based on purely morphological criteria. The algorithm uses as input a pre-selection of potential lens galaxies, hence producing so-called "lens-selected" samples. The present work sets the basis of an algorithm using machine learning techniques. Although focused on finding Einstein rings, it can be adapted to other types of lenses, such as those consisting of multiple, relatively pointlike, components. This paper is organised as follows. In Sections \ref{PCA} and \ref{Finder} we outline our algorithm and introduce the principles behind each step of the process. In section \ref{Euclid} we show the performance of our algorithm using a set of simulations designed to reproduce Euclid images in the optical. We discuss the completeness and purity of our algorithm as a function of signal-to-noise (SNR) and caustic radius of the lensing systems. Section \ref{Stripe82} shows results of our galaxy subtraction algorithm compared to those of {\tt galfit} software \citep[][]{Peng2011} on images from the CFHT optical imaging of SDSS stripe 82 and Section \ref{conclusion} summarizes our main results. | \label{conclusion} The two lens finder algorithms developed here all rely on a good subtraction of lensing galaxies with machine learning methods; different ideas for ring detection then allow objects with different properties to be detected on the residual images: \begin{itemize} \item The polar transform method enhances the signal in the residual image by applying curvelet denoising and uses a polar transform of the images to turn the problem of a circle detection to a line detection. It is designed to detect full or partial rings with or without ellipticity. \item The "Island finding algorithm" uses {\tt SExtractor} to detect structures in the PCA-subtracted images and to determine whether they correspond to lensed sources according to their elongation, orientation and bending. This algorithm is expected to be more efficient in finding partial arcs and multiple images. \end{itemize} The method is successfully applied to Euclid-like simulations. With the polar transform method, a completeness of 90\% is reached for data where the signal-to-noise in the Einstein ring is at least 30. The same simulations show that the purity of the derived ring sample reaches 86\% of the non lensed galaxies detected as false positives. The galaxy subtraction algorithm occurs to be efficient when applied to real data as well: our tests with CFHT images of SDSS Stripe 82 surpasses in quality the subtraction obtained with direct model fitting. In future work, ways to increase the purity of the algorithms will be investigated by using adapted dictionary learning \citep[e.g.][]{Beckouche2013} for galaxy subtraction. The strength of those machine learning methods should allow us to build bases adapted to more complicated problems, such as the subtraction of galaxies in clusters to detect rings produced by multiple galaxies. Better morphological selection based on PCA "clustering" or beamlet analysis \citep[e.g.][]{Donoho&Huo2002} can be used to discriminate ring-like shapes, to classify rings and arcs and to carry out galaxy classification in general, as has been done in the past with quasar spectra \citep{Boroson2010} and, more recently, with galaxy multi-band photometry \citep{Wild2014}. | 14 | 3 | 1403.1063 |
1403 | 1403.5640_arXiv.txt | We present high-spatial resolution spectropolarimetric observations of a quiescent hedgerow prominence taken in the \ion{He}{1}~1083.0~nm triplet. The observation consisted of a time series in sit-and-stare mode of $\sim$~36 minutes of duration. The spectrograph's slit crossed the prominence body and we recorded the time evolution of individual vertical threads. Eventually, we observed the development of a dark Rayleigh-Taylor plume that propagated upward with a velocity, projected onto the plane of the sky, of 17\kms. Interestingly, the plume apex collided with the prominence threads pushing them aside. We inferred Doppler shifts, Doppler widths, and magnetic field strength variations by interpreting the \ion{He}{1} Stokes profiles with the HAZEL code. The Doppler shifts show that clusters of threads move coherently while individual threads have oscillatory patterns. Regarding the plume we found strong red-shifts ($\sim$9-12\kms) and large Doppler widths ($\sim$10\kms) at the plume apex when it passed through the prominence body and before it disintegrated. We associate the red-shifts with perspective effects while the Doppler widths are more likely due to an increase in the local temperature. No local variations of the magnetic field strength associated with the passage of the plume were found; this leads us to conclude that the plumes are no more magnetized than the surroundings. Finally, we found that some of the threads oscillations are locally damped, what allowed us to apply prominence seismology techniques to infer additional prominence physical parameters. | \label{sec1} Quiescent hedgerow prominences are seen as sheet-like plasma structures standing vertically above the solar surface. They are characterized by the presence of thin, vertically oriented and highly dynamic columns of plasma (hereafter threads) supported against gravity \citep[e.g.,][]{2008ApJ...676L..89B,2008ApJ...689L..73C}. They also show plumes that eventually rise from below the prominence and propagate upward with speeds of $\sim$~15\kms\/ \citep{2010ApJ...716.1288B}. These plumes have been recently associated with the magnetic Rayleigh-Taylor (R-T) instability that explains how hot plasma and magnetic flux can be transported upwards through the prominence (e.g., \citealt{2005Natur.434..478I,2012ApJ...746..120H}). If the highly dynamic plasma is coupled with the magnetic field, the latter might show local variations, at scales comparable to or smaller than the typical sizes of the prominence threads. However, there are no direct observational constraints on magnetic properties of the fine-scale structures seen in hedgerow prominences or on the effects produced by upward plumes. So far, we only have moderate resolution information about the global magnetic structuring and about line-of-sight velocities (LOS) and velocities perpendicular to the LOS thought time-slice techniques using high-spatial resolution filtergrams. (e.g., \citealt{1983SoPh...89....3A,1994SoPh..154..231B,2003ApJ...598L..67C,1983SoPh...83..135L,2005SoPh..226..239L,2009ApJ...704..870L,1976ApJ...210L.111L,1983A&A...119..197M,1981SoPh...69..301M,2006ApJ...642..554M,2012ApJ...761L..25O,2013hsa7.conf..786O,1988A&A...197..281S,2010A&A...514A..68S,2013arXiv1309.1568S,1979SoPh...61...39V,1998Natur.396..440Z}). Here, we report high-resolution full spectropolarimetric measurements taken in the \ion{He}{1}~1083.0~nm triplet, that recorded the temporal evolution of quiescent prominence threads and the passing of a plume generated by a R-T instability through the spectrograph slit. \begin{figure}[!t] \begin{center} \resizebox{\hsize}{!}{\includegraphics{fig1.eps}} \caption{Observed quiescent solar prominence as seen with the H$_\alpha$ slit-jaw camera. The box outlines the area shown in figure 2 that contains a prominence plume. The dotted line represents the TIP-II spectrograph slit, which forms an angle of $\sim$45\degree\/ with the solar limb direction. The observing time (in UT) is shown at the bottom-left.} \label{fig1} \end{center} \end{figure} | \label{sec5} We have presented full spectropolarimetric observations in the \ion{He}{1}~1083.0~nm triplet that recorded the evolution of quiescent hedgerow prominence threads and the passage of a prominence plume along the slit and evidence of standing damped oscillations in some of the threads. According to the H$_\alpha$ slit-jaw images, the plume develops at the prominence-cavity interface (probably via the R-T instability) and rises through the prominence body at about 17~\kms, displacing the thread material horizontally. The rise of the plume coincides with the disappearance of the underlying cavity. Eventually, the plume disintegrates distorting the thread pattern. The \ion{He}{1}~1083.0~nm peak intensity shows that the plume apex pushes the threads aside. Doppler shift measurements indicate that the plasma with which the plume first collides is strongly redshifted ($\sim$9-12~\kms). Strong redshifts ($<$10~\kms) are also detected below the plume during and after the pass of the plume. If we assume that the plume rises vertically and along the prominence sheet and that the strong red-shifts at the plume apex correspond to plasma that is being pushed upwards (in other words, we consider that the velocity component perpendicular to the plane of the sky is negligible) then, the prominence threads and plume should be slightly inclined about 30\degr\/ from the vertical and away to the observer LOS in order to detect red-shifts of about 9-12\kms. In this scenario, and since the observed velocity component in the plane of the sky is about 17~\kms, the plasma at the apex of the plume would be experimenting an upward velocity of $\sim$~20\kms, which may exceed typical sound speeds in prominences. Other possibility is that the strong red-shifts are associated with a horizontal (along the LOS) net plasma displacement. The inferred flows would be then associated with thread material falling along the boundaries of the plume. In this scenario, the plane containing the prominence threads and plume should also be slightly inclined with respect to the LOS to detect a net flow. The Doppler width of the line increases slightly before the plume crosses the slit. It is maximal within the plume and persists after the plume has disappeared. The larger Doppler widths within the plume may be due to local temperature enhancements resulting from the injection of cavity's hot plasma into the prominence body. On the other hand, the strong redshifts and the larger Doppler widths after the passage of the plume could be, in addition, associated with local turbulence generated by the disintegration of plume. Regarding the field strength, it shows a gradient from left (limb side) to right (corona). The presence of the plume does not modify the inferred field strengths. Since it is believed that the prominence material is in frozen in conditions, we would expect an increase of magnetic flux at the boundary between the prominence and the plume apex resulting from the squeezing of the field lines in that area. However, we do not detect any sign of flux intensification. Thus, we believe that the plume neither interacts with the magnetic structure of the prominence nor it is more magnetized that the surroundings, which is in line with recent simulation results \citep{khomenko}. Finally, we found that clusters of threads move together in phase while individual threads show their own (of less amplitude) oscillatory patterns. The presence of oscillations in individual threads have already been detected in solar filaments using the \ion{He}{1}~1083.0~nm multiplet (e.g., \citealt{1991SoPh..132...63Y}). Some of the oscillations are clearly damped and can be associated with transverse kink modes. This allowed us to apply seismology techniques and infer the product $(\rho_\mathrm{p}Lw)$ using the averaged field strength derived from the interpretation of the Stokes profiles with the HAZEL code. Unfortunately, we did not detect other clear decaying oscillations as to compare the results from other threads and determine the length of the field lines, although it is well established that threads tend to oscillate independently and their standing modes are only excited for certain type of perturbations, or oscillate in a plane where little $\mathrm{V}_\mathrm{LOS}$ modulation is produced (\citealt{2002ApJ...580..550D, 2007A&A...469.1135T, 2008ApJ...676..717L}). | 14 | 3 | 1403.5640 |
1403 | 1403.0854_arXiv.txt | {}{The Galileon model is a modified gravity model that can explain the late-time accelerated expansion of the Universe. In a previous work, we derived experimental constraints on the Galileon model with no explicit coupling to matter and showed that this model agrees with the most recent cosmological data. In the context of braneworld constructions or massive gravity, the Galileon model exhibits a disformal coupling to matter, which we study in this paper.}{After comparing our constraints on the uncoupled model with recent studies, we extend the analysis framework to the disformally coupled Galileon model and derive the first experimental constraints on that coupling, using precise measurements of cosmological distances and the growth rate of cosmic structures.}{In the uncoupled case, with updated data, we still observe a low tension between the constraints set by growth data and those from distances. In the disformally coupled Galileon model, we obtain better agreement with data and favour a non-zero disformal coupling to matter at the $2.5\sigma$ level. This gives an interesting hint of the possible braneworld origin of Galileon theory.}{} | Dark energy remains one of the deepest mysteries of cosmology today. Even though it has been fifteen years since the discovery of dark energy \citep{bib:riess,bib:perlmutter}, its fundamental nature remains unknown. Adding a cosmological constant ($\Lambda$) to Einstein's general relativity is the simplest way to account for this observation, and leads to remarkable agreement with all cosmological data so far (see e.g. \cite{bib:planck}). However, the cosmological constant requires considerable fine-tuning to explain current observations and motivates the quest for alternative explanations of the nature of dark energy. Modified gravity models aim to provide such an explanation. The Galileon theory, first proposed by \cite{bib:nicolis} involves a scalar field, hereafter called $\pi$, whose equation of motion must be of second order and invariant under a Galilean shift symmetry $\partial_\mu \pi \rightarrow \partial_\mu \pi + b_\mu$, where $b_\mu$ is a constant vector. This symmetry was first identified as an interesting property in the DGP model \citep{bib:dgp}. \cite{bib:nicolis} derived the five possible Lagrangian terms for the field $\pi$, which were then formulated in a covariant formalism by \cite{bib:deffayet} and \cite{bib:deffayetb}. This model forms a subclass of general tensor-scalar theories involving only up to second-order derivatives originally found by Horndeski \citep{bib:horndeski}. Later, Galileon theory was also found to be the non-relativistic limit of numerous broader theories, such as massive gravity \citep{bib:deRhamMasGra} or brane constructions \citep{bib:deRhamDBI,bib:hinterbichler,bib:acoleyen}. Braneworld approaches give a deeper theoretical basis to Galileon theories. The usual and simple construction involves a 3+1 dimensional brane, our Universe, embedded in a higher dimensional bulk. The Galileon field $\pi$ can be interpreted as the brane transverse position in the bulk, and the Galilean symmetry appears naturally as a remnant of the broken space-time symmetries of the bulk \citep{bib:hinterbichler}. The Galilean symmetry is then no longer imposed as a principle of construction, but is a consequence of space-time geometry. Models that modify general relativity have to alter gravity only at cosmological scales in order to agree with the solar system tests of gravity (see e.g. \cite{bib:will}). % The Galileon field can be coupled to matter either explicitly or through a coupling induced by its temporal variation \citep{bib:babichev13}. This leads to a so-called fifth force that by definition modifies gravity around massive objects like the Sun. But the non-linear Lagrangians of the Galileon theory ensure that this fifth force is screened near massive objects in case of an explicit coupling of the form $c_0 \pi T^\mu_{\ \mu}/M_P$ (where $T^\mu_{\ \mu}$ is the trace of the matter energy-momentum tensor, $c_0$ a dimensionless parameter, and $M_P$ the Planck mass) or in the case of an induced coupling. This is called the Vainshtein effect (\cite{bib:vainshtein} and \cite{bib:babichev13b} for a modern introduction). The fifth force is thus negligible with respect to general relativity within a certain radius from a massive object, that depends on the object mass and Galileon parameters \citep{bib:vainshtein,bib:nicolis,bib:brax11}. Braneworld constructions and massive gravity models give rise to an explicit disformal coupling to matter of the form $\sim \partial_\mu \pi \partial_\nu \pi T^{\mu\nu}$. As shown, for example, in \cite{bib:brax12b}, this coupling does not induce a fifth force on massive objects since it does not apply to non-relativistic objects when the scalar field is static. In a cosmological context, the scalar field $\pi$ evolves with time but the fifth force introduced by the disformal coupling to matter can be masked thanks to a new screening mechanism \citep{bib:koivisto,bib:zumalacarregui}. However, the disformal coupling still plays a role in the field cosmological evolution, which makes this kind of Galileon model interesting to compare with cosmological data. The action of the model is \begin{equation}\label{eq:action} S=\int d^4x \sqrt{-g}\left( \frac{M_P^2R}{2} - \frac{1}{2} \sum_{i=1}^{5} c_i L_i - L_m - L_G\right), \end{equation} with $L_m$ the matter Lagrangian, $R$ the Ricci scalar, and $g$ the determinant of the metric. The $c_i$s are the Galileon model dimensionless parameters weighting different covariant Galileon Lagrangians $L_i$ \citep{bib:deffayet}: \begin{align} L_1 = & M^3\pi,\quad L_2=\pi_{;\mu}\pi^{;\mu},\quad L_3=(\pi_{;\mu}\pi^{;\mu})(\square \pi)/M^3, \notag \\ L_4 = & (\pi_{;\mu}\pi^{;\mu})\left[ 2(\square \pi)^2 - 2 \pi_{;\mu\nu}\pi^{;\mu\nu} - R(\pi_{;\mu}\pi^{;\mu})/2 \right]/M^6, \notag \\ L_5 = & (\pi_{;\mu}\pi^{;\mu}) \left[ (\square \pi)^3 - 3(\square \pi) \pi_{;\mu\nu}\pi^{;\mu\nu} +2\pi_{;\mu}\ ^{;\nu}\pi_{;\nu}^{\ ;\rho}\pi_{;\rho}^{\ ;\mu} \right. \notag \\ & \left. -6 \pi_{;\mu}\pi^{;\mu\nu}\pi^{;\rho}G_{\nu\rho}\right]/M^9, \end{align} where $M$ is a mass parameter defined as $M^3=H_0^2M_P$ with $H_0$ the Hubble parameter current value. $L_G$ is the disformal coupling to matter: \begin{equation} L_G=\frac{c_G}{M_P M^3}\partial_\mu \pi \partial_\nu \pi T^{\mu\nu}, \end{equation} where $c_G$ is dimensionless. Interestingly, \cite{bib:babichev} showed that $c_0\lesssim 10^{-2}$ by comparing local time variation measurements of the Newton constant $G_N$ in the Lunar Laser Ranging experiments, to predictions derived in the Galileon theory with the Vainshtein mechanism accounted for and boundary conditions set by the cosmological evolution. % In the more general context of scalar field theories, the disformal coupling has been recently constrained in particle physics using Large Hadron Collider data \citep{bib:brax14,bib:monophoton}. Thus the disformal coupling should be the first explicit Galileon coupling to look at considering the actual existing constraints. The uncoupled Galileon model ($c_G=0$) has already been constrained by observational cosmological data in \citet{bib:appleby2}, \citet{bib:okada}, \citet{bib:nesseris}, and more recently in \cite{bib:neveu} (hereafter \citetalias{bib:neveu}) and \cite{bib:barreira13} (hereafter \citetalias{bib:barreira13}). In \citetalias{bib:neveu}, we introduced a new parametrisation of the model and developed a likelihood analysis method to constrain the Galileon parameters independently of initial conditions on the $\pi$ field. The unknown initial condition for the Galileon field was absorbed into the original $c_i$ parameters to form new parameters $\bar c_i$ defined by $\bar c_i = c_i x_0^i$, where $x_0$ encodes the initial condition for the Galileon field. The same methodology was adopted here, and we refer the interested reader to \citetalias{bib:neveu} for more details. Same datasets were used % for baryonic acoustic oscillations (BAO) \citep{bib:beutler,bib:padmanabhan,bib:sanchez}, and for growth of structure joint measurements\footnote{In order to ensure that the measurements do not depend of a fiducial cosmology.} of $f\sigma_8(z)$ and the Alcock-Paczynski parameter $F(z)$, mainly from \cite{bib:percival04,bib:blake11b,bib:beutler12, bib:samushia12a,bib:reid}. For the cosmic microwave background (CMB), we updated our analysis to use the WMAP9 distance priors \citep{bib:wmap9} instead of the WMAP7 ones \citep{bib:komatsu11}. Concerning type Ia supernovae (SNe Ia), we also updated our sample from the high-quality data of the SuperNova Legacy Survey (SNLS) collaboration \citep{bib:guy2010,bib:conley,bib:sullivan} to the recent sample published jointly by the SNLS and Sloan Digital Sky Survey (SDSS) collaborations \citep{bib:jla}, which we will refer to as the Joint Light-curve Analysis (JLA) sample in the following. Interesting constraints on the uncoupled Galileon model using the full CMB power spectrum were published in \citetalias{bib:barreira13}, with a different methodology. In the following, we show that the results from both studies agree. However, in our study we used growth data, despite our using a linearised version of the theory, while \citetalias{bib:barreira13} preferred not to use those data until the Galileon non-linearities responsible for the Vainshtein effect are precisely studied. We include a discussion on that important point in this paper.% Section~\ref{sec:data} describes our updated datasets. Section~\ref{sec:uncoupled} provides an update of the constraints on the uncoupled Galileon model, using WMAP9 and JLA data, and a comparison with \citetalias{bib:barreira13} results. Section~\ref{sec:coupled} gives constraints on the disformally coupled Galileon model derived from the same dataset. Section~\ref{sec:disc} discusses these results and their implications, as well as the state of the art of growth rate of structure modelling in Galileon theory. We conclude in Section~\ref{sec:concl}. | \label{sec:concl} We have compared the uncoupled and disformally coupled Galileon models to the most recent cosmological data, using the methodology from our previous work \citepalias{bib:neveu}. An update of the uncoupled Galileon model experimental constraints using WMAP9 $\left\lbrace l_a,R,z_* \right\rbrace$ constraints was derived jointly with the new JLA SN~Ia sample, BAO measurements, and growth data with the Alcock-Paczynski effect taken into account. The $\sigma_8(z=0)$ value used to compute the growth of structure observable was also updated to the \cite{bib:planck} value. The JLA sample allowed us to derive better constraints on the $\bar c_i$ parameters. When we kept the SNLS3 sample, our constraints did not change significantly, but led to an interesting comparison with the Galileon best-fit values published in \citetalias{bib:barreira13}. They used the full WMAP9 power spectrum to derive their constraints, and thus brought tighter constraints, but both best-fit scenarios agree. This validates both methodologies despite their differences. As expected, WMAP9 distance priors are less constraining than the full CMB spectrum but provide a simpler and faster way to derive constraints on the Galileon model. We provided the first experimental constraints on the disformal coupling parameter in the framework of the Galileon model. This coupling between matter and the Galileon field is natural when building the theory from massive gravity or extra-dimension considerations. Our final $\chi^2$'s are comparable to the one obtained for the $\Lambda$CDM model. Galileon theories are thus competitive to explain the nature of dark energy. We also showed that a null disformal coupling to matter is excluded at the $2.5\sigma$ level when using growth data, and at the 1.4$\sigma$ level when using distances only. % This gives some interesting clues, from experimental data, on the possible extra-dimension origin of Galileon theories. Better constraints would be possible including the ISW effect as shown in \citetalias{bib:barreira13}. The galaxy velocity field could also be a decisive probe to test modified gravity theories, as advocated in \citep{bib:zu,bib:hellwing}. However, this probe would require to have a correct modelling of the Galileon model non-linearities. % Interestingly, the disformal coupling couples to light and thus can have an impact on gravitational lensing \citep{bib:wyman}. Lensing experiments such as LSST \citep{bib:lsst} % or the future satellite Euclid \citep{bib:euclid}, or laboratory tests with light shining through a wall experiments \citep{bib:brax12b} can provide more data to constrain this interesting coupling. CMB spectral distortion studies \citep{bib:brax13} will also give further insight into the braneworld origin of the Galileon theory. | 14 | 3 | 1403.0854 |
1403 | 1403.2302.txt | {We test the evolutionary model of cool close binaries developed by one of us (KS) on the observed properties of near contact binaries (NCBs). These are binaries with one component filling the inner critical Roche lobe and the other almost filling it. Those with a more massive component filling the Roche lobe are SD1 binaries whereas in SD2 binaries the Roche lobe filling component is less massive. Our evolutionary model assumes that, following the Roche lobe overflow by the more massive component (donor), mass transfer occurs until mass ratio reversal. A binary in an initial phase of mass transfer, before mass equalization, is identified with SD1 binary. We show that the transferred mass forms an equatorial bulge around the less massive component (accretor). Its presence slows down the mass transfer rate to the value determined by the thermal time scale of the accretor, once the bulge sticks out above the Roche lobe. It means, that in a binary with a (typical) mass ratio of 0.5 the SD1 phase lasts at least 10 times longer than resulting from the standard evolutionary computations neglecting this effect. This is why we observe so many SD1 binaries. Our explanation is in contradiction to predictions identifying the SD1 phase with a broken contact phase of the Thermal Relaxation Oscillations model. The continued mass transfer, past mass equalization, results in mass ratio reversed. SD2 binaries are identified with this phase. Our model predicts that the time scales of SD1 and SD2 phases are comparable to one another. Analysis of the observations of 22 SD1 binaries, 27 SD2 binaries and 110 contact binaries (CBs) shows that relative number of both types of NCBs favors similar time scales of both phases of mass transfer. Total masses, orbital angular momenta and orbital periods of SD1 and SD2 binaries are indistinguishable from each other whereas they differ substantially from the corresponding parameters of CBs. We conclude that the results of the analysis fully support the model presented in this paper.} {Stars: activity -- binaries: close -- Stars: evolution -- Stars: late-type -- Stars: rotation} | Near contact binaries (NCBs) are a class of cool close binaries showing eclipses, with one component filling the inner critical equipotential surface (Roche lobe) and the other almost filling it. The name was suggested by Shaw (1990) who dis-\break \newpage\noindent tinguished two types of NCBs: those with the more massive component filling the Roche lobe were named V1010 Oph type and binaries with the less massive component filling the Roche lobe were named FO Vir type. As Shaw states, the massive components look in both types as normal, or ``a bit evolved'' Main Sequence (MS) stars, whereas low mass components are oversized for their masses: $\approx1.2$ times in V1010~Oph type and 2--3 times in FO~Vir type binaries. NCBs of V1010~Oph type show shortening of the orbital period and O'Connell effect in their light curves, interpreted as resulting from a hot spot situated on the trailing side of the less massive component. NCBs of FO~Vir type never show O'Connell effect and period lengthening prevails in them. Yakut and Eggleton (2005) suggested the name SD1 and SD2 for NCBs of V1010 Oph and FO~Vir type, respectively. We will use their designations in the following. The ranges of component masses and orbital periods of NCBs overlap with the ranges of cool contact binaries (CB), which implies a relationship between these two kinds of binaries. The shapes of light curve differ, however, substantially: while equal, or almost equal depth minima are observed for CBs, the minima of NCBs are distinctly different. SD1 binaries have sometimes been identified with the broken contact phase of the Thermal Relaxation Oscillation (TRO) model of CBs described in detail below. The presence of such a phase is an important constituent of this model. Because, however, SD2 binaries do not fit to the TRO model, several authors suggested that they may represent another route to CB formation, resulting from mass transfer between the components with mass ratio reversed (as in case of Algols). The evolutionary model of CBs suggested by one of us (KS) assumes that all cool CBs are formed this way and their components are in thermal equilibrium with no need for TROs. The main purpose of the present investigation is to show that the observed properties of NCBs cannot be reconciled with the TRO model but they fit well into our model. Before we place NCBs into the evolutionary sequence leading to CB formation, we describe first the historical development of our understanding of origin, evolution and observational properties of cool CBs. Eclipsing binaries of W~UMa-type were discovered more than a century ago (M{\"u}ller and Kempf 1903). The analysis of the light and velocity curves carried out then showed that the binaries were very unusual, with the components in contact and the uniform surface brightness. According to the present definition, a cool CB, or W~UMa-type binary consists of two lower MS stars surrounded by a common envelope lying between the inner and outer Lagrangian zero velocity equipotential surfaces (called also the Roche lobes) and possessing almost identical mean surface brightnesses (Mochnacki 1981). The more massive, primary component is a MS star, lying often close to Zero Age MS (ZAMS), and the secondary component is oversized, compared to its expected ZAMS size. The accepted upper limit is 1~d for the orbital period and 2.5--3~\MS\ for the total mass of a cool CB although some authors prefer somewhat higher values. The observed lower limits for the orbital period and total mass are about 0.2~d and 1.1~\MS, respectively. Based on early observations, several papers explaining the observed properties of CBs were published in 50-ties and 60-ties of the past century but no satisfactory model was obtained. Since then, an enormous amount of new data have been collected on these stars, yet their structure and evolutionary status still remain obscured. Following the original suggestion by Jeans (1928) it was believed for a long time that CBs are formed by fission of the protostellar core. An apparently satisfactory agreement of the observed basic parameters of W~UMa type stars with predictions resulting from the fission mechanism was obtained by Roxburgh (1966). This strengthened the conviction that CBs are born as contact systems with a uniform chemical composition. Yet, a fundamental difficulty in explaining their structure remained. As Kuiper (1941) demonstrated, the ratio of the thermal equilibrium radii for two ZAMS stars is approximately directly proportional to the mass ratio whereas the geometry of the inner critical Roche lobes requires that it scales as, approximately, a square root of mass ratio. These two conditions can be fulfilled only when both components have identical masses. Two different zero age stars in thermal equilibrium do not fit into their Roche lobes. This is still true for the (coeval) binary components burning hydrogen in their cores as long as their masses are close to their initial values. The fact that we do observe contact binaries with different component masses, is known as the Kuiper paradox. Let us note in this place, however, that the Kuiper paradox does not apply to evolved binaries past mass exchange with mass ratio reversal (\eg Algols) because each component obeys a different mass-radius relation, depending on its evolutionary status. We will discuss this problem later. A very convincing attempt to solve the Kuiper paradox was undertaken by Lucy (1968). To explain the existence of two unevolved stars in contact, he noted that the mass-radius relation for stars with proton-proton (pp) nuclear cycle has a different slope, compared to the same relation for stars with CNO cycle. As a result, the Kuiper paradox can be solved by assuming that the pp cycle dominates in one component and the CNO cycle dominates in the other one, and that convection zones of both stars share the same adiabatic constant. This situation requires a very efficient energy transport from primary to secondary component through the common part of the convective envelopes. However, detailed calculations showed that realistic models can only be produced within a narrow range of component masses, contrary to what was observed. A model giving more flexibility in selection of the component masses was suggested several years later also by Lucy (1976). He still came out from the two fundamental assumptions: first, that CBs are formed at ZAMS and second, that the specific entropy is identical in the convection zones of both components. To explain the Kuiper paradox for a broad range of component masses he abandoned the assumption of thermal equilibrium for each component separately. A similar model was concurrently developed by Flannery (1976). The model is known as TRO model. Both components are supposed to oscillate about the equilibrium state, with the whole binary remaining in the global thermal equilibrium. The energy is transported from primary to secondary {\it via} a turbulent convection which results in equal entropies of both convective envelopes, hence equal surface brightnesses. Lucy did not consider details of the energy transfer; he simply assumed that on reaching contact between the components, entropies of both convection zones equalize instantaneously. Later, TRO model was also applied to initially detached binaries in which a primary reaches its Roche lobe after some time spent on MS (\eg Webbink 1976, 1977ab, Sarna and Fedorova 1989, Yakut and Eggleton 2005). Detailed modeling of such binaries shows that, following the Roche lobe overflow (RLOF), the primary transfers about 0.1~\MS\ to the secondary which expands and fills its Roche lobe, forming a CB. Then, the TRO paradigm applies with a direction of secular mass transfer reversed, \ie from the secondary to primary, until both components merge. TRO model explains two basic observational facts about W~UMa-type stars: the geometry of the binary where the primary component is an ordinary MS star and the secondary is also a MS star but swollen to the size of its Roche lobe by energy transfer, and equal apparent effective temperatures of both components resulting in a characteristic light curve with two equal minima. It also gives an additional observational prediction, that a binary oscillates between two states: contact -- when both stars fill their respective Roche lobes and mass flows from the secondary to the primary, and semidetached -- when the primary still fills its Roche lobe but the secondary detaches from its lobe and mass flows from the primary to the secondary (Lucy 1976). Time scales of both states should be comparable to one another. Additional effects, like stellar evolution and/or angular momentum loss (AML) can influence the ratio of both time scales reducing the duration of the semidetached state (Robertson and Eggleton 1977, Rahunen 1983, Yakut and Eggleton 2005, Li, Han and Zhang 2005). In the most extreme case a binary can remain in contact all the time if AML rate is high enough but then its lifetime as a CB must be as short as $\approx10^8$~y as noted by Webbink (2003). Such binaries would be rare in space, contrary to observations. As more and more theoretical and observational data on CBs are accumulated, the TRO model encounters increasing difficulties. In particular, its both basic assumptions, \ie zero age of CBs and identical specific entropy in the convection zones of both components, are questionable and its basic prediction of the broken contact phase seems to be at odds with observations. Fission of a contracting protostellar core has been abandoned many years ago and it is no longer considered a feasible mechanism for binary formation. Numerical simulations of the bar-like instability developing in a rapidly rotating liquid body showed that it never results in a fission if the liquid is compressible (which a star is). Instead, a spiral arm structure develops resulting in a disk, or ring containing the excess of angular momentum (AM) and a stable core (Bonnell 2001). At present, the early fragmentation of a protostellar cloud resulting in two protostellar cores orbiting each other is considered to be a dominating mechanism for binary formation (Machida \etal 2008 and references herein). In effect, the orbit size of a freshly formed binary must be large enough to accommodate both pre-MS components. In particular, the low period limit for the isolated progenitors of W UMa-type binaries with total masses between 1.5~\MS\ and 3~\MS\ is about 1.5--2.0~d. Recently, a mechanism for tightening of the originally wide, eccentric orbit by an interaction with a properly placed, distant third companion has been suggested. The interaction enforces the, so called, Kozai cycles which, together with the tidal friction (KCTF), make the period of the inner binary shorten. Detailed calculations showed that the inner period can be shortened down to a value of about 2--3~d only (Eggleton and Kiseleva-Eggleton 2006, Fabrycky and Tremaine 2007). The orbit is circularized at this value and the mechanism does not work any more. So, excluding very exceptional cases, we do not expect the KCTF mechanism to produce binaries with periods shorter than this limit. The typical time scale of the period shortening of a binary with the initial period of 10--20~d is of the order of $10^6{-}10^7$~y. We should then observe an excess of young binaries with periods of 2--3~d compared to the ``canonical'' Duquenoy and Mayor (1991) distribution. This is indeed observed among binaries in Hyades (Griffin 1985, Stêpieñ 1995). Tokovinin \etal (2006) demonstrated, on the other hand, that almost all field binaries with periods shorter than~3 d are in fact triple systems, compared to only about one third of long period binaries possessing a tertiary companion. This suggests that the KCTF mechanism works indeed efficiently, producing large numbers of short period binaries compared to those formed as isolated systems. The observations of pre-MS and young binaries are in a full agreement with the above expectations. HD155555 with $P=1.7$~d has the shortest known period among pre-MS binaries (although some authors suggest that it may already be on MS). All other binaries of T~Tau type and members of young clusters with masses corresponding to CBs have periods longer than 2~d. We conclude that theoretical, as well as observational data show that detached binaries with initial periods of the order of 2--3~d are dominant progenitors of CBs. Substantially shorter periods of a fraction of a day may be encountered among young binaries only exceptionally, \eg as a result of a hard collision with another object in a dense stellar environment but they should be very rare (Bradstreet and Guinan 1994). Note that this conclusion restricts an acceptable range for initial orbital periods when modeling CBs. It is incorrect to adopt initial orbital periods shorter than, say, 1.5~d when considering a model of a typical contact binary, as some authors do (\eg Webbink 1976, 1977ab, Sarna and Fedorova 1989, and more recently Jiang \etal 2012). Binaries with components possessing subphotospheric convection zones show hot coronae and magnetized winds carrying away mass and AM. This is a mechanism of magnetic braking (MB). The time scale for AML of a binary with a period of 2~d is approximately of the same order as the MS life time of the primary component (Stêpieñ 2011a). We should expect then that a primary is close to, or even beyond terminal age MS (TAMS) when it fills the Roche lobe. It can fill the Roche lobe at the earlier stages of MS life only if its mass is lower than about 1.1~\MS\ and the initial period is shorter than 2~days (Stêpieñ and Gazeas 2012). In other words, RLOF occurs when a typical progenitor of CB is rather old, with an age comparable to the MS life time of its primary which under the circumstances has substantially, or even completely depleted hydrogen in the core. Such stars lie close to TAMS on the Hertzsprung-Russell diagram. As primaries retain their status within the framework of the TRO model until coalescence, we should not observe primaries of W~UMa type stars close to ZAMS. If, however, CBs are past mass transfer with the mass ratio reversed, the present primary consists of a little evolved former secondary and matter coming from the outer layers of a former primary. These stars should lie close to ZAMS. The accurate data for a number of W~UMa type stars show that most of their primaries lie at, or close to ZAMS (Yakut and Eggleton 2005, Stêpieñ 2006a, Siwak \etal 2010). Only the most massive primaries with masses higher than 1.5~\MS, for which the evolutionary time scale shortens substantially as a result of increasing mass transferred slowly from secondaries, lie farther from ZAMS. Observations of W~UMa-type stars in stellar clusters confirm their advanced age. They are absent in young and intermediate-age clusters while they appear abundantly in clusters with age exceeding 4--4.5~Gyr (Rucinski 1998, 2000). Kinematical analysis of field W UMa-type stars also shows that the binaries have an average age of several Gyr (Guinan and Bradstreet 1988, Bilir \etal 2005). The second basic assumption of the TRO model deals with the energy transfer between the components. Lucy (1968, 1976) did not consider the mechanism for it. Instead, he assumed that the transport is very efficient so that entropies of both convection zones equalize immediately after a contact between the components is established. Detailed mechanisms of the energy transfer have been discussed by several authors. Applying different simplifying assumptions, some of them argued for turbulent, small-scale transport (\eg Moses 1976), while others considered large-scale circulations (Hazlehurst and Meyer-Hofmeister 1973, Webbink 1977c, Robertson 1980). However, no satisfactory result was obtained. As Yakut and Eggleton (2005) summarized: ``... there is still remarkably little understanding of how the heat transport manages to be as efficient as it must be''. The problem of the energy transfer can be solved if the assumption of the equal entropy in both convection zones is dropped (see below). In addition, the prediction of the TRO model that each CB should spend part of its life as a semi-detached system finds no observational support. Rucinski (1998) noted that CBs with distinctly different depths of minima (suggesting poor thermal contact) are quite rare. A recent photometric sky survey ASAS (Pojmañski 2002) detected several thousand eclipsing binaries with periods shorter than 1~d in the solar neighborhood (Paczyñski \etal 2006). Classification of the light curves resulted in a significant proportion of semi-detached systems. This would seemingly solve the problem and support TRO model, yet a closer look at the sample shows that there is very few semi-detached binaries among stars with periods shorter than 0.45~d (Pilecki 2010) whereas an overwhelming majority of CBs has periods within this range (Rucinski 2007). On the other hand, semi-detached binaries are quite common among binaries with periods between 0.7~d and 1~d where few CBs are observed. Moreover, values of global parameters were obtained recently for several CBs and some NCBs using the high-precision photometric and spectroscopic observations, together with improved modeling procedure. The results show that the global parameters of NCBs are distinctly different from those of CBs as will be demonstrated later. So, the problem of the lack of binaries in a semi-detached phase of TRO model still remains. To solve the problems with the existing model of cool CBs, an alternative model has been developed by one of us (Stêpieñ 2006ab, 2009, 2011a). The model assumes that CBs originate from young cool binaries with initial orbital periods close to 2~d. Both components rotate synchronously with the orbital period and have initial masses lower than 1.3~\MS. Such stars show strong magnetic activity resulting in MB. Permanent AML makes the orbit tighten and the components approach each other until RLOF by the primary occurs. Rapid mass transfer follows, up to the equalization of the component masses. Mass transfer continues until both components regain thermal equilibrium. The NCB configuration is identified with the mass transfer phases when at least one component is out of thermal equilibrium. After regaining thermal equilibrium by both components, a contact, or Algol-type configuration is assumed. Depending on the amount of AM left in the system, mass transfer rate and AML rate, the Algol-type configuration may then evolve into contact or may widen the orbit and stay as semi-detached until the presently more massive component leaves MS and a common envelope develops. The evolution of several exemplary CBs was computed by Stêpieñ (2006a), Gazeas and Stêpieñ (2008) and Stêpieñ and Gazeas (2012) whereas a more systematic calculations of the cool binary evolution from the initial state till RLOF by the primary component in a number of systems with different initial masses and orbital periods was carried out by Stêpieñ (2011a). Energy flow by a large scale circulation between the components of a contact binary past rapid mass exchange was considered in detail by Stêpieñ (2009). The present paper investigates the relatively short-lasting but crucial evolutionary phase of a cool close binary when the mass exchange occurs following RLOF and the binary assumes a NCB configuration. Section~2 considers in detail the process of mass transfer including, hitherto neglected, dynamics of the matter flowing from a donor to an accretor. The flow forms an equatorial bulge influencing the accretion rate when the accretor almost fills its Roche lobe. Its presence lengthens substantially the SD1 phase of the mass transfer. This explains the observed similar frequency of SD1 binaries, compared to SD2 binaries. In Section~3 observational data are analyzed. In particular, it is demonstrated that the basic parameters of SD1 and SD2 binaries are very similar to each other which favors the view that they correspond to a single process of mass transfer. The parameters of NCBs are, on the other hand, distinctly different from the observed parameters of CBs which contradicts an assumption that SD1 binaries correspond to the broken contact phase of CBs. Section~3 contains a discussion of the results and Section~4 gives conclusions. \vspace*{9pt} | The observed properties of cool close binaries with one component filling, and the other nearly filling its Roche lobe (called NCBs) fit to the recent model of origin and evolutionary status of cool CBs developed by one of us (Stêpieñ 2006ab, 2009, 2011a, Gazeas and Stêpieñ 2008, Stêpieñ and Gazeas 2012). An important starting point of the model is based on the observational, as well as theoretical, arguments that the orbital period distribution of young cool binaries is concentrated around 2--3~d. This fact is supplemented with an assumption that components of these binaries possess magnetic winds carrying mass and AM in the same way as single stars of the lower MS. Mass loss is rather moderate (of the order of 0.1~\MS\ during the whole MS age) so it influences little a nuclear time scale of either component. But, as detailed computations of the evolution of cool close binaries show, the AM loss time scale is close to MS life time of a primary component for typical values of the initial orbital period (Stêpieñ 2011a). In effect, the typical primary reaches RLOF when it is close to TAMS. Following RLOF, a mass transfer occurs. With dynamical effects taken into account, it can be shown that, until mass reversal, the process takes time comparable to the thermal time scale of the secondary component, as opposed to the conventional models of mass transfer neglecting dynamics of the transferred matter. SD1 variables are identified with this phase of mass transfer. After mass ratio reversal a CB, or SD2 binary is formed, depending on the amount of AM left in the system. Further evolution of an SD2 binary is affected by two factors acting in the opposite direction: mass transfer from the present secondary to the present primary makes period increase whereas the AML makes it shorten. Depending on the relative importance of these processes the binary evolves either into contact or becomes an Algol (Stêpieñ 2011b). \Acknow{We thank Wojtek Dziembowski, the referee, for a very careful reading of the manuscript and numerous remarks which substantially improved the original version of the paper. This research was partly supported by the National Science Centre under the grant DEC-2011/03/B/ST9/03299. We acknowledge the use of the SIMBAD database, operated at CDS, Strasbourg, France.} | 14 | 3 | 1403.2302 |
1403 | 1403.0586_arXiv.txt | {Observations of secondary eclipses of hot Jupiters allow one to measure the dayside thermal emission from the planets' atmospheres. The combination of ground-based near-infrared observations and space-based observations at longer wavelengths constrains the atmospheric temperature structure and chemical composition.} {This work aims at detecting the thermal emission of \object{WASP-5b}, a highly irradiated dense hot Jupiter orbiting a G4V star every 1.6 days, in the $J$, $H$ and $K$ near-infrared photometric bands. The spectral energy distribution is used to constrain the temperature-pressure profile and to study the energy budget of \object{WASP-5b}.} {We observed two secondary-eclipse events of \object{WASP-5b} in the $J$, $H$, $K$ bands simultaneously using the GROND instrument on the MPG/ESO 2.2 meter telescope. The telescope was in nodding mode for the first observation and in staring mode for the second observation. The occultation light curves were modeled to obtain the flux ratios in each band, which were then compared with atmospheric models.} {Thermal emission of \object{WASP-5b} is detected in the $J$ and $K$ bands in staring mode. The retrieved planet-to-star flux ratios are $0.168^{+0.050}_{-0.052}$\% in the $J$ band and $0.269\pm0.062$\% in the $K$ band, corresponding to brightness temperatures of $2996^{+212}_{-261}$\,K and $2890^{+246}_{-269}$\,K, respectively. No thermal emission is detected in the $H$ band, with a 3-$\sigma$ upper limit of 0.166\% on the planet-to-star flux ratio, corresponding to a maximum temperature of 2779~K. On the whole, our $J$, $H$, $K$ results can be explained by a roughly isothermal temperature profile of $\sim$2700~K in the deep layers of the planetary dayside atmosphere that are probed at these wavelengths. Together with {\it Spitzer} observations, which probe higher layers that are found to be at $\sim$1900~K, a temperature inversion is ruled out in the range of pressures probed by the combined data set. While an oxygen-rich model is unable to explain all the data, a carbon-rich model provides a reasonable fit but violates energy balance. The nodding-mode observation was not used for the analysis because of unremovable systematics. Our experience reconfirms that of previous authors: staring-mode observations are better suited for exoplanet observations than nodding-mode observations.} {} | \label{sec:intro} Currently, the most fruitful results on the characterization of exoplanetary atmospheres come from transiting planets. Since the first transiting planet \object{HD 209458b} was discovered in 1999 \citep{2000ApJ...529L..45C}, more than 400 are confirmed\footnote{http://exoplanet.eu/}. The orbital parameters of these planets are well constrained when transit observations were combined with radial velocity measurements. Precise planetary parameters such as mass and radius can be determined as well, which leads to a preliminary view of the internal structure of a planet, and thus to constrain the formation and evolutionary history of the planet \citep{2005AREPS..33..493G,2007ApJ...659.1661F}. Furthermore, transiting planets provide unprecedented opportunities to probe their atmospheres, not only from wavelength-dependent effective radius variations determined from the transit \citep[e.g.:][]{2002ApJ...568..377C}, but also from differential planetary photon measurements from occultation \citep[e.g.:][]{2005Natur.434..740D}. In the latter case, the planet passes behind the star, which leaves us only stellar emission during a total eclipse. As a subset of transiting planets that are exposed to high irradiation in close orbits around their host stars, hot Jupiters are the most favorable targets for thermal emission detection through secondary-eclipse observation. Their close orbits translate into a high occultation probability and frequency, while their high temperatures and large sizes make the planet-to-star flux ratio favorable. The first thermal emission detections of hot Jupiters have been achieved with the {\it Spitzer Space Telescope} \citep{2005Natur.434..740D,2005ApJ...626..523C}, which operates in the mid-infrared (MIR) wavelength range. Since then, a flood of such detections have been made with {\it Spitzer} observations, resulting in better knowledge of the chemical composition and thermal structure of the planetary atmosphere. Compared with the MIR, the near-infrared (NIR) wavelength range covers the peak of the spectral energy distribution (SED) of a planet and probes deeper into the atmosphere, therefore it can be used to constrain the atmosphere's temperature structure and energy budget. While the {\it Hubble Space Telescope} has contributed much to the NIR observation on planetary secondary eclipses \citep[e.g.:][]{2009ApJ...690L.114S,2009ApJ...704.1616S}, now more observations with high precision are starting to come from ground-based mid-to-large aperture telescopes thanks to the atmospheric window in the NIR \citep[e.g.:][]{2010ApJ...717.1084C,2010ApJ...718..920C,2011AJ....141...30C, 2011A&A...530A...5C,2012A&A...542A...4G}. As shown for example by \citet{2012ApJ...758...36M}, these ground-based NIR measurements play a crucial role in determining the C/O ratio when combined with measurements from {\it Spitzer} observations. \object{WASP-5b} was first detected by \citet{2008MNRAS.387L...4A} as a hot Jupiter orbiting a 12.3 mag G4V type star every 1.628 days. Its mass and radius are derived to be 1.58 and 1.09 times of the Jovian values, respectively, which places it among the relatively dense hot Jupiters. Several follow-up transit observations have refined its density to be nearly the same as our Jupiter \citep{2009MNRAS.396.1023S, 2011PASJ...63..287F}. Its host star has a slightly supersolar metallicity ([Fe/H]=+0.09$\pm$0.09), according to the high-resolution VLT/UVES spectroscopy of \citet{2009A&A...496..259G}. The planetary orbit might have a marginally nonezero eccentricity based on the joint analysis of RV and photometric measurements \citep{2009A&A...496..259G,2010A&A...524A..25T,2012MNRAS.422.3151H}. \citet{2010A&A...524A..25T} studied the Rossiter-McLaughlin effect in the \object{WASP-5} system and found a sky-projected spin-orbit angle compatible with zero ($\lambda$=12.1$^{+10.0\circ}_{-8.0}$), indicating an orbit aligned with the stellar rotation axis. Furthermore, several studies focused on the potential transit-timing variations (TTVs) of this system. \citet{2009A&A...496..259G} first noticed that a linear fit cannot explain the transit ephemeris very well, which was later suspected to be caused by the poor quality of one timing \citep{2009MNRAS.396.1023S}. \citet{2011PASJ...63..287F} studied its TTVs in detail with an additional seven new transit observations and calculated a TTV rms of 68\,s, only marginally larger than their mean timing uncertainty of 41\,s. \citet{2012ApJ...748...22H} revisited this TTV signal by combining their nine new epochs and suggested that this TTV might be introduced by data uncertainties and systematics and not by gravitational perturbations. From these intensive previous studies, \object{WASP-5b} has become an intriguing target for atmospheric characterization. It is not bloated, although it receives a relatively high irradiation of $\sim$2.1$\times$10$^9$~erg\,s$^{-1}$\,cm$^{-2}$ from its 5700~K \citep{2009A&A...496..259G} host star \citep[assuming a scaled major-axis $a/R_*$=5.37,][]{2011PASJ...63..287F}, which would place it in the pM class in the scheme proposed by \citet{2008ApJ...678.1419F}. Its proximity to the host star results in an equilibrium temperature of 1739~K assuming zero albedo and isotropic redistribution of heat across the whole planet, which could be as high as 2223~K in the extreme case of zero heat-redistribution. Its \ion{Ca}{II} H and K line strength \citep[$\log R'_{\rm{HK}}$=$-$4.72$\pm$0.07,][]{2010A&A...524A..25T} suggests that the activity of the host star might prevent it from having an inverted atmosphere, given the correlation proposed by \citet{2010ApJ...720.1569K}. Recently, \citet{2013ApJ...773..124B} reported thermal detections from the Warm {\it Spitzer} mission, suggesting a weak thermal inversion or no inversion at all, with poor day-to-night energy redistribution. In this paper, we present the first ground-based detections of thermal emission from the atmosphere of \object{WASP-5b} in the $J$ and $K$ bands through observations of secondary eclipse. Section~\ref{sec:obs} describes our observations of two secondary-eclipse events and the process of data reduction. Section~\ref{sec:lc} summarizes the approaches that we employed to remove the systematics and to optimally retrieve the flux ratios. In Sect.~\ref{sec:discuss}, we discuss remaining systematic uncertainties and orbital eccentricity, and we also offer explanations for the thermal emission of \object{WASP-5b} with planetary atmosphere models. Finally, we conclude in Sect.~\ref{sec:con}. | \label{sec:con} We observed two secondary eclipses of \object{WASP-5b} simultaneously in the $J$, $H$ and $K$ bands with GROND on the MPG/ESO 2.2 meter telescope, one in nodding mode and the other in staring mode. Although we failed to extract useful results from the nodding-mode observation due to the associated complicated systematics, we did measure the occultation dips from the staring-mode observation with reasonable precision, reconfirming that the staring mode is more suited than the nodding mode for exoplanet observations. We have successfully detected the thermal emission from the dayside of \object{WASP-5b} in the $J$ and $K$ bands, with flux ratios of $0.168^{+0.050}_{-0.052}$\% and 0.269$\pm$0.062\%, respectively. In the $H$ band we derived a 3-$\sigma$ upper limit of 0.166\%. The brightness temperatures inferred from the $J$ and $K$ bands are consistent with each other ($2996^{+212}_{-261}$\,K and $2890^{+246}_{-269}$\,K, respectively), but the upper limit in the $H$ band rules out temperatures above 2779\,K at $3\sigma$ level. While a slight difference might exist, together they indicate a roughly isothermal lower atmosphere of $\sim$2700~K. We modeled the GROND data together with the Warm {\it Spitzer} data using the spectral retrieval technique, ruling out a thermal inversion. We fit our data with two different models: an oxygen-rich atmosphere and a carbon-rich atmosphere. The O-rich model requires a very low day-to-night-side heat redistribution but satisfies energy balance. The C-rich model fits our data better, but violates energy balance in that it radiates 70\% more energy than it receives. To constrain the chemical composition of \object{WASP-5b} and to distinguish atmospheric models, more observations in the NIR, in particular spectroscopy, are required. | 14 | 3 | 1403.0586 |
1403 | 1403.8096_arXiv.txt | We analyze high-resolution spectra obtained with the Space Telescope Imaging Spectrograph onboard the \emph{Hubble Space Telescope} toward 34 nearby stars ($\leq$100 pc) to record \ion{Mg}{2}, \ion{Fe}{2} and \ion{Mn}{2} absorption due to the local interstellar medium (LISM). Observations span the entire sky, probing previously unobserved regions of the LISM. The heavy ions studied in this survey produce narrow absorption features that facilitate the identification of multiple interstellar components. We detected one to six individual absorption components along any given sight line, and the number of absorbers roughly correlates with the pathlength. This high-resolution near-ultraviolet (NUV) spectroscopic survey was specifically designed for sight lines with existing far-UV (FUV) observations. The FUV spectra include many intrinsically broad absorption lines (i.e., of low atomic mass ions) and often observed at medium resolution. The LISM NUV narrow-line absorption component structure presented here can be used to more accurately interpret the archival FUV observations. As an example of this synergy, we present a new analysis of the temperature and turbulence along the line of sight toward $\epsilon$ Ind. The new observations of LISM velocity structure are also critical in the interpretation of astrospheric absorption derived from fitting the saturated \ion{H}{1} Lyman-$\alpha$ profile. As an example, we reanalyze the spectrum of $\lambda$ And and find that this star likely does have an astrosphere. Two stars in the sample that have circumstellar disks (49 Cet and HD141569) show evidence for absorption due to disk gas. Finally, the substantially increased number of sight lines is used to test and refine the three-dimensional kinematic model of the LISM, and search for previously unidentified clouds within the Local Bubble. We find that every prediction made by the \cite{redfield07lism4} kinematic model of the LISM is confirmed by an observed component in the new lines of sight. | \label{introduction.s} The interstellar medium (ISM) connects many fundamental areas of astrophysics. The morphology, density, and temperature of the ISM control star formation \citep{evans99}; the dynamics of the ISM provides information on stellar winds \citep{linsky96,frisch95,muller06}; nearby electron density enhancements cause the scintillation of distant radio sources \citep{linsky08}; the ionization of the ISM yields clues to the interstellar radiation field \citep{vallerga98}; and the chemical abundances and enrichment of the ISM are tracers for the death of low-mass stars as well as the supernovae of massive stars \citep{mccray79}. Theoretical studies of the phases of the ISM have produced classic works \citep[e.g.,][]{field69,mckee77}, presenting ideas which are still being analyzed and discussed today \citep{heiles01}. The local interstellar medium (LISM) is clearly important in the context of the general ISM, as it provides the best opportunity to study in great detail many of the physical processes that dictate its structure and evolution, such as gas dynamics, pressure balance, and the effects of the radiation field. Not only are these phenomena widespread in the ISM throughout our own Galaxy, but also in other galactic environments even at high redshift \citep{frisch95,mckee98}. LISM studies can also have a surprising impact on fields as disparate as astrobiology and geophysics. For example, the interaction of the LISM with solar and stellar winds controls the size and properties of the heliosphere and astrospheres \citep{shapley21, begelman76, zank99,redfield06, wyman13}, which in turn affect cosmic ray fluxes in the associated planetary systems. Finally, a densely sampled model of the LISM could be used to predict and remove foreground contamination due to local interstellar absorption in order to aid interpretation of spectra of more distant targets in our Galaxy. The Sun and nearby stars reside in a region of ionized material known as the Local Bubble (or Local Cavity). The first evidence for this arguably hot cavity came from color excess maps indicating a large pocket in the dust at its edge and observations of diffuse soft X-ray background observed across the entire sky (\citealt{frisch11} and references therein). The edge of the Local Bubble can be traced by the onset of \ion{Na}{1} and \ion{Ca}{2} absorption, indicators of colder material. This edge begins anywhere from 65 to 250 pc depending on the observed direction \citep{sfeir99,welsh10}. The initial carving of the Local Bubble was likely the result of stellar winds or supernova explosions. Within the Local Bubble, isolated clouds of warm, partially ionized gas are observed \citep{redfield07lism4}, each distinguished by its own unique properties (e.g., density, temperature, projected velocity). The predominant strategy to study the LISM is to observe its absorption signatures against bright, nearby background sources. The shape and Doppler shift of absorption features offer insight into the nature of the ISM along each line of sight. % Since resonance lines of common ions in the ISM are formed mainly in the ultraviolet (UV), the advent of space-based high-resolution UV spectrographs, largely thanks to the {\it Hubble Space Telescope} (\emph{HST}), has made it possible to study the warm material in the LISM in unprecedented detail. The proximity of the LISM material permits detailed scrutiny currently impractical for longer distance scales; for sight lines of hundreds to thousands of parsecs, ISM absorptions are often blended and/or saturated. Conversely, by observing nearby stars, multiple LISM component absorption profiles are frequently fully resolved, allowing the identification and characterization of the constituent clouds. The observation of heavier elements in warm clouds has proven to be a boon to the understanding of the structure of the LISM. Their relatively large masses reduce thermal broadening, and thus blending, allowing for more precise measurements of cloud velocities and straightforward identification of multiple structures along a line of sight. Of particular importance are \ion{Mg}{2} and \ion{Fe}{2}, which have high cosmic abundance and are the dominant ionization stages in the LISM \citep{slavin08}. Both produce multiple spectral lines that provide redundant measurements of each ion along a given line of sight. These heavy ions have been exploited extensively to characterize the global structure of the LISM. \cite{genova90} used the {\it International Ultraviolet Explorer} (\emph{IUE}) to observe the \ion{Mg}{2} $h$ and $k$ lines of cool stars within 30 pc of the Sun. ISM absorption superimposed on the \ion{Mg}{2} chromospheric emission profiles hinted at heterogeneities in the column density distribution, as well as unresolved clouds beyond the ``Local Cloud." Later studies using Goddard High Resolution Spectrograph (GHRS) onboard {\it HST}, identified the two nearest clouds --- the Local Interstellar Cloud (LIC) and the Galactic (G) Cloud --- and established a velocity vector with only $\sim$10 lines of sight \citep{lallement92,lallement95}. \cite{redfield02} analyzed and compiled the (then) complete LISM sample of \ion{Mg}{2} and \ion{Fe}{2} observations taken at high resolution with {\it HST}'s GHRS and the Space Telescope Imaging Spectrograph (STIS). \citet{redfield07lism4} used these data to develop a kinematic model of the LISM and to identify 15 distinct clouds each with a unique velocity vector. Observations of multiple ions and ionization levels in these clouds have enabled determinations of ionization structure \citep{wood02}; abundances and element depletions \citep{redfield04a}; and temperature and turbulence \citep{redfield04b}. Furthermore, increased numbers of sight lines have made it possible to examine the small-scale structure of the LIC \citep{redfield01}. The goal of the present study is to build on this historical body of data by adding a large number of observations of heavy ions along more distant sight lines, thereby extending and refining measurements of the LISM. \begin{deluxetable}{llcccccccccl} \rotate \tablewidth{0pt} \tabletypesize{\tiny} \tablecaption{Parameters for Stars in the LISM SNAP Program\tablenotemark{a} \label{tab1}} \tablehead{& & Spectral & $m_V$ & $v_R$ & $l$ & $b$ & Distance & S/N\tablenotemark{b} & S/N\tablenotemark{b} & S/N\tablenotemark{b} & Other \\ HD No. & Other Name & Type & (mag) & (km s$^{-1}$) & (deg) & (deg) & (pc) & (\ion{Mg}{2}) & (\ion{Fe}{2}) & (\ion{Mn}{2}) & Spectra} \startdata 209100 & $\epsilon$ Ind & K5V & 4.833 & --40.4 & 336.2 & --48.0 & 3.62 & 29 & 6 & 5 & GHRS/Ech-A (Ly$\alpha$)\\ 115617 & 61 Vir & G5V & 4.74 & --8.5 & 311.9 & 44.1 & 8.56 & 18 & 6 & 7 & STIS/E140M E230M\\ 114710 & $\beta$ Com & G0V & 4.311 & 6.1 & 43.5 & 85.4 & 9.13 & 21 & 8 & 8 & FUSE\\ & WD1620--391 & DA & 10.974 & 43.2\tablenotemark{c}&341.5&7.3&13.2&6&7& 7 & GHRS/G160M, FUSE\\ 72905 & $\pi^1$ UMa & G1.5V & 5.706 & --12.0 & 150.6 & 35.7 & 14.4 & 22 & 8 & 7 & FUSE\\ 217014 & 51 Peg & G5V & 5.524 & --31.2 & 90.1 & --34.7 & 15.6 & 8 & 5 & 6 & STIS/G140M (Ly$\alpha$), FUSE\\ 120136 & $\tau$ Boo & F7V & 4.541 & --15.6 & 358.9 & 73.9 & 15.6 & 17 & 8 & 10 & STIS/G140M (Ly$\alpha$)\\ 142373 & $\chi$ Her & F9V & 4.672 & --55.4 & 67.7 & 50.3 & 15.9 & 8 & 8 & 16 & STIS/E140M \\ 220140 & V368 Cep & G9V & 7.622 & --16.8 & 118.5 & 16.9 & 19.2 & 19 & 5 & 2 & GHRS/G140M G160M G270M\\ 97334 & MN UMa & G0V & 6.476 & --2.6 & 184.3 & 67.3 & 21.9 & 16 & 5 & 3 & STIS/E140M E230M\\ & WD1337+705 & DA & 12.8 & 26 & 117.2 & 46.3 & 26.1 & 2 & 4 & 4 & STIS/G430M, FUSE\\ 222107 & $\lambda$ And & G8III--IV&3.975& 6.8 & 109.9 & --14.5 & 26.4 & 54 & 11 & 6 & GHRS/Ech-A (Ly$\alpha$), FUSE\\ 180711 & $\delta$ Dra & G9III & 3.188 & 24.8 & 98.7 & 23.0 & 29.9 & 20 & 5 & 5 & FUSE\\ 12230 & 47 Cas & F0V & 5.26 & --26 & 127.1 & 15.0 & 33.2 & 12 & 17 & 19 & GHRS/G140M, FUSE \\ 163588 & $\xi$ Dra & K2III & 3.867 & --26.4 & 85.2 & 30.2 & 34.5 & 23 & 4 & 3 & FUSE\\ 216228 & $\iota$ Cep & K0III & 3.621 & --12.6 & 111.1 & 6.2 & 35.3 & 24 & 5 & 5 & FUSE\\ 93497 & $\mu$ Vel & G5III & 2.818 & 6.2 & 283.0 & 8.6 & 35.9 & 39 & 11 & 8 & STIS/E140M, FUSE\\ 149499 & V841 Ara & K0V & 8.737 & --24.8 & 329.9 & --7.0 & 36.4 & 10 & 2 & 0 & STIS/E140M, FUSE\\ 131873 & $\beta$ UMi & K4III & 2.238 & 17.0 & 112.6 & 40.5 & 40.1 & 9 & 2 & 3 & FUSE\\ 210334 & AR Lac & G2IV & 6.203 & --34.6 & 95.6 & --8.3 & 42.8 & 13 & 5 & 5 & GHRS/G160M G270M, FUSE\\ 28911 & HIP21267 & F5V & 6.619 & 35 & 183.4 & --22.6 & 44.7 & 12 & 6 & 10 & FUSE\\ 28677 & 85 Tau & F4V & 6.02 & 36 & 180.9 & --21.4 & 45.2 & 11 & 13 & 16 & FUSE\\ 204188 & IK Peg & A8 & 6.06 & --11.4 & 70.4 & --22.0 & 46.4 & 7 & 12 & 15 & GHRS/G160M, FUSE\\ & WD0549+158 & DA & 13.06 & 12.0 & 192.0 & --5.3 & 49\tablenotemark{d} & 4 & 5 & 5 & STIS/G140M G230M, FUSE\\ & WD2004--605 & DA & 13.14 & --26.5 & 336.6 & --32.9 & 58\tablenotemark{d} & 3 & 4 & 5 & FUSE\\ 9672 & 49 Cet & A1V & 5.62 & 12.1\tablenotemark{e}&166.3&--74.8&59.4&24&37&37& FUSE\\ 43940 & HR2265 & A2V & 5.88 & 24.0\tablenotemark{f}&244.6&--22.4&61.9&19&29&30& FUSE\\* 137333 & $\rho$ Oct & A2V & 5.57 & --11 & 307.0 & --23.0 & 66.1 & 14 & 25 & 31 & FUSE\\* & WD1631+781 & DA & 13.03 & \nodata &111.3& 33.6 & 67\tablenotemark{d} & 0 & 0 & 0 & FUSE\\* 3712 & $\alpha$ Cas & K0II--III &2.377&--4.3& 121.4 & --6.3 & 70.0 & 21 & 6 & 5 & FUSE\\* 149382 & HIP81145 & B5 & 8.872 & 3 & 11.8 & 27.9 & 73.9 & 21 & 24 & 20 & FUSE\tablenotemark{g}\\* & WD0621--376 & DA & 11.99 & 40.5\tablenotemark{c}&245.4&--21.4&78\tablenotemark{d}&8&9& 9 & FUSE \\* 75747 & RS Cha & A7V & 6.02 & 26.0 & 292.6 & --21.6 & 92.9 & 9 & 17 & 18 & STIS/E230M, FUSE\\* & IX Vel & O9 & 9.503 & 20 & 264.9 & --7.9 & 96.7 & 9 & 10 & 10 & STIS/E140M, FUSE\\* 141569 & HIP77542 & B9 & 7.143 & --7.6\tablenotemark{h}&4.2&36.9&116&11&14&13 & FUSE\\* 149730 & R Ara & B9IV/V & 6.73 & $\pm$100\tablenotemark{i}&330.4&--6.8&124&14&20&21&FUSE \enddata \tablenotetext{a}{All stellar parameters taken from the SIMBAD database unless otherwise stated.} \tablenotetext{b}{S/N calculated over 10 km~s$^{-1}$ bins on either side of any LISM absorption.} \tablenotetext{c}{\cite{holberg98}} \tablenotetext{d}{\cite{vennes97}} \tablenotetext{e}{\cite{hughes08}} \tablenotetext{f}{\cite{gontcharov06}} \tablenotetext{g}{Planned FUSE observations that were not completed before the end of the mission.} \tablenotetext{h}{\cite{dent05}} \tablenotetext{i}{\cite{reed10}} \end{deluxetable} | \label{conclusion} High-resolution NUV SNAP observations of 34 stars within $\sim$100 pc broadly distributed across the sky reveal widespread \ion{Mg}{2}, \ion{Fe}{2}, and \ion{Mn}{2} absorption in the LISM. Among these sight lines, we detected 76 \ion{Mg}{2} components, 71 \ion{Fe}{2} components, and 11 \ion{Mn}{2} components. Each \ion{Fe}{2} and \ion{Mn}{2} component matches an \ion{Mg}{2} component to within 3 km s$^{-1}$ in radial velocity, evidence that they arise from the same LISM clouds. The distribution of radial velocities is consistent with the bulk flow of the cluster of local interstellar clouds, and the Doppler parameters reflect the greater contribution of thermal broadening for the lighter \ion{Mg}{2} ion. The average number of components per sight line remains flat beyond 10 pc, and only begins rising beyond $\sim$60 pc, evidence that LISM clouds are concentrated close to the Sun, and that a considerable accumulation of material traces the edge of the Local Bubble. Every prediction made by the \cite{redfield07lism4} kinematic model of the LISM is confirmed by an observed component in the new lines of sight. The success of the model points to the value of these observations for understanding the velocity structure of the LISM. Many velocity components not predicted by the model for the observed lines of sight agree with the projected velocities of nearby clouds within small angular separations from these lines of sight. In these cases, the cloud boundaries will need to be redrawn. For longer lines of sight, we detected many absorption components not consistent with previously identified clouds. These can be compared with unidentified components along nearby sight lines to construct velocity vectors for new clouds. Three close pairs of sight lines in this sample, separated by $<$3$^{\circ}$, were scrutinized for evidence of small scale structure. While slight variations in the absorption profiles can be seen, we find little evidence for significant small scale structure. For the dominant ions, the radial velocities, Doppler widths, and column densities are consistent for scales on the order of 10,000 AU or 0.05 pc. All of the new NUV SNAP spectra are along sight lines with existing FUV spectra, typically taken at medium resolution because of the low intrinsic stellar flux. The new high-resolution NUV spectra provide critical information regarding the velocity structure of the LISM absorbers, which can then be applied to the blended medium-resolution spectra of the lighter ions to deduce fundamental physical properties. For example, the widths of LISM absorption lines contain information on the temperature and turbulent velocity of the gas. We use the line widths measured in this paper, together with archived FUV absorption lines to make the first measurement of temperature and turbulent velocity along the sight line to $\epsilon$ Ind. The absorption is associated with the LIC, and the temperature and turbulent velocity are consistent with other measurements of the LIC. Accumulating a large sample of these combined NUV $+$ FUV measurements will be critical in evaluating the homogeneity of LISM clouds. Clouds detected towards $\epsilon$ Ind and $\lambda$ And are of particular interest because these stars show evidence of astrospheres. Understanding the LISM cloud velocity structure in the foreground of these stars influences the fitting of the often blended and saturated Ly$\alpha$ lines used to detect the subtle astrospheric absorption. The $\epsilon$ Ind sight line shows evidence for only one interstellar cloud, which was assumed in the original Ly$\alpha$ fitting. On the other hand, we detected three components toward $\lambda$ And, which was previously modeled assuming only a single high temperature cloud. We analyzed the Ly$\alpha$ line with three ISM clouds included in the fit. An astrosphere detection remains viable in our analysis, which highlights the importance of high-resolution LISM spectra to constrain the velocity structure of the interstellar absorption. Two stars in the sample have known circumstellar disks. 49 Cet, which has an edge-on debris disk, shows \ion{Mg}{2}, \ion{Fe}{2}, and \ion{Mn}{2} absorption at the stellar velocity; and likewise for the \ion{Mg}{2} and \ion{Fe}{2} components towards HD141569. In both sight lines, the proposed disk components do not agree with any model LISM cloud predictions. Eliminating the possibility that this absorption is from the ISM would require further examination of nearby sight lines. Such an analysis of two nearby sight lines (HD28911 and 85 Tau) in the SNAP sample to the sight line toward HD32297, an edge-on debris disk located 112 pc away, supports the detection of disk absorption in the HD32297 spectrum. The results presented here are only the beginning in a series of investigations that will characterize the LISM and its constituent clouds. When combined with archived FUV spectra, often obtained at medium resolution, it will be possible to measure the temperature and turbulence of LISM clouds as was shown with the LIC towards $\epsilon$ Ind. Furthermore, observations of different ionization stages of Mg, Fe, and Mn along the same sight lines can help describe the interstellar radiation field. Similarly, a comparison of column densities of various ions, across many sight lines, provides a valuable inventory of the abundances and depletions of LISM clouds. With more sight lines, tighter constraints can be placed on the three dimensional morphology of the LISM, including the small scale structure of the clouds. Due to the proximity of LISM clouds, a large number of sight lines must be observed in order to adequately sample the cloud structures. As this sample grows, it will be possible to integrate the various fundamental measurements into a self-consistent model of the morphology and physical characteristics of the structures inhabiting our local interstellar environment. | 14 | 3 | 1403.8096 |
1403 | 1403.5088_arXiv.txt | Solar coronal shocks are very common phenomena in the solar atmosphere and are believed to be the drivers of solar type II radio bursts. However, the microphysical nature of these emissions is still an open problem. This paper proposes that electron cyclotron maser (ECM) emission is responsible for the generation of radiations from the coronal shocks. In the present model, an energetic ion beam accelerated by the shock excites first Alfv\'en wave (AW) and then the excited AW leads to the formation of a density-depleted duct along the foreshock boundary of the shock. In this density-depleted duct, the energetic electron beam produced via the shock acceleration can effectively excite radio emission by the ECM instability. Our results show that this model may have potential application to solar type II radio bursts. | A shock standing ahead of a magnetic structure ejected from the Sun is a very common phenomenon in solar and interplanetary physics. This idea of the shock was proposed by \citet{gol55p03,gol62p00}, which was confirmed subsequently via in situ observations \citep{son64p53}. In the solar corona, the shock is believed to be driven by fast coronal mass ejection \citep{man02p67,lar03p16,cli04p05,liu09p51,che11p01,ram12p07}, or by the pressure pulse of a flare \citep{har65p61,gop98p07,nio11p31,mag08p05,mag10p66,mag12p52}. The early known signatures of coronal shocks are type II radio bursts which often appear in a form of two intense emission bands drifting gradually from higher to lower frequencies as revealed from the solar radio dynamic spectra \citep{pay47p56,wil50p87,nel85p33}. Other evidences of coronal shocks are suggested in terms of Moreton waves \citep{mor60p94,mor60p57,che02p99}, streamer deflections \citep{gos74p81,mic84p11,she00p81}, and magnetohydrodynamic simulations \citep{che00p75,man04p07}. In recent studies, the existences of coronal shocks have been shown by direct observations both in white light \citep{vou03p92,ont09p67,gop09p27,gop11p17,she13p43} and the extreme ultraviolet \citep{bem10p30,koz11p25,mas11p60,gop12p72}. One can refer to the recent reviews for details of theory and properties of shocks \citep{vrs08p15,tre09p09,war10p27,pat12p87}. For the coronal shock, one of the most challenging and fascinating questions is how it can result in emission of radiation. Two elements are required for the emission of radiation of the shock. The first one is the energetic electrons produced by the shock, and the second one is the emission mechanism by which part of kinetic energy of the energetic electrons can be converted to radiation. For the energetic electrons, many authors found that their acceleration mechanism, in terms of shock drift acceleration \citep{hol83p37,ste84p93,bal01p61} or fast fermi acceleration \citep{wuc84p57,ler84p49}, is actually simple and effective for the case of nearly perpendicular shocks (NPSs). The key point is that these NPSs can act as fast-moving magnetic mirrors which reflect upstream electrons along the ambient magnetic field, and consequently one can obtain energetic electrons characterized by beam with a loss-cone \citep[or "hollow beam", "ring beam" in literatures;][]{wuc86p92,man05p19,yoo07p01}. For the emission mechanism two theories, related to induced (or coherent in literatures) emissions, have been proposed. One is so called plasma-emission suggested by \citet{gin58p53}. This theory posits that electrostatic waves are first generated by instabilities and then are converted to electromagnetic waves via nonlinear wave$-$wave interaction \citep{mer85p77,ben88p67}. Here, both the high level of electrostatic waves and conversion efficiency are required to explain the unusually high brightness temperature (up to $10^{13}$ K) from the observations of type II bursts \citep[][and references therein]{nel85p33}. The other is the theory of direct excitation of radiations in which electromagnetic waves can be amplified efficiently by perpendicular free energy of energetic electrons via wave$-$particle interaction \citep{twi58p64,wuc85p15}. Based on this theory, for nearly perpendicular coronal shocks two papers have been presented to show the emission processes related to synchrotron maser emission \citep{wuc86p92} or electron cyclotron maser emission \citep[ECME;][]{yoo07p01}. ECME from interplanetary shocks or other quasi-perpendicular astrophysical shocks were also discussed \citep[see,][]{far01p01,bin03p79}. ECME is a well-known emission mechanism and has been extensively discussed as a dominant mechanism of producing high-power radiation in magnetized plasmas \citep[e.g., see a review by][]{tre06p29}. In the discussion of ECME a low-density region, with plasma frequency lower than electron cyclotron frequency, is important so that the energetic electrons with perpendicular free energy can efficiently drive ECME \citep{bin03p79,lee13}. This low-density region, if the ECME is responsible for the radio emission of coronal shocks, should be necessary for the ECME to effectively emit radiations near both the fundamental (F) and its second harmonic (H). This is because observations showed that two emission bands (F and H) of type II bursts in general have their frequency ratio of about $1:2$ \citep[e.g.,][]{nel85p33,man95p75}. However, the existence of a low-density region related to coronal shocks, to the best of our knowledge, has not been discussed. Only a relevant study of the depletion of plasma density in a flux tube in the solar corona was presented \citep{wuc06p17}. According to the study by \citet{wuc06p17}, Alfv\'en waves (AWs) excited by ion beam can deplete plasma density and result in the formation of a density-depleted duct on the path of the ion beam traveling due to the pressure of the AWs. This process is expected to be effective in a low-beta plasma in which the magnetic pressure dominates the plasma pressure \citep[e.g.,][]{dul85p19}. The present paper is devoted to further reveal the physical processes of radio emission from solar coronal shocks based on ECME, in which AWs generated by ion beam are taken into account self-consistently. The paper is organized as follows. In Section 2 the basic physical model is given, in which the ion and electron beams in the foreshock boundary, excitation of AWs by ion beams, density depletion by AWs, and ECME in the presence of AWs are described, respectively. The calculated results based on solar coronal parameters are presented in Section 3. Several characters of the present model related to type II radio bursts are discussed in Section 4. Finally, the conclusions with some brief discussion are given in Section 5. | This paper reveals the physical processes of radio emission from solar coronal shocks based on ECME, in which AWs are introduced and play an important role. The present discussion consists of three elementary processes based on (1) excitation of AWs, (2) depleting density and forming a duct, and (3) ECME in the duct. AWs is first excited by ion beams accelerated by NPSs. The generated AWs deplete the local density through magnetic compression in a low-beta plasma \citep{wuc06p17}. Consequently a density-depleted duct is made along the ion foreshock boundary where the ion beams have the highest energy \citep{eas05p41}. Then, the ECME works when energetic electrons with a crescent-shaped beam distribution move through the duct. As shown in the Section 3.2, the ECME is more efficient when the plasma frequency is smaller than the electron gyrofrequency (i.e., $\omega_{pe}/\Omega_e \lesssim 1$) in the duct. And, both the F and H are excited when $\omega_{pe}/\Omega_e \lesssim 1$ is fulfilled. The present study is different from the preceding works \citep{wuc86p92,yoo07p01}. The key difference is that the present study introduces AWs which lead to three important plasma processes. They are the depleting density, pitch-angle scattering energetic electrons, and influencing the basic physics of ECME. Among these processes the first one is vitally significant because this process leads to the condition of $\omega_{pe}/\Omega_e \lesssim 1$ in favor of the ECME to excite both the F and H. Furthermore, on the basis of density depletion a duct is made, which can inherently explain the outstanding fact that the observed source regions of the F and H of type II bursts are nearly overlapping at a fixed frequency \citep{saw82p49,nel85p33}. In addition, the present model implies that the observed radiation has a frequency close to the ambient plasma frequency of exit point, which is compatible with the observations of the height of type II bursts. Finally, it should be noted that the observed frequency drift of type II bursts is due to the decreasing magnetic field strength rather than the density as described in the section 4 based on the present model. Certainly, the present discussion of radio emission from coronal shocks is preliminary. The radiation from shocks is by no means simple. Based on the preceding works \citep{wuc86p92,yoo07p01}, this paper mainly investigates the physical process of radio emission from solar coronal shocks and shows that the AWs play a vitally important role. More researches are required to fully understand the related details of the present discussion. | 14 | 3 | 1403.5088 |
1403 | 1403.2985_arXiv.txt | We show that in clustering dark energy models the growth index of linear matter perturbations, $\gamma$, can be much lower than in $\Lambda$CDM or smooth quintessence models and presents a strong variation with redshift. We find that the impact of dark energy perturbations on $\gamma$ is enhanced if the dark energy equation of state has a large and rapid decay at low redshift. We study four different models with these features and show that we may have $0.33<\gamma\left(z\right)<0.48$ at $0<z<3$. We also show that the constant $\gamma$ parametrization for the growth rate, $f=d\ln\delta_{m}/d\ln a=\Omega_{m}^{\gamma}$, is a few percent inaccurate for such models and that a redshift dependent parametrization for $\gamma$ can provide about four times more accurate fits for $f$. We discuss the robustness of the growth index to distinguish between General Relativity with clustering dark energy and modified gravity models, finding that some $f\left(R\right)$ and clustering dark energy models can present similar values for $\gamma$. | The understanding of the accelerated expansion of the universe is one of the greatest challenges in physics. It may be caused by a yet unknown form of energy with negative pressure, generically called dark energy, or by a new theory of gravity and space-time. Since different theoretical scenarios and their various models are designed to reproduce the expansion history, from the observational point of view we certainly need to analyze the evolution of cosmological perturbations in order to be able to falsify the models and have a better indication of what drives the accelerated expansion. One particular simple and powerful tool to study the linear growth of cosmic structures and discriminate between the various theoretical possibilities is the growth rate of matter perturbations, $f=d\ln\delta_{m}/d\ln a$, which is usually parametrized by $f=\Omega_{m}^{\gamma}$, where $\Omega_{m}$ is the matter density parameter and $\gamma$ is the so-called growth index. It is well-known that $\Lambda$CDM and quintessence models (minimally coupled canonical scalar fields) can be well described by a scale independent and constant $\gamma\simeq0.55$ \cite{Wang:1998gt,Linder:2005in,Linder2007} with very small corrections \cite{Tsujikawa2013}. Since the underlying theory of gravity in such models is the General Relativity, it is usual to refer to $\gamma_{GR}\simeq0.55$ as the value of the growth index in General Relativity. On the other hand, modified gravity models such as $f\left(R\right)$ models may have $0.40\lesssim\gamma\lesssim0.43$ at $z=0$, besides being scale dependent \cite{Tsujikawa2009,Gannouji2009}, and Dvali-Gadabadze-Porrati (DGP) braneworld gravity model \cite{Dvali2000b} has $\gamma\simeq0.68$ \cite{Linder2007}. It has been shown by reference \cite{Heavens2007} that, ongoing observational projects, like Dark Energy Survey \cite{Abbott:2005bi}, should be able to distinguish a deviation of $0.179$ from $\gamma_{GR}$ and future space based projects, like \textit{Euclid} \cite{Laureijs2011}, a deviation of $0.048$, which proves the power of the growth index to falsify the various models of cosmic acceleration. In the context of quintessence models, dark energy perturbations are relevant for dark matter growth only on Hubble scales and then are usually neglected on small scales, which are the observationally relevant for the determination of $f$. This is due to the fact that quintessence perturbations have unitary effective sound speed (in its rest frame), $c_{{\rm eff}}^{2}=\left(\delta p/\delta\rho\right)_{{\rm rest}}=1$ \cite{Hu1998c}. Hence its sound horizon, $\sim c_{{\rm eff}}H^{-1}$, is of the order of the Hubble radius and dark energy perturbations are strongly suppressed on smaller scales. However, there are models of dark energy based on non-canonical scalar fields in which the effective sound speed is variable and even negligible \cite{Chiba2000,Armendariz-Picon2001,Chimento2005c,Creminelli2009,Lim2010}. When $c_{{\rm eff}}\ll1$ dark energy perturbations grow at the same pace as matter perturbations \cite{Abramo:2008ip,Sapone2009} and can be as large as them when $w=p_e/\rho_e\simeq0$ \cite{Batista:2013oca}, like during the matter dominated period in Early Dark Energy models. Hence it is possible that in such models the growth of matter perturbations is quite different from quintessence or $\Lambda$CDM models. In this case, we have to ask whether the values of $\gamma$ could be mistaken for modified gravity models. The issue of how to differentiate a new energy component from a new gravity theory has been discussed a lot in the literature, e.g., \cite{Kunz2007,Jain2008,Bertschinger2008,Dossett:2013npa}. Although most smooth dark energy models can be distinguished from modified gravity models, if dark energy can cluster this task can be much more difficult. However, reference \cite{Dossett:2013npa} has recently claimed that clustering dark energy models do not impact the growth index severely, and its value remains near the $\Lambda$CDM one, so these models could be easily distinguished from modified gravity. Moreover, it was found that clustering dark energy models with constant equation of state differ only about $5\%$ from $\gamma_{GR}$ \cite{Ballesteros2008}. In this paper we will show that if clustering dark energy is allowed to have a large and rapid decay of its equation of state at low redshift, a situation that was not considered in references \cite{Ballesteros2008,Dossett:2013npa}, then dark energy perturbations will strongly impact the growth index and it would be difficult to distinguish this model from some $f\left(R\right)$ models. Although these features may seem unnatural in the context of a single canonical scalar field model, there are at least two other possible ways to construct models with this evolution. One can construct a k-essence model requiring negligible effective sound speed \cite{Creminelli2009} and tracking behavior \cite{Chiba2002}, which can in principle induce a fast transition of the equation of state at low redshift. It is also possible to make use of two scalar fields, one of which is a Lagrange multiplier that enforces the sound speed to be exactly zero, regardless of the background evolution \cite{Lim2010}, which can also present the tracking behavior. For the purpose of this paper, however, it will be sufficient to describe dark energy as a perfect fluid with a parametrized evolving equation of state and a constant effective sound speed. This paper is organized as follows. In section II we present the background evolution of four dark energy models that we will use to illustrate the impact of dark energy perturbations on the growth index. In section III we present the equations which we use to evolve the linear perturbations. The results for the growth index and the comparison with some modified gravity models are shown in section IV. We present the conclusions in section V. | We have shown that clustering dark energy models with a rapid and large decay of equation of state at low redshift have a growth index much lower than in $\Lambda$CDM or quintessence models. When fitting a constant growth index, we found values in the range $0.43<\gamma_{0}<0.51$ for the four representative clustering models that we have considered. However, we also have observed that the constant $\gamma_{0}$ fit is not very accurate to represent the numerical solution for the growth rate, $f$, being almost $6\%$ inaccurate for our models B and D. When fitting $f$ with the redshift dependent parametrization for $\gamma$ proposed in reference \cite{Dossett2010}, the accuracy is about four times better, but can still be as large as $1\%$. In this parametrization, the $\gamma_{b}$ parameter, associated with the time dependence of $\gamma$, is always positive, and one order of magnitude larger for clustering dark energy models when compared to their non-clustering versions. This behavior can be useful in order to distinguish between smooth and clustering dark energy. The general trend we have found is that clustering dark energy lowers $\gamma$ and induces an important time variation to it. This is the same behavior found in some $f\left(R\right)$ models \cite{Gannouji2009,Tsujikawa2009}. Therefore, we conclude that if future data on the growth index points to values much lower than in the $\Lambda$CDM model, the interpretation of the result as a clear evidence of modified gravity is not straightforward. \subsection* | 14 | 3 | 1403.2985 |
1403 | 1403.5277_arXiv.txt | Natural inflation is a good fit to all cosmic microwave background (CMB) data and may be the correct description of an early inflationary expansion of the Universe. The large angular scale CMB polarization experiment BICEP2 has announced a major discovery, which can be explained as the gravitational wave signature of inflation, at a level that matches predictions by natural inflation models. The natural inflation (NI) potential is theoretically exceptionally well motivated in that it is naturally flat due to shift symmetries, and in the simplest version takes the form $V(\phi) = \Lambda^4 [1 \pm \cos(N\phi/f)]$. A tensor-to-scalar ratio $r>0.1 $ as seen by BICEP2 requires the height of any inflationary potential to be comparable to the scale of grand unification and the width to be comparable to the Planck scale. The Cosine Natural Inflation model agrees with all cosmic microwave background measurements as long as $f \gae \mpl$ (where $\mpl = 1.22 \times 10^{19}\ {\rm GeV}$) and $\Lambda \sim \mgut \sim 10^{16}\ {\rm GeV}$. This paper also discusses other variants of the natural inflation paradigm: we show that axion monodromy with potential $V\propto \phi^{2/3}$ is inconsistent with the BICEP2 limits at the 95\% confidence level, and low-scale inflation is strongly ruled out. Linear potentials $V \propto \phi$ are inconsistent with the BICEP2 limit at the 95\% confidence level, but are marginally consistent with a joint Planck/BICEP2 limit at 95\%. We discuss the pseudo-Nambu Goldstone model proposed by Kinney and Mahanthappa as a concrete realization of low-scale inflation. While the low-scale limit of the model is inconsistent with the data, the large-field limit of the model is marginally consistent with BICEP2. All of the models considered predict negligible running of the scalar spectral index, and would be ruled out by a detection of running. | Introduction} In a paper published in 1981, Guth proposed inflation \cite{Guth:1980zm} to solve several cosmological puzzles: an early period of accelerated expansion explains the homogeneity, isotropy, and flatness of the universe, as well as the lack of relic monopoles. Subsequently, Linde \cite{Linde:1981mu}, as well as Albrecht and Steinhardt \cite{Albrecht:1982wi} suggested rolling scalar fields as a mechanism to drive the dynamics of inflation (see \cite{Kazanas:1980tx,Starobinsky:1980te,Sato:1981ds,Sato:1980yn,Mukhanov:1981xt,Mukhanov:2003xw,Linde:1983gd} for important early work). While inflation results in an approximately homogeneous universe, inflation models also predict small inhomogeneities. Observations of inhomogeneities via the cosmic microwave background (CMB) anisotropies and structure formation provide strong tests of inflation models. In 1990, Freese, Frieman, and Olinto proposed the paradigm of natural inflation \cite{Freese:1990rb} to solve theoretical problems of rolling inflation models. Most inflation models suffer from a potential drawback: to match various observational constraints, namely CMB anisotropy measurements and the requirement of sufficient inflation, the height of the inflaton potential must be of a much smaller scale than that of the width, by many orders of magnitude (\ie, the potential must be very flat). This requirement of two very different mass scales is what is known as the ``fine-tuning'' problem in inflation, since very precise couplings are required in the theory to prevent radiative corrections from bringing the two mass scales back to the same level. The natural inflation model (NI) uses shift symmetries to generate a flat potential, protected from radiative corrections, in a natural way \cite{Freese:1990rb}. Natural inflation models use ``axions'' as the inflaton, the field responsible for inflation, where the term ``axion'' is used loosely for a field which has a flat potential as a result of a shift symmetry, i.e. the potential is unchanged under the transformation $\phi \rightarrow \phi + {\rm constant}$. During the early Universe, the inflaton field rolls along this flat potential for a long time, giving rise to the long period of inflationary expansion that solves the cosmological problems described above. Of course the shift symmetry must eventually be broken to allow the inflaton to roll to a minimum of the potential and inflationary expansion to proceed and finally stop. In this sense the inflaton in NI is an ``axion,'' or a ``pseudo-Nambu-Goldstone boson,'' with a nearly flat potential, exactly as required by inflation. In the original natural inflation model proposed in 1990, the inflaton was directly modeled after the QCD axion, though with different mass scales. In this original model, the shape of the potential is a cosine, exactly as for the QCD axion. To match CMB observations, the height of the potential in the original Cosine NI is required to be $\sim 10^{16}$ GeV while the width is required to be $\gae 10^{19}$ GeV, as we will see in detail later in the paper. In 1995, WHK and K.T.\ Mahanthappa considered NI potentials generated by radiative corrections in models with explicitly broken Abelian \cite{Kinney:1995xv} and non-abelian \cite{Kinney:1995cc} symmetries. We will call these models KM Natural Inflation. Since that time many other variants of natural inflation have been proposed. A notable example is axion monodromy, where an axion arising in string compactification is the inflaton; the potential in this case is not periodic and instead can be linear or increasing as $\phi^{2/3}$. Remarkably, the data are now of sufficient accuracy to differentiate between these different types of NI models. Over the past decade Cosmic Microwave Background (CMB) observations have confirmed basic predictions of inflation and are in addition providing stringent tests of individual inflationary models. First, generic predictions of inflation match the observations: the universe has a critical density ($\Omega=1$), the density perturbation spectrum is nearly scale invariant, and superhorizon fluctuations are evident. Second, current data differentiate between inflationary models and rule some of them out \cite{Spergel:2006hy,Alabidi:2006qa,Peiris:2006ug,Easther:2006tv,Seljak:2006bg,Kinney:2006qm,Martin:2006rs,Martin:2013tda,Martin:2013nzq,Peiris:2006sj}. For example, quartic potentials and generic tree-level hybrid models were disfavored already by WMAP data. The Planck satellite data has produced powerful tests of single-field rolling models \cite{Ade:2013uln}. It has placed strong bounds on non-Gaussianity of the data, ruling out many non-minimal models including variants with multiple fields, non-canonical kinetic terms, and non-Bunch-Davies vacua \cite{Ade:2013ydc}. To quote the Planck team, ``With these results, the paradigm of standard single-field inflation has survived its most stringent tests to date.'' Most recently, BICEP2 has made a ground-breaking discovery \cite{Ade:2014xna}. In addition to density perturbations, quantum fluctuations in inflation should produce gravitational waves that would appear as B-modes in polarization data. BICEP2 reported the first discovery of these gravity waves. They find that the observed B-mode power spectrum is well- fit by a lensed $\Lambda$-CDM + tensor theoretical model with tensor/scalar ratio $r = 0.20^{+0.07}_{-0.05}$, with the null hypothesis disfavored at 7.0 $\sigma$. Alternatively, if running of the spectral index is allowed, the combined Planck and BICEP data could have a different best fit. In this paper we restrict our studies to the case of no running, consistent with the predictions of the simplest Natural Inflation models. Thus we will take as our lower bound on $r$: \begin{equation} \label{eq:lowerbound} r > 0.15\ {\mathrm{at}}\ 1 \sigma\ {\mathrm{and}}\ r>0.1\ {\mathrm{at}}\ 2 \sigma. \end{equation} It is the purpose of this paper to test natural inflation models with the Planck and BICEP2 data. For comparison with the approach of taking the lower bound on $r$ from BICPE2, we also perform a joint likelihood analysis of Planck and BICEP2 (including data from some other experiments as described below). We compare the predictions of the Cosine NI model with the 68\% and 95\% confidence level regions of this joint likelihood analysis. Inflation models predict two types of perturbations, scalar and tensor, which result in density and gravitational wave fluctuations, respectively. Each is typically characterized by a fluctuation amplitude ($\Pscalarrt$ for scalar and $\Ptensorrt$ for tensor, with the latter usually given in terms of the ratio $r \equiv \Ptensor/\Pscalar$) and a spectral index ($\ns$ for scalar and $\nt$ for tensor) describing the mild scale dependence of the fluctuation amplitude. The amplitude $\Pscalarrt$ is normalized by the height of the inflationary potential. The inflationary consistency condition $r = -8 \nt$ further reduces the number of free parameters to two, leaving experimental limits on $\ns$ and $r$ as the primary means of distinguishing among inflation models. Hence, predictions of models are presented as plots in the $r$-$\ns$ plane. The amplitude of the gravity waves and hence the value of $r$ is determined by the height of the potential, i.e., the energy scale of inflation. The relationship is given by \begin{equation} V = (2.2 \times 10^{16} {\rm GeV})^4 \frac{r}{0.2} . \end{equation} Thus the BICEP2 bound $r>0.1$ at 2$\sigma$ requires the height of the potential to be at least $10^{16}$ GeV. Inflation is probing the GUT scale. Further, the width of the potential must exceed the the well-known Lyth Bound for single-field inflation \cite{Lyth:1996im}, which relates the tensor/scalar ratio to the field excursion $\Delta \phi$ during inflation, \begin{equation} \Delta\phi \geq \mpl \sqrt{\frac{r}{4 \pi}}. \end{equation} With $r \sim 0.2$, inflation potentially becomes an interesting test of physics beyond the Planck scale. The major results of this paper can be seen in Figures 1-5. The predictions of natural inflation models are plotted in the $r$-$\ns$ plane and compared to data from the Planck and BICEP2/Keck data. The predictions are plotted for various parameters: the width $f$ of the potential and number of e-foldings $N$ before the end of inflation at which present day fluctuation modes of scale $k=0.002$ Mpc$^{-1}$ were produced. $N$ depends upon the post-inflationary universe and is $\sim 46-60$. Also shown in the figure are the observational constraints from Planck and BICEP2. Figures 1-4 apply the lower bound on $r$ in Eqn(\ref{eq:lowerbound}). Figure 1 shows the original Cosine NI model; Figure 2 the KM NI model, and Figure 3 summarizes a variety of potentials. Figure 4 shows a Higgs potential for comparison. In Figure 5 (for comparison with Figure 1), we plot the predictions of the Cosine NI model vs. the 68\% and 95\% confidence level regions of the joint likelihood analysis of Planck and BICEP2 data. Our primary result is that the original Natural Inflation Model and KM NI are consistent with current observational constraints. In this paper we take $\mpl = 1.22 \times 10^{19}$ GeV. Our result extends upon previous analyses of NI \cite{Freese:2004un} and \cite{Savage:2006tr} that was based upon WMAP's first year data \cite{Spergel:2003cb} and third year data. Even earlier analyses \cite{Adams:1992bn,Moroi:2000jr} placed observational constraints on this model using COBE data \cite{Smoot:1992td}. Other papers have studied inflation models (including NI) in light of the WMAP1 and WMAP3 data \cite{Alabidi:2006qa,Alabidi:2005qi} and in light of Planck data \cite{Tsujikawa:2013ila}. In previous papers \cite{Savage:2006tr} \cite{Freese:2008if}, we found how far down the potential the field is at the time structure is produced, and found that for $f \gg \mpl$ the relevant part of the potential is indistinguishable from a quadratic potential (yet has the advantage that the required flatness is well- motivated). Indeed one can see that $V\sim m^2 \phi^2$ matches all the data. We will examine one other model with a GUT-scale Higgs-like potential, and show that it too can match the data. The BICEP2 data have substantially reduced the number of inflationary models that agree with data. We will begin by discussing the model of natural inflation in \refsec{NI}: the motivation, the potential, and relating pre- and post-inflation scales. We will describe which of the natural inflation models we plan to compare to data. In \refsec{Fluctuations}, we will examine the scalar and tensor perturbations predicted by NI models and compare them with Planck and BICEP2 data in \refsec{Results}. We conclude in \refsec{Conclusion}. | Conclusion} Remarkable advances in cosmology have taken place in the past decade thanks to Cosmic Microwave Background experiments. The release of the BICEP2 data is revolutionary and will lead to even more exciting times for inflationary cosmology. The success of BICEP2 should motivate future missions even going to space. Not only have generic predictions of inflation been confirmed by a series of CMB experiments (though there are still outstanding theoretical issues), but indeed individual inflation models are being tested with large classes already ruled out. Currently the natural inflation model, which is well-motivated on theoretical grounds of naturalness, is a good fit to existing data. In Figure 1, we showed that for the cosine potential with width $f \gae \mpl$ and height $\Lambda \sim \mgut$ the model is in good agreement with all CMB data. Natural inflation predicts very little running, at the level of $10^{-3}$, and this will become a test of the model. Even for values $f\gg \mpl$ where the relevant parts of the potential are indistinguishable from quadratic, natural inflation provides a framework free of fine-tuning for the required potential. Other than natural inflation, single-field models compatible with all existing data sets include the $m^2 \phi^2$ quadratic potential (to which natural inflation asymptotes for large $f$ as mentioned above) as well as the potential for a Higgs-like particle at the GUT scale (see Figure 4). The BICEP2 data have substantially reduced the number of inflationary models that agree with data. In summary, Natural Inflation represents a model which is both well-motivated and testable. It is a good fit to all cosmic microwave background (CMB) data and may be the correct description of an early inflationary expansion of the Universe. | 14 | 3 | 1403.5277 |
1403 | 1403.2727_arXiv.txt | We show that the existence of new, light gauge interactions coupled to Standard Model (SM) neutrinos give rise to an abundance of sterile neutrinos through the sterile neutrinos' mixing with the SM. Specifically, in the mass range of MeV-GeV and coupling of $\gZp\sim 10^{-6} - 10^{-3}$, the decay of this new vector boson in the early universe produces a sufficient quantity of sterile neutrinos to account for the observed dark matter abundance. Interestingly, this can be achieved within a natural extension of the SM gauge group, such as a gauged $L_\mu-L_\tau$ number, without any tree-level coupling between the new vector boson and the sterile neutrino states. Such new leptonic interactions might also be at the origin of the well-known discrepancy associated with the anomalous magnetic moment of the muon. | 14 | 3 | 1403.2727 |
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1403 | 1403.3271_arXiv.txt | {}{The association of very-high energy sources with regions of the sky rich in dust and gas has been noticed in the study of individual VHE sources. However, the statistical significance of such correlation for the whole population of TeV detections has not been assessed yet. Here we present a study of the association of VHE sources in the central Galactic region with positions of enhanced material content.}{ We obtain estimates of the material content through two classical tracers: dust emission and intensity of the $^\textrm{12}$CO(1$\rightarrow$0) line. We make use of the recently released all-sky maps of astrophysical foregrounds of the Planck Collaboration and of the extensive existing CO mapping of the Galactic sky. In order to test the correlation, we construct randomized samples of VHE source positions starting from the inner Galactic plane survey sources detected by the \hess array.}{ We find hints of a positive correlation between positions of VHE sources and regions rich in molecular material, which in the best of cases reaches the 3.9$\sigma$ level. The latter confidence is however decreased if variations in the selection criteria are considered, what lead us to conclude that a positive correlation cannot be firmly established yet. Forthcoming VHE facilities will be needed in order to firmly establish the correlation.}{} | Most of the very-high energy (VHE; E$\gtrsim$100 GeV) sources were discovered in the last decade through a scan of the Galactic plane region by the High Energy Stereoscopic System (\hessns). In many cases, multiwavelength studies of the position of VHE emission allowed the classification of the source within a given class of known VHE emitters. Still, many sources are unidentified. It would seem that the Galactic VHE sources are in regions of the sky where the surrounding is rich in molecular material, but no correlation is established up to date. Such a relation would be expected in a scenario where the VHE emission has an hadronic origin: the accelerated cosmic rays (CRs, protons or heavier nuclei) interact with the surrounding material, leading to VHE emission through the decay of the produced $\pi^0$ \citep{ginzburg1964}. Such emission can be boosted by the presence of an enhancement of target material above the ISM contribution \citep[see e. g., ][]{w28hess}. Mass enhancements (or simply enhancements of the dust content) can also be associated with regions of high stellar activity, which are in turn associated with known or predicted VHE emitters, such as Pulsar Wind Nebulae (PWN), Supernova remnants (SNR), binaries or regions of massive-star formation. In the case of PWN, the VHE emission needs to take into account also the inverse Compton scattering (ICS) of the accelerated electrons off the thermal radiation associated to the dust \citep[e.g.,][]{JonMartin2012}. VHE emission has also been predicted to be produced in regions of massive-star formation, where apart from being obvious sites prone to the appearance of SNRs and other accelerators, the strong winds of the hot OB stars in the clusters form acceleration region at wind interaction zones. These regions are rich in molecular material and dust and are hence expected to be bright regions for the tracers that we consider here. The extreme cases in this sense are the ULIRGs and starburst galaxies \citep[e.g.,][]{voelkstarbust,diegostarburst,decea,lackistarburst}, some of which have also been established as high energy emitters both in GeV and TeV \citep{starb_lat,starb_hess}. Mass content is usually obtained trough well established tracers. The most commonly used is the intensity of the $^\textrm{12}$CO(1$\rightarrow$0) line at 115 GHz (2.6 mm), used as tracer of H2 \citep{dame_co}. However, if the gas is diffuse, the line cannot be excited and this method fails to trace all the mass content of the region. The gas in this phase is usually referred to as ``\textit{dark gas}'' and can be better studied through HE (E$\gtrsim$100 MeV) \gr emission or dust emission \citep{planckdark,planckdust}. In this work, we will use both the CO line and dust emission as tracers. Thanks to the increase of the VHE detections and the richness of data released by the Planck Collaboration \citep[see, e.g., ][]{planckco, planckdust}, it is possible to estimate quantitatively the possible correlation of the population of Galactic VHE sources with enhancements of the mass distribution. We do so next. | We studied the possible correlation of VHE emission and matter content enhancement in the inner Galactic region ($|l|<30^\circ$ and $|b|<2^\circ$). We constructed the probability distribution function of the number of positions in the inner galaxy associated with a mass enhancement. The value of surface density threshold to define enhancement is derived for the inner Galaxy distribution. The results for a representative subsample of the performed tests are summarized in Table \ref{tbl:results}. Independently from the tracer used to estimate the surface density, we conclude that a positive correlation cannot be firmly established yet. The number of sources discovered from the \hess galactic plane scan keeps on increasing with larger observation time and refined analysis. This study will benefit from a substantial increase of the number of sources, like the one we can expect from the Galactic plane scan with the forthcoming CTA array. | 14 | 3 | 1403.3271 |
1403 | 1403.1873_arXiv.txt | We discuss the recent Baryon Oscillation Spectroscopic Survey measurement of a rather high bias factor for the host galaxies/haloes of Damped Lyman-alpha Absorbers (DLAs), in the context of our previous modelling of the physical properties of DLAs within the $\Lambda$ cold dark matter paradigm. Joint modelling of the column density distribution, the velocity width distribution of associated low ionization metal absorption, and the bias parameter suggests that DLAs are hosted by galaxies with dark matter halo masses in the range $10 < \log M_v < 12$, with a rather sharp cutoff at the lower mass end, corresponding to virial velocities of $\sim 35 \kmsec$. The observed properties of DLAs appear to suggest efficient (stellar) feedback in haloes with masses/virial velocities below the cutoff and a large retained baryon fraction ($\ga 35 \%$) in haloes above the cutoff. | Lyman alpha (\lya), seen in absorption in the spectra of quasars, is the most sensitive method for detecting baryons at high redshift \citep[e.g.][]{1998ARA&A..36..267R}. \lya absorbers are classified according to their neutral hydrogen column density, \nhi. \lya forest absorbers have $\nhi < 10^{17} \cm$, making them optically thin to ionising radiation. Lyman limit systems (LLS) have $10^{17} \cm < \nhi < 10^{20.3} \cm$. Damped Lyman alpha absorbers (DLAs) are the highest column density systems, with $\nhi > 10^{20.3} \cm$ and have long been known to probe sightlines passing through the interstellar medium (ISM) of high-redshift galaxies \citep{2005ARA&A..43..861W}. Direct observations of the stellar emission of DLA host galaxies are made difficult by the overwhelmingly bright background QSO, meaning that their precise nature has remained controversial \citep{1997ApJ...487...73P,2000ApJ...536...36K, 2007A&A...468..587C,2012MNRAS.424L...1K}. Some consensus has been reached that the absorption cross-section-selected DLA host galaxies are generally less massive than typical spectroscopically confirmed emission-selected galaxies at the same redshift \citep{1999MNRAS.305..849F, 2000ApJ...534..594H,2001ApJ...559L...1S,2008ApJ...683..321F, 2008MNRAS.390.1349P,2013arXiv1308.2598B,2013arXiv1310.3317R}. The most important observational properties of DLAs can be summarised by their distribution of column density (\nhi), velocity width ($v_w$) from associated low ionization metal absorbers, metallicity, and redshift. These properties have proven challenging for models of DLAs to reproduce, especially the velocity width distribution of low ionization metal absorption. Many simulations which otherwise account very well for both DLA properties and for galaxy properties today struggle to produce enough large-velocity width DLAs \citep{2008ApJ...683..149R,2008MNRAS.390.1349P, 2009MNRAS.397..411T,2010arXiv1008.4242H}. The most comprehensive DLA survey to date comes from the Baryon Oscillation Spectroscopic Survey \citep[BOSS][]{2013AJ....145...10D}, which is part of the Sloan Digital Sky Survey III \citep[SDSS III][]{2011AJ....142...72E}. The full sample, based on SDSS Data Release 9, contains over 150,000 quasar spectra over the redshift range $2.15 < z < 3.5$ and has discovered 6,839 DLAs, which is an order of magnitude larger than SDSS II. In particular, BOSS has for the first time estimated the bias of DLA host galaxies $(b_{\rm DLA})$ with respect to the matter distribution by cross-correlating DLA absorption with \lya forest absorption \citep{2012JCAP...11..059F}. The surprisingly large value of $b_\ro{DLA} = (2.17 \pm 0.20) ~ \beta_F^{0.22}$, where $\beta_F \approx 1$ is the \lya forest distortion parameter, provides an important constraint on the distribution of the host halo masses of the DLA population. Figure \ref{fig:biasM} shows the bias of dark matter haloes as a function of halo mass, for a range of redshifts including the mean redshift of the BOSS bias data, $\langle z \rangle = 2.3$. The measured value of the DLA bias suggests a typical DLA halo mass of $\sim 10^{11.5} \Msol$, significantly larger than is found in many simulations \citep[e.g.][]{2008MNRAS.390.1349P, 2013arXiv1310.3317R}. \begin{figure} \centering \includegraphics[width=0.45\textwidth]{yy_bias_M.eps} \caption{The bias of dark matter haloes, calculated following \citet{2002MNRAS.329...61S} for a range of redshifts including the mean redshift of the BOSS bias data, $\langle z \rangle = 2.3$. The observed bias and its 1 $\sigma$ error are shown as a grey shaded region, suggesting a typical DLA mass scale of $\sim 10^{11.5} \Msol$.} \label{fig:biasM} \end{figure} In \citet{2009MNRAS.397..511B,2010MNRAS.403..870B} we proposed a simple model for DLAs that simultaneously accounts for their absorption properties, and also reproduces the emission properties of a population of very faint \lya emitters observed by \citet{2008ApJ...681..856R}. Here we revisit our model to see whether it can also account for the observed DLA bias. In Section \ref{s:DLAmodel} we describe our model for the DLA population. Section \ref{s:obs} compares our modelling to observations. Section \ref{s:metal} uses our model to place constraints on the mass-metallicity relation of DLAs, and compares this relation to the corresponding relation for luminosity-selected galaxies. In Section \ref{s:Discussion} we discuss our results and give our conclusions. | \label{s:Discussion} We have investigated whether our previous modelling of the physical properties of DLAs and faint \lya emitters can account for the bias parameter estimated by BOSS for DLAs at $z\sim 2.3$. We have found that a model in which the fraction of neutral hydrogen in DM haloes drops sharply below $\sim 35$ \kmsec reproduces the observed value of the DLA bias, in broad agreement with the properties of DLAs we derived from their \lya absorption and emission. As in \citet{2010MNRAS.403..870B}, our model puts DLAs in more massive host haloes than, for example, the numerical simulations of \citet{2008MNRAS.390.1349P}. This implies that stellar feedback in shallow potential wells is quite efficient at $z \ga 2.3$. \citet{2012JCAP...11..059F} parameterised the absorption cross-section of DLAs as a power law $\sigma_\ro{DLA} \propto M_v^\alpha$. They report that, \emph{if} they fix their minimum halo mass of a DLA at $10^9 \Msol$, their observed value for the DLA bias is best fit by $\alpha = 1.1 \pm 0.1$. At $z = 2.3$, $10^9 \Msol$ corresponds to $v_{\ro{v}} = 21 \kmsec$. Such a population of DLAs in small haloes may conflict with the observed distribution of DLA velocity width, as shown in Figure \ref{fig:vw}. \citet{2013arXiv1308.2598B} investigated the properties of DLAs in semi-analytics models of galaxy formation. They report that their favoured ``BRj25'' model produces a slope of $\alpha = 0.91$, which is closest to the slope reported by \citet{2012JCAP...11..059F}. However, their simulations were limited to haloes with masses $\ga 10^{9.7}$\Msol, and the predicted bias is very sensitive to the low-mass cutoff of the DLA cross-section. If we extrapolate their $\alpha = 0.91$ model to $10^9 \Msol$, the predicted bias is $\ga 2 \sigma$ below the observed value. Fixing the slope, the best fit low-mass cutoff is at $10^{10.3} \Msol$, which corresponds to a \emph{step-function} cutoff at $v_{\ro{v}} = 56 \kmsec$. The modelling of \citet{2012JCAP...11..059F} appears therefore to be consistent with our conclusion that some physical process needs to effectively remove or ionize gas in low mass haloes/shallow potential wells. We use our constrained model to investigate the DLA halo mass-metallicity relation, finding $[M/H]_\ro{mean} = (0.47 \pm 0.1) \log \left( M_v / 10^{11} \Msol \right) -1.34$, with no significant metallicity-velocity width relation at fixed halo mass. Comparison with the galaxy stellar mass-metallicity relation finds that DLAs are typically $\Delta \log(O/H) \sim 1$ more metal-poor than luminosity-selected galaxies at all masses. We interpret this effect as evidence that DLA sightlines probe the outer regions of less-evolved galaxies. Our modelling of DLA properties, updated to account for the large BOSS DLA bias parameter, suggests that stellar feedback in shallow potential wells is more efficient than realized in many current numerical galaxy formation models. Efficient feedback in such rather massive haloes appears also to be suggested by halo abundance matching analyses \citep{2013MNRAS.428.3121M,2013ApJ...762L..31B}. As many implementations of galactic winds in numerical simulations already struggle to be energetically viable, this adds to the growing consensus that either the physical mechanism behind driving galactic winds has not yet been correctly realized in numerical simulations of galaxy formation, or that other physical processes than efficient outflows are responsible for the rapidly decreasing stellar and \hi mass fraction in shallow potential wells. Further consolidation and extension of the redshift range of measurements of the bias of DLA host galaxies in combination with improved measurements of the velocity width distribution of the associated metal distribution based on larger samples should thus provide important bench marks for the modelling of stellar feedback in galaxy formation. | 14 | 3 | 1403.1873 |
1403 | 1403.0044_arXiv.txt | The estimation and utilization of photometric redshift probability density functions (photo-$z$ PDFs) has become increasingly important over the last few years and currently there exist a wide variety of algorithms to compute photo-$z$'s, each with their own strengths and weaknesses. In this paper, we present a novel and efficient Bayesian framework that combines the results from different photo-$z$ techniques into a more powerful and robust estimate by maximizing the information from the photometric data. To demonstrate this we use a supervised machine learning technique based on random forest, an unsupervised method based on self-organizing maps, and a standard template fitting method but can be easily extend to other existing techniques. We use data from the DEEP2 and the SDSS surveys to explore different methods for combining the predictions from these techniques. By using different performance metrics, we demonstrate that we can improve the accuracy of our final photo-$z$ estimate over the best input technique, that the fraction of outliers is reduced, and that the identification of outliers is significantly improved when we apply a Na\"{\i}ve Bayes Classifier to this combined information. Our more robust and accurate photo-$z$ PDFs will allow even more precise cosmological constraints to be made by using current and future photometric surveys. These improvements are crucial as we move to analyze photometric data that push to or even past the limits of the available training data, which will be the case with the Large Synoptic Survey Telescope. | Spectroscopic galaxy surveys have played an important role in understanding the origin, composition, and evolution of our Universe. Surveys like the Sloan Digital Sky Survey (SDSS;~\citealt{York2000}), WiggleZ~\citep{Drinkwater2010}, and BOSS~\citep{Dawson2013} have imposed important constraints on the allowed parameter values of the standard cosmological model ~\citep[\eg][]{Percival2010,Blake2011,Sanchez2013}. However, spectroscopic measurements are considerable more expensive to obtain than photometric data, they are more likely to suffer from selection effects, and they provide much smaller galaxy samples per unit telescope time. As a consequence, current ongoing and future galaxy surveys like the Dark Energy Survey (DES\footnote{http://www.darkenergysurvey.org/}) and the Large Synoptic Survey Telescope (LSST\footnote{http://www.lsst.org/lsst/}) are pure photometric surveys. These surveys will enable cosmological measurements on galaxy samples that are currently at least a hundred times larger than comparable spectroscopic samples, that have relatively simple and uniform selection functions, that extend to fainter flux limits and larger angular scales, thereby probing much larger cosmic volumes and will photometrically detect galaxies that are too faint to be spectroscopically observed. With the growth of these large photometric surveys, the estimation of galaxy redshifts by using multi band photometry has grown significantly over the last two decades. As a result, a variety of different algorithms for estimating \pz's based on statistical techniques have been developed ~\citep[see, \eg][for a review of current \pz techniques]{Hildebrandt2010,Abdalla2011,Sanchez2014}. Over the last several years, particular attention has been focused on techniques that compute a full probability density function (PDF) for each galaxy in the sample. A \pz PDF contains more information than a single \pz estimate, and the use of \pz PDFs has been shown to improve the accuracy of cosmological measurements ~\citep[\eg][]{Mandelbaum2008,Myers2009,Jee2013}. \PZ techniques can be broadly divided into two categories: spectral energy distribution (SED) fitting, and training based algorithms. Template fitting approaches \citep[see \eg][]{Benitez2000,Bolzonella2000,Feldmann2006,Ilbert2006,Assef2010} estimate \pzns s by finding the best match between the observed set of magnitudes or colors, and the synthetic magnitudes or colors taken from the suite of templates that are sampled across the expected redshift range of the photometric observations. This method is often preferred over empirical techniques as they can be applied without obtaining a high-quality spectroscopic training sample. However, these techniques do require a representative sample of template galaxy spectra, and they are not exempt from uncertainties due to measurement errors on the survey filter transmission curves, mismatches when fitting the observed magnitudes or colors to template SEDs, and color--redshift degeneracies. The use of training data that include known redshifts can also improve these predictions~\citep[\eg][]{Ilbert2006, Newman2013b}. On the other hand, machine learning methods have been shown to have similar or even better performance~\citep[\eg][]{Collister2004, CarrascoKind2013a} when the spectroscopic training sample is populated by representative galaxies from the photometric sample. Machine learning methods have the advantage that it is easier to include extra information, such as galaxy profiles, concentrations, or different modeled magnitudes within the algorithm. However, they are only reliable within the limits of the training data, and one must exercise sufficient caution when extrapolating these algorithms. These techniques can be sub-categorized into supervised and unsupervised machine learning approaches. For supervised techniques~\citep[\eg][]{Connolly1995,Brunner1997, Collister2004,Wadadekar2005,Ball2008,Lima2008,Freeman2009,Gerdes2010, CarrascoKind2013a}, the input attributes (e.g., magnitudes or colors) are provided along with the desired output (e.g., redshift). This training information is directly used by the algorithm during the learning process. In this case, the redshift information from the training set \textit{supervises} the learning process and decisions are made by using this information. On the other hand, unsupervised machine learning \pz techniques \citep[\eg][]{Geach2012,Way2012, CarrascoKind2014a} are less common as they do not use the desired output value (e.g., redshifts from the spectroscopic sample) during the training process. Only the input attributes are processed during the training, leaving aside the redshift information until the evaluation phase. Given the importance of these \pz PDFs, there is a present demand to compute them as efficiently and accurately as possible. Additional requirements include the need to understand the impact of systematics from the spectroscopic sample on the estimation of these PDFs~\citep[\eg][]{Oyaizu2008,Cunha2012a,Cunha2012b}, and to maximally reduce the fraction of catastrophic outliers~\citep[\eg][]{Gorecki2014}. Considerable effort has, therefore, been put into both the development of different techniques and the exploration of new approaches in order to maximize the efficacy of \pz PDF estimation. Yet, the combination of multiple, independent \pz PDF techniques has remained under explored~\citep[\eg][]{CarrascoKind2013b, Dahlen2013}. In this paper we extend our previous exploratory work in combining machine learning techniques with template fitting methods~\citep{CarrascoKind2013b} to explicitly address this issue by presenting a novel Bayesian framework to combine and fully exploit different \pz PDF techniques. In particular, we show that the combination of a standard template fitting technique with both a supervised and an unsupervised machine learning method can improve the overall accuracy over any individual method. We also demonstrate how this combined approach can both reduce the number of outliers and improve the identification of catastrophic outliers when compared to the individual techniques. Finally, we show that this methodology can be easily extended to include additional, independent techniques and that we can maximize the complex information contained within a photometric galaxy sample. This paper is organized as follows. In Section 2 we present the algorithms used in this work to generate the individual \pz PDF estimates and we provide a brief description on their individual functionality. We describe, in Section 3, the different Bayesian approaches by which different \pz techniques are combined. Section 4 introduces the data sets employed to test this Bayesian approach taken from the SDSS and DEEP2 surveys. In Section 5 we present the main results of our combination approach and compare these results to those from the individual \pz PDF methods. In Section 6 we discuss the application of a Na\"{\i}ve Bayes combination technique for outlier detection. In Section 7 we conclude with a summary of our main points and a more general discussion of this new approach. | We have presented and analyzed different techniques for combining \pz PDF estimations on galaxy samples from the DEEP2 and SDSS projects. In particular, we use three independent \pz PDF estimation methods: \tpzns, a supervised machine learning technique based on prediction trees and a random forest; \somzns, an unsupervised machine learning approach based on self organizing maps and a random atlas; and \bpzns, a standard template-fitting method that we have slightly modified to parallelize the implementation. Both \tpz and \somz are currently available within a new software package entitled \texttt{MLZ}\footnote{http://lcdm.astro.illinois.edu/code/mlz.html}. We developed seven different combination methods that employ ensemble learning with cross-validation data to maximize the information extracted. Of these seven methods, four employ a weighted average where the weights can either be selected to be uniform across the input methods, to be determined from the shape of the \pz PDF (e.g., by using the $zConf$ parameter), to be determined by an \textit{oracle} estimator where one (ideally the best) method is preferentially selected, and where the weights are obtained by a fitting procedure applied to the OOB data. Three of the combination methods were Bayesian techniques: Bayesian Model Averaging (BMA), Bayesian Model Combination (BMC), and Hierarchical Bayes (HB). We expect the individual \pz PDF estimation techniques to perform differently across the parameter space spanned by our galaxy samples; for example, template-fitting techniques are expected to work better at higher redshifts than machine learning methods, which perform optimally when provided high-quality, representative training data. Thus we construct a two-dimensional, $10 \times 10$ self-organizing map (SOM) to subdivide the high-dimensional parameter space occupied by the galaxy samples. We apply different \pz PDF estimation techniques within each cell in this map, since each cell should contain galaxies with similar properties. A visual inspection of these maps indicates that the two machine learning methods: \tpz and \somz are generally complementary, and that in combination with a model based technique such as \bpz we are able to maximize the coverage of this multidimensional space efficiently. We also verified that by using the OOB data, as introduced in CB13, we can an obtain an accurate, unbiased and \textit{honest} estimation of the performance of a \pz PDF estimation technique on the test data. We also computed the correlation coefficient and the error distribution and showed they also behave similarly for the cross-validation (\ie the OOB data) and the test data. These computations are extremely important when combining \pz PDF techniques as we can learn from the OOB data the optimal parameters needed for a specific ensemble learning approach, and thereby maximize the performance of that combination technique when applied to \textit{blind} test data. Overall, we found that the BMA and BMC are the best \pz PDF combination techniques as they have better performance metrics when compared to the individual \pz PDF estimation techniques, especially when unbiased cross-validation data is available. This result is true for both the DEEP2 and the SDSS data. When OOB data is not available, we can instead use the $zConf$ parameter as a weight for each method after first renormalizing the individual \pz PDFs. We can also use the Hierarchical Bayes method to combine these predictions, which we demonstrated can also lead to better results. Within this Bayesian Framework, we also developed a novel, Na\"{\i}ve Bayesian Classifier (NBC) that efficiently identifies outliers within the galaxy sample. The approach we present gathers all available information from the different \pz PDF estimation techniques regarding the shape of the PDF, the location of the mean and mode, and the magnitudes and colors, which are all \textit{naively} assumed to be independent, in order to compute a Bayesian posterior probability that a certain galaxy is an outlier. The distribution of these probabilities for an entire galaxy sample indicate that this is a very powerful method to separate outliers from inliers (\ie \textit{good} galaxies), and we further demonstrated that this approach can produce a more accurate and cleaner sample of galaxies than competing techniques, such as the use of the $zConf$ parameter. An important takeaway point is that all information provided by the catalogs and the \pz PDF methods, no matter how redundant the information might appear, helps in building this discriminant probability. Given the probabilistic nature of this computation, the final application of this technique can be chosen to maximize the scientific utility of the resulting galaxy data for a specific application. The computational cost to apply these Bayesian models to galaxy samples will depend directly on the size of the data set, the number of \pz estimation techniques used, and the resolution of the given \pz PDFs. In~\cite{CarrascoKind2014b} we demonstrate how a sparse basis representation can reduce the storage significantly and that manipulation of these PDFs can be improved within the bases framework thereby reducing computational costs. We plan to adopt this representation framework to compute the combination models, which will allow fast and accurate combination of multiple \pz PDFs. Finally, we have demonstrated that even when a \pz PDF technique is very accurate, we can still make improvements by extracting additional information about the distribution of galaxies in the higher dimensional parameter space and the individual performance of the \pz PDF algorithms. There are currently a large number of published algorithms to compute \pz's, many of which also compute \pz PDFs. Even if their performance is similar, these techniques will all have their own advantages and disadvantages. Thus we believe the combination of different techniques is the future of \pz research, and we expect additional research to be forthcoming in this area. Overall, the combination of \pz PDFs is a powerful, new approach that can be easily extended to incorporate new techniques in order to generate a meta-predictor that accelerate our knowledge and understanding of the Universe. | 14 | 3 | 1403.0044 |
1403 | 1403.7949_arXiv.txt | In this paper we demonstrate an efficient method for including both CMB temperature and polarisation data in optimal non-Gaussian estimators. The method relies on orthogonalising the multipoles of the temperature and polarisation maps and results in a reduction by a factor of over 3 the terms required to calculate the estimator. The method is illustrated with the modal method applied to bispectrum estimation via the CMB with the trispectrum included as an appendix. However, the method is quite general and can be applied to any optimal bispectrum or trispectrum estimator including the KSW, binned and wavelet approaches. It would also be applicable to any situation where multiple data sets with known correlations are being considered. | The paradigm of slow-roll single field inflation is now strongly favoured due to the recent results obtained by Planck \cite{1303.5082} and BICEP \cite{1403.3985}. One of the most promising areas to search for deviations from this standard model is through non-Gaussianities of the primordial density perturbation. If detected, the form the non-Gaussianity took would point to specific mechanisms at play during inflation (see reviews \cite{1001.4707,1002.1416,1003.6097,1006.0275}). The recent Planck papers contained the strongest constraints on non-Gaussianity that currently exist \cite{1303.5084}. No deviations from a Gaussian spectrum were found except some weak hints for oscillatory-type models. As the temperature data is almost cosmic variance limited, for these constraints to be improved we need additional data sets. In the future large scale structure may provide stronger constraints (see, for example, \cite{1206.1225}) but various theoretical and observational challenges remain before LSS becomes competitive with the CMB. The easiest additional data set to include is the polarisation of the CMB. This has been measured by the current Planck satellite and will likely be part of the next release. Hence the question of how to include polarisation data into current methods in an efficient manner is a pressing question. Here we present an approach which greatly simplifies the complexity of the equations required for constraining non-Gaussianity via the bispectrum and trispectrum. The method is general to any optimal bi- or tri-spectrum estimator however we use the modal estimator as an illustrative example. We begin by reviewing some basic equations for the CMB bispectrum which provide the starting point for our discussion. The primordial and CMB bispectrum are defined from the three-point correlators of the primordial density perturbation, $\Phi$, and the CMB multipoles, $a^X_{lm}$, respectively. For the CMB the superscript $X$ can be one of ($T$,$E$) denoting whether the multipoles were derived from temperature or E-mode polarisation CMB maps. Statistical isotropy demands that the primordial bispectrum has no angular dependence which translates to the CMB bispectrum having no $m$ dependence. Momentum conservation demands the three $\bk$ vectors form a triangle and this is enforced via a delta function. This leads to the following expressions: \begin{align} \< \Phi(\bk_1) \Phi(\bk_2) \Phi(\bk_3)\> &= \(2\pi\)^3\delta(\bk_1+\bk_2+\bk_3) B(k_1,k_2,k_3)\,,\\ \< a^{X_1}_{\ell_1 m_1} a^{X_2}_{\ell_2 m_2} a^{X_3}_{\ell_3 m_3} \> &= \curl{G}^{\ell_1 \ell_2 \ell_3}_{m_1 m_2 m_3} b^{X_1X_2X_3}_{\ell_1 \ell_2 \ell_3}\,, \end{align} and $\curl{G}$ is the Gaunt integral, which is the projection of the angular part of the primordial delta function, and is defined as follows \begin{align} \nonumber\curl{G}^{\ell_1 \ell_2 \ell_3}_{m_1 m_2 m_3} &= \int d\Omega_{\un} Y_{\ell_1 m_1 }(\un) Y_{\ell_2 m_2 }(\un) Y_{\ell_3 m_3 }(\un) = \(\begin{array}{ccc}\ell_1 & \ell_2 & \ell_3 \\ m_1 & m_2 & m_3 \end{array}\) h_{\ell_1 \ell_2 \ell_3}\,, \\ h_{\ell_1 \ell_2 \ell_3} &= \sqrt{\frac{(2\ell_1+1)(2\ell_2+1)(2\ell_3+1)}{4\pi}}\(\begin{array}{ccc}\ell_1 & \ell_2 & \ell_3 \\ 0 & 0 & 0 \end{array}\)\,. \end{align} If we wish to constrain the amplitude of the bispectrum from the CMB we need to construct an estimator. The simplest form was written down and shown to be optimal in \cite{0503375}. A linear term was added in \cite{0509029} to restore optimality in the presence on anisotropic noise and sky cuts. This estimator was then extended to include polarisation in \cite{0701921,0711.4933}. In its most general form the estimator is \begin{align}\label{eq:estimator} \nonumber \curl{E} &= \frac{1}{N}\sum_{X^{\phantom{'}}_i X'_i}\sum_{\ell^{\phantom{'}}_i \ell'_i m^{\phantom{'}}_i m'_i} \curl{G}^{\ell^{\phantom{'}}_1 \ell^{\phantom{'}}_2 \ell^{\phantom{'}}_3}_{m^{\phantom{'}}_1 m^{\phantom{'}}_2 m^{\phantom{'}}_3} b^{X^{\phantom{'}}_1X^{\phantom{'}}_2X^{\phantom{'}}_3}_{\ell^{\phantom{'}}_1 \ell^{\phantom{'}}_2 \ell^{\phantom{'}}_3} (C^{-1})^{X^{\phantom{'}}_1X'_1}_{\ell^{\phantom{'}}_1\ell'_1m^{\phantom{'}}_1m'_1} (C^{-1})^{X^{\phantom{'}}_2X'_2}_{\ell^{\phantom{'}}_2\ell'_2m^{\phantom{'}}_2m'_2} (C^{-1})^{X^{\phantom{'}}_3X'_3}_{\ell^{\phantom{'}}_3 \ell'_3 m^{\phantom{'}}_3 m'_3}\\ &\times \(a^{X'_1}_{\ell'_1 m'_1} a^{X'_2}_{\ell'_2 m'_2} a^{X'_3}_{\ell'_3 m'_3} - \<a^{X'_1}_{\ell'_1 m'_1} a^{X'_2}_{\ell'_2 m'_2}\> a^{X'_3}_{\ell'_3 m'_3} - \<a^{X'_2}_{\ell'_2 m'_2} a^{X'_3}_{\ell'_3 m'_3}\> a^{X'_1}_{\ell'_1 m'_1} - \<a^{X'_1}_{\ell'_1 m'_1} a^{X'_3}_{\ell'_3 m'_3}\> a^{X'_2}_{\ell'_2 m'_2}\)\,, \end{align} where the normalisation, $N$, is defined by \begin{align}\label{eq:norm} N \equiv \sum_{X^{\phantom{'}}_i X'_i}\sum_{\ell^{\phantom{'}}_i\ell'_i}\curl{G}^{\ell^{\phantom{'}}_1 \ell^{\phantom{'}}_2 \ell^{\phantom{'}}_3}_{m^{\phantom{'}}_1 m^{\phantom{'}}_2 m^{\phantom{'}}_3} b^{X^{\phantom{'}}_1 X^{\phantom{'}}_2 X^{\phantom{'}}_3}_{\ell^{\phantom{'}}_1 \ell^{\phantom{'}}_2 \ell^{\phantom{'}}_3} (C^{-1})^{X^{\phantom{'}}_1X'_1}_{\ell^{\phantom{'}}_1\ell'_1m^{\phantom{'}}_1m'_1} (C^{-1})^{X^{\phantom{'}}_2X'_2}_{\ell^{\phantom{'}}_2\ell'_2m^{\phantom{'}}_2m'_2} (C^{-1})^{X^{\phantom{'}}_3X'_3}_{\ell^{\phantom{'}}_3\ell'_3m^{\phantom{'}}_3m'_3} \curl{G}^{\ell'_1 \ell'_2 \ell'_3}_{m'_1 m'_2 m'_3} b^{X'_1 X'_2 X'_3}_{\ell'_1 \ell'_2 \ell'_3}\,, \end{align} and $(C^{-1})^{XX'}_{\ell \ell' m m'}$ is the $XX'$ element of the inverse of the covariance matrix for the $a^X_{lm}$ \begin{align}\label{eq:covariance} \(\begin{array}{cc} C^{TT}_{\ell \ell' m m'} & C^{TE}_{\ell \ell' m m'} \\ C^{TE}_{\ell \ell' m m'} & C^{EE}_{\ell \ell' m m'} \,. \end{array}\)^{-1} \end{align} The normalisation is related to the Fisher matrix by $N = 6F$. We can relate the primordial and CMB bispectra by a convolution \begin{align}\label{eq:projection} b^{X_1X_2X_3}_{\ell_1 \ell_2 \ell_3} = \(\frac{2}{\pi}\)^3\int_{\curl{V}_k} \(k_1 k_2 k_3\)^2 B(\klist) \D^{X_1 X_2 X_3}_{\ell_1 \ell_2 \ell_3}(k_1,k_2,k_3) d\curl{V}_k\,, \end{align} where $d\curl{V}_k$ is the region of k space allowed by the triangle condition and we have defined the bispectrum transfer function $\D^{X_1 X_2 X_3}_{\ell_1 \ell_2 \ell_3}$ to be \begin{align} \D^{X_1 X_2 X_3}_{\ell_1 \ell_2 \ell_3}(k_1,k_2,k_3) \equiv \D^{X_1}_{\ell_1}(k_1) \D^{X_2}_{\ell_2}(k_2) \D^{X_3}_{\ell_3}(k_3) \int x^2 dx j_{\ell_1}(xk_1) j_{\ell_2}(xk_2) j_{\ell_3}(xk_3)\,. \end{align} where the $\D_l$ are the radiation transfer functions as produced by CMB anisotropy codes such as CAMB \cite{0205436}. The integral over the spherical Bessel functions $j_l$ is a geometric factor from the projection of the radial part of the primordial delta function. The above equations, while seemingly simple, are impossible to evaluate in general (excepting very small $l_{max}$). The convolution to calculate a single $\ell$-triple of $b_{\ell_1 \ell_2 \ell_3}$ requires a 4D integration and there are in general $\ell^3/2$ triples to calculate. Also the estimator requires a sum over $\ell^{11}$ terms, which reduces to $\ell^5$ if we assume the covariance matrices are diagonal. This is beyond current computational resources. Fortunately the equations simplify greatly if we consider primordial bispectra which are separable. This fact was exploited, in multiple ways relating to different choices of separable functions to filter the data with, in the recent Planck experiment to obtain constraints on a wide variety of primordial \cite{1303.5084} and late time models \cite{1303.5079, 1303.5085}. The methods fall into 4 main categories, KSW-type \cite{0302223, 0305189}, Binned \cite{0911.1642}, Modal \cite{0612713,0912.5516} and Wavelet \cite{9808.3987,0111284,0211399} approaches. Each approach has its own particular advantages and disadvantages which are briefly discussed later on. Non-Gaussianity can also be constrained with other estimators, like Minkowski functionals \cite{0302223,0401276}, but these are suboptimal and so the method we describe in this paper is not applicable to them. In the following section we will review the temperature-only modal approach as used by Planck before demonstraiting a novel method for including polarisation in the subsequent section which comprises the focus of this paper. The choice of the modal approach is for illustration only and the method could be applied equally to any of the other methods. This method is also applicable in the case of trispectrum estimation and the extension to it is included as an appendix. | Here we have presented a simple way to rewrite the optimal estimator for the bispectrum with temperature and polarisation CMB data. The new form significantly reduces the number of calculations required. In the simplest case, where we consider the bispectrum with just $T$ and $E$, the number of terms in the estimator is reduces by over a factor of three or by over four for the trispectrum. The method was illustrated using the modal method but is applicable to any optimal approach including KSW, binned and wavelet methods. In addition to the great simplification of the equations this method also allows us calculate the correct signal-to-noise weight for each term. This ensures that the convergence of the decompositions required for the modal, binned and wavelet methods is optimised. The method has a straight-forward extension to higher order correlators like the trispectrum. It would also apply more generally to any situation where we need to consider multiple data sets with known correlations. One possible example would be calculating the galaxy bispectrum with multiple redshift bins. It also presents a simple method for producing non-Gaussian simulations for any given model. The method is currently being implemented for the modal method and will be applied to the Planck data with results appearing at the end of the year. | 14 | 3 | 1403.7949 |
1403 | 1403.0758_arXiv.txt | { We present a sample of 383 X-ray selected galaxy groups and clusters with spectroscopic redshift measurements (up to $z \sim 0.79$) from the 2XMMi/SDSS Galaxy Cluster Survey. The X-ray cluster candidates were selected as serendipitously detected sources from the 2XMMi-DR3 catalogue that were located in the footprint of the Sloan Digital Sky Survey (SDSS-DR7). The cluster galaxies with available spectroscopic redshifts were selected from the SDSS-DR10. We developed an algorithm for identifying the cluster candidates that are associated with spectroscopically targeted luminous red galaxies and for constraining the cluster spectroscopic redshift. A cross-correlation of the constructed cluster sample with published optically selected cluster catalogues yielded 264 systems with available redshifts. The present redshift measurements are consistent with the published values. The current cluster sample extends the optically confirmed cluster sample from our cluster survey by 67 objects. Moreover, it provides spectroscopic confirmation for 78 clusters among our published cluster sample, which previously had only photometric redshifts. Of the new cluster sample that comprises 67 systems, 55 objects are newly X-ray discovered clusters and 52 systems are sources newly discovered as galaxy clusters in optical and X-ray wavelengths. Based on the measured redshifts and the fluxes given in the 2XMMi-DR3 catalogue, we estimated the X-ray luminosities and masses of the cluster sample. } | Galaxy clusters are the largest gravitationally bound objects in the Universe. They have been formed from the densest regions in the large-scale matter distribution of the Universe and have collapsed to form their own proper equilibrium structure. Their form can be well assessed by observations and well described by theoretical modelling \citep[e.g.][]{Sarazin88, Bahcall88, Voit05, Boehringer06, Ota12}. X-ray and optical observations show that galaxy clusters are clearly defined connected structural entities, where the diffuse X-ray emission from the hot intracluster medium (ICM) trace the whole structure of the cluster. They are excellent giant laboratory sites for several astrophysical studies, for example, investigating galaxy evolution in their dense environments \citep[e.g.][]{Dressler80, Goto03}, evolution of the dynamical and thermal structure \citep[e.g.][]{Balestra07, Maughan08, Anderson09}, chemical enrichment of the intracluster medium \citep[e.g.][]{Cora06, Heath07}, studying lensed high-redshift background galaxies \citep[e.g.][]{Metcalfe03, Santos04, Bartelmann10}, and investigating the evolution of the Universe to test the cosmological models \citep[e.g.][]{Rosati02, Reiprich02, Voit05, Vikhlinin09a, Allen11}. Owing to the multi-component nature of galaxy clusters, they can be observed and identified through multiple observable signals across the electromagnetic spectrum. Tens of thousands of galaxy clusters have been identified by detecting their galaxies in the optical and near-infrared (NIR) bands \citep[e.g.][]{Abell58, Abell89, Zwicky61, Gladders05, Merchan05, Koester07, Wen09, Hao10, Szabo11, Geach11, Durret11, Wen12, Gettings12, Rykoff13}. Recently, several galaxy cluster surveys have been conducted at mm wavelengths using the Sunyaev-Zeldovich (SZ) effect based on observations made by several instruments, for example, the Atacama Cosmology Telescope \citep[ACT,][] {Hasselfield13}, the South Pole Telescope \citep[SPT,][]{Reichardt13}, and the Planck Satellite \citep[][]{Planck13}. These surveys have provided cluster samples that contain several hundreds of SZ-selected clusters. X-ray cluster surveys provide pure and complete cluster catalogues, in addition, their X-ray observables correlate tightly with masses of clusters \citep[e.g.][]{Allen11}. Several hundreds of galaxy clusters were detected in X-rays based on previous X-ray missions mainly from ROSAT data \citep[e.g.][]{Ebeling98, Boehringer04, Reiprich02, Ebeling10, Rosati98, Burenin07}. The current X-ray telescopes (XMM-Newton, Chandra, Swift/X-ray) provide contiguous cluster surveys for small areas \citep[e.g.][]{Finoguenov07, Finoguenov10, Adami11,Suhada12}, in addition to serendipitous cluster surveys \citep[e.g.][]{Barkhouse06, Kolokotronis06, Lamer08, Fassbender11, Takey11, Mehrtens12, Clerc12, Tundo12, de-Hoon13, Takey13}. So far, these surveys have provided a substantial cluster sample of several hundreds up to a redshift of 1.57. We have conducted a systematic search for X-ray detected galaxy clusters based on XMM-Newton fields that are located in the footprint of the SDSS-DR7. The catalogue of serendipitously detected sources (extended) in XMM-Newton EPIC images was the basic database from which we selected a list of X-ray cluster candidates, comprising 1180 objects. The main goal of the survey is to construct a large catalogue of newly discovered X-ray emitting groups and clusters. Due to the higher sensitivity of XMM-Newton the compiled cluster sample extends ROSAT cluster samples to fainter X-ray fluxes. The sample, which comprised galaxy groups and clusters, allows us to investigate the evolution of X-ray scaling relations as well as the correlation between the X-ray and optical properties. Other long-term goals of the survey are the selection of distant clusters beyond the SDSS detection limit and, in general terms, the preparation for the eROSITA mission, which will uncover a similar cluster population as in our survey. The main way to obtain the cluster redshifts is based on the optical data. This can be achieved by either cross-matching the X-ray cluster candidates with the available optically selected galaxy cluster catalogues in the literature or by measuring the cluster photometric redshifts based on galaxy redshifts given in the SDSS catalogues. Using these two methods, we were able to establish an optically confirmed cluster sample comprising 530 groups/clusters with redshift measurements. From these optically confirmed groups/clusters with redshift measurements, we derived their X-ray luminosities and temperatures and investigated the X-ray luminosity-temperature relation. The selection criteria of the X-ray cluster candidates and redshift measurements as well as the X-ray properties of the optically confirmed sample were described in more detail by \citet[][Paper I, Paper II, hereafter]{Takey11, Takey13}. In this work, we compile a sample of X-ray detected galaxy clusters among the X-ray cluster candidate list that are associated with luminous red galaxies (LRGs), which have spectroscopic redshift measurements out to 0.8 in the SDSS-DR10. We present the procedure we used for constructing this cluster sample that is spectroscopically confirmed and for measuring their redshifts. We also present estimates of X-ray bolometric luminosity and luminosity-based mass at $R_{500}$ (the radius at which the cluster mean density is 500 times the critical density of the Universe at the cluster redshift) of the cluster sample. The compiled cluster sample can be used to investigate various relations among the cluster physical properties, for example, the correlations between the properties of the BCG and its hosting cluster. By measuring the X-ray temperature of the cluster sample, one can extend the \ltr relation in Paper II to slightly higher redshifts. Moreover, the cluster sample is expected to permit studies of the relations between the cluster optical properties (richness and luminosity) and the cluster X-ray properties (X-ray temperature, luminosity, and mass). These correlations will be discussed in an upcoming paper. The article is organized as follows: Section 2 gives a short overview on the selection procedure of the X-ray cluster candidates. In Section 3, we describe the construction of the cluster sample associated with LRGs and their redshift measurements. The X-ray parameters of the cluster sample are presented in Section 4. The summary of the paper is presented in Section 5. Throughout this paper, we used the cosmological parameters $\Omega_{\rm M}=0.3$, $\Omega_{\Lambda}=0.7$ and $H_0=70$\ km\ s$^{-1}$\ Mpc$^{-1}$. | We presented a sample of 383 X-ray selected galaxy groups and clusters associated with at least one LRG, which has a spectroscopic redshift in the SDSS-DR10. The redshifts of the associated LRGs were used to identify BCGs and other cluster galaxies with spectroscopic redshifts. The cluster spectroscopic redshift was computed as the weighted average of the available spectroscopic redshifts of the cluster galaxies within 500 kpc from the X-ray emission peak. The cluster sample spans a wide redshift range of $0.05 \le z \le 0.79$ with a median of $z = 0.34$. Of the cluster sample, 264 are previously known as optically selected galaxy clusters. In addition to re-identifying and confirming the redshift estimates of 316 clusters in common with the published cluster sample from our survey, we extended the optically confirmed cluster sample by 67 objects. Of this new sample that comprises 67 systems, about 75 percent are newly discovered groups and clusters, and about 80 percent are new X-ray detected clusters. Comparing the BCGs of the cluster sample with the colour and magnitude cuts of LRGs in the BOSS survey yielded that 92 percent of the BCGs are considered LRGs. However, this percentage is dependent on the selection of the spectroscopically targeted LRGs in SDSS as well as on the current cluster identification procedure. The measured redshift and the X-ray flux in 0.5-2.0 keV given in the 2XMMi-DR3 catalogue were used to determine the X-ray luminosity in 0.5-2.0 keV of the cluster sample. We converted the X-ray luminosity in 0.5-2.0 keV into bolometric luminosity $L_{500}$ based on the available properties of the published cluster sample with X-ray spectroscopic parameters from our survey. This conversion yielded a scaling relation, which could be used to derive bolometric $L_{500}$ from the luminosity (0.5-2.0 keV) that is computed based on the $\beta$ model flux (0.5-2.0 keV) given in the 2XMMi-DR3 catalogue. We also derived X-ray-luminosity-based masses of the cluster sample based on published scaling relation in the literature. Comparing the current estimates of the X-ray bolometric luminosity, $L_{500}$, with the available values from the XCS project, we found a good agreement between the two measurements. The distribution of X-ray luminosities of our cluster sample and ROSAT clusters with redshifts showed that we detected less-luminous groups and clusters at each redshift interval, and added a few tens of clusters at high redshifts. | 14 | 3 | 1403.0758 |
1403 | 1403.5661_arXiv.txt | Recent released Planck data and other astronomical observations show that the universe may be anisotropic on large scales. Inspired by this, anisotropic cosmological models have been proposed. We note that the Finsler-Randers spacetime provides an appropriate framework for the anisotropic cosmology. By adding an arbitrary 1-form to the Friedmann-Robertson-Walker (FRW) line element, a privileged axis in the universe is picked out. The distance-redshift relation is modified to be direction-dependent. We wish that the anisotropic cosmological model may be tested crossly by independent observations. Type-Ia supernovae (SNe Ia) calibrated from four different light curve fitters are used to constrain possible anisotropy of the universe. The magnitudes of anisotropy are all between 2\% \--- 5\%, but the systematic uncertainty cannot be excluded. The directions of privileged axis seem to differ from each other. The statistical significance is not high enough to make a convincing conclusion. Nevertheless, the $1\sigma$ contours in the $(l,b)$ plane obtained from four groups of SNe Ia have an overlap, centering at $(l,b)\approx (170^{\circ},0^{\circ})$. Monte Carlo simulation shows that the anisotropy is unlikely to be caused by selection effect. | The ${\rm \Lambda}$CDM model is well known as the standard model of modern cosmology. It is based on the fundamental assumption called cosmological principle, which states that the universe is homogeneous and isotropic at large scales. The general geometric structure of the universe can be described by the spherically symmetric Friedmann-Robertson-Walker (FRW) metric. The ${\rm \Lambda}$CDM model is well consistent with the seven-year WMAP observations \cite{Spergel:2007hy,Komatsu:2011fb} and the recent released Planck 2013 results \cite{Ade:2013ktc,Ade:2013nlj}. The tiny fluctuation of cosmic microwave background (CMB) radiation implies that the cosmological principle is an excellent approximation \cite{Smith:2009jr}. However, recent observations show that the universe may be deviated from isotropy. For example, the large-scale bulk flow \cite{Kashlinsky:2009ut,Watkins:2009hf,Lavaux:2010th}, the alignments of low multipoles in CMB angular power spectrum \cite{Lineweaver:1996xa,Tegmark:2003,Bielewicz:2004en,Copi:2010,Frommert:2010qw}, the large-scale alignments of the quasar polarization vectors \cite{Hutsemekers:2005iz,Hutsemekers:2008iv}, the spatial variation of fine-structure constant \cite{Dzuba:1999,Murphy:2001,Murphy:2003,King:2012}, the CMB hemispherical asymmetry observed by WMAP \cite{Bennett:2011,Bennett:2012zja} and Planck satellite \cite{Ade:2013nlj}. Type-Ia supernovae (SNe Ia) are widely used as the standard candle to test possible anisotropy of the universe. Schwarz \& Weinhorst \cite{Schwarz:2007wf} used four groups of SNe Ia with redshift $z<0.2$ to test the isotropy of the Hubble diagram, and found a maximal hemispheric asymmetry towards a direction close to the equatorial poles. Using the hemisphere comparison method, Antoniou \& Perivolaropoulos \cite{Antoniou:2010} found that the highest expansion direction of the universe points towards $(l,b)=(309^{\circ}\,^{+23^{\circ}}_{-03^{\circ}}, 18^{\circ}\,^{+11^{\circ}}_{-10^{\circ}})$ in the Union2 compilation. The maximum anisotropy level is about $\Delta\Omega_M/\Omega_M\approx 0.43\pm 0.06$. Using the same method and dataset, Cai \& Tuo \cite{CaiTuo:2012} found that the maximum accelerating expansion direction points to $(l,b)=(314^{\circ}\,^{+20^{\circ}}_{-13^{\circ}}, 28^{\circ}\,^{+11^{\circ}}_{-33^{\circ}})$, and the maximum anisotropy is at the order of magnitude $\Delta q_0/q_0\approx 0.79^{+0.27}_{-0.28}$. Kalus et al. \cite{kalus:2013} tested the anisotropy of local universe using low-redshift ($z<0.2$) SNe Ia calibrated from four different light curve fitters. The highest expansion rate is found to be in the direction $(l, b)\approx (325^{\circ}, -19^{\circ})$\footnote{In the original paper of Kalus et al., the authors used the convention that the galactic longitude $l$ is from $-180^{\circ}$ to $+180^{\circ}$. In order to make the comparison easier, we convert it to the range $l\in[0^{\circ},360^{\circ}]$.}, and the magnitude of Hubble anisotropy is about $\Delta H/H\approx 0.026$. Zhao et al. \cite{Zhao:2013yaa} studied the anisotropy of cosmic acceleration by dividing the Union2 dataset into 12 subsets according to their positions, and found a significant dipole effect in the $q_0$-maps. The direction of this dipole is nearly perpendicular to the CMB kinematic dipole. The redshift of SNe Ia is usually no more than 2. As a supplementary to SNe Ia, gamma-ray bursts (GRBs) are also used by some authors to test anisotropy of the universe \cite{Cai:2013lja}. However, there are many controversies in calibrating GRBs data. The systematic uncertainty of GRBs is much larger than that of SNe Ia. In the theoretical aspect, some anisotropic cosmological models have been studied \cite{Mimoso:1993,Kumar:2011ui,Verma:2011,Singh:2012}. We note that the Finsler-Randers spacetime \cite{Randers:1941,Li:2010,Li:2012,Chang:2013} provides an appropriate framework for the anisotropic cosmology. The line element in Finsler-Randers spacetime can be described by the FRW line element with an extra 1-form \cite{Chang:2013}. This 1-form picks out a privileged axis so that the universe becomes axis-symmetric. The luminosity distance depends on not only the redshift, but also the direction. A direct fit to the Union2 dataset shows that the magnitude of anisotropy is about $D\approx 0.03\pm 0.03$, and the privileged axis points towards $(l,b)=(304^{\circ}\pm 43^{\circ},-27^{\circ}\pm 13^{\circ})$ in galactic coordinate system (GCS) \cite{Chang:2013}. This axis is close to the direction of highest expansion of the universe found by Kalus et al. \cite{kalus:2013}. Nevertheless, The statistical significance of this result is too low to be conclusive. The anisotropic magnitude is small enough such that the ${\rm \Lambda}$CDM model is still a good approximation. We cannot make a convincing conclusion from only one dataset. Anisotropy may come from systematic uncertainty, as well as the intrinsic property of the universe. In this paper, we use different datasets published by literatures to constrain possible anisotropy of the universe. If the privileged axes derived from different datasets are close to each other, we can safely conclude that anisotropy is an intrinsic property of the universe. Otherwise, systematic uncertainty may dominate. The rest of the paper is arranged as follows: In section \ref{sec:model}, we briefly introduce the anisotropic cosmological model in the Finsler-Randers spacetime. In section \ref{sec:numerical}, SNe Ia data calibrated from four different light curve fitters are used to constrain the model parameters. We first fit the data of each group independently. Then, the intersection of four groups is picked out to fit the model. Finally, we re-analyze the data by restricting the redshift to $z<0.2$. In section \ref{sec:MCsimulation}, Monte Carlo simulation is performed to rule out the selection effect. Discussions and conclusions are given in section \ref{sec:conclusions}. | \label{sec:conclusions} Recent observations on large-scale structure of the universe imply that the cosmos may be anisotropic. As an intrinsically anisotropic geometry, the Finsler geometry provides us an ideal framework to describe the anisotropic universe. An anisotropic cosmological model was proposed in the background of the Finsler-Randers spacetime. An arbitrary 1-form adding to the FRW line element picks out a privileged axis in the universe, such that the universe becomes axis-symmetric. Giving some assumptions to the 1-form, the distance-luminosity relation was modified to be direction-dependent. SNe Ia data calibrated from four different light curve fitters were used to test possible anisotropy of the universe. The anisotropy constrained from four groups is found to be at the same order of magnitude, while the directions of privileged axis differ from each other. The statistical uncertainty is too large to make a convincing conclusion. Picking out the intersection of four groups does not significantly improve the results. Interestingly, the $1\sigma$ contours in the $(l,b)$ plane obtained from four groups overlap with each other, centering at $(l,b)\approx (170^{\circ},0^{\circ})$. This direction is approximately in the galactic plane. Monte Carlo simulation excludes the selection effect. | 14 | 3 | 1403.5661 |
1403 | 1403.7208_arXiv.txt | We have developed a maximum-likelihood procedure to fit theoretical isochrones to the observed cluster color-magnitude diagrams of NGC 6866, an open cluster in the Kepler Spacecraft field of view. The Markov-Chain Monte Carlo algorithm permits exploration of the entire parameter space of a set of isochrones to find both the best solution and the statistical uncertainties. For clusters in the age range of NGC 6866, with few if any red giant members, a purely photometric determination of the cluster properties is not well-constrained. Nevertheless, based on our UBVRI photometry alone, we have derived the distance, reddening, age and metallicity of the cluster and established estimates for the binary nature and membership probability of individual stars. We derive the following values for the cluster properties: $(m-M)_V = 10.98\pm 0.24$, $E(B-V) = 0.16\pm 0.04$ (so the distance = 1250 pc), age $= 705\pm170$\ Myr and $Z = 0.014\pm 0.005$. | The four open clusters located in NASA's Kepler spacecraft field of view (NGC 6866, NGC 6811, NGC 6819 and NGC 6791), which range in age from less than 1 Gyr to more than 8 Gyr, are ideal targets for a variety of astrophysical investigations. The two older clusters, NGC 6819 and NGC 6791 have been thoroughly studied \citep[see, e.g.,][for recent Kepler-related papers]{corsaro12, sandquist13, yang13}, but the other two are less well-known. We recently completed an analysis of NGC 6811 \citep[][hereafter Paper I]{janes13} and we report here on NGC 6866. Recent publications on NGC 6866 include \citet{frolov10}, who did a proper motion and CCD photometric study of the cluster; photometric studies by \citet{molenda09} and \citet{joshi12}; and an investigation by \citet{balona13} of rotations and pulsations of stars in the cluster using Kepler data. Frolov et al. found 423 likely cluster members and estimated the age of the cluster at 560 Myr. Joshi et al. derived $E(B-V) = 0.10$\ mag., an age of 630 Myr and a distance of 1.47 kpc. From an analysis of 2MASS JHK photometry, \citet{gunes12} derived an age 0.8$\pm$0.1 Gyr, E(B-V) = 0.19$\pm$0.06 and $(m-M)_{\circ} = 11.08\pm0.11$. Molenda-\.Zakowicz et al. and Joshi et al. both found several variable stars in the cluster. In a survey of a number of clusters, \citet{frinchaboy08} derived a radial velocity of 12.18 $\pm$\ 1.14 km s$^{-1}$ and proper motions $\mu_{\alpha}cos\delta = -5.52 \pm 1.17$\ mas yr$^{-1}$ and $\mu_{\delta} = -7.97 \pm 1.09$\ mas yr$^{-1}$\ for the cluster. The traditional approach to deriving the properties of star clusters from broad-band photometry is to ``fit'' theoretical stellar isochrones to the observed color-magnitude diagram (CMD). But an isochrone is simply the locus of possible stars over a range of masses at fixed age in the CMD (see Figure \ref{theory}a). So at a given time, in a cluster with a finite number of stars, it is unlikely that any stars will actually be found along some sections of an isochrone. We have chosen instead to find the maximum-likelihood probability that the observed cluster stars embedded in a background population of field stars (Figure \ref{allbv}a) could be drawn from a theoretical CMD, created by choosing a sample of stars from the models with a range of masses, as in Figure \ref{theory}b. \begin{figure} \epsscale{1.05} \plotone{fig1.eps} \caption{(a) A typical isochrone \citep{bressan12} with age = 700 Myr and Z = 0.014 (see Table \ref{final}), (b) A theoretical CMD consisting of 100 stars selected at regular mass intervals from the same isochrone. We use the theoretical CMD for our analysis rather than the isochrone. \label{theory}} \end{figure} By posing the problem in this way, we can take a modern Bayesian approach to derive not only the cluster parameters, but also their uncertainties. In \S 2 we describe the photometry; \S 3 is a discussion of the structural properties of the cluster; The Bayesian analysis is the topic of \S 4; \S 5 is a discussion of our results; and \S 6 summarizes our conclusions. | We have produced a catalog of high-quality Johnson/Cousins UBVRI photometry of stars in a large field around the cluster NGC 6866. Our photometry has been carefully transformed to the standard system as defined by the \citet{landolt09} standard stars. Using a Bayesian analytical procedure, we derived the following values for the cluster properties: $(m-M)_V = 10.98\pm 0.24$, $E(B-V) = 0.16\pm 0.04$, age $= 705\pm170$\ Myr and $Z = 0.014\pm 0.005$ (see also Table \ref{final}). Assuming a canonical extinction-to-reddening ratio $R_V = A_V / E(B-V) = 3.1$, the distance to the cluster is about 1250 parsecs. Our results are in rough agreement with previous work on this cluster as discussed in the introduction \citep[see also][and references therein]{balona13} As mentioned above, the lack of independent membership information, or, alternatively the cluster metallicity or reddening, limits the accuracy of photometric measurements of its age and distance. Furthermore, most of the previous results were based, directly or indirectly, on visual comparisons of observed color-magnitude diagrams with theoretical isochrones of solar composition only; for that reason, the quoted errors are likely to be highly optimistic, since they do not include the metallicity uncertainty. In particular, our analysis, as shown in Figures \ref{margins} and \ref{twod}, do not support a metallicity as high as solar. Solar metallicity would require a reddening of essentially zero, unlikely in this direction in the galaxy. \begin{figure} \plotone{fig6.eps} \caption{Two-dimensional marginal distribution of the numbers of trials in the E(B-V), Z plane for the Yale chain. The plus sign marks the peak of the Yale chain distributions for E(B-V) and Z (see Table \ref{final}). \label{twod}} \end{figure} Finally, the errors given in Table 3 do not include any uncertainty in the theoretical models. In particular, Figure \ref{cmdfits} suggests that there may be a small inconsistency between the theoretical models and the observed CMD. \begin{deluxetable}{ccccc} \tabletypesize{\small} \tablewidth{0pt} \tablecaption{NGC 6866 --- Summary of MCMC Analysis \label{final}} \tablehead{\colhead{ } &\colhead{E(B-V)} & \colhead{$(m-M)_V$} & \colhead{Age (Myr)} & \colhead{Z}} \startdata Padova &0.17$\pm$0.05 & 11.15$\pm$0.36 & 730$\pm$320 & 0.014$\pm$0.008 \\ Yale-Yonsei &0.14$\pm$0.05 & 10.82$\pm$0.32 & 680$\pm$340 & 0.013$\pm$0.007 \\ Average &0.16$\pm$0.04 & 10.98$\pm$0.24 & 705$\pm$170 & 0.014$\pm$0.005 \\ \enddata \end{deluxetable} | 14 | 3 | 1403.7208 |
1403 | 1403.7500_arXiv.txt | Neutron stars undergoing r-mode oscillation emit gravitational radiation that might be detected on earth. For known millisecond pulsars the observed spindown rate imposes an upper limit on the possible gravitational wave signal of these sources. Taking into account the physics of r-mode evolution, we show that only sources spinning at frequencies above a few hundred Hertz can be unstable to r-modes, and we derive a more stringent \textit{universal r-mode spindown limit} on their gravitational wave signal, exploiting the fact that the r-mode saturation amplitude is insensitive to the structural properties of individual sources. We find that this refined bound limits the gravitational wave strain from millisecond pulsars to values below the detection sensitivity of next-generation detectors. Young sources are therefore a more promising option for the detection of gravitational waves emitted by r-modes and to probe the interior composition of compact stars in the near future. | With the significant sensitivity improvement of forthcoming next generation gravitational wave detectors like advanced LIGO \cite{Harry:2010zz}, advanced Virgo \cite{Weinstein:2011kh} and the LCGT \cite{Kuroda:2010zzb} there is a realistic chance that gravitational waves may be directly observed. In addition to transient events such as neutron star and/or black hole mergers or supernovae, which require that an event happens sufficiently near to us during the observation period \cite{Abadie:2012rq}, it is important to also consider continuous sources. Millisecond pulsars are a particularly promising class since they are very old and stable systems and therefore could be reliable sources of gravitational waves. Their fast rotation strongly favors gravitational wave emission \cite{Aasi:2013sia}, and the fact that their timing behavior is known to high precision \cite{Manchester:2004bp} greatly simplifies the analysis required to find a signal in the detector data. Emission due to deformation of these objects (``mountains''), which is usually parametrized by an ellipticity, is the standard paradigm for continuous gravitational wave searches \cite{Collaboration:2009rfa}, but global oscillation modes of a star can also emit copious gravitational waves that could be detectable if the oscillation reaches sufficiently high amplitudes. R-modes are the most interesting class \cite{Andersson:1997xt,Andersson:2000mf,Lindblom:1998wf,Owen:1998xg}, because they are generically unstable in millisecond pulsars and therefore will be present unless the dissipative damping is strong enough. If r-modes arise in a spinning neutron star, they affect the spindown (since they cause the star to lose angular momentum via gravitational radiation) and the cooling (since the the damping forces on the r-mode generate heat). To understand the interplay of these effects we have developed \cite{Alford:2012yn,Alford:2013pma} an effective description of the spindown evolution where complicated details about the star's interior are absorbed into a few effective parameters. The resulting spindown can be rather different from that predicted by simpler approaches, and includes strict bounds on the uncertainties in the final results. In this paper we will use this method to analyze the possible r-mode gravitational radiation of old neutron stars. Firstly, however, we provide some background and motivation. R-modes can occur in young or old pulsars. In the case of young sources \cite{Aasi:2013sia,Abadie:2010hv,Abbott:2008fx,Wette:2008hg} we have analyzed their r-mode evolution \cite{Alford:2012yn} and found that r-modes can provide a \textit{quantitative} explanation for their observed low spin rates. Moreover, the r-mode gravitational emission is expected to be strong, because a large r-mode amplitude would be required to spin down the known young pulsars to their current low spin frequencies within their lifetimes which are as short as a thousand years. These known pulsars are no longer in their r-mode spindown epoch, but there may be unobserved young neutron stars, e.g. associated with known supernova remnants such as SN 1987A, that are currently undergoing r-mode spindown, and several of them would be in the sensitivity range of advanced LIGO \cite{Alford:2012yn}, allowing this scenario to be falsified by future measurements. In this paper we focus on old neutron stars which have been spun up by accretion, and we perform an analysis of their expected r-mode gravitational wave radiation. In \cite{Alford:2013pma} novel r-mode instability regions in spindown timing parameter space have been derived that allow us to decide if r-modes can be present in old millisecond radio pulsars. As discussed there, there are two scenarios to explain the observed timing data. It might be that the ordinary nuclear matter model of neutron stars is incomplete, and there is additional damping (e.g.~from exotic forms of matter or currently overlooked physical processes) that stops r-modes from growing in these stars. In this case there will be no r-mode gravitational radiation from old neutron stars. The other possibility is the conventional scenario where only standard damping mechanisms are present in neutron stars. In this scenario most old millisecond pulsars \textit{will be} undergoing r-mode oscillations, since for expected r-mode saturation amplitudes the dissipative heating ensures that fast spinning sources can neither cool nor spin out of the parameter region were r-modes are unstable \cite{Alford:2013pma}. Yet, some slower spinning sources can escape the instability region and we will determine the limiting frequency. Therefore, there will be gravitational radiation from most old neutron stars in this scenario, and the purpose of this paper is to find out whether it could be detected on earth. The detectability of known continuous sources is generally described by the ``spindown limit'' which is, for a specific source with known timing data, the maximum gravitational wave strain that can be emitted by that source. Despite the quite restrictive limits set by the spindown data, the large spin frequencies of millisecond pulsars could nevertheless lead to a detectable signal. Present gravitational wave detectors---like the original LIGO interferometer---did not probe the spindown limit for millisecond pulsars. However, next generation detectors including the advanced LIGO detector will be able to beat the spindown limit for various sources. Therefore, it is interesting to assess the chance to detect gravitational emission from oscillating millisecond pulsars. We will introduce here the \textit{universal r-mode spindown limit} on the gravitational wave strain, which is more restrictive since it takes into account our understanding of the r-mode spindown and the complete information we have about these systems. Whereas deformations of a given source depend on its evolutionary history and could therefore vary significantly from one source to another, for proposed saturation mechanisms the r-mode saturation amplitude proves to be rather insensitive to details of a particular source, like its mass or radius \cite{Bondarescu:2013xwa,Alford:2011pi,Haskell:2013hja}. The expected gravitational wave strain of a given source can then be strongly constrained by the timing data of the \textit{entire set} of millisecond pulsars. Using our semi-analytic approach to pulsar evolution, and assuming that the same saturation and cooling mechanism (with given power-law dependence on temperature) operates in all the stars, we can then obtain the universal limit given in Eq.~(\ref{eq:universal-spindown-limit}). We will see that this is considerably below the standard spindown limits, indicating that it will be harder than previously expected to see r-mode gravitational waves from these sources. | We have analyzed the continuous gravitational wave emission of millisecond radio pulsars due to r-modes. As an improvement to the usual bound, given by the spindown limit, we have derived the \textit{universal r-mode spindown limit} which takes into account the fact that proposed r-mode saturation mechanisms are insensitive to the macroscopic star configuration (mass, radius, moment of inertia, etc) and takes into account the whole class of sources. Using this additional information, we find that the universal spindown limit for the intrinsic gravitational wave strain amplitude can be significantly smaller than the usual spindown limit. Furthermore, we show that r-modes are damped in old millisecond radio pulsars spinning with frequencies below about $150-200\,{\rm Hz}$ so that corresponding gravitational wave emission is not expected to be present. Our results do not rely on explicit estimates for the r-mode saturation amplitude, which depend on the microphysics and are still very uncertain, but merely on the parametric temperature and frequency dependence which is generic for a given saturation mechanism and given by characteristic rational power-law exponents. We compare our improved bounds to the detection thresholds for realistic searches with next generation detectors like advanced LIGO using a year of coherent data and find that for none of the known millisecond radio pulsars would r-mode gravitational waves be detectable in the near future. This is in contrast to r-mode emission from young sources, where several potential sources are in reach of advanced LIGO \cite{Alford:2012yn}. However, if the sensitivity could be improved by the combination of different detectors, the analysis of larger coherent data sets or other enhancements, the universal spindown limits of selected millisecond pulsars which are close to the the detection limit might be beaten by next generation searches. For third generation detectors, like the planned Einstein telescope, there is a realistic chance to detect dozens of sources and our refined bounds identify those that are most promising. In contrast to the conventional spindown limit (triangles in fig.~\ref{fig:universal-spindown-limits}), which is sizable for some lower frequency sources, the universal spindown limit (circles or rectangles in fig.~\ref{fig:universal-spindown-limits}) shows that it is actually the mid- to high-frequency sources which feature the largest bounds. The universal spindown limit relies on the assumption that the same r-mode saturation mechanism is operating in the entire set of radio pulsars. In principle it cannot be completely excluded that different saturation mechanisms are at work in different sources. This could happen if there were classes of sources with qualitatively different structural or phase compositions. For the recycled old radio pulsars that we focus on in this paper, this is not a likely scenario. These stars are very stable systems that hardly change over time and have very similar properties. For instance the magnetic fields that could distinguish different radio pulsars are all rather small and are not expected to strongly affect the r-mode evolution besides the additional magnetic spindown. However, it is quite possible that old and young stars have different saturation mechanisms, in fact such a difference is required to explain the low spin frequencies of young pulsars \cite{Alford:2012yn} and the low spindown limits of old radio pulsars \cite{Alford:2013pma}. One possibility is enhanced dissipation due to the transformation of a neutron star or its core into a quark star owing to the density increase during the initial spindown \cite{Alford:2013rea}. Another option would be enhanced dissipation in a superfluid/superconductor \cite{Haskell:2013hja} which is only present below the superfluid melting temperature and this transition might have been explicitly observed in the cooling of the neutron star in Cassiopeia A \cite{Page:2010aw}. Both of these transitions would happen in the dynamic early evolution of young sources, before they are a few hundreds of years old. In contrast, recycled old radio pulsars are very stable systems that hardly change over time and have very similar properties. For instance the magnetic fields that could distinguish different radio pulsars are all rather small and are not expected to strongly affect the r-mode evolution besides the additional magnetic spindown. Therefore, the assumption that the same saturation mechanism is realized in the entire class of old millisecond radio pulsars is reasonable. In addition to the exciting prospect of directly detectable gravitational waves, the emission from oscillating pulsars presents a unique chance to directly probe the interior of a compact star. The amplitude of r-modes, which is encoded in the gravitational wave signal, can directly reveal the damping properties of the matter inside the star and thereby its composition. In addition to thermal measurements from low mass x-ray binaries \cite{Lindblom:1998wf,Haskell:2012} and pulsar timing data \cite{Alford:2013pma,Manchester:2004bp}, gravitational waves would provide a third messenger to probe the interior star composition via r-modes. The combined analysis of these different data sets would provide a clearer picture of the star's interior and could allow us to discriminate different star compositions in the future. | 14 | 3 | 1403.7500 |
1403 | 1403.0050_arXiv.txt | We report the selection and spectroscopic confirmation of 129 new late-type (SpT$=$K3--M6) members of the Tucana-Horologium moving group, a nearby ($d \sim 40$ pc), young ($\tau \sim 40$ Myr) population of comoving stars. We also report observations for 13 of the 17 known Tuc-Hor members in this spectral type range, and that 62 additional candidates are likely to be unassociated field stars; the confirmation frequency for new candidates is therefore $129/191 = 67\%$. We have used radial velocities, H$\alpha$ emission, and Li$_{6708}$ absorption to distinguish between contaminants and bona fide members. Our expanded census of Tuc-Hor increases the known population by a factor of $\sim$3 in total and by a factor of $\sim$8 for members with SpT$\ge$K3, but even so, the K-M dwarf population of Tuc-Hor is still markedly incomplete. Our expanded census allows for a much more detailed study of Tuc-Hor than was previously feasible. The spatial distribution of members appears to trace a two-dimensional sheet, with a broad distribution in $X$ and $Y$, but a very narrow distribution ($\pm$5 pc) in $Z$. The corresponding velocity distribution is very small, with a scatter of $\pm$1.1 km/s about the mean $UVW$ velocity for stars spanning the entire 50 pc extent of Tuc-Hor. We also show that the isochronal age ($\tau \sim 20$--30 Myr) and the lithium depletion boundary age ($\tau \sim 40$ Myr) disagree, following the trend in other pre-main sequence populations for isochrones to yield systematically younger ages. The H$\alpha$ emission line strength follows a trend of increasing equivalent width with later spectral type, as is seen for young clusters. We find that moving group members have been depleted of measurable lithium for spectral types of K7.0--M4.5. None of our targets have significant infrared excesses in the WISE W3 band, yielding an upper limit on warm debris disks of $F < 0.7\%$. Finally, our purely kinematic and color-magnitude selection procedure allows us to test the efficiency and completeness for activity-based selection of young stars. We find that 60\% of K-M dwarfs in Tuc-Hor do not have ROSAT counterparts and would have been omitted in X-ray selected samples. In contrast, GALEX UV-selected samples using a previously suggested criterion for youth achieve completeness of 77\% and purity of 78\%, and we suggest new SpT-dependent selection criteria that will yield $>$95\% completeness for $\tau \sim 40$ Myr populations with GALEX data available. | Over the past 20 years, co-moving associations of young stars ($\tau \la 100$ Myr) have been identified among the nearby field population \citep[][]{Kastner:1997kx,Webb:1999tw,Mamajek:1999ul,Torres:2000qy,Zuckerman:2000uq,Zuckerman:2004fj}. These moving groups represent the dispersed remnants of coeval stellar populations \citep[e.g.,][]{Weinberger:2012qy} that apparently formed in the same star-forming region, and might be older analogs to unbound associations like Taurus-Auriga and Upper Scorpius \citep[][]{Kraus:2008fr}. Most of these populations are associated with well-known isolated classical T Tauri stars (such as the TW Hya Association, or TWA) or debris disk hosts (such as the $\beta$ Pic moving group, or BPMG), an association which provided the first indication that they were post-T Tauri associations. Surveys to identify active young stars within the solar neighborhood ($d \la 50$ pc) have subsequently identified several additional populations, including the AB Dor, Carina-Near, Hercules-Lyra, and Tucana-Horologium associations \citep[][]{Zuckerman:2004fj,Zuckerman:2006fk,Torres:2008lr,Eisenbeiss:2013qy}. Young moving groups ($\tau \sim 8$--300 Myr) provide a critical link between star-forming regions (which can be recognized by the presence of molecular cloud material and the preponderance of protoplanetary disk hosts) and the old field population. The close proximity of these young moving groups makes them especially advantageous for the study of circumstellar processes that depend on angular resolution (such as multiple star formation; \citealt[][]{Brandeker:2003wd,Brandeker:2006cr,Evans:2012wd}) and searches for extrasolar planets \citep[][]{Marois:2008zt,Lagrange:2009fc}. The low distances also result in additional sensitivity for flux-limited studies of disks \citep[][]{Low:2005lq,Bouwman:2006yq,Plavchan:2009dp} and the (sub)stellar mass function \citep[][]{Gizis:2002lr,Lyo:2006fk,Murphy:2010lr,Shkolnik:2011qf}. Finally, these stellar populations record a key epoch of planet formation, representing the end of giant planet formation and the onset of terrestrial planet assembly. The Tucana-Horologium moving group (hereafter Tuc-Hor) is a particularly intriguing stellar population. Its members were first identified separately as the Tucana association and the Horologium association \citep[][]{Torres:2000qy,Zuckerman:2000uq}, but were subsequently recognized to represent a single comoving population with an age of $\tau \sim 30$ Myr. Tuc-Hor is host to at least 12 BAF-type stars \citep[e.g.,][]{Zuckerman:2004fj,Torres:2008lr}, similar in size to the BPMG (also with 12 BAF-type stars) and much larger than the TWA (with a single BAF-type member). Tuc-Hor is likely one of the largest young stellar populations within $d < 100$ pc, making it a robust site for measuring population statistics (the IMF, multiplicity properties, disk frequencies, and activity rates). As an ``intermediate age'' moving group, Tuc-Hor represents a key calibration for age indicators like H$\alpha$ emission, UV and X-ray excesses, rotational velocities, and age-dependent spectral features like $Li_{6708}$, and $Na_{8189}$. If these indicators can be robustly calibrated for the age of Tuc-Hor, then their measurement for stars unaffiliated with any moving group can distinguish analogs to stars in star-forming regions ($\tau = 1$--20 Myr) from the young ($\tau = 50$--300 Myr) field population \citep[][]{Shkolnik:2012ee} and old field stars \citep[][]{Reid:2004rw}. The current census of Tuc-Hor is largely restricted to the higher-mass (AFGK-type) stars, which can be selected via all-sky activity indicators like ROSAT and confirmed with high-quality proper motions from Hipparcos. There are $<$10 spectroscopically confirmed M dwarfs in Tuc-Hor, even though these stars represent the peak of the IMF and thus should comprise the majority of the population by both number and mass. The reason for this paucity is straightforward. M dwarfs are fainter both optically and in the Xray/UV, so they have been more difficult to mine out of all-sky surveys. \citet[][]{Malo:2012fv} and \citet[][]{Rodriguez:2013vn} have begun to identify significant samples of low-mass candidate members, based on proper motions and ROSAT/GALEX excesses, but they spectroscopically confirmed only a handful of late-type members. In this paper, we present the discovery and spectroscopic confirmation of 129 new K3--M6 members of the Tuc-Hor moving group, along with the recovery of most known $\ge$K3 members, and compute isochronal sequences for several spectroscopic signatures of youth. We also use this sample to characterize the age, mass function, spatial and velocity distribution, disk population, and activity of Tuc-Hor members. In Section 2, we describe our candidate selection procedures. In Section 3, we describe our high-resolution optical spectroscopic observations, and in Section 4, we summarize the analysis methods used to measure each candidate's spectroscopic properties. In Section 5, we combine all of the signatures of youth and membership to identify a sample of bona fide moving group members with spectral types mid-K to mid-M, and compare our results to those of previous surveys. Finally, in Section 6, we discuss the population statistics of the Tuc-Hor moving group. | 14 | 3 | 1403.0050 |
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1403 | 1403.1583.txt | Nearly sixty percent or more of the Solar neighborhood stars are binaries or multiple systems \citep{Duquennoy93}. Binaries are important for astrophysicists not only because they over populate single stars, but also because they provide basic stellar parameters as independent observed quantities used in testing astrophysical theories. Stellar masses can be determined directly via application of Kepler's law for the visual binaries if apparent orbital parameters were calibrated to be real. A calibration is possible for a visual pair if its distance (parallax) is known. Reliable stellar masses could also be obtained from the radial velocity curves without distance, but only if orbital inclinations were known. The resolved double stars (visual binaries confirmed to be spectroscopic binaries), therefore, are a special case to provide reliable stellar masses, since the orbital inclinations are from the apparent orbit and the absolute orbital sizes are from the radial velocity curves. Gainfully, the light curves of eclipsing binaries could provide orbital inclinations and the radii relative to the semi-major axis of the orbit. But, if both stars are resolved spectroscopically, accurately determined radii and masses could be obtained from the simultaneous solutions of the light and the radial velocity curves. In addition to the radii, which are not available from visual binaries, the eclipsing spectroscopic binaries provide masses, effective temperatures and the absolute dimensions of the orbit, from which absolute brightnesss could be calculated. Provided with a parallax, either the physical parameters or the parallax could mutually be tested by comparing the photometric and the trigonometric distance moduli. Otherwise, a proper solution would provide not only the most reliable stellar parameters, but also a reliable photometric distance (parallax) as an independent quantity. The critical compilations of stellar parameters and absolute dimensions of binary components were initiated, and continued with increasing quantity and quality especially by \citet{Popper80} and \citet{Harmanec88}. \citet{Andersen91} collected accurate stellar masses and radii with uncertainties less than 2 per cent from the detached, double-lined eclipsing systems. The list contained 45 (90 stars) binaries which are all non-interacting, so that each star could be accepted as if evolved as single stars. Accuracies of 1-2 per cent were found to be significant for deeper astrophysical insight than merely improving the spectrum of masses and radii. Due to great sensitivity of other parameters, only limited amount of useful results could be extracted up to $\pm$5 per cent uncertainties. \citet{Malkov93} announced a catalog of astrophysical parameters of binary systems containing 114 systems including all pre and out of main sequence, contact and semi-contact systems. \citet{Gorda98} collected stellar masses and radii with accuracies better than 2-3 per cent from photometric, geometric, and absolute elements of 112 eclipsing binaries with both components on the main sequence, for studying the mass-luminosity and mass-radius relations. Ages and metallicities for the components of 43 eclipsing binaries with lines of both components visible on the spectra were studied by \citet{Kovaleva01}. As the number of stars with reliable physical parameters is increasing, the studies concentrated more on the precision and accuracy. Therefore, \citet{Ibanoglu06} did not combine 74 double-lined detached eclipsing Algols and 61 semi-detached Algols when plotting mass-radius, mass-T$_{eff}$, radius-T$_{eff}$, and mass-luminosity data. \citet{Lastennet02} compiled 60 non-interacting, well-detached systems with typical errors smaller than 2 per cent for masses and radii, while 5 per cent for the effective temperatures. The core of the sample was the large catalogue of \citet{Andersen91}. As being satisfied with 10 per cent accuracy for the main-sequence stars, \citet{Hillenbrand04} studied dynamical mass constraints on pre-main-sequence evolutionary tracks with 148 stars, 88 are on the main-sequence, 27 are on the pre main-sequence and 33 are on the post main-sequence, where the source of data were \citet{Andersen91}, \citet{Ribas00} and \citet{Delfosse00}. Despite, the number of eclipsing binaries was 6330 in ``the catalogue of eclipsing binaries'' by \citet{Malkov06}, but \citet{Malkov07} was able to select only 215 stars (114 binaries) which are detached-main-sequence and double-lined eclipsing binary with uncertainties for masses, radii, $\log T_{eff}$, $\log L$, and $\log M$ were assumed to be 10, 10 per cent, 0.03, 0.03 and 0.1 mag or better respectively. Eclipsing binaries are not only recognized with their accuracy, but also known to have larger spectrum of mass range especially towards larger masses in compared to visual binaries including {\em Hipparcos} detections \citep{Malkov03}. Improvements in observing and analysis techniques never stop, and collection of reliable light and radial velocity curve solutions continue. Recently, \citet*{Torres10} updated the critical compilation of detached, double-lined eclipsing binaries with accurate masses and radii. Superseding \citet{Andersen91} list, this new list contains 190 stars (94 eclipsing binaries and $\alpha$ Cen). In order to fill the gaps in different mass ranges, further compilations on the accurate absolute dimensions of the eclipsing double lined spectroscopic binaries are inevitable. The aim of this paper is to present our compilation of 514 stars which are from 257 detached eclipsing double-lined spectroscopic binaries (SB2) of the Milky Way. The number of stars in our list with reliable masses, spectroscopic mass ratios, orbital inclinations, radii, $T_{eff}$, $\log g$, and $v\sin i$ values as collected from the literature supersede similar compilations before. Selecting criteria and data collection from binaries and the descriptions of the quality of the data are given in Section 2. The H-R diagram, space distributions and how good a typical single star represented were discussed in Section 3 and finally conclusions were provided in Section 4. | \begin{itemize} \item The most accurate stellar parameters (masses, radii, temperatures, surface gravities, luminosities, projected rotational velocities, radial velocity amplitudes, mass ratio, orbital period, orbital inclination, semi-major axis, eccentricity) were compiled from the simultaneous solutions of light and radial velocity curves of detached double-lined eclipsing binaries. \item The masses and radii were homogenized using most recent values of $GM_{\odot}=1.3271244\times10^{20}$ m$^{3}$s$^{-2}$ \citep{Standish95} and $R_{\odot}=6.9566\times10^{8}$m \citep{Haberreiter08}. Surface gravities and luminosities recomputed using homogenized masses and radii. \item Apparent magnitudes, orbital periods, masses, radii, mass ratios, spectral types and space distribution of the present sample were discussed. \item The number of stars with both mass and radius as accurate as 1 per cent is 93, as accurate as 3 per cent is 311, and as accurate as 5 per cent is 388. \item Filling ratios of the current sample were studied. Thus, the geometrical shapes of the component stars were determined. Up to 75 per cent of filling factors, stars are found almost spherical within 1 per cent uncertainty. \item Giants and supergiants are missing in the present sample. Observational astronomers are encouraged to explore eclipsing binaries among giants and supergiants. Improving light curve observing techniques for discovering small amplitude SB2 eclipsing systems is a challenge \end{itemize} | 14 | 3 | 1403.1583 |
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1403 | 1403.4029_arXiv.txt | We present a comparison of the {\it Solar Dynamics Observatory} (SDO) analysis of NOAA Active Region (AR) 11158 and numerical simulations of flux-tube emergence, aiming to investigate the formation process of the flare-productive AR. First, we use SDO/{\it Helioseismic and Magnetic Imager} (HMI) magnetograms to investigate the photospheric evolution and {\it Atmospheric Imaging Assembly} (AIA) data to analyze the relevant coronal structures. Key features of this quadrupolar region are a long sheared polarity inversion line (PIL) in the central $\delta$-sunspots and a coronal arcade above the PIL. We find that these features are responsible for the production of intense flares including an X2.2-class event. Based on the observations, we then propose two possible models for the creation of AR 11158 and conduct flux emergence simulations of the two cases to reproduce this AR. Case 1 is the emergence of a single flux tube, which is split into two in the convection zone and emerges at two locations, while Case 2 is the emergence of two isolated but neighboring tubes. We find that, in Case 1, a sheared PIL and a coronal arcade are created in the middle of the region, which agrees with the AR 11158 observation. However, Case 2 never build a clear PIL, which deviates from the observation. Therefore, we conclude that the flare-productive AR 11158 is, between the two cases, more likely to be created from a single split emerging flux than two independent flux bundles. | } Solar flares are catastrophic eruptions produced around active regions (ARs). Also, AR is the product of emerging magnetic flux from the deep convection zone ({\it e.g.} \opencite{fan09}). Observations have revealed that intense flares often occur near polarity inversion lines (PILs) of ARs, especially those with strong magnetic shear ({\it e.g.} \opencite{hag84}). This is due to the availability of free magnetic energy in the sheared coronal arcades over such PILs. When a flare occurs, the stored energy is released via magnetic reconnection (see \opencite{shi11}, and references therein). \inlinecite{kus12} carried out a systematic study of three-dimensional magnetohydrodynamic (3D MHD) simulations to investigate the triggering mechanism of solar flares. It was found that a solar flare occurs at the highly sheared PIL and the overlying coronal arcade above it. The flare is triggered by a small-scale magnetic field that initiates the reconnection between the coronal arcades. The magnitude of flare eruptions ({\it e.g.} maximum kinetic energy) was found to increase with a shear angle of the arcade, which is measured from the axis normal to the PIL. As demonstrated by \inlinecite{kus12}, the creation of a sheared PIL is critical for the production of flares. Here, the PIL in an AR is formed through the large-scale flux emergence of the entire AR. If the emerging flux transports larger magnetic helicity, it may build up a more sheared PIL and may produce stronger flares. If the flux is severely deformed before it appears at the surface, it may develop a more complex AR ($\delta$-sunspots, possibly with a sharp, sheared PIL), which is known to produce larger flares \citep{sam00}. Therefore, intense flares at a highly sheared PIL are likely to reflect the evolutionary history of emerging magnetic flux while in the convection zone (see also \opencite{poi13}). In this article, we present a detailed analysis of NOAA AR 11158 and a comparison with numerical simulations of emerging magnetic flux. The aim of this work is to study the subsurface/global structure of a flare-productive AR. For this purpose, we first analyze observational data of AR 11158 obtained by the {\it Helioseismic and Magnetic Imager} (HMI: \opencite{sche12}; \opencite{scho12}) and {\it Atmospheric Imaging Assembly} (AIA: \opencite{lem12}) onboard the {\it Solar Dynamics Observatory} (SDO: \opencite{pes12}) to investigate the photospheric and coronal evolution of this AR. Thanks to the continuous, full-disk observation by SDO, we are able to investigate the evolution of this AR from its earliest stage. Then, we conduct numerical simulations of emerging flux tubes to reproduce AR 11158. By comparing the observational and the numerical results, particularly the geometrical evolution of surface magnetic fields around the PIL and of overlying coronal arcades, we search for a possible scenario of the large-scale emerging flux that creates a sheared PIL in AR, which is largely responsible for producing strong flares. The rest of the article is organized as follows: We first describe the observations and the simulations in Sections \ref{sec:observation} and \ref{sec:simulation}, respectively. Then, a comparison of observations and simulations is given in Section \ref{sec:comparison}. We discuss the results in Section \ref{sec:discussion} and, finally, we summarize the article in Section \ref{sec:conclusion}. | } In this study, we compared the SDO/HMI and AIA observations of NOAA AR 11158 with the numerical simulations of the flux tube emergence, aiming to study the formation of this flare-productive AR. AR 11158, basically composed of two emerging bipoles, is one of the most flare-productive ARs in Solar Cycle 24. SDO's continuous observation of the full solar disk at multiple wavelengths allows us to investigate the photospheric and coronal evolution of this AR from the first minutes to the moments of strong flares. The key features of this AR that we found are i) the long sheared PIL between the elongated magnetic elements of opposite polarity that produced a $\delta$-configuration in the central region and ii) the sheared coronal arcade above the PIL created by magnetic reconnection between $\Omega$-shaped loops of two major bipoles. Based on the SDO observations, we inferred two possible scenarios for the formation of AR 11158: emergence of a single split tube {\it versus} two different tubes. According to the numerical simulations, AR 11158 is more likely to be made by a single flux tube than two tubes. The single tube is severely deformed and split in two while in the convection zone. The two major bipoles at the photosphere, which share the common subsurface structure, recover their original shape during flux emergence by releasing magnetic free energy within the sheared coronal arcade in the form of solar flares including X- and M-class events. Our study suggests that a solar flare in an AR naturally reflects the large-scale magnetic structure beneath the surface. From this point of view, flares can be thought as a process to relax magnetic shear produced by a helical and/or deformed emerging flux from the solar interior. However, we cannot observe the subsurface structure of flare-productive ARs from direct optical observations. Helioseismic detection of the emerging subsurface flux ({\it e.g.} \opencite{ilo11}; \opencite{tor13b}) may improve our understanding of the nature of such ARs. Regarding the numerical simulations, neither case reproduced flare reconnection, since the evolution of the flare trigger, which may be coupled with thermal convection, was beyond the scope of the simulation code. Also, the origin of the perturbation that splits the emerging flux in two, which was mimicked by the sinking of the tube, remained unclear. These topics will be addressed in future investigations. \begin{acks}[Acknowledgments] The authors thank K. Hayashi (Stanford University) for providing HMI data and P. D\'{e}moulin (Paris Observatory) for fruitful discussions. The authors are grateful to the anonymous referee for improving the manuscript and the SDO team for distributing HMI and AIA data. Numerical computations were carried out on Cray XC30 at the Center for Computational Astrophysics, National Astronomical Observatory of Japan. ST is supported by Grant-in-Aid for JSPS Fellows. This work was supported by a Grants-in-Aid for Scientific Research (B) ``Understanding and Prediction of Triggering Solar Flares'' (23340045, Head Investigator: K. Kusano) from the Ministry of Education, Science, Sports, Technology, and Culture of Japan. \end{acks} | 14 | 3 | 1403.4029 |
1403 | 1403.1326_arXiv.txt | We report on the diffusive-ballistic thermal conductance of multi-moded single-crystal silicon beams measured below 1 K. It is shown that the phonon mean-free-path $\ell$ is a strong function of the surface roughness characteristics of the beams. This effect is enhanced in diffuse beams with lengths much larger than $\ell$, even when the surface is fairly smooth, 5-10 nm rms, and the peak thermal wavelength is 0.6 $\mu$m. Resonant phonon scattering has been observed in beams with a pitted surface morphology and characteristic pit depth of 30 nm. Hence, if the surface roughness is not adequately controlled, the thermal conductance can vary significantly for diffuse beams fabricated across a wafer. In contrast, when the beam length is of order $\ell$, the conductance is dominated by ballistic transport and is effectively set by the beam area. We have demonstrated a uniformity of $\pm$8\% in fractional deviation for ballistic beams, and this deviation is largely set by the thermal conductance of diffuse beams that support the micro-electro-mechanical device and electrical leads. In addition, we have found no evidence for excess specific heat in single-crystal silicon membranes. This allows for the precise control of the device heat capacity with normal metal films. We discuss the results in the context of the design and fabrication of large-format arrays of far-infrared and millimeter wavelength cryogenic detectors. | The management of heat in dielectric beams and membranes is an important part of the design in micro-electro-mechanical systems (MEMS)~\cite{Savin,Maldovan,Yefremenko1}. While the physics of thermal transport in dielectric materials is well understood, the effect of fabrication processes on the surface physics is less clear and widely treated as a hidden variable in the evaluation of the device performance. This uncertainty can prolong the design-test cycle, where a parameter such as beam geometry is iterated until the target thermal conductance $G$ is obtained~\cite{ACTPol,SPT90GHz}. In our application, the MEMS is a cryogenic detector known as the Transition-Edge Sensor (TES)~\cite{TESIrwinHilton}. Figure~\ref{fig:Q-band-detector} shows a TES designed for measurements of the polarization state of the Cosmic Microwave Background~\cite{Rostem,Eimer}. The TES is comprised of a superconducting MoAu bilayer deposited on a single-crystal silicon substrate. The silicon is etched around the bilayer and other electrical components to form a membrane that is supported by dielectric beams. The total thermal conductance $G(T)$ of the beams is a critical parameter that determines the sensitivity ($\propto \sqrt{G}$), response time ($\propto 1/G$), and saturation power of the TES detector ($\propto \int G\,dT$) (saturation energy in the case of a TES micro-calorimeter)~\cite{TESIrwinHilton}. The response time is also a function of the total heat capacity $C(T)$ of the detector, which is the sum of the heat capacity of the silicon membrane and normal metal films. \begin{figure}[htbp] \begin{center} \includegraphics[width=8.5cm]{Q-band-detectors-SEM-01.eps} \caption{SEM image of a TES detector fabricated for a 40 GHz focal plane~\cite{Rostem}. The single-crystal silicon membrane volume is $5\times350\times450$ $\mu$m$^3$. The thermal conductance from the membrane to the frame is effectively set by the ballistic-dominated thermal conductance of the short beam (magnified). The long silicon beams are $5\times15\times785$ $\mu$m$^3$, and merely support TES bias and rf leads. The thermal conductance of the long silicon beams is diffusive-ballistic and sub-dominant to the conductance of the ballistic beam. The Pd layer deposited on the membrane sets the detector heat capacity. }% \label{fig:Q-band-detector} \end{center} \end{figure} At temperatures far below the Debye temperature of the lattice ($\Theta_{Si}=645$ K), anharmonic phonon collisions in the bulk of the dielectric are negligible, and the phonon-mean-free path $\ell$ is restricted by the cross sectional dimensions of the beam~\cite{Kittel}. In state-of-the-art far-infrared and millimeter TES detectors operating at sub-Kelvin temperatures~\cite{Khosropanah,ACTPol,SPT90GHz}, the beam length $L$ is much larger than $\ell$, and the thermal conductance is often described by the Fourier law for phonon diffusion, $G(T) = \kappa(T)\,wt/L$, where $w$ and $t$ are the width and thickness of the beam, and $\kappa(T)$ is the bulk thermal conductivity of the dielectric. $\kappa(T)$ is determined empirically with the fabrication and testing of numerous beams of varying width and length, and the aspect ratio $w/L$ is tuned to achieve the desired conductance. However, this approach rarely provides a complete view of the thermal physics, and higher order effects such as surface roughness of the beams have been identified as the likely cause of the reported non-uniformity in $G$ across detector arrays~\cite{ACTPol,SPT90GHz}. A simple analysis can readily show the sensitivity of phonon propagation in long beams ($L\gg\ell$) to the details of the surface physics. For a random Gaussian surface, the roughness can be characterized by the ratio of the standard deviation $\sigma$ of the surface features to the peak thermal wavelength $\lambda_{th}(T)$ of the incident phonon field. When $\sigma/\lambda_{th} \ll 1$, phonons are reflected specularly from the surface~\cite{Beckmann}. As the wavelength becomes much smaller than the scale size of the surface, $\sigma/\lambda_{th}\gg1$, phonons are scattered over all angles, or diffused. Assuming isotropic diffusion, it can be shown that for a rectangular beam, the phonon mean-free-path $\ell$ scales logarithmically with $r = w/t$ ($\ell\approx0.75\,wr^{-1}\ln2r$ for $r>1$~\cite{Wybourne}). Hence, in a beam where $L\gg\ell$, phonons experience a large number of scattering events, $N\sim L/\ell$, and the heat flux entering the beam at one end $P_0(T)$ is reduced to $P(T) = P_0(T)\,(1-f)^N$ at the exit port, where $f$ is the diffuse fraction. The derivative $dG/dN$ is a measure of the sensitivity of $G$ to changes in $N$ and proportional to the power-law function $(1-f)^N$. In practice, the statistics of the surface roughness can be heavily biased by the fabrication and is likely non-Gaussian. Dielectric beams can be roughened in various forms depending on the compatibility and properties of the etchants with the dielectric material. Preliminary tests can shed light on the roughening steps, however, fabrication processes can be difficult to control in practice. Details such as base pressure and process chamber conditioning during dry-etch steps can vary between batches of devices, especially in shared facilities. As a result, the characteristics of the roughness of a single surface can change significantly over spatial scales shorter than the beam length, and between wafers. Furthermore, not all surfaces of a beam are rough to the same degree. These effects add to the unpredictable variability in $N$ and therefore $G$ in beams dominated by diffusive thermal transport. The work in this paper is focused on understanding the effects of fabrication on the thermal conductance in single-crystal silicon beams. The beam geometries explored span several orders of magnitude in $L/wt$. The results demonstrate that $G$ in short ($L\lesssim10$ $\mu$m, $L/\ell\le$ 1) uniform beams with ballistic-dominated phonon transport is insensitive to the fabrication conditions and can be realized with precision in devices on different wafers. This approach is suitable for TES detector arrays in ground-based and air-borne telescopes, where the detector noise equivalent power requirements is greater than 10$^{-18}$ W/$\sqrt{\rm Hz}$. Throughout this paper, the terms \emph{diffuse} and \emph{ballistic} are used to describe the scale size of the phonon transport in a silicon beam. In the presence of surface roughness, the thermal transport in a long beam with $L/wt\gg1$ is dominated by diffuse reflections off the beam walls, and $L/\ell\gg1$. For a short beam, ballistic transport dominates and $L/\ell\le1$. We emphasize that these limits bound the diffusive-ballistic conductance observed in practice. In Sec.~\ref{sec:method}, we briefly describe the device fabrication and readout hardware employed for the low-temperature measurements of $G$ and $C$. In Sec.~\ref{sec:model}, we describe the theory of radiative phonon transport in diffusive-ballistic beams. In Sec.~\ref{sec:diff-ball}, we present results that illustrate the effect of fabrication on the diffusive-ballistic nature of the thermal conductance. In Sec.~\ref{sec:controlG}, we describe the superior performance of ballistic beams for the control of $G$ of TES detectors. Finally, we demonstrate that because of the low specific heat capacity of single-crystal silicon, the heat capacity of the detectors fabricated on this substrate can be effectively controlled using a normal metal film with high specific heat. | The thermal conductance of single-crystal silicon devices can be precisely controlled using a short beam with ballistic-dominated phonon transport. The conductance of the short beam is largely set by its area and is insensitive to the details of the fabrication conditions that can vary over time. This approach is superior to the conventional use of long beams for the control of thermal conductance. Phonon transport in long beams is diffusive-ballistic and very sensitive to the detailed surface physics of the beams. The conductance is thus boundary-limited, and has been observed in beams with modest surface roughness (5-10 nm rms in surface height). Resonant phonon scattering has also been observed at 300 mK in beams with highly pitted surfaces with pit depths of order 30 nm. Boundary-limited scattering has contributed to a large variance, up to a factor of 5, in the conductance of devices fabricated and tested during this work. In contrast, when a beam with ballistic-dominated thermal transport is integrated into the design, the uniformity in conductance is reduced to a fractional deviation of $\pm$8\% in devices fabricated across two wafers, and this variability is largely set by the conductance of diffuse beams that support electrical and microwave leads to the device. In addition, we have found no evidence of excess specific heat in single-crystal silicon membranes. Hence, the total heat capacity of the detector can be effectively controlled with a normal metal film. For the transition-edge sensors (TESs) described in this work, the heat capacity was determined by a Pd layer 400 nm thick. Hence, the strategies outlined for the precision control of thermal conductance and heat capacity are well suited to the fabrication of uniform large-format arrays of TESs with sensitivities approaching 10$^{-18}$ W/Hz$^{1/2}$. | 14 | 3 | 1403.1326 |
1403 | 1403.5325_arXiv.txt | We report on intriguing photometric properties of Galactic stars observed in the GALEX satellite's far-UV (FUV) and near-UV (NUV) bandbasses as well as from the ground-based SDSS survey and the Kepler Input Catalog. The first property is that the (FUV-NUV) color distribution of stars in the Kepler field consists of two well separated peaks. A second and the more perplexing property is that for stars with spectral types G or later the mean (FUV-NUV) color becomes much bluer, contrary to expectation. Investigating this tendency further, we found in two samples of mid-F through K type stars that 17-22\% of them exhibit FUV-excesses relative to their NUV fluxes and spectral types. A correction for FUV incompleteness of the FUV magnitude limited star sample brings this ratio to 14-18\%. Nearly the same fractions are also discovered among members of the Kepler Eclipsing Binary Catalog and in the published list of Kepler Objects of Interest. These UV-excess (``UVe") colors are confirmed by the negative UV continuum slopes in GALEX spectra of members of the population. The SDSS spectra of some UVe stars exhibit metallic line weakening, especially in the blue. This suggests an enhanced contribution of UV flux relative to photospheric flux of a solar-type single star. We consider the possibility that the UV excesses originate from various types of hot stars, including white dwarf DA and sdB stars, binaries, and strong chromosphere stars that are young or in active binaries. The space density of compact stars is too low to explain the observed frequency of the UVe stars. Our model atmosphere-derived simulations of colors for binaries with main sequence pairs with a hot secondary demonstrate that the color loci conflict with the observed sequence. As a preferred explanation we are left with the active chromospheres explanation, whether in active close binaries or young single stars, as a still tentative explanation for the UVe population - despite the expected paucity of young, chromospherically-active stars in the field. We also address a third perplexing color property, namely the presence of a prominent island of ``UV red" stars surrounded by ``UV blue" stars in the diagnostic $(NUV-g)$, $(g-i)$ color diagram. We find that the subpopulation comprising this island are mainly horizontal branch stars. These objects do not exhibit UV excesses and therefore have UV colors typical for their spectral types. This subpopulation appears ``red" in the UV only because their colors are not pulled to the blue by the inclusion of UVe stars. | Although the Kepler program was conceived as a NASA space-borne mission dedicated to the discovery of Earth-sized exoplanets, its data archive is now being mined as an important resource for determining fundamental properties of late-type stars, including their evolution and variability, as well as a resource for the discovery of new stellar populations. The ensuing literature promises to mark the Kepler mission's Field of View (FOV) as a region of dedicated study of Galactic disk stars for some time to come. The study of Kepler light curves has required complementary ground-based observations to determine basic stellar parameter. To take one example, a planetary host star's radius is used with the eclipse depth to determine the radius of a transiting planet. The first large ground-based effort was the construction of the Kepler Input Catalog (KIC), which contained mean magnitudes obtained from the clones of the ${\it g, r, i, z}$ filters introduced by the Sloan Digital Sky Survey (SDSS) project\footnote{The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. Funding for SDSS was provided by the Alfred P. Sloan Foundation, Participating Institutions, the National Science Foundation, U.S. Department of Energy, and the National Aeronautics \& Space Administration. The 2.5m SDSS telescope is described by Gunn et al. (2006). Technical summary of the SDSS project are given by York et al. (2000) and Stoughton et al. (2002). } before the launch of the Kepler spacecraft. Described by T. Brown et al. (2011), the KIC provided optical and near-IR magnitudes for nearly all stars down to magnitude 17 in the region of the sky where Kepler's camera would be pointed. The ``Kepler magnitude" (K$_p$) used by the KIC is a weighted mean of the $g$ and $r$ magnitudes. The catalog also included ${\it JHK}$ infrared observations from the {\it 2MASS} survey. Because foremost the SDSS was a survey of extragalactic objects, the sky coverage of the principal SDSS data releases avoided low Galactic latitude sky zones and this avoidance included the Kepler FOV. The FOV is a 105 deg.$^{2}$ field and lies within Galactic latitudes 5-22$^{\circ}$ toward the constellations Lyra and Cygnus. Building on the success of the SDSS project, Groot et al. (2009) and Verbeek et al. (2012) published the ``UVEX catalog," a SDSS filter-based photometric survey of objects with strong UV excess fluxes in a 1850 deg.$^{2}$ region of the Northern Galactic plane. Steeghs et al. (2012) used SDSS filter copies to observe 98\% of the area comprising the Kepler FOV, which as we have noted likewise substantially restricts studies to stars in the Galactic (thin) disk. This work is known as the Kepler Isaac Newton Telescope Survey (``KIS," Steeghs et al. 2012), is calibrated in the Vega magnitude system, and is distributed by MAST. Our work includes the results of both releases, that is the union of both sky areas. A spectroscopic follow up to the UVEX catalog by Verbeek et al. (2012b) confirmed the catalog authors' conclusions that 95\% of UVEX objects are hot objects such as DA and DB white dwarfs (WD), WD binaries, hot subdwarf (sdO, sdB) stars, and QSOs. Rounding out the other 5\% are upper main sequence stars and members of the Blue and Extreme Horizontal Branches. The addition of UV sky surveys from the GALEX satellite extended the wavelength coverage to simultaneous observations in the near-UV (NUV, centered at 2271\,\AA) and far-UV (FUV, centered at 1528\,\AA) wavebands. The photometric depth of these surveys depended on the wavelength band and exposure time associated with the survey (e.g., Morrissey et al. 2007, Bianchi 2009, 2011). Like the SDSS the GALEX surveys avoided the low Galactic latitude sky regions owing to safety limits imposed by diffuse glow and bright stars (m$_{NUV} <$ 9.5). For completeness, we note that an electrical overcurrent in the FUV camera caused its shutdown in May, 2009. NASA funding for the GALEX mission was terminated in early 2012. As for the Kepler spacecraft, the failure of a reaction wheel in May 2013 brought to a close its search for exoplanets in the FOV. Despite the extensive GALEX literature, rather few studies of stellar properties have been published to date that combine optical, IR, and GALEX photometry in the Kepler FOV. One reason for this still incomplete record is that whereas IR magnitudes form an important complement, the UV magnitudes are faint and are generally less important to characterizing a cool star. Also, because of the diffuse UV glow in the Galactic Plane, a homogeneous GALEX survey could not cover more than half the Kepler FOV. The optical and GALEX imaging surveys can accumulate strong UV fluxes of several important stellar populations which are largely unrelated to Kepler's core mission studies. By making use of the (UV/optical) $U$ filter, KIS provides a bridge between the KIC optical and the GALEX NUV and FUV magnitudes and facilitates the discovery of Galactic stars with UV excesses in this important sky field. Several studies that combine SDSS and GALEX data have contributed to our understanding of stellar populations, particularly by deriving photometric spectral types for Galactic stars. Bianchi et al. (2005, 2007, 2011) and Bianchi (2011) have published initial results from these comprehensive photometric surveys. These authors computed colors of galaxies, QSOs, and well represented populations of Galactic stars (main sequence, giants/supergiants, white dwarfs) through the SDSS and GALEX filters. This body of work demonstrated that unresolved galaxies and QSOs can be differentiated well by using GALEX UV colors combined with the SDSS ground-based data. Comparison of the GALEX and SDSS surveys shows that in both the Medium and All-Sky Imaging Surveys, the number of Galactic stars per square degree falls off and equals the number (rapidly rising with magnitude) of GALEX-identified galaxies at K$_p$ = 17-18 magnitude. While the addition of GALEX UV colors has facilitated searches for hot objects with UV excesses, new binary classes have been found that include cool companions. Thus, GALEX and SDSS colors together have enabled the discovery of White Dwarf-Main Sequence systems (WDMS), i.e., binaries with WD primaries and late-type main sequence secondaries (see Rebassa-Mansergas et al. 2010, 2012, Girven et al. 2012b, N\'emeth et al. 2012). Herein we extend previous work by examining a newly discovered population of Galactic disk stars with GALEX far-UV excesses. Although these stars were first discovered in sky areas common to both GALEX and SDSS, our emphasis will be on the properties of similar objects that lie within the Kepler FOV chiefly because of the promised rich harvest from ground-based follow-up campaigns on them. Thus, primarily we relied on the stars observed by the GALEX GR6/GR7 surveys in the FOV. Secondarily, we relied on stars observed by GALEX and SDSS DR7 imaging surveys, i.e. in sky regions not covered by the FOV and used by Smith \& Shiao (2011). Moreover, the SDSS filter colors used in each case are taken from different magnitude systems. Because the samples are independent, we will treat them separately. Both samples were created by adopting cross-correlation search radii of 5 arcsec and restricting matches that were closest neighbor members of one survey to the other and vice versa. The magnitude and error limits are discussed below. Also, unless stated otherwise we generally constrained our study of the Kepler FOV to objects considered probable stars brighter than K$_p$ = 16.0 and within 0.55\,$^{\circ}$ of the GALEX tile centers.\footnote{For the SDSS/GALEX population the faint limit was K$_p$= 18.} This is also the practical limit for KIS recommended by Steeghs et al. (2012). | Spurred by curious features in GALEX-SDSS color diagrams found by Smith \& Shiao (2011), we have investigated populations of solar-type stars (F-K dwarfs and some giants) with K$_p$ $\le$ 16.0 to demonstrate that at least 17\% of them are observed with FUV excesses of about 3-4 magnitudes. The existence of these excesses is robust, and they are present with nearly the same frequency for three stellar samples we investigated: (1) the GALEX-SDSS overlap region of the sky, (2) those overlap regions of the Kepler FOV observed by the GALEX surveys, (3) the systems listed in the Kepler Eclipsing Binary Catalog. Among a smaller number taken from the KOI list, a subsample (2 of 12 stars) exhibits UV excesses consistent with these populations. GALEX and SDSS spectra of stars show that these excesses diminish from the far-UV wavelength region and are still visible in the blue and even through the visible region. The distribution of UVe stars in Fig.\,\ref{fngi} suggests that the $(g-i)$ color is redder than the UV-normal stars that have the same spectral type and T$_{\rm eff}$. We speculate that the reddening of the visible band color arises from the protrusion of a strong chromosphere into the photosphere. The warmer temperature would produce a shift of the primary continuum contributor from the H$^{-}$ ion to bound-free transitions of hydrogen. This in turn shifts the formation of the near infrared continuum ($i$ filter) deeper into the atmosphere, resulting in relatively more IR flux relative to the optical ($g$ filter). A similar explanation may hold for the reddening in (r-K) color by UVe stars. Thus, the reddening of this color could be consistent with the strong chromosphere hypothesis. In all, degenerate star populations (DA and sdOB stars) and especially chromospherically active F-K stars could contribute a minor fraction to the population of UVe stars. We estimate from their occurrence rates a total of no more than 2\% and 4\%, respectively. From the expectation that the number of young F-G main sequence stars is low, we are hard pressed to accept that they are numerous to account for the full UVe population by themselves. Considering the similar UVe population fractions in the GALEX-SDSS sky (Fig.\,\ref{fnteff}), we estimate a floor of perhaps 15-17\% of the apparent UVe population. One or more other populations are evidently needed to explain their numbers. With correction for the FUV incompleteness, this floor falls to 12-14\%. We summarize our evaluation of the contributions of the likeliest contributors to the UVe population in Table\,1. Our estimates in the table for old yet chromospherically active stars and close binaries are taken from Pace (2013). Our assessment of the contributions of extragalactic and compact objects (WDs, sdBs) come our assessments in $\S$\ref{discs}. We have added halo stars to the latter group as a minor possibility. Their expected numbers (Gilmore \& Zeilik 2000) are only about one sixtieth of the UVe population. Moreover, their UVe excesses are not as large the as 3-4 magnitudes observed, and their rotations are slower than the moderate ones reported above. As noted, we estimate that roughly 4\% of the F-K stars can be young ($\approx$0.5 Gyr). Our total of $\ltsim$15\% in the table is already optimistic and yet it falls short of our estimate of the observed fraction, 17-22\%. However, if we multiply the observed rate by the FUV-incompleteness factor 0.82, estimated in $\S$\ref{genproc}, the corrected observed UVe rate becomes 14-18\%. This puts us within striking distance of agreement to the {\rm SUBTOTAL} line in the table. We represent this correction exercise in Table\,1 by bringing the predicted component population rates to the observed values, i.e., by applying the factor's reciprocal, 1.22, to the {\rm TOTAL} line. The agreement is only modestly comforting because most of the estimated percentages are upper limits. Hence, we cannot be assured that we have identified all the components of the UVe population or their relative proportions. As this paper was being refereed, A. Brown et al. (2013) reported on a study of young G-K\,V bright dwarfs in a 5 deg.$^{2}$ Kepler field. They found that spectra of 51 out of 300 stars in their sample exhibit strong lithium lines and concluded tentatively that approximate equal numbers of the sample are young single stars and active binaries. This is consistent with our findings in Table\,1. \begin{table}[h!] % \tablenum{1} % \begin{center} % \center{\caption{Contributors to the UVe population among F-K stars }} % \begin{tabular}{lc} % \\ % \tableline\tableline % Contributing Population & ~~~~Estimated Percentage \\ % \tableline % Extragalactic & ~~~~~$<$1 \\ WD, sdB, halo & ~~~~$\le$2 \\ Old active Stars & ~~~~$\le$5 \\ Active binaries & ~~~~$\le$4 \\ Young stars & ~~~$\approx$4 \\ & \\ SUBTOTAL: & ~~~~$\le$16\% \\ FUV incompleteness corr.: & ~~~1.22$\times$ \\ TOTAL: & ~~~~$\le$20\% \\ \tableline % \end{tabular} % \end{center} % \end{table} % The existence of the UVe population influences the mean UV colors of another stellar group. Our UVe group consists mainly of late F to G and K stars. Yet the A/early-F stars, especially giants. are not among them. The AF stars constitute a distinct ``UV blue" population because of their higher effective temperatures. In contrast, the UVe frequency is higher among GK and early M-type main sequence stars. This strongly pulls their mean (FUV-NUV) colors to the blue (Fig.\,\ref{fndist}). These late-type stars comprise the UV-blue stars in Fig.\,\ref{ging1}, and thus they appear to surround a ``UV-red clump." To complete this discussion, notice that the {\it blue} peak of the histogram in Fig.\,\ref{fndist} is significantly augmented by the addition of {\it } faint, point-like extragalactic objects (Bianchi et al. 2007). This can be seen in the 17$<$ K$_p$ $<$ 19 mag. distribution broken out in this figure. We look forward to detailed studies of the EBC systems and particularly KOI stars with UVe colors. These can determine if near-UV fluxes from the secondaries influence the colors of the primaries as they eclipse them. We also anticipate that radial velocity studies of many of these stars will refine the frequency estimates of active binaries. A study of the ages of these objects via asteroseismology will also address whether young active chromospheres can be expected to be prevalent after all. In that event one can hope to amass a sample of young planet-hosting stars to compare with older stars to find out how planet-bearing incidence changes with time and also to map the evolution of planetary system properties. | 14 | 3 | 1403.5325 |
1403 | 1403.2219_arXiv.txt | Our recent search for the presence of a magnetic field in the bright early A-type supergiant HD\,92207 using FORS\,2 in spectropolarimetric mode indicated the presence of a longitudinal magnetic field of the order of a few hundred Gauss. Assuming the ideal case of a non-variable star, this discovery has recently been questioned in one work trying to demonstrate the importance of non-photon noise in FORS\,2 observations. The assumption of non-variability of HD\,92207 can, however, not be held since substantial profile variations of diverse lines on a time scale of minutes or maybe even a fraction of a minute are detected in FORS\,2 spectra. The presence of short-term spectral variability in blue supergiants, which are considered as type~II supernova progenitors, has not been a subject of systematic studies before and is critical for the current theoretical understanding of their physics. Given the detected short term variability, the question of the presence of a magnetic field cannot be answered without proper modeling of the impact of such a variability on the measurements of the magnetic field. Since the short-term periodicity does not fit into the currently known domain of non-radially pulsating supergiants, its confirmation is of great importance for models of stellar evolution. | \label{sect:intro} Recent developments in observational techniques and theories reveal the potential significance of magnetic fields for stellar structure, evolution, and circumstellar environment. At present, the distribution of magnetic field strengths in massive stars from the zero-age main sequence to more evolved stages, which would shed light on the origin of the magnetic field, has not been systematically studied. Our recent search for the presence of a magnetic field in the visually brightest early A-type supergiant HD\,92207, using FORS\,2 in spectropolarimetric mode, resulted in the discovery of a rather strong mean longitudinal magnetic field of the order of a few hundred Gauss \citep{Hubrig2012}. The photometrically and spectroscopically variable bright A0 supergiant star HD\,92207 is of particular interest for spectropolarimetric studies. It has been monitored for several years in the $uvby$-Str\"omgren system by \citet{Sterken1983} and spectroscopically by \citet{Kaufer1996,Kaufer1997}, who found cyclical changes of the brightness and substantial profile changes for metal lines and at H$\alpha$, and suggested that the observed photometric and H$\alpha$ line variations are the result of a corotating structure in the wind, which they considered to be in the star's equatorial plane. Furthermore, their study of the line profile variations revealed clear pulsation-like structures, indicating the presence of non-radial pulsations (NRPs) with a period of 27\,days, while the stellar rotation period is of the order of several months. \citet{Ignace2009} measured linear polarisation in the spectra of this star on seven different nights, spanning approximately three months in time. For the continuum polarisation, the spiral-shaped wind density enhancement in the equatorial plane of the star suggested by \citet{Kaufer1996} was explored. Importantly, the authors reported that the polarisation across the H$\alpha$ line on any given night is typically different from the degree and position angle of the polarisation in the continuum. These night-to-night variations in the H$\alpha$ polarisation are hard to understand in terms of the spiral structure that was considered for the continuum polarisation. Recently, \citet{Bagnulo2013} claimed that the discovery of a longitudinal magnetic field in FORS\,2 data is spurious due to non-photon noise, more specifically due to small offsets in the parallel and perpendicular beams, or non-predictable instrument instabilities or flexures, evidenced by changes in the individual spectra. In all considerations of possible culprits playing a role in the magnetic field determination, Bagnulo et al.\ explicitly exclude the role of intrinsic spectral variations, assuming the ideal case of a non-variable star, referring to HARPSpol observations obtained in 2013. In this study, we present a careful inspection of the FORS\,2 spectra used for the magnetic field determination in HD\,92207 in our previous work. We report on the detection of short-term variability in this object, implying that the assumption of an ideal case of a non-variable star cannot be held. | \label{sect:disc} The main conclusion by \citet{Bagnulo2013} on the discrepancies between their and our earlier determination of the longitudinal magnetic field seems to be a wrong relative wavelength calibration on our side, especially due to the impact of wavelength shifts when rotating the retarder waveplate. While the assessment of a potential influence of a wrong relative wavelength calibration seems to be correct, it is not plausible that this is actually an issue for the data from the first epoch, where the longitudinal magnetic field is detected. Directly after the observations of HD\,92207, we observed the hot massive star HD\,93843 close to the position of HD\,92207, at the same air mass and with similar short exposure times. We do not find any distinct Zeeman features for HD\,93843 and the determined longitudinal magnetic field is compatible with zero. HD\,93843 also does not show strong spectral variability on a short time scale, ruling out that spectral variability is introduced due to imperfections within FORS\,2. The same results are obtained from observations of $\zeta$\,Oph, with an exposure time of 0.2\,s. In the same night, we also observed the two Of?p stars HD\,148937 and CPD\,$-$28\,2561 \citep{Hubrig2013}. The measurement of a magnetic field of $139\pm33$\,G in HD\,148937 using the same wavelength calibration is perfectly in line with earlier measurements by ourselves \citep{Hubrig2011a,Hubrig2013} and \citet{Wade2012}, following the 7.032\,d period determined by \citet{Naze2010}. For CPD\,$-$28\,2561, we find a magnetic field of $269\pm81$\,G, which is supported by \citet{Petit2013}, who give a polar field strength larger than 1.7\,kG for CPD\,$-$28\,2561. All these measurements indicate that there is nothing wrong with the wavelength calibration for that night. This still leaves room for a spontaneous instability in the FORS\,2 wavelength calibration that affects the observations of HD\,92207 but no other object. While we can not rule this out, there is no evidence that could support this speculation in this or any other FORS\,1/2 data set. Another point raised by \citet{Bagnulo2013} was that we could underestimate our magnetic field errors. We have used the mechanism to estimate the ``external'' error, as described by \citet{Bagnulo2012} and can conclude that there is also no issue with the data in that respect. We also used the Monte Carlo bootstrapping tests proposed by \citet{Rivinius2010}, which indicate that we only slightly understimated our initial errors. We suggest that what \citet{Bagnulo2013} claim to result from non-photon noise, most probably can be traced back to spectral variability of HD\,92207 on short time scales. The available FORS\,2 polarimetric spectra clearly show the presence of short-term spectral variability, which was not previously discussed in the literature for any blue supergiant and certainly needs further investigation. In particular, a careful search for periodicity and identification of pulsation modes causing the remarkable changes in the line intensity and position on time scales of the order of minutes are urgently needed. With the current data, it can not be decided, if the variations are of periodic or stochastic nature. In any case, given the size of the supergiant, it is clear that the variability can not be referred to coherent line variations across the entire surface on such short time scales. Obviously, seismic studies are of great importance to constrain physical processes in stars, e.g. differential rotation, mixing, mass loss, etc.. Despite several decades of observational efforts with ground-based photometry and spectroscopy of bright blue supergiants, it is not yet certain what portion of their variability is periodic, or how far they deviate from strict periodicity. On the other hand, in the most recent observational studies of massive stars, evidence is accumulating that some BA supergiants exhibit multiperiodic NRPs. As an example, short-term variability was already identified on a time scale of 1--3\,hours \citep{Lefever2007,Kraus2012}. However, a variability on time scales of the order of minutes has not been detected so far, mostly due to the fact that telescopes with large collecting areas are needed for studies with spectral time sampling of a few minutes. Clearly, it is not possible to use the low-resolution FORS\,2 spectra to model the effect of pulsations on the magnetic field measurements, and the potential of high-resolution spectropolarimetric observations should be used in the search of short-term variations (e.g.\ \citealt{Hubrig2011b}). We need to note that due to the proprietary time of one year for ESO observations, we are not yet able to study the spectral variability of this star in the high resolution HARPSpol spectra mentioned in the work of \citet{Bagnulo2013}. The question how pulsations affect the magnetic field measurements is not yet solved in spite of the fact that the number of studies of pulsating $\beta$~Cephei and slowly pulsating B (SPB) stars is gradually increasing. Already in \citeyear{Schnerr2006}, \citeauthor{Schnerr2006} discussed the influence of pulsations on the analysis of the magnetic field strength in the $\beta$~Cephei star $\nu$~Eri in MUSICOS spectra and tried to model the signatures found in Stokes $V$ and $N$ spectra. Although the authors claim that using some modeling they are able to quantitatively establish the influence of pulsations on the magnetic field determination, they still detect profiles in Stokes $N$ and $V$ that are the result of the combined effects of the pulsations and the inaccuracies in wavelength calibration that were not removed by their imperfect modeling of these effects. Another important effect in the measurements of magnetic fields in pulsating stars, applying the LSD method to high-resolution polarimetric spectra, is that the line profiles belonging to different elements show different profile shapes and different displacements. The authors usually use essentially all metallic lines and He lines (up to several hundred lines) to calculate a "mean" LSD line profile, although the behaviour of lines of different elements during the pulsation cycle is frequently different (e.g.\ \citealt{Hubrig2011b}). Blue supergiants are considered as type~II supernova progenitors. A careful study of their variability provides important diagnostic means for internal and atmospheric structure. The need for multiple modes to fit to the spectroscopic data sets has already been presented in several works analysing BA supergiants. According to the study of Rigel by \citet{Moravveji2012}, periods shorter than about a week can only be caused by the $\kappa$-mechanism if other sources such as spots, variable winds, and propagating shocks can be excluded. The goal of future studies should be to search for the presence of short-term variability and periodicities in bright A0 supergiants with similar stellar parameters. Moreover, since the short-term periodicity does not fit into the currently known domain of non-radially pulsating supergiants, its confirmation is of great importance for the models of stellar evolution. | 14 | 3 | 1403.2219 |
1403 | 1403.2733_arXiv.txt | We present the first high resolution spectroscopic observations of one red giant star in the ultra-faint dwarf galaxy Segue~2, which has the lowest total mass (including dark matter) estimated for any known galaxy. These observations were made using the MIKE spectrograph on the Magellan~II Telescope at Las Campanas Observatory. We perform a standard abundance analysis of this star, SDSS~J021933.13$+$200830.2, and present abundances of 21~species of 18~elements as well as upper limits for 25~additional species. We derive [Fe/H]~$= -$2.9, in excellent agreement with previous estimates from medium resolution spectroscopy. Our main result is that this star bears the chemical signatures commonly found in field stars of similar metallicity. The heavy elements produced by neutron-capture reactions are present, but they are deficient at levels characteristic of stars in other ultra-faint dwarf galaxies and a few luminous dwarf galaxies. The otherwise normal abundance patterns suggest that the gas from which this star formed was enriched by metals from multiple Type~II supernovae reflecting a relatively well-sampled IMF. This adds to the growing body of evidence indicating that Segue~2 may have been substantially more massive in the past. | \label{introduction} In the last decade, we have witnessed the discovery of extremely low-luminosity dwarf galaxies, largely due to the advent of the Sloan Digital Sky Survey (SDSS). The innovative searches for these galaxies were pioneered by \citet{willman05}, \citet{belokurov07}, and others. One member of this class of ultra-faint dwarf galaxies, \seggal, was initially identified by \citet{belokurov09} as a stellar overdensity on the sky in images obtained as part of the Sloan Extension for Galactic Understanding and Exploration (SEGUE) and by using matched filters in colour-magnitude space. Deeper imaging and followup spectroscopy confirmed this detection, identified the presence of a cold velocity structure with a non-zero velocity dispersion, and indicated a mean metallicity of approximately 1/100$^{\rm th}$ solar. \citet{kirby13} used the DEIMOS spectrograph to obtain red and near-infrared spectra of 25~probable members of \seggal. These medium resolution spectra allowed \citeauthor{kirby13}\ to constrain the line-of-sight velocity dispersion of \seggal\ to be $<$~2.6~\kmsec\ at 95~per cent confidence. This corresponds to a mass $<$~2.1~$\times$~10$^{5}$~\msun\ within the half-light radius assuming \seggal\ is in dynamical equilibrium. That study also derived abundances of iron (Fe) and the $\alpha$ elements magnesium (Mg), silicon (Si), calcium (Ca), and titanium (Ti) for the 10~brightest members of \seggal\ based on fits to a grid of synthetic spectra. \citeauthor{kirby13}\ confirmed that stars in \seggal\ span a range in metallicity of more than 1.5~dex. The [$\alpha$/Fe] ratios in \seggal\ generally decrease with increasing [Fe/H], as seen in classical dwarf galaxies (e.g., \citealt{shetrone03}; \citealt{kirby11a}) but not all of the ultra-faint dwarf galaxies \citep{frebel10,vargas13}. \seggal\ is the least-massive galaxy currently known based on its inferred dynamical mass. Yet with a mean metallicity of [Fe/H]~$= -$2.2 it does not obey the mass-metallicity relationship established by \citet{kirby11b} for classical and ultra-faint dwarf galaxies. \seggal, along with \segigal\ and \wilgal, may reveal the existence of a metallicity floor in galaxy formation. Alternatively, \seggal\ may have been substantially more massive before being tidally stripped down--by a factor of several hundred in stellar mass--to the remnant observed today. We present the first high resolution spectroscopic observations of one red giant in \seggal, \seg, the only star reasonably bright enough for such observations. By coincidence, this star happens to be the most metal-poor star identified by \citet{kirby13} as a probable member. We use these data to confirm the radial velocity measured by \citeauthor{kirby13}\ and derive detailed abundances of 21~species of 18~elements. We also present upper limits derived from non-detections of 25~additional species. Throughout this work we adopt the standard definitions of elemental abundances and ratios. For element X, the logarithmic abundance is defined as the number of atoms of X per 10$^{12}$ hydrogen atoms, $\log\epsilon$(X)~$\equiv \log_{10}(N_{\rm X}/N_{\rm H}) +$~12.0. For elements X and Y, [X/Y] is the logarithmic abundance ratio relative to the solar ratio, defined as $\log_{10} (N_{\rm X}/N_{\rm Y}) - \log_{10} (N_{\rm X}/N_{\rm Y})_{\odot}$, using like ionization states; i.e., neutrals with neutrals and ions with ions. We adopt the solar abundances listed in \citet{asplund09}. Abundances or ratios denoted with the ionization state indicate the total elemental abundance as derived from transitions of that particular state. | \label{discussion} \subsection{Metal Production in Segue 2} \label{metals} The [Mg/Fe], [Ca/Fe], and possibly [Ti/Fe] ratios in \seg\ are enhanced relative to the solar ratios and are not subsolar like those found in the more metal-rich stars of classical Local Group dwarf galaxies. Neither the intermediate odd-$Z$ elements (Na, Al, K) nor the iron group elements show any significant deviations from the abundance patterns commonly found in field stars or dwarf galaxies. Ratios among the neutron-capture elements and iron ([Sr/Fe], [Ba/Fe]) are subsolar by more than 1~dex, but these deficiencies are common in the ultra-faint dwarf galaxy populations and lie at the low ends of the halo star distributions. This abundance pattern can be attributed to enrichment by Type~II supernovae. In Type~II supernovae, magnesium is produced via hydrostatic carbon and neon burning, and calcium is produced via oxygen burning during the explosion (e.g., \citealt{woosley95}). Fig.~\ref{abundplot5} illustrates that the [Mg/Ca] ratio in \seg\ is the same as in the majority of stars in the field, \umigal, and the ultra-faint dwarf galaxies with similar [Mg/H] ratios. Fig.~3 of \citet{feltzing09} and Figures~20 and 21 of \citet{venn12} demonstrate that the [Mg/Ca] ratios in several other classical and ultra-faint dwarf galaxies match this ratio within a factor of $\approx$~2, regardless of whether [Mg/Fe] and [Ca/Fe] are solar or supersolar. To place this result in context, it may be helpful to examine stars with non-standard [Mg/Ca] ratios. In the dwarf galaxy population, these include one star found in \dragal\ \citep*{fulbright04}, two stars in \hergal\ \citep{koch08}, and one star in \cargal\ \citep{venn12}. In these stars, the hydrostatic $\alpha$ elements O and Mg are enhanced relative to the explosive $\alpha$ element Ca. These authors interpreted the enhanced [Mg/Ca] ratios as a consequence of stochastic sampling of the high end of the Type~II supernova mass function. \citet{gilmore13} report a star in \boogal, \mbox{Boo-119}, with a high [Mg/Ca] ratio. This star also shows enhanced [C/Fe] \citep{lai11} and [Na/Fe], suggesting it is a member of the class of carbon-enhanced metal-poor stars with no enhancement of neutron-capture elements. Such stars have been suggested as some of the earliest to have formed from the remnants of zero-metallicity Pop~III stars (e.g., \citealt{norris13}). \citet{feltzing09} reported another star with enhanced [Mg/Ca] in \boogal, \mbox{Boo-127}, but that result was not confirmed by \citeauthor{gilmore13}\ and \citet{ishigaki14}. The similarity of the [Mg/Ca] ratios in \seg, the field giants, and most classical dwarfs suggest that the Type~II supernovae reflect a relatively well-sampled initial mass function (IMF) in \seggal. \citet{kirby13} excluded inhomogeneous mixing as the source of the metallicity spread in \seggal\ on account of the dispersion in the [Si/Fe] and [Ti/Fe] ratios. Downward trends in these ratios (and possibly [Mg/Fe]) with increasing [Fe/H] suggest that star formation in \seggal\ occurred over a timescale long enough to incorporate the products of multiple supernovae. Abundance information for more metal-rich stars in \seggal\ is limited to the [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe] ratios derived by \citeauthor{kirby13} % These data may indicate that the additional metals were manufactured by Type~Ia supernovae, which produce intrinsically lower [$\alpha$/Fe] ratios. \citet{mcwilliam13} offer an alternative hypothesis that better explains the declining [$\alpha$/Fe] ratios and low ratios of hydrostatic to explosive $\alpha$ elements in the \sgrgal\ dwarf galaxy. In this scenario, an extension of that proposed initially by \citet{tolstoy03} for other classical dwarf galaxies, a low star formation rate produces a top-light IMF. The yields of hydrostatic $\alpha$ elements increase with increasing stellar mass, so they will naturally be deficient in such a scenario. The extant data are insufficient to distinguish between these scenarios in \seggal, but the composition of at least one of the most metal-poor stars in \seggal\ is dominated by products of fairly normal Type~II supernovae. Either way, the \citeauthor{kirby13}\ abundance data indicate that \seggal\ experienced self-enrichment, excluding it from the list of candidates for the ``one-shot enrichment'' scenario proposed by \citet{frebel12}. \begin{figure} \begin{center} \includegraphics[angle=00,width=3.0in]{fig7.eps} \end{center} \caption{ \label{abundplot5} The [Mg/Ca] ratios as a function of [Mg/H]. Symbols are the same as in Fig.~\ref{abundplot1}. } \end{figure} \subsection{The Original Mass of Segue 2} \label{originalmass} \seggal\ has a present-day stellar mass of $\approx$~10$^{3}$~\msun\ \citep{kirby13}, assuming $M_*/L_V = 1.2$, as is typical for dwarf spheroidal galaxies \citep{woo08}. The [Sr/Fe] ratio in \seggal\ more closely matches that found in the ultra-faint dwarf galaxies than in \umigal. This could be an indication that the original mass of \seggal\ was not quite as large as the original mass of \umigal. Similarly low [Sr/Fe] ratios are also found, however, in a few stars in the more luminous systems \dragal\ \citep{fulbright04}, \hergal\ \citep{koch08}, and \cargal\ \citep{venn12}. We consider the low [Sr/Fe] ratio in \seg\ inconclusive regarding the original mass of \seggal. On one hand, the total mass of metals, $\sim$~0.1~\msun, in a galaxy as small as \seggal\ is consistent with the predicted yields of a single zero-metallicity supernova (cf.\ \leogal; \citealt{simon10}). Substantial metal loss from dwarf galaxies seems unavoidable, however, so multiple supernovae may be necessary to account for the small fractions of metals retained, even in the lowest metallicity stars. \citet{kirby11c} estimate that this fraction could be 1~per cent or less for dwarf galaxies like \umigal. For a \citet{salpeter55} IMF, only $\sim$~2~stars with $M >$~8~\msun\ would be expected for every 10$^{3}$~\msun\ of stars formed. \citeauthor{tumlinson06}'s (2006) chemical evolution model predicts that the average halo star with [Fe/H]~$\sim -$3 and normal abundance ratios has $\sim$~10 enriching progenitors. This model might also be applicable to \seg\ because this star has abundance ratios like halo stars of similar metallicity. Therefore, \seg\ might also require at least $\sim$~10 enriching progenitors to explain its chemical abundances, or $\sim$~5 times as many as would be expected from a \citeauthor{salpeter55} IMF for a galaxy with \seggal's current stellar mass. Consequently, we infer that the stellar mass of \seggal\ was at least $\sim$~5 times greater when it first formed stars than it is today. Following a different line of reasoning, \citet{kirby13} estimated that \seggal\ must have had $\ga$~150~times its current stellar mass in order to retain the ejecta of one supernova. This missing mass could be dark matter or other stars that are no longer part of \seggal. \citeauthor{kirby13}\ also note that \seggal\ does not lie on the (present-day) luminosity-metallicity relation, which predicts that a galaxy of \seggal's luminosity should have a mean metallicity of [Fe/H]~$= -$2.83~$\pm$~0.16 \citep{kirby11b}, a factor of 4~lower than derived by \citet{kirby13}. % Therefore \seggal\ would have shed $\approx$~99.7~per cent of its original stellar mass if it obeyed the luminosity-metallicity relation at the time it was born. Presumably this mass loss would have occurred as \seggal\ fell into the Milky Way halo. Low surface brightness tidal tails have not yet been detected around \seggal, and unfortunately no proper motions are available to calculate the orbit of \seggal\ with respect to the Milky Way. \subsection{The Origin of the Neutron-Capture Elements in Segue 2} \label{ncaps} Despite our best efforts, no heavy elements except strontium and barium can be detected in our spectrum of \seg. In Section~\ref{results} we presented some typical \rpro\ and \spro\ ratios of [Sr/Ba] for comparison, and the [Sr/Ba] ratio in \seg\ is suggestive of an \rpro\ origin. Yet the [Sr/Ba] ratio alone is hardly sufficient to unambiguously determine what kind of nucleosynthesis reactions may have produced the heaviest elements found in \seg. Strontium may be produced by a myriad of neutron-capture and charged-particle reactions, and the abundance patterns resulting from $r$- and \spro\ nucleosynthesis depend on the physical conditions at the time of nucleosynthesis. The barium abundance and our upper limit on the europium abundance in \seg\ ([Eu/Ba]~$< +$0.70) cannot exclude the main component of the \rpro\ as exemplified by the abundance pattern in the metal-poor halo star \cs\ (e.g., \citealt{sneden03}; [Eu/Ba]~$= +$0.65). Prodigious lead production also did not occur, and the low [Sr/Fe] and [Ba/Fe] ratios suggest that large amounts of \spro\ material were not present in the gas from which \seg\ formed. Without additional information it is best to avoid making any definitive statements regarding the origin of the neutron-capture elements. The unmistakable presence of strontium and barium in the most metal-poor star known in \seggal\ indicates that at least one neutron-capture nucleosynthesis mechanism operated prior to the formation of this star. \citet{roederer13} showed that this is a characteristic of all other systems that have been studied, and our observations demonstrate that \seggal\ is no exception. \citeauthor{tumlinson06}'s (2006) model also predicts that $\sim$~90~per cent of the supernova progenitors of the average halo star with [Fe/H]~$\sim -$3 are zero-metallicity progenitors. While this prediction remains unverified, the presence of neutron-capture elements in \seggal\ and all other systems hints that neutron-capture reactions may have occurred in at least some zero-metallicity stars (cf.\ \citealt{roederer14b}). | 14 | 3 | 1403.2733 |
1403 | 1403.2505_arXiv.txt | {We investigate the influence of Asymptotic Giant Branch stars on integrated colours of star clusters of ages between $\sim$100~Myr and a few gigayears, and composition typical for the Magellanic Clouds. We use state-of-the-art stellar evolution models that cover the full thermal pulse phase, and take into account the influence of dusty envelopes on the emerging spectra. We present an alternative approach to the usual isochrone method, and compute integrated fluxes and colours using a Monte Carlo technique that enables us to take into account statistical fluctuations due to the typical small number of cluster stars. We demonstrate how the statistical variations in the number of Asymptotic Giant Branch stars and the temperature and luminosity variations during thermal pulses fundmentally limit the accuracy of the comparison (and calibration, for population synthesis models that require a calibration of the Asymptotic Giant Branch contribution to the total luminosity) with star cluster integrated photometries. When compared to observed integrated colours of individual and stacked clusters in the Magellanic Clouds, our predictions match well most of the observations, when statistical fluctuations are taken into account, alhough there are discrepancies in narrow age ranges with some (but not all) set of observations.} | \label{s:intro} Stars of moderate mass, between approximately 1 and 8~$M_\odot$, spend less than 1 percent of their lifetime in the phase of double-shell (H- and He-) burning, generally called the Asymptotic Giant Branch (AGB) phase, after exhaustion of central helium-burning and before turning into white dwarfs. For an even shorter fraction of their nuclear life, of order $10^{-3}$, they experience the thermal pulses (TP-AGB phase), during which temperature and brightness vary significantly on timescales of a few thousand years. On the other hand, in these evolutionary stages they are much brighter than they were on the main-sequence (MS): stars of intermediate mass ($\approx 2 - 2.3 \cdots 6 - 8\, M_\sun$) that do not develope electron degenerate He-cores after the MS (the exact mass range depending on the initial chemical composition and treatment of core convection) have a bolometric luminosity larger by a factor of up to 100 compared to the MS turn-off. For low-mass stars the difference is even larger. However, for the latter the difference between the TP-AGB luminosity and that on the tip of the Red Giant Branch (RGB) is closer to a factor of only 10. Since AGB stars are also much cooler than MS stars of comparable mass, they may completely dominate the IR integrated light of a stellar population. The integrated red magnitudes and colours of a single-age stellar population will be dominated by AGB-stars at an epoch when intermediate mass stars have reached this evolutionary stage. At earlier times massive stars dominate, but they contribute much less in the red, because they increase their brightness relatively moderately in post-MS phases and spend a much larger fraction in the blue, anyway. At later times low-mass stars reach the AGB, but here the longer-lived RGB stars dominate the IR output, and thus the importance of the AGB stars is reduced. The age range, during which intermediate-mass AGB stars are significant for the integrated spectrum, is therefore between $\sim$100~Myr and $\sim$1Gyr, varying somewhat with metallicity. This has been demonstrated frequently \citep{lm:00,bch:2003,mar:05,zlhzk:2013,ip:2013} in models of population synthesis \citep[see, for example,][for a recent review]{mgba:2010}. In a broader context, the correct prediction of the IR integrated flux of a stellar population is crucial, for example, to disentangle the age-metallicity degeneracy in integrated colours of unresolved stellar populations \citep[see, e.g.,][]{anders, j:06}, and determine stellar masses of high-redshift objects \citep[see, e.g.][]{mar:05}. New fully evolutionary AGB stellar models for moderate-mass stars, which treat the effects of nucleosynthesis and mixing of carbon on stellar effective temperatures and mass loss consistently, are now available \citep[][hereinafter WF09]{wf:2009}, and in a recent paper \citep[Paper~I]{cp:2013} we have presented new population synthesis models where the contribution of AGB-stars to integrated spectra and colours made use of these AGB calculations\footnote{Both WF09 AGB evolutionary models and the population synthesis models of Paper~I are available upon request}. In the same Paper~I, the reprocessing of stellar light by the dusty circumstellar shell, as obtained from the stellar models, was taken into account by a library of spectral energy distribution (SED) models for such cases. In doing so, we could investigate the role of dust in models of population synthesis for intermediate age populations \citep[see, e.g,][for earlier works on this subject]{ptc:2003, mar:08}. Paper~I was the first attempt, to date, to include fully evolutionary AGB calculations in the predictions of integrated spectra of stellar populations. The standard approach is to include instead simplified treatments of the AGB phase \citep{mar:05}, or synthetic AGB calculations \citep[see, e.g.,][]{mar:08}. However, in several aspects Paper~I remained restricted to conventional assumptions and procedures. First, a preexisting widely used set of isochrones \citep{bbcfn:94} is employed for the pre-AGB phase, and the AGB part is {\sl attached} after appropriate $T_\mathrm{eff}$ and bolometric luminosity shifts, to ensure continuity. This procedure destroys in principle the self-consistency of the AGB calculations; just as an example, the mass loss rates depend on the model luminosity and $T_\mathrm{eff}$, and shifting the tracks would require rates different from the ones actually used, thus a different AGB evolution. Besides this intrinsic inconsistency, the contribution of the AGB (calculated from the shifted tracks) to the integrated flux can be potentially significantly different from what predicted by the {\sl original} AGB calculations. We notice here that shifts in ${T_\mathrm{eff}}$ and luminosity of existing AGB calculations to match pre-AGB models and/or satisfy empirical constraints, are adopted also in other population synthesis models, like the Flexible Stellar Population Synthesis model by \citet{conroy:10}. Second, the TP-AGB portion of the tracks is {\sl pre-smoothed} to eliminate the complicated and irregular loops in the ${T_\mathrm{eff}}$-$L$ plane, and allow a simple interpolation when calculating the full isochrones. This is similar to reducing the TP-AGB phase to the evolution during quiescent H-shell burning as usually done when synthetic AGB models \citep[that nowadays can also take into account the detailed varition of luminosity and sometimes also $T_\mathrm{eff}$ along the pulse cycles, see i.e.][]{itk04, mg07} are implemented in the calculation of integrated spectra of stellar populations \citep[see][for an example]{mar:08}, although the (generally small) contribution of the He-shell burning on the timescales is retained. Third, the distribution of stars along the AGB is computed according to an analytical integration of the initial mass function (IMF). This is certainly appropriate (in the approximation of {\sl smooth} TP-AGB tracks) for well populated massive galaxies, e.g., in case of a well sampled AGB sequence, but it is well known that for stellar clusters and low-mass galaxies the number of AGB stars can be so low that statistical fluctuations of AGB-dominated magnitudes become important \citep{cbb:1988,fmb:1990,sf:1997,b:02,bch:2003,ko:13}. This is relevant when taking into account that tests and calibrations of AGB calculations (evolutionary or synthetic) are typically performed on star clusters of the Magellanic Clouds. In this study we investigate the effects of these three ingredients of the standard approach to include the AGB phase in stellar population synthesis models followed in Paper~I. To this purpose we extend WF09 calculations to models with masses below 1$M_{\odot}$ (the lower limit of WF09 computations), to calculate self-consistent isochrones for the pre-AGB evolution. We also provide extended tests of the accuracy of integrated magnitudes obtained from WF09 calculations --using several sets of data suitable for testing predicted integrated magnitudes/colours that are dominated by AGB stars-- and study the differences with selected integrated colours predicted in Paper~I and by other population synthesis models in the literature. Our approach is the following. We use the AGB evolutionary tracks and all spectral libraries of Paper~I, restricted, however, to two metallicities, $Z=0.004$ and 0.008, appropriate for most of the SMC and LMC clusters, that are used to test/calibrate AGB models. Section~\ref{s:models} presents a brief discussion of the models, introduces the extension of WF09 calculations to low-mass stars, and describes a new Monte Carlo (MC) based approach to calculate the resulting integrated photometric properties, taking into account the oscillatory behaviour of stellar parameters during the TPs. Section~\ref{s:prediction} discusses the effect of statistical fluctuations on magnitudes/colours dominated by the AGB contribution, and evaluates the effect on IR integrated magnitudes of smoothing the TP-AGB tracks and shifting AGB models to match different sets of pre-AGB isochrones as in Paper~I. We also compare predictions for selected colours with independent models in the literature. Section~\ref{s:calibrations} compares our predictions with several observational data, taking into account the effect of statistical fluctuations, followed by Sect.~\ref{s:conclusion} that closes the paper with our conclusions. | \label{s:conclusion} Star clusters in the Magellanic Clouds are of special interest as they cover an age range in which stars of low- and intermediate mass develop into double-shell burning objects, populating the AGB, and can be massive enough to host at least a few AGB stars. Such clusters therefore serve as template and calibration objects for population synthesis aimed at understanding the star formation history of distant galaxies during the last few hundred million to a few billion years. Observations, such as those shown in Fig.~\ref{f:LkLtot_cl}, however, display a large variation of integrated IR colours for clusters of presumably very similar age and composition. It is therefore unclear to what accuracy theoretical population synthesis models could be calibrated or verified against such variations. It was recognized early-on \citep{cbb:1988,fmb:1990} that the low number of AGB stars in individual clusters results in statistical fluctuations of the AGB integrated luminosity that, given the important contribution of late-type luminous stars to the integrated IR-light, explains the variation of IR integrated colours. In this paper we have presented new theoretical predictions of near-IR colours of intermediate-age populations, and tested them against data about clusters in the LMC and SMC, taking into account their low number of AGB-stars. Our predictions rest on the new WF09 fully evolutionary AGB stellar models for stars of low and intermediate mass, and a detailed treatment of the effect of their surrounding dust shells, to achieve the most realistic description of their stellar energy distribution. In Paper~I we have already introduced the new AGB models and the treatment of the dusty envelope, and applied it to observations of galaxies. In that paper, however, WF09 AGB tracks were smoothed out (to calculate AGB isochrones) and shifted in both luminosity and $T_\mathrm{eff}$ to match an independent set of isochrones that model the pre-AGB evolution. Here we employ the full evolution until the end of the TP-AGB phase from WF09 calculations. One new aspect of our predictions is the treatment of the TP-AGB phase in the construction of isochrones (Sect.~\ref{s:spectra}). We have used a MC scheme to populate what we call an {\sl evolutionary HRD} with a given number of AGB stars, comparable to that of observed clusters, and combine it with a standard isochrone for earlier evolutionary phases. This way we have been able to take into account all temperature and luminosity variations that occur during the TP-AGB cycles as well as the statistical fluctuations due to finite star numbers. Our results, presented in Sect.~\ref{s:prediction}, quantitatively demonstrate the possible range of both IR colours (we consider $(V-K_s)$ in Fig.~\ref{f:VKdistr}) and the contribution of AGB stars to the integrated $K_s$-luminosity (Fig.~\ref{f:LkLtotdistr}), how they approach a mean value for large ($\sim 1000$) numbers of AGB stars, and how they distribute almost uniformly over a wide range for low numbers (the case of 10 AGB stars). In $(V-K_s)$ the colour of any cluster can vary by as much as $\pm 0.37$~mag ($1 \sigma$; Table~\ref{t:3}). Our models cover in fact a range up to $\sim$1.2~mag for ages close to 1~Gyr, when AGB stars are most dominant. We have also shown that the luminosity and $T_\mathrm{eff}$ variations during the TP-AGB cycles do not contribute significantly to the total statistical fluctuations of the AGB integrated light, such that interpolations amongst smoothed AGB-tracks as in Paper~I, can also be used, when carefully constructed. They allow construction of conventional isochrones for any desired age, while our --in principle-- more accurate method is restricted by default to the ages of the available stellar model tracks. We have then extended our analysis to investigate the additional contribution of the fluctuations of the RGB integrated luminosity for poorly populated clusters. We found that, as expected, the RGB contribution is negligible for ages below log(t)$\sim$=9.1 (ages younger than the transition to electron degenerate He-cores), while it becomes comparable to the AGB fluctuations at older ages. In terms of consequences for population synthesis of younger stellar clusters, e.g. in star forming regions of distant galaxies, our results imply that for any given age in the range between $\sim$0.1 and $\sim$1 Gyr, infrared colours may vary --due to statistical fluctuations in the number of AGB stars-- to an extent that the cluster age cannot be determined more accurately than a factor $\sim$10. This is already implied by the observational data used in this paper, but substantiated now by our theoretical models. We have taken into account these AGB statistical fluctuations to compare our predictions with empirical data on Magellanic Cloud clusters, the standard bench tests of near-IR population synthesis models. The comparison with empirical estimates of the $L_{K_s}^{AGB}/L_{K_s}^{tot}$ ratio by \cite{ko:13} shows very good agreement in general: when considering the appropriate number of AGB stars, the statistical scatter of our predictions covers the observed distribution, and the variation of $K_s$-band luminosity with age for stacked clusters (or {\em supercluster}) also agrees very well with their data (Figs.~\ref{f:LkLtot_cl} and \ref{f:LkLtot_scl}). When considering integrated near-IR colours, the level of agreement with empirical data for several samples of superclusters \citep{noel:13,Pessev:2008,gonzalez:04} depends somehow on the selected colour, but also on the sample. Clearly, the construction of superclusters as well as the individual observations themselves, are sometimes not consistent. These discrepancies need clarification, and should be a warning to population synthesis models that require calibration with such observed superclusters. In general, our predictions pass the observational tests well, and can also be properly applied to study individual clusters hosting a low number of AGB stars. A comparison with integrated colours from other population synthesis models, including the results of Paper~I, reveals significant discrepancies with results from \citet{mar:08} and \citet{mar:05}. \citet{noel:13} have already discussed how these models disagree (they are generally too red) with the integrated colours of their superclusters for ages between $\sim 10^8$ and $\sim 10^9$~years. The agreement with the model of Paper~I and with the BaSTI-model by \citet{cordier} is, in contrast, excellent. In summary, we have presented a statistical approach to model integrated colours of intermediate-age populations with a small number of stars that makes use of new state-of-the-art stellar evolution models, the effect of dusty envelopes, quantifies statistical fluctuations and matches well observations of individual Magellanic Cloud clusters as well as artificial superclusters. The predictive power of theoretical models, which are not calibrated beforehand on a specific set of observations --this calibration being difficult because of the statistical effects-- should be sufficient for wider applications. | 14 | 3 | 1403.2505 |
1403 | 1403.5922_arXiv.txt | { An inflationary gravitational wave background consistent with BICEP2 is difficult to reconcile with a simple power-law spectrum of primordial scalar perturbations. Tensor modes contribute to the temperature anisotropies at multipoles with $l\lesssim 100$, and this effect --- together with a prior on the form of the scalar perturbations --- was the source of previous bounds on the tensor-to-scalar ratio. We compute Bayesian evidence for combined fits to BICEP2 and \Planck\ for three nontrivial primordial spectra: a) a running spectral index, b) a cutoff at fixed wavenumber, and c) a spectrum described by a linear spline with a single internal knot. We find no evidence for a cutoff, weak evidence for a running index, and significant evidence for a ``broken'' spectrum. Taken at face-value, the BICEP2 results require two new inflationary parameters in order to describe both the broken scale invariance in the perturbation spectrum and the observed tensor-to-scalar ratio. Alternatively, this tension may be resolved by additional data and more detailed analyses. } | The BICEP2 experiment \cite{Collaboration:2014wq,Collaboration:2014xx} has reported a detection of primordial B-modes in the cosmic microwave background (CMB).\footnote{B-mode polarization from CMB lensing was detected earlier by the POLARBEAR experiment \cite{Ade:2014afa}.} The most natural explanation for a B-mode signal is a stochastic background of long-wavelength gravitational waves, or tensor perturbations \cite{Seljak:1996gy}. This constitutes strong {\em prima facie\/} evidence for an inflationary phase in the early universe, the most widely-studied source for a stochastic background of gravitational waves. If the observational data and theoretical explanation are confirmed, the B-mode signal will provide unprecedented insight into the mechanism responsible for inflation. The measured tensor-to-scalar ratio has a $68\%$ confidence-interval (CI) of $r=0.20^{+0.07}_{-0.05}$ and differs from zero with a statistical significance of $5.9 \sigma$. However, the temperature data from \emph{Planck} \cite{Ade:2013xsa,Ade:2013zuv,Ade:2013uln}, SPT \cite{Hou:2012vk}, and ACT \cite{Das:2013wg}, combined with WMAP \cite{Hinshaw:2012aka} polarization, yields $r \lesssim 0.11$ at the $95\%$ CI, in significant tension with the BICEP2 result. There are several potential explanations for this discrepancy. The first is that the BICEP2 analysis over-estimates the amplitude of the B-mode itself {{\cite{Mortonson:2014bja}}. The second possibility is that the primordial B-mode is accurately measured, but sourced by a mechanism unrelated to the standard assumptions for the primordial inflationary phase \cite{Seljak:1997ii,Pogosian:2007gi,JonesSmith:2007ne,Kobayashi:2010pz,Cook:2011hg,Senatore:2011sp,Barnaby:2012xt,Carney:2012pk,Contaldi:2014zua,Czerny:2014wua}. Conversely, existing CMB data may have been misanalysed, although this appears unlikely given the agreement of \emph{Planck} with WMAP at large and intermediate scales and with ACT and SPT at small scales. Another suggestion is that the large-scale scalar power spectrum is suppressed relative to that predicted by the best-fit $\Lambda$CDM scenario. Pre-BICEP2 constraints on the inflationary gravitational wave background were driven primarily by the contribution of tensor modes to the temperature-temperature (TT) anisotropies. This is illustrated in Fig.~\ref{cl_tt_fig}, which shows the contribution to $C_l^{TT}$ at low-$l$ from a tensor background with $r=0.2$. The tensor contribution to individual $C_l^{TT}$ is small, but systematically increases the TT multipoles for all $l\lesssim 100$. However, to constrain the primordial tensor background using this signal we must have an independent estimate of the contributions $C_l^{TT}$ from scalar perturbations alone. Moreover, the measured low-multipole $C_l^{TT}$ typically lie below the best fit values for simple power-law spectra, so the inclusion of a tensor background is likely to reduce the likelihood relative to $r=0$. Fig.~\ref{cl_tt_fig} also shows a sample angular power spectrum derived from a primordial scalar spectrum with a sharp cut-off in power at a comoving wavenumber $k=0.002 \, \impc$. This particular scenario has a very low likelihood relative to the \emph{Planck} and WMAP datasets, but provides an extreme illustration of how a scalar spectrum with a cutoff could compensate for a tensor contribution to the $C_l^{TT}$ for $l\lesssim 100$. In this paper we focus on the implications of the BICEP2 result for the scalar power spectrum $\Delta^2(k)$, performing joint analyses of the BICEP2 and \emph{Planck} datasets. We consider three possibilities: (i) a running spectral index, (ii) a sharp cut-off in power at scale $k_\mathrm{cut}$, and (iii) a discontinuity in the spectral index at scale $k_\mathrm{knot}$. The latter two scenarios are implemented via the algorithm described by us in Ref.~\cite{Aslanyan:2014mqa}. The BICEP2 analysis \cite{Collaboration:2014wq,Collaboration:2014xx} presents joint constraints from BICEP2 and \Planck\ with a running index, but focusses primarily on the polarization and B-mode amplitude and does not discuss the issue in detail. We reproduce the BICEP2 constraints on a running index, and compute Bayesian evidence (relative to $\Lambda$CDM) of $\Delta \log Z=1.1$ for the running case. The cutoff spectrum does not give a significant improvement, since it suppresses the scalar power by a factor far larger than the corresponding increase in power due to tensor contributions. Finally, a break in the spectral index --- implemented as a splined $P(k)$ with a single ``interior'' point at an arbitrary amplitude and location --- provides the best fit to the data. With a broad, uninformative prior we find the change in the logarithmic evidence ratio is $\Delta \log Z=1.6$. However, using a prior that includes information from our investigation of the \Planck\ data alone, which disfavors knots at $k_\mathrm{knot} \gtrsim 10^{-2} \, \impc$ or dramatic changes in amplitude, we infer an evidence ratio of $\Delta \log Z=3.1$, a ``significant'' to ``strong'' detection according to conventional model selection criteria. Consequently, this analysis would suggest that BICEP2 has actually made {\em three\/} significant discoveries about inflation: the first is to confirm its existence, and the second is to show that it took place at a relatively high energy scale. Thirdly, these results also suggest that the primordial scalar spectrum has a nontrivial structure which is \emph{inconsistent} with simple models of inflation. Alternatively, the tensor spectrum may differ from the ``standard'' inflationary form, due to either a variant model of inflation \cite{Miranda:2014wga} or a mechanism that is independent of inflation \cite{Seljak:1997ii,Pogosian:2007gi,JonesSmith:2007ne,Senatore:2011sp,Contaldi:2014zua}. Of course, the conservative explanation of our findings is that they point to tension between the \Planck\ and BICEP2 datasets which will be resolved by more complete analyses and/or additional data. \begin{figure} \centering \includegraphics[width=1.0\textwidth]{cl_tt.pdf} \caption{\label{cl_tt_fig} The contribution to the (lensed) TT power spectrum from scalar and tensor modes ($r=0.2$). The left panel shows a standard power law primordial power spectrum with typical values of the cosmological parameters. The right panel shows the same primordial power spectrum but cut-off below $k=0.002 \, \impc$ (corresponding to $l\sim30$). } \end{figure} | Using data from \emph{Planck} and BICEP2 we perform parameter estimates and calculate Bayesian evidence in order to explore the implications of the BICEP2 result for different parameterisations of the primordial scalar power spectrum. In agreement with the BICEP2 analysis we find that the posterior probability for a running spectral index excludes zero at the 95\% confidence interval. Similarly, a spectrum defined by a linear spline with one internal knot shows a distinct preference for a suppression of power in the scalar spectrum at large angular scales, $k \lesssim 10^{-3} \, \impc$. For an informative prior incorporating the results of the \Planck-only analysis \cite{Aslanyan:2014mqa} the corresponding Bayesian model selection criteria show a pronounced preference for a model with broken scale invariance, with $\Delta \ln Z = 3.6$. This paper extends the analysis of Ref.~\cite{Aslanyan:2014mqa}, which reconstructs the primordial scalar power spectrum from \emph{Planck} temperature data alone. In particular, Ref.~\cite{Aslanyan:2014mqa} shows that the evidence for extra structure in the scalar power spectrum is negligible and that this reconstruction technique successfully recovers artificial signals injected into simulated temperature maps. Consequently, these results quantify the impact of the additional information provided by BICEP2.% If the scalar power spectrum is not well described by the usual power-law form, the estimated values of other novel cosmological parameters may also be modified, including sum of the neutrino masses or the number of effective relativistic degrees of freedom, which can be degenerate with features in the scalar power spectrum \cite{2013PhRvD..87l3528H,2011NJPh...13j3024S,2003MNRAS.342L..72B,2002PhRvD..66j3508T,2001PhRvD..63d3001K,dePutter:2014vd}. Likewise, the BICEP2 data does not put robust constraints on the tensor index $n_T$. Generically, the expectation from inflation is that $n_T=-r/8$ to first order in slow-roll, so we assume a scale-invariant tensor spectrum in this analysis. However, while a blue (or sharply peaked) tensor background would also alleviate the tension between \emph{Planck} and BICEP2, the physical processes that generated this spectrum would at least be as radical as considering a non--power-law scalar spectrum. The recent BICEP2 result provides strong evidence for a primordial tensor background, from which it is inferred that the very early universe underwent an inflationary phase. However, the results presented here imply that BICEP2 also suggests that this inflationary phase yields a non-trivial scalar power spectrum, and that the underlying inflationary mechanism is not well-described by a simple, smooth single-field potential. The inverse problem associated with reconstructing the inflationary potential from data has been widely discussed \cite{Copeland:1993ie, Copeland:1993jj,Lidsey:1995np,Hansen:2001eu,Leach:2002ar, Leach:2002dw, Leach:2003us,Kinney:2006qm,Peiris:2006ug,Peiris:2006sj,Martin:2006rs,Lesgourgues:2007gp, Lesgourgues:2007aa, Peiris:2008be,Adshead:2008vn,Hamann:2008pb,Kinney:2008wy,Martin:2010hh,Easther:2011yq} and these methods would have at least three nontrivial input parameters in such a scenario. Likewise, with a large negative running similar to the central value found here, simple inflationary models typically yield an unacceptably small number of e-foldings, implying that the running itself must be scale dependent \cite{Easther:2006tv}. Needless to say, this analysis takes both the current \Planck\ and BICEP2 data-products at face-value. The most conservative explanation for these result is that future analyses will eliminate much of the apparent tension between BICEP2 and other cosmological datasets. From this perspective our analysis quantifies the extent of that tension. | 14 | 3 | 1403.5922 |
1403 | 1403.7266_arXiv.txt | How dust scatters and absorbs starlight in the interstellar medium (ISM) contains important clues about the size and composition of interstellar dust. While the ultraviolet (UV) and visible interstellar extinction is well studied and can be closely fitted in terms of various dust mixtures (e.g., the silicate-graphite mixture), the infrared (IR) extinction is not well understood, particularly, the mid-IR extinction in the 3--8$\mum$ wavelength range is rather flat (or ``gray'') and is inconsistent with the standard Mathis, Rumpl, \& Nordsieck (MRN) silicate-graphite dust model. We attempt to reproduce the flat IR extinction by exploring various dust sizes and species, including amorphous silicate, graphite, amorphous carbon and iron. We find that the flat IR extinction is best explained in terms of micrometer-sized amorphous carbon dust which consumes $\simali$60 carbon atoms per million hydrogen atoms (i.e., C/H\,$\approx$\,60\,ppm). To account for the observed UV/visible and near-IR extinction, the silicate-graphite model requires Si/H\,$\approx$\,34\,ppm and C/H\,$\approx$\,292\,ppm. We conclude that the extinction from the UV to the mid-IR could be closely reproduced by a mixture of submicrometer-sized amorphous silicate dust, submicrometer-sized graphitic dust, and micrometer-sized amorphous carbon dust, at the expense of excess C available in the ISM (i.e., this model requires a solid-phase C abundance of C/H\,$\approx$\,352\,ppm, considerably exceeding what could be available in the ISM). | } The interstellar extinction is one of the primary sources of information about the interstellar dust size and composition. The interstellar extinction varies from one sightline to another in the ultraviolet (UV) and optical wavelength range. This variation in the Milky Way galaxy can be described by a single parameter, i.e., $R_{\rm V}$ (Cardelli et al.\ 1989; hereafter CCM).\footnote{% $R_V\,\equiv\,A_V/E(B-V)$ is the total-to-selective extinction ratio, where $E(B-V)\equiv A_B-A_V$ is the reddening which is the difference between the extinction in the blue band ($A_B$) and the extinction in the visual band ($A_V$). } The average extinction law for the Galactic diffuse interstellar medium (ISM) corresponds to $R_V\approx 3.1$. Based on the interstellar extinction curve observed for the diffuse ISM $R_V\approx 3.1$, Mathis et al.\ (1977) constructed a simple interstellar dust model to fit the interstellar extinction observed over the wavelength range of $0.11\mum < \lambda < 1\mum$. This classic model --- known as the ``MRN'' model --- consists of silicate and graphite grains\footnote{% Hoyle \& Wickramasinghe (1962) first proposed that graphite grains of sizes a few times 0.01$\mum$ could condense in the atmospheres of cool N-type carbon stars, and these grains would subsequently be driven out of the stellar atmospheres and injected into the interstellar space by the stellar radiation pressure. Similarly, Kamijo (1963) suggested that nanometer-sized SiO$_2$ grains could condense in the atmospheres of cool M-type stars. Gilman (1969) argued that grains around oxygen-rich cool giants could mainly be silicates such as Al$_2$SiO$_5$ and Mg$_2$SiO$_4$. Silicates were first detected in emission in M stars (Woolf \& Ney 1969, Knacke et al.\ 1969). After blown out of the stellar atmospheres and injected into the interstellar space, silicates could become an interstellar dust component. Hoyle \& Wickramasinghe (1969) first modeled the interstellar extinction in terms of a mixture of silicate grains of radii $\simali$0.07$\mum$ and graphite grains of radii $\simali$0.065$\mum$. Wickramasinghe \& Nandy (1970) found that a mixture of silicate, graphite, and iron grains achieved a rough fair fit to the interstellar extinction curve at $\lambda^{-1} < 8\mum^{-1}$. } and takes a simple power-law size distribution $dn/da \propto a^{-\alpha}$ with $\alpha\approx 3.5$ for the size range of $50\Angstrom < a < 0.25\mum$, where $a$ is the radius of the dust which is assumed to be spherical.\footnote{% To be precise, the MRN model actually derived a {\it wider} size range of $50\Angstrom < a < 1\mum$ for the graphite component and a {\it narrower} size range of $0.025\mum < a < 0.25\mum$ for the silicate component (and for other components such as SiC, iron and magnetite), with $\alpha$\,$\approx$\,3.3--3.6. In the literature, the MRN model is customarily taken to be a mixture of silicate and graphite with $\alpha=3.5$ and $50\Angstrom < a < 0.25\mum$. This is probably because (1) in their Figure~4 the demonstrated model fit to the observed UV/visible extinction was provided by the olivine-graphite mixture with $\alpha=3.5$ and $50\Angstrom < a < 0.25\mum$ for both dust components; and (2) Draine \& Lee (1984) also derived $\alpha=3.5$ and $50\Angstrom < a < 0.25\mum$ for both dust components using improved optical constants for these two substances. The sudden cutoff at $\amin=50\Angstrom$ and $\amax=0.25\mum$ is not physical. Kim et al.\ (1994) and WD01 adopted a more smooth size distribution function which extends smoothly to $a>1\mum$. But the dust with $a>1\mum$ takes only a negligible fraction of the total dust mass. } This model was further developed by Draine \& Lee (1984) who extensively discussed the optical properties of ``astronomical'' silicate and graphite materials. Subsequent developments were made by Draine and his coworkers (Weingartner \& Draine 2001 [hereafter WD01], Li \& Draine 2001) who extended the silicate-graphite grain model to explicitly include polycyclic aromatic hydrocarbon (PAH) molecules to explain the so-called ``unidentified infrared emission'' (UIE) bands at 3.3, 6.2, 7.7, 8.6, and 11.3$\mum$ (see L\'eger \& Puget 1984, Allamandola et al.\ 1985). With the wealth of available data from space-borne telescopes (e.g., {\it Infrared Space Observatory} [ISO] and {\it Spitzer Space Telescope}) and ground-based surveys (e.g., {\it Two Micron All Sky Survey} [2MASS]) in the near- and mid-infrared, in recent years we have seen an increase in interest in the infrared (IR) extinction. Understanding the effects of dust extinction in the IR wavelengths is important to properly interpret these observations. While the UV/optical extinction has been extensively observed for a wide variety of environments and modeled in terms of various dust models, our understanding of the near- and mid-IR extinction is still somewhat poor and controversial, despite that in this spectral domain many advances have been made in the past few years (see \S1 of Wang et al.\ 2013). \begin{figure}[h!] \centering \vspace{-0.0in} \includegraphics[angle=0,width=5.0in]{f1.eps} \vspace{-0.1in} \caption{\footnotesize \label{fig:IRExtObs} Comparison of the IR extinction observed for various interstellar regions with that predicted from the MRN (red dot-dashed line) and WD01 (black solid line) silicate-graphite models for the diffuse ISM of which the UV/optical extinction is characterized by $R_V\approx 3.1$. The little bump at 6.2$\mum$ arises from the C--C stretching absorption band of PAHs (see Li \& Draine 2001). } \end{figure} As shown in Figure~\ref{fig:IRExtObs}, WD01 silicate-graphite grain model predicts a power-law of $A_\lambda \propto \lambda^{-1.74}$ for the IR extinction at $1\mum < \lambda < 7\mum$, while the MRN model predicts a steeper power-law of $A_\lambda \propto \lambda^{-2.02}$.\footnote{% At $\lambda>7\mum$, the extinction increases because of the 9.7$\mum$ silicate Si--O stretching absorption band. } The model IR extinction curves reach their minimum at $\simali$7$\mum$ where the extinction power-law intersects the blue-wing of the 9.7$\mum$ silicate absorption band. Rieke \& Lebofsky (1985) measured the IR extinction from 1$\mum$ to 13$\mum$ for the lines of sight toward $o$ Sco, a normal A5\,II star behind the edge of the $\rho$ Oph cloud obscured by $A_V\approx 2.92\magni$,\footnote{% The extinction toward $o$ Sco at $\lambda> 0.55\mum$ can be well described by the $R_V=3.1$ extinction law. At $\lambda<0.55\mum$, the observed colors of $o$ Sco are much bluer than expected from those of a normal A5\,II star obscured by $A_V=2.92\magni$ with the $R_V=3.1$ extinction law, leading to the assignment of $R_V\approx 4.0$ (see Rieke \& Lebofsky 1985). } and toward a number of stars in the galactic center (GC). Rieke \& Lebofsky (1985) derived a power-law of $A_\lambda\propto \lambda^{-1.62}$ for $1\mum < \lambda < 7\mum$ for $o$ Sco and the GC sources. Draine (1989) compiled the IR extinction observed for a range of galactic regions including diffuse clouds, molecular clouds, and HII regions. He derived a power-law of $A_\lambda\propto \lambda^{-1.75}$ for $1\mum < \lambda < 7\mum$. More recently, Bertoldi et al.\ (1999) and Rosenthal et al.\ (2000) also derived a power-law extinction of $A_\lambda\propto \lambda^{-1.7}$ for $2\mum <\lambda < 7\mum$ for the Orion molecular cloud (OMC).\footnote{% The OMC extinction also displays an absorption band at 3.05$\mum$ attributed to water ice. } However, numerous recent observations suggest the mid-IR extinction at $3\mum <\lambda< 8\mum$ to be almost {\it universally} flat or ``gray'' for both diffuse and dense environments (see \S1.4 of Wang et al.\ 2013 for a summary), much flatter than that predicted from the MRN or WD01 silicate-graphite model for $R_V=3.1$ (see Figure~\ref{fig:IRExtObs}). Lutz et al.\ (1996) derived the extinction toward the GC star Sgr A$^{\ast}$ between 2.5$\mum$ and 9$\mum$ from the H recombination lines. They found that the GC extinction shows a flattening of $A_\lambda$ in the wavelength region of $3\mum <\lambda < 9\mum$, clearly lacking the pronounced dip at $\simali$7$\mum$ predicted from the $R_V=3.1$ silicate-graphite model (see Figure~\ref{fig:IRExtObs}). This was later confirmed by Lutz (1999), Nishiyama et al.\ (2009), and Fritz et al.\ (2011). Indebetouw et al.\ (2005) used the photometric data from the {\it 2MASS} survey and the {\it Spitzer}/GLIMPSE Legacy program to determine the IR extinction. From the color excesses of background stars, they derived the $\simali$1.25--8$\mum$ extinction laws for two very different lines of sight in the Galactic plane: the $l=42^{\rm o}$ sightline toward a relatively quiescent region, and the $l=284^{\rm o}$ sightline which crosses the Carina Arm and contains RCW~49, a massive star-forming region. The extinction laws derived for these two distinct Galactic plane fields are remarkably similar: both show a flattening across the 3--8$\mum$ wavelength range, consistent with that derived by Lutz et al.\ (1996) for the GC. Jiang et al.\ (2006) derived the extinction at 7 and 15$\mum$ for more than 120 sightlines in the inner Galactic plane based on the ISOGAL survey data and the near-IR data from DENIS and 2MASS, using RGB tip stars or early AGB stars (which have only moderate mass loss) as the extinction tracers. They found the extinction well exceeding that predicted from the MRN or WD01 $R_V=3.1$ model. Flaherty et al.\ (2007) obtained the mid-IR extinction laws in the {\it Spitzer}/IRAC bands for five nearby star-forming regions. The derived extinction laws at $\simali$4--8$\mum$ are flat, even flatter than that of Indebetouw et al.\ (2005). Gao et al.\ (2009) used the {\it 2MASS} and {\it Spitzer}/GLIPMSE data to derive the extinction in the four IRAC bands for 131 GLIPMSE fields along the Galactic plane within $|l|\leq65^{\rm o}$. Using red giants and red clump giants as tracers, they also found the mean extinction in the IRAC bands to be flat. Wang et al.\ (2013) determined the mid-IR extinction in the four {\it Spitzer}/IRAC bands of five individual regions in Coalsack, a nearby starless dark cloud, spanning a wide variety of interstellar environments from diffuse and translucent to dense clouds. They found that all regions exhibit a flat mid-IR extinction. All these observations appear to suggest an ``universally'' flat extinction law in the mid-IR, with little dependence on environments.\footnote{% We should note that an ``universally'' flat mid-IR extinction law does not necessarily mean an identical mid-IR extinction law for all regions, instead, it merely means a flattening trend of $A_\lambda$ with $\lambda$ in the mid-IR. Chapman et al.\ (2009), McClure (2009), and Cambr\'{e}sy et al.\ (2011) found that the shape of the mid-IR extinction law appears to vary with the total dust extinction. But also see Rom{\'a}n-Z{\'u}{\~n}iga et al.\ (2007) and Ascenso et al.\ (2013) who found no evidence for the dependence of the mid-IR extinction law on the total dust extinction. } While rapid progress has been made in observationally determining the mid-IR extinction and numerous IR extinction curves have been accumulated both for the Milky Way and for the Magellanic Clouds (e.g., see Gao et al.\ 2013a), theoretical understanding of the nature and origin of the flat mid-IR extinction lags well behind the observations. We plan to model the interstellar extinction from the far-UV to the far-IR for a wide range of interstellar environments. In this work we present our first attempts to understand the nature of the flat mid-IR extinction. In \S\ref{sec:status} we summarize the current status in interpreting the flat mid-IR extinction. \S\ref{sec:mod} describes our model. \S\ref{sec:rst} presents the results and discussions. \begin{figure}[h!] \centering \vspace{-0.0in} \includegraphics[angle=0,width=5.0in]{f2.eps} \vspace{-0.1in} \caption{\footnotesize \label{fig:IRExtMod} Comparison of the IR extinction observed for various interstellar regions with that predicted from the WD01 model for $R_V=5.5$ (black solid line) and the iron needle model (red dot-dashed line) of Dwek (2004) which is a combination of the $R_V=3.1$ silicate-graphite model of Zubko et al.\ (2004; green dashed line) and iron needles (blue dashed line). } \end{figure} | } To testify our model, we first fit the UV/optical and near-IR extinction curve of $R_V=3.1$. We assume that silicate and graphite have the same size distribution (i.e., $\alphaS=\alphaC$, $\acS=\acC$). Figure~\ref{fig:WLJUVOpt} shows the best-fit results. The best-fit model parameters are listed in Table~\ref{tab:uvpara}. The abundances of the dust-forming heavy elements locked up in the dust can be derived from the following equation: \begin{eqnarray} \nonumber \left[{\rm X}/{\rm H}\right] & = & 4\pi/3 \times \rho_{\rm X}/m_{\rm H} \times N_{\rm X}/\mu_{\rm X}\\ && \times \int_{\amin}^{\amax} N_{\rm X}^{\prime}\,a^{3-\alphaX}\,\exp\left(-a/\acX\right)\,da ~~, \end{eqnarray} where $m_{\rm H} = 1.66 \times 10^{-24}\g$ is the mass of a hydrogen atom, $\rho_{\rm X}$ and $N_{\rm X}^\prime$ are respectively the mass density and column density of the dust species containing element X, and $N_{\rm X}$ and $\mu_{\rm X}$ are respectively the number of X atoms in and molecular weight of a molecule of the dust species containing element X. We consider elements Si and C and dust species amorphous silicate and graphite: $\mu_{\rm C} \approx 12$, $N_{\rm C}=1$, $\mu_{\rm S} \approx 172$, and $N_{\rm Si}=1$.\footnote{% For silicate dust, we assume its chemical composition to be MgFeSiO$_4$. } We derive the C and Si abundances required to be locked up in dust to be $\cdust\approx 292\ppm$ and $\sidust\approx\mgdust\approx\fedust\approx 34\ppm$ (ppm refers to ``parts per million''). For the dust-forming element ${\rm X}$, let $\xism$ be the ``interstellar abundance'' -- the total abundance of this element in the ISM, both in gas and in dust; and $\xgas$ be the gas-phase abundance of this element. The abundance of this element in dust is $\xdust = \xism-\xgas$. The gas-phase Mg, Si and Fe abundances are negligible (i.e. these rock-forming elements are almost completely depleted from the gas phase; see Li (2005) and references therein). Therefore, for Si we have $\sidust\approx\siism$. The interstellar abundance of Si (i.e. $\siism$) is not known. Traditionally, one often adopts the solar photospheric abundances (e.g. Asplund et al.\ 2009) of heavy elements as their interstellar abundances. However, Lodders (2003) argued that the currently observed solar photospheric abundances (relative to H) must be lower than those of the proto-Sun because helium and other heavy elements have settled toward the Sun's interior since the time of the Sun's formation some 4.55\,Gyr ago. She further suggested that protosolar abundances derived from the photospheric abundances by considering settling effects are more representative of the solar system elemental abundances. On the other hand, it has also been argued that the interstellar abundances might be better represented by those of B stars and young F, G stars (because of their young ages) which are just $\simali$60--70\% of the solar values (i.e., ``subsolar''; Snow \& Witt 1996, Sofia \& Meyer 2001). However, Li (2005) showed that if the interstellar abundances are indeed ``subsolar'' like B stars and young F, G stars, there might be a lack of raw material to form the dust to account for the interstellar extinction. We also note that Przybilla et al.\ (2008) derived the photospheric abundances of heavy elements for six unevolved early B-type stars in the solar neighborhood OB associations and the field using NLTE techniques. They found that the photospheric abundances of those B stars are in close agreement with the solar values. Nieva \& Przybilla (2012) further derived the photospheric abundances of 29 slowly-rotating early B-type stars. These stars exhibit $<$10\% abundance fluctuations and their abundances are also similar to that of the Sun. The Si abundance of the Sun, proto-Sun, and early B stars are respectively $\sisun\approx 32\ppm$ (Asplund et al.\ 2009), $41\ppm$ (Lodders 2003), and $32\ppm$ (Przybilla et al.\ 2008, Nieva \& Przybilla 2012). The model which best fits the UV/optical extinction requires $\sidust\approx 34\ppm$, consistent with the solar, proto-Sun or B stars Si abundance. For C, it is more complicated since the gas-phase C abundance is recently under debate. Earlier studies reported $\cgas\approx 140\ppm$ from the weak intersystem absorption transition of C\,II] at 2325$\Angstrom$ (Cardelli et al.\ 1996; Sofia et al.\ 2004). Very recently, Sofia et al.\ (2011) derived $\cgas\approx 100 \ppm$ for several interstellar sightlines from the strong transition of C\,II] at 1334$\Angstrom$. They argued that the oscillator strength for the C\,II] transition at 2325$\Angstrom$ previously used by Cardelli et al.\ (1996) and Sofia et al.\ (2004) to obtain $\cgas\approx 140\ppm$ might have been underestimated. The solar C abundance and proto-Sun C abundance are respectively $\csun\approx 224\ppm$ (Asplund et al.\ 2009) and $288\ppm$ (Lodders 2003). The C abundance of the early B stars which are thought to be ideal indicators for the present-day interstellar abundances since they preserve their pristine abundances is close to the solar C abundance: $\cBstar\approx 214\pm20\ppm$ (Przybilla et al.\ 2008) and $\cBstar\approx 209\pm15\ppm$ (Nieva \& Przybilla 2012). If the interstellar C abundance is like that of the early B stars (i.e., $\cism\approx209\ppm$) or that of the proto-Sun (i.e., $\cism\approx288\ppm$), with the gas-phase C abundance of $\cgas\approx 100 \ppm$ (Sofia et al.\ 2011) subtracted, there will be only $\simali$109$\ppm$ or $\simali$188$\ppm$ of C available to make the carbonaceous dust. However, the model which best fits the UV/optical extinction requires $\cdust\approx 292\ppm$, substantially exceeding what would be available to be locked up in dust.\footnote{% We note that, except the composite dust model of Mathis (1996) which only requires $\cdust\approx 155\ppm$ (and $\sidust\approx 31\ppm$, but see Dwek 1997), all interstellar grain models consume more C than the available value of $\simali$109$\ppm$ or $\simali$188$\ppm$ in the ISM: $\cdust\approx 194\ppm$ (and $\sidust\approx 20\ppm$) of Li \& Greenberg (1997), $\cdust\approx 231\ppm$ (and $\sidust\approx 48\ppm$) of WD01, $\cdust\approx 244\ppm$ (and $\sidust\approx 36\ppm$) of Zubko et al.\ (2004), $\cdust\approx 233\ppm$ (and $\sidust\approx 50\ppm$) of Jones et al.\ (2013). } As shown in Figure~\ref{fig:WLJUVOpt}, the silicate-graphite mixture model with $\sidust\approx 34\ppm$ and $\cdust\approx 292\ppm$ closely reproduces the observed UV/optical/near-IR extinction. However, it fails in fitting the flat 3--8$\mum$ mid-IR extinction (see Figure~\ref{fig:WLJIR1}a). According to light scattering theory, dust absorbs and scatters starlight most effectively if its size is comparable to the starlight wavelength. Therefore, the dust which dominates the mid-IR extinction at $\simali$3--8$\mum$ should be in micrometer size scale, as inferred from the consideration of $a\sim \lambda/2\pi$. This leads us to add an extra population of large, $\mu$m-sized dust to account for the mid-IR extinction. We explore the size of the dust ranging from $a=0.5\mum$ to $a=3.5\mum$. For simplicity, we only consider dust of single sizes. In principle, we could assume a log-normal size distribution or the WD01-type size distribution for this $\mu$m-sized dust population. But we do not expect that a distribution of dust sizes would affect the conclusion drawn from the single-size model. A distribution of sizes would remove the ripple structures in the extinction curve of single-sized dust. The observed mid-IR extinction is commonly derived from broad-band photometry and therefore could tolerate the wavy ripples. As shown in Figure~\ref{fig:WLJIR1}a, the $R_V=3.1$ model together with spherical amorphous carbon dust of radius of $a\approx1.5\mum$ and C/H\,$\approx$\,60$\ppm$ could closely fit the mid-IR extinction. These $\mu$m-sized amorphous carbon grains, with $2\pi a/\lambda\gg 1$, are ``gray'' in the UV/optical wavelength regime. Therefore, the addition of $\mu$m-sized dust does not distort the fit to the observed $R_V=3.1$ extinction curve provided by the silicate-graphite model. In total, this model requires $\cdust\approx 352\ppm$ to account for the observed extinction from the UV to the mid-IR, with $\simali$17\% of the C atoms locked up in the $\mu$m-sized amorphous carbon component. We have also considered $\mu$m-sized graphite, amorphous silicate, and iron dust. As shown in Figure~\ref{fig:WLJIR1}b, graphite of radius of $a=1.5\mum$ is also capable of reproducing the flat mid-IR extinction. However, the $\mu$m-sized graphite population requires C/H\,$\approx$\,92$\ppm$. Therefore, amorphous carbon, with C/H\,$\approx$\,60$\ppm$, seems more favorable since the $R_V=3.1$ silicate-graphite model already encounters a ``carbon crisis'' problem: the model consumes more C/H than what is available. As shown in Figure~\ref{fig:WLJIR1}c, amorphous silicate could not fit the mid-IR extinction for two reasons: (1) the best-fit model with $a=3\mum$ predicts a prominent dip at $\lambda$$\simali$8$\mum$ which is not seen in the observed mid-IR extinction; this dip is due to the onset of the 9.7$\mum$ Si--O stretch at $\lambda$$\simali$8$\mum$; (2) this model requires Si/H\,$\approx$\,21,000$\ppm$ to be locked up in the $\mu$m-sized silicate dust, which is far more than the available amount of $\siism$\,$\approx$\,32--41$\ppm$ in the ISM. Figure~\ref{fig:WLJIR1}d shows the fit obtained with Fe/H\,$\approx$\,84$\ppm$ in iron spheres of $a=1.5\mum$. Although the fit to the mid-IR extinction is excellent, this model requires a total depletion of Fe/H\,$\approx$\,116$\ppm$,\footnote{% To account for the UV/optical extinction, the submicrometer-sized amorphous silicate component consumes Fe/H\,$\approx$\,32$\ppm$. } while the Fe abundance of the Sun, proto-Sun, and early B stars is only $\fesun\approx 27.5\ppm$ (Asplund et al.\ 2009), $\fesun\approx 34.7\ppm$ (Lodders 2003), and $\feBstar$$\approx$\,28--33$\ppm$ (Przybilla et al.\ 2008, Nieva \& Przybilla 2012), respectively. \begin{table}[h!] {\footnotesize \begin{center} \caption{\footnotesize \label{tab:uvpara} Model parameters for fitting the UV/optical and near-IR extinction. } \begin{tabular}{ccccccccc} \hline \hline Extinction & $A_{\Ks}/N_{\rm H}$ & $\alphaS$ & $\alphaC$ & $\acS$ & $f_{\rm C2S}$ & $\NS$ & $\sidust$ & $\cdust$\\ Type & ($10^{-23}\magni\cm^2$) & & & ($\mu$m) & & ($\cm^{-2}$) & (ppm) & (ppm)\\ \hline $R_V=3.1$ & 6.26 & 3.2 & 3.2 & 0.14 & 0.6 & $4.687\times10^{-24}$ & 34.0 & 292\\ $R_V=4.0$ & 6.85 & 2.7 & 2.7 & 0.12 & 0.6 & $1.669\times10^{-21}$ & 30.7 & 264\\ $R_V=5.5$ & 7.40 & 2.1 & 3.0 & 0.16 & 0.3 & $1.047\times10^{-18}$ & 40.0 & 172 \\ \hline \end{tabular} \end{center} } \end{table} We have also considered models for the $R_V=4.0$ and $R_V=5.5$ extinction curves since the flat mid-IR extinction has also been seen in dense regions (see \S\ref{sec:status}). For the $R_V=4.0$ case, we also assume that both silicate and graphite have the same size distribution. The results are shown in Figure~\ref{fig:WLJIR2} and Table~\ref{tab:uvpara}. It is seen that both amorphous carbon of $a\approx1.6\mum$ and graphite of $a\approx1.5\mum$ could fit the flat mid-IR extinction. Again, amorphous carbon is preferred since it requires C/H\,$\approx$\,72$\ppm$, less than that of graphite of C/H\,$\approx$\,92$\ppm$. For the $R_V=5.5$ case, we could not fit the UV/optical/near-IR extinction if we assume the same size distribution for both silicate and graphite. We therefore set $\acS=\acC$, but allow silicate and graphite to have different $\alpha$ values (i.e., $\alphaS\ne\alphaC$). The best-fit results are shown in Figure~\ref{fig:WLJIR3} and the model parameters are tabulated in Table~\ref{tab:uvpara}. Similar to the $R_V=3.1$ and $R_V=4.0$ models, $\mu$m-sized amorphous carbon and graphite could closely fit the mid-IR extinction, with amorphous carbon being preferred since it does not consume as much C/H as graphite. Finally, we note that it is not clear how $\mu$m-sized interstellar dust is formed. However, there are several pieces of evidence suggesting its presence in the ISM: (1) measurements by dust impact detectors on the interplanetary spacecrafts {\it Ulysses} and {\it Galileo} appear to indicate a substantial flux of interstellar particles with masses $>$\,10$^{-12}\g$ (corresponding to $a>0.4\mum$ for silicate and $a>0.5\mum$ for graphite) entering the heliosphere (see Landgraf et al.\ 2000, Kr\"uger et al.\ 2007); (2) Taylor et al.\ (1996) reported radar detection of $a\approx 30\mum$ particles entering the Earth's atmosphere on solar-hyperbolic trajectories implying that they are arriving from interstellar space. Socrates \& Draine (2009) discussed the detectability of very large interstellar grains of $a$$\simali$1\,mm (``pebble'') through optical scattered light halos. | 14 | 3 | 1403.7266 |
1403 | 1403.0670_arXiv.txt | Based on two-dimensional high resolution hydrodynamic numerical simulation, we study the mechanical and radiative feedback effects from the central AGN on the cosmological evolution of an isolated elliptical galaxy. Physical processes such as star formation and supernovae are considered. The inner boundary of the simulation domain is carefully chosen so that the fiducial Bondi radius is resolved and the accretion rate of the black hole is determined self-consistently. In analogy to previous works, we assume that the specific angular momentum of the galaxy is low. It is well-known that when the accretion rates are high and low, the central AGNs will be in cold and hot accretion modes, which correspond to the radiative and kinetic feedback modes, respectively. The emitted spectrum from the hot accretion flows is harder than that from the cold accretion flows, which could result in a higher Compton temperature accompanied by a more efficient radiative heating, according to previous theoretical works. Such a difference of the Compton temperature between the two feedback modes, the focus of this study, has been neglected in previous works. Significant differences in the kinetic feedback mode are found as a result of the stronger Compton heating and accretion becomes more chaotic. More importantly, if we constrain models to correctly predict black hole growth and AGN duty cycle after cosmological evolution, we find that the favored model parameters are constrained: mechanical feedback efficiency diminishes with decreasing luminosity (the maximum efficiency being $\simeq 10^{-3.5}$) and X-ray Compton temperature increases with decreasing luminosity{, although models with fixed mechanical efficiency and Compton temperature can be found that are satisfactory as well.} {We conclude that radiative feedback in the kinetic mode is much more important than previously thought}. | \label{sec:introduction} There is accumulating evidence showing that the evolution of host galaxies is tightly related to their central supermassive black holes (SMBHs) \citep{Fabian2012, Kormendy2013}. The most linkages are the strong correlations between the mass of SMBH and properties of the galactic spheroid, including luminosity \citep{Kormendy1995}, stellar velocity dispersion \citep{Gebhardt2000, Ferrarese2000, Tremaine2002, Gueltekin2009, Graham2011} and stellar mass \citep{Magorrian1998, Marconi2003, Haering2004}. The general consensus is that powerful feedback from the central active galactic nuclei (AGNs) should play an important role in the formation and evolution processes of their host galaxies. Simple energetic arguments indicate that AGNs should be capable of heating the inner regions of galaxies to offset radiative cooling and further regulate the black hole growth \citep[e.g.,][]{Ciotti1997,Binney2001,Fabian2012}. Many authors have proposed and performed successful theoretical models and numerical simulations to investigate how the feedback plays the role. However, because the length scales associated with AGN activity are so tiny compared to their host galaxy, the feedback process must operate over a huge dynamical range. This implies that the detailed AGN feedback mechanisms must be diverse and explains why this process is still incompletely understood \citep[for reviews, see][]{Ostriker2005,Peterson2006, McNamara2007, Cattaneo-Best2009, Fabian2012, Yuan-Narayan2014}. To study AGN feedback, ideally, we should cover the whole range of lengths and timescales, from black hole event horizon to the galactic scales. Obviously, such a huge dynamical range is technically almost impossible to achieve by current 2- and 3-dimensional numerical simulations. In reality, different works focus on feedback at different scales. At the smallest black hole accretion scale, works have been done on outflow production driven by line force \citep[e.g.,][]{Kurosawa-Proga2009a, Kurosawa-Proga2009b, Liu2013a}, and on the radiative feedback due to the global Compton scattering \citep{Park-Ostriker1999, Park-Ostriker2001, YXO2009}. The latter effect has been invoked to explain the intermittent behavior of the black hole activity of some compact young radio sources \citep{Yuan-Li2011}. On the other hand, many works \citep[e.g.][]{DiMatteo2005,Johansson2009} have focused on the much larger galactic scale, from $\simeq 100$ pc to tens of kpc and the timescale from a fraction of Myr to several Gyr. Brighenti \& Mathews (e.g., \citeyear{Brighenti2002}; \citeyear{Brighenti2003}, see also \citeauthor{Mathews2003} \citeyear{Mathews2003}) investigated the AGN heating on the ISM in details, and found that the thermal feedback could break the cool-core structures which are observed in many clusters, i.e., the over-heating problem. Gaspari et al. (e.g., \citeyear{Gaspari2012}; \citeyear{Gaspari2013}) performed detailed simulations on the mechanical feedback, and they found that the mechanical feedback is favoured to solve the cooling flow problem, to explain to cold rims, and meantime to avoid over-heating. Many works on the AGN feedback have been done in the context of isolated elliptical galaxies by Ciotti, Ostriker and their collaborators, both in one dimension \citep{Ciotti1997,Ciotti2001,Ciotti2007,Ciotti2009b,Shin2010,Ostriker2010,Jiang2010} and two dimensions \citep{Novak2011,Novak2012}. In these works, the inner boundary is small enough to resolve the black hole accretion flow, typically a few pc. This is important since it can compile the accretion rate in a physical way, which is crucial to evaluate the effect of AGN feedback \citep{Novak2011}. When the Bondi radius \citep{Bondi1952} is not resolved, other more approximate methods of estimating the accretion rate \citep[e.g., see][]{Springel2005} must be utilized. The outer boundary is large enough to reach hundreds of kpc, i.e, the galactic outskirts. The timescale also covers a large range, from accretion timescale to galaxy evolution timescale. The interaction of the radiation and winds from the inner AGNs with the galactic gas and their effects on regulating the accretion are considered, together with physical processes such as supernovae heating and star formation. Overall, the above mentioned works evidenced that the most satisfactory models are the combined models with both mechanical feedback and radiative feedback, in which mechanical feedback is very efficient to regulate the black hole growth, and radiative feedback can help to balance cooling and modulate the gas dynamics on the galactic scale. As is well-known, two ``modes'' of AGN feedback have been identified \citep{Fabian2012, Kormendy2013}. When the mass accretion rate is relatively large, $\ga 0.1 \dot{M}_{\rm Edd}$ (where the Eddington rate is defined as $\dot{M}_{\rm Edd}\equiv 10L_{\rm Edd}/c^2$), we have the radiative or quasar mode. In this regime, a standard thin disk is operating in the central region of AGNs, the luminosity is high, and a strong wind is observed (see \citeauthor{Fabian2012} \citeyear{Fabian2012} for a review). When the accretion rate is lower, the AGN is said to be in the kinetic mode, also known as the ``radio'' or ``maintanence'' mode. This mode corresponds to low-luminosity AGNs (LLAGNs). In this regime, the accretion flow is expected to be in the hot phase (Narayan \& Yi \citeyear{Narayan1994}, \citeyear{Narayan-Yi1995}; see Yuan \& Narayan \citeyear{Yuan-Narayan2014} for a recent review of the theoretical aspects of this model and its various astrophysical applications). The spectrum from a hot accretion flow is quite different from that of a standard thin disk, as we will describe in more detail in \S\ref{sec:radio-mode-feedback}. Moreover, recent theoretical studies indicate that, in addition to jet, winds also exist in hot accretion flows \citep{Yuan2012b,Narayan2012,Sadowski2013,Li2013}. Observationally, such a theoretical prediction has been confirmed by the Chandra observation to the accretion flow around the supermassive black hole in our Galactic center \citep{Wang2013}. The importance of radiative feedback in the quasar mode is obvious and well recognized. However, in the radio mode, the role of radiation is usually assumed to be minor compared to mechanical feedback by winds or jet. The reasons are possibly twofold. First, it is usually thought that the radiative power is low compared to the kinetic power of jet. Second, the efficiency of radiative heating of the emitted radiation on the interstellar medium is assumed to be not high. However, the radiative luminosity may actually be larger than the kinetic outflow power for luminosities $\ga 10^{-4}L_{\rm Edd}$ \citep{Fender2003}. It should be noted that, regarding the radiative heating efficiency, it depends not only on the bolometric luminosity, but also the spectral energy distribution. Taking the Compton heating as an example, the Compton heating is proportional to both the total radiative flux and the Compton temperature $T_C$ \citep[defined as the effective temperature of the radiation field,][]{Sazonov2005}, and the value of $T_C$ is determined by the spectral energy distribution (see eq. \ref{eq:compton-temperature}): in the quasar mode, typically $T_C\simeq 10^7$K \citep{Sazonov2005}, while in the radio mode, as we will describe in detail in \S\ref{sec:radio-mode-feedback}, $T_C$ is likely to be as high as $10^9$K, which is about two orders of magnitude higher than that in the quasar mode \citep{YXO2009}. Such a difference of $T_C$ in the two feedback modes has not been considered in the works mentioned above; rather, it is often assumed to maintain the same $T_C$ at different feedback modes. Therefore, the radiative feedback in the radio mode could potentially be much more important than previous thought. For example, \citet{Novak2011} studied two models with different mechanical feedback efficiency $\epsilon_W$. In the first class of models (``Models A''), $\epsilon_W$ is a constant. In another family (``Models B''), the efficiency decreases with the decreasing luminosity. Although there are some initial evidence that the assumption of Model B leads to more realistic results, \citet{Novak2011} find that Model B predicts too much growth of black hole mass, and incorrect AGN duty cycle. Will the results be changed when we correctly consider a stronger Compton heating in the radio mode? One of our main aims of the present work is to study the effect of a variable $T_C$. In the present paper, following \citet{Novak2011}, we perform two-dimensional high resolution hydrodynamical numerical simulations to study the effect of AGN feedback on the evolution of an isolated elliptical galaxy. Both mechanical and radiative interaction are considered. Special attention is paid to the effect of radiative feedback. Especially, the Compton temperature is self-consistently determined from the different accretion modes and a high (consistent) $T_C$ is adopted when the accretion is in the hot mode. The paper is organized as follows. In \S2, we introduce the physics of our model, including how do we treat mechanical and radiative feedback, the galaxy model we adopt, and the numerical treatments of stellar mass loss, supernovae, and star formation. The setup and boundary conditions of numerical simulation are described in \S3. Our results are presented in \S4, while \S5 is devoted to summary and discussion. | We have performed two-dimensional high resolution hydrodynamical simulations to investigate the AGN feedback in an isolated elliptical galaxy, focusing in particular on the so far unexposed regime of an accretion-dependent Compton temperature $T_C$. Both radiative and mechanical feedback are taken into account and also physical processes on galactic scales such as star formation and supernovae are considered in the calculation. The inner boundary of our computational domain is carefully chosen so as to make sure that the fiducial Bondi radius is resolved in our simulation, allowing for a robust estimate of the black hole accretion rate, which is crucial to study AGN feedback. Following previous works, two types of models have been considered. In ``A'' models, the mechanical efficiency of winds is a constant, while in ``B'' models, it decreases with the decreasing luminosity of AGN as would be expected from radiatively driven winds \citep{Proga2008}. By construction models in the B family are perhaps more realistic than in the A family. However a few important systematic problems have been detected in the B family in previous works. In particular, previous calculations have shown that Model B predicts a too high final black hole mass and incorrect AGN duty cycle compared to observations. A major improvement of the present work compared with previous ones is that we allow for a different Compton temperature of the radiation spectrum from the central AGN. In the radiation mode, the accretion flow is described as a standard thin disk thus the corresponding Compton temperature is relatively low, $T_C\simeq 10^7$K. But in the kinetic mode, the accretion flow is described by a hot accretion flow thus the corresponding Compton temperature should be higher. Following previous theoretical work, we adopt $T_C\simeq 10^9$K. This in general results in a stronger radiative feedback as adopted in \citet{Ciotti2001}. Consequently, we find that the accretion processes are more chaotic and further suppressed. Specifically, we find that Model B now predicts a correct range of black hole mass and AGN duty cycle. In more general sense, our study indicate that in the kinetic mode, radiative feedback is much more important than previous thought and should be seriously considered in future studies. Some improvements can be made based on the present work in the future. First, as we have mentioned in the paper, we have simply chosen $T_C \simeq 10^9$ K as the Compton temperature of the emitted spectrum from the hot accretion flows. This value comes from the calculation based on the theoretical spectrum from a hot accretion flow. In reality, the accretion flow is composed of an inner hot accretion flow plus an outer truncated thin disk (see \citeauthor{Yuan-Narayan2014} \citeyear{Yuan-Narayan2014} for a review). The best way is to combine the observed spectral energy distribution of LLAGNs with various luminosities and calculate the Compton temperature as a function of luminosity. Moreover, relativistic effect may be important in calculating $T_C$ which was unfortunately neglected in the previous work. A complementary aspect of this study that needs an improvement is the description of the properties of the nuclear wind as a function of the black hole accretion state. In particular, issues line the mechanical efficiency $\epsilon_W$, the wind speed and its angular distribution. In fact, as we have shown in this paper, $\epsilon_W$ is of crucial importance for the evaluation of mechanical feedback. But unfortunately this value is still poorly constrained by observations or by theories so we have to treat it as a free parameter, although some initial results have been obtained, e.g., in the study of hot accretion flows \citep{Yuan2012b,Li2013}. The angular distribution of wind, which is also expected to be important to mechanical feedback, is again poorly constrained. In this paper we assume a ``bipolar-like'' angular distribution function of the wind. In the future, it is expected that the theoretical studies will be able to better constrain these two properties. In fact, we are using the MHD numerical simulation data to study the wind from hot accretion flows and some initial results have been obtained. For example, we find that the winds do have a wide range of distribution angles, from $\simeq 0-45^{\circ}$. But different from the ``bipolar-like'' structure, we find that most of the mass flux of wind seem to be concentrate on the disk surface. It will be interesting to examine its effect in cooperation with the variations of $T_C$. | 14 | 3 | 1403.0670 |
1403 | 1403.5055_arXiv.txt | Large field inflation models are favored by the recent BICEP2 that has detected gravitational wave modes generated during inflation. We study general large field inflation models for which the potential contains (constant) quadratic and quartic terms of inflaton field. We show, in this framework, those inflation models can generate the fluctuation with the tensor-to-scalar ratio of $0.2$ as well as the scalar spectral index of $0.96$: those are very close to the center value of the tensor-to-scalar ratio reported by BICEP2 as well as Planck. Finally, we briefly discuss the particle physics model building of inflation. | The inflationary cosmological model is the standard paradigm of modern cosmology because an inflationary expansion in the very early Universe solves various problems in the standard big bang cosmology~\cite{Inflation} and also provides the seed of large scale structure in our Universe from the quantum fluctuation of an inflaton field $\phi$~\cite{InflationFluctuation}. The property of the generated density fluctuation from a single-field slow-roll inflation model, namely adiabatic, Gaussian, and its almost scale-invariant spectrum, is quite consistent with various cosmological observations. As the scalar perturbation is generated from the inflaton's quantum fluctuation during inflationary expansion, the tensor perturbation also is generated from graviton's one~\cite{Tensor}. The tensor perturbation induces $B$-mode polarization of the temperature anisotropy in the cosmic microwave background radiation and is important for inflationary cosmology because the tensor perturbation directly tells us the energy scale of inflation. Recently, the BICEP2 collaboration reported the detection of the tensor mode through the $B$-mode polarization with the corresponding tensor-to-scalar ratio~\cite{Ade:2014xna} \begin{equation} r_T = 0.20^{+0.07}_{-0.05} . \label{rT:BICEP} \end{equation} Its cosmological implications also have been studied~\cite{AfterBICEP}. It has been well known that theoretically such a large tensor-to-scalar ratio can be generated only by so-called large field models, where its potential, as of a polynomial function of $\phi$, is convex and the variation of the inflaton field value during inflation $\Delta\phi$ is as large as of the Planck scale~\cite{LythBound}. On the other hand, the Planck satellite~\cite{Ade:2013zuv,Ade:2013uln} has reported the scalar spectral index as \begin{equation} n_s \simeq 0.96 . \label{ns:Planck} \end{equation} Now, if we compare the central values of Eqs.~(\ref{rT:BICEP}) and (\ref{ns:Planck}) with the predicted values of well-studied potential models such as $V \propto \phi^2 $ or $\phi^4$, there is a discrepancy. Namely, $r_T$ from $V \propto \phi^2 $ is too low and that from $\phi^4$ is too high~\cite{Ade:2013uln}. ~\footnote{The $V \propto \phi^3$ potential would well agree with data. However, naively, this potential is pathological because the potential is not bounded from below. Note, however, an effective realization would be possible with a field redefinition from ${\cal L} \sim \phi^2(\partial\phi)^2 - \phi^6$. } In this paper, we extend analysis to general polynomial models of inflation for which the potential is expressed as~\cite{Poly} \begin{equation} V = c_1 + c_2 \phi^2 +c_4 \phi^4 , \label{potential:general} \end{equation} to examine whether this form of potential can reconcile the mismatch mentioned above, by taking the latest BICEP2 data into account. Since it is not easy to control so many parameters, in practice, we will consider terms up to $\phi^4$, which might be motivated by the renormalizability of quantum field theory. | We have shown that general polynomial inflation models are fit well to the observed data including the tensor-to-scalar ratio recently reported by BICEP2. In other words, after we know the size of $r_T$, we are able to determine more parameters of inflation models. In fact, for $V \sim + \phi^2 + \phi^4$ with $N=60$, we find $m^2 \simeq 3\times 10^{-11}$ and $\lambda \simeq 1\times 10^{-14}$. A double-well potential also can be fit nicely to the data; then, the VEV should be $\langle\phi\rangle \simeq 13$, and the self-coupling constant is $\lambda \simeq 4.5\times 10^{-14}$ for $N=60$. Finally, we note here possible directions of particle physics model construction for inflation. Being aware of the above size of self-coupling, an inflaton's Yukawa coupling $y$ to fermion $\psi$, ${\cal L} = y \bar{\psi}\phi\psi$, should be smaller than ${\cal O}(10^{-4})$ because it induces a ${\cal O}(y^4)$ self-coupling by radiative corrections. Supersymmetric construction of a large field inflation model has been challenging~\cite{Yamaguchi:2011kg}. F-term inflation suffers from so-called ``$\eta$ problem'' due to higher-order terms from the Kahler potential. Imposing shift symmetry $\phi \rightarrow \phi + C$ is one of a few effective manners to overcome the problem~\cite{Kawasaki:2000yn,Kaloper:2008fb}. While D-term inflation has been regarded as an example of hybrid inflation~\cite{Binetruy:1996xj}, in fact, D-term chaotic inflation is also possible~\cite{Kadota:2007nc}. Such a model interestingly does not suffer from the $\eta$ problem even if we consider a general Kahler potential because the field redefinition to the canonical field absorbs higher-order corrections and the Lagrangian is reduced to a quartic or double-well potential. Since a self-coupling is given by the square of a gauge coupling in the D-term, we need to introduce a new gauge interaction with the gauge coupling constant of ${\cal O}(10^{-7})$. If we could realize a large VEV about $10$ by any means, as we have shown, such a model would easily reproduce the data. We have restricted the polynomial potential (\ref{potential:general}) in this paper. It would be important to add higher-order terms $\phi^n$ as well as the cubic term $\phi^3$. We will study it elsewhere. | 14 | 3 | 1403.5055 |
1403 | 1403.6056_arXiv.txt | {\sao, the exciting star of the Stingray nebula, is rapidly evolving. Previous analyses suggested that it has heated up from an effective temperature of about 21\,kK in 1971 to over 50\,kK in the 1990s. Canonical post-asymptotic giant branch evolution suggests a relatively high mass while previous analyses indicate a low-mass star. } {A comprehensive model-atmosphere analysis of UV and optical spectra taken during 1988\,--\,2013 should reveal the detailed temporal evolution of its atmospheric parameters and provide explanations for the unusually fast evolution. } {Fitting line profiles from static and expanding non-LTE model atmospheres to the observed spectra allowed us to study the temporal change of effective temperature, surface gravity, mass-loss rate, and terminal wind velocity. In addition, we determined the chemical composition of the atmosphere. } {We find that the central star has steadily increased its effective temperature from 38\,kK in 1988 to a peak value of 60\,kK in 2002. During the same time, the star was contracting, as concluded from an increase in surface gravity from \loggw{4.8} to 6.0 and a drop in luminosity. Simultaneously, the mass-loss rate declined from $\log$(\Mdot\,/\,\Msol\,yr$^{-1})=\,-9.0$ to $-11.6$ and the terminal wind velocity increased from $v_\infty = 1800$\,km/\,s to $2800$\,km/\,s. Since around 2002, the star stopped heating and has cooled down again to 55\,kK by 2006. It has a largely solar surface composition with the exception of slightly subsolar carbon, phosphorus, and sulfur. The results are discussed by considering different evolutionary scenarios. } {The position of \sao in the log \Teff\ -- \logg\ plane places the star in the region of sdO stars. By comparison with stellar-evolution calculations, we confirm that \sao must be a low-mass star ($M < 0.55$\,\Msol). However, the slow evolution of the respective stellar evolutionary models is in strong contrast to the observed fast evolution and the young planetary nebula with a kinematical age of only about 1000 years. We speculate that the star could be a late He-shell flash object. Alternatively, it could be the outcome of close-binary evolution. Then \sao would be a low-mass (0.354\,\Msol) helium prewhite dwarf after the common-envelope phase, during which the planetary nebula was ejected. } | \label{sect:introduction} The long stellar evolutionary time scales mean it is in general impossible for an astronomer to ``watch'' a star evolving in real time. Intermediate-mass stars ($M_{\mathrm{ZAMS}}=0.8-8$\,\Msol) experience their most rapid evolution close to the end of their nuclear-burning phase. Observing stars during this period provides the unique opportunity to investigate on the stellar asymptotic giant branch (AGB) and post-AGB evolution, including the AGB mass-loss phase, and the ejection, shaping, and excitation of planetary nebulae (PNe) -- phases that are still not fully understood. \sao, the exciting star of the \object{Stingray Nebula} (\object{Henize 3$-$1357}, \citealt{henize1976}), is an unusually fast evolving star. It was first classified to be a hot post-AGB star \citep{partha1989} based on the discovery of a circumstellar dust shell with far-IR (IRAS) colors and flux distribution similar to that of PNe. Based on a spectral classification of the optical spectrum obtained in 1971, \cite{partha1995} concluded that the star was a B1 or B2 supergiant. From the UBV colors and the 1971 spectrum, they estimated \Teffw{21}. However, they found that the optical spectra from 1990 and 1992 as well as the IUE\footnote{International Ultraviolet Explorer} spectra (1992 $-$ 1996) display many nebular emission lines, indicating that \sao has turned into a central star of a PN (CSPN) within a time span of only 20 years. Furthermore, when omparing the IUE spectra from 1988 and 1995 \cite{partha1995} discovered it is the only known CSPN that faded by a factor of 2.83 in its flux level within seven years. In addition, it was possible for them to observe how the stellar wind gradually decreased. From the IUE spectrum obtained in 1988, \cite{partha1995} measured a terminal wind velocity of $v_{\infty}=3500$\,km/s from the \ion{C}{IV} resonance doublet. The IUE spectrum in 1994 showed that the stellar wind vanished. Based on the IUE spectra, they estimated that \Teff\ must be around 55\,kK. Assuming a distance of 5.6\,kpc \citep{kozok1985} and an expansion velocity of 8\,km/s, \citet{partha1993} found that the post-AGB time of \sao is about 2700 years. Furthermore, they estimated the luminosity and core mass of the CS to be 3000\,\Lsol\,\,and 0.55\,\Msol, respectively. The first optically resolved images of the Stingray Nebula were presented by \citet{Bobrowsky1994} and \citet{Bobrowsky1998} using the Wide Field and Planetary Camera 1 (WFPC1) and WFPC2, respectively. \citet{Bobrowsky1994} found that in H\,$\beta$, the Stingray Nebula appears to have an equatorial ring of enhanced density tilted approximately 56$\degr$ from the line of sight. In addition, he found bubbles of gas above and below the ring with areas of decreased brightness near the poles where a fast stellar wind has broken through the red giant envelope. From the H\,$\beta$ flux, he derived an ionized mass of 0.2\,\Msol, $L=5000$\,\Lsol\, and a stellar core mass of 0.59\,\Msol. Thanks to the superior spatial resolution of the WFPC2 \citet{Bobrowsky1998} found evidence of collimated outflows, which are focused by the nebula bubbles and function like nozzles, with gas leaving through the polar holes. They also report a possible detection of a late type companion star at a distance of 2200\,AU from the central star. \citet{Umana2008} present the first detailed radio study of the Stingray Nebula by using the Australian Telescope Compact Array (ATCA). They find that the Stingray Nebula is still embedded in the dusty remnant of the AGB phase. Depending on their models, they derived an ionized mass of 0.057\,--\,0.07\,\Msol\,\, and a total dust mass of 2$\times 10^{-4}$\,\Msol\ in the case of silicates and 7.5$\times 10^{-5}$\,\Msol\,\,in case of graphite. \citet{Arkhipova2013} performed an analysis of the nebula spectra taken in 1990, 1992, and 2011. They find significant changes in the relative line intensities. The low-excitation $[$\ion{O}{I}$]$, $[$\ion{O}{II}$]$, and $[$\ion{N}{II}$]$ lines became stronger relative to H\,$\beta$ by a factor of two, while the $[$\ion{O}{III}$]$ lines weakened by a factor of $\approx 2$. Using a formula of \citet{Kaler1978}, they estimated that \Teff\ decreased from 1990 (\Teffw{57}) to 2011 (\Teffw{40}). \cite{partha1995} first discovered that the observed properties of \sao, e.g\@. the rapid changes in \Teff\ and the drop of luminosity, contradict with canonical post-AGB evolution. For such a rapid evolution, the core mass should be 0.8\,\Msol\,\,or even more \citep{partha1995, Bobrowsky1998}. The evolutionary time scales for CSs with core masses of 0.6\,\Msol\,\,or less are predicted to be much longer \citep{bloecker1995}. To address the evolution of the properties of SAO 244567 quantitatively for the first time, we carried out a spectral analysis based on all available spectra from 1988 until 2006 taken with IUE, FUSE\footnote{Far Ultraviolet Spectroscopic Explorer}, HST/STIS\footnote{Hubble Space Telescope / Space Telescope Imaging Spectrograph}, and HST/FOS\footnote{Faint Object Spectrograph}. The comparison of the results to different evolutionary models should help provide conclusions on the nature of \sao. This paper is organized as follows. In \se{sect:observation}, we describe the observations. The spectral analysis follows in \se{sect:analysis}. In \se{sect:discussion}, we summarize our results and derive the distance and the mass of \sao. We discuss possible stellar evolutionary scenarios and compare \sao to other low-mass CSPNe. We conclude in \se{sect:conclusions}. | \label{sect:conclusions} \sao is a rapidly evolving object. Its evolutionary status remains unclear. The most reasonable explanations are a late He-shell flash or CE evolution with a remnant that is in thermal non-equilibrium after the CE ejection. However, respective models are lacking that match the position of \sao in the $\log$ \Teff\,-- \logg plane. The contradiction between observations and theory make \sao particularly interesting. Its fast evolution gives us the unique opportunity to study stellar evolution in real time and establishes constraints for stellar evolutionary theory. Further observations, in the next years, decades and even centuries, are essential for monitoring whether the rapid evolution of \sao is still going on and to see if it is directly evolving to the white dwarf domain or back to the AGB. The detection of a close binary would support the scenario of a CE ejection, whereas an increase in brightness and decrease in \Teff\ over the next decades, would indicate an evolution back to the AGB and hence speak for a LTP scenario. | 14 | 3 | 1403.6056 |
1403 | 1403.3997_arXiv.txt | {The cosmological birefringence caused by the coupling between the cosmic scalar field and the cosmic microwave background (CMB) photons through the Chern-Simons term can rotate the polarization planes of the photons, and mix the CMB E-mode and B-mode polarizations. The rotation angle induced by the dynamical scalar field can be separated into the isotropic background part and the anisotropic fluctuations. The effect of the background part has been be studied in the previous work (Zhao \& Li, arXiv:1402.4324). In this paper, we focus on the influence of the anisotropies of the rotation angle. {\tc{ We first assume that the cosmic scalar field is massless, consistent with other works, we find that the rotation spectrum can be quite large, which may be detected by the potential CMB observations. However, if the scalar field is identified as the quintessence field, by detailed discussing both the entropy and adiabatic perturbation modes for the first time, we find that the anisotropies of the rotation angle are always too small to be detectable.}} {\tc {In addition, as the main goal of this paper, we investigate the effect of rotated polarization power spectrum on the detection of relic gravitational waves. we find that, the rotated B-mode polarization could be fairly large, and comparable with those generated by the gravitational waves. This forms a new contamination for the detection of relic gravitational waves in the CMB. In particular, we also propose the method to reconstruct and subtract the rotated B-mode polarization, by which the residuals become negligible for the gravitational-wave detection.}} } | Inflation is the most popular scenario of the extremely early Universe \cite{guth1981}. In addition to elegantly solve the flatness puzzle, the horizons puzzle and the monopoles puzzle in the hot bag-bang universe, inflationary models predict the primordial scalar and tensor fluctuations with the nearly scale-invariant power spectra \cite{inflation-perturbation}. The scalar perturbations seeded the large-scale structure, which is highly consistent with the current observations on temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation \cite{wmap,planck0} and the distributions of the galaxies in various large-scale structure observations. The primordial tensor perturbations, i.e., relic gravitational waves, encoded all the evolution information of the Universe \cite{grishchuk}. The amplitude corresponds to the energy scale of inflation, and the spectral index reflects the evolution of scale factor in the inflation stage. So, the detection of relic gravitational waves is always treated as the smoking-gun evidence of the inflation, which mainly depends on the observation of the CMB polarization, in particular the so-called B-mode polarization \cite{ref-Bmode}. The current observations, including those of WMAP and Planck missions, are yet to detect a definite signal of relic gravitational waves. However, the recent observations of BICEP1, SPTPOL and POLARBEAR telescopes have given some interesting results for the B-mode polarizations \cite{bicep,spt,polarbear}, which encourage us to put the gravitational-wave detection through the CMB polarizations as a highest priority task for the next generations of CMB experiments \cite{task}. The CMB B-mode polarization is contaminated by many sources, including the instrumental noises, various foreground emissions, the E-B mixture due to the partial sky observations, the leakage of E-mode polarizations caused by the cosmic weak lensing, as well as the cosmic birefringence. It is well known that the cosmic birefringence can be caused by the possible interaction between the photons and the cosmic scalar field $\varphi$ in the Universe \cite{carroll1990,kamionkowski1998}. The birefringence induces rotation of the polarization plane of CMB, and converts E-mode and B-mode polarization, which forms a new contamination for the gravitational-wave detection. Recently, numerous attentions have been attracted to study this effect from both theoretical and observational sides \cite{other-cpt,other-constraints}. The cosmic scalar field may or may not be identified as the quintessence dark energy. {\tc{ In the previous works \cite{li2008,kamionkowski2008,kamionkowski2009,zaldarriaga2009,Caldwell:2011}, the main attentions have been payed to the case, where the scalar field is massless. Consistent with these works, we find that, although the background rotation angle is absent in this case, the spatial fluctuations could be quite large, and could be well detected by the potential observations of Planck satellite, CMBPol mission or some other experiments. In this paper, we also consider the case where the scalar field is identified with the quintessence dark energy, and the background rotation angle can be large. For the first time, we detailed discuss both the entropy and the adiabatic perturbation modes, and find that the fluctuations in this case are always very small, and beyond the future detection abilities.}} {\tc{As the main task of this paper, we focus on the influence of the cosmological birefringence on the detection of relic gravitational waves. For the former case, where the cosmic scalar field is massless, we investigate in detail the rotated B-mode polarization, and find they can be fairly large and comparable with (or even larger than) those caused by relic gravitational waves or cosmic weak lensing. So, it is important to reduce it in the future gravitational-wave detections. By utilizing the statistical properties of the reconstructed rotation angle coefficients $\alpha_{\ell m}$ and those of the E-mode coefficients $E_{\ell m}$, we propose the method to reconstruct the rotated B-mode polarization. We find that the rotated polarization can be reconstructed and removed at the very high level, if considering the noise levels of CMBPol mission or the better experiments, which become completely negligible for the detection of relic gravitational waves in the CMB.}} The outline of this paper is as follows. In Sec. \ref{sec2}, we briefly introduce the cosmological birefringence and focus on the rotation angle fluctuations. In Sec. \ref{sec3}, we discuss the fluctuations of the rotation angle in both the massless scalar field and the quintessence field models. In Sec. \ref{sec4}, we investigate the possible detection of the fluctuations of the rotation angle by the potential CMB observations. In Sec. \ref{sec5}, we discuss the reconstruction and subtraction of the rotated B-mode polarization, and their effect on the gravitational-wave detection. Sec. \ref{sec6} summarizes the main results of this paper. | } The detection of relic gravitational waves through the CMB B-mode polarization is rightly considered a highest priority task for the future observational missions. In addition to the contaminations and noises in the observations, in the real Universe, the primordial B-mode was also polluted by some other cosmological effects. One of them is the cosmological birefringence, which can be caused by the possible coupling between CMB photons and the cosmic scalar field through the Chern-Simons term. The cosmological birefringence rotates the polarization planes of CMB photons, and mixes the E-type and B-type polarizations. Due to the perturbations of the scale field, the fluctuations of the rotation angle naturally exist. In this paper, we studied the fluctuations of cosmological birefringence in various scalar-field models. {\tc{By detailed discussing both entropy and adiabatic perturbation modes for the first time, we find that, if the cosmic scalar field is identified with the quintessence component, the fluctuations of the rotation angle are always too small, and beyond the detection abilities of future detectors. However, if the scalar field is a massless field, consistent with the previous works, we find that the fluctuation power spectrum could be fairly large and detectable for the potential observations, although the uniform rotation angle is absent in this case.}} {\tc{As the main task of this paper, the B-mode polarization caused by the rotation angle fluctuations are also studied in details. We found that, the converted B-mode polarizations could be comparable with (or even larger than) those generated by the primordial gravitational wave or those caused by the cosmic weak lensing. However, this B-mode can be well reconstructed and subtracted at the very high level. In this paper, we proposed the method to de-rotate the B-mode polarization by utilizing the statistical properties of the coefficients $\alpha_{\ell m}$ and $E_{\ell m}$. We found that, if the de-rotating is done by considering the noise level of CMBPol mission or the better experiment, the B-mode residuals become much smaller than those caused by weak lensing, which is entirely negligible for the future gravitational-wave detections.}} ~ ~ {\tc{Note: In the same day of the submission of the paper, BICEP2 \cite{bicep2} released its data which indicates a discovery of the primordial gravitational waves with $r = 0.20^{+0.07}_{-0.05}$ and $r = 0$ disfavored at $7.0\sigma$, which confirmed the hint of gravitational waves in the WMAP and Planck low-multipole data \cite{zhao2010,zhao2014}.}} ~ ~ {\it Acknowledgments:} W.Z. is supported by project 973 under Grant No.2012CB821804, by NSFC No.11173021, 11322324 and project of KIP of CAS. M.L. is supported by Program for New Century Excellent Talents in University and by NSFC under Grants No. 11075074. \appendix | 14 | 3 | 1403.3997 |
1403 | 1403.3445_arXiv.txt | Blackman \& Brandenburg argued that magnetic helicity conservation in dynamo theory can in principle be captured by diagrams of mean field dynamos when the magnetic fields are represented by ribbons or tubes, but not by lines. Here we present such a schematic ribbon diagram for the $\alpha^2$ dynamo that tracks magnetic helicity and provides distinct scales of large scale magnetic helicity, small scale magnetic helicity, and kinetic helicity involved in the process. This also motivates our construction of a new ``2.5 scale'' minimalist generalization of the helicity-evolving equations for the $\alpha^2$ dynamo that separately allows for these three distinct length scales while keeping only two dynamical equations. We solve these equations and, as in previous studies, find that the large scale field first grows at a rate independent of the magnetic Reynolds number $R_M$ before quenching to an $R_M$ dependent regime. But we also show that the larger the ratio of the wavenumber where the small scale current helicity resides to that of the forcing scale, the earlier the non-linear dynamo quenching occurs, and the weaker the large scale field is at the turnoff from linear growth. The harmony between the theory and the schematic diagram exemplifies a general lesson that magnetic fields in MHD are better visualized as two-dimensional ribbons (or pairs of lines) rather than single lines. | Dynamo theory has long been a topic of active research in astrophysical and geophysical magnetohydrodynamics, and describes how magnetic energy can be amplified and/or sustained in the presence of a turbulent diffusion that would otherwise rapidly dissipate the field (e.g. Glatzmeier 2002, Brandenburg \& Subramanian 2005a, Blackman 2014). In particular, large scale dynamo (LSD) theory in astrophysics is aimed at understanding the \emph{in situ} physics of magnetic field growth, saturation, and sustenance on time or spatial scales large compared to the turbulent scales of the host rotator. Galaxies, stars, planets, compact objects, and accretion engines (via their jets) often show direct or indirect evidence for large scale magnetic fields. The extent to which magnetic fields are a fossil vestige of the formation of the object, or primarily generated via LSDs, is itself a question of active research; but observations of the sun for example (e.g. Wang \& Sheely 1993; Schrijver \& Zwaan 2000) prove that LSDs do operate in nature since a frozen-in field could not exhibit sign reversals. LSDs are also commonly seen in accretion disc or shearing box simulations (e.g. Brandenburg et al. 1995; Lesur \& Ogilive 2008; Davis et al. 2009; Gressel et al. 2010; Simon et al. 2011; Sorathia et al. 2012; Suzuki \& Inutsuka 2013; Ebrahimi \& Bhattacharjee 2014), with observed large scale field reversals occurring on time scales of order $10$ orbits. The presence of magnetohydrodynamic turbulence makes the study of LSDs highly nonlinear, exacerbating the importance of numerical simulations. However, large scale spatial symmetry and the slow evolution of large scale fields compared to turbulent fluctuation time scales motivates a mean field approach in which statistical, spatial, or temporal averages are taken, and the evolution of the mean field studied (Moffatt 1978 Parker 1979; Krause \& R\"adler 1980). For many decades, mean field dynamo theory was studied assuming a prescribed flow that was not affected by the growing magnetic field. This is a problem because the field does exert Lorentz forces back on the flow. Moreover, unless the back reaction is incorporated into the theory, it is impossible to make a dynamical prediction of LSD saturation. The 21st century has brought progress in this endeavor as the growth and saturation of LSDs seen in simple closed box simulations (Brandenburg 2001) are reasonably matched by newer mean field dynamo theories that follow the time dependent dynamical evolution of magnetic helicity (e.g. Blackman \& Field 2002, for reviews see Brandenburg \& Subramanian 2005a; Blackman 2014). These newer 21st century mean field dynamos are discrete scale theories that capture the basic principles of the inverse transfer of the magnetic helicity first derived in the spectral model of Pouquet et al. (1976), which revealed the fundamental importance of magnetic helicity evolution for large scale field growth. The simplest example of a mean field dynamo for which this saturation theory has been tested dynamically (Field \& Blackman 2002; Blackman \& Field 2002) and compared to simulations (Brandenburg 2001) is the $\alpha^2$ dynamo in a closed or periodic box. In this dynamo, the system is forced with kinetic helicity in a closed or periodic system at some wavenumber, say $k_f=5$ where the box wavenumber is $k_1=1$. The large scale field growth at $k_1$ is captured by an equation which is coupled to the equation for small scale magnetic helicity because the sum of small and large scale magnetic helicity is conserved up to resistive terms. The growth of large scale helicity thus also implies the growth of small scale helicity of the opposite sign. Because the growth driver turns out to be the difference between small scale kinetic and small scale current helicities (the latter related to the small scale magnetic helicity), the growth of the small scale magnetic helicity offsets the kinetic helicity driver, eventually halting the growth. While $\alpha^2$ dynamos are simple theoretical models for study, they are also important for the generation of large scale fields in stars that lack strong differential rotation. Blackman and Brandenburg (2003) argued that textbook diagrams of mean field dynamos do not properly capture the near conservation of magnetic helicity because they display a growth of large scale magnetic helicity without any corresponding oppositely signed small scale helicity to compensate. If instead the field is displayed as a ribbon or tube, any writhing of the large scale field is naturally accompanied by a corresponding twisting of the small scale field. On a related theme, Pfister \& Gekelman (1991) showed that magnetic helicity conservation during a magnetic reconnection of linked loops can be captured when the field lines are represented as ribbons but not as lines. See also Bellan (2000) in this context. In this paper we revisit the $\alpha^2$ dynamo to show more specifically how to visually represent its large scale and small scale magnetic helicity growth. The resulting diagram has also stimulated us to introduce a minimalist generalization of the helicity evolving $\alpha^2$ dynamo equations which allows for scale separation between the large scale, forcing scale, and scale of the small scale current helicity, whilst keeping only two dynamical equations. Normally the latter two latter scales are taken to be the same, but there is evidence from simulations that they can be different (Park \& Blackman 2012). In section 2 we discuss the different conceptual representations of magnetic helicity. In section 3 we discuss the schematic diagram of the $\alpha^2$ dynamo. In section 4 we derive the the equations for the $\alpha^2$ dynamo based on previous work but with the new scale separation feature. We solve these equations in section 5 and discuss their solutions and the correspondence with the schematic diagram. We conclude in section 6. | We have shown how considering the magnetic field to be a 2-D ribbon rather than 1-D line leads to a schematic diagram that correctly captures the conservation of magnetic helicity for the $\alpha^2$ dynamo during its evolution to saturation unlike traditional dynamo diagrams that treat the magnetic field as a line. In addition, the diagram illustrates the need to allow for a distinction of 3 scales: (i) the helical forcing scale (ii) the small scale magnetic helicity (ii) the large scale magnetic helicity. Toward this end, we introduced a simple generalization to the two-scale equations of the $\alpha^2$ dynamo to allow for the fact the the forcing scale and and scale of current helicity buildup may not be equal without having to introduce a third dynamical equation. Solving these equations shows that when the scale of the current helicity buildup is much smaller than that of the forcing scale (though still well above the resistive scale), the quenching of the dynamo is exacerbated when compared to the case in which these latter two scales are equal. This provides a simpler framework to study the separation of these scales than has been considered before (Park \& Blackman 2013). In short, the near conservation of magnetic helicity in MHD dynamos for a large $R_M$ closed system is well captured visually when magnetic fields are represented by ribbons but poorly captured when the fields are represented as lines. The associated diagram of the $\alpha^2$ dynamo also captures the potential richness of an additional scale separation which, as we have shown, affects predictions of dynamo saturation when incorporated into the theory. {There is opportunity for future work to assess the efficacy of the 2.5 scale model of the $\alpha^2$ dynamo herein with simulations and to develop a theory to predict $k_2/k_2$ for a given $k_f$.} Because dynamos are so representative of how magnetic fields and flows interact in MHD, the lesson learned seemingly has very broad implications for high $R_M$ MHD beyond that of dynamo theory: {\it Magnetic fields are better visualized as 2-D ribbons than 1-D lines. } Magnetic reconnection provides another example which bears this out \cite{1991AmJPh..59..497P}. | 14 | 3 | 1403.3445 |
1403 | 1403.4115_arXiv.txt | { We present a study of $\sim$100 high redshift ($z \sim $~2-4) extremely strong damped Lyman\,$\alpha$ systems (ESDLA, with $N(\HI)\ge 0.5 \times 10^{22}$~\cmsq) detected in quasar spectra from the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey (SDSS-III) Data Release 11. We study the neutral hydrogen, metal, and dust content of this elusive population of absorbers and confirm our previous finding that the high column density end of the $N(\HI)$ frequency distribution has a relatively shallow slope with power-law index $-$3.6, similar to what is seen from 21-cm maps in nearby galaxies. The stacked absorption spectrum indicates a typical metallicity $\sim$1/20$^{\rm th}$ solar, similar to the mean metallicity of the overall DLA population. The relatively small velocity extent of the low-ionisation lines suggests that ESDLAs do not arise from large-scale flows of neutral gas. The high column densities involved are in turn more similar to what is seen in DLAs associated with gamma-ray burst afterglows (GRB-DLAs), which are known to occur close to star forming regions. This indicates that ESDLAs arise from lines of sight passing at very small impact parameters from the host galaxy, as observed in nearby galaxies. This is also supported by simple theoretical considerations and recent high-$z$ hydrodynamical simulations. We strongly substantiate this picture by the first statistical detection of \lya\ emission with $\avg{L_{\rm ESDLA}(\lya)} \simeq (0.6\pm0.2) \times 10^{42}~\ergs$ in the core of ESDLAs (corresponding to about 0.1\,$L^{\star}$ at $z\sim 2-3$), obtained through stacking the fibre spectra (of radius 1\,$\arcsec$ corresponding to $\sim$\,8\,kpc at $z \sim 2.5$). Statistical error on the \lya\ luminosity are of the order of $0.1 \times 10^{42}~\ergs$ but we caution that the measured \lya\ luminosity may be overestimated by $\sim 35\%$ due to sky light residuals and/or FUV emission from the quasar host and that we have neglected flux-calibration uncertainties. We estimate a more conservative uncertainty of $0.2 \times 10^{42}~\ergs$. The properties of the \lya\ line (luminosity distribution, velocity width and velocity offset compared to systemic redshift) are very similar to that of the population of Lyman-$\alpha$ emitting galaxies (LAEs) with $L_{\rm LAE}(\lya) \ge 10^{41} \ergs$ detected in long-slit spectroscopy or narrow-band imaging surveys. By matching the incidence of ESDLAs with that of the LAEs population, we estimate the high column density gas radius to be about $r_{\rm gas}=2.5$~kpc, i.e., significantly smaller than that corresponding to the BOSS fibre aperture, and making fibre losses likely negligible. Finally, the average measured Ly\,$\alpha$ luminosity indicates a star-formation rate consistent with the Schmidt-Kennicutt law, SFR (\msyr)~$\approx 0.6/f_{\rm esc}$, where $f_{\rm esc} < 1$ is the \lya\ escape fraction. Assuming the typical escape fraction of LAEs, $f_{\rm esc} \sim 0.3$, the Schmidt-Kennicutt law implies a galaxy radius of about $r_{\rm gal} \approx 2.5$~kpc. Finally, we note that possible overestimation of the \lya\ emission would result in both smaller $r_{gas}$ and $r_{gal}$. Our results support a close association between LAEs and strong DLA host galaxies. } | In the past two decades, astronomers have found several efficient observational strategies to detect and study galaxies in the early Universe. Each strategy targets a subset of the overall population of galaxies, which is then named after the selection technique. Lyman-break galaxies \citep[LBGs,][]{Steidel96} are selected in broad-band imaging using colour cuts around the Lyman-limit at 912~{\AA}. Because of this selection, LBGs probe mostly bright massive galaxies with strong stellar continuum \citep[e.g.][]{Steidel03, Shapley03, Shapley11}. Since hydrogen recombination following ionisation by young stars produces \lya\ emission, this line can also be used to detect star-forming galaxies at high-redshift, where it is conveniently redshifted in the optical domain. \lya\ emitting galaxies (more generally called Lyman-$\alpha$ emitters: LAEs, \citealt[][]{Cowie98, Hu98}) are detected using narrow-band filters tuned to the wavelength of \lya\ \citep[e.g.][]{Rhoads00, Ouchi08, Ciardullo12}, long-slit spectroscopy \citep{Rauch08,Cassata11} or integral field spectroscopy \citep[e.g.][]{Petitjean96,Adams11}. Because their selection is independent of the stellar continuum, these galaxies are often faint in broad-band imaging and likely represent low-mass systems with little dust attenuation \citep{Gawiser07}. Several studies have attempted to relate these two populations in a single picture by studying how the \lya\ emission line properties are related to the galaxy stellar populations \citep[e.g.][]{Lai08,Kornei10}. Additionally, infrared observations together with detections of molecular emission have opened a new and very promising way to study galaxies at high redshift \citep[e.g.][]{Omont96, Daddi09}. Another and very different technique to detect high-redshift galaxies is based on the absorption they imprint on the spectra of bright background sources, such as quasi-stellar objects (QSOs) or gamma ray burst (GRB) afterglows. These detections depend only on the gas cross-section and are thus independent of the luminosity of the associated object. Large surveys have demonstrated that Damped Lyman-$\alpha$ systems (DLAs, see \citealt{Wolfe05}), characterised by $N(\HI) \ge 2\times 10^{20}$~cm$^{-2}$, contain $\ge$80\% of the neutral gas immediately available for star formation \citep{Peroux03, Prochaska05, Prochaska09, Noterdaeme09dla, Noterdaeme12c,Zafar13}. Constraints on the star-formation activity associated with DLAs can be obtained by measuring the metal abundances in the gas \citep[e.g.][]{Prochaska03, Petitjean08} and their evolution with cosmic time \citep[e.g.][]{Rafelski12}. The excitation of different atomic and/or molecular species provides indirect constraints on instantaneous surface star-formation rates \citep{Wolfe03, Srianand05, Noterdaeme07lf, Noterdaeme07}. \citet{Prochaska97,Prochaska98} tested a variety of models and concluded that the DLA kinematics, as traced by the profiles of low-ionisation metal absorption lines, could be characteristic of rapidly rotating discs. This interpretation is, however, problematic in the cold dark matter models that predict low rotation speeds \citep{Kauffmann96}. Alternatively, \citet{Ledoux98} showed that merging protogalactic clumps can explain the observed profiles, as expected in the now prevailing hierarchical models of galaxy formation \citep[see e.g.][]{Haehnelt98}. \citet{Schaye01} proposed that large scale outflows would also give rise to DLAs when seen in absorption against a background QSO and that the outflows would have sufficiently large cross-section to explain a significant fraction of DLAs. It has also been proposed that the fraction of neutral gas in cold streams of gas infalling onto massive galaxies is non-negligible at high redshift, where this is an important mode of galactic growth \citep[e.g.][]{Moller13}. This gas potentially gives rise to DLAs \citep{Fumagalli11} with moderate column densities. Although the chemical and physical state of the gas in DLAs is relatively well understood, we still know little about the properties (mass, kinematics, stellar content) of the associated galaxy population. Since the total cross-section of DLAs is much larger than that of starlight-emitting regions in observed galaxies, a large fraction of DLAs potentially arises from atomic clouds in the halo or circumgalactic environments, as supported by high-resolution galaxy formation simulations \citep[e.g.][]{Pontzen08}. Direct detection of galaxies associated with DLAs (hereafter ``DLA-galaxies'') is needed to address these issues. This has appeared to be a very difficult task, mainly due to the faintness of the associated galaxies and their unknown location (i.e. impact parameter) with respect to the quasar line of sight. Thankfully, substantial progress has been made in the past few years, owing to improved selection strategies and efficient instrumentation on large telescopes \citep{Bouche12, Fynbo10, Fynbo11, Noterdaeme12a, Peroux11}. Although still rare, these observations show that it is possible to relate the properties of the gas to star formation activity in the host galaxy \citep[e.g.][]{Krogager12}. For example, large scale kinematics have recently been invoked to link the absorbing gas with star-forming regions located 10-20~kpc away \citep[e.g.][]{Bouche13,Fynbo13,Krogager13,Kashikawa13}. Here, we aim to study the link between star formation and the absorbing gas within or very close to the host galaxy. Our rationale is that this can be achieved by selecting DLAs with very high column densities of neutral hydrogen, which will be closely connected both spatially and physically to star forming regions in galaxies, since a Schmidt-Kennicutt law is expected to apply to quasar absorbers \citep[e.g.][]{Chelouche10}. This idea is also supported by 21-cm maps of nearby galaxies \citep[e.g.][]{Zwaan05,Braun12} and existing observations of impact parameters for high-$z$ DLA galaxies that decrease with increasing column density \citep{Krogager12}, an effect which is also seen in simulations \citep[e.g.][]{Pontzen08,Yajima12,Altay13b}. Until recently, very high column density DLAs, with $\log N(\HI)\sim 22$, were very rare occurrences (\citealt{Guimaraes12}, \citealt{Noterdaeme12a}, see also \citealt{Kulkarni12}), but the steadily increasing number of quasar spectra obtained by the Sloan Digital Sky Survey \citep[SDSS,][]{York00} and more recently by the Baryon Oscillation Spectroscopy Survey \citep[BOSS,][]{Dawson13} component of SDSS-III \citep[][]{Eisenstein11} opens the possibility to study such a population. We present our DLA sample in Sect.~\ref{sample} and its column density distribution in Sect.~\ref{fhi}. We then study the metal content of our DLA sample and compare it to the population of DLAs associated with GRB afterglows (Sect.~\ref{metals}). In Sect.~\ref{colours}, we analyse the colour distortions that DLAs induce on their background QSOs. The rest of the paper explores the \lya\ emission detected using stacking procedures and discusses the nature of DLA galaxies. Throughout the paper, we use standard $\Lambda$CDM cosmology with $\Ho=70$~\kms\,Mpc$^{-1}$, $\Omega_{\Lambda}=0.7$ and $\Omega_{\rm m}=0.3$. | The historical $N(\HI)$-threshold for DLAs, $\log N(\HI) \ge 20.3$, was originally chosen mostly for observational reasons \citep{Wolfe86} and was found similar to \HI\ column densities measured in the disks of local spiral galaxies. However, it is becoming more and more clear that a significant fraction of DLAs at high redshift probe gas on the outskirts of a galaxy. Recent 21-cm observations of nearby galaxies have shown that higher \HI\ column densities are mostly found at small impact parameters \citep[$\sim$~80\% probability of being located at less than 5~kpc for $\log N(\HI)\ge 21.7$,][]{Zwaan05}. At high redshift, simulations also indicate that only the highest column density absorptions probe ISM gas that feeds star formation \citep[e.g.][]{Altay13,Rahmati13,Rahmati14}. Here, we have studied an elusive population of extremely strong DLAs detected in BOSS. The small incidence of these systems reflects their small cross-section. Confirming our previous result in \citep[see][]{Noterdaeme12c}, the high column density end of the $N(\HI)$-distribution function has a moderate power-law slope, similar to that of the local Universe. We find that the metallicities and dust-depletion of ESDLAs are similar to those of the overall DLA population and thus indicate that they are related to a similar population of galaxies. Their higher column densities are mainly the consequence of small impact parameters. Indeed, we found that the absorption characteristics are very similar to what is seen in DLAs associated with GRB afterglows, which are known to be intimately related to star-formation regions. Using stacking techniques, we detect \lya\ emission in the core of ESDLAs with a mean luminosity $\avg{L_{Ly\,\alpha}} \simeq (0.6 \pm 0.1 ({\rm stat}) \pm 0.2 ({\rm syst})) \times 10^{42}\,\ergs$ which corresponds to that of $L_{Ly\,\alpha} \ge 10^{41}$~\ergs\ Lyman-$\alpha$ emitting galaxies. We also show that the distribution of luminosities measured in individual spectra, although noisy, is also consistent with that of the above LAE population. The incidences of ESDLAs and LAEs indicates impact parameters $b <2.5$~kpc. The properties of the Ly$\alpha$ emission in both populations are very similar. All of this strongly suggests that the ESDLA host galaxies are actually LAEs that emit most of their light well within the area covered by the the BOSS fibre (8~kpc radius) and obey the Schmidt-Kennicutt law. We caution however that the measured \lya\ luminosity may be overestimated by $\sim 35\%$ due to sky light residuals and/or FUV emission from the QSO host and that we have neglected flux-calibration uncertainties. However, this has little consequence on our overall picture. Indeed, a lower \lya\ luminosity would imply a fainter but more numerous LAE population (hence a smaller extent of gas to match the incidence of ESDLAs) and at the same time a smaller galactic size according to the Schmidt-Kennicutt law. \citet{Hashimoto13} recently suggested that LAEs should have small neutral hydrogen column densities. However, this suggestion arises from considerations based on homogeneous expanding shell models \citep{Verhamme06}, while the true configuration is probably much more complicated \citep[e.g.][]{Kulas12}. Indeed, recent works have highlighted the importance of ISM clumpiness and geometry in allowing \lya\ photons to escape from star-forming regions \citep[e.g.][]{Laursen13}, even at high integrated \HI\ column densities \citep[e.g.][]{Noterdaeme12a}. Finally we note that the viewing angle seems to play an important role in anisotropic configurations \citep{Zheng13}. Interestingly, using very deep (92\,h of VLT/FORS2) long-slit spectroscopy, \citet{Rauch08} revealed a population of faint LAEs with $L$(\lya)~$\sim 10^{41}$~\ergs\ that have a total cross-section consistent with that of DLAs \citep[see also][]{Barnes09}. Targeting high-metallicity DLAs has successfully produced a number of host galaxy detections with higher SFR, but the host galaxies are frequently at large impact parameters and either have no \lya\ emission or a suppressed blue peak \citep[see][]{Fynbo10,Fynbo11,Fynbo13,Krogager12,Krogager13}. This indicates that high metallicity DLAs could be associated with massive and luminous galaxies, but their cross-section selection increases the probability that the DLAs will probe the galaxy outskirts. This is in line with other studies suggesting that the large cross-section of gas around massive galaxies is responsible for higher metallicities in sub-DLAs on average \citep{Khare07,Kulkarni10}. ESDLAs, however, are selected solely on the basis of high \HI\ column densities. They should arise in more typical galaxies that have not yet converted their gas reservoirs into stars and thereby produced little metals, as seen from the low metallicities. Follow-up studies of ESDLAs and their host galaxies will contribute important clues for understanding galaxy formation at high redshift and constrain crucial parameters for numerical simulations such as the amount of stellar feedback and the gas consumption rate. In particular, deep multi-wavelength spectroscopy, covering both \lya\ and nebular emission lines (redshifted in the near-infrared) are required to measure accurately the star-formation rate and hence the \lya\ escape fraction as well as bringing constraints on the \lya\ transfer. | 14 | 3 | 1403.4115 |
1403 | 1403.1506_arXiv.txt | {The search for the solar siblings has been particularly fruitful in the last few years. Until now, there are four plausible candidates pointed out in the literature: HIP21158, HIP87382, HIP47399, and HIP92831. In this study we conduct a search for solar siblings among the HARPS high-resolution FGK dwarfs sample, which includes precise chemical abundances and kinematics for 1111 stars. Using a new approach based on chemical abundance trends with the condensation temperature, kinematics, and ages we found one (additional) potential solar sibling candidate: HIP97507.} | Nowadays, it is accepted that most stars are born in clusters \citep{Lada-03}, as it is also believed to have happened in the case of our Sun. According to \cite{Wielen-1996}, the Sun was born in the inner part of the Milky Way, perhaps 1.9 kpc closer to the galactic center than its current location. The stars that have born in the same cluster as the Sun, called solar siblings, were spread away from their initial orbits over the Galaxy. In this scenario, mechanisms such as spiral density waves may play an important role \citep[e.g.][]{Lepine-03}. \cite{Zwart-09} quote that if the parental cluster of our Sun had 10$^{3}$ stars, at least 1\% of the solar siblings (about 10 - 60) should still be located within 100 pc and that more than 10\% should be within a region of 1 kpc, around the present location of our Sun. On their hand, \cite{Mishurov-11} showed that this result is only true in the most optimistic case. Identifying the Sun's siblings would put constraints on the number of stars in the original cluster. Moreover, reconstructing the orbits of the siblings in the Galaxy would help us to understand the Sun's accurate birth location. The search for solar siblings is an ambitious task, strongly restricted by their ages, metallicities, and kinematics. The latter has been particularly fruitful during the last few years. A search for solar siblings conducted among the Hipparcos catalogue, provided a list of 6 potential candidates \citep{Brown-10}: HIP21158; HIP30344; HIP51581; HIP80124; HIP90122; HIP99689. Due to relatively low age estimates or low metallicity values or high radial velocities, only the star HIP21158 was pointed out as being a real potential candidate. The same work, also discussed five more stars, which were found close to the solar isochrones: HIP56287, HIP57791, HIP89825, HIP92381, and HIP101911. However, all of these stars were discarded either because of their radial velocities, or due to the lack of age estimates or metallicity values. \cite{Bobylev-11} introduced a new kinematic approach to search for solar siblings. They found two potential candidates: HIP87382 and HIP47399. More recently, the first giant, HIP175740, was pointed out as a potential solar sibling candidate \citep{Batista-12}. In addition, they also discuss a potential candidate, which has known orbiting planets (HIP115100). However, the latter star was discarded due to its supersolar metallicity. Very recently, \cite{Adibekyan-14} used a sample of 148 solar-type stars from \cite{Jonay-10, Jonay-13} to explore the main factors responsible for the abundance trends with condensation temperature (T$_{c}$ hereafter). The authors found that the slope of this trend (T$_{c}$ slope hereafter) significantly correlates (at more than 4$\sigma$) with the stellar age. They also found an evidence that the T$_{c}$ slope correlates with the mean galactocentric distance of the stars (R$_{mean}$), indicating that stars originated in the inner Galaxy have less refractory elements relative to the volatiles. Thus the authors concluded that the age and the Galactic birth place are determinant for the chemical structure of stars and they also determine the T$_{c}$ slopes. This means that stars which were born in the same cluster should have a similar metallicity and should show similar abundance trends with the T$_{c}$. The search for solar siblings is strongly dependent on the ability of finding compatible metallicities between surveys \citep{Batista-12}. In this work, we conducted a search for solar siblings among the HARPS high-resolution FGK dwarfs sample \citep{Adibekyan-12a} using a new approach based on the observed chemical abundance trends with the T$_{c}$. The paper is organized as follows. In Sect. 2, we present the sample. Section 3 presents the considered criteria to conduct this search and the potential candidates. Finally, in Sect. 4, we summarize the results. | Despite not being the most abundant element, iron is usually used as a proxy of the overall metallicity of a star, due to its high number of available spectral lines to measure in solar-type stars. Indeed, the metallicity criterion, used in many studies, can be improved by using additional chemical abundances of other elements. For the first time, this study provides a search for solar siblings in a very homogeneous sample, in terms of the metallicity, and chemical abundances in general. We constrained our search for solar siblings among the HARPS FGK dwarfs sample \citep{Adibekyan-12a}, based on the trends observed between the chemical abundances of the stars and condensation temperature. Further applying the kinematics criteria we found two solar sibling candidate, HIP97507 and HIP61173, which have a peculiar velocity of about 12 km s$^{-1}$. Our estimation of the age for these stars are very close to the age of our Sun (within the errors). The [X/H] versus T$_{c}$ for the solar sibling candidates are shown in Fig.~\ref{fig_el_tc}. As one can see although HIP61173 shows a practically negligible slope, abundances of all the individual elements are higher than 0.05 dex. Since this star is a ``solar analog'' the derived stellar parameters and chemical abundances are very precise \citep[see][]{Sousa-08, Adibekyan-12a}, which forces us to conclude that HIP61173 does not have solar composition, and hence cannot be a solar sibling plausible candidate. On the meantime time our paper was submitted, \cite{Ramirez-14} made a detailed analysis of chemical composition of 30 solar sibling candidates listed in the literature with the goal to select the most probable candidate(s). The authors also showed that several key elements, like Na, Al, V, B, and Y can be used for a chemical tagging of solar siblings. Following the referee’s suggestion, we derived abundances of several heavy elements including Ba and Y for our candidate star (HIP97507): [Cu/H] = 0.02, [Zn/H] = 0.04, [Ba/H] = 0.07 dex, and [Y/H] = 0.00 dex \citep[see][for details on derivation of these elements]{Jonay-10}. These values are quite compatible with the composition of the Sun, probably expect Ba. However, several studies showed that the dispersion in Ba abundance within open clusters can be higher than 0.1 dex \citep[e.g.][]{Jacobson-13, Mishenina-13}. Chemical abundances for the aforementioned elements also suggest a slightly enhanced metallicity for HIP61173: [Cu/H] = 0.14, [Zn/H] = 0.07, [Ba/H] = 0.05 dex, and [Y/H] = 0.00 dex. Summarizing, we can state that in the sample of 1111 FGK dwarfs from the HARPS GTO subsample \citep{Adibekyan-12a} there is only one promising potential candidate: HIP97507 (HD186302). We note, that the simulations done by \cite{Zwart-09} predict only very few solar siblings within 100 pc from the Sun, and probably with masses lower than that of the Sun (mostly M dwarfs). With the new astrometric measurements that will be done by Gaia, the knowledge of the stars kinematics of the solar neighborhood will be improved. Consequently, the kinematics and age criteria to search for the solar siblings will also be improved. | 14 | 3 | 1403.1506 |
1403 | 1403.4924_arXiv.txt | We show that the B-mode polarization signal detected at low multipoles by BICEP2 cannot be entirely due to topological defects. This would be incompatible with the high-multipole B-mode polarization data and also with existing temperature anisotropy data. Adding cosmic strings to a model with tensors, we find that B-modes \emph{on their own} provide a comparable limit on the defects to that already coming from \Planck\ satellite temperature data. We note that strings at this limit give a modest improvement to the best-fit of the B-mode data, at a somewhat lower tensor-to-scalar ratio of $r \simeq 0.15$. | The detection of low-multipole B-mode polarization anisotropies by the BICEP2 project \cite{Ade:2014xna} opens a new observational window on models that generate the primordial perturbations leading to structure formation. The leading candidate to explain such a B-mode signal is primordial gravitational wave (tensor) perturbations generated by the inflationary cosmology. For a tensor-to-scalar ratio $r$ of around $0.2$, these give a good match to the spectral shape in the region $\ell \simeq 40$ -- $150$, while falling some way short of the observed signal at higher multipoles for reasons yet to be uncovered. An alternative mechanism of generating primordial B-modes is the presence of an admixture of topological defects (see e.g.\ Refs.~\cite{VilShe94,Hindmarsh:1994re,Durrer:2001cg,Copeland:2009ga,Hindmarsh:2011qj} for reviews). Many inflation scenarios, particularly of hybrid inflation type, end with a phase transition. Defect production at such a transition is natural and plausibly a sub-dominant contributor to the total temperature anisotropy. Many papers have used recent data to impose constraints on the fraction of defects, typically obtaining limits of a few percent contribution to the large-angle temperature anisotropies \cite{Wyman:2005tu,Bevis:2007gh,Battye:2010xz,Dunkley:2010ge,Urrestilla:2011gr,Avgoustidis:2011ax,Ade:2013xla}. The tensor and defect spectra were previously compared in Refs.~\cite{Urrestilla:2008jv,Mukherjee:2010ve}. An important question then arises: does the observed B-mode polarization confirm the existence of a primordial gravitational wave background due to inflationary dynamics in the early Universe, or could it instead be entirely due to the presence of topological defects? In this \emph{Letter} we show that topological defects alone cannot explain the BICEP2 data points. \begin{figure}[t] \resizebox{1.05\columnwidth}{!}{\includegraphics{Fig1.eps}} \caption{\label{pol}The \CMB temperature and polarization power spectra contributions from inflationary scalar modes (black solid), inflationary tensor modes (black dashed), and cosmic strings (blue dot-dashed) \cite{Bevis:2007qz}. The inflationary tensors have $r=0.2$ while the string contribution has $\fd=0.03$.} \end{figure} \begin{figure}[t] \resizebox{1.05\columnwidth}{!}{\includegraphics{Fig2_NewColors.eps}} \caption{\label{polar} B-mode polarization power spectra for textures (solid red), semilocal strings (dashed black), and Abelian Higgs strings (dot-dash blue). All the curves are normalized to make the temperature spectra match the \Planck\ $\ell=10$ value. We see that all these types of topological defects predict similar shapes in the BICEP2 data range $30 \lesssim \ell \lesssim 300$, though they become different for $\ell>300$. } \end{figure} | If this detection of B-mode polarization is confirmed, then primordial gravitational waves appear to be a necessary addition to the standard cosmological model. However, the BICEP2 data points do not agree well with expectations at higher $\ell$. It is intriguing that an admixture of topological defects appears able to improve the fit, while reducing the tensor-to-scalar ratio to $r \simeq 0.15$. But precise quantitative statements for such a model, which would simultaneously include primordial tensors, defects, and perhaps also a running of the scalar spectral index, require a more careful numerical analysis. In conclusion, we have shown that topological defects alone cannot explain the BICEP2 data points, and that B-modes already give a constraint on defects competitive with that from temperature anisotropies. | 14 | 3 | 1403.4924 |
1403 | 1403.4609_arXiv.txt | We present an analysis of the star formation history (SFH) of a field near the half light radius in the Local Group dwarf irregular galaxy IC~1613 based on deep {\it Hubble Space Telescope} Advanced Camera for Surveys imaging. Our observations reach the oldest main sequence turn-off, allowing a time resolution at the oldest ages of $\sim 1$ Gyr. Our analysis shows that the SFH of the observed field in IC~1613 is consistent with being constant over the entire lifetime of the galaxy. These observations rule out an early dominant episode of star formation in IC~1613. We compare the SFH of IC~1613 with expectations from cosmological models. Since most of the mass is in place at early times for low mass halos, a naive expectation is that most of the star formation should have taken place at early times. Models in which star formation follows mass accretion result in too many stars formed early and gas mass fractions which are too low today (the ``over-cooling problem''). The depth of the present photometry of IC~1613 shows that, at a resolution of $\sim 1$ Gyr, the star formation rate is consistent with being constant, at even the earliest times, which is difficult to achieve in models where star formation follows mass assembly. | \label{secint} \subsection{Motivation} The present paper is part of the Local Cosmology from Isolated Dwarfs (LCID)\footnote{Local Cosmology from Isolated Dwarfs: http://www.iac.es/project/LCID/} project. We have obtained deep {\it Hubble Space Telescope} (HST) photometry, reaching the oldest main sequence turn-off points, of six isolated dwarf galaxies in the Local Group: IC~1613, Leo~A, Cetus, Tucana, \objectname[]{LGS-3}, and Phoenix. Five galaxies were observed with the Advanced Camera for Surveys \citep[ACS,][]{ford98}, while Phoenix was observed with the Wide Field and Planetary Camera-2 \citep[WFPC2,][]{holtzman1995}. The main goal of the LCID project is to derive the star formation histories (SFHs), age-metallicity relations (AMRs), variable star populations, and stellar population gradients of this sample of galaxies. Our objective is to study their evolution at early epochs and to probe effects of cosmological processes, such as the cosmic UV background subsequent to the onset of star formation in the universe or physical processes such as the gas removal by supernovae (SNe) feedback. Our sample consists of field dwarfs which were chosen in an effort to study systems as free as possible from environmental effects due to strong interactions with a host, massive galaxy. The SFH is a powerful tool to derive fundamental properties of dwarf galaxies and their evolution \citep{tolstoy2009}, but to study the earliest epochs of star formation, deep CMDs, reaching the oldest main sequence turn-offs, are required \citep[cf.,][]{gallart2005}. Our impressions of the evolution of dwarf galaxies are biased by studies of the nearby, gas-poor dSph companions of the Milky Way. Because of their proximity, deep CMDs are obtainable from ground-based observatories. In contrast, the gas-rich, dIrr galaxies, which are found at greater distances, have few studies with comparable photometric depth. The Magellanic Clouds represent the one exception to this generalization, but, because of they are substantially more massive than the typical dwarf galaxy and have potentially complex histories due to their current interactions \citep[see][and references therein]{kalli2013}, they present less than ideal targets for study. Because of the larger distances to the dIrrs, until the LCID project, none have had resolved star studies which reach down to the oldest main sequence turnoff stars. Thus, our view of the SFHs of dwarf irregular galaxies has been shaped by relatively indirect measures. The work by \citet{gallagher84} represents a seminal contribution to our understanding of the SFHs of dIrrs. Based on galaxy mass estimates, blue luminosities, and H$\alpha$ luminosities, they demonstrated that most irregular galaxies were consistent with nearly constant star formation over their lifetimes (as opposed to the larger spiral galaxies which showed declining star formation rates, hereafter SFRs). Most importantly, they pointed out that ``The constant SFR history implies that the simple classical model in which star formation is proportional to gas density in a closed system cannot be correct for irregular galaxies.'' Modern observations of nearby dIrrs have been collected and summarized by \citet{weisz2011}, and indicate that, on average, SFRs are higher at early times, but that there are some dIrrs for which constant SFRs are a good approximation. Recently, there have been theoretical papers emphasizing the difficulty in making models of galaxies which have nearly constant SFRs. \citet{orban08}, \citet{sawala2011}, \citet{weinmann2012}, and \citet{kuhlen12} have all highlighted the difficulty of producing dwarf galaxies with properties comparable to those observed in the current universe. The degree of failure is greatest in the amount of mass converted into stars, which is of order one magnitude too large in cosmological simulations. This overproduction of stars in dwarfs is an extreme symptom of the ``over-cooling problem'' \citep[c.f.,][]{benson03} faced by all galaxy modeling. Without deep imaging of resolved stars in dIrr galaxies, we lack sufficient time resolution to study SFHs at the earliest times. For example, the earliest time bin used by \citet{weisz2011} is 4 Gyr in duration. At this time resolution, we cannot distinguish between SFRs that are constant at all times, or SFRs that show considerable variation (most importantly evidence for an early dominant episode of SF). The initial time bin of 4 Gyr covers the time range from before re-ionization up to a redshift of $\sim$2 \citep[which is approaching the peak of in the history of universal star formation, e.g.,][]{madau1998}, and represents this entire important range with a single average number. The observations of IC~1613 presented here resolve this initial period and represent a small step into this relatively unexplored territory. \subsection{The Normal, Isolated, Low Mass, Dwarf Irregular Galaxy IC 1613} Here we present our analysis of a deep HST/ACS observation of a field in IC~1613. As we discuss in section \ref{repfield}, the SFH that we derive for this field is likely a good representation for the entire galaxy. IC~1613 is a low-luminosity, Local Group, dIrr galaxy which is one of the nearest gas-rich irregular galaxies \citep[for a review of the properties of IC~1613 see][]{vdb2000}. Because of its proximity, IC~1613 offers the opportunity to reconstruct a detailed SFH of a relatively isolated and non-interacting dwarf irregular galaxy. IC~1613 also has very low foreground and internal reddening (although it lies within 5 degrees of the ecliptic). There have been several determinations of its distance based on Cepheid and RR~Lyr variable stars and the tip of the red giant branch. Using all three methods, \citet{dolphin2001} derived a distance of 730 kpc. In a comparison of all of the literature values (which included their own measurement using RR Lyrae and Cepheid data of 770 Kpc), \citet{bernard2010} determine a mean distance of 760 kpc. The most recent determination is by \citet{tammann2011} who derived a distance of 740 kpc using Cepheids. For consistency with the other LCID studies, we will adopt the distance estimate from \citet{bernard2010} which corresponds to scales of 221 pc arcminute$^{-1}$, 3.7 pc arcsecond$^{-1}$, and $\sim$ 0.2 pc pixel$^{-1}$. IC~1613 is not considered to be a satellite of either the Milky Way or M31. \citet{mateo1998} included IC~1613 in the diffuse ``Local Group Cloud,'' and \citet{mcc2012} determined a distance of 517 kpc and a velocity of $-$90 km s$^{-1}$ relative to the Local Group barycenter. As such, it is located very close to the zero velocity surface for M~31 and well within the zero velocity surface for the Local Group \citep{mcc2012}. Given its isolated position and velocity, IC~1613 has not had any recent interactions, although interactions with other galaxies long ago cannot be ruled out. To date, there are no proper motion studies of IC~1613, which would be very valuable in determining its potential interaction history. The physical parameters of IC~1613 were summarized in \citet{cole1999}. These properties are normal for an Im~V galaxy with a moderate luminosity ($M_V = -$15.2) and a small value of the maximum amplitude of the rotation curve \citep[V$_{max}$ $=$ 25 km s$^{-1}$;][]{lake1989}. Its SFR of 0.003~$M_{\odot}$~yr$^{-1}$ \citep{mateo1998} is also normal for its type and luminosity. The most recent ISM oxygen abundance measurement was made by \citet{lee2003}, who obtained a spectrum where the $\lambda$4363 auroral line of [\ion{O}{3}] was detected resulting in a measurement of 12 $+$ log (O/H) $=$ 7.62 $\pm$ 0.05. This corresponds to 8.5\% of the solar oxygen abundance \citep[as determined by][]{asplund2009}, which is slightly less than that of the SMC, and normal for a galaxy of its luminosity \citep[e.g.,][]{skillman1989, berg2012}. This combination of proximity and normality makes IC~1613 one of the best opportunities to study the properties of a dwarf star-forming galaxy that is relatively isolated (as is typical for Im~V galaxies). The overall structure of IC~1613 is also typical of an Im~V galaxy. Ground-based studies have provided an overview of the stellar population distributions. \citet{bor2000} studied the distribution of luminous cool stars from J and K-band imaging and found AGB stars covering a wide range in age in all of their inner galaxy fields. \citet{albert2000} conducted a wide field survey of IC~1613 for C and M stars, and found the (intermediate age) C stars extended out to 15 arcminutes, well beyond the regions where star formation currently is active. Recently, \citet{bernard2007} have conducted a wide field optical survey of IC~1613, and trace red giant branch (RGB) stars out to radii $\ge$ 16.5 arcminutes ($\sim$ 3.6 kpc), showing the galaxy to be more extended than previously thought. The resolved stellar populations of IC~1613 have been studied with the HST twice in the past, both times using the WFPC2 camera. \citet{cole1999} studied a central field and found IC~1613 to be a smoothly evolving galaxy with a relatively constant SFR over the last Gyr. Horizontal branch (HB) stars were detected, indicating the presence of an old population. \citet{skillman2003a} obtained deep imaging for a field located 7.4 arcminutes southwest of the center. While that imaging was not quite deep enough to reach to the oldest main sequence turnoff stars, greatly limiting the time resolution at the oldest ages, the derived SFRs were constant within a factor of three over the entire lifetime of the galaxy. In this paper, we present the SFH of IC~1613 obtained from observations with the ACS on the HST. The photometry reaches the oldest main sequence turn-offs of the galaxy, allowing us to obtain an accurate SFH even for the oldest stellar populations. \citet{bernard2010} have already used these observations to conduct a study of the variable star content of IC~1613. The structure of the paper is as follows: in \S\ref{secred} the observations and data reduction are discussed and the CMD is presented. The derived SFH of IC~1613 is presented in \S\ref{secsfhresult} and is compared with those of other LCID galaxies in \S\ref{seclcid}. The implications of the SFH of IC~1613 for galaxy modeling, and, in particular, the over-cooling problem are discussed in \S\ref{seccosmo}. The main conclusions of the work are summarized in \S\ref{seccon}. As with the previous LCID papers, cosmological parameters of $H_0=70.5\rm~km~s^{-1}~Mpc^{-1}$, $\Omega_m=0.273$, and a flat Universe with $\Omega_\Lambda = 1 - \Omega_m$ are assumed \citep[i.e.,][]{kom_etal2009}. \begin{figure}[h] \epsscale{1.0} \includegraphics[width=8.6cm,angle=0]{f1.jpg} \caption[ ]{The location of the newly observed HST ACS field in IC~1613 (rectangle, upper right). The optical center of the galaxy is indicated by the white cross. The two dashed ellipses correspond to the core radius (r$_c$) at 4\farcm5 ($\sim$ 1.0 kpc) and the half-light radius (r$_h$) at 6\farcm5 ($\sim$ 1.4 kpc). As can be seen from the figure, the HST ACS field is located between the two. Also indicated are the positions of the two previous HST WFPC2 fields (chevrons) from \citet{cole1999} (inner) and \citet{skillman2003a} (outer). \label{f1}} \end{figure} | \label{seccon} We have presented the SFH of the dIrr galaxy IC~1613, based on deep HST photometry obtained with the ACS. \begin{itemize} \item The SFH with relatively small uncertainties has been obtained for the entire lifetime of the galaxy. The solution shows that the SFH of IC~1613 is consistent with a constant SFR over its entire lifetime. \item Most or all the star formation was produced in IC~1613 after the reionization epoch, assumed to occur $\sim 12.8$ Gyr ago. There is no evidence of an early dominant episode of star formation in IC~1613. \item A comparison of the derived SFH of IC~1613 with the models of \citet{sawala2011} reinforce their observation that models where star formation follows mass assembly form too many stars too early. This well known aspect of the so called ``over-cooling problem'' appears to be universal, but now, with the deep HST photometry of IC~1613, we see that the problem reaches back to the very earliest times in the evolution of galaxies. \item There are proposed solutions to the over-cooling problem for dwarf galaxies. The solutions discussed in this paper rely on an efficient coupling of supernova feedback to the ISM. The predictions of very efficient coupling may be confirmed or refuted with future generations of simulations that model the relevant processes directly and through future observations of dwarf galaxy SFHs with similar quality to the LCID studies. \end{itemize} | 14 | 3 | 1403.4609 |
1403 | 1403.6000_arXiv.txt | Scattering in central attractive potentials is investigated systematically, in the limit of strong interaction, when large-angles scattering dominates. In particular, three important model interactions (Lennard-Jones, Yukawa, and exponential), which are qualitatively different from each other, are studied in detail. It is shown that for each of these interactions the dependence of the scattering angle on the properly normalized impact parameter exhibits a quasi-universal behavior. This implies simple scaling of the transport cross sections with energy in the considered limit. Accurate fits for the momentum transfer cross section are suggested. Applications of the obtained results are discussed. | The classical problem of elastic collisions between interacting particles has numerous applications, in particular to the transport properties of gases, plasmas, and other related systems. The properties of the scattering depend strongly on the exact form of the interaction potential. Since the interaction potential differs greatly from one system to another, it is not surprising that numerous studies addressing classical scattering for various model potentials have been published in the literature. Numerical calculations are required for most of the potentials, and thus the volume of published works showed explosive growth as appropriate computational tools became widely available. For example, collision integrals for scattering in the Lennard-Jones (12-6) and Buckingham (exp-6) potentials were evaluated in Refs.~\cite{Hirschfelder} and \cite{Mason1}, in order to model transport properties of non-polar gases. Collisional integrals for the Stockmayer (12-6-3) potential were evaluated in connection with transport properties of polar gases~\cite{Monchick1}. Scattering in the attractive and repulsive screened Coulomb (Yukawa) potentials has been investigated in the context of transport properties of ionized gases~\cite{Lane,Mason2,Hahn}. Other idealized model potentials, as e.g. inverse power law~\cite{Kihara} and exponential~\cite{Monchick2} have been investigated as well. However, not all cases of practical interest were explored in these early studies. One relevant example is scattering in the Yukawa potential in the limit of very strong interaction~\cite{id2,idIEEE,MT}. This limit received attention only after it was recognized that it applies to elastic collisions involving highly (negatively) charged particles in complex (dusty) plasmas~\cite{Book,FortovUFN,FortovPR}. The interaction can be either repulsive (particle-particle collisions) or attractive (particle-ion collisions). More recently, the results for classical scattering in the Yukawa potential in the limit of strong interaction~\cite{id2,idIEEE,MT} have been used in the context of transport properties of strongly coupled plasmas~\cite{Baalrud} and to describe self-scattering of dark matter particles~\cite{Feng,Buckley,Tulin}. An interesting result from the studies of classical scattering in the strongly attractive Yukawa potential~\cite{id2,idIEEE} is that the scattering angle $\chi$ is a quasi-universal function of the properly normalized impact parameter $\rho$: The shape $\chi(\rho)$ has only very weak dependence on other parameters (e.g. energy). In this paper we show that this quasi-universal behavior is not a special properties of the Yukawa potential. It applies to a wider class of strongly attractive potentials, among them are three qualitatively different interactions -- Lennard-Jones, Yukawa, and exponential. The quasi-universality is in fact most pronounced for the Lennard-Jones potential. In each case, the universality of $\chi(\rho)$ leads to simple scaling of the transport cross sections with energy. Accurate fits for the dependence of the momentum transfer cross section on energy in the considered regime are proposed. Possible applications of the results to practical problems are discussed. | One of the main results of this study is that quasi-universality in the low-energy scattering can be expected for a wide class of realistic interaction potentials. This has applications for the direct simulation Monte Carlo (DSMC) method employed to model various aspects of rarefied gas flows~\cite{BirdBook}. Appropriate modeling of intermolecular collisions is an important element of this method. The calculation of the scattering angle for each pair of colliding particles is computationally expensive, since it depends on the energy and impact parameter of the colliding particles. Therefore, simplified collision models such as variable hard sphere, variable soft sphere, and their modifications are widely employed. The present observation, that in the low-energy regime the scattering angle becomes a quasi-universal function of the (properly normalized) impact parameter and is practically independent of energy, can significantly simplify the simulations. Remarkably, the universality is most pronounced for the LJ potential, which is extensively used in DSMC. The reader is referred to Refs.~\cite{Sharipov,Bird} for a recent discussion of some related issues. The proposed simple and accurate fits for the momentum transfer cross sections are also useful. As has been pointed out, the attractive Yukawa potential in the high-$\beta$ regime is relevant to complex plasmas and to the dark matter. The typical values of the thermal scattering parameter for ion-particle interactions ($\beta$ evaluated at an average kinetic energy of the ions) under normal condition are expected to lie in the range between $\simeq 1$ and $\simeq 30$ for micron-size particles~\cite{MT}. Higher values, up to $\beta\simeq 70$, have been reported in experiments with big hollow microspheres of a diameter $\simeq 60$ $\mu$m~\cite{Nosenko, NosenkoCorr}. This range has already been covered in previous studies~\cite{id2,idIEEE}. In the context of dark matter, however, the regime $\beta > 10^3$ is not unrealistic~\cite{FengPRD}. The present results, which extend previous studies and provide more accurate fit in the high-$\beta$ regime, are therefore recommended for use. Our result for the momentum transfer cross section for the LJ interaction potential, exhibits the expected scaling $\sigma_{\rm MT}\propto \beta^{1/3}\propto v^{-2/3}$ at low velocities. On the other hand, the generalized soft-sphere model (GSS, also based on the LJ potential) proposed in Ref.~\cite{Fan}, is accurate at high velocities but shows the incorrect scaling $\sigma_{\rm MT}\propto v^{-2.5}$ at low velocities. This results in unphysically high collision frequencies and an overall loss of simulation accuracy and efficiency at low temperatures~\cite{Gu}. The simple and accurate fit of Eq.~(\ref{fit_LJ}) can easily be implemented to eliminate these unphysical characteristics of GSS. The quasi-universality discussed above clearly requires some attraction. Moreover, the attractive potential should decay more rapidly than $r^{-2}$ and be sufficiently strong (in terms of $\beta$) so that a barrier in the effective potential emerges. These are all necessary but not sufficient conditions of qusai-universality. It would be interesting to investigate the ``quality'' of the universality as a function of the range and strength of the attractive part of the interaction potential. One of the possible strategies would be to analyze in detail scattering in the generalized ($m$-$n$) Mie potential. This is, however, beyond the scope of the present study. Regarding the repulsive potentials, there is indeed a natural quasi-universality of another kind. As the interaction becomes steeper, the scattering resembles more and more that from a hard sphere. The distance at which the potential is equal to the kinetic energy of colliding particles approximately determines the radius of this hard sphere and sets up the scaling of the transport cross sections with energy. This has been investigated in detail earlier, see e.g. Refs.~\cite{Baroody,Smirnov}. To summarize, classical scattering in the limit of strong attractive interaction has been investigated in detail and interesting generic properties have been identified. The results are useful in a wide interdisciplinary context. | 14 | 3 | 1403.6000 |
1403 | 1403.6831_arXiv.txt | \kepb\ (= KOI-13.01) is a unique transiting hot Jupiter. It is one of very few known short-period planets orbiting a hot A-type star, making it one of the hottest planets currently known. The availability of \ik\ data allows us to measure the planet's occultation (secondary eclipse) and phase curve in the optical, which we combine with occultations observed by warm \is\ at 4.5~\mic\ and 3.6~\mic\ and a ground-based occultation observation in the \ks\ band (2.1~\mic). We derive a day-side hemisphere temperature of 2,750$\pm$160 K as the effective temperature of a black body showing the same occultation depths. Comparing the occultation depths with one-dimensional planetary atmosphere models suggests the presence of an atmospheric temperature inversion. Our analysis shows evidence for a relatively high geometric albedo, \ag = $0.33^{+0.04}_{-0.06}$. While measured with a simplistic method, a high \ag\ is supported also by the fact that the one-dimensional atmosphere models underestimate the occultation depth in the optical. We use stellar spectra to determine the dilution, in the four wide bands where occultation was measured, due to the visual stellar binary companion 1\farcs15$\pm$0\farcs05 away. The revised stellar parameters measured using these spectra are combined with other measurements leading to revised planetary mass and radius estimates of $M_p$ = 4.94--8.09~\mjup\ and $R_p$ = 1.406$\pm$0.038~\rjup. Finally, we measure a \ik\ mid-occultation time that is 34.0$\pm$6.9 s earlier than expected based on the mid-transit time and the delay due to light travel time, and discuss possible scenarios. | \label{sec:intro} The study of exoplanetary atmospheres is one of the most exciting aspects of the discovery of planets outside the Solar System. When the system is in a favorable edge-on geometric configuration the atmosphere of the unseen planet can be probed by measuring the decrease in observed flux during planetary transit (planet moves across the disk of its host star) or planetary occultation (secondary eclipse, when the planet moves behind the star), at different wavelengths. This approach favors large, hot, gas giant planets with large atmospheric scale heights, commonly known as hot Jupiters. This class of planets earns its name by having a radius about the radius of Jupiter while orbiting at short orbital periods, close-in to their host star. Tidal interaction is expected to lock (synchronize) the planet spin with the orbit, keeping the same planetary hemisphere constantly facing the star (a permanent day side) and the other hemisphere constantly facing away from the star (a permanent night side). Such planets do not exist in the Solar System, so only by probing the atmospheres of these distant worlds can we learn about atmospheric processes and atmospheric chemistry at such exotic environments. The number of hot Jupiters whose atmospheres were studied using occultations is continuously rising and currently number in the several dozens. As the field transitions from the detailed study of individual objects to the characterization of a significant sample, several correlations, or patterns, are emerging. Several authors \citep[e.g.,][]{cowan11, perna12, perez13} have noticed that among the hot Jupiters, the hottest planets tend to have a low albedo and poor heat redistribution from the day side hemisphere to the night side hemisphere, pointing to a decreased advection efficiency. \cite{knutson10} noticed that planets with an inversion layer in their upper atmosphere, where temperature increases with decreasing pressure, tend to orbit chromospherically quiet (i.e.~non-active) stars, while planets with no inversion layer orbit chromospherically active stars. The inversion can be attributed to an absorber in the upper atmosphere that is being destroyed by UV radiation from chromospherically active stars \citep{knutson10}. Although, the occurrence of atmospheric inversions might also be related to atmospheric chemical composition, specifically the C to O elemental abundance ratio compared to the Solar composition value \citep{madhu11, madhu12}. Another interesting correlation involving chromospheric activity was identified by \cite{hartman10} who showed that planets with increased surface gravity tend to orbit stars with increased chromospheric activity. The patterns mentioned above are not fully explained. Gaining a better understanding of these patterns requires testing them with a larger sample, and studying planets at extreme environments and/or different characteristics, while observing over a wide range of wavelengths and obtaining a rough characterization of their spectrum. \kepb\ is such an extreme hot Jupiter, orbiting an A-type star every 1.76~days at a distance of only 0.034~AU. The close proximity to a hot, early-type star makes this planet one of the hottest currently known. With an irradiation at the planetary surface over 15,000 times that of Jupiter in the Solar System, the expected black body temperature of \kepb\ is up to over 3,000~K (for zero albedo and no heat redistribution from the day to night sides), comparable to the smallest stars, motivating the study of its atmosphere. Moreover, main-sequence A-type stars are inaccessible to spectroscopic radial velocity (RV) planet searches since their spectrum does not allow high precision RV measurements, making this a unique opportunity to study a planet in a short-period orbit around a main-sequence A-type star. The only other currently known hot Jupiter orbiting a bright A-type star is WASP-33b \citep{collier10, kovacs13}, although, that system is not in the \ik\ field and the host star's pulsating nature hampers the measurement of occultation depths. Here we carry out an atmospheric characterization of \kepb\ by measuring its occultation in four different wavelength bands, from the infrared (IR; \is/IRAC 4.5~\mic\ and 3.6~\mic), through the near-IR (NIR; \ks\ band), to the optical (\ik). We also analyze the \ik\ phase curve and obtain Keck/HIRES spectra that result in revised parameters for the objects in the system. We describe the analysis of our various data sets in \secr{dataanal}. In \secr{atm} we study the planet's atmosphere, and in \secr{dis} we discuss our results. \subsection{The \kep\ System} \label{sec:kepler13} The \kep\ system is a four body system, as far as we currently know. A high angular resolution image is shown in \figr{fchart}, taken from the publicly accessible \ik\ Community Follow-up Observing Program (CFOP) website\footnote{https://cfop.ipac.caltech.edu/}. The image was obtained in \ks\ (K short) band with the PHARO camera \citep{hayward01} and the adaptive optics system mounted on the Palomar 200 inch (5 m) Hale telescope (P200). The two bright components seen in \figr{fchart} are two A-type stars, where the brighter one, the primary (\kepA), hosts a transiting planet (\kepAb\footnote{In the literature it is occasionally referred to as simply Kepler-13b.}), while the fainter one, the secondary (\kepB), is orbited by a third star (\kepBB) of spectral type G or later \citep{santerne12}. The observed angular separation between the two A-type stars was measured to be 1\farcs12$\pm$0\farcs08 by \cite[][E.~Adams private communication]{adams12} and 1\farcs16$\pm$0\farcs06 by \cite{law13}, resulting in a weighted mean of 1\farcs15$\pm$0\farcs05. The distance to the system is 530~pc \citep{pickles10} with an uncertainty of 20\% (A.~Pickles, private communication), giving a sky-projected separation of $610 \pm 120$~AU. \begin{figure} \begin{center} \includegraphics[scale=0.40]{fchart.eps} \caption{\label{fig:fchart} High angular resolution adaptive optics imaging of the \kep\ system, obtained with P200/PHARO in the \ks\ band. North is up and East is to the left. The system is a visual binary, composed of two A-type stars at a sky-projected separation of 1\farcs15$\pm$0\farcs05. The brighter one, the primary, \kepA, is to the East (left), and is the planet host. The fainter component, the secondary, \kepB, is to the West (right) and is itself a stellar binary system, where the A-type star hosts a late-type star \citep{santerne12}. } \end{center} \end{figure} The availability of \ik\ data for a short-period planet transiting an A-type star in a bright ($V$~=~9.95~mag) hierarchical system makes it an interesting astrophysical laboratory. It is the first planet whose mass was estimated using photometric light curves \citep{shporer11, mazeh12, mislis12, esteves13, placek13}, and the first star-planet system where the star's obliquity was measured by modeling the asymmetric transit light curve due to stellar gravity darkening \citep{szabo11, barnes11}. In addition, orbital precession was also identified \citep{szabo12, szabo14}. | \label{sec:dis} We present here a multi band study of the atmosphere of \kepb. We measured the occultation depth of \kepb\ in four wide bands, from the IR (\is/IRAC 4.5~\mic\ and 3.6~\mic), through the NIR (P200/WIRC/\ks), to the optical (\ik). We also used \ik\ data along the entire orbit to measure the planetary reflected and thermally emitted light, and measure the planetary mass from the beaming and ellipsoidal effects. Finally, we used Keck/HIRES spectroscopic data to characterize the planet host star and calculate the dilution of the observed occultations due to the presence of a blended A-type companion star. The measured occultation depths are listed in \tabr{res} including both the directly measured depths, not accounting for the dilution, and the corrected depths while accounting for the dilution. The corrected depths are simply the measured depths multiplied by the dilution factor at the respective wavelength, also listed in \tabr{res}. The corrected depth uncertainties account for both the measured depth uncertainties and dilution factor uncertainties. Comparing the \ik\ mid-occultation time derived here (see \tabr{fitparams} and \secr{kepler_occ}) to the mid-transit time from the literature shows that the mid-occultation time occurs about half a minute earlier, with a significance of almost \sig{5} (\secr{timecomp}). This can be attributed to either a non-zero orbital eccentricity, or, an asymmetric distortion in the light curve ingress and egress shape due to asymmetric planetary surface brightness distribution, meaning the brightest region on the planet's surface is shifted away from the substellar point. An early mid-occultation time can be the result of super-rotating winds causing the planet's most reflective region to be shifted westward, as already identified for Kepler-7b by \cite{demory13}. Interestingly, Kepler-7b's high geometric albedo and day-side brightness temperature in the optical \citep{demory11, kipping11}, as well as the planet and host star radii \citep{latham10}, are all comparable to those of \kepb. However, Kepler-7b's mass is only $0.433 \pm 0.040$ \mjup, more than ten time less massive than \kepb\ mass, and its host star has a mass of about 1.35 \msun\ and effective temperature of about 6,000 K \citep{latham10}. By analyzing the \ik\ phase curve we have identified a discrepancy between the beaming-based and ellipsoidal-based planet's mass estimates (see \tabr{planetmass} and \secr{planetmass}), which was already noticed before \citep{shporer11, mazeh12}. We chose to take a conservative approach and give a wide range for the planet's mass that includes both estimates. If the early mid-occultation time is indeed due to the brightest region of the planetary atmosphere being shifted away from the substellar point then that may also affect the observed phase curve. Specifically, that will insert a phase shift to the reflection component in \eqr{beer} which includes both thermal emission and reflected stellar light from the planet's atmosphere. In that case the measured coefficients $a_{1c}$ and $a_{1s}$ would not correspond separately to the reflection and beaming amplitudes but a linear combination of them, meaning the model will include a degeneracy. This was already noted by \cite{faigler13} who analyzed the phase curve of Kepler-76b. Although the host star in that system is an F-star, so it is different than the host star in the \kepA\ system, they have shown that adding a phase shift to the reflection component results in a decreased beaming-based mass estimate for Kepler-76b and makes it consistent with the ellipsoidal-based mass estimate. Following a similar scheme \citep[see][ Eq.~1]{faigler13}, the required phase shift of the reflection component that will resolve the corresponding discrepancy for \kepb\ (see \tabr{planetmass}) is $1.49 \pm 0.48$ deg. However, such a phase shift will put the planet's brightest region eastward of the substellar point, so the resulting asymmetry in the occultation light curve ingress and egress will make the mid-occultation time later than expected, not earlier as we measure here. We conclude that if the measured early mid-occultation time is due to a planetary asymmetric surface brightness distribution we cannot detect direct evidence for it in the phase curve. Our revised host star parameters show it is smaller than previous estimates \citep{szabo11}, leading to a smaller planetary radius of $R_p = 1.406 \pm 0.038$~\rjup\ where we assume the planet to star radii ratio reported by \cite{barnes11}. This revised planet radius is comparable with the radii of other hot Jupiters, although given the planet's relatively high mass it is positioned in a sparse region in the planetary radius-mass diagram for the currently known planets. We have followed two approaches for interpreting our measurements and characterizing \kepb's atmosphere. In \secr{energybudget} we study the atmospheric energy budget, and in \secr{atm_model} we compare our wide-band measurements to various spectral atmospheric models. We must caution here that our conclusions about \kepb's atmosphere are based on sparse data. Although covering a wide wavelength range, from the IR to the optical, we have at hand the occultation depth measured in only four wide bands and the phase curve measured in only one wide band. Such sparse data could, in principle, lead to systematically biased results when fitted with over-simplified atmospheric models (see \citealt{burrows13} for a more detailed discussion). Despite the limited data, our analysis here, including the two different approaches (\secr{energybudget} and \secr{atm_model}), is an attempt to extract as much science as possible from the data while not over interpreting it. In the future, more detailed data, including panchromatic spectra and phase curves at various wavelengths, will allow a more comprehensive characterization of the planet's atmosphere. The four occultation measurements enable us to identify the relation between the day-side brightness temperature and geometric albedo in each band (see \eqr{depth} and \figr{ag_td}). Assuming the geometric albedo does not change significantly between the four bands these relations allow us to derive the effective temperature of a black body that will show the same occultation depths, $\tdeff = 2,750 \pm 160$ K. This also results is a high geometric albedo, of $\ag = 0.33^{+0.04}_{-0.06}$, which assuming \ab = (3/2)\ag\ (Lambert's Law) leads to \ab = $0.50^{+0.06}_{-0.09}$. Such an albedo is at the high end of the range spanned by other hot Jupiters \citep[e.g.,][]{rowe08, cowan11, coughlin12, evans13, demory13, heng13}. The night-side brightness temperature in the optical is \tn = 2,537 $\pm$ 45 K, measured from the difference between the \ik\ occultation depth and the reflection component amplitude (see \eqr{ns}). \tn\ is smaller than \tdeff\ but not by much. Comparing \tn, \tdeff, and \ab\ results in inconsistencies, indicating the night side does not behave as a black body in the optical. A possible explanation for the small difference between \tn\ and \tdeff\ is the planet's high mass, from at least five to nearly ten times larger than that of typical hot Jupiters, which gives a correspondingly large surface gravity with $\log_{10}(g\ [\rm g\ cm^{-2}])$ in the range of 3.79--4.01. Increased gravity leads to increased photospheric pressure which in turn increases the radiative time constant in the atmospheric layers probed by our measurements \citep{iro05, showman08}. As shown in idealized dynamical models by \cite{perez13}, atmospheres with greater radiative time constants exhibit smaller day-night thermal contrasts. Comparing the wide-band occultation depths measured here to the spectral atmospheric models of \cite{fortney08} and \cite{burrows08} shows that our measurements are better described by models that include an atmospheric inversion and a weak day-night energy circulation. As can be seen in \figr{atm_model} the current atmospheric spectral models underestimate the occultation depth in the optical. Since the \ik\ occultation depth measurement is of much higher precision than occultation depths measured here in other bands, and than other occultations in the optical in other studies involving \ik\ data \citep[e.g.,][]{desert11a, desert11b, fortney11}, this discrepancy could be attributed to limits of the one-dimensional spectral models. If the \ik\ band measurement uncertainty was similar to that in the other bands then it would have been consistent with the models. Still, the fact that all models underestimate the \ik\ occultation depth suggests a higher geometric albedo in the optical than the typical 0.05 -- 0.10 predicted by the models. This supports the high geometric albedo of $\ag = 0.33^{+0.04}_{-0.06}$ derived in \secr{energybudget} for the equivalent black-body object showing the same occultation depths. If indeed \kepb\ day-side atmosphere has a high \ag\ then this could be used as a clue to identify the material dominating the day-side reflectivity, along with the day-side temperature and the possible existence of atmospheric inversion. Short-period planets are expected to reach full orbital circularization and spin-orbit synchronization due to tidal interaction with the host star, an interaction that grows stronger with decreasing period \cite[e.g.,][]{mazeh08}. However, our measurement of the mid-occultation time suggests a possible small but finite orbital eccentricity (see \secr{timecomp}). If confirmed, it can lead to a non-synchronized planetary rotation \citep[e.g.,][]{correia11}, meaning the day and night sides are not permanent, which could explain the small brightness temperature difference detected between them in the optical. Our comparison between the atmospheres of \kepb\ and WASP-33b shows that despite the similarity between the host stars and other similarities between the two star-planet systems, the planetary atmospheres seem to be different. If confirmed, it is yet another example of the diversity of exoplanets and exoplanet atmospheres, emphasizing the need to discover more exoplanets that allow the study of their atmosphere, in particular those orbiting early-type stars like the one investigated here. Although spectra of such stars (currently) do not allow for high-precision RV measurements, preventing precise planet mass measurement \citep[but see][]{galland05, lagrange09}, the planetary nature of massive close-in planets can be confirmed with high-quality space-based photometry of bright stars. This was done using \ik\ data for \kepb\ and can potentially be done in the future with data from the NASA K2 mission \citep{howell14}, the NASA TESS mission\footnote{Scheduled for launch in 2017, see \url{http://tess.gsfc.nasa.gov}}, and the ESA PLATO mission \citep{rauer13}. In addition, detailed follow-up studies are also possible, like the measurement of stellar obliquity \citep{collier10} and investigation of the planet atmosphere. The host star's increased mass, radius, temperature, and younger age, compared to Sun-like stars, will allow testing planet formation and evolution theory. | 14 | 3 | 1403.6831 |
1403 | 1403.1620_arXiv.txt | Massive young stellar clusters are strong sources of radiation and mechanical energy. Their powerful winds and radiation pressure sweep-up interstellar gas into thin expanding shells which trap the ionizing radiation produced by the central clusters affecting the dynamics and the distribution of their ionized gas. Here we continue our comparison of the star cluster winds and radiation pressure effects on the dynamics of shells around young massive clusters. We calculate the impact that radiation pressure has on the distribution of matter and thermal pressure within such shells as well as on the density weighted ionization parameter $U_w$ and put our results on the diagnostic diagram which allows one to discriminate between the wind-dominated and radiation-dominated regimes. We found that model predicted values of the ionization parameter agree well with typical values found in local starburst galaxies. Radiation pressure may affect the inner structure and the dynamics of wind-driven shells significantly but only during the earliest stages of evolution (before $\sim 3$~Myr) or if a major fraction of the star cluster mechanical luminosity is dissipated or radiated away within the star cluster volume and thus the star cluster mechanical energy output is significantly smaller than star cluster synthetic models predict. However, even in these cases radiation dominates over the wind dynamical pressure only if the exciting cluster is embedded into a high density ambient medium. | \label{sec:1} HII regions are fundamental to our understanding of young stellar clusters radiative and mechanical feedback on the interstellar medium (ISM). They are strong sources of emission-line radiation and thus serve as a powerful diagnostic tool to study star formation and the chemical composition of nearby and distant galaxies \citep{CapriottiKozminski2001,Dopitaetal2005, Dopitaetal2006, YehMatzner2012}. They have even been used as tracers of the Hubble expansion \citep{Chavezetal2012}. The idealized \citep{Stromgren1939} model for spherical static HII regions with a homogeneous density distribution was a revolutionary step forward in the study of photoionized nebulae. However the consideration of a number of physical effects have led to a much more robust paradigm. Winds produced by the exciting clusters \citep{CapriottiKozminski2001,Arthur2012,SilichTenorioTagle2013} and the impact that radiation pressure provides on the swept-up interstellar gas \citep{ElmegreenChiang1982, CapriottiKozminski2001, Matzner2002, KrumholzMatzner2009, NathSilk2009, SharmaNath2012} are among such major physical effects. As recently shown by \citet{Draine2011}, the absorption of photons emerging from an exciting cluster by either dust grains and recombining atoms, leads to a non homogeneous density distribution even within static or pressure confined HII regions and under certain conditions, radiation pressure may pile up the ionized gas into a thin outer shell, as assumed by \citet{KrumholzMatzner2009}. The action of cluster winds, as well as the strong evolution that the ionizing photon flux and the star cluster bolometric luminosity suffer after the first supernova explosion make the situation even more intricate \citep{SilichTenorioTagle2013}. The thermalization of the stellar winds and supernovae mechanical energy through nearby random collisions leads to a high central overpressure which forms a strong shock that moves supersonically and sweeps the ambient ionized gas into a thin, wind-driven shell. This shell cools down in a short time scale and begins to absorb ionizing photons causing the ionization front to move back towards the cluster and finally become trapped within the shell. The size and density distribution of such ionized shells have little to do with the original Str\"omgren model. Their evolution depends not only on the ambient gas density distribution and the available Lyman continuum, but also on the mechanical power of the exciting cluster. \citet[hereafter ST13]{SilichTenorioTagle2013} discussed the impact that radiation pressure has on the dynamics of wind-driven shells powered by young star clusters and found radiation pressure not to be a dominant factor. They, however, did not consider the detailed impact that radiation pressure provides on the inner shell structure. They also assumed that shells absorb all photons escaping from the central cluster and thus found an upper limit to the radiative feedback from the central cluster on the dynamics of the swept-up shell. Here we extend the analysis provided in \citetalias{SilichTenorioTagle2013} and discuss how radiation pressure affects the distribution of density and thermal pressure within a shell and thus how it may affect the velocity of the outer shock and the dynamics of the ionized gas around young stellar clusters. The paper is organized as follows: we first present in section \ref{sec:2} the major equations formulated by \citet{Draine2011} for static spherically symmetric HII regions and discuss how the inner and outer boundary conditions affect the solution. In section \ref{sec:3} we discuss different hydrodynamic regimes and also show how \citetalias{Draine2011}'s equations may be applied to the whole shell, including the outer, non-ionized segments. The results of the calculations are presented and discussed in section \ref{sec:4} where we compare different hydrodynamical models (standard energy and momentum dominated, leaky and low star clusters heating efficiency), calculate the model-predicted values of the ionization parameter and compare them to typical values found in local starburst galaxies. Our results are also placed onto a diagnostic diagram which allows one to discriminate between the radiation pressure and wind pressure (thermal or ram) dominated regimes. The summary of our major results is given in section \ref{sec:5}. | \label{sec:4} \subsection{Shells evolving in a low density ISM} We first explore the impact that radiation provides on the wind-driven shells expanding into a low density ambient medium (Table \ref{tab:2}, LDS model). Models LDSa, LDSb and LDSc present different evolutionary stages of the ``standard bubble model''. In this case the wind-driven shell expands into a low density (1 cm$^{-3}$) ISM in the energy-dominated regime. In all cases the mass of the driving cluster is $10^6$\Msol \, and the selected times allow one to see how the ionization structure of the shell changes with time due to the bubble and radiation field evolution. Figure \ref{fig:3} displays the density (solid lines), thermal pressure (dashed lines) and ram pressure (dotted lines) distributions within and at both sides of the expanding shell, while this is exposed to the radiation from the central cluster. \begin{figure*}[htp] \plotone{f3.eps} \caption{The wind-blown shell structure for a low-density environment. Zoom at the density (left-hand axes) and pressure (right-hand axes) distributions across and at both sides of the expanding shell. The left-hand panels present the results of the calculations for models LDSa (top panel), LDSb (middle panel) and LDSc (bottom panel). The right-hand panels displays the results for models with gas leakage: models LDLa (top panel), LDLb (middle panel) and LDLc (bottom panel), respectively. Solid lines show the radial density distribution in the shocked/free wind region, in the ionized and neutral shell and in the ambient ISM. Dashed and dotted lines display the distribution of thermal pressure inside the shell and in the ambient ISM and that of the ram pressure in the free wind region, respectively. The Mach number for the LDS models a, b and c is 6.6, 59 and 50, respectively, while for the LDL models a, b and c is 4.9, 2.7 and 31.4.} \label{fig:3} \end{figure*} The sudden density jumps at the inner edge of the ionized shell result from the fact that the thermal pressure there must be equal to the thermal pressure of the hot thermalized cluster wind (equations \ref{eq2c}) while the temperature in the ionized gas is $10^4$~K. As shown in Figure \ref{fig:3}, in the case of model LDSa ($t = 1$~Myr) the swept up shell has already cooled down and is completely photo-ionized by the Lyman continuum from the young central cluster. Furthermore, a fraction of the ionizing photons still escapes from the shell into the ambient ISM keeping it also at $T = 10^4$ K. Model LDSb presents the shell structure at the trapping time, $\tau_{trap} = 3.3$~Myr. At this time the shell absorbs all ionizing photons, and the mass of the ionized matter is exactly that of the swept-up shell: $M_{ion} = M_{sh}$. The thermal pressure outside of the shell then falls by two orders of magnitude as it is assumed that the temperature of the ambient neutral gas in this case is $100$~K (see the left-hand middle and bottom panels in Figure \ref{fig:3}). The first supernova explosion also occurs at this time and thus the number of ionizing photons emerging from the central cluster begins to decay rapidly afterwards. Model LDSc presents the shell structure at a later time, $t = 5$~Myr, when all ionizing photons are absorbed in the inner segments of the shell and thus the outer skin of the shell remains neutral. The conditions for model LDL assume a leaky bubble model \citep[see, for example,][]{Matzner2002, Harper-ClarkMurray2009}. In this case, the thermal pressure inside the wind-driven bubble drops below the \citet{Weaveretal1977} model predictions due to the escape of hot shocked-wind plasma through holes in the wind-driven shell. In this case individual bow shocks around the shell fragments should merge to create a coherent reverse shock near the contact discontinuity, or inner side of the broken shell \citep[see][]{TenorioTagleetal2006,RogersPittard2013}. We thus assume that the minimum driving force on the shell in the leaky bubble model is determined by the cluster wind ram pressure at the shell location and can never fall below such value (\citetalias{SilichTenorioTagle2013}). Hereafter we will assume that in the leaky case the transition from energy to momentum dominated regimes occurs at $0.13$~Myr, just after the shell cools down and begins to absorb ionizing photons. Equations (\ref{eq2a}-\ref{eq2c}) are replaced with equations (\ref{eq13a} - \ref{eq13c}) at this time. Certainly, this time is arbitrary, but warrants the maximum possible effect of radiation pressure. The density and thermal pressure distributions within and at both sides of the shell in the leaky case are shown on the right-hand panels of Figure \ref{sec:3}. Here the top middle and bottom panels correspond to models LDLa, LDLb and LDLc and thus present the density, thermal pressure and ram pressure profiles at the same evolutionary times $t = 1$, $3.3$ and $5$ Myr, respectively. The size of the leaky shell is smaller and its thickness larger than those predicted by the standard bubble model (model LDS) and the difference grows with time (compare the right and left-hand panels in Figure \ref{fig:3}). Note also that the leaky shell is not able to trap all ionizing photons and form an outer neutral skin for a much longer time (in this case $\tau_{trap} \approx 5$~Myr). This is because in the leaky bubble model the driving pressure and thus the ionized gas density at the inner edge of the shell are much smaller than those in the standard case (LDS). The expectations resulting from calculations of the ionized gas distribution in static configurations with low pressure central cavities (section \ref{sec:2}) had been that radiation pressure would lead to a non homogeneous thermal pressure and density distributions inside the wind-driven shell. Both, density and thermal pressure should grow from a low value at the inner edge of the shell to a maximum value at the outer edge, as in the high density static models (see section \ref{sec:2}). The calculations however, do not show such large enhancements in density and in the leading shock driving pressure relative to that at the inner edge of the shell. The density enhancement is about $\sim 1.04$ and $\sim 1.09$ at $1$~Myr, $\sim 1.07$ and $\sim 1.18$ at $3.3$~Myr and $\sim 1.04$ and $\sim 1.12$ at $5$~Myr in the standard and the leaky bubble model, respectively (see the left-hand and right-hand panels of Figure \ref{fig:3}). We then provided similar calculations for an order of magnitude less massive cluster (10$^5$ M$_{\sun}$) and did not find significant difference with the above results. In all calculations with a 10$^5$ M$_{\sun}$ cluster the density enhancement does not exceed $\sim 1.1$ despite radii of the shells differ significantly from those obtained in the more energetic models LDS and LDL. These results demonstrate how significantly the inner boundary condition (the value of thermal pressure at the inner edge of the HII region) may change the ionized gas density distribution. They also imply that the impact from radiation pressure on the dynamics of shells formed by massive young stellar clusters embedded into a low density ambient medium is not significant throughout their evolution even if all of the hot plasma leaks out from the bubble interior into the surrounding medium. Consequently, allow for the use of equations (\ref{eq2a}-\ref{eq2b}) and (\ref{eq13a}-\ref{eq13b}), ignoring the impact of the starlight momentum. \subsection{Shells evolving in a high density ISM} The high-density models (Table \ref{tab:2}, models HDS and HDE) are evaluated at the same dynamical times: $t $= 1, 3.3 and 5~Myr and are displayed in Figure \ref{fig:4}. In these cases the model predicts that the transition from energy to the momentum dominated regime occurs at much earlier times (see equation \ref{eq15}). For example, in the case of model HDS, $\tau_{tran} \approx 1.58$~Myr. Thus, models HDSb and HDSc correspond to a shell expanding in the momentum dominated regime. The size of the shell in this case is much smaller than when it expands into a low density ISM, however the shell is much denser and thus recombines faster. Therefore in the high density cases the ionizing radiation is not able to photoionize the whole shell from the very early stages of the bubble evolution (see the top left-hand panel in Figure \ref{fig:4}). The density in the ionized shell drops when the transition to the momentum-dominated regime occurs. This allows the central cluster to photoionized a larger fraction of the swept-up material. Therefore the relative thickness of the ionized shell increases between the 1~Myr and 3.3~Myr (compare panels HDSa and HDSb in Figure \ref{fig:4}). After 3.3~Myr the number of ionizing photons decreases rapidly (Figure \ref{fig:2}) and the relative thickness of the ionized shell becomes smaller again despite the drop in driving pressure and the consequent drop in the ionized gas density (see panel HDSc). The density gradient also reaches the maximum value at $3.3$~Myr and then drops at latter times. The density (and thermal pressure) gradient across the ionized shell in the high density models is larger than in the low density cases. For example, the enhancement of density relative to that at the inner edge of the shell in model HDSa is $\sim 1.14$, in model HDSb is $\sim 1.67$ and in model HDSc $\sim 1.25$ (see the left-hand panels in Figure \ref{fig:4}). This is because the inner radius of the ionized shell in the high density case is smaller and thus the impact that radiation pressure provides on the shell is larger. \begin{figure*}[htp] \plotone{f4.eps} \caption{The wind-blown shell structure for a high-density environment. The left-hand column shows the results for models HDSa (top panel), HDSb (middle panel) and HDSc (bottom panel). The right-hand column displays the results for models with a low cluster heating efficiency: HDEa (top panel), HDEb (middle panel) and HDEc (bottom panel). Solid lines correspond to the radial density distribution (left axis) for the free wind, shocked wind, ionized shell, neutral shell and the ambient ISM. Long-dashed and short-dashed lines depict the radial thermal and ram pressure distributions (right axis), respectively. The Mach number for the HDS models a, b and c is 23.9, 8.2 and 5.8, respectively, while for the HDE models a, b and c is 12.5, 3.9 and 3.0.} \label{fig:4} \end{figure*} The right-hand panels in Figure \ref{fig:4} present the results of the calculations when the driving cluster has a low heating efficiency (models HDEa, HDEb and HDEc). These calculations were motivated by the discrepancy between the \citet{Weaveretal1977} model predictions and the observed sizes and expansion velocities of the wind-blown bubbles known as ``the growth-rate discrepancy'' \citet{Oey1996} or ``the missing wind problem'' (\citealt{Freyeretal2006, Dopitaetal2005,Smithetal2006,Silichetal2007, Silichetal2009}) and by the fact that at the initial stages of the bubble evolution the star cluster mechanical luminosity still does not reach the average value adopted in our calculations (see Figure \ref{fig:2}). The heating efficiency may also be small if the kinetic energy of stellar winds is converted to turbulence and radiated away in young stellar clusters \citep{Bruhweileretal2010}. At later stages of evolution a low heating efficiency may be physically justified by assuming mass loading of the matter left over from star formation, as in \citet{Wunschetal2011}, or an oversolar metallicity of the SN ejecta what enhances the cooling rate, as in \citet{TenorioTagleetal2005}. More recently, a low heating efficiency has been shown to also arise from the consideration of a continuous presence of dust within the cluster volume, dust produced within the ejecta of the multiple core-collapsed SN expected in young clusters \citep[see][]{TenorioTagleetal2013}. In this case, we keep the values of $L_i$, $L_n$ and $Q_0$ equal to those predicted by the Starburst99 synthetic model for a $10^6$\Msol \, cluster, but instead of using $L_{mech}=10^{40}$~erg s$^{-1}$, as in our models HDSa - HDSc, we use an order of magnitude smaller mechanical luminosity: $L_{mech} = 10^{39}$~erg s$^{-1}$. The transition to the momentum dominated regime in this case occurs at $\approx 0.84$~Myr. The relative thickness of the ionized shell is much larger than that in model HDS as the size of the shell is about two times smaller and thus the flux of the ionizing radiation is about four times larger than in model HDS (compare the left-hand and right-hand panels in Figure \ref{fig:4}). This leads to the largest calculated enhancement in the shell density (and thus thermal pressure) relative to that at the inner edge of the shell which is: $\sim 6.41$ at $t=1$~Myr, $\sim 7.26$ at $3.3$~Myr and $\sim 3.47$ at $5$~Myr. These results imply that radiation pressure must be taken into consideration in calculations with low heating efficiency and that \citet{Weaveretal1977} model (equations \ref{eq2a}-\ref{eq2b} and \ref{eq13a}-\ref{eq13b}) must be corrected in this case. The radiation pressure may also contribute to the shell dynamics at very early stages (before 3~Myr) of the wind-blown bubbles evolution (see also Figure 3 in \citetalias{SilichTenorioTagle2013}). Similar results were obtained for the less massive ($10^5\Msol$) clusters. In this case the maximum enhancement of density is $\sim 1.43$ in the standard (HDS) case and $\sim 4.68$ in the low heating efficiency (HDE) model, respectively. The time evolution of the thermal pressure excess, $P_{edge}/P_s$, where $P_{edge}$ and $P_s$ are the values of the thermal pressure behind the leading shock and at the inner edges of the wind-driven shell, is shown in Figure \ref{fig:5}. In the high density models (dashed and dash-dotted lines) this ratio decreases first as the flux of ionizing energy at the inner edge of the shell drops faster (as $R_s^{-2}$) than thermal pressure in the shocked wind region which drops as $R_s^{-4/3}$ (see equation \ref{eq2b}). It then grows to a larger value when the hydrodynamic regime changes from the energy to a momentum-dominated expansion and the wind pressure at the inner edge of the shell drops abruptly. After this time both, the flux of radiation energy and the wind ram pressure at the inner edge of the shell drop as $R_s^{-2}$. The $P_{edge}/P_s$ ratio then grows slowly as the number of non-ionizing photons absorbed by the outer neutral shell increases with time. The slow increase of the $P_{edge}/P_s$ ratio continues until the number of ionizing photons begins to drop after the first supernova explosion at 3.3~Myr when the $P_{edge}$ over $P_s$ ratio reaches 1.67 ($\log{P_{edge} / P_s} \approx 0.22$) in the case of model HDSb and 7.26 ($\log{P_{edge} / P_s} \approx 0.86$) in the case of model HDEb. In the low density cases (solid and dotted lines) the swept-up shell is not able to absorb all ionizing photons until it grows thick enough and therefore the number of ionizing photons trapped inside the completely ionized shell grows continuously until the first supernova explosion at 3.3~Myr. This compensates the $R_s^{-2}$ drop of the ionizing energy flux and leads to a continuously growing $P_{edge}/P_s$ ratio at this stage. However, in the standard (solid line) case and leaky (dotted line) bubble model this ratio remains always smaller than $\sim 1.7$. In the low density models LDS and LDL it is even smaller (less than 1.2) and is below the upper limit obtained in \citetalias{SilichTenorioTagle2013}. This is because in the low density cases wind-driven shells absorb only a fraction of the star cluster bolometric luminosity. The fraction of the star cluster bolometric luminosity trapped within a shell as a function of time in models LDS, LDL, HDS and HDE is shown in Figure \ref{fig:6} by solid, dotted, dashed and dash-dotted lines, respectively. Note that dashed and dash-dotted lines overlap rapidly as in the high density calculations expanding shells absorb all available (ionizing and non ionizing) photons at the very beginning of their time evolution (at $t << 1$~Myr). However, even in this case the shell remains optically thin to the IR photons re-emitted by dust grains, as shown in Figure \ref{fig:7}. Here we adopted for the dust opacity $\kappa_d = 2.3$~cm$^2$ g$^{-1}$ \citep[see Table 1 in][]{Novaketal2012} and calculated the optical depth for the IR radiation as $\tau_{IR} = \kappa_d \Sigma_s$, where the column density of the shell, $\Sigma_s$, is $\Sigma_s = \rho_{ISM} R_s / 3$. The amplification of radiation pressure by the multiple re-emitted IR photons which is $\sim \tau_{IR} L_{bol} / c$ \citep[see][]{Hopkinsetal2011,KrumholzThomson2012} thus remains less than unity. In all our calculations, the amplification factor never exceeds 2, even if one uses a larger dust opacity, $\kappa_d = 5$~cm$^2$ g$^{-1}$ adopted by \citet{Hopkinsetal2011}. This implies that the star cluster wind-driven shells expand in the radiation momentum rather than in the radiation energy dominated regime \citep[see][for the detailed discussion of the two limiting cases]{Falletal2010,KrumholzThomson2012}. \begin{figure*}[ht] \plotone{f5.eps} \caption{The $P_{edge}/P_s$ ratio time evolution. The solid, dotted, dashed and dash-dotted lines display the logarithm of the $P_{edge}$ over $P_s$ ratio, $\log{P_{edge}/P_s}$, at different times $t$ in the case of models LDS, LDL, HDS and HDE, respectively.} \label{fig:5} \end{figure*} \begin{figure*}[htp] \plotone{f6.eps} \caption{Fraction of the star cluster bolometric luminosity trapped within the shell as a function of time. The solid, dotted, dashed and dash-dotted lines display the $L_{abs}$ over $L_{bol}$ ratio at different evolutionary times $t$ for models LDS, LDL, HDS and HDE, respectively. Note that dashed and dash-dotted lines overlap into a single horizontal line $L_{abs} / L_{bol} = 1$ at the earliest stages of the shell evolution.} \label{fig:6} \end{figure*} We also computed how radiation pressure affects the density and thermal pressure distribution in the case when the exciting cluster is embedded into a low ($n_{ISM} = 1$~cm$^{-3}$) density ISM and has a low heating efficiency and in the case of a leaky shell moving into a high ($n_{ISM} = 1000$~cm$^{-3}$) density medium. We found a little difference between these calculations and models LDL and HDS, respectively. For example, the enhancement of density from the inner to the outer edge of the shell in the low density calculations with a 10\% heating efficiency is about 1.13, 1.2 and 1.11 at 1~Myr, 3.3~Myr and 5~Myr, whereas in the leaky bubble model LDL it is $\sim 1.1$, $\sim 1.19$ and $\sim 1.12$, respectively. In the case when a leaky shell expands into a high density medium, the enhancement of density is : $\sim 1.61$ at 1~Myr, $\sim 1.67$ at 3.3~Myr and $\sim 1.25$ at 5~Myr, whereas in model HDS it is $\sim 1.14$, $\sim 1.67$ and $\sim 1.25$, respectively, and thus the only difference between the last two models is that the transition from energy to momentum dominated regimes occurs at different times. Therefore we do not present the detailed description of these calculations in our further discussion. \begin{figure*}[htp] \plotone{f7.eps} \caption{The star cluster wind-driven shell optical depth for the IR radiation as a function of time. The solid, dotted, dashed and dash-dotted lines show $\tau_d$ for models LDS, LDL, HDS and HDE, respectively.} \label{fig:7} \end{figure*} \subsection{Comparison to other models and observations} Having the exciting cluster parameters and the distribution of the ionized gas density in the surrounding shell, one can obtain the model predicted values for diagnostic parameters often used in observations and compare them to the typically observed ones. In this section we first calculate the values of the ionization parameter and then put our results onto a diagnostic diagram proposed by \citet{YehMatzner2012} which allows one to conclude if radiation or the wind dynamical pressure dominates the dynamics of the ionized gas around young stellar clusters. The ionization parameter $U$ is defined as the flux of ionizing photons per hydrogen atom. It is directly related to the state of ionization and to the radiation pressure over gas thermal pressure ratio and is usually calculated at the inner edge of the ionized medium \citep[e.g.][]{Dopitaetal2005}: \begin{eqnarray} \label{eq:U1} U=\frac{Q_{0}}{4\pi n R_{s}^2 c} = \frac{\mu_i}{\mu_a}\frac{k T_{i}}{\langle h\nu\rangle_i}\frac{P_{rad}}{P_{HII}} . \end{eqnarray} The ionization parameter may be measured observationally from the emission line ratios \citep[e.g.][and references therein]{RigbyRieke2004, Snijdersetal2007,YehMatzner2012} and thus is a powerful tool to measure the relative significance of the radiation and gas thermal pressure around young stellar clusters. However, the number of ionizing photons varies radially within HII regions and therefore the measured values of $U$ are weighted by the density distribution in the ionized nebula. This led \citet{YehMatzner2012} to propose as a relevant model parameter \begin{equation} \label{eq:U2} U_w = \displaystyle \frac{\int 4 \pi r^2 n^2 U(r) \mbox{d}r }{\int 4 \pi r^2 n^2 \mbox{d}r} , \end{equation} where the integrals are evaluated from the inner to the outer edge of the HII region. In our approach, we have neglected the presence of any neutral gas and dust able to deplete the radiation field in the free and hot shocked wind regions and thus assumed that all the photons produced by the star cluster are able to impact the shell. The integrals in equation \ref{eq:U2} thus were evaluated with the lower and upper limits $R_{s}$ and $R_{HII}$, respectively. Here we make use of our models to obtain the ionized gas density distribution within wind-driven shells expanding into different interstellar media and calculate the ionization parameter $U_w$ at different times $t$. The results of the calculations are presented in Figure \ref{fig:8}. One can note, that the time evolution of the ionization parameter $U_w$ in the wind-driven bubble model is complicated as it depends not only on the varying incident radiation, but also on the hydrodynamics of the wind-driven shell. In all cases the value of $U_w$ drops first as the wind-driven shell expands and the photon flux at the inner edge of the shell drops accordingly. In the standard case (LDS, solid line) the value of $U_w$ drops continuously but turns to decrease faster after the first supernova explosion as since that time the flux of incident photons per unit area drops not only because of the shell expansion, but also because of the reduced value of $Q_0$. In the high density model HDS (dashed line) the value of the ionization parameter increases by about an order of magnitude after the transition to the momentum-dominated regime as when the transition occurs, the wind pressure and the ionized gas density at the inner edge of the shell drop, what enhances the value of $U_w$ significantly (see equations \ref{eq:U1} and \ref{eq:U2}). The value of the ionization parameter then remains almost constant until the first supernova explodes at about 3.3~Myr as at this stage both, the flux of ionizing photons and the ram pressure of the wind at the inner edge of the shell drop as $R_s^{-2}$ and thus the radiation over the dynamical pressure ratio depends only on the $L_{bol} / L_{mech}$ ratio \citepalias[see][]{SilichTenorioTagle2013} which in our calculations does not change much at this stage. After 3.3~Myr the value of the ionization parameter drops as the number of massive stars and the number of available ionizing photons $Q_0$ decline rapidly. The behavior of $U_w$ in the leaky (model LDL, dotted line) and low heating efficiency (model HDE, dash-dotted line) cases is very similar to that in the high density case HDS. The only difference is that the transition to the momentum-dominated regime in these cases occurs at earlier times and the maximum values of the ionization parameter are larger than that in model HDS. One can also note that the ionization parameter reaches the maximum possible value, $log U_w \approx - 1.5$, in the low heating efficiency model HDL and that the model predicted values of the ionization parameter fall into the range of typical values found in local starburst galaxies: $-3 \le log U_w \le -1.5$, \citep[see Figure 10 in][]{RigbyRieke2004}. The larger values of the ionization parameter \citep[e.g.][]{Snijdersetal2007} either require a lower heating efficiency, as was also claimed in \citet{Dopitaetal2005}, or a more complicated physical model than a single ionized shell formed by a young stellar cluster \citep[see the discussion in][]{Snijdersetal2007}. Finally, we put our results onto a diagnostic diagram proposed by \citet{YehMatzner2012} in order to show where physically motivated models are located in this diagram. For example, their model with more than an order of magnitude increasing density (see Figure 7 in their paper), $L_i = 10^{42}$~erg s$^{-1}$, $\log{\Phi} = -1.09$ and $\log{\Omega} = -1.56$ corresponds, according to our calculations, to a very compact ($R_{HII}$ less than 3~pc) and very dense ($n_s$ is a few hundred particles per cm$^{3}$) shell at the age of 2~Myr what implies that the HII region is quasi-static and requires a very low star cluster heating efficiency and a large confining (thermal/turbulent) pressure in the ambient ISM \citep[see][]{Smithetal2006,Silichetal2007,Silichetal2009}. Two-dimensional parameter space introduced by \citet{YehMatzner2012} is related to the compactness of the HII region (parameter $\Psi$) and to the relative strength of different driving forces (parameter $\Omega$). Parameter $\Psi$ is defined as the $R_{HII} / R_{ch}$ ratio, where $R_{HII}$ is the radius of the ionization front (in our case this is the radius of the outer edge of the ionized shell) and $R_{ch}$ is the radius of a uniform density Str\"omgren sphere whose thermal pressure is equal to the maximum possible unattenuated radiation pressure at the edge of the HII region $P_{rad} = L_{bol} / 4 \pi c R^2_{st}$: \begin{equation} \label{eq:rch} R_{ch} = \frac{\beta_2 \mu^2_a L^2_{bol}}{12 \pi \mu^2_i (k T_i c)^2 Q_0} . \end{equation} Parameter $\Omega$ is related to the volume between the ionization front and the inner edge of the HII region and to the values of thermal pressure at its inner and outer edges: \begin{equation} \label{eq:omega1} \Omega = \frac{P_s R^3_s}{P_{edge} R^3_{edge} - P_s R^3_s} . \end{equation} We obtain parameter $\Omega$ by calculating the volume between the outer and the inner edge of the ionized shell and the values of thermal pressure $P_s$ and $P_{edge}$ even at earlier stages of models LDS and LDL when the ionized shell is still embedded into an extended diffuse HII region. As long as the ionized shell is thin, parameter $\Omega$ is: \begin{equation} \label{eq:omega2} \Omega \approx 4 \pi c R^2_s P_s / L_{bol} , \end{equation} and thus measures the wind dynamical over the radiation pressure ratio (the shell moves in the radiation-dominated regime if $\log{\Omega} < 0$ and in the wind-dominated regime if $\log{\Omega} > 0$). \begin{figure}[htp] \plotone{f8.eps} \caption{The ionization parameter time evolution. The solid, dotted, dashed and dash-dotted lines correspond to models LDS, LDL, HDS and HDE, respectively (see Table \ref{tab:2}). The horizontal lines display the range of typical values for the ionization parameter found in local starburst galaxies \citep[see][]{RigbyRieke2004}.} \label{fig:8} \end{figure} In all static models discussed in section \ref{sec:2} the parameter $\Omega$ is very small ($\log{\Omega}\sim-15$) what implies that radiation pressure controls the ionized gas distribution in all static configurations with low-pressure central cavities. In the wind-blown cases the parameter $\Psi$ is a function of time as both radii, $R_{HII}$ and $R_{ch}$, change with time. Therefore it is instructive to show first how parameter $\Omega$ changes with time. This is shown in Figure \ref{fig:9} , panel a. Panel b in this figure displays the evolutionary tracks of our models in the $\Omega - \Psi$ parameter space. The initial points for models LDS, LDL, HDS and HDE were calculated at the star cluster age of 0.13~Myr. The initial values of the normalization radius $R_{ch}$ then are: $\sim 72$~pc in model LDL and $\sim 70$~pc in models LDS, HDS and HDE, respectively. As both star cluster parameters, $L_{bol}$ and $Q_0$, change with time, the value of $R_{ch}$ also changes with time significantly and by 10~Myr reaches $\approx 720$~pc. In cases LDS and LDL parameter $\Omega$ grows continuously (see panel a, solid and dotted lines). In the high density cases parameter $\Omega$ drops drastically when the transition occurs to the momentum dominated regime, then slightly declines and increases again after the first supernova explosion as the number of the ionizing photons then drops rapidly. The strong time evolution of $R_{ch}$ leads to the intricate tracks of the ionized shells in the $\log{\Omega} - \log{\Psi}$ diagram (see panel b). In the low density models LDS and LDL the tracks go to the left and up because the normalization radius $R_{ch}$ grows with time faster than the radius of the shell and thus the ionization front radius $R_{HII}$. In the high density cases HDS and HDE the tracks are more intricate. They first go to the right, then drop down when the transition to the momentum dominated regime occurs, make a loop and finally go back to the left and up. Thus, in the low density cases the impact of radiation pressure on the shell dynamics is always negligible and declines with time. In the high density model HDS the contribution of radiation pressure to the shell dynamics becomes more significant when the shell makes a transition from the energy to the momentum dominated regime. However, in this case parameter $\log{\Omega}$ also remains positive and thus in all models with a 100\% heating efficiency the shells expand in the wind-dominated regime. Parameter $\log{\Omega}$ falls below a zero value only in the low heating efficiency case HDE. Thus, only in this case radiation pressure may dominate the shell dynamics. The radiation dominated phase lasts from the beginning of the momentum dominated regime at $\sim 0.85$~Myr till $\sim 7.36$~Myr (see panel a). This implies that radiation pressure may dominate the dynamics of the gas around young stellar clusters either at early stages of evolution (before $\sim 3$~Myr) or if the major fraction of the star cluster mechanical luminosity is dissipated or radiated away within the star cluster volume and thus the energy of the star cluster driven winds is significantly smaller than what star cluster synthetic models predict. However, even if this is the case, radiation pressure will dominate only if the exciting cluster is embedded into a high density ambient medium. \begin{figure}[htp] \plotone{f9.eps} \caption{Evolutionary tracks of the expanding ionized shells in the diagnostic parameter space. The evolution of the diagnostic parameter $\Omega$ (see text) is presented in panel a. Panel b displays the location of the expanding shell exposed to the radiation from the central cluster in the $\log{\Omega} - \log{\Psi}$ diagram at different times $t$. The solid, dotted, dashed and dash-dotted lines correspond to models LDS, LDL, HDS and HDE, respectively. The circles, diamonds and triangles mark the evolutionary times of 1 Myr, 3.3 Myr and 5 Myr, respectively.} \label{fig:9} \end{figure} | 14 | 3 | 1403.1620 |
1403 | 1403.3555_arXiv.txt | {} {We aim to examine the relative cross-calibration accuracy of the on-axis effective areas of the XMM-Newton EPIC pn and MOS instruments.} {Spectra from a sample of 46 bright, high-count, non-piled-up isolated on-axis point sources are stacked together, and model residuals are examined to characterize the EPIC MOS-to-pn inter-calibration. } {The MOS1-to-pn and MOS2-to-pn results are broadly very similar. The cameras show the closest agreement below 1\,keV, with MOS excesses over pn of 0-2\% (MOS1/pn) and 0-3\% (MOS2/pn). Above 3\,keV, the MOS/pn ratio is consistent with energy-independent (or only mildly increasing) excesses of 7-8\% (MOS1/pn) and 5-8\% (MOS2/pn). In addition, between 1-2\,keV there is a `silicon bump' $-$ an enhancement at a level of 2-4\% (MOS1/pn) and 3-5\% (MOS2/pn). Tests suggest that the methods employed here are stable and robust.} {The results presented here provide the most accurate cross-calibration of the effective areas of the XMM-Newton EPIC pn and MOS instruments to date. They suggest areas of further research where causes of the MOS-to-pn differences might be found, and allow the potential for corrections to and possible rectification of the EPIC cameras to be made in the future. } | XMM-Newton (Jansen \etal\ 2001), a cornerstone mission of ESA's Horizon 2000 science program, was designed as an X-ray observatory able to spectroscopically study cosmic X-ray sources with a very large collecting area in the 0.2$-$10\,keV band. This high throughput is achieved primarily through the use of 3 highly nested Wolter type {\rm I} imaging telescopes. One of the three co-aligned XMM-Newton X-ray telescopes has an unimpeded light path to the primary focus, where the European Photon Imaging Camera (EPIC) pn camera (Str\"{u}der \etal\ 2001) is positioned. The two other telescopes have EPIC-MOS cameras (Turner \etal\ 2001) at their primary foci, but receive only approximately half of the incoming radiation, the remainder being diffracted away by Reflection Grating Assemblies (RGAs) towards the secondary foci (where the Reflection Grating Spectrometers (RGS; den Herder \etal\ 2001) are situated). The effective area of the EPIC instruments is defined here as the product of the mirror effective area, the detector quantum efficiency and the filter transmission, and is an extremely important quantity to have accurately established. In detail, further complications can include: that the effective area for the MOSs includes the RGA transmission factors, that one cannot extract 100\% of the source counts, unless one uses unworkably large extraction regions (i.e. Point Spread Function [PSF] issues), that contamination of the mirror and/or detector may be present, that the full detector efficiency can include other effects in addition to the quantum efficiency, such as out-of-time events, and that the mirror effective area includes vignetting, which, though minimised on-axis, is still important. Furthermore, as the EPIC CCDs are sensitive to IR-UV light, a filter wheel provides a choice of optical blocking filter, including thin, medium and thick filters (plus open and closed). Usage of these filters alters the low-energy X-ray transmission and requires extra specific detailed calibration. Many attempts have been made to quantify more and more precisely the effective area of the EPIC instruments (and other instruments, both on XMM-Newton and on other X-ray observatories), and this has been one of the main drivers behind IACHEC\footnote{http://web.mit.edu/iachec/} $-$ the International Astronomical Consortium for High Energy Calibration, formed to provide standards for high-energy calibration and to study in detail the cross-calibration between different high-energy observatories. This work describes a new attempt to establish the relative cross-calibration accuracy of the on-axis effective areas of the XMM-Newton EPIC pn and MOS instruments, using a sample of bright, isolated point sources, selected from the 2XMM catalogue. The results provide the most accurate cross-calibration to date of the EPIC pn and MOS effective areas. The structure of the paper is as follows: Sec.~2 describes the sample selection and analysis. Sec.~3 describes the results obtained. In Sec.~4 we discuss these results and further tests that were made, and in Sec.~5 we present our conclusions. Unless otherwise stated, a reference to the term MOS1, MOS2 or pn indicates that particular `whole telescope' system. | \label{sec_conc} We have examined the accuracy of the relative cross-calibration of the on-axis effective areas of the XMM-Newton EPIC pn and MOS instruments. A sample of 46 bright, high-count, non-piled-up, isolated, on-axis point sources was selected from the 2XMM catalogue. After flare- and background-cleaning, and applying common GTI filtering, source and background spectra extracted from the 46 sources were stacked together, and the individual response files were averaged in an exposure-weighted manner. Spectral fitting was applied, and the MOS and pn model residuals were examined in order to characterize the EPIC MOS-to-pn inter-calibration. It was seen that the MOS1-to-pn and MOS2-to-pn results are broadly very similar, with the cameras showing the closest agreement below 1\,keV, with MOS excesses over pn of 0-2\% (MOS1/pn) and 0-3\% (MOS2/pn). Above 3\,keV, the MOS/pn ratio is consistent with an energy-independent (or only mildly increasing) ratio, with MOS excesses of 7-8\% (MOS1/pn) and 5-8\% (MOS2/pn). In addition to this, between 1-2\,keV there is a further excess $-$ a `silicon bump' $-$ at a level of 2-4\% (MOS1/pn) and 3-5\% (MOS2/pn). Tests reveal that the `stack \& fit' methods employed here appear to be stable and robust, and the results presented here provide the most accurate to date cross-calibration of the on-axis effective areas of the XMM-Newton EPIC pn and MOS instruments. Areas of research where possible causes of the MOS-to-pn mismatches might be found are suggested by the analysis, and we note the potential for future corrections to and possible rectification of the EPIC MOS and pn cameras to be made. | 14 | 3 | 1403.3555 |
1403 | 1403.1285_arXiv.txt | The design of a neutron source capable of producing 24 and 70 keV neutron beams with narrow energy spread is presented. The source exploits near-threshold kinematics of the \iso{7}{Li}(p,n)\iso{7}{Be} reaction while taking advantage of the interference `notches' found in the scattering cross-sections of iron. The design was implemented and characterized at the Center for Accelerator Mass Spectrometry at Lawrence Livermore National Laboratory. Alternative filters such as vanadium and manganese are also explored and the possibility of studying the response of different materials to low-energy nuclear recoils using the resultant neutron beams is discussed. | Characterizing the response of radiation detector media to low-energy $\mathcal{O}$(keV) recoiling atoms, often referred to in the literature as nuclear recoils, is necessary to accurately understand the sensitivity of radiation detectors to light weakly interacting massive particles (WIMPS) \cite{Gaitskell,Chepel} and coherent elastic neutrino-nucleus scattering (CENNS) \cite{Hagmann,AkimovCNNS,Freedman,Drukier,Barbeau2}. To produce nuclear recoils of known energy, several different types of experiments have been proposed; the use of monoenergetic neutron sources and tagging the scattered neutron \cite{Manzur,Gastler,PhysRevC.88.035806}, exploiting time of flight and neutron tagging with a pulsed neutron source \cite{Alexander}, end-point measurements using a monoenergetic neutron source \cite{Jones2,PhysRevLett.110.211101}, use of broad spectrum neutron sources and comparison with monte carlo simulations \cite{Sorensen}, and tagged resonant photo-nuclear scatter \cite{Joshi}. With the exception of the proposal to use resonant photo-nuclear scatter, these experimental designs have all been employed, however successful characterization of sub-keV nuclear recoils has been limited to several results in germanium \cite{Barbeau2,Jones,Jones2}. A quasi-monoenergetic $\mathcal{O}$(10 keV) neutron source that can be easily constructed at small proton accelerators would enable further characterization of low-energy nuclear recoils in candidate detector materials. More generally, such a source would be useful for characterizing the response of detector materials to $\mathcal{O}$(10 keV) neutrons. In this article we present the design of a neutron source capable of producing such a beam. The design employs the near-threshold kinematics of the \iso{7}{Li}(p,n)\iso{7}{Be} reaction to target resonance interference notches present in the neutron scattering cross-section of certain isotopes. The use of resonance interference notches as neutron filters, only transmitting neutrons within a narrow energy range, has been successfully demonstrated for many years using nuclear reactors \cite{Barbeau,RussianFilter}, however the availability of research reactors instrumented and available for this type of work is limited. Using a nuclear reaction as the source of neutrons allows production of neutron beams with narrow energy spread at proton accelerator beam-lines capable of producing 2 MeV beams. A prototype neutron source was constructed at the target station of the microprobe beam line at the Center for Accelerator Mass Spectrometry (CAMS) at Lawrence Livermore National Laboratory (LLNL) \cite{uprobe}. In Sec.~\ref{sec:nearthreshold} we discuss the characteristics of near-threshold \iso{7}{Li}(p,n)\iso{7}{Be}. In Sec.~\ref{sec:filtering} we discuss the use of interference notches in iron, vanadium, or manganese as neutron filters. The results from characterization of the neutron source using an iron filter are described in Sec.~\ref{sec:Validation} and a discussion of possible low-energy nuclear recoils measurements that may be performed with such a neutron source is included in Sec.~\ref{sec:Target}. | The near-threshold kinematics of the \iso{7}{Li}(p,n)\iso{7}{Be} reaction combined with the neutron transmission properties of materials such as iron, vanadium, and manganese provide the ability to produce neutron beams with narrow energy spreads using a small proton accelerator. We have designed such a source, and demonstrated production of 24 and 70 keV neutron beams using an iron filter. This neutron source may be useful for measuring the response of relevant detector materials to $\mathcal{O}$(10 keV) neutrons. One specific application being the study of detector response to low energy nuclear recoils. Measurements of this type can provide information about the energy loss mechanisms of low-energy nuclear recoils, the recombination effects when electric fields are present within the targets, and the sensitivity of different detector media. Additionally, such characterization would enable accurate calculation of the sensitivity of different detector media to CENNS of reactor anti-neutrinos. The authors would like to thank Vincent Meot for production of the Li targets, Sergey Kucheyev for Rutherford Backscatter measurements of the lithium targets, Jason Burke for his help with the experimental effort, and Tom Brown for his assistance at CAMS. T.H.~Joshi would like to acknowledge the funding of the Lawrence Scholars Program at LLNL and the Department of Homeland Security. A portion of M. Foxe's research was performed under the Nuclear Forensics Graduate Fellowship Program, which is sponsored by the U.S. Department of Homeland Security, Domestic Nuclear Detection Office and the U.S. Department of Defense, Defense Threat Reduction Agency. We gratefully acknowledge the LDRD program (LDRD 13-FS-005) at LLNL. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. LLNL-JRNL-651154% | 14 | 3 | 1403.1285 |
1403 | 1403.7189_arXiv.txt | \pagenumbering{arabic} During the last few years we witnessed several radically different trends in the development of inflationary cosmology. Prior to the Planck data release \cite{ade}, there were rumors of the possible discovery of large non-Gaussianity, which was supposed to rule out 99\% of all existing inflationary models. Many people worked on the remaining 1\% of the models, which where rather exotic and complicated. The Planck data revealed that the $f^{\rm local}_{\rm NL}$ is as small as one could expect from the simplest inflationary models, so we were able to return to the investigation of more regular versions of inflationary theory. However, the results by Planck and other experiments suggested that the amplitude of tensor modes is very small, $r \lesssim 0.1$. Consequently, attention was attracted to the models predicting very small values of $r$, such as the Starobinsky model, new inflation, Higgs inflation, and many versions of string theory inflation predicting $r \ll 0.01$. The simplest versions of the chaotic inflation scenario, such as the model with a quadratic potential ${m^{2}\over 2} \phi^{2}$ \cite{chaotic} were disfavored. Now, in a surprising twist of fortune, the chaotic inflation models such as ${m^{2}\over 2} \phi^{2}$ are at the center of attention, but all models predicting small values of $r$ are strongly disfavored by the recent BICEP2 data, which found B-modes and concluded that $\ensuremath{r = 0.2^{+ 0.07}_{- 0.05}}$, \cite{bicep}. In particular, according to \cite{bicep}, the Starobinsky model \cite{Starobinsky:1980te,Starobinsky:1983zz}, predicting $r \sim 0.004$, is disfavored at a level greater than $5\sigma$. It is too early to discard models with small $r$ which have been popular since the latest Planck data release, especially since there is a broad class of theories continuously interpolating between the models with $r < 0.01$ and the models with $r \gtrsim 0.2$ \cite{Kallosh:2013tua,Kallosh:2013yoa}. Also, some of the models predicting $r < 0.01$ can be modified in a way making them consistent with the BICEP2 data. In a recent paper \cite{Ferrara:2014ima} it was argued that the supersymmetric generalization of the theory $R+ R^{2}$ developed by Cecotti back in 1987 \cite{Cecotti:1987sa} may allow two different inflationary regimes. One of them, driven by the real part of the scalar field $T$ present in this model, coincides with Starobinsky inflation, predicting $r \sim 0.004$, whereas another one, driven by the imaginary part of the field $T$, describes chaotic inflation with the quadratic potential \cite{chaotic}, predicting $r \sim 0.15$. Of course, the possibility of such a regime does not make the original Starobinsky model consistent with the BICEP2 results, but nevertheless it would be very interesting if its supersymmetric generalization, containing 3 extra scalar degrees of freedom as compared to the original Starobinsky model, were able to describe an inflationary regime providing a good match to the recent BICEP2 data. In this paper we will analyze this issue and show that there is no inflationary regime driven by the imaginary part of the field $T$ because large field ${\rm Im} T$ destabilizes the real part of the field $T$ in a way to be described shortly. It is possible to solve this problem by stabilizing the real part of the field $T$, but this requires a strong modification of the model of \cite{Cecotti:1987sa}, after which it ceases to have any relation to the original Starobinsky model $R+R^{2}$, as well as to pure higher derivative supergravity. | A unique supersymmetric model with higher curvature (up to 4-derivative terms) without matter was constructed by Cecotti in \cite{Cecotti:1987sa}. It is dual to a standard 2-derivative supergravity interacting with two chiral matter multiplets. This model provides a supersymmetric generalization of the Starobinsky model \cite{Starobinsky:1983zz}, when the imaginary part of the modulus $T$ vanishes and the real part of $T$ evolves \cite{Kallosh:2013lkr}. However this regime produces very low amplitude of tensor modes, which is strongly disfavored by BICEP2. It was argued in \cite{Ferrara:2014ima} that if one studies an opposite regime, when the imaginary part of $T$ evolves and the real part of $T$ vanishes, the same model \cite{Cecotti:1987sa} leads to realization of the simplest chaotic inflation scenario \cite{chaotic} with predictions matching the BICEP2 results. This would be a very attractive feature of the model \cite{Cecotti:1987sa}: It would be able to describe two radically different inflationary regimes, corresponding to two simplest models of inflation, \cite{chaotic} and \cite{Starobinsky:1983zz}. However, we have shown here that the general regime where both the real and imaginary parts of $T$ are allowed to evolve leads to the same predictions as the usual Starobinsky model. If the BICEP2 result and their interpretation in \cite{bicep} are valid, one concludes that the higher derivative pure curvature supergravity \cite{Cecotti:1987sa} does not describe the early universe inflation. Some matter multiplets have to be present, even in models with higher curvatures, as argued in \cite{CK}, where the relevant chaotic inflation models supporting inflation with high level of gravity waves were studied both in the standard 2-derivative supergravity as well as when higher derivatives terms are present. This does not mean that the model \cite{Cecotti:1987sa} cannot be generalized in such a way as to describe chaotic inflation with a quadratic or nearly quadratic potential. Indeed one can do so e.g. by modifying the \K\ potential of the theory. For example, one can strongly stabilize the real part of the field $T$ by adding to the \K\ potential a term such as $S\bar S (T+\bar T)$ or $S\bar S (T+\bar T)^2$ under the logarithm. We checked that in this case the real part of the field $T$ becomes strongly stabilized at the minimum of its potential, and chaotic inflation driven by the imaginary part of the field $T$ becomes possible. The potential along the inflationary trajectory will be approximately quadratic. However, strong stabilization of the real part of the field $T$ is possible only at the expense of a dramatic modification of the potential. As a result, the stabilized version of the model \cite{Cecotti:1987sa} entirely loses its original relation to the theory $R +R^2$ and the Starobinsky model. This conclusion is fully consistent with the recent results obtained in \cite{CK}. \ \subsubsection* | 14 | 3 | 1403.7189 |
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1403 | 1403.0626_arXiv.txt | It has recently been proposed that the dwarf spheroidal galaxies located in the Local Group disks of satellites (DoSs) may be tidal dwarf galaxies (TDGs) born in a major merger at least 5 Gyr ago. Whether TDGs can live that long is still poorly constrained by observations. As part of deep optical and \HI\ surveys with the CFHT MegaCam camera and Westerbork Synthesis Radio Telescope made within the ATLAS$^{\rm 3D}$ project, and follow-up spectroscopic observations with the Gemini-North telescope, we have discovered old TDG candidates around several early-type galaxies. At least one of them has an oxygen abundance close to solar, as expected for a tidal origin. This confirmed pre-enriched object is located within the gigantic, but very low surface brightness, tidal tail that emanates from the elliptical galaxy, NGC~5557. An age of 4 Gyr estimated from its SED fitting makes it the oldest securely identified TDG ever found so far. We investigated the structural and gaseous properties of the TDG and of a companion located in the same collisional debris, and thus most likely of tidal origin as well. Despite several Gyr of evolution close to their parent galaxies, they kept a large gas reservoir. Their central surface brightness is low and their effective radius much larger than that of typical dwarf galaxies of the same mass. This possibly provides us with criteria to identify tidal objects which can be more easily checked than the traditional ones requiring deep spectroscopic observations. In view of the above, we discuss the survival time of TDGs and question the tidal origin of the DoSs. | The discovery that a large fraction of Local Group (LG) dwarf galaxies are located within narrow planar structures, the so-called Disk of Satellites (DoSs), first speculated by \cite{Lynden-Bell76}, and confirmed through a number of deep surveys, raised the question of their origin \citep{Metz07,Ibata13}. Whether conventional $\Lambda$CDM cosmology can produce or not such DoSs is actively debated \citep{Libeskind11,Pawlowski12,Bellazzini13}. Alternatively, the presence of DoSs might simply be accounted for if all dwarfs were formed simultaneously within a single parent structure, e.g. the collisional debris of a merger \citep{Hammer13}. Objects born with that process are known as tidal dwarf galaxies (TDGs). The importance of TDGs among the dwarf population is rather controversial. On the one hand, the idealized numerical simulations of galaxy-galaxy collisions made by \cite{Bournaud06} suggest that only fine-tuned orbital parameters, mass ratio and initial gas content are needed for a merger to produce long-lived TDGs. \cite{Bournaud06} estimate that, at most, ten percent of dwarfs are of tidal origin. On the other hand, according to other numerical models \citep{Dabringhausen13} and an extrapolation at high redshift of the TDG production rate \citep[e.g.][]{Okazaki00}, the majority of nearby dwarfs should be of tidal origin. The actual number of TDGs in the Universe is poorly constrained by observations. All TDGs so far unambiguously identified and studied in detail are found in on--going or very recent mergers: they are still linked to their parents by an umbilical cord -- the tidal tail in which they were born --, are extremely gas-rich compared to other dwarfs and most likely have just become gravitationally bound \citep[see review by][]{Duc12}. Among the TDG candidates identified so far with \Ha\ or UV surveys \citep[e.g.][]{Weilbacher00,Mendes01,Neff05,Hancock09,Smith10,Kaviraj12,Miralles-Caballero12}, a large fraction are certainly gravitationally unbound star-forming knots that will quickly dissolve, or young compact star clusters that might evolve into globular clusters. In such conditions, estimates of the TDG fraction among regular galaxies substantially vary from one study to the other. This fraction may also depend on the large-scale environment. \cite{Kaviraj12} estimated it to 6~\% in clusters, \cite{Sweet14} to 16~\% in groups, whereas \cite{Hunsberger96} claimed that it could be as high as 50~\% in compact groups. How TDGs evolve and for how long they survive is largely uncertain. Objects that are not kicked out from their parents are subject to dynamical friction, the gradual loss of orbital energy plunging them into the host system again, to destructive tidal forces generated by the deep gravitational potential of the host galaxies \citep{Mayer01,Fleck03}, or even to the destabilizing effect of ram pressure \citep{Smith13}. The scenarios leading to a tidal origin for the MW and M31 satellites assume a very old merger \citep[5--9~Gyr,][]{Hammer13}. Can TDGs survive that long, and after several Gyr of evolution resemble present day Local Group dSphs, as proposed by \cite{Dabringhausen13}? Besides, the morphological and color evolution of TDGs will depend on their ability to continue forming stars, and thus to retain their original large gas reservoir. TDGs have a star-formation efficiency which is comparable to that of spiral galaxies \citep{Braine01}. Thus, compared to regular dwarfs, their gas depletion time scale is rather large, and star-formation activity may in principle continue for a Hubble time. However, the quenching mechanisms that apply to regular satellites, such as ram pressure \citep{Mayer06} should also apply to TDGs and even be reinforced \citep{Smith13}, presumably leading to a rapid reddening of their stellar populations. The observation of several Gyr old TDGs is thus most needed to investigate the various scenarios proposed so far for the long-term evolution of such objects. Unfortunately when the tidal features in which they were born gradually evaporate -- in typically 2 Gyr, according to numerical simulations \citep{Hibbard95,Michel-Dansac10} --, galaxies of tidal origin become more difficult to distinguish from classical ones. In principle, clear distinguishing criteria exist: a lack of dark matter \footnote{The material forming TDGs emanate from the dark matter poor disk of spiral galaxies.}, and an unusually high metallicity for their mass \citep[e.g. ][]{Hunter00,Duc07,Sweet14}. In practice, such characteristics need to be checked with high-resolution spectroscopic data, which are expensive in terms of telescope time. This is in particular the case for the low-surface-brightness dwarfs in which star-formation has already been quenched. The oldest TDGs disclosed so far based on their excess of metals and deficit of dark matter are located in the vicinity of advanced but still relatively recent mergers: e.g., NGC~7252 \citep{Belles14}, or highly perturbed early-type galaxies, like NGC~4694 in the Virgo Cluster \citep{Duc07}. These TDGs may be 0.5-2 Gyr old. In this paper we detail the properties of a sample of dwarf galaxies which are satellites of early-type galaxies (ETGs). They were initially found during a systematic deep imaging survey of ETGs with the Canada-France-Hawaii Telescope made as part of the ATLAS$^{\rm 3D}$ project \citep{Cappellari11}. Their location towards faint streams of stars, visible on CFHT MegaCam images, or neutral hydrogen clouds, imaged by the Westerbork Synthesis Radio Telescope \citep[WSRT,][]{Serra12}, also as part of ATLAS$^{\rm 3D}$, made them putative TDG candidates \citep{Duc11}. Their association with fully relaxed galaxies, classified as lenticulars or ellipticals, rather than on-going mergers, ensured they are at least 2~Gyr old. The objects were followed up with the spectrograph GMOS installed on the Gemini-North telescope. The spectroscopic observations are presented in Section~\ref{spec}. Results on the metallicity and light profiles of the TDG candidates are given in Section~\ref{res}. Finally, Section~\ref{dis} discusses the implications of these observations on the long-term evolution of TDGs and proposes new diagnostics of a tidal origin that are based on scaling relations. They are applied to the Local Group dwarfs. \begin{figure*} % \includegraphics[width=\textwidth]{sample.pdf} \caption{ {\it Central panels:} composite g'+r' or g'+r'+i' MegaCam images of the early-type galaxies hosting the dwarf galaxies studied here. The faintest low surface brightness features are shown as inverted grey maps for better contrast. The ETG satellites for which a spectroscopic follow-up was carried out are indicated with the squares. {\it Top and bottom panels:} MegaCam g'--band surface brightness maps of the pre-selected satellites. The field of view of each panel is 3 $\times$ 3 arcmin. Each bar corresponds to a physical length of 10~kpc. Greyscale levels range between 22 and 28.5 mag.arcsec$^{-2}$. \HI\ contours from the WSRT observations are superimposed. Levels correspond to 0.7, 1.4 and 2.1 $\times$ 10$^{20}$ cm$^{-2}$.} \label{ETGsample} \end{figure*} | We have obtained with Gemini-North optical long-slit spectra of a sample of 7 dwarf galaxies in the vicinity of 5 early-type galaxies (ETGs) selected from the ATLAS$^{\rm 3D}$ survey. Deep optical CFHT/MegaCam images and WSRT radio observations had previously detected around the selected ETGs gaseous and/or stellar streams that made the host galaxies likely old gas-rich mergers, and their dwarf satellites excellent tidal dwarf galaxy (TDGs) candidates. The spectroscopic observations were aimed at measuring the oxygen abundance of the ETG satellites, and investigate any deviation from the mass-metallicity relation that may indicate a tidal origin. We furthermore used the MegaCam images to determine the morphological properties of the dwarfs and their behavior with respect to standard scaling relations. We obtained the following results: \begin{itemize} \item One dwarf, referred as NGC~5557-E1, located in the vicinity of the massive elliptical, NGC~5557, has a gas-phase metallicity of about solar; its oxygen abundance is 0.6 dex above that typical of regular dwarf galaxies, or conversely its abundance corresponds to that of a galaxy ten times more massive. This dwarf, together with two fainter companion objects, E2 and E3 (for which no spectra could be extracted), lie along an extended, very low surface brightness tidal tail, most likely formed during a major merger that occurred at least 2 Gyr ago. A burst model fitting the spectral energy distribution of NGC~5557-E1 provides an age for the dwarf of about 4 Gyr, consistent with the age estimate of the merger at the origin of NGC~5557. Object E1, plus most likely its companions located in the same tidal structure, in particular the apparently relaxed object E2, would thus be the oldest confirmed tidal dwarf galaxies so far identified. \item Like regular dwarf ellipticals/spheroidals, NGC~5557-E1/E2 are well fitted by exponential light profiles. However, they have an unusually large effective radius, and low central surface brightness for their mass. This may be an intrinsic characteristic of old TDGs. Besides, contrary to typical satellites of massive galaxies, NGC~5557-E1/E2 managed to retain a large gas reservoir despite several Gyr of evolution and interaction with their parent galaxy. They may preserve it for several additional Gyr, given their very low current star-formation rate, as measured from the UV and/or \Ha\ luminosity, unless stripping mechanisms become important. \item Among the four other ETG satellites in our survey, three that are more massive than NGC~5557-E1/E2 tend to also have rather low central surface brightness and large effective radius. However unlike the confirmed TDGs, they are not clear outliers of the luminosity-metallicity relation. In fact, the method to identify TDGs using deviations from scaling relations only works well for low-mass objects. Future systematic surveys of tidal dwarfs should thus rather focus on the least massive ones, identified in deep images. They may tell whether the large effective radius found for the old TDGs NGC~5557-E1/E2, but also for young TDGs, is a durable, intrinsic characteristic of a tidal origin. If this is the case, it is then unlikely that the dwarfs in the disk of satellites around our Milky Way and Andromeda are old TDGs made in gas--rich major mergers. \end{itemize} | 14 | 3 | 1403.0626 |
1403 | 1403.0410_arXiv.txt | We show that the recently proposed multi-natural inflation can be realized within the framework of 4D ${\cal N}=1$ supergravity. The inflaton potential mainly consists of two sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase. For a sub-Planckian decay constant, the multi-natural inflation model is reduced to axion hilltop inflation. We show that, taking into account the effect of the relative phase, the spectral index can be increased to give a better fit to the Planck results, with respect to the hilltop quartic inflation. We also consider a possible UV completion based on a string-inspired model. Interestingly, the Hubble parameter during inflation is necessarily smaller than the gravitino mass, avoiding possible moduli destabilization. Reheating processes as well as non-thermal leptogenesis are also discussed. | The recent observations of the cosmic microwave background (CMB) by the Planck satellite \cite{Ade:2013uln} showed that $\Lambda$CDM cosmology is consistent with the data and fluctuations in the cosmic microwave background (CMB) can be explained by single-field inflation \cite{Guth:1980zm,Linde:1981mu}, which solves the fine-tuning problems in the early universe. The spectral index $n_s$ and the tensor-to-scalar ratio $r$ are tightly constrained by the Planck data combined with other CMB observations \cite{Ade:2013uln}: \bea \label{planck} n_s &=& 0.9603 \pm 0.0073, \\ r &<& 0.11 ~(95\%~{\rm CL}). \eea The index $n_s$ is determined by the shape of the inflaton potential, whereas the ratio $r$ is done by the energy scale of the potential:\footnote{After submission of this paper, the BICEP2 collaboration announced the detection of the primordial B-mode polarization, which can be explained by $r = 0.20^{+0.07}_{-0.05}$~\cite{Ade:2014xna}. See note added at the end of this paper.} \bea H_{\rm inf} \simeq 8.5 \times 10^{13}~{\rm GeV} \left( \frac{r}{0.11} \right)^{1/2}. \label{stratio} \eea Here, $H_{\rm inf}$ is the Hubble scale during inflation. To construct a viable inflation model, the inflaton potential should be under good control so as not to break the slow-roll condition and to suppress the inflation scale compared with the the Planck scale. There have been many attempts to accomplish this. One way is to introduce a certain symmetry which keeps the inflaton potential flat. See Refs.~\cite{Linde:1983gd,Kawasaki:2000yn,Kawasaki:2000ws, Kallosh:2010ug,Kallosh:2010xz,Takahashi:2010ky,Nakayama:2010kt,Harigaya:2012pg,Silverstein:2008sg,McAllister:2008hb,Kaloper:2008fb,Croon:2013ana, Nakayama:2013jka,Ellis:2013xoa,Kallosh:2013pby} for various chaotic inflation models along this line. In this sense, an axion is a good candidate for the inflaton due to the approximate shift symmetry \bea \phi \to \phi + {\rm const}. , \eea which controls its potential structure and suppresses the scale of inflation to be consistent with observation. Here, $\phi$ is an axion. So, it is possible to consider a natural inflation model \cite{Freese:1990ni,Adams:1993ni} with an axion potential $V(\phi)$ given by: \bea V(\phi) = \Lambda^4 \bigg[1 - \cos\left(\frac{\phi}{f}\right) \bigg] . \eea In this model, the shift symmetry is broken non-perturbatively by the dynamical scale $\Lambda$ much smaller than the Planck scale. However, the decay constant $f$ is required to be larger than the Planck scale\footnote{ See \cite{Kim:2004rp} for realizing a large decay constant effectively, \cite{Mohanty:2008ab,Germani:2010hd} for other ways to relax the bound on the decay constant, and \cite{Kaplan:2003aj,BlancoPillado:2004ns,Dimopoulos:2005ac,Silverstein:2008sg,McAllister:2008hb} for other models with axion(s). }, $f \gtrsim 5M_{\rm Pl}$ \cite{Ade:2013uln}, for the predicted $n_s$ and $r$ to be consistent with the observed values, where $M_{\rm Pl} \simeq 2.4 \times 10^{18}$GeV is the reduced Planck mass.\footnote{ Hereafter, we take the Planck unit of $M_{\rm Pl}=1$ for a simplicity, unless otherwise stated. } So, one might worry about the control of the correction $f/M_{\rm Pl}$ after all. Recently, two of the present authors (MC and FT) proposed an extension of natural inflation, called multi-natural inflation~\cite{Czerny:2014wza}, in which the inflaton potential mainly consists of two (or more) sinusoidal functions. Interestingly, multi-natural inflation is versatile enough to realize both large-field and small-field inflation. In the case of large-field inflation with super-Planckian decay constants, the predicted values of the spectral index as well as the tensor-to-scalar ratio can be closer to the center values of the Planck results, with respect to the original natural inflation. In the case of small-field inflation with sub-Planckian decay constants, we arrange those sinusoidal functions so that they conspire to make the inflaton potential sufficiently flat for slow-roll inflation. In a certain limit, this axion hilltop inflation is equivalent to hilltop quartic inflation \cite{Linde:1981mu}. The hilltop quartic inflation has been studied extensively so far, and it is known that, for the e-folding number $N_e \simeq 50$, its predicted spectral index tends to be too low to explain the Planck results [\ref{planck}]. There are various proposals for resolving this tension in the literature. The purpose of this paper is twofold. First, we will show that the predicted spectral index for the axion hilltop inflation can be increased with respect to the hilltop quartic inflation case by including a relative phase between two sinusoidal functions. This gives a better fit to the Planck data. Second, we consider a UV completion of multi-natural inflation within supergravity(SUGRA)/string theory. This is because a viable inflation model can be easily realized for large decay constants close to the GUT or Planck scale, and because the string theory offers many axions~through compactifications \cite{Svrcek:2006yi,Blumenhagen:2006ci,Arvanitaki:2009fg}, some of which could play an important role in inflation. Also, non-perturbative dynamics which explicitly break the axionic shift symmetry can be studied rigorously in a supersymmetric (SUSY) framework. The rest of this paper is organized as follows. In Sec.\ref{SecSUGRA} we build an axion hilltop inflation model with one axion multiplet in the context of SUGRA, taking into account SUSY breaking effects. In Sec.\ref{Secstring}, we consider a UV completion of multi-natural inflation in the string-inspired model, which is reduced to the model analyzed in Sec.\ref{SecSUGRA} in the low energy effective theory. The last section is devoted to discussion and conclusions. | \label{Secsum} We have studied multi-natural inflation~\cite{Czerny:2014wza} in SUGRA for a UV completion. In this model the inflaton potential mainly consists of two sinusoidal functions that are comparable in size, but have different periodicity. For sub-Planckian values of the decay constants, this model is reduced to the hilltop quartic inflation in a certain limit. It is known however that the predicted spectral index, $n_s \simeq 0.94$, for the e-folding number $N_e \simeq 50$ tends to be too low to explain the Placnk results. We have shown that, allowing a relative phase between the two sinusoidal functions, the spectral index can be increased to give a better fit to the Planck data based on the axion hilltop inflation in SUGRA. We have also considered a further UV completion based on a string-inspired framework, and have shown that the axion hilltop inflation model can be indeed obtained in the low energy limit. The axion hilltop inflation requires a rather flat potential near the (local) potential maximum. For realizing the flat-top potential, there should exist a relation between the ratio of the decay constants and the dynamical scale: $(f_1/f_2)^2 \approx A/B$. This in turn implies that in string theory there should be a relation between the world volume of D-branes where the non-perturbative effects occur and the number of such branes. It is also noted that because we have used supergravity, the gravitino mass is related to physical quantities. For successful inflation, the typical scale of the gravitno mass is $m_{3/2} \sim \GEV{13}$, whereas the soft mass is about one order of magnitude smaller, $m_{\rm soft} = \GEV{12}$, while the inflaton mass is $m_\phi \sim \GEV{11}$. Thus, the SUSY particles are not produced in the Universe after reheating. The dark matter candidates can be considered such as the QCD axion, axion-like particles, or sterile neutrinos, if they exist. In particular, a light dark matter is interesting in light of its longevity. The recently discovered X-ray line at $3.5$\,keV~\cite{Bulbul:2014sua,Boyarsky:2014jta} may be due to the decay of one of such light dark matter\footnote{See the recent works on explaining the $3.5$\,keV X-ray line by axions~\cite{Higaki:2014zua} or sterile neutrinos~\cite{Ishida:2014dlp}.}. It may be possible to explain the baryon asymmetry from the inflaton decay into right-handed neutrinos. \vspace{5mm} {\it Note added:} After the submission of our paper, the BICEP2 experiment found the primordial B-mode polarization~\cite{Ade:2014xna}, which suggests $r = 0.20^{+0.07}_{-0.05}$. Although we have focused on the hilltop inflation limit of the multi-natural inflation when we evaluate the spectral index and the tensor-to-scalar ratio, most of the discussion including the realization of the multi-natural inflation in supergravity and string-inspired set-up, the reheating, and leptogenesis is applicable to a more general multi-natural inflation. In particular, for such a large value of $r$, the inflaton mass will be of order $\GEV{13}$, leading to the reheating temperature close to $\GEV{9}$ (cf. \EQ{TR}). Therefore, thermal leptogenesis will be possible. See also the related papers on the multi-natural inflation~\cite{Czerny:2014qqa, Czerny:2014wua} that appeared after BICEP2. | 14 | 3 | 1403.0410 |
1403 | 1403.6416_arXiv.txt | The nearby group centered on its bright central galaxy NGC~1407 has been suggested to be an unusually dark system from previous kinematic studies. It is also known for hosting a bright galaxy, NGC~1400, with a large radial velocity (1200 km~s$^{-1}$) with respect to the group center. Previous {\sl ROSAT} X-ray observations revealed an extended region of enhanced surface brightness just eastward of NGC~1400. We investigate the NGC~1407/1400 complex with {\sl XMM-Newton} and {\sl Chandra} observations. We find that the temperature and metallicity of the enhanced region are different (cooler and more metal rich) than those of the surrounding group gas, but consistent with those of the ISM in NGC~1400. The relative velocity of NGC~1400 is large enough that much of its ISM could have been ram pressure stripped while plunging through the group atmosphere. We conclude that the enhanced region is likely to be hot gas stripped from the ISM of NGC~1400. We constrain the motion of NGC~1400 using the the pressure jump at its associated stagnation front and the total mass profile of the NGC~1407 group. We conclude that NGC~1400 is moving within $\sim30^{\circ}$ of the line-of-sight with Mach number $\mathcal{M}\lesssim3$. We do not detect any obvious shock features in this complex, perhaps due to the highly line-of-sight motion of NGC~1400. With an {\sl XMM-Newton} pointing on the relatively relaxed eastern side of NGC~1407, we derive a hydrostatic mass for this group of $\sim1\times 10^{13}$ $M_\odot$ within 100 kpc. The total mass extrapolated to the virial radius (681 kpc) is 3.8$\times 10^{13}$ $M_\odot$, which puts an upper limit of $\sim$300 $M_\odot/L_{B_\odot}$ on the mass-to-light ratio of this group. This suggests that the NGC~1407 group is {\sl not} an unusually dark group. | \smallskip The nearby group centered on the elliptical galaxy NGC~1407 is notable because it appears to contain a bright lenticular galaxy, NGC 1400, with a very large velocity (1200 km s$^{-1}$) relative to NGC~1407. This has led to suggestions that the NGC 1407 group is one of the darkest known galaxy systems (Gould 1993). This group belongs to the Eridanus supergroup, which contains three main groups: the NGC~1407 group, the NGC~1332 group and the Eridanus group (Brough et al.\ 2006). Among them the NGC~1407 group is the most dynamically and morphologically relaxed and NGC~1407 is the brightest galaxy in the supergroup. The NGC~1407 group has relatively relaxed X-ray morphology and has a cool core centered on NGC~1407 (Zhang et al.\ 2007). NGC~1407 is X-ray luminous ($L_X=8.6\times10^{40}$ erg s$^{-1}$ in 0.1--2.0 keV, within two optical effective radii; Su \& Irwin 2013), with evidence for recurrent radio outbursts (Giacintucci et al.\ 2012). The Eridanus supergroup may collapse into a massive cluster in the future, with NGC~1407 as its future brightest cluster galaxy (BCG). Hierarchical structure formation theory predicts an upper limit for the total $M/L$ of galaxy systems, assuming high mass systems are formed from low mass systems with similar stellar mass fractions (Kauffmann et al.\ 1999; Marinoni \& Hudson 2002). The observational discovery of galaxy groups and clusters with extremely small baryonic mass fractions may indicate a gap in our knowledge about the current structure formation paradigm (Balogh et al.\ 2008; Bower at al.\ 2006; Giodini et al.\ 2009; Lin et al.\ 2003). The NGC~1407 group is a possible example of such a system. Romanowsky et al.\ (2009) found a very low baryon mass fraction $f_b$ in the NGC 1407 group, after using globular cluster kinematics (within 60 kpc of NGC~1407) to measure the group mass; extrapolating their results to the virial radius, they found $M/L \sim800$ $M_\odot/L_{B_\odot}$ and $f_b \sim 0.004$, the latter being much lower than the cosmological value of $f_b=0.17$ (Hinshaw et al.\ 2009). Zhang et al.\ (2007) studied the hot gas of this group with {\sl Chandra} ACIS-S X-ray observations centered on NGC~1407, as well as {\sl ROSAT} observations extending out to 75 kpc from NGC~1407. Assuming hydrostatic equilibrium, they inferred a smaller value of $M/L=311\pm60$ $M_\odot/L_{B_\odot}$ within its virial radius. The large velocity difference places NGC~1400's group membership in doubt and casts more doubt on the total mass (hence, mass-to-light ratio) estimates for this group. Brough et al.\ (2006) studied the galaxy dynamics of this group and derived the total mass by both excluding and including NGC~1400 and five other galaxies, which yielded low and high $M/L$ estimates of 600 and 1200 $M_\odot/L_{B\odot}$, respectively. In estimating masses of galaxy groups, both X-ray techniques and dynamical probes have their drawbacks. X-ray techniques assuming hydrodynamic equilibrium may be affected by group gas being out of equilibrium, having significant non-thermal pressure support, and/or containing multi-phase gas. Dynamical analyses tend to lack the spatial extent of X-ray observations and require assumptions about velocity distributions. Despite the fact that there is no general consensus about the $M/L$ of the NGC~1407 group, all estimates to date are above the typical range for groups, which is $M/L_B \sim 60-300$ $M_\odot/L_{B_\odot}$ (Eke et al.\ 2006). In this paper, we reveal some thermal substructures in the gas associated with NGC~1400, which undermines the assumption of hydrostatic equilibrium for X-ray analyses. This motivated us to propose an {\sl XMM-Newton} pointing on the eastern side of the NGC~1407 group out to 100 kpc, where the thermal structure is relatively relaxed, in order to better estimate the total mass of this possibly dark system through hydrostatic X-ray techniques. We also analyzed the existing archival {\sl XMM-Newton} pointing on the western side of NGC~1407, which covers both NGC~1407 and NGC~1400. {\sl XMM-Newton} imaging reveals an extended region of enhanced surface brightness just east of NGC~1400 (Figure~\ref{fig:1407}), which was attributed to be a background object in the previous {\sl ROSAT} study (Zhang et al.\ 2007). We suspect that this enhanced region is hot gas stripped out of NGC~1400 due to its large relative velocity through the group. Furthermore, we found an apparently heated region between NGC~1407 and NGC~1400, potentially an indicator of an ongoing collision. An additional {\it XMM-Newton} pointing covering the eastern side of NGC~1407 provides us an azimuthally complete coverage. This helps us to diagnose whether the apparently heated region between NGC~1400 and NGC~1407 is indeed non-gravitational heating or simply a reflection of the gravitational well of the NGC~1407 group. To further unveil the dynamical state of this complex, we also acquired an additional {\sl Chandra} ACIS-S pointing covering NGC~1400 and the enhanced region, which allows us to infer the gas dynamics of the enhanced region. In this paper, we present these observations and discuss their implications. We assume $H_0 = 70$ km~s$^{-1}$ Mpc$^{-1}$, $\Omega_{\Lambda}=0.7$, and $\Omega_M=0.3$. The central dominant galaxy NGC 1407 resides at a luminosity distance of $D_L$ = 22.08 Mpc ($1^{\prime}$ = 6.5 kpc; NED\footnote{\url{http://ned.ipac.caltech.edu}}). Throughout this paper, all uncertainties are given at the $90\%$ confidence level unless otherwise stated. Observations and data reduction are described in \S2. We report our results in \S3 and describe our proposed scenario in \S4. We summarize our main conclusions in \S5. \bigskip \medskip | Here we consider a scenario where NGC~1400 is moving towards us through the atmosphere of the NGC~1407 group, with a velocity mostly along the line-of-sight and slightly westward, as illustrated in Figure~\ref{fig:tv}. The outer ISM of NGC~1400 has been stripped and trails behind, creating the region of enhanced surface brightness east of NGC~1400. \subsection{\sl The motion of NGC~1400 and the length of its stripped tail} NGC~1400 has a line-of-sight velocity of 1200 km~s$^{-1}$ relative to NGC~1407. The projected distance between NGC~1407 and NGC~1400 is 78 kpc (11.9$^{\prime}$). Here we try to place some rough limits on the total velocity of NGC~1400 relative to NGC~1407. The position of the enhanced region implies that NGC~1400 has a westward velocity component. We estimate the westward velocity of NGC~1400 through the pressure jump it has induced beyond the western leading edge. We follow the treatment of Vikhlinin et al.\ (2001) for the motion of a blunt body through intracluster gas: the pressure difference between a distant ``free stream" region and the stagnation point (where the local relative velocity is brought to zero at the body's leading edge) is related to the velocity (Mach number) in that direction (Landau \& Lifshitz 1987): \begin{equation} \frac{p_1}{p_2}=\left(1+\frac{\gamma-1}{2}\mathcal{M}_{\rm ap}^{2}\right)^{\frac{\gamma}{\gamma-1}} ~~~{\rm for}~ \mathcal{M}_{\rm ap} \le 1 ~{\rm (subsonic}); \end{equation} \begin{equation} \frac{p_1}{p_2}=\left(\frac{\gamma+1}{2}\right)^{\frac{\gamma+1}{\gamma-1}}\mathcal{M}_{\rm ap}^{2}\left(\gamma-\frac{\gamma-1}{2\mathcal{M}_{\rm ap}^2}\right)^{-\frac{1}{\gamma-1}} ~~~{\rm for}~ \mathcal{M}_{\rm ap} > 1 ~{\rm (supersonic)}; \end{equation} where the adiabatic index $\gamma = 5/3$. We were unfortunately unable to identify a clear leading edge, likely due to the highly line-of-sight motion of NGC~1400 and the tenuousness of the group gas west of NGC~1400. Instead, we obtained a constraint from the (factor of 3.4) jump in surface brightness in the {\sl Chandra} profile westward of NGC~1400 from 50$^{\prime\prime}$ to 100$^{\prime\prime}$, which likely spans a range of radii from just within the stagnation radius to the free stream region. We assume the density jump equals the square root of surface brightness jump (thus, a factor of 1.85). The temperature of the group gas at the stagnation point ($\sim$1 keV) is calculated from eq.~(4) for regions at the same radius from NGC~1407 as NGC~1400. We take the temperature of the enhanced region (0.8 keV) as the temperature of regions just inside the leading edge. The apparent pressure jump is thus 1.5, corresponding to an apparent Mach number of $\mathcal{M}_{\rm ap}=0.74$. The sound speed of the NGC~1407 group gas is $c_{\rm s}=({\gamma kT/\mu m_H})^{1/2}$ = 507 km~s$^{-1}$, where the group gas temperature $kT\approx1$ keV. The inferred tangential velocity is $v_{\rm tan}$ = $\mathcal{M}_{\rm ap} c_{\rm s}$ = $0.74\times 507$~km\,s$^{-1}$ = 375~km\,s$^{-1}$. This gives us a total velocity of 1257~km\,s$^{-1}$ ($\mathcal{M}\approx2.5$) for NGC~1400, in a direction $\theta = 20^{\circ}$ from the line-of-sight. However, unlike cases in Abell~3667 (Vikhlinin et al.\ 2001), NGC~1404 (Machacek et al.\ 2005), and Abell~194 (Bogdan et al.\ 2011), the motion of NGC~1400 seems highly line-of-sight, which makes it difficult to infer its tangential velocity through this method. We used the total mass profile of the NGC~1407 group (derived in \S3.3 and indicated by the green line in Figure~\ref{fig:mass}) to provide an additional constraint on the motion of NGC~1400. We first constrained the total velocity of NGC~1400 by assuming it resides at the same distance as NGC~1407, so their physical separation is the same as their projected distance. If NGC~1400 experienced free-fall from infinity to its current position, we deduced from the group mass profile that NGC~1400's total relative velocity would be 1500 km\,s$^{-1}$. Considering that NGC~1400 has a line-of-sight velocity $v_{\rm los}=1200$ km~s$^{-1}$ and its projected separation from NGC~1407 is only a lower limit to NGC~1400's distance from the group center, we infer that NGC~1400's velocity in the plane of sky is $<$ 900 km~s$^{-1}$ and $\vert \theta \vert < 36.9^{\circ}$. If we instead assume that NGC~1400 has no velocity component in the plane of sky ($\theta$ $=$ 0$^{\circ}$), its current velocity ($v= 1200$ km~s$^{-1}$) then requires that NGC~1400 resides at a distance 400 kpc closer (or farther) than NGC~1407. Given a possible velocity range of $1200-1500$ km s$^{-1}$, the Mach number $\mathcal{M}\equiv v/c_{\rm s}$ would be in the range of 2.4--3. Our previous estimate of the motion (Mach number) of NGC~1400, derived from the observed pressure jump at its leading edge, lies in this range. Since the strength of ram pressure stripping is proportional to the ambient gas density, significant stripping is most likely to occur near the group center, given the low average gas density of this group. Given the proximity of the stripped tail to NGC~1400, this implies that NGC~1400 likely resides near the group center, so its projected distance from NGC~1407 should be comparable to its physical separation. This leads us to prefer the higher total velocity estimates. If the surface brightness enhancement east of NGC~1400 is indeed the stripped tail of NGC~1400 (see \S3.1), the direction of NGC~1400's motion allows us to infer the tail length, assuming the tail is aligned with the current direction of NGC~1400's motion. The projected length of NGC~1400's tail (the projected northeast-southwest extent of the enhanced region) is $\sim25$ kpc. Since NGC~1400 is estimated to be moving at an angle $\theta\approx30^{\circ}$ from the line-of-sight, the actual tail length is $\sim50$ kpc. In numerical simulations of ram pressure stripping, typical lengths of stripped tails are $\sim40$ kpc (Roediger \& Bruggen 2008). Observationally, there is a large scatter in reported tail lengths (Sun et al.\ 2007b) and some can be as long as $\sim380$ kpc (M86 -- Randall et al.\ 2008). There are various factors that can affect the length (or morphology) of stripped tails, such as the velocity of the moving galaxy, the time scale of the stripping process, the relative emissivities of the tail and the ambient ICM, and projection effects (Ruszkowski et al.\ 2012). In summary, our preferred scenario is illustrated in Figure~\ref{fig:tv}, where NGC~1400 is moving through the atmosphere of the NGC~1407 group at an angle of $\sim30^{\circ}$ from the line-of-sight, with a total relative velocity of $\sim1400$ km~s$^{-1}$. \subsection{\sl The apparent absence of shock heating} Most merger shocks reported to date have been found in galaxy clusters (e.g.\ Abell~3376, Sarazin 2013), rather than in galaxy groups. Shocks found in groups are usually related instead to AGN feedback (HCG 62 -- Gitti et al.\ 2010). One exception is Abell~194, a poor cluster ($kT\sim2$ keV) observed to have a merger shock: its member galaxy NGC~541 has a velocity of 788 km~s$^{-1}$ with respect to the cluster center and has a reverse shock with $\mathcal{M}\approx0.9$ (derived from a discontinuity in its pressure profile; Bogdan et al.\ 2011). In the NGC~1407 group, NGC~1400 has a velocity of at least 1200 km~s$^{-1}$ ($\mathcal{M} \gtrsim 2.4$) relative to the group center. Thus, we expect to observe some evidence of a shock, such as density discontinuities and shock heating. From the Rankine-Hugoniot jump conditions (Laudau \& Lifshitz 1987), the expected density and temperature jumps can be expressed as a function of the Mach number: \begin{equation} \frac{{\rho}_2}{{\rho}_1}=\frac{\mathcal{M}^2(\gamma+1)}{2+\mathcal{M}^2(\gamma-1)}, \end{equation} \begin{equation} \frac{T_2}{T_1}=\frac{[(\gamma-1)\mathcal{M}^2+2][2\gamma \mathcal{M}^2-(\gamma-1)]}{(\gamma+1)^2\mathcal{M}^2}. \end{equation} NGC~1400 is moving with $\mathcal{M}\gtrsim2.4$, so the expected density jump is $\rho_2/\rho_1\gtrsim 2.6$ and the expected temperature jump is $T_2/T_1\gtrsim2.6$. Given that the group gas temperature is $\sim1$ keV, we expect to observe some gas heated to $\gtrsim2.6$ keV in the field of view. However, we do not detect obvious shock features. A similar situation has been reported for M86 in the Virgo cluster. It has a line-of-sight velocity difference of 1550 km~s$^{-1}$ with respect to M87 at the cluster center, which is almost twice the sound speed of the cluster gas (850 km~s$^{-1}$). In spite of a Mach number $\mathcal{M}\approx2$, no shock feature has been found around M86 (Randall et al.\ 2008); the absence of shock features has been attributed to projection effects (Mazzotta et al.\ 2001; Rangarajan et al.\ 1995). Akahori \& Yoshikawa (2010) simulated cluster shock features as a function of viewing angle. They found that sharp surface brightness discontinuities at shock layers are clearly visible only when the collisional direction is nearly perpendicular to the line-of-sight ($\theta$ = 90$^{\circ}$). The apparent Mach number can be reduced by more than 60\% when $\theta$ is smaller than 30$^{\circ}$. The motions of M86 and NGC~1400 are nearly line-of-sight ($\theta$ $\lesssim30^{\circ}$), so shock features may be smeared out by projection effects. This is in sharp contrast to the case of Abell~194, where the motion of NGC~541 is almost perpendicular to the line of sight (Bogdan et al.\ 2011). Our current X-ray data do not allow us to constrain spectrally whether there is a layer of shocked group gas superposed on ISM stripped from NGC~1400, as well as unshocked group gas. In addition to being washed out by projection effects, the observability of a shock may be affected by ions and electrons being out of thermal equilibrium. The ion temperature may indicate a shock, but it takes a finite time for the electrons to equilibrate with the ions and also exhibit the shock temperature. Most of the shock energy would be initially converted to the thermal energy of ions in the post-shock region, due to the mass difference between ions and electrons (Spitzer 1962; Wong \& Sarazin 2009; Akahori \& Yoshikawa 2010). The time scale for electron-ion thermal equilibration through Coulomb collisions is given by \begin{equation} t_{\rm ei} \approx6.3 \times 10^7 \frac{(T_{\rm e}/10^7 ~{\rm K})^{3/2}}{(n_{\rm e}/10^{-4}~{\rm cm}^{-3})({\rm ln}~\Lambda/40)}~{\rm yr}, \end{equation} (Rudd \& Nagai 2009), where ln~$\Lambda$ $\approx40$ is the Coulomb logarithm. Electron-ion thermal equilibrium usually is achieved in the inner regions of galaxy clusters, where the equilibration time is shorter than the dynamical time scale. Departure from this equilibrium has been proposed to occur in the outskirts of galaxy clusters, where the electron density is small and the equilibration time is relatively long (Fox \& Loeb 1997; Hoshino et al.\ 2010). The group gas of NGC~1407 has a smaller gas density ($n_{\rm e}\sim10^{-4}$ cm$^{-3}$) compared to similar regions in galaxy clusters. Thus, we examined the thermal equilibrium condition for this system. We assume that the shock has started at what is now the end of the tail (corresponding to the 7th bin of the western pointing) and propagate following the motion of NGC~1400, as indicated in Figure~\ref{fig:ts} ({\sl left}). For regions between the end of the tail and NGC~1400, we calculated $t_{\rm ei}$ as a function of (projected) distance to NGC~1400\footnote{$n_{\rm e}$ and $T_{\rm e}$ are calculated from eq.~(4) and eq.~(5) respectively, derived with the eastern pointing}. We estimated the time elapsed since the passage of a putative shock ($t_{\rm elapsed}$), assuming NGC~1400 has tangential velocity of 800 km~s$^{-1}$ along the (projected) length of the stripped tail. We compare $t_{\rm ei}$ and $t_{\rm elapsed}$ in Figure~\ref{fig:ts} ({\sl right}). For regions within 25 kpc (projected) of NGC~1400, the electrons might not have had enough time to equilibrate with ions, consequently leading to the absence of evidence for shock heating. The end of the tail (beyond 25 kpc) should be in thermal equilibrium. Interestingly, we did observe slight extra heating (temperature increasing by 0.2 keV or $\sim20$\%) in the 7th bins with {\sl XMM-Newton} observations. In principle, we should observe transitional shock heating regions along the path of NGC~1400 (on its eastern side), as ion-electron equilibrium is gradually established. Unfortunately, these {\sl XMM-Newton} and {\sl Chandra} data do not allow us to resolve this; we would need deeper {\sl Chandra} observations with more areal coverage to test this. \subsection{\sl Stripping conditions} \subsubsection{\sl Ram pressure stripping} For a consistency check, we studied the conditions for ram pressure stripping in the NGC 1407 group. The ISM of NGC~1400 would be stripped when the ram pressure ($P_{\rm ram}=\rho_{\rm gas}v^2$) exceeds the gravitational restoring force per unit area (Gunn \& Gott 1972): \begin{equation} P_{\rm ram} > \frac{F}{A} ~\Rightarrow ~\rho_{_{\rm ICM}}v^2 > \frac{GM_{\rm tot}}{{R_{_{\rm ISM}}}^2}\frac{M_{_{\rm ISM}}}{\pi {R_{_{\rm ISM}}}^2}, \end{equation} for a galaxy with a total mass of $M_{\rm tot}$ and a characteristic radius of $R_{_{\rm ISM}}$ (the radius of the galaxy at which the stripping occurs), moving with total velocity $v$ through cluster gas with density $\rho_{_{\rm ISM}}$. While this was originally derived for disk galaxies, McCarthy et al.\ (2008) developed an analogous model for the ram pressure stripping of galaxies with spherically-symmetric gas distributions. Their model, which is more suitable for early-type galaxies with an extended atmospheres, yields the ram pressure stripping condition: \begin{equation} P_{\rm ram} = \rho_{_{\rm ICM}}v^2 >\frac{\pi}{2}\frac{GM_{\rm tot}\rho_{_{\rm ISM}}}{R_{_{\rm ISM}}}, \end{equation} where $\rho_{_{\rm ISM}}$ is the ISM gas density in the galaxy. To examine this condition, we first fit the surface brightness profile of the ``middle" direction from NGC~1400 (shown in Figure~\ref{fig:sur}) to a $\beta$-profile: \begin{equation} I(r)=I_{0}\left[1+\left(\frac{r}{r_c}\right)^2\right]^{-3\beta/2+1/2}. \end{equation} We obtained $\beta$=0.27 and $r_c$=0.93 kpc. Assuming isothermal gas, this corresponds to an ISM density profile of \begin{equation} \rho_{_{\rm ISM}}(r)=\rho_{0}\left[1+\left(\frac{r}{r_c}\right)^2\right]^{-3\beta/2}. \end{equation} The X-ray luminosity of the enhanced region is comparable to the hot gas luminosity of NGC~1400. Thus, roughly half of NGC~1400's ISM has been stripped, corresponding to a radius ranging from 6.4 kpc to 8.7 kpc, derived from the volume integration of the ISM density profile. Thus, we adopted a characteristic radius of $R_{_{\rm ISM}}$=7.6 kpc for this ram pressure stripping process. This calculation also lead us to obtain the value of $\rho_{0}$=0.012 cm$^{-3}$, using the ISM mass of NGC~1400, determined through the best-fit normalization in the spectral analysis of \S3.1. The density of group gas is chosen to be $\rho_{_{\rm ICM}}=2.5\times 10^{-4}$ cm$^{-3}$, calculated from eq.~(5) for regions at the same radius from NGC~1407 as the enhanced region. The ISM density $\rho_{_{\rm ISM}}=2.2\times 10^{-3}$ cm$^{-3}$ is calculated from eq.~(21) at a radius of $R_{_{\rm ISM}}$=7.6 kpc. We estimated the total mass of NGC~1400 enclosed within a spherical radius $r$ through the hydrostatic equilibrium equation shown in eq.~(6). We chose $r$ to be the same as $R_{_{\rm ISM}}$=7.6 kpc. The gas density gradient is chosen to be -3$\beta = -0.81$ at this radius and we assume the temperature gradient is is zero. We obtained a total enclosed mass of $M_{\rm tot}$ = 1.5$\times 10^{11}$ $M_\odot$. We calculated through eq.~(19) that the relative velocity of NGC~1400 needs to be $\sim1275$ km\,s$^{-1}$ to have the gas in the enhanced region stripped via ram pressure. This value lies in a possible range (1200 -- 1500 km\,s$^{-1}$) of its total velocity estimated in \S4.1. Therefore, ram pressure stripping alone is capable of forming the enhanced region. Once the stripping condition is satisfied, we can estimate the time scale for the ram pressure stripping process, which is given by \begin{equation} t_{\rm ram}=({\rm d}~{\rm{ln}}~m_{_{\rm ISM}}/{\rm d}t)^{\rm -1}, \end{equation} so that \begin{equation} t_{\rm ram}\approx~\frac{R}{v}\left(\frac{2\rho_{_{\rm ISM}}}{\rho_{_{\rm ICM}}}\right)^{1/2} \approx3\times10^7 \left(\frac{\rho_{_{\rm ISM}}}{\rho_{_{\rm ICM}}}\right)^{1/2}\left(\frac{\it v}{10^3~ \rm km~s^{-1}}\right)^{-1} \left(\frac{\it R}{20~ \rm kpc}\right) {\rm yr}. \end{equation} (Takeda et al.\ 1984). It takes $\sim30$ Myr to have the hot gas in the enhanced region stripped from NGC~1400 through ram pressure. Given that NGC~1400 may have a tangential velocity of $\approx800$ km~s$^{-1}$ (\S4.1), it may have travelled for $\gtrsim25$ kpc in the plane of sky within this time. This is in excellent agreement with the projected tail length. \subsubsection{\sl Turbulent and Viscous Stripping} Ram pressure is not the only possible stripping mechanism. There are other processes such as turbulence and viscosity which may contribute to the stripping of ISM, as noted by Nulsen (1982). The Reynolds number ($Re$) is the ratio of inertial to viscous forces, which can be obtained through \begin{equation} Re = 2.8\,(r/\lambda)(v_{\rm gal}/c_{\rm s}) \end{equation} (Batchelor 1967); $r$ and $v_{\rm gal}$ are the radius and velocity of the moving galaxy respectively; $\lambda$ is the effective mean free path of ions in the hot gas, which can be calculated through \begin{equation} \lambda = 23 \left(\frac{T}{10^8\,{\rm K}}\right)\left(\frac{n_{\rm e}}{10^{-3}\,{\rm cm^{-3}}}\right)^{-1}\,\rm kpc \end{equation} Sarazin (1988). For low Reynolds numbers ($\sim$ 10), laminar viscous flow occurs, characterized by smooth constant fluid motion, while for high Reynolds numbers ($\sim$ 2000), turbulent flow occurs, producing various instabilities. For NGC~1400 we assume $r=8.6$ kpc and $v=1400$ km\,s$^{-1}$; $T$ and $n_{\rm e}$ are taken to be 1.1 keV and 2.5$\times 10^{-4}$\,cm$^{-3}$, respectively, derived from eqs.\ (4) and (5); thus, we estimate that $Re = 5.9$, so laminar viscous stripping is preferred (in the absence of magnetic fields). For turbulent stripping, the typical mass-loss rate of the ISM is approximately (Nulsen 1982): \begin{equation} \dot{M}_{\rm tur}\approx\pi r^2\rho_{_{\rm ICM}} v_{\rm gal} =0.69\left(\frac{n_{e,_{\rm ICM}}}{10^{-3}\,\rm cm^{-3}}\right)\left(\frac{r}{2.5\,\rm kpc}\right)^2\left(\frac{v_{\rm gal}}{1200\,\rm km\,s^{-1}}\right) M_\odot\,{\rm yr^{-1}}. \end{equation} This gives a typical stripping time scale of (Sun et al.\ 2007b): \begin{equation} t_{\rm strip}=\int{\frac{d M}{\dot{M}}}=\frac{4}{n_{_{\rm ICM}}v_{\rm gal}}\int n(r)dr$$ $$=0.224\,g_1\left(\frac{n_{\rm e0}}{0.2~ \rm cm^{-3}}\right)\left(\frac{n_{_{\rm ICM}}}{10^{-3}\,\rm cm^{-3}}\right)^{-1}\left(\frac{r_0}{0.4\,\rm kpc}\right)\left(\frac{v_{\rm gal}}{1400~ \rm km\,s^{-1}}\right)^{-1} \rm Gyr, \end{equation} $${\rm where} ~~g_1=\int(1+x^2)^{-1.5\beta}dx, ~x=r/r_0,$$ and $r_0$ and $\beta$ are the parameters in the $\beta$-model of the deprojected electron density profile. A stripped radial range from 6.4 to 8.7 kpc corresponds to $g_1=0.41$. We estimate from eq.~(27) that the enhanced region has been stripped during the last $19$ Myr. For viscous stripping, the typical mass-loss rate of the ISM is approximately (Nulsen 1982): \begin{equation} \dot{M}_{\rm vis}\approx\pi r^2\rho_{_{\rm ICM}} v_{\rm gal}\,(12/Re) \end{equation} In the case of NGC~1400, $\dot{M}_{\rm vis} \approx 2.1 \dot{M}_{\rm tur}$, so the time scale for viscous stripping is half that of turbulent stripping. Although analytical methods show that viscous stripping can be very efficient in extracting gas from galaxies (e.g., Nulsen 1982), some (hydro)dynamical simulations indicate that magnetic fields could greatly reduce the effects of viscosity (e.g., Roediger \& Bruggen 2008). Measurements of radio continuum emission and Faraday rotation show that magnetic fields commonly exist in galaxy clusters, with strengths of the order of 1$\mu$G (Govoni \& Feretti 2004; Bonafede et al.\ 2010). To include the effects of magnetic fields, we invoke a suppression factor ($f_{\rm v}$), relating a corrected Reynolds number to the original unmagnetized version: $Re_{\rm m}=Re\,f_{\rm v}^{-1}$. Narayan \& Medvedev (2001) found $f_{\rm v}$ of 0.01--0.2 in intracluster gas, so the corrected Reynolds number $Re_{\rm m}$ should be in the range of 30--550 for NGC~1400 and the enhanced region. This points to a more turbulent, less viscous case compared with our original estimate. Roediger \& Bruggen (2008) demonstrate through simulations that intracluster gas flows through galaxies more smoothly in the viscous case, while Kelvin-Helmhotz and Rayleigh-Taylor instabilities occur when the viscosity is suppressed, leading to vortices and turbulence. \subsection{\sl $M/L$ and the group membership of NGC~1400} Romanowsky et al.\ (2009) studied this group using the kinematics of its globular clusters within 60 kpc. They extrapolated a virial mass of $\sim6\times10^{13}$ $M_\odot$ and an associated $M/L$ of $\sim800$ $M_\odot/L_{B_\odot}$. This large $M/L$ would make NGC~1407 an unusually dark system and may require a large amount of baryons to be lurking in an undetected phase (Romanowsky et al.\ 2009). In our study, we derived the hydrostatic mass of this group with an {\sl XMM-Newton} pointing east of NGC~1407. We determined a total mass within 100 kpc of $\sim1\times10^{13} M_\odot$ and an extrapolated virial mass of only $3.75\times10^{13}$ $M_\odot$ for this group. The disagreement between the total mass estimated through globular cluster kinematics and that determined through X-ray analysis of hot gas is rather common for early-type galaxies, some of which are at group centers (e.g, M87: Murphy et al.\ 2011; NGC~4636: Johnson et al.\ 2009; NGC~4649: Shen \& Gebhardt 2010; NGC~3923: Norris et al.\ 2012). The biggest problem with the X-ray modeling involves the possible lack of hydrodynamic equilibrium or the presence of non-thermal pressure support, due to magnetic fields, gaseous turbulence or cosmic rays (Churazov et al.\ 2010; Shen \& Gebhardt et al.\ 2010). Some studies show that the contribution from non-thermal pressure is much smaller than thermal pressure for early-type galaxies (Brighenti et al.\ 2009), as well as within $R_{500}$ for groups and clusters (Shaw et al.\ 2010). Moreover, the eastern side of NGC~1407 that we used to derive a hydrostatic mass appears relatively relaxed, thus is likely to be close to hydrostatic equilibrium. On the other hand, the biggest concerns with the globular cluster probe include the unknown galaxy inclination and potentially complex orbit structure (Gavazzi 2005; Thomas et al.\ 2007). Romanowsky et al.\ (2009) found that their results are in better agreement with the previous {\sl Chandra} X-ray study (Zhang et al.\ 2007, within 20 kpc of NGC~1407) if the globular clusters are assumed to have a peculiar orbit distribution. In short, we believe that the total mass estimated through X-ray analysis may be relatively more robust in this case. Nevertheless, even a virial mass as low as $3.75\times10^{13}$ $M_\odot$ may still be able to keep NGC~1400 bound. According to Romanowsky et al.\ (2009), the minimum virial mass necessary to keep NGC~1400 bound is only $3\times10^{13}$ $M_\odot$, provided that the apocenter of NGC~1400 is at $R_{\rm vir}$. The upper limit of $M/L\approx300$ $M_\odot/L_{B_\odot}$ that we determined with the hot gaseous X-ray emission is half that estimated by Romanowsky et al.\ (2009), although their uncertainty is as large as a factor of two. Our results suggest that NGC~1407 is {\it not} an unusually dark system, with a group $M/L$ that is comparable to that of Fornax group ($\sim300$ $M_\odot/L_B$; Drinkwater et al.\ 2001). Another important observable is the baryon mass fraction. We determined an enclosed baryon mass fraction of 0.06 within 100 kpc for this group, which is much larger than previously determined by Romanowsky et al.\ (2009). This value is still smaller than the cosmological value of $0.17$, but comparable to other galaxy groups with similar temperatures (Dai et al.\ 2010). Thus, this baryon deficit is not unusual for groups. However, galaxy groups as a population do tend to have smaller baryon fractions than clusters (Dai et al.\ 2010). One explanation is that galaxy groups have shallower gravitational potentials, making them more vulnerable to AGN feedback and/or galactic winds. Thus, their atmospheres may have been redistributed to large radii (beyond $R_{500}$). There are a number of {\sl Suzaku} X-ray observatory studies of clusters reaching $R_{200}$. In contrast, there are only a few such studies of galaxy groups to comparable radii, due to their relatively lower X-ray surface brightness. Thus far, there are three such investigations involving poor clusters: Hydra A (3.0 keV; Sato et al.\ 2012), RXJ1159+5531 (2.0 keV; Humphrey et al.\ 2012) and ESO 3060170 (2.7 keV; Su et al.\ 2013). The enclosed baryon mass fractions in these systems are 0.23, 0.17 and 0.13, respectively. The surprisingly high value of Hydra A (higher than cosmic) may result from its total mass being underestimated, due to non-thermal pressure support at large radii. The observations of RXJ1159+5531 are consistent with theoretical predictions, with no baryons missing. Baryons may have been lost from ESO 3060170, likely due to central feedback. We speculate that the diversity of gas properties at $R_{200}$ should be larger among galaxy groups than galaxy clusters. Note that if NGC~1400 were not present, the NGC~1407 group would qualify as a fossil group, which is defined as a group with a central dominant galaxy at least two magnitudes brighter in $R$-band than the second brightest galaxy within half a virial radius (Jones et al.\ 2003). It has been debated whether fossil groups are the end results of galaxy mergers within groups or are instead a transitional stage. Our study indicates that NGC~1400, as a newly infalling galaxy, only temporarily disqualifies the NGC~1407 group as a fossil group. This is consistent with some simulation work that shows that the gap between the brightest and the second brightest galaxy may be intermittently filled over time by newly infalling galaxies (von Benda-Beckmann et al.\ 2008). Group/cluster scaling relations (such as X-ray luminosity -- temperature) show that fossil groups lie between groups and clusters in many of their properties (Khosroshahi et al.\ 2007; Miller et al.\ 2012). Thus, we speculate that fossil groups may be a transient phase as groups evolve into clusters in the hierarchical Universe. This also sheds light on the puzzling fact that a large fraction of fossil groups lack cool cores, although they are usually thought to be highly evolved, undisturbed systems (Dupke et al.\ 2010). We anticipate that recent mergers, as exhibited in the NGC~1407/1400 complex, may inhibit the monotonic growth of cool cores in many fossil groups. | 14 | 3 | 1403.6416 |
1403 | 1403.4625_arXiv.txt | In this paper we investigate the constant volume exponential solutions (i.e. the solutions with the scale factors change exponentially over time so that the comoving volume remains the same) in the Einstein-Gauss-Bonnet gravity. We find conditions for these solutions to exist and show that they are compatible with any perfect fluid with the equation of state parameter $\omega<1/3$ if the matter density of the Universe exceeds some critical value. We write down some exact solutions which generalize ones found in our previous paper for models with a cosmological constant. | Exact solutions play important role in any gravitational theory, especially nonlinear. Indeed, using numerical recipes one almost always can build a solution, but its viability will be questioned. This is especially true for nonlinear theories where even numerical solutions are sometimes hard to find. Lovelock gravity~\cite{Lovelock} is the striking example of the nonlinear theory of gravity. It is the most general metric theory of gravity yielding conserved second order equations of motion (in contrast to $f(R)$ gravity which gives fourth order dynamical equations) in arbitrary number of spacetime dimensions. One can say that the Lovelock gravity is a natural generalization of Einstein's General Relativity in the following sense: it is known~\cite{etensor1, etensor2, etensor3} that the Einstein tensor is, in any dimension, the only symmetric and conserved tensor depending only on the metric and its first and second derivatives (with a linear dependence on second derivatives); if one drops the condition of linear dependence on second derivatives, one can obtain the most general tensor which satisfies other mentioned conditions -- the Lovelock tensor. The Lovelock gravity has been intensively studied in the cosmological context (see, e.g.,\cite{add_1, add_2, add_3, add_4, add_6, add_7, add_8, add_10, add13, add_11, mpla09, prd10}). Particularly, many interesting results have been obtained for flat anisotropic metrics due to the fact that its cosmological dynamics is much richer in the Lovelock gravity than in the Einstein one. Since the resulting equations of motion turn out to be complicated enough, researchers usually study some special kind of metric (e.g. with only two different scale factors~\cite{add13, CGP}) or consider Lagrangian that contain the highest order Lovelock term only (e.g., deleting Einstein term and keeping Gauss-Bonnet term in a Lagrangian in the cases of (4+1)- and (5+1)-dimensional spacetimes one get so called ``pure'' Gauss-Bonnet model -- see, for instance, \cite{Pavluchenko, grg10, Ivashchuk}). In the latter approach solutions with power-law and exponential time dependence of scale factors were found. The first of them is an analog of Kasner solution~\cite{Deruelle1,Deruelle2} -- scale factors in this solution have power-law behavior, though relations between power indices is different from the Kasner solution in Einstein gravity~\cite{add_12, Pavluchenko, PT}. Special features of the second type of solutions -- Hubble parameters are constant, so in a flat metric differential equations of motion become algebraic -- allows us to study them in more complicated theories~\cite{KPT, PT}. There is a meaning behind considering these two metric {\it ansatz} -- power-law and exponential -- while looking for exact solutions. The former of them could be considered as a ``classical'' Friedman power-law expansion, but generalized for flat anisotropic metric. So that finding generalized Kasner power-law solutions we find possible ``Friedman-like'' attractors in high-curvature regime for the general system. The latter could be considered as anisotropic generalization of the de Sitter (exponential) expansion. Unlike power-law solutions which could be build only when one (usually highest) Lovelock term is considered, exponential solutions could be obtained when a mixture of Lovelock terms is considered. It makes exponential solutions more related to general Lovelock theory then power-law ones; from physical point of view they could be considered as ``inflation-like'' attractors\footnote{ But the analogy is not totally correct -- indeed, generally by ``inflation'' is meant not any exponential expansion stage, but the one with a mechanism to end this stage, from this point of view exponential solution cannot be called ``inflation'' for it will never ends.}. For this reason we are looking for exact solutions of this kind. When considering general cases, solutions of this kind also often are found (see e.g.~\cite{add13, CGP, MO14}; in particular, in~\cite{CGP} solutions of this kind were found in the model with non-flat spatial sections), and as one of the goals we want to describe the general conditions for these solutions to exist. In our previous paper~\cite{CST} we started to investigate the exponential solutions in Einstein-Gauss-Bonnet gravity. In the course of the study we have shown that these solution are divided into two different types -- with constant volume and with volume changing in time. The paper~\cite{CST} is devoted to the latter case. In the present paper we consider solutions with constant volume. The structure of the manuscript is as follows: in the second section we introduce the set-up we are working on and very briefly reintroduce the results from our previous paper. Then in Section III we write down solutions of a special structure which generalize those found in~\cite{CST} and in Section IV finally we work with a general case. Section V concludes the results of this paper and compares them with results of our previous paper~\cite{CST}. | 14 | 3 | 1403.4625 |
|
1403 | 1403.1693_arXiv.txt | We have pioneered a new method for the measurement of extragalactic distances. This method uses the time-lag between variations in the short wavelength and long wavelength light from an active galactic nucleus (AGN), based on a quantitative physical model of dust reverberation that relates the time-lag to the absolute luminosity of the AGN. We use the large homogeneous data set from intensive monitoring observations in optical and near-infrared wavelength bands with the dedicated 2-m MAGNUM telescope to obtain the distances to 17 AGNs in the redshift range $z=0.0024$ to $z=0.0353$. These distance measurements are compared with distances measured using Cepheid variable stars, and are used to infer that $H_0$ $=$ 73 $\pm$ 3 (random) km s$^{-1}$ Mpc$^{-1}$. The systematic error in $H_0$ is examined, and the uncertainty in the size distribution of dust grains is the largest source of the systematic error, which is much reduced for a sample of AGNs for which their parameter values in the model of dust reverberation are individually measured. This AGN time-lag method can be used beyond 30 Mpc, the farthest distance reached by extragalactic Cepheids, and can be extended to high-redshift quasi-stellar objects. | \citet{Hubb29} discovered that the universe is expanding by finding a correlation between a galaxy's recession velocity and its distance. Since then, a reliable estimate of the expansion rate of the universe at the current epoch has been a central subject in observational cosmology. This expansion rate is denoted by the Hubble constant, $H_0$, and it characterizes the nature of the universe, such as the age of the universe, $t_0=1/H_0$, the observable size of the universe, $R_0=c/H_0$, and the critical mass density of the universe, $\rho_{\rm {crit,0}}=3H_0^{2}/(8\pi G)$, where $c$ is the speed of light, and $G$ is the gravitational constant. A variety of empirical distance-ladder methods have been proposed, which determine the distance to a galaxy through a series of steps, with each step calibrating the next more distant step, such as those with final steps based upon the period--luminosity relation for Cepheid variable stars, the maximum luminosity of type Ia supernovae, etc. The results from these empirical methods have almost converged to a value of $H_0$ at around 73 km s$^{-1}$ Mpc$^{-1}$ \citep{Free01,Free10}. On the other hand, a physical method has the advantage over the empirical methods in that it could, in principle, determine $H_0$ through a reasonable model parameterization without resorting to an empirical distance ladder. The Sunyaev--Zel'dovich effect \citep{Birk99} and the use of gravitational lensing \citep{Blan86} have been proposed. However, their results for $H_0$ have not converged to agree with those from the empirical methods, because uncertainties associated with parameters in these particular methods do not allow an accuracy comparable to the empirical methods \citep{Free10}. Consequently, other physical methods that enable the measurement of extragalactic distances with higher accuracy are eagerly sought. In this Letter, we propose a new physical method, using a model with simple physics, for extragalactic distance determination. Our model is based on the dust reverberation in active galactic nuclei (AGNs). We demonstrate the effectiveness of this method by determining $H_0$ with a value and accuracy comparable to that obtained by the Hubble Key Project using Cepheid variable stars. \begin{figure*} \epsscale{0.81} \plotone{figure1_color.eps} \caption[The light curves of Seyfert galaxies]{ Light curves for two Seyfert 1 galaxies demonstrating the time-lag between variations at short wavelength ($V$ band) and long wavelength ($K$ band). Filled circles (colored red in the online version) represent the $K$-band light curve, and open circles (filled green circles in the online version) represent the $V$-band light curve. Changes in the $V$-band are mimicked in the $K$-band after a time-lag related to the $V$-band absolute magnitude. The observations span more than 2000 days. (a) Observations of NGC 5548 in the $V$ and $K$ bands. (b) Observations of IRAS03450$+$0055 in the $V$ and $K$ bands.}\label{fig:lc} \end{figure*} | In Figure 2, we present the velocity-distance diagram to compare the extragalactic distances measured using our AGN time-lag method with distances obtained from Cepheid variable stars. Our AGN time-lag method determines the distance, $d$, through a reasonable physical parameterization, and directly provides the first step in the distance ladder. We obtain the Hubble constant, $H_0 = 73 \pm 3$ km s$^{-1}$ Mpc$^{-1}$ from a least squares fit to $v = H_0d$ using our AGN time-lag distances. The Hubble constant found from empirically calibrated Cepheid distances is $H_0 = 75 \pm 10$ \citep{Free01}. Our AGN time-lag method, which is based upon a physical model with no empirical calibration, agrees well with the Cepheid distances and other empirical distance ladders \citep{Free01,Free10}, but extends to galaxies 10 times more distant than where Cepheid distances can be measured, to where the cosmic recession velocity is not so badly afflicted by the local velocity flow. The systematic error in $H_0$ is estimated by changing the parameter values of $\alpha_{\rm UV}$ and $T_{\rm d}$ in their respective ranges of uncertainty, and by changing the distribution of $a$, assumed to have a power-law form of $f(a) = Ka^{-p}$. \footnote{ The observer's viewing angle has also been considered as a possible source of the systematic error \citep[e.g.,][]{KW11}. However, we do not explicitly consider this possibility here, because we have not found any systematic difference in the time lag measurements for our target AGNs of different Seyfert subclasses (S. Koshida et al., in preparation). } Our calculation gives $\Delta H_{0,\alpha}=\pm 5$ km s$^{-1}$ Mpc$^{-1}$ and $\Delta H_{0,T_{\rm d}}=\pm 3$ km s$^{-1}$ Mpc$^{-1}$ for the uncertainty in $\alpha_{\rm UV}$ and $T_{\rm d}$, respectively. The systematic error in $H_0$ from the uncertainty in $f(a)$ is estimated using two extreme size distributions, such as the standard ``MRN'' distribution in the local interstellar medium for our Galaxy \citep[$p=3.5$, $a_{\rm min}=0.005\ \mu$m, $a_{\rm max}=0.25\ \mu$m;][]{Math97}, and the larger grain enhanced distribution for AGNs ($p=2.05$, $a_{\rm min}=0.005\ \mu$m, $a_{\rm max}=0.20\ \mu$m), because smaller dust grains are more efficiently sublimated by UV radiation from the central engine \citep{Gask04}. We adopt an intermediate value of $p=2.75$ with $a_{\rm min}=0.005\ \mu$m and $a_{\rm max}=0.20\ \mu$m as our standard grain size distribution. NIR flux-weighted averaging scheme over the full range of $a$ is then applied to Equation (1), and the calibration factor $g$ is calculated for the two extreme distributions as well as the intermediate one. The uncertainty in $g$ is within the limits of $\Delta g=\pm 0.5$, so that $\Delta H_{0,a}$ is at most $\pm 0.1$ dex from Equation (2), which is currently the largest source of the systematic error in $H_0$. This error in $H_0$ is much reduced for a sample of AGNs for which their $\alpha_{\rm UV}$, $T_{\rm d}$, and $f(a)$ are individually measured, because the target to target variation of these parameters also contributes to the random error in the $H_0$ fitting. In particular, if monitoring observations of high-redshift AGNs were obtained, their UV--optical spectrum could be determined directly from ground based spectroscopic observations, and the accuracy of the $H_0$ determination would be significantly improved. Alternatively, if many of target AGNs were calibrated by other reliable distance indicators such as Cepheids and type Ia supernovae, their calibrated distances would not only provide a cross check on our method of distance determination, but also independently constrain the parameter values in a physical model of dust reverberation. Two other reverberation methods of distance determination of AGN have been proposed. One is a method based on the reverberation mapping of the broad line emitting region (BLR) in AGN \citep{Wats11,Cze03}, using an empirical relation between the radial distance of BLR from the AGN center and the AGN luminosity. Although the radius-luminosity relation of BLR is well established now \citep{Bent13}, the exact size of BLR cannot be predicted theoretically. Therefore, this method remains as an empirical method in the sense that it must use empirical distance-ladder methods for calibration. Another is a method based on the wavelength-dependent time delay of UV--optical continuum emission from the central accretion disk in AGN \citep{Coll99,Cack07}. This method is a physical one, like our method, which could, in principle, determine the distance without any distance calibration. However, this method gives $H_0=$42--44 km s$^{-1}$ Mpc$^{-1}$, which is about a factor of 1.7 smaller than current standard estimates, and even below the recent lower estimate of 67 km s$^{-1}$ Mpc$^{-1}$ based on Planck measurements of the cosmic microwave background temperature \citep{Plan13}. Thus, this method seems to have some difficulties to be resolved, such as the adequacy of modeling the X-ray reprocessing for the flux variation of UV--optical continuum emission. In fact, while some AGNs show a delay of the optical flux variation behind that of X-ray, which is consistent with the X-ray reprocessing, some others show a delay of the X-ray variation behind that of optical, or they show a poor correlation between the X-ray and optical variations \citep[e.g.,][]{Uttl06}. In summary, we have demonstrated that our AGN time-lag method can be used to measure extragalactic distances beyond what is possible with Cepheids, and we have obtained a value of the Hubble constant with our AGN time-lag method of $H_0 = 73 \pm 3\ ({\rm random})$ km s$^{-1}$ Mpc$^{-1}$ for a sample of 17 Seyfert 1 galaxies observed with the MAGNUM telescope. We suggest that this method can be used with QSOs to study the dark energy in the universe beyond what is possible with type Ia supernovae. | 14 | 3 | 1403.1693 |
1403 | 1403.4249_arXiv.txt | We report ALMA Early Science observations of the Abell 1835 brightest cluster galaxy (BCG) in the CO (3-2) and CO (1-0) emission lines. We detect $5\times 10^{10}~\rm M_\odot$ of molecular gas within 10 kpc of the BCG. Its {ensemble velocity profile} width of $\sim 130 ~\rm km~s^{-1}$ FWHM is too narrow for the molecular clouds to be supported in the galaxy by dynamic pressure. The gas may instead be supported in a rotating, turbulent disk oriented nearly face-on. Roughly $10^{10}~\rm M_\odot$ of molecular gas is projected $3-10 ~\rm kpc$ to the north-west and to the east of the nucleus with line of sight velocities lying between $-250 ~\rm km~s^{-1}$ to $+480 ~\rm km~s^{-1}$ with respect to the systemic velocity. {The high velocity gas may be either inflowing or outflowing. However, the absence of high velocity gas toward the nucleus that would be expected in a steady inflow, and its bipolar distribution on either side of the nucleus, are more naturally explained as outflow. Star formation and radiation from the AGN are both incapable of driving an outflow of this magnitude. The location of the high velocity gas projected behind buoyantly rising X-ray cavities and favorable energetics suggest an outflow driven by the radio AGN.} If so, the molecular outflow may be associated a hot outflow on larger scales reported by Kirkpatrick and colleagues. {The molecular gas flow rate of approximately $200~\rm M_\odot ~yr^{-1}$ is comparable to the star formation rate of $100-180~\rm M_\odot ~yr^{-1}$ in the central disk.} How radio bubbles would lift dense molecular gas in their updrafts, how much gas will be lost to the BCG, and how much will return to fuel future star formation and AGN activity are poorly understood. Our results imply that radio-mechanical (radio mode) feedback not only heats hot atmospheres surrounding elliptical galaxies and BCGs, it is able to sweep higher density molecular gas away from their centers. | Brightest cluster galaxies (BCGs) are the largest and most luminous galaxies in the universe. Like normal elliptical galaxies, their stellar populations are usually old and dormant. BCGs residing in cooling flow clusters are exceptional (Fabian 1994). Fueled by unusually large reservoirs of cold molecular clouds (Edge et al. 2001, Salome \& Combes 2003), many form stars at rates of several to several tens of solar masses per year (O'Dea et al. 2008). Extreme objects, such as the Phoenix and the Abell 1835 BCGs, are forming stars at rates upward of $100~\rm M_\odot ~yr^{-1}$ (McDonald et al. 2012, McNamara et al. 2006, hereafter M06). {The origin of star formation in a population of normally ``red and dead" galaxies is not entirely clear. In some instances, BCGs may be rejuvenated by collisions with gas-rich galaxies. However, wet mergers must be uncommon in BCGs due to a dearth of gas-rich donor galaxies in cluster cores. A wealth of data suggests that molecular clouds and young stars forming in BCGs are usually fueled instead by gas cooling from hot atmospheres.} For example, bright nebular emission and young stars are observed preferentially when the central cooling time of a cluster atmosphere falls below $\sim 1$ Gyr (Heckman 1981, Hu et al. 1985). Furthermore, high resolution X-ray imaging has since revealed that nebular emission and star formation appear at a sharp threshold or transition as the central cooling time falls below $\sim 5 \times 10^8~\rm yr$ (Rafferty et al. 2008, Cavagnolo et al. 2008). {Voit and others} have attributed this threshold to cooling instabilities and thermal conduction in hot atmospheres (Voit et al. 2008, Voit 2011, Gaspari et al. 2012, Guo \& Mathews 2013). Despite strong indications that cold clouds are condensing out of hot atmospheres, only a few percent of the mass expected to cool actually does so (Peterson \& Fabian 2006). Feedback from active galactic nuclei (AGN) is almost certainly suppressing cooling below the levels expected in an unimpeded cooling flow (reviewed by McNamara \& Nulsen 2007, 2012, Fabian 2013). So-called radio-mode or radio-mechanical feedback operates primarily on the hot, volume-filling atmosphere. {The energy released by radio AGN increases the entropy of the hot gas (O'Neill \& Jones 2010) and drives the most rapidly cooling gas outward, thereby regulating the cooling rate, the star formation rate, and the power output of the AGN itself. } {Despite the widely held view that radio-mechanical feedback maintains BCGs and giant elliptical galaxies in dormancy, little is known of its effect on molecular gas. This is potentially significant issue because the rate of cold accretion onto AGN may be a crucial element of an operational feedback loop (Pizzolato \& Soker 2010, Gaspari et al. 2013)}. {Radio jets are known to interact with nebular gas surrounding them (eg. Villar-Mart{\'{\i}}n et al. 2006, Nesvadba et al. 2006), which are likely to be the ionized skins of molecular clouds (Wilman et al. 2006, Emonts et al. 2013). } Furthermore, blueshifted absorption lines of neutral atomic hydrogen have been observed toward several radio galaxies (Morganti et al. 2005, 2013), indicating that radio jets couple effectively to cold clouds and are able to drive them out at high speed. {NGC 1275 in the Perseus cluster is a striking example of radio lobes interacting with molecular clouds (Salome et al. 2006, 2011). Both inflow and outflow are observed in what appears to be a molecular "fountain" (Lim et al. 2008). Abell 1835, discussed here, may be similar to Perseus.} Here we examine the effects of feedback on the molecular gas located near the nucleus of the Abell 1835 BCG. The BCG contains upward of $\simeq 5 \times 10^{10}~\rm M_\odot$ of molecular gas (Edge 2001) and star formation proceeding at a rate of between $100-180~\rm M_\odot ~yr^{-1}$ (M06). The AGN launched a pair of cavities into its hot atmosphere a few $10^7 \rm yr$ ago, each of which is 20 kpc in diameter and projected roughly 20 kpc from the nucleus. The AGN's radio synchrotron luminosity, $3.6\times 10^{41}~\rm erg~s^{-1}$, is dwarfed by its mechanical power, $ L_{\rm mec} \simeq 10^{45}~\rm erg s^{-1}$(M06), which is typical of radio AGN (Birzan et al. 2008). Abell 1835 is an archetypal cooling flow regulated by radio-mode feedback. The ALMA Early Science observations reported here and in a companion paper on Abell 1664 (Russell et al. 2013), explore for the first time at high resolution, the relationships between molecular gas, star formation, and radio AGN feedback. At the emission line redshift z = 0.252 (Crawford et al. 1999), 1 arcsec = 3.9 kpc. | We have shown that the BCG in Abell 1835 contains roughly $5\times 10^{10}~\rm M_{\odot}$ of molecular gas, most of which is associated with stars forming at a rate of $100-180 ~\rm M_{\odot}~yr^{-1}$, in a thick, turbulent disk projected face-on. We discovered a $\sim 10^{10}~\rm M_{\odot}$ bipolar molecular flow traveling between $-250~\rm and~ +480 ~\rm km~s^{-1}$ that {we suggest} is being accelerated outward by mechanical energy associated with rising X-ray bubbles. Whether the bubbles accelerated the molecular clouds themselves, or whether the molecular clouds cooled out of the hot plasma in the updraft behind the bubbles is unclear. {We highlight the difficulty lifting dense molecular gas out of the central disk and we propose that the molecular gas in the flow may have cooled in the updraft of hot plasma behind the bubbles. The problem would be mitigated if the outflowing mass were lower than we have estimated, for example, if the $\rm X_{\rm CO}$ parameter were lower than the value we assumed. } Our result has broader implications. Molecular gas abundance is a sharply declining function of a galaxy's stellar mass. Above $3\times 10^{10}~M_\odot$ most are elliptical galaxies. Of these, only $\sim 22\%$ contain molecular gas, and only at levels between $10^7-10^9~\rm M_\odot$ (Young et al. 2011). On the other hand, radio power is a steeply increasing function of stellar mass (Best et al. 2005, Best \& Heckman 2012). Their radio detection fraction rises from $0.01\%$ at $3\times 10^{10}~M_\odot$ to upward of $30\%$ at $5\times 10^{11}~M_\odot$ (Best et al. 2005). Therefore, molecular gas mass must also be a declining function of radio power. While a number of environmental factors may be contributing to this decline (Young et al. 2011), the radio source itself may play a role, albeit a complex one. Radio synchrotron power represents only a small fraction of a radio AGN's total mechanical power (Birzan et al. 2008). Therefore, relatively low power radio synchrotron sources can be mechanically potent. Mechanical heating of hot atmospheres in elliptical galaxies by radio mode feedback is likely to be the primary mechanism maintaining ``red and dead" elliptical galaxies (e.g., Bower et al. 2006, Croton et al. 2006). {However, radio AGN are likely fed by cold clouds. A feedback loop may be difficult to sustain unless the radio jets are also affecting the rate of cold gas accretion by driving it away from the nucleus.} The relatively efficient coupling between the molecular gas and radio bubbles {inferred here in Abell 1835 and in other radio galaxies (eg., Morganti, Tadhunter, \& Oosterloo 2005) } suggests that radio mode feedback may also be regulating the amount of molecular gas reaching the centers of galaxies. BRM thanks Tom Jones and Christine Jones for helpful comments. HRR and BRM acknowledge generous financial support from the Canadian Space Agency Space Science Enhancement Program. BRM, RAM, HRR, and ANV acknowledge support from the Natural Sciences and Engineering Research Council of Canada. ACE acknowledges support from STFC grant ST/I001573/1 PEJN is supported by NASA grant NAS8-03060. We thank the ALMA scientific support staff members Adam Leroy and St\'ephane Leon. The paper makes use of the following ALMA data: ADS/JAO.ALMA\#2011.0.00374.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This paper is dedicated to Jim Pisano, who helped make ALMA the marvelous facility it is. \appendix | 14 | 3 | 1403.4249 |
1403 | 1403.2659_arXiv.txt | The study of symbiotic systems is of considerable importance in our understanding of binary system stellar evolution in systems where mass loss or transfer takes place. Elemental abundances are of special significance since they can be used to track mass exchange. However, there are few symbiotic giants for which the abundances are fairly well determined. Here we present for the first time a detailed analysis of the chemical composition for the giants in the RW Hya and SY Mus systems. The analysis is based on high resolution (R $\sim$ 50000), high S/N, near-IR spectra. Spectrum synthesis employing standard LTE analysis and atmosphere models was used to obtain photospheric abundances of CNO and elements around the iron peak (Sc, Ti, Fe, and Ni). Our analysis reveals a significantly sub-solar metallicity, [Fe/H]$\sim$\mbox{-0.75}, for the RW\,Hya giant confirming its membership in the Galactic halo population and a near-solar metallicity for the SY\,Mus giant. The very low $^{12}$C/$^{13}$C isotopic ratios, $\sim$6--10, derived for both objects indicate that the giants have experienced the first dredge-up. | Binary systems are an invaluable source of knowledge of the physical parameters of the stars. During some stage of stellar evolution most binary stellar systems undergo interactions between the components. The interactions turn on and off at various evolutionary stages, depending on the separation of components. Among the most interesting examples of such systems are the symbiotic systems. These are still often called symbiotic stars because their binary nature which we now consider obvious was controversial only thirty years ago. Symbiotic systems are long-period interacting binaries in which an evolved giant transfers material to a hot and luminous companion surrounded by an ionized nebula. The hot component of the vast majority of symbiotic systems is a white dwarf (WD) although in two cases, V2116\,Oph \citep{Dav1977} and V934\,Her \citep{Gar1983}, a neutron star has been found. There are two distinct classes of symbiotic binaries. The S-type (stellar) have normal red giants and orbital periods in the range $\sim$1--15 years. The D-type (dusty) have Mira primaries usually surrounded by a warm dust shell and orbital periods of typically decades to centuries. Mass exchange is the property that defines the symbiotic class. Even in the D-type systems the components are still close enough to allow the WDs to accrete material from the giant's stellar wind. Symbiotic systems are the interacting binaries with the longest orbital periods. Their study is essential to understand the evolution and interaction of detached and semi-detached binary stars. The rich and luminous circumstellar environment surrounding the interacting symbiotic stellar members results from the presence of both an evolved giant with a heavy mass loss and a hot companion copious in ionizing photons often producing its own wind. The cool giant and the hot dwarf produce strongly different environments such as ionized and neutral regions, dust forming region(s), accretion/excretion disks, interacting winds, bipolar outflows, and jets. Such a complex multi-component structure makes symbiotic stars a very attractive laboratory to study many aspects of stellar evolution in binary systems. Firming links between symbiotic systems and related objects are essential to the understanding, for instance, of the role of interacting binaries in the formation of stellar jets, planetary nebulae, novae, supersoft X-ray sources (SSXS), and supernovae type Ia (SN Ia). Many of these issues concerning the late stages of stellar evolution are presently poorly understood but have important implications on our understanding of the stellar population and chemical evolution of galaxies as well as the extragalactic distance scale. Chemical composition is one of the major parameters along with initial mass that determine stellar evolution. Chemical composition has a strong influence on many important astrophysical processes. In the case of symbiotic stars it is generally believed that the symbiotic appearance and activity is triggered by high mass-loss rate of the giant \citep[see e.g.][and references therein]{Mik2003} possibly due to its enhanced metallicity \citep{Jor2003}. The apparent deficit of extrinsic C or S stars, i.e. cool components polluted by the s-process and C-rich material from the former TP-AGB companion, is among the most interesting problems raised by the S-type symbiotic binaries. There are other red giant -- white dwarf binary star families with abundance peculiarities, for instance the barium stars and Tc-poor S stars. These families have orbital parameters similar to those of symbiotic systems but do not exhibit symbiotic activity. The hot component of most symbiotic systems is a white dwarf and, at least in some systems, the white dwarf mass is higher than 0.5~$M_\odot$ \citep{Mik2003}. White dwarfs of this type have gone through the TP-AGB phase. Moreover, the orbital periods of the S-symbiotic systems are generally less than $\sim$1000 days with circular orbits. Interaction of these systems is via Roche-lobe overflow. \citet{Jor2003} suggested that either the former AGB star did not go through the TP-AGB or its high metallicity hindered the efficiency of the s-process and the mass transfer during the TP-AGB. The first possibility could apply to a small number of red symbiotic systems with low mass ($M_{\rm WD}$ $\sim$0.4 $M_\odot$) companions such as AX\,Per and CI\,Cyg. However, in order to account for the absence of the barium syndrome in systems like AR\,Pav ($M_{\rm WD}$ $\sim$1 $M_\odot$) or FN Sgr ($M_{\rm WD}$ $\sim$0.7 $M_\odot$) the second possibility must be invoked. \begin{table} \centering \caption{Parameters of RW\,Hya and SY\,Mus}\label{T1} \begin{tabular}{@{}lccl@{}} \hline Parameter & RW\,Hya & SY\,Mus & Reference\\ \hline $P_{\rmn{orb}}$ & 370.2 days & 625 days & \citet{KeMi1995}\\ & & & \citet{Dum1999} \\ Sp Type & M2 & M5 & \citet{Bel2000} \\ $M_{\rmn{cool}}$ & 1.6$\pm$0.3 & 1.30$\pm$0.25 & \citet{Rut2007} \\ $M_{\rmn{hot}}$ & 0.48$\pm$0.06 & 0.43$\pm$0.05 & \citet{Rut2007} \\ $R_{\rmn{cool}}$ & 122\,$R_{\sun}$ & 135\,$R_{\sun}$ & \citet{Rut2007} \\ \hline \end{tabular} \end{table} There are contradictory arguments provided by the photospheric abundance analysis of symbiotic giants. In particular, the so-called yellow symbiotic systems, AG Dra, BD-21 3873, and He2-467, all contain K-type giants that are metal poor and s-process over abundant (\citealt[][1997;]{Smi1996} \citealt{Per1998}). These systems seem to belong to the Galactic halo and are probably low-metallicity relatives of Ba stars. On the other hand, HD\,330036, AS\,201, and StHA\,190, members of another small subclass of symbiotic stars with G-type giants and warm dust shells (D'-type), have very high rotational velocities, solar metallicities, and are also s-process over abundant (\citealt{Smi2001}, \citealt{Per2005}). The vast majority of symbiotic systems, however, seem to contain normal M-type giants with very little known about their abundances and no published information about the presence of any s-process enrichments \citep[][and references therein]{Sch2006}. Thus far most information about the red giant nature and chemistry is derived either from the abundance studies based on nebular emission lines (\citealt{Nus1988}) or (mostly) TiO molecular absorption bands (\citealt{Mue1999}). In addition, analysis of the first-overtone CO absorption features in $K$-band spectra of a dozen symbiotic systems indicate sub-solar carbon abundances and $^{12}$C/$^{13}$C $\sim$ 3 to 30 (\citealt{Sch1992}, \citealt{Sch2003}, \citealt{Sch2006}). All these have indicated that the surveyed symbiotic giants are indistinguishable from local M giants in agreement with abundance studies based on nebular emission lines. \begin{table} \centering \caption{Journal of spectroscopic observations}\label{T2} \begin{tabular}{@{}lcccc@{}} \hline Object & Band & Date & HJD(mid) & Orbital phase$\,^a$\\ \hline & $H$ & 16.02.2003 & 2452686.8380 & 0.57 \\ RW\,Hya & $K$ & 20.04.2003 & 2452749.6295 & 0.74 \\ & $K$ & 13.12.2003 & 2452986.8656 & 0.38 \\ & $K_r$& 03.04.2006 & 2453828.6308 & 0.65 \\ \hline & $H$ & 17.02.2003 & 2452687.7566 & 0.02 \\ SY\,Mus & $K$ & 20.04.2003 & 2452749.5817 & 0.12 \\ & $K$ & 13.12.2003 & 2452986.8250 & 0.50 \\ & $K_r$& 03.04.2006 & 2453828.5767 & 0.84 \\ \hline \end{tabular} \begin{list}{}{} \item[$^a$] Orbital phases calculated for RW\,Hya from orbital ephemerides of \citet{KeMi1995} or \citet{Sch1996} and for SY\,Mus from orbital ephemerides of \citet{Dum1999} \end{list} \end{table} Despite the significant role that knowledge of chemical composition has to play in improving our understanding of the symbiotic systems, there are few cases in which abundances are fairly well determined. Analysis of photospheric chemical abundances has been performed only for a few bright systems: CH\,Cyg - the brightest symbiotic system \citep{Sch2006}, V2116\,Oph - the symbiotic system with a neutron star \citep{Hin2006}, and the symbiotic recurrent novae T\,CrB and RS\,Oph \citep{Wal2008}. In all these cases a solar or nearly solar metallicity was found with Li enhancements in RS\,Oph and T\,CrB the only peculiarity. For CH\,Cyg \citet{Sch2006} found that the isotopic ratios of $^{12}$C/$^{13}$C and $^{16}$O/$^{17}$O are close to the mean values for single M giants that have experienced the first dredge-up. The relatively high metallicity of CH\,Cyg accounts for the absence of chemical peculiarities similar to those seen in Ba stars. The analysis of \citet{Sch2006} has also revealed significant differences between the C/N and O/N ratios derived from nebular emission lines versus those from photospheric absorption lines. This indicates that an analysis based on emission lines can, for some circumstances, seriously overestimate the N abundance. A direct high resolution spectroscopic determination of the photospheric chemical abundances of red symbiotic giants is needed to settle this issue and to explore the abundances of more members of the symbiotic family. We have undertaken an extensive research program to perform detailed chemical composition analysis of a sample of over 30 symbiotic systems. The analysis is based on near-$IR$ spectra observed at high-resolution (R $\sim$ 50000) and high S/N ($\sim$100) during the years 2003-2006 with the Phoenix spectrometer on the Gemini South telescope. The spectral regions observed are located in the $H$ and $K$ photometric bands. Spectrum synthesis employing standard LTE analysis and current model atmospheres was used to determine abundances of CNO and elements around the iron peak (Sc, Ti, Fe, and Ni) in the stellar photospheres. We expect our study to provide clues to resolve the metallicity problem in symbiotic systems as well as important information for understanding the history of these systems. In this paper we present the first analysis of the photospheric chemical abundances (CNO and elements around iron peak: Sc, Ti, Fe, and Ni) for two classical S-type symbiotic systems, RW\,Hya and SY\,Mus. Both of these systems have well known basic parameters (Table\,\ref{T1}) with effective temperatures estimated from the near-IR colors. Both systems also have well established orbital solutions with circular orbits. Near-IR light curves of both systems show ellipsoidal variations which permit an estimation of their red giant radii \citep{Rut2007}. These two systems have tidally distorted giants similar to those in the classical Z\,And-type symbiotic systems but unlike these systems they do not show outburst activity. \begin{table} \centering \caption{Velocity parameters$\,^a$ of the cool components obtained via cross-correlation technique} \label{TvsiC} \begin{tabular}{@{}lccc@{}} \hline & \multicolumn{3}{c}{RW\,Hya} \\ \hline & $(V_{\rmn{rot}}^2 \sin^2{i} + \xi^2_{\rmn{t}})^{0.5}$ & $V_{\rmn{rad}}$ & Orbital phase \\ Feb\,2003 & 5.74 & 11.13 $\pm$ 0.15 & 0.57 \\ Apr\,2003 & 6.63 &~~3.04 $\pm$ 0.34 & 0.74 \\ Dec\,2003 & 6.25 & 18.44 $\pm$ 0.32 & 0.38 \\ Apr\,2006 & 5.57 &~~5.33 $\pm$ 0.41 & 0.65 \\ \hline & \multicolumn{3}{c}{SY\,Mus} \\ \hline & $(V_{\rmn{rot}}^2 \sin^2{i} + \xi^2_{\rmn{t}})^{0.5}$ & $V_{\rmn{rad}}$ & Orbital phase \\ Feb\,2003 & 3.88 & 19.39 $\pm$ 0.15 & 0.02 \\ Apr\,2003 & 5.98 & 19.66 $\pm$ 0.29 & 0.12 \\ Dec\,2003 & 6.84 & 13.14 $\pm$ 0.41 & 0.50 \\ Apr\,2006 & 5.01 &~~4.42 $\pm$ 0.37 & 0.84 \\ \hline \end{tabular} \begin{list}{}{} \item[$^{a}$]\,Units $\rmn{km}\,\rmn{s}^{-1}$ \end{list} \end{table} \begin{table} \centering \caption{Quadrature sums of the projected rotational velocities and microturbulence $(V_{\rmn{rot}}^2 \sin^2{i} + \xi^2_{\rmn{t}})^{0.5}$ from $K$-band \mbox{Ti\,{\sc i}}, \mbox{Fe\,{\sc i}} and \mbox{Sc\,{\sc i}} lines$\,^a$}\label{TvsiF} \begin{tabular}{@{}lcc@{}} \hline & RW\,Hya & SY\,Mus \\ \hline Apr\,2003 & 6.73 $\pm$ 0.60 & 6.91 $\pm$ 0.33 \\ Dec\,2003 & 6.35 $\pm$ 0.24 & 6.97 $\pm$ 0.33 \\ both$\,^{b}$ & 6.54 $\pm$ 0.32 & 6.94 $\pm$ 0.22 \\ \hline \end{tabular} \begin{list}{}{} \item[$^{a}$]\,Units $\rmn{km}\,\rmn{s}^{-1}$ \item[$^{b}$]\,Used for synthetic spectra calculations \end{list} \end{table} \section[]{Observations and data reduction} Spectra of RW\,Hya and SY\,Mus were observed at high-resolution ($R = \lambda/\Delta\lambda \sim 50000$) and high S/N ratio ($\ga$\,100) in the near-IR using the Phoenix cryogenic echelle spectrometer on 8\,m Gemini South telescope. For both objects one spectrum was observed at 1.56$\,\mu$m ($H$-band) during February 2003, two spectra at 2.23$\,\mu$m ($K$-band) during April and December 2003, and one spectrum at 2.36$\,\mu$m ($K_{\rm r}$-band) during April 2006. All the spectra cover a narrow spectral range of $\sim$100\AA. The spectra were extracted and wavelength calibrated using standard reduction techniques \citep{Joy1992} and all were heliocentric corrected. In all cases telluric lines were either not present in the interval observed or were removed by reference to a hot standard star. For all spectra the Gaussian instrumental profile is about of $6\,\rmn{km}\,\rmn{s}^{-1}$ FWHM, corresponding to instrumental profile widths of 0.31\,\AA\ , 0.44\,\AA\, and 0.47\,\AA\ for the $H$-band, $K$-band, and $K_{\rm r}$-band spectra, respectively. The journal of our spectroscopic observations is given in Table\,\ref{T2} and the spectra of RW\,Hya and SY\,Mus are shown in Figures \ref{FRWSc1_H}--\ref{FRWSc1_Kb} and \ref{FSYSc2_H}--\ref{FSYSc2_Kb}, respectively. \begin{table} \centering \caption{Calculated abundances and relative abundances$\,^a$, velocity parameters$\,^b$, and uncertainties$\,^c$ for RW\,Hya and SY\,Mus }\label{TaSc1} \begin{tabular}{@{}lccccr@{}} \hline &\multicolumn{2}{c}{RW\,Hya} &\multicolumn{2}{c}{SY\,Mus} &\\ $X$ & $\log{\epsilon(X)}$ & [$X$] & $\log{\epsilon(X)}$ & [$X$] & n$\,^d$\\ \hline $^{12}$C & 7.53$\pm$0.02 & -0.90$\pm$0.07 & 8.17$\pm$0.01& -0.26$\pm$0.06 & 90\\ N & 7.46$\pm$0.03 & -0.37$\pm$0.08 & 8.11$\pm$0.02& +0.28$\pm$0.07 & 62\\ O & 8.17$\pm$0.01 & -0.52$\pm$0.06 & 8.66$\pm$0.01& -0.03$\pm$0.06 & 49\\ Sc & 2.71$\pm$0.05 & -0.44$\pm$0.09 & 3.97$\pm$0.05& +0.82$\pm$0.09 & 1\\ Ti & 4.49$\pm$0.05 & -0.46$\pm$0.10 & 5.12$\pm$0.03& +0.17$\pm$0.08 & 9\\ Fe & 6.74$\pm$0.02 & -0.76$\pm$0.06 & 7.42$\pm$0.02& -0.08$\pm$0.06 & 21\\ Ni & 5.63$\pm$0.03 & -0.59$\pm$0.07 & 6.37$\pm$0.03& +0.15$\pm$0.07 & 3\\ $^{12}$C/$^{13}$C& 6$\pm$2~ & ... & 10$\pm$3~ & ... & $\frac{66}{16}^e$\\ \hline $\xi_{\rmn{t}}$ &\multicolumn{2}{c}{1.8$\pm$0.2} &\multicolumn{2}{c}{2.0$\pm$0.2} & ... \\ $V_{\rmn{rot}} \sin{i}$ &\multicolumn{2}{c}{6.3$\pm$0.2} &\multicolumn{2}{c}{6.6$\pm$0.2} & ... \\ \hline \end{tabular} \begin{list}{}{} \item[$^a$] Relative to the Sun [$X$] abundances estimated in relation to the solar composition of \citet{Asp2009} \item[$^b$] Units $\rmn{km}\,\rmn{s}^{-1}$ \item[$^c$] 3$\sigma$ \item[$^d$] Number of lines used \item[$^e$] Number of lines used to estimate $^{12}$C/$^{13}$C isotopic ratio: 66 lines for $^{12}$C and 16 lines for $^{13}$C.\\ \end{list} \end{table} | We have performed a detailed analysis of the photospheric abundances of CNO and elements around the iron peak (Sc, Ti, Fe, and Ni) for the red giant components of RW Hya and SY Mus. Our analysis reveals a significantly sub-solar metallicity ([Fe/H]$\sim$\mbox{-0.75}) for the RW\,Hya giant, confirming its membership in the Galactic halo population, and a near-solar metallicity in SY\,Mus. The very low $^{12}$C/$^{13}$C isotopic ratios, $\sim$6--10, derived for both objects and their N enrichment indicate that the giants have experienced the first dredge-up. | 14 | 3 | 1403.2659 |
1403 | 1403.5553_arXiv.txt | We formulate and solve the Slepian spatial-spectral concentration problem on the three-dimensional ball. Both the standard Fourier-Bessel and also the Fourier-Laguerre spectral domains are considered since the latter exhibits a number of practical advantages (spectral decoupling and exact computation). The Slepian spatial and spectral concentration problems are formulated as eigenvalue problems, the eigenfunctions of which form an orthogonal family of concentrated functions. Equivalence between the spatial and spectral problems is shown. The spherical Shannon number on the ball is derived, which acts as the analog of the space-bandwidth product in the Euclidean setting, giving an estimate of the number of concentrated eigenfunctions and thus the dimension of the space of functions that can be concentrated in both the spatial and spectral domains simultaneously. Various symmetries of the spatial region are considered that reduce considerably the computational burden of recovering eigenfunctions, either by decoupling the problem into smaller subproblems or by affording analytic calculations. The family of concentrated eigenfunctions forms a Slepian basis that can be used be represent concentrated signals efficiently. We illustrate our results with numerical examples and show that the Slepian basis indeeds permits a sparse representation of concentrated signals. | It is well-known that functions cannot have finite support in both the spatial~(or time) and spectral~(or frequency) domain at the same time~\cite{Slepian:1960,Slepian:1983}. This fundamental problem of finding and representing the functions that are optimally energy concentrated in both the time and frequency domains was solved by Slepian, Landau and Pollak in the early 1960s~\cite{Slepian:1960,Landau:1961,Landau:1962,Slepian:1965}. This problem, herein referred to as the \emph{Slepian spatial-spectral concentration problem}, or \emph{Slepian concentration problem} for short, gives rise to the orthogonal families of functions that are optimally concentrated in the spatial (spectral) domain and exactly limited in the spectral (spatial) domain. These families of functions and their multidimensional extensions~\cite{Slepian:1964} have been extensively used in various branches of science and engineering~(e.g., signal processing~\cite{Thomson:1982,Mathew:1985}, medical imaging~\cite{Jackson:1991}, geophysics~\cite{Thomson:1976}, climatology~\cite{Thomson:1990}, to name a few). Although the the Slepian spatial-spectral concentration problem was initially formulated and solved in the Euclidean domain, generalizations for various geometries and connections to wavelet analysis have also been well-studied~(e.g., \cite{Meaney:1984,Daubechies:1988,Cohen:1989,Daubechies:1990,Albertella:1999,Mortlock:2002,Fernández:2003,Wieczorek:2005,Simons:2006}). We note that the Slepian concentration problem for functions defined on the two-sphere $\untsph$ has been thoroughly revisited and investigated~\cite{Albertella:1999,Simons:2006,Wieczorek:2005}. The resulting orthogonal family of band-limited spatially concentrated functions have been applied for localized spectral analysis~\cite{Wieczorek:2007} and spectral estimation~\cite{Dahlen:2008} of signals~(finite energy functions) defined on the sphere. There are also many applications~\cite{Leistedt:2012,Simons:2011_1,Simons:2011_2} where signals or data are defined naturally on the three-dimensional ball, or ball for short. For example, signals defined on the ball arise when observations made on the sphere are augmented with radial information, such as depth, distance or redshift. Recently, a number of signal processing techniques have been tailored and extended to deal with signals defined on the ball (e.g., \cite{Simons:2011_1,Lanusse:2012,Leistedt:2012}). In this paper, we pose, solve and analyse the Slepian concentration problem of simultaneous spatial and spectral localization of functions defined on the ball. By considering Slepian's quadratic~(energy) concentration criterion, we formulate and solve the problems to: (1) find the band-limited functions with maximum concentration in some spatial region; and (2) find the space-limited functions with maximum concentration in some region of the spectral domain. Each problem is formulated as an eigenvalue problem, the solution of which gives the orthogonal family of functions, referred as eigenfunctions, which are either spatially concentrated while band-limited, or spectrally concentrated while space-limited. These eigenfunctions serve as an alternative basis on the ball, which we call a Slepian basis, for the representation of a band-limited or space-limited signal. We show, and also illustrate through an example, that the representation of band-limited spatially concentrated or space-limited spectrally concentrated functions is sparse in the Slepian basis, which is the essence of the Slepian spatial-spectral concentration problem. We also derive the spherical Shannon number as an equivalent of the Shannon number in the one dimensional Slepian concentration problem~\cite{Slepian:1965,Percival:1993}, which serves as an estimate of the number of concentrated functions in the Slepian basis. For the spectral domain characterization of functions defined on the ball we use two basis functions: (1) spherical harmonic-Bessel functions, which arise as a solution of Helmholtz's equation in three-dimensional spherical coordinates, and are referred to as \emph{Fourier-Bessel}\footnote{A more appropriate terminology would be spherical harmonic-Bessel basis, however we adopt the established convention of using the term Fourier to denote the spherical harmonic part.} basis functions; and (2) spherical harmonic-Laguerre functions, which are referred to as \emph{Fourier-Laguerre} basis functions. We consider the Fourier-Laguerre functions in addition to the standard Fourier-Bessel functions, as the Fourier-Laguerre functions serve as a complete basis for signals defined on the ball, enable the decoupling of the radial and angular components of the signal, and support the exact computation of forward and inverse Fourier-Laguerre transforms~\cite{Leistedt:2012}. We show that the eigenvalue problem to find the eigenfunctions or Slepian basis can be decomposed into subproblems when the spatial region of interest is symmetric in nature. We consider two types of symmetric regions: (1) circularly symmetric regions; and (2) circularly symmetric and radially independent regions. As Slepian functions on the one-dimensional Euclidean domain~\cite{Slepian:1960,Landau:1961,Landau:1962,Slepian:1965}, and other geometries~\cite{Slepian:1964,Meaney:1984,Albertella:1999,Fernández:2003,Simons:2006}, have been widely useful in a diverse variety of applications, we hope that the proposed orthogonal family of Slepian eigenfunctions on the ball will find similar applications in fields such as cosmology, geophysics and planetary science, where data/signals are often inherently defined on the ball. For example, the band-limited spatially concentrated eigenfunctions can be used as window functions to develop multi-window spectral estimation techniques~\cite{Thomson:1982,Thomson:1990,Dahlen:2008,Wieczorek:2005} for the estimation of the signal spectrum from observations made over the limited spatial region. We organize the remainder of the paper as follows. The mathematical preliminaries for functions on the ball are presented in \secref{sec:maths}. The Slepian concentration problem is posed as an eigenvalue problem in \secref{sec:conc_problem} and the resulting eigenfunctions are analysed in \secref{sec:eignfunctions_analysis}. The decomposition of the eigenvalue problem into subproblems for the case of special, but important, symmetric spatial regions is presented in \secref{sec:special_regions}. The representation of spatially concentrated band-limited functions in the Slepian basis is discussed and illustrated in \secref{sec:Applications}. Concluding remarks are made in \secref{sec:conclusions}. | \label{sec:conclusions} We have formulated and solved the Slepian spatial-spectral concentration problem on the ball. We consider two domains for the spectral characterization of the signal defined on the ball, namely the Fourier-Bessel domain and the Fourier-Laguerre domain. The Fourier-Laguerre domain is considered in addition to the standard Fourier-Bessel domain since the former has a number of practical advantages. The orthogonal families of band-limited spatially concentrated functions and of space-limited spectrally concentrated functions can be computed as solutions of eigenvalue problems. The spatially and spectrally concentrated eigenfunctions that arise as solutions of these eigenvalue problems coincide with each other inside both the spatial and spectral regions of interest. The eigenvalue associated with each eigenfunction is a measure of both the spatial concentration of the band-limited function and of the spectral concentration of the space-limited function. The number of well-concentrated~(significant) eigenfunctions depends on the spherical Shannon number, which also serves as the dimension of the space of functions that can be concentrated in both the spatial and spectral domains at the same time. When the spatial region of interest is rotationally symmetric and/or radially independent, the eigenvalue problem decomposes into subproblems, which reduces the computational burden significantly. The family of concentrated eigenfunctions can be used to form an orthonormal basis, or Slepian basis, which provides a sparse representation of concentrated functions. Just as the Slepian basis in the one-dimensional Euclidean domain and other geometries have proven to be extremely valuable, we hope the Slepian eigenfunctions on the ball developed in this work will prove useful in a variety of applications in various fields of science and engineering~(e.g., geophysics, cosmology and planetary science), where signals are inherently defined on the ball. Some applications where the proposed orthogonal family of eigenfunctions~(Slepian basis) are likely to be of use are the estimation of signals, their power spectrum, and other statistics, when noisy observations on the ball can only be made over partial fields-of-views. For example, surveys of the distribution of Galaxies in our Universe are observed only over partial fields-of-view \cite{ahn:2012} on the ball, while their statistical properties can be used to infer the physics of our Universe, such as the nature of dark energy and dark matter. | 14 | 3 | 1403.5553 |
1403 | 1403.0006_arXiv.txt | In our own solar system, the necessity of understanding space weather is readily evident. Fortunately for Earth, our nearest stellar neighbor is relatively quiet, exhibiting activity levels several orders of magnitude lower than young, solar-type stars. In protoplanetary systems, stellar magnetic phenomena observed are analogous to the solar case, but dramatically enhanced on all physical scales: bigger, more energetic, more frequent. While coronal mass ejections (CMEs) could play a significant role in the evolution of protoplanets, they could also affect the evolution of the central star itself. To assess the consequences of prominence eruption/CMEs, we have invoked the solar-stellar connection to estimate, for young, solar-type stars, how frequently stellar CMEs may occur and their attendant mass and angular momentum loss rates. We will demonstrate the necessary conditions under which CMEs could slow stellar rotation. | On young stars, we observe flares hundreds to ten thousand times more energetic and frequent than solar flares. Along with energy scales greater by orders of magnitude, we also observe physical scales far greater than in the solar case: while solar prominences soar around 1 R$_{\odot}$ above the solar surface and CMEs launch from similar radii in the Sun's atmosphere, magnetic structures on T Tauri Stars (TTS, young solar analogs)--post-flare loops and prominences--can extend tens of stellar radii from the star's surface. The discovery of such large magnetic structures arose from solar-stellar analogy, applying solar flare models to the X-ray light curve data from young stars \cite[(e.g., Reale et al. 1998)]{Reale:1998}. In characterizing the solar-stellar connection, overwhelming evidence has been found in support of the idea that the fundamental physics of magnetic reconnection is the same, despite differences in stellar parameters (e.g., mass, radius, $B$, age). As such, we approach analysis of young stars' flares and CMEs under this supposition, and aim to assess how the physical properties of these events--and their frequency--may scale accordingly with stellar parameters. Ultimately, we seek to understand the consequences of exoplanetary space weather on protostellar systems and their forming planets. | \label{disc} We have shown that for young, solar-type stars, spin down due to CMEs might play a significant role in stellar rotation evolution after the star has ceased accreting. Our Figs. \ref{fig1} and \ref{fig2} illustrate a critical selection effect in performing this kind of calculation: we only have data for the most active young stars, or the star conveniently located at 1 AU. There is a dearth of data for older, less active stars, and we suggest that filling in the gaps in flare X-ray energy could trace age evolution in these parameter spaces. The addition of data from the $\sim$20-50 Myr old K dwarfs in Fig. \ref{fig1} hints at this, but more data are needed to conclusively show age dependence. In both figures, we have taken care to specify the masses of the stars involved: how would evolution with stellar age look in these parameter spaces as a function of stellar mass? While the fundamental physics are the same, the scaling could change, and the ramifications certainly would. For low-mass stars in particular, high activity levels are observed for longer fractions of the stars' lives; this could have grave implications for exoplanets as these stars' habitable zones could be within range of extreme exo-weather. | 14 | 3 | 1403.0006 |
1403 | 1403.5547_arXiv.txt | {} { We present a new set of weak-line abundances of HII regions in M81, based on Gemini Multi-Object Spectrograph (GMOS) observations. The aim is to derive plasma and abundance analysis for a sizable set of emission-line targets to study the galactic chemical contents in the framework of galactic metallicity gradients.} {We used the weak-line abundance approach by deriving electron density and temperatures for several HII regions in M81. Gradient analysis is based on oxygen abundances.} {Together with a set of HII region abundances determined similarly by us with Multi-Mirror Telescope (MMT) spectra, the new data yield to a radial oxygen gradient of -0.088$\pm$0.013 dex kpc$^{-1}$, which is steeper than the metallicity gradient obtained for planetary nebulae (-0.044$\pm$0.007 dex kpc$^{-1}$). This result could be interpreted as gradient evolution with time: Models of galactic evolution with inside-out disk formation associated to pre-enriched gas infall would produce such difference of gradients, although stellar migration effects would also induce a difference in the metallicity gradients between the old and young populations. } {By comparing the M81 metallicity gradients with those of other spiral galaxies, all consistently derived from weak-line analysis, we can infer that similar gradient difference is common among spirals. The metallicity gradient slopes for HII regions and PNe seem to be steeper in M81 than in other galactic disks, which is likely due to the fact that M81 belongs to a galaxy group. We also found that M81 has experienced an average oxygen enrichment of 0.14$\pm$0.08 dex in the spatial domain defined by the observations. Our data are compatible with a break in the radial oxygen gradient slope around R$_{25}$ as inferred by other authors both in M81 and in other galaxies.} | The metallicity of a galaxy carries the signature of its history, including various phenomena such as gas accretion during the first epochs (infall), star formation, and subsequent gas outflow/inflow. Among the various observational constraints that can shed light on the galaxy past, an important one is the radial metallicity gradient-- and its evolution with time-- which is sensitive to the assembly history at different radii, and thus tells a story about galaxy formation and evolution processes. From an observational point of view, during the last decades the study of the gradient evolution has been mainly investigated through the determination of the metallicity of resolved populations with different ages in the Milky Way and in nearby galaxies. Measurements of metallicity of different targets in the Local Universe (for instance young OB stars and HII regions, Cepheids, open clusters, red giant stars) have shown that disk galaxies usually exhibit negative radial metallicity gradients, with higher metallicity in their inner regions and lower metallicity at larger galactocentric radii (e.g., Vila-Costas \& Edmunds 1992; Zaristisky et al. 1994; Rupke et al. 2010). It was also found that, in several cases, the radial gradient becomes flatter at large radii (e.g., Werk et al. 2011; Bresolin et al. 2012; CALIFA survey results described in Sanchez et al. 2013). Very recently, more attention has also been devoted to measurements of the time evolution of metallicity gradients and its consequent implications for galaxy formation and evolution. In the Galaxy, two stellar tracers have been essentially used to investigate the time evolution of the radial gradient: open clusters and planetary nebulae (PNe). Open clusters represents a reliable approach to the study of the time evolution of the metallicity gradient, since it is possible to firmly determine their age, Galactocentric distances, and abundances of a large number of elements (see, e.g., Janes 1979; Freeman \& Bland-Hawthorn 2002; Friel et al. 2002; Magrini et al. 2009a; Bland-Hawthorn et al. 2010; Kobayashi \& Nakasato 2011, Yong et al. 2012). From the recent high spectral resolution studies of open clusters in the inner Galaxy (R$_{\rm G}<$ 13~kpc) the older open clusters show a steeper abundance gradient than the younger clusters, implying thus a slight gradient flattening with time in the inner Galaxy. Planetary nebulae in principle should allow to detect the time evolution of the gradient by comparing the present-time gradient, as outlined by HII regions, with that of PNe of different ages. In our Galaxy however the distances to PNe are affected to large uncertainties that restrict their use as tracers of the past evolution of metallicity gradients. The best distance scale available to date is the one calibrated on the Magellanic Cloud PNe observed with the {\it Hubble Space Telescope (HST)} (Stanghellini et al. 2008). This distance scale is very similar to Cahn et al. (1992)'s scale, the most commonly used to date. Stanghellini \& Haywood (2010) used Stanghellini et al. (2008)'s scale and oxygen abundances from weak-line analysis to determine Galactic metallicity gradients with PNe of different progenitor ages. The sample of PNe analyzed by Stanghellini \& Haywood (2010) had been parsed into age bins based on their location with respect to the Galactic plane, their peculiar radial velocity, and their nitrogen and helium contents. In fact, the mass range of PN progenitors can be constrained by comparing the observed N and He enrichment to the yields from stellar evolution; this allows to mark the time of PN progenitor formation, and consequently allows the determination of chemical enrichment when comparing $\alpha$-element abundances in young and old populations. The nebular parameters listed above have typically low uncertainties, and are only marginally dependent on assumptions. Stanghellini \& Haywood (2010) found a very mild steepening of the gradient with time, but the evolution is not significant given the distance scale uncertainties. On the other hand, Maciel and Costa (2013) determined the radial metallicity gradients of several PN populations with Cahn et al. (1992)'s distance scale, and by using the PN central star properties to date the PN populations; they found radial gradients almost invariant with time, with differences consistent with the age-metallicity dispersion. The different results by the two PN teams could be ascribed to uncertainties associated with dating PN based on central stars -- given that stellar progenitors could have had a non-conventional evolution such as common envelope binaries -- rather than to the distance scale used. In external galaxies, where PNe can be assumed, to first order, at the same distance of the host galaxy, the comparison of PNe and HII region abundances, investigated with similar observational and analysis techniques, has given reliable results (e.g., Magrini et al. 2007, 2010; Stanghellini et al. 2010; Stasinska et al. 2013). The large database of PNe and HII regions in M33 indicate that the galaxy underwent a global enrichment similar at all radii, and that the slope of the gradient was essentially unvaried (Magrini et al. 2010). For NGC~300, Stasinska et al. (2013) found that the formal abundance gradients of PNe are shallower than for HII regions. However, their large observed abundance dispersion and the small statistics on which their results are based make any conclusion on a possible steepening of the gradients with time only tentative. An alternative approach to the study of the time evolution of metallicity gradients is to derive them at different cosmic epochs, and to compare with local $z$=0 galaxies, taking care of considering galaxies with equivalent dark matter halos. Some pioneering studies have found unexpected results that suggest that some massive galaxies may show positive gradients with lower metallicity in the central regions (Cresci et al. 2010; Queyrel et al. 2012) at very high redshift ($z$$\sim$3). These galaxies, however, are likely progenitors of present time massive elliptical galaxies and should be not compared with present disk galaxies. Other recent studies were instead based on the analysis of high-$z$ lensed galaxies: Jones at al. (2010) measured the metallicity gradient of a gravitationally lensed galaxy at $z$=2 finding it significantly steeper than in local disk galaxies. A similar result was obtained in another lensed galaxy at $z$=1.5 (Yuan et al. 2011). Other four lensed galaxies were studied very recently by Jones et al. (2013) who compared them with galaxies at lower redshift selected to occupy equivalent dark matter halos. They found that, on average, gradients flatten by a factor of $\sim$2.6 between $z$=2.2 and $z$=0, in agreement with size evolution measured for more massive galaxies by van Dokkum et al. (2010). The emerging scenario at this time is that several Local Universe observations have shown the presence of metallicity gradients in old populations, such as PNe and open clusters. Since radial migration is able only to flatten the gradient redistributing the stars of different ages (see, e.g., Fig.~2 of Roskar et al 2008; Michev et al. 2013), the observations of non null gradients in old population imply that the effect of radial migration of stellar population is not so strong to cancel them. To date, we do not have a firm conclusion on the evolution of the gradients in the Local Universe since different authors found discordant results. However we can conclude that all results are in the framework of a limited evolution of the slope with time. From the high-$z$ Universe observations, the new set of observations of lensed galaxies (consistent to be present disk-galaxy progenitors) show steeper gradients than that observed presently in disk galaxies. If we compare the high-$z$ results with Fig.~2 in Roskar et al. (2008), we can see that they are not inconsistent with what observed with old stellar population in Local Universe galaxies. From a theoretical point of view, different types of classical chemical evolution models --where "classical" means that they do not consider the cosmological context, and they do not consider dynamical effects--predict different temporal behaviors of the metallicity gradients due to the different rates of the chemical enrichment in inner and outer regions of the galactic disk related to the star formation and infall processes. The models can be broadly divided in those where the metallicity gradients steepen with time (Chiappini et al. 1997; Chiappini et al. 2001) and those where they flatten with time (Moll{\'a} et al. 1997; Portinari \& Chiosi 1999; Bossier \& Prantzos 1999; Hou et al. 2000; Magrini et al. 2007, 2009b). However, classical models have been recently overcame by the development of models of formation and evolution of galaxies created in a cosmological context (see, e.g., Rahimi et al. 2011, Pilkington et al. 2012, Gibson et al. 2013) and by models that join chemical evolution with dynamical aspects (see. e.g., Michev et al. 2013). Only recently these new set of models reached a spatial resolution able to investigate the shape of the metallicity gradients and its evolution with time. The conclusions given by Gibson et al. (2013) are instructive of the present time situation. With their modeled galaxies, realized with different assumptions (e.g., with different feedback implementations) they can obtain both gradients that only mildly steepen with time, and metallicity gradients steeper at high redshift, that subsequently flatten with time. Both results have an observational counterparts, and thus they conclude that more constraints from the local and high-redshift Universe are necessary to provide more definitive conclusions on the time evolution of the gradients. To a similar conclusions arrives Moll{\'a} et al. (2014), where spectro-photometric models show a moderate flattening of the radial gradients with decreased redshift, flattening that tend to be less noticeable when only the inner parts of the galaxies are accounted for. Aiming at adding more constraints to the evolution of radial metallicity gradients, we embarked in observing a significant sample of HII regions in M81, a nearby (3.63$\pm$0.34 Mpc, Freedman et al. 2001) spiral galaxy whose membership to a tidal group is evident from its extended tidal streams, clearly observed in the HI emission line (Gottesman \& Weliachew 1975; Yun et al. 1994). Several tools are available to understand the chemical evolution of the M81 disk: star clusters (Ma et al. 2005, Nantais et al. 2011), young supergiant stars (Davidge 2006), X-ray sources (Sell et al. 2011), and color-magnitude diagram fitting to the HST-resolved stellar population (Kudritzki et al., 2012). Nonetheless, emission-line targets such as HII regions and PNe have advantages over their stellar counterparts since PNe and HII region spectra are analyzed in similar ways, making the comparison of the two sets of probes more direct than when comparing sources of different nature. HII regions and PNe represent different star formation epochs in the galaxy evolutionary history, HII regions probing the stellar population currently formed, and PNe being the gaseous remnants of stars formed 1-10 Gyr ago; studied together the two populations provide the temporal dimension of galactic evolution. The study of chemical evolution through emission-line probes in M81 has been attempted before. Garnett \& Shields (1987) have used strong-line abundances to constrain the radial metallicity gradient of the M81 disk with oxygen abundances of HII regions, finding a negative gradient of about -0.08 dex kpc$^{-1}$ at intermediate (4-12 kpc) galactocentric radii. The strong-line method provides estimate of elemental abundances, while the weak-line method utilizes auroral line strengths to determine electron temperatures directly, and it is much more accurate in determining ionic abundances. M81 has a well-defined, shallow PN metallicity gradient from weak-line analysis (Stanghellini et al. 2010); several HII regions have been studied within the same paper as well, but the characterization of the radial metallicity gradient has not been possible given the limited number of probes observed. While direct comparison of emission line abundances from probes of different progenitors has been attempted successfully in M33 and NGC 300, to date there are no other nearby spirals where adequate spectroscopy is available for both PNe and HII regions to determine weak-line abundances. This paper represents a continuation of these abundance studies started by us with M33 (Magrini et al. 2009b, 2010), and M81 (Stanghellini et al. 2010). Here, we present the weak-line abundances from a new dataset of HII region spectroscopy in the inner 12 kpc of M81. We observed two M81 fields with the Gemini Multi-Object Spectrograph (GMOS) on Gemini North with the aim of obtaining weak-line abundances for HII regions that would define the radial metallicity gradient in the inner parts of M81, with the main goal to study their metallicity gradient and chemical enrichment. We present the data acquisition and analysis in $\S$2; the radial metallicity gradients and metal enrichment of M81 based on our data are in $\S$3; the discussion, in $\S$4, includes a comparison of M81 weak-line abundance gradients with those of other galaxies. The conclusions are given in $\S$5. | Weak-line abundance analysis is performed for a sample of HII regions in M81, based on GMOS/Gemini multi-object spectroscopy. Together with other datasets we have collected in the past with the MMT we found oxygen enrichment of 0.14$\pm$0.08 dex in M81. We also found a radial metallicity gradient $\Delta$log(O/H)/$\Delta$R$_{\rm G}=-0.088\pm$0.013 dex kpc$^{-1}$, when using HII regions as probes. Compared to the PN gradient, which is recalculated here based on new PN identifications, to be -0.044$\pm$0.007 dex kpc$^{-1}$, this result is consistent with the metallicity gradient steepening with time since galaxy formation, if stellar migration is not accounted for. Compared to other galaxies for which these diagnostics are available, there is consistency of gradient steepening with time in the Galaxy, M33, and NGC 300, in addition to M81. It appears that the gradient has steepened in M81 more than in the other galaxies examined by weak-line abundances. Our M81 data are consistent with a negative HII region oxygen gradient in the inner galaxy, but they can not exclude a flat gradient in the outer galactic regions, as indicated by Patterson et al.'s (2012). A better handle on this possibility could be offered by observing other M81 fields in the outer zones where the gradient seems to break. This would actually be the first direct test of a radial metallicity break by using only weak-line abundances. The results obtained in this work are based solely on weak-line abundances, from direct empirical methods. We avoid to mix the weak-line and strong-line derived abundances in order to obtain as pure a sample as possible. By deriving abundance using the strong-line method, possibly based on calibrations within our own observations, would have certainly enlarged the sample size and lower the formal gradient errors. Abundances derived from the two methods have different errors and might have different systematics. Furthermore, abundances from strong-line fitting formulae can have intrinsic errors of $\sim$0.5 dex, and the gradients in spiral galaxies are very shallow in general, which makes a bad combination for precise gradient studies. Both the abundances presented here for M81 from GMOS, and those from the MMT observations, have large error bars. We also note that, while statistically accurate, the difference in gradient is below 3$\sigma$ and can be seen as tentative at this stage. Although we have been conservative in the error bar estimates, it is clear that this abundance determination method has been pushed very far here. It is worth noting that the GMOS time allocated for this project was about 70$\%$ of the time requested, thus the S/N ratio for some of the diagnostics lines of regions that are listed now as lower limits to fluxes could have been completely analyzed with the original allocation of time. We plan in the future to observe additional HII regions to better define the metallicity gradient both for the inner and outer regions of this galaxy, in particular to augment the radial extent of the analysis. Also, we plan to extend this type of analysis to other spiral galaxies with different masses, metallicities, and environment conditions, to enlarge the database to study metallicity gradients and their evolution. More progress could be taken forward with the data on hand by modeling the regions studied with photoionization analysis in a self-consistent way. We aim to reproduce the observed abundances with the observed emission lines, and to continue enriching the sample of spiral galaxies for which these diagnostics will be available. | 14 | 3 | 1403.5547 |
1403 | 1403.5292_arXiv.txt | We explore secular dynamics of a recently discovered hierarchical triple system consisting of the radio pulsar PSR J0337+1715 and two white dwarfs (WDs). We show that three body interactions endow the inner binary with a large forced eccentricity and suppress its apsidal precession, to about $24\%$ of the rate due to the general relativity. However, precession rate is still quite sensitive to the non-Newtonian effects and may be used to constrain gravity theories if measured accurately. Small value of the free eccentricity of the inner binary $e_{i}^{\rm free}\approx 2.6\times 10^{-5}$ and vanishing forced eccentricity of the outer, relatively eccentric binary naturally result in their apsidal near-alignment. In addition, this triple system provides a unique opportunity to explore excitation of both eccentricity and inclination in neutron star-WD (NS-WD) binaries, e.g. due to random torques caused by convective eddies in the WD progenitor. We show this process to be highly anisotropic and more effective at driving eccentricity rather than inclination. The outer binary eccentricity as well as $e_{i}^{\rm free}$ exceed by more than an order of magnitude the predictions of the eccentricity-period relation of Phinney (1992), which is not uncommon. We also argue that the non-zero mutual inclination of the two binaries emerges at the end of the Roche lobe overflow of the outer (rather than the inner) binary. | \label{sect:intro} Recent discovery of a triple system harboring two white dwarfs (WDs) and a millisecond pulsar PSR J0337+1715 (Ransom \etal 2014) is intriguing because of the complicated evolutionary history that this system must have undergone (Tauris \& van den Heuvel 2014, hereafter TvdH14). It also represents an interesting testbed of the Newtonian dynamics which can be explored at very high accuracy. In particular, high masses of the WD companions make gravitational three body effects quite significant. A pulsar for which such study has been done previously is PSR 1257+12 (Wolszczan \& Frail 1992) but it is orbited by three planetary mass objects (Rasio \etal 1992, Malhotra 1993). In addition, high timing accuracy of PSR J0337+1715 (Ransom \etal 2014) makes this system well suited for studying orbital dynamics. Mutual gravitational interactions between the orbiting bodies are also being explored in systems of multiple extrasolar transiting planets discovered by {\it Kepler} satellite, using the so-called {\it transit timing variations} (TTVs; e.g. Mazeh \etal 2013). However, planetary transits usually have timing accuracy of order minutes, while PSR J0337+1715 already yields median arrival time uncertainty of $0.8\mu$s in 10 s integrations. Moreover, pulsar timing has the benefit of revealing the variations of orbital parameters over the {\it full orbit}, while TTVs inform us only about the system parameters at the moments of mutual conjunctions of eclipsing bodies. Our present goal is to explore secular evolution of the PSR J0337+1715 system and to provide possible connections to its origin. This system is hierarchical in nature, with the semi-major axis of the outer binary $a_o=1.76498\times 10^{13}$ cm far exceeding that of the inner binary $a_i=4.776\times 10^{11}$ cm. The two features of its present day dynamical architecture are rather intriguing. First, the orbits of the inner and outer binaries are highly coplanar: their mutual inclination $i=1.2\times 10^{-2\circ}$ is small but is certainly non zero. Second, the orbital ellipses of the inner and outer orbits are quite well aligned: the difference of their apsidal angles is small, $\varpi_i-\varpi_o=1.9987^\circ$. Understanding the origin of these dynamical peculiarities of the PSR J0337+1715 system will be one of the goals of this work. | \label{sect:disc} Small value of the forced eccentricity of the outer binary implies that its eccentricity vector ${\bf e}_o$ is always very well aligned with the forced eccentricity vector of the inner binary ${\bf e}_i^{\rm forced}$, see equations (\ref{eq:in_decomp})-(\ref{eq:in_forced}) and (\ref{eq:out_decomp})-(\ref{eq:out_forced}). The only significant source of misalignment between ${\bf e}_i$ and ${\bf e}_o$ is due to the non-zero value of ${\bf e}_i^{\rm free}$. However, because $e_i^{\rm free}\ll e_i^{\rm forced}$ this misalignment is also rather small. Thus, the eccentricity vectors of both binaries are guaranteed to be {\it locked in near-alignment}. As a result, the observed close apsidal alignment between the two binaries at present epoch ($|\varpi_i-\varpi_o|=1.9987^\circ$) does not require unique circumstances such as observing the system at a special moment of time. The inferred misalignment is in fact close to the maximum possible max$|\varpi_i-\varpi_o|=\mbox{asin} \left|e_i^{\rm free}/e_i^{\rm forced}\right| \approx 2.16^\circ$, given the smallness of $e_i^{\rm free}$. Collinearity of ${\bf e}_o$ and ${\bf e}_i^{\rm forced}$ also explains why $\dot\varpi_i$ and $\dot\varpi_o$ are of the same order of magnitude --- they would be exactly equal if ${\bf e}_i^{\rm free}$ were zero. However, because ${\bf e}_i^{\rm free}$ is not zero and period of free precession of the inner binary is shorter that that of the ${\bf e}_i^{\rm forced}$ circulation, we find that $\dot\varpi_i$ exhibits significant variability around the value corresponding to $\dot\varpi_o$, see Figure \ref{fig:inner_ev}. \begin{figure} \plotone{sec_ev_out.ps} \caption{Same as Figure \ref{fig:inner_ev} but for the outer binary. \label{fig:outer_ev}} \end{figure} Note that these conclusions rely on the use of secular approximation and strictly speaking apply to the orbital evolution of the system on long ($\sim P_+$ and longer) intervals. In reality orbital parameters of both binaries will also oscillate on shorter timescales (e.g. $P_o$) due to the short-period terms in the expansion of the disturbing function (Murray \& Dermott 1999). We cannot capture such effects with our orbit-averaged approach. However, we expect the amplitude of short-term variations to be small compared to the secular ones. The general behavior of the system should still be reasonably well described by our results. \subsection{Period-eccentricity relation} \label{sect:P-e} Millisecond radio pulsars with WD companions are known to obey the so-called {\it eccentricity-period relation}, which states that the eccentricity of the neutron star (NS)-WD binary $e_b$ increases with its orbital period $P_b$ (Lorimer 2008). Phinney (1992) suggested that this correlation emerges at the last stage of the Roche lobe overflow (RLOF) leading to the formation of the WD: random density fluctuations in the envelope of the WD progenitor caused by the convective motions induce stochastic variations of the gravitational quadrupole tensor $Q_{ij}$ of the progenitor. This results in random quadrupole accelerations acting on the NS and drives eccentricity of the binary. Random walk of $e_b$ is balanced by the tidal dissipation in the WD envelope, which results in a well-defined theoretical correlation between $e_b$ and $P_b$. This theory predicts, in particular, the rough equipartition between the kinetic energy of individual convective eddies in the envelope of the WD progenitor and the energy of eccentric motion of the binary. More recent compilations of the binary pulsar properties (Ng \etal 2014) show that many systems deviate from $e_b-P_b$ relation suggested by Phinney (1992) by orders of magnitude in $e_b$. Nevertheless, the general trend of $e_b$ increasing with growing $P_b$ is still observed, see Figure \ref{fig:ecc_per} in which we display properties of 72 binary pulsars with both CO and He WD companions. The data are from the ATNF pulsar catalogue\footnote{http://www.atnf.csiro.au/people/pulsar/psrcat/} (Manchester \etal 2005) and include only NS-WD systems which do not reside in globular clusters. The system of PSR J0337+1715 provides two tests of the $e_b-P_b$ relation, for both binaries. This is because the system must have undergone {\it two} RLOF episodes, within the inner and outer binaries, to arrive to its present configuration with two WDs (TvdH14). \begin{figure} \plotone{ecc_period.ps} \caption{ Eccentricity-period ($e_b-P_b$) relation for binary pulsars with WD companions. Red points are for systems with CO WDs, green are for systems with He WDs. Binaries comprising the system PSR J0337+1715 are indicated with blue points: inner eccentricity $e_i$ (open hexagon), inner free eccentricity $e_i^{\rm free}$ (filled hexagon), outer eccentricity $e_o$ (filled square), and mutual inclination $i$ (dotted line). Downward arrows are the theoretical upper limits on the mutual eccentricity given by equations (\ref{eq:Ie_b_i}) for the inner and (\ref{eq:Ie_b_o}) for the outer binaries. Solid curve shows theoretical $e_b-P_b$ relation from Phinney and Kulkarni (1994), with dashed curves encompassing $95\%$ deviations. \label{fig:ecc_per}} \end{figure} Present day eccentricity of the inner binary, $e_i\approx 6.9\times 10^{-4}$ is more than two orders of magnitude larger $e_b\sim 10^{-6}$ implied by the $e_b-P_b$ relation of Phinney (1992), see Figure \ref{fig:ecc_per}. However, as mentioned in \S \ref{sect:inner}, almost all of this eccentricity is forced by the gravitational perturbations due to the outer WD. Only the free eccentricity $e_i^{\rm free} =e_{i,+}\approx 2.6\times 10^{-5}$, which is much smaller than $e_i$, carries information about the initial conditions for the evolution of the inner binary. Even this low value is still about an order of magnitude higher than the prediction of Phinney (1992), see Figure \ref{fig:ecc_per}. However, same Figure also shows several other NS-WD systems with $P_b$ of order several days and $e_b$ deviating from this relation upward by at least an order of magnitude. Thus, the inner binary of PSR J0337+1715, while disagreeing with the theoretical $e_b-P_b$ correlation, is not an extreme outlier in the general population of the short-period NS-WD binaries. For the outer binary the non-Keplerian gravitational perturbations due to the inner binary play negligible role and its free eccentricity is essentially equal to its current eccentricity $e_0\approx 0.035$. This is more than an order of magnitude higher than $e_b\sim 10^{-3}$ predicted by Phinney (1992) for the orbital period of $P_o=$327 d, see Figure \ref{fig:ecc_per}. On the other hand, there is another pulsar (PSR J1822-0848, Lorimer \etal 2006) in a similar orbit with $P_b=287$ d and high $e_b=0.059$, which also strongly deviates from the $e_b-P_b$ relation, see Figure \ref{fig:ecc_per}. Thus, systems like the outer binary of PSR J0337+1715 are not unique and have been previously known. \subsection{Origin of the binary eccentricities} \label{sect:e_origin} We now explore what do the measurements of binary eccentricities in the PSR J0337+1715 triple tell us about the past history of the system and the $e_b$-excitation mechanisms, focussing on the theory of Phinney (1992). During the RLOF phase of the inner binary its eccentricity has already been driven by the outer WD. Tidal dissipation in the inner WD damps $e_i$ on the characteristic {\it circularization} timescale (Correia 2009; Correia \etal 2011) \ba t_{\rm tid}^e & = & \frac{2}{21}\frac{Q}{k_2}n_i^{-1}\frac{m_i}{m_p} \left(\frac{a_i}{R_i}\right)^5 \label{eq:tidal}\\ & \approx & 1.6\times 10^5 \mbox{yr}\frac{Q/k_2}{10^7}\left(\frac{0.227}{R_i/a_i}\right)^5, \nonumber \ea assuming present-day orbital parameters of the inner binary and $R_i\approx 0.227a_i$ given by the Roche radius formula of Eggleton (1983) for $q=m_i/m_p=0.137$; $k_2$ is the Love number and $Q$ is the tidal quality factor. This timescale is much longer than the characteristic secular timescale $P_+$ of the inner binary, see equation (\ref{eq:P_pm}). It has been shown by Mardling (2007) and Batygin \etal (2009) that in these circumstances tidal dissipation drives ${\bf e}_i$ towards the {\it fixed point} state, in which $|{\bf e}_i|$ is finite and fixed and apsidal lines of the inner and outer binaries are strictly aligned. In this configuration the free eccentricity of the inner binary is damped to zero by tides. One can also show that as long as $\left(A_i-A_0\right) t_{\rm tid}^e\gg 1$ the forced eccentricity of the inner WD is given by the expression computed in the absence of tidal dissipation. Moreover, the stochastic excitation of $e_i$ by the convective eddies has likely been negligible, since it did not result in large present day value of $e_i^{\rm free}$. Thus, during the RLOF phase $e_i$ should have been close to the present-day forced eccentricity $e_i^{\rm forced}=e_{i,-}\approx 6.8\times 10^{-4}$, if the orbital parameters of the triple did not change since then. The tidal dissipation rate due to this non-zero $e_i$ is too small to affect the semi-major axis of the inner binary --- $a_i$ would appreciably change only on timescale $\sim e_i^{-2}t_{\rm tid}^e\gtrsim 10^{11}$ yr. However, the persistent non-zero eccentricity at the RLOF stage might have interesting consequences for the dynamics of the mass transfer through the inner Lagrange point. As the inner WD loses its outer envelope and accretion onto the NS ceases, $t_{\rm tid}^e$ becomes very long, about $2\times 10^{11}$ yr for the present-day inner WD radius $R_i\approx 0.091R_\odot$ (Ransom \etal 2014; Kaplan \etal 2014) and $Q/k_2=10^7$. Any $e_i^{\rm free}$ that is imparted by e.g. the convective eddies in the vanishing envelope of the inner WD at the ``freeze-out'' moment, when $t_{\rm tid}^e$ becomes comparable to the internal evolution timescale of the inner WD, gets inherited by the binary until present time. Whatever process was responsible for the eccentricity excitation, it must have been very efficient at that moment since currently measured $e_i^{\rm free}$ considerably exceeds the prediction of Phinney (1992). Anomalously high eccentricity of the outer binary might be due to the same physical mechanism that excited $e_i$ but operating during the earlier RLOF phase of the outer WD (TvdH14). However, this is just a possibility. Since ${\bf e}_o^{\rm forced}\ll {\bf e}_o^{\rm free}$, it is very hard to imagine that the inner binary has exchanged enough angular momentum with the outer one to excite $e_o$ to the present day value, especially in light of the evolutionary scenario favored by TvdH14, in which the inner binary has always been essentially circular after the birth of the outer WD. Thus, we conclude that non-zero $e_o$ was induced when the outer companion was turning into the WD, either via a very efficient version of the Phinney (1992) mechanism, or by some other means. \subsection{Origin of the mutual inclination} \label{sect:inclin} Triple nature of the PSR J0337+1715 system presents us with a unique chance to explore excitation of the epicyclic motion in a NS-WD binary not only in the orbital plane but also {\it in the direction normal to it}. Measurement of the non-zero angle between the orbital planes of the two binaries, $i=1.2\times 10^{-2~\circ}\approx 2.1\times 10^{-4}$ (Ransom \etal 2014) has a potential to provide us with important clues to the processes sculpting the dynamical architecture of the system. This measurement is interesting because one expects $i$ to be reduced to zero during the RLOF phase of the outer binary, when an accretion disk coplanar with it was engulfing the inner binary. During this stage that could have lasted for $\sim 17$ Myr (TvdH14) gravitational torques acting on the inner binary must have reduced its inclination to zero: the angular momentum deposited into the disk by the inner binary, regardless of whether it was able to clear out an inner cavity in the disk or not, gets communicated by pressure and viscous stresses out to the outer binary, effectively damping their mutual inclination (Artymowicz 1994; Terquem 1998). After the complete orbital alignment of the two binary planes, their non-zero mutual inclination could have been excited by the same underlying mechanism as the binary eccentricity, or a completely different one. Here we will focus on the former possibility, i.e. epicyclic excitation by random forces due to stochastically generated quadrupole in the convective envelope of the WD progenitor (Phinney 1992). This mechanism should naturally drive out-of-plane motion. Indeed, the r.m.s. radial and vertical components of the pulsar acceleration due to stochastically varying WD quadrupole are \ba a_r^{\rm rms}=\frac{3}{2}\frac{G Q_{rr}^{\rm rms}}{a^4},~~~ a_z^{\rm rms}=\frac{G Q_{rz}^{\rm rms}}{a^4}, \label{eq:accels} \ea where $Q_{rr}^{\rm rms}$ and $Q_{rz}^{\rm rms}$ are the r.m.s. values of the relevant diagonal and off-diagonal components of the WD quadrupole tensor. Since non-zero $Q_{ij}$ is due to a superposition of many randomly varying convective eddies, one can show (Phinney 1992) that $Q_{rz}^{\rm rms}=\left(3/4\right)^{1/2}Q_{rr}^{\rm rms}$, so that \ba \frac{a_z^{\rm rms}}{a_r^{\rm rms}}=3^{-1/2}, \label{eq:accel_rat} \ea i.e. inclination is driven somewhat less efficiently than eccentricity. Excitation of $e_b$ and mutual inclination $I$ by the WD quadrupole is balanced by the tidal dissipation and one expects (Phinney 1992) their equilibrium values to scale as $e_b\propto \left(t_{\rm tid}^e\right)^{1/2}a_r^{\rm rms}$, $I\propto \left(t_{\rm tid}^i\right)^{1/2}a_z^{\rm rms}$, where $t_{\rm tid}^e$ is given by equation (\ref{eq:tidal}) and $t_{\rm tid}^i$ is the inclination damping time. Thus, one expects \ba \frac{I}{e_b}\approx \frac{a_z^{\rm rms}}{a_r^{\rm rms}} \left(\frac{t_{\rm tid}^i}{t_{\rm tid}^e}\right)^{1/2}. \label{eq:Ie_b} \ea Note that this relation does not make assumptions about the physical nature of the random acceleration, however the value of $I/e_b$ depends on the knowledge of $t_{\rm tid}^i$. Because of tidal dissipation, over the long time interval the hierarchical triple system like PSR J0337+1715 tends to converge to an equilibrium configuration in which the inner and outer orbits are coplanar and the inner WD obliquity $\theta_i$ --- the angle between its spin axis ${\bf S}_i$ and the orbital angular momentum ${\bf L}_i$ of the inner binary --- is zero. In this state ${\bf L}_i$ is aligned with the orbital angular momentum of the outer binary ${\bf L}_o$, which dominates over ${\bf L}_i$, and the WD rotation is synchronized with the orbital motion (we neglect the eccentricity of the inner binary). Next we discuss the way in which convergence to this equilibrium state takes place and the value of inclination damping timescale $t_{\rm tid}^i$. We do this for two alternative scenarios of the inclination driving, depending on whether it is excited by processes operating during the RLOF phase of the inner or outer binaries. \subsubsection{Excitation of $I$ during the inner RLOF phase} \label{sect:inn_RLOF} TvdH14 advocate an evolutionary scenario in which the inner WD undergoes RLOF {\it after} the outer one. We explore whether the mutual inclination could have been imprinted at the end of this phase, simultaneously with the free eccentricity excitation for the inner binary. Random torques driven by the convection in the WD progenitor excite both the mutual inclination of the two binaries $\delta I$ (assuming initial coplanarity) and the obliquity of the inner WD $\delta \theta$. Angular momentum conservation ensures that \ba \delta\theta=\frac{|{\bf L}_i|}{|{\bf S}_i|}\delta I, \label{eq:theta_I} \ea so that $\delta\theta\gg \delta I$ since $|{\bf L}_i|\gg|{\bf S}_i|$ for a synchronized WD progenitor. Obliquity of the WD damps on the {\it synchronization} timescale (Correia \etal 2011) \ba t_{{\rm sync},i} & = & \frac{2}{3}\frac{\xi Q}{k_2}n_i^{-1}\frac{m_i(m_p+m_i)} {m_p^2}\left(\frac{a_i}{R_i}\right)^3 \label{eq:t_theta}\\ & \approx & 600~\mbox{yr}~ \frac{Q/k_2}{10^7}\frac{\xi}{0.01}\frac{0.227}{R_i/a_i}, \nonumber \ea which is much shorter than the circularization timescale $t_{\rm tid}^e$, see equation (\ref{eq:tidal}). Because of the relation (\ref{eq:theta_I}) mutual inclination decays due to tides on the same short timescale $t_{{\rm sync},i}$, simultaneous with the excitation by random quadrupole torques. Substituting $t_{{\rm sync},i}$ for $t_{\rm tid}^i$ in equation (\ref{eq:Ie_b}) we find \ba \frac{I}{e_i} & \approx & \chi \left(7\xi\frac{m_i+m_p}{m_p}\right)^{1/2}\frac{R_i}{a_i}= \chi\left(7\frac{|{\bf S}_i|}{|{\bf L}_i|}\right)^{1/2} \label{eq:Ie_b_i}\\ & \approx & 0.064~\chi\left(\frac{\xi}{0.01}\right)^{1/2} \frac{R_i/a_i}{0.227}, \nonumber \ea where we defined $\chi\equiv a_z^{\rm rms}/a_r^{\rm rms}$. Equation (\ref{eq:Ie_b_i}) implies that even for $\chi=1$ the mutual inclination $I$ excited during the inner binary RLOF should be {\it much smaller} than the free eccentricity of the inner WD, at the level of $\lesssim 10^{-6}$. This is because spin angular momentum of the pulsar companion is much smaller than the orbital angular momentum of the binary. However, the present day value of $I=i$ is about an order of magnitude {\it higher} than $e_i^{\rm free}$, $i/e_{i,+}\approx 8.2$, exceeding the prediction (\ref{eq:Ie_b_i}) by more than two orders of magnitude, see the upper limit at $P_i$ in Figure \ref{fig:ecc_per}. The discrepancy can in fact be even worse as the assumption of $\chi\sim 1$ suggested by the estimate (\ref{eq:accel_rat}) may be too optimistic. Indeed, the final value of $i$ gets established at the freeze-out time when $t_{{\rm sync},i}$ becomes comparable to the WD evolution timescale at a stage when mass transfer stops and $R_i$ becomes smaller than the Roche radius. Since $t_{{\rm sync},i}\ll t_{\rm tid}^e$ and $t_{{\rm sync},i}$ scales with $R_i/a_i$ slower than $t_{\rm tid}^e$, the inclination freeze-out must occur {\it considerably later} than the eccentricity freeze-out of the inner binary. At that stage convective envelope of the WD progenitor is less massive than at $e_i$ freeze-out, resulting in less vigorous quadrupole fluctuations and $a_z^{\rm rms}$ being likely smaller than $a_r^{\rm rms}$ was when $e_i$ attained its final value. As a result, one should expect $\chi\ll 1$, exacerbating the discrepancy between the theoretical and measured values of $i$. For these reasons we believe that the present day mutual inclination could not have been established at the end of the RLOF phase of the inner binary. In conclusion we would like to address a subtle point related to the energy equipartition between individual convective eddies and the binary epicyclic motion. Phinney (1992) has shown that the mean energy of the random epicyclic motion in the binary plane $E_e=(1/2)\mu v_K^2 e_b^2$ ($\mu$ is the reduced mass, $v_K$ is the Keplerian speed) is of order the kinetic energy of an individual eddy driving $Q_{ij}$ fluctuations. Equation (\ref{eq:Ie_b_i}) then suggests that the mean energy of the random epicyclic motion normal to the binary plane $E_i=(1/2)\mu v_K^2 I^2\ll E_e$ and is not in equipartition with individual convective eddies. This paradox is easily resolved when one notices that inclination variations unavoidably cause much larger obliquity variations of the WD progenitor, see equation (\ref{eq:theta_I}). Because both are driven by equal (but opposite) torques, the energy stored in the obliquity wobble of the pulsar companion $E_\theta$ must be larger than $E_i$ by a factor $\delta \theta/\delta I=|{\bf L}_i|/|{\bf S}_i|\gg 1$. Using equations (\ref{eq:accel_rat}) and (\ref{eq:Ie_b_i}) one then trivially finds that $E_\theta\approx (7/3)E_e$. Thus, the full binary energy $E_\theta+E_i\approx E_\theta$ associated with the out-of-plane torques is in fact in equipartition with the kinetic energy of individual eddies in the WD progenitor envelope. \subsubsection{Excitation of $I$ during the outer RLOF phase} \label{sect:out_RLOF} Results of \S \ref{sect:inn_RLOF} can be trivially extended to study the possibility of the mutual inclination excitation by the random $Q_{ij}$ fluctuations during the RLOF phase of the {\it outer} binary. The same logic applies in that case as well if we consider inner binary as a point mass (which is reasonable for an hierarchical system) and replace $m_p\to m_p+m_i$ and $m_i\to m_o$ in all equations. As a result, we find that random fluctuations of the mutual inclination during the outer RLOF get damped on timescale \ba t_{{\rm sync},o} & = & \frac{2}{3}\frac{\xi Q}{k_2}n_o^{-1}\frac{m_om_3} {(m_p+m_i)^2}\left(\frac{a_o}{R_o}\right)^3 \label{eq:t_theta_o}\\ & \approx & 1.6\times 10^5~\mbox{yr} \frac{Q/k_2}{10^7}\frac{\xi}{0.01}, \nonumber \ea assuming the present day masses of all components. If we follow TvdH14 and adopt $m_p=1.3M_\odot$ and $m_i=1.12M_\odot$ (mass of the inner WD progenitor) during the outer binary RLOF, prior to the inner RLOF episode, this timescale does not change significantly, $t_{{\rm sync},o}\approx 10^5$ yr. This is shorter than the expected duration of the outer RLOF phase, $\sim 17$ Myr (TvdH14). Analogously, equation (\ref{eq:Ie_b_i}) becomes \ba \frac{I}{e_o} & \approx & \chi \left(7\xi\frac{m_3}{m_i+m_p}\right)^{1/2}\frac{R_o}{a_o} \label{eq:Ie_b_o}\\ & \approx & 0.08~\chi\left(\frac{\xi}{0.01}\right)^{1/2} \frac{R_o/a_o}{0.268}, \nonumber \ea where we used $R_o=0.268a_o$ for $q=m_o/(m_p+m_i)=0.251$. Adopting the parameters of the inner binary before its RLOF phase we get $q=m_o/(m_p+m_i)=0.17$, $R_o=0.24a_o$, and essentially the same value of $I/e_o$. This estimate shows that if the observed outer binary eccentricity $e_o\approx 0.035$ was excited by randomly varying $Q_{ij}$ of the WD progenitor at the end of the RLOF phase, then the same process must have given rise to the mutual inclination $I\approx 2.8\times 10^{-3}\chi\left(\xi/0.01\right)^{1/2}$. This can be easily reconciled with the present day value of $i=2.1\times 10^{-4}$ (see the upper limit on $I$ at $P_o$ in Figure \ref{fig:ecc_per}) if either $\chi\lesssim 10^{-2}$, which is quite plausible for an extended WD progenitor in long-period orbit, or $\chi\lesssim 1$, which is also expected, as we described in \S \ref{sect:inn_RLOF}. However, this comparison of $I$ and the current mutual inclination $i$ is meaningful only if $I$ did not change since the outer binary RLOF phase, which may have occurred $\sim 5$ Gyr ago (TvdH14). Mutual inclination would decay because for non-zero $I$ the steady state obliquity $\theta_i$ of the inner pulsar companion (WD or its progenitor) does not converge to $\theta_i=0$. Instead, tidal dissipation in the companion drives the system towards the so-called Cassini state (Colombo 1966; Peale 1969), in which the companion spin vector ${\bf S}_i$, the angular momentum of the inner binary ${\bf L}_i$, and the total angular momentum of the system ${\bf J}$ are coplanar and precess at the same rate $A_i^{\rm sec}$. Convergence of the companion spin to this configuration happens on relatively short synchronization timescale $t_{{\rm sync},i}$ given by equation (\ref{eq:t_theta}). Obliquity in the low-obliquity Cassini state (the one relevant for our purposes) is non-zero and is given in the case of weak dissipation by $\theta_i^{\rm Cas}\approx \lambda_i^{-1}I$ (Ward \& Hamilton 2004), where the dimensionless parameter \ba \lambda_i & = & \frac{2}{3}\frac{k_2}{\xi} \frac{m_p(m_p+m_i)}{m_i m_o}\left(\frac{R_i}{a_i}\right)^3 \left(\frac{a_o}{a_i}\right)^3 \label{eq:lambda_i}\\ & \approx & 1.1\times 10^4\frac{k_2}{\xi} \left(\frac{R_i/a_i}{0.227}\right)^3 \nonumber \ea is the ratio of the pulsar companion spin precession rate to the nodal precession rate of the inner binary. Tidal dissipation affects the value of $\theta_i^{\rm Cas}$ (Fabrycky \etal 2007) but for $A_i^{\rm sec}t_{\rm tid}^e \gg 1$ the effect is small and will be neglected. The numerical estimate in equation (\ref{eq:lambda_i}) applies during the inner binary RLOF, when $\lambda_i\gg 1$. During other evolutionary phases $R_i/a_i$ is smaller and $\lambda_i$ is lower. But in any case it is reasonable to expect $\lambda_i\gtrsim 1$ so that $\theta_i^{\rm Cas}\lesssim I$. Non-zero obliquity in presence of tidal dissipation results in a torque acting on the inner binary, which over time damps the mutual inclination $I$ of the two orbits. Its evolution is described by (Correia \etal 2011) \ba \frac{dI}{dt}= - \frac{\sin\theta_i}{t_I}, \label{eq:Iev} \ea where $t_I\equiv 7t_{\rm tid}^e\gg t_{{\rm sync},i}$. Thus, ${\bf S}_i$ settles into a Cassini state before $I$ has a chance to change. Plugging the dissipationless $\theta_i^{\rm Cas}\approx \lambda^{-1}I$ for the Cassini state into equation (\ref{eq:Iev}) we find that subsequently $I$ decays on a timescale \ba t_I^{\rm Cas} & = & \lambda_i t_I=\frac{4}{9}\frac{Q}{\xi}n_i^{-1} \frac{m_i+m_p}{m_o}\left(\frac{a_o}{a_i}\right)^3 \left(\frac{a_i}{R_i}\right)^2, \label{eq:t_I}\\ & \approx & 12~\mbox{Gyr}~\frac{Q/\xi}{10^7} \left(\frac{0.227}{R_i/a_i}\right)^2, \nonumber \ea see equation (\ref{eq:tidal}). Now we need to distinguish two possibilities. First, TvdH14 favor evolutionary scenario in which the inner binary underwent RLOF phase {\it after} the outer one. Given the scaling $t_I^{\rm Cas}\propto R_i^{-2}$ one expects fastest $I$ decay to occur during the RLOF. But even then the estimate (\ref{eq:t_I}) shows that $t_I^{\rm Cas}$ is much longer than the expected duration of the inner RLOF episode, $\sim 2$ Gyr (TvdH14). As a result, mutual inclination does not decay during this phase by more than $\sim 20\%$. Before and after that phase, the inner WD or its progenitor have $R_i/a_i$ smaller than during the overflow, resulting in much longer $t_I^{\rm Cas}$. Thus, $I$ stays constant during these time intervals. Second, TvdH14 also do not exclude the possibility of the outer WD to be the {\it last} one to form via the RLOF, after the inner WD has already formed. In this case $R_i/a_i$ is always very small and $t_I^{\rm Cas}$ is much longer than the lifetime of the system. High degree of the orbital coplanarity of the system also strongly argues against the outer binary eccentricity $e_o$ being excited by some external process, e.g. gravitational perturbation by a passing star. Such perturbation is expected to excite $I$ on par with $e_o$ so that an encounter driving $e_o$ two orders of magnitude stronger than $i$ seems extremely improbable. Needless to say, stellar encounter is in any case highly unlikely for an object in the field as excitation of $e_o=0.035$ would require stellar passage within $\sim 10$ AU from the system (Heggie \& Rasio 1996). Thus, we conclude that the combination of arguments presented here and in \S \ref{sect:inn_RLOF} does not contradict the scenario in which the present day mutual inclination $i$ was excited by convectively-driven random $Q_{ij}$ fluctuations at the end of the outer binary RLOF phase, simultaneous with the excitation of its eccentricity $e_o$. On the other hand, we cannot exclude the possibility that $I$ and/or $e_o$ were produced by a mechanism completely unrelated the stochastic $Q_{ij}$ variations of the WD progenitor, e.g. as a result of incomplete damping of the mutual misalignment by disk torques during the outer binary RLOF. This possibility may be hinted at by the large difference between $e_o$ and the prediction of Phinney (1992), see \S \ref{sect:P-e}. Finally, the weak decay of mutual inclination after its excitation in the outer binary does not allow us to distinguish between the two alternative evolutionary scenarios presented in TvdH14, in which the outer WD is either the first or last one to form. \subsection{Implications for timing measurement} \label{sect:timing} Strong Newtonian three-body coupling between the components of PSR J0337+1715 system should make the measurement of the general relativistic effects in it difficult, even despite the high timing accuracy of this pulsar (Ransom \etal 2014). In particular, as shown in \S \ref{sect:inner} apsidal precession of the inner binary is no longer set by the GR precession alone but is instead strongly suppressed by the three-body effects, so that $\dot\varpi_i\approx 0.24 \dot\varpi_{\rm GR}$. At the same time, we find that measurement of $\dot\varpi_i$ is quite sensitive to the actual value of $\dot\varpi_{\rm GR}$. Artificially varying $\dot\varpi_{\rm GR}$ by $1\%$ results in roughly $4\%$ variation of $\dot\varpi_i$. This is especially surprising given that $\dot\varpi_{\rm GR}$ provides only a $29\%$-contribution to $A_i$, see equations (\ref{eq:A_in})-(\ref{eq:omGR}). Such a disproportionate response can be understood if one manipulates the expression for $\dot\varpi_i$ using solutions (\ref{eq:h_i})-(\ref{eq:k_i}) and the fact that $e_{i,+}/e_{o,+}\gg e_{i,-}/e_{o,-}$, $g_+\approx A_i$, $g_-\approx A_o$. As a result, one can write the following expression for the apsidal rate of the inner binary at the present time: \ba \dot\varpi_i(0)\approx A_i+B_i\frac{{\bf e}_i\cdot {\bf e}_o} {e_i^2}, \label{eq:varpinow} \ea where ${\bf e}_i$ and ${\bf e}_o$ are the eccentricity vectors of the inner and outer binaries at present day. This formula clearly shows the near cancellation of the two large contributions (two terms in the r.h.s.), since $\dot\varpi_i(0)\ll A_i$ according to our estimate (\ref{eq:dvarpi_i}). Because of that even a small variation in the value of $A_i$ in equation (\ref{eq:varpinow}), e.g. due to the deviation of $\dot\varpi_{\rm GR}$ from the GR prediction (Damour \& Taylor 1992), drives large change in the value of $\dot\varpi_i$. Thus, given a significantly accurate measurement of $\dot\varpi_i$ one may still be able to use timing of PSR J0337+1715 to constrain non-GR contributions to the apsidal precession rate of the inner binary, even in presence of the three-body effects. The problem may be in measuring $\dot\varpi_i$ accurately enough, given the low value of $e_i$ (Ransom, private communication). Another complication for timing may arise from the short-term effects, neglected in our calculations. Small variations of the orbital parameters on the orbital timescales of both binaries may be at least partly degenerate with the post-Newtonian contributions to timing (Damour \& Deruelle 1986; Damour \& Taylor 1992). This is likely to make the problem of extracting post-Newtonian parameters of the system quite challenging. | 14 | 3 | 1403.5292 |
1403 | 1403.2856.txt | Recent analysis of the interstellar helium fluxes measured in 2009-2010 at Earth orbit by the Interstellar Boundary Explorer (IBEX) has suggested that the interstellar velocity (both direction and magnitude) is inconsistent with that derived previously from Ulysses/GAS observations made in the period from 1990 to 2002 at 1.5-5.5 AU from the Sun. Both results are model-dependent and models that were used in the analyses are different. In this paper, we perform an analysis of the Uysses/GAS and IBEX-Lo data using our state-of-the-art 3D time-dependent kinetic model of interstellar atoms in the heliosphere. For the first time we analyze Ulysses/GAS data from year 2007, the closest available Ulysses/GAS observations in time to the IBEX observations. We show that the interstellar velocity derived from the Ulysses 2007 data is consistent with previous Ulysses results and does not agree with the velocity derived from IBEX. This conclusion is very robust since, as is shown in the paper, it does not depend on the ionization rates adopted in theoretical models. We conclude that Ulysses data are not consistent with the new LISM velocity vector from IBEX. In contrast, IBEX data, in principle, could be explained with the LISM velocity vector derived from the Ulysses data. This is possible for the models with the interstellar temperature increased from 6300 K to 9000 K. There is a need to perform further study of possible reasons for the broadening of the helium signal core measured by IBEX. This could be an instrumental effect or due to unconsidered physical processes. | The Solar System is surrounded by the partially ionized plasma of the Local Interstellar Medium (LISM). The most abundant neutral component in the LISM is atomic hydrogen. Minor neutral components in the LISM are atomic helium, oxygen, nitrogen, and others. The Sun is moving through the LISM with a relative velocity about 20-30~km/s. The supersonic solar wind (SW) interacts with the charged component of the interstellar plasma and the result is the SW/LISM interaction region, which is called the heliospheric interface \citep{bm_1993}. The mean free path of interstellar neutrals is comparable to the size of the heliospheric interface \citep[see e.g.][]{izmod_etal_2001}. Therefore, neutral atoms penetrate through this region into the heliosphere, where they can be measured directly or indirectly. Being measured in the heliosphere, the interstellar neutrals are the main source of information on the LISM parameters, because charged LISM particles are deflected by the solar wind and do not enter the heliosphere. Although hydrogen (H) atoms have the largest number density of interstellar neutrals, they are not the easiest to study from inside the heliosphere, because during their motion through the heliospheric interface H atoms interact with the interstellar and solar wind protons by charge exchange ($H+H^{+} \leftrightarrow H^{+}+H$). As a result, new so-called secondary interstellar H atoms are created, and their distribution function depends on local plasma parameters. Therefore, hydrogen distributions in the heliosphere (e.g. at the heliospheric termination shock) are considerably disturbed compared with the original distribution in the LISM \citep[see][]{izmod_etal_2001}. In addition, near the Sun hydrogen atoms are affected by substantial solar radiation pressure, varies with time and the velocity of particles, which results in more complications for modelling of hydrogen distribution as compared with helium (radiation pressure is negligible for helium). That is why it becomes challenging to use the hydrogen distribution, for example at 1 AU, to derive the LISM parameters, because one needs to take into account perturbation of the hydrogen parameters in the heliospheric interface \citep{kat_izmod_2010, kat_izmod_2011}. On the other hand, due to the charge exchange interactions, interstellar hydrogen distributions inside the heliosphere can be used as remote diagnostics of the heliospheric interface. Since 1970s, interstellar hydrogen in the heliosphere has been studied remotely by numerous measurements of backscattered solar Lyman-alpha radiation by, e.g., OGO-5 \citep{thomas_krassa_1971, bertaux_blamont_1971}, Prognoz-5 and 6 \citep{bertaux_etal_1985}, SOHO/SWAN \citep{costa_etal_1999, quemerais_izmod_2002}, Voyager-1/2 \citep{quemerais_etal_2010}, Hubble Space Telescope \citep{vincent_etal_2011} and others. Nowadays interstellar hydrogen atoms for the first time are measured directly at Earth orbit by the IBEX-Lo sensor on board the Interstellar Boundary Explorer (IBEX) spacecraft. Some data and results of these observations are presented in \citet{saul_etal_2012} and \citet{schwadron_etal_2013}. Contrary to the H atoms, it is known that interstellar helium (He) atoms penetrate into the heliosphere almost freely. They only weakly interact with protons ($H^{+}$) and helium ions ($He^{+}$) by charge exchange, due to small charge exchange cross sections \citep[see, e.g., section~7 in][]{bzowski_etal_2012}. %\textbf{Bzowski et al. (2012) have % shown that the main charge exchange reaction for helium atoms is % $He+He^+\rightleftarrows He^++He$ (cross section of this reaction is only % several times less than for similar resonant charge exchange reaction of % hydrogen atoms). However, even for this reaction its rate is quiet small and % mean free path of helium atoms in the heliospheric interface is much more % than for hydrogen atoms due to small abundance of helium in the LISM. % Therefore, it is usually assumed that interstellar helium flow is not % disturbed at the heliospheric interface region}. This means that measurements of the interstellar helium near the Sun can be used to determine the temperature ($T_{LISM}$) and relative velocity vector ($\textbf{V}_{LISM}$) of the LISM. Inside the heliosphere, the interstellar helium flow suffers from effects of solar photoionization and electron impact ionization. Rates of these processes are partially known from different observations of the solar irradiance and the solar wind \citep{mcmullin_etal_2004, bzowski_etal_2012}. So, to obtain the LISM parameters from the local observations inside the heliosphere one should use a theoretical model of interstellar helium distributions in the heliosphere, which takes into account all important ionization processes, and then solves the inverse problem to find the LISM parameters providing the best agreement between results of the numerical modeling and the experimental data. Such a technique to derive the LISM parameters from the interstellar helium measurements in the heliosphere was applied to data from the GAS instrument on board the Ulysses spacecraft \citep{banaszkiewicz_etal_1996, witte_etal_1993, witte_etal_1996, witte_2004}. The Ulysses/GAS instrument was designed for direct measurements of interstellar helium. These measurements were performed from 1990 to 2007. Analysis of the Ulysses/GAS data from 1990 to 2002 by \citet{witte_2004} yielded the following LISM parameters: number density of interstellar helium $n_{He,LISM}=0.015 \pm 0.003$~cm$^{-3}$, temperature $T_{LISM}=6300 \pm 340$~K, relative SW/LISM velocity $V_{LISM}=26.3 \pm 0.4$~km/s, and direction of the interstellar wind in J2000 ecliptic coordinates at longitude $\lambda_{LISM}=75.4^{\circ} \pm 0.5^{\circ}$ and latitude $\beta_{LISM}=-5.2^{\circ} \pm 0.2^{\circ}$. These parameters were found to be consistent with other experimental data \citep{moebius_etal_2004, lallement_etal_2004, vallerga_etal_2004} and remained canonical until recently. In October 2008 a new NASA mission, IBEX, was launched \citep{mccomas_etal_2009}. The main goal of IBEX is to study the three-dimensional structure of the heliosphere using measurements of heliospheric neutrals (hydrogen, helium and oxygen) in different energy channels \citep{mccomas_etal_2009, moebius_etal_2009}. IBEX is primarily designed to study high energy neutrals formed by charge exchange between the termination shock and the heliopause rather than LISM neutrals, but the IBEX-Lo sensor is also capable of observing the LISM neutrals at certain times of the year. IBEX-Lo \citep{fuselier_etal_2009} is designed to measure the low-energy neutrals in the energy range from 0.01 to 2 keV. IBEX-Lo measurements of interstellar helium in 2009-2010 were analyzed recently by \citet{bzowski_etal_2012} and \citet{moebius_etal_2012}. The analysis of \citet{bzowski_etal_2012} was based on a model of the helium distribution similar to that of \citet{witte_2004}, but taking into account more recent data on the helium ionization rates. \citet{moebius_etal_2012} have performed an analytical analysis of the IBEX-Lo measurements in the context of a stationary and axisymmetric model \citep[the so-called ``classical hot model'', see,][]{meier_1977, wu_judge_1979, lallement_etal_1985, lee_etal_2012}.The following LISM parameters were obtained as the result of these investigations: $T_{LISM}=6300$~K, $V_{LISM}=23.2$~km/s, $\lambda_{LISM}=79^{\circ}$, $\beta_{LISM}=-4.98^{\circ}$. These mean values were taken from \citet{mccomas_etal_2012}, who used weighted means to combine the two independent results of \citet{bzowski_etal_2012} and \citet{moebius_etal_2012}. The IBEX-Lo analysis of possible values of the interstellar parameters ($V_{LISM}, \lambda_{LISM}, \beta_{LISM}, T_{LISM}$) suggests a ``tube'' of allowable fits in the 4D parameter space. This ``tube'' is characterized by 1) uncertainties that represent the widths of the ``tube'', and 2) bounding ranges that characterize the length of the ``tube'' \citep[see][for details]{mccomas_etal_2012}. The uncertainties and the bounding ranges are shown in Table~1 of \citet{mccomas_etal_2012}. %\textbf{Let us emphasize that the bounding ranges presented in \citet{mccomas_etal_2012} are quite larger than 1-$\sigma$ uncertainties \citep[see table 1 from][]{mccomas_etal_2012}. Theoretical analysis of IBEX-Lo data provided several combinations of the LISM parameters ($V,\lambda,\beta,T$), which are consistent with the observations. These combinations represent the ``tube'' in 4-dimension space of the LISM parameters. The widths of the ``tube'' in all directions are uncertainties, while the length of the tube represents the bounding ranges.} The velocity of the interstellar flow obtained from the IBEX-Lo data is about 3~km/s less and its direction 4$^{\circ}$ different compared with the previous results of \citet{witte_2004}. Note that results of both \citet{witte_2004} and \citet{mccomas_etal_2012} are model-dependent, and different models have been used. Therefore, it is worthwhile to analyze both GAS and IBEX-Lo data in the context of one model. Although the differences in the LISM parameters may not seem large, they may actually be physically significant. For example, the low velocity measurement from IBEX has stimulated a debate about the existence of the Bow Shock \citep{mccomas_etal_2012, zank_etal_2013}. Also, changes in the $\textbf{V}_{LISM}$ direction influence the orientation of the hydrogen deflection plane (HDP) \citep{lallement_etal_2005, lallement_etal_2010}, which in turn leads to a different inferred configuration of the interstellar magnetic field within the HDP. Changes in the SW/LISM relative velocity could also affect the position of the heliopause (i.e. the contact discontinuity where dynamic pressure of the interstellar plasma and the solar wind are equal to each other). This is very important for interpreting data from the Voyager spacecraft, which are approaching the heliopause. Voyager~1 in fact may have already crossed the heliopause \citep{gurnett_etal_2013}. %---- m.b. perenesti eto vse v konec discussion-section ? %%------------------------------------------ % % What are the reasons of the differences in the SW/LISM velocity vector revealed by the analysis of Ulysses/GAS and IBEX-Lo data? %In principle, there are four possibilities. % %\begin{enumerate} % \item The first one is connected with difference in the ionization rate (which is a sum of photoionization, electron-impact and charge-exchange ionization rates) in the periods of observations %by Ulysses and IBEX. Some uncertainties might be also connected with our unperfect knowledge of the ionization rate, i.e. its latitudinal and time variations. So, the ionization rates adopted in the models of \textbf{Witte (2004)} and \textbf{Bzowski et al. (2012)} could be potentially the source of uncertainty. %Note, also that models of \textbf{Witte (2004)} and \textbf{Bzowski et al. (2012)} differ only in the ionization rates. % \item The second possibility deals with some additional physical processes, which are not taken into account in the models. For example, it might be the influence of the secondary interstellar helium atoms created during charge exchange %at the heliospheric boundary, or heating of the interstellar helium atoms due to elastic collisions (\textbf{Gruntman, 1986; Chassefiere et al., 1986, %Gruntman, 2013}). % \item The third possibility, could be connected with some physical changes in the interstellar helium flow outside the heliosphere during the time period between measurements of Ulysses and IBEX (i.e. from 2004 to 2009). Changing of the interstellar medium parameters at short time scales are discussed by \textbf{Frisch (2012)}. % \item The fourth possible reason of the difference may be connected with the specifics of data collection and data analyzes inherent to each of the experiments. %\end{enumerate} %In this work we modelled the interstellar helium fluxes measured by Ulysses (in 2001 and 2007) and IBEX (in 2009) and explore the first possibility. %Calculations were performed for the ``old'' and ``new'' LISM parameters and for different ionization rates adopted in the model. % % The comparison of the model results with the Ulysses/GAS data in 2001 and 2007 years was performed. We intentionally chose these periods of time: on the one hand, this allows us to check the results of \textbf{Witte (2004)} for year 2001 with the independent model, and on the other hand, we take Ulysses/GAS data for 2007, because it is closer to time of IBEX's observations. %\textbf{Our study of the Ulysses/GAS data is focused on the position of the center of the He beam (i.e. direction on the sky, where observed helium fluxes are maximal). %Center of the helium beam is convenient for the analysis, because it should be mostly determined by the LISM velocity vector as opposed to the %helium fluxes itself, which strongly depend on the local ionization rate. %However, since the helium ionization rate is varying with time and %heliolatitude, some portions of the helium atoms are more ionized than other portions (so called ``selection'' effect). In this case ionization rate, in principle, can change the position of the center of the He beam. This effect is not expected to be large at least for the Ulysses data, because %losses of helium atoms from the interstellar medium to 2-4 AU (where Ulysses was located) are only about 10-12~\%. But, in respect that differences %in the LISM velocity vectors between Ulysses and IBEX are quite small too (3~km/s or 12~\% in magnitude and 3.5$^{\circ}$ in direction), we need to study influence of the ionization rate and check is it possible to get an agreement between Ulysses and IBEX data by changing of the ionization rate.} % %We also performed the calculations of the interstellar helium fluxes measured by IBEX during the orbits from 13-th to 19-th and found that model results with the ``old'' %and ``new'' LISM parameters differ substantially only in the peak width of the angular distribution of helium fluxes. While other parameters of the distribution (peak high and position of the peak) are approximately the same for different LISM velocity vectors. Influence of the ionization rates adopted in the %model on the peak width is studied. In this paper, we perform an analysis of both Uysses/GAS data (in years 2001 and 2007) and IBEX-Lo data (in year 2009) using our state-of-the-art 3D time-dependent kinetic model of interstellar atoms in the heliosphere. We do not aim to repeat the detailed analyses performed previously by Witte and Bzowski et al., and restrict ourselves to a few individual observations from both spacecraft. We provide the first analysis of Ulysses/GAS data obtained in 2007, which is closer in time to the observations of IBEX. Calculations were performed for the ``old'' and ``new'' LISM velocity vectors, and for different ionization rates adopted in the model. We explore the role of the ionization rates on the differences in the LISM velocity vector obtained from the GAS and IBEX-Lo data. | %Main points: % %- new parameters contradict to the Ulysses data in direction of the He beam for both 2001 and 2007 years %- this direction does not depend on the ionization rate, hence errors in Witte's ionization rates could not be a reason of the differences %- old parameters contradict to the IBEX data in peak width of the fluxes %- peak width does not depend on the ionization rate, hence again ionization rate is not a reason of the differences %- is is possible to obtain an agreement between the model and the IBEX data in peak width by increasing of the LISM temperature. %- different other reasons of the differences (real changes in the LISM, other physical processes, etc) %- conclusions %It was shown, that the positions of the He beam obtained from the model with the ``new'' LISM parameters deviate from the positions of the He beam in the Ulysses/GAS data by several degrees. In the same time for the theoretical maps obtained with ``old'' LISM parameters the positions of the He beam are in a good agreement with the Ulysses/GAS data in 2001 and 2007 years. %This result for 2001 is not surprising, it is just a confirmation of the results of \textbf{Witte (2004)} analysis by using our model. %However, Ulysses/GAS data for 2007 were not analyzed by Witte. %Nevertheless, our analysis of the 2007 data shows perfect agreement with previously obtained Ulysses/GAS results. % %Calculations of the helium fluxes %measured by IBEX showed that the main difference between the model results with the ``old'' and ``new'' LISM parameters is in the peak width of the angular helium distribution. Employing of the ``old'' LISM parameters leads to systematic underestimation of the peak width as compared with the IBEX data, while %model results with the ``new'' LISM parameters show a good agreement of the peak width with the IBEX data. It was shown that increasing of the LISM %temperature up to 9000~K in the model with the ``old'' LISM velocity vector allows to obtain a good agreement with the IBEX data. % %We have also demonstrated that position of the interstellar helium beam on the Ulysses's maps and peak width of the angle-distribution of helium %fluxes in the IBEX data do not depend on the ionization rate adopted in the model. It means that uncertainties in the ionization rate connected either with the model assumptions or with luck of our knowledge could not be a reason of the presented differences. % %The following conclusions can be made: % \begin{itemize} % \item ``new'' LISM velocity vector from IBEX data contradicts to the Ulysses data in direction of the helium beam for the whole period of observations; % \item ``old'' LISM velocity vector from the Ulysses data contradicts to the IBEX data in a peak width of the interstellar helium angular distribution; % \item both previous conclusions do not depend on the ionization rate adopted in the model; % \item it is possible to enhance the peak width and obtain a good agreement between the IBEX data and the model results with the ``old'' LISM velocity % vector by increasing of the LISM temperature from 6300~K to 9000~K. % \end{itemize} % %Note, that increasing of the LISM temperature to 9000~K is not an ``ideal'' solution, because such a high temperature contradicts to the results of %Witte (2004), who obtained $T_{LISM}=6300\pm340$~K from the analysis of the Ulysses data for 1990-2002 years. However, in our opinion, %determination of the LISM temperature has less precision as compared with a determination of the LISM velocity vector. Because %in order to obtain temperature one need to analyze a width of the measured helium beam, while to obtain the velocity vector one need to %analyze the position of the beam. Probably, width of the beam could be affected by some instrumental effects, and some systematic inaccuracies %may exist. From the naive point of view, position of the helium beam is easier to determine precisely from the experimental data than the width of the beam. % %It was shown that any changes in the ionization rate adopted in the models could not be a reason of the different LISM parameters % obtained by Witte (2004) and Bzowski et al. (2012). Therefore the following remaining possibilities should be considered: 1) there are some physical processes, which are not considered in the models, and which can influence the interstellar helium fluxes %measured by Ulysses and IBEX in different ways; 2) there are very short time scale (order of year) variations in the interstellar velocity parameters; and 3) there are some unknown uncertainties connected with Ulysses/GAS and/or IBEX-Lo data analysis or data selection. % %The second case has been discussed by \textbf{Frisch (2012)}. However, in our opinion such variations are hardly probable, especially, for the time scale of 2 years (from 2007 to 2009), because of large mean free path of the interstellar atoms. % %%For the first of the considered possibilities, we should look into the physical process, which affect the interstellar helium fluxes more effectively at 1 AU %%(where IBEX is orbiting) than at 2-4~AU (where Ulysses has performed its measurements). %%%Indeed, if we assume that there is a process that is important for the solar minimum in 2009, it should also was important for the previous solar minimum in 1996-1997 %%%and should changed the distribution of the interstellar helium measured by Ulysses. %%A physical process known for us that is more important %%at the small heliocentric distances is electron impact ionization. However, both \textbf{Witte (2004)} and \textbf{Bzowski et al. (2012)} took into account this ionization in their models. %%They used some reasonable assumptions for the distributions of the electrons in the solar wind. %%Therefore, the electron impact can not cause the differences in \textbf{Witte (2004)} and \textbf{Bzowski et al. (2012)}, unless some dramatic changes in the electron impact ionization appeared in 2004-2009. % %Another physical process, which leads to broadening of the helium beam is elastic collisions with the solar wind protons. This effect was studied in \textbf{Gruntman (2013)}. Rate of the elastic collisions is proportional to the solar wind number density. Hence, this process should be more effective at small heliocentric distances, where the solar wind is denser. \textbf{Gruntman (2013)} has shown that elastic collisions result in the formation of the wings in angular distribution of interstellar helium fluxes. Probably, this effect may be pronounced in the IBEX data. | 14 | 3 | 1403.2856 |
1403 | 1403.4599.txt | We investigate the cosmological implications of the latest growth of structure measurement from the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS Data Release 11 with particular focus on the sum of the neutrino masses, $\sum m_{\nu}$. We examine the robustness of the cosmological constraints from the Baryon Acoustic Oscillation (BAO) scale, the Alcock-Paczynski effect and redshift-space distortions ($D_V/r_s$, $F_{\rm AP}$, $f\sigma_8$) of~\citet{Beutler:2013b}, when introducing a neutrino mass in the power spectrum template. We then discuss how the neutrino mass relaxes discrepancies between the Cosmic Microwave Background (CMB) and other low-redshift measurements within $\Lambda$CDM. Combining our cosmological constraints with WMAP9 yields $\sum m_{\nu} = 0.36\pm0.14\,$eV ($68\%$ c.l.), which represents a $2.6\sigma$ preference for non-zero neutrino mass. The significance can be increased to $3.3\sigma$ when including weak lensing results and other BAO constraints, yielding $\sum m_{\nu} = 0.35\pm0.10\,$eV ($68\%$ c.l.). However, combining CMASS with Planck data reduces the preference for neutrino mass to $\sim 2\sigma$. When removing the CMB lensing effect in the Planck temperature power spectrum (by marginalising over $A_{\rm L}$), we see shifts of $\sim 1\sigma$ in $\sigma_8$ and $\Omega_m$, which have a significant effect on the neutrino mass constraints. In case of CMASS plus Planck without the $A_{\rm L}$-lensing signal, we find a preference for a neutrino mass of $\sum m_{\nu} = 0.34\pm 0.14\,$eV ($68\%$ c.l.), in excellent agreement with the WMAP9+CMASS value. The constraint can be tightened to $3.4\sigma$ yielding $\sum m_{\nu} = 0.36\pm 0.10\,$eV ($68\%$ c.l.) when weak lensing data and other BAO constraints are included. \vspace{1cm} | The measurement of neutrino oscillations in neutrino detection experiments using solar, atmospheric and reactor neutrinos has now convincingly shown that neutrinos cannot be massless. Neutrino oscillation experiments are sensitive to the mass differences between the neutrino eigenstates, and the current data imply $|\Delta m^2_{31}| \cong 2.4\times 10^{-3}$eV$^2$ and $\Delta m^2_{21} \cong 7.6\times 10^{-5}$eV$^2$~\citep{Beringer:1900zz}. These measurements provide a lower limit for the sum of the neutrino masses of $\sim 0.06\,$eV. Using the mass difference constraints above and knowing that $\Delta m^2_{21} > 0$, one can construct two mass hierarchies for neutrinos. The so-called ``normal'' hierarchy suggests $m_{\nu_1} < m_{\nu_2} \ll m_{\nu_3}$, where we have one heavy neutrino and two lighter ones, while the so-called ``inverted'' hierarchy suggests $m_{\nu_3} \ll m_{\nu_1} < m_{\nu_2}$, where we have one light neutrino and two heavy ones. Because of the extremely low cross-section of neutrinos it is difficult for laboratory experiments to measure the neutrino mass directly. The current best upper bounds on the neutrino mass from particle physics experiments are from Troitsk~\citep{Lobashev:1999tp} and Mainz~\citep{Weinheimer:1999tn} tritium beta-decay experiments that found $m_{\beta} < 2.3\,$eV ($95\%$ confidence level), where $m_{\beta}$ is the mass to which beta-decay experiments are sensitive (see section~\ref{sec:particle} and eq.~\ref{eq:mbeta}). The KArlsruhe TRItium Neutrino experiment (KATRIN) aims to measure $m_{\beta}$ with a sensitivity of $\sim 0.2\,$eV~\citep{Wolf:2008hf}, which would constrain $\sum m_{\nu} \lesssim 0.6\,$eV. Also, neutrino-less double beta decay ($0\nu\beta\beta$) experiments such as KamLAND-Zen will assess the effective mass of Majorana neutrinos at the level of $\mathcal{O}$($0.1-1$)eV~\citep{Gando:2012zm} depending on the nuclear matrix element. With the advent of precision cosmology, it was realised that the neutrino mass has an effect on the matter distribution in the Universe and that this could be used to indirectly measure the sum of the neutrino masses, $\sum m_{\nu}$. The neutrino mass introduces a scale-dependent suppression of the clustering amplitude with the scale-dependency set by $f_{\nu} = \Omega_{\nu}/\Omega_m$. The suppression of clustering is caused by the large thermal velocity of neutrinos which leads to a large free-streaming scale. Many recent publications have attempted to constrain $\sum m_{\nu}$, but most were only able to set upper limits~\citep{Seljak:2006bg, Hinshaw:2008kr,Dunkley:2008ie,Reid:2009nq,Komatsu:2010fb,Saito:2010pw,Thomas:2009ae,Tereno:2008mm,Gong:2008pg,Ichiki:2008ye,Li:2008vf,Zhao:2012xw,Hinshaw:2012aka,dePutter:2012sh,Xia:2012na,Sanchez:2012sg,Riemer-Sorensen:2013jsa,Giusarma:2013pmn} with some exceptions based on cluster abundance results, e.g.,~\citet{Hou:2012xq,Ade:2013lmv,Battye:2013xqa,Wyman:2013lza,Burenin:2013wg,Rozo:2013hha}. Introducing a neutrino mass suppresses clustering power between the epoch of decoupling and today below the free streaming scale, as massive neutrinos affect the cosmological expansion rate, but free-stream out of matter perturbations. The clustering amplitude is often parameterised by the r.m.s. mass fluctuations in spheres of $8\,$Mpc$/h$ at the present epoch and denoted $\sigma_8$. Given the clustering amplitude at decoupling measured by the CMB, we can predict the $z=0$ value of $\sigma_8$, within a certain cosmological model. However, this $\sigma_8$ prediction depends on the initial assumption of the neutrino mass, introducing a degeneracy between $\sigma_8$ and $\sum m_{\nu}$. In fact, if there were no other effect of the neutrino mass on the CMB, the neutrino mass parameter would be completely degenerate with $\sigma_8$. Luckily there are several other effects of the neutrino mass on the CMB, which can be used to break this degeneracy. If neutrinos would exceed the limit $\sum m_{\nu} \lesssim 1.8\,$eV, they would trigger more direct effects in the CMB~\citep{Dodelson:1995es,Ichikawa:2004zi}, which are not observed. This represents probably the most robust limit on the neutrino mass from cosmology. Apart from this there are other, more subtle effects on the CMB anisotropies. Changing the neutrino mass and keeping the redshift of matter-radiation equality fixed will change the low-redshift value of $\Omega_mh^2$. This will change the angular diameter distance to the last scattering surface, $D_A(z_*)$. Since such changes can be absorbed by changes in the Hubble parameter there is a (geometric) degeneracy between $\sum m_{\nu}$ and $H_0$ in the CMB. Beside the angular diameter distance the neutrino mass also impacts the slope of the CMB power spectrum at low multipoles due to the Integrated Sachs-Wolfe (ISW) effect~\citep{Lesgourgues:2006nd,Ade:2013dsi}. The ISW effect describes the energy change of CMB photons caused by the decay of the gravitational potentials during radiation domination (early ISW effect) or $\Lambda$ domination (late ISW effect). If instead $\Omega_mh^2$ is kept fixed when varying the neutrino mass, the redshift of matter-radiation equality will change, which affects the position and amplitude of the acoustic peaks in the CMB power spectrum (for more details see e.g.~\citealt{oai:arXiv.org:1212.6154}). Weak gravitational lensing of the CMB photons encodes information about the late-time Universe with the Planck kernel peaking at around $z\sim 2$~\citep{Ade:2013aro}. The lensing deflections are caused by an integrated measure of the matter distribution along the line of sight. Using these additional signals, the CMB data are able to break the $\sum m_{\nu}$-$\sigma_8$ degeneracy to some extent. The remaining degeneracy can be broken by including low-redshift $\sigma_8$ measurements from other datasets. Low-redshift measurements of the clustering amplitude ($\sigma_8$) are notoriously difficult, and to some extent require priors from the CMB. Most low-redshift probes which are sensitive to $\sigma_8$ require the understanding of non-linear effects and usually carry large systematic uncertainties. In this paper we demonstrate that recent constraints on the growth rate $f\sigma_8$, the Baryon Acoustic Oscillation (BAO) scale $D_V/r_s$ and the Alcock-Paczynski effect $F_{\rm AP}$ from the Baryon Oscillation Spectroscopic Survey (BOSS) are robust against variations of $\sum m_{\nu}$ in the theoretical template. We also show that the constraint on ($\Omega_m$, $\sigma_8$) from the shear correlation function of the weak lensing signal of CFHTLenS is robust against variations of $\sum m_{\nu}$. We therefore claim that combining CMB datasets with these low-redshift growth of structure measurements provides a reliable approach to break the $\sum m_{\nu}$-$\sigma_8$ degeneracy in the CMB. This paper is organised as follows. In section~\ref{sec:theory} we give a brief summary of the effect of neutrinos on the matter perturbations. In section~\ref{sec:tension} we introduce constraints on $\sigma_8$ from different datasets. In section~\ref{sec:reliability} we investigate the robustness of different low redshift $\sigma_8$ constraints, with particular focus on the BOSS growth of structure constraint. In section~\ref{sec:mnu} we investigate the parameter $\sum m_{\nu}$ as one approach to relieve the tension between these different datasets. In section~\ref{sec:dis} we discuss the cosmological implications of our results, and we conclude in section~\ref{sec:conclusion}. | \label{sec:conclusion} This paper presents an investigation of the cosmological implications of the CMASS-DR11 anisotropic analysis including the growth of structure measurement, with particular focus on the sum of the neutrino masses $\sum m_{\nu}$. First we examine the robustness of the CMASS constraints of~\citet{Beutler:2013b} when changing the power spectrum template including $\sum m_{\nu} = 0.4\,$eV. Our main cosmological parameters change by $<0.5\sigma$ and therefore are robust against variations in the neutrino mass. We perform similar tests for the weak lensing results from CFHTLenS, finding that these results show only weak dependence on the initial assumption of the neutrino mass parameter. We use the WMAP9 and Planck MCMC chains where the sum of the neutrino masses is varied as a free parameter and importance sample these chains. When combining WMAP9 with the three constraints $(D_V/r_s,F_{\rm AP},f\sigma_8)$ of~\citet{Beutler:2013b} we obtain $\sum m_{\nu} = 0.36\pm0.14\,$eV, which represents a $2.6\sigma$ preference for the neutrino mass. If we also include CFHTLenS, galaxy-galaxy lensing and the BAO constraints from 6dFGS and LOWZ, we find $\sum m_{\nu} = 0.35\pm0.10\,$eV ($3.3\sigma$). Using the Planck dataset the preference for a neutrino mass is reduced to $\sim 2\sigma$. However, marginalising over the $A_{\rm L}$-lensing contribution to the temperature power spectrum of Planck leads to $\sim 1\sigma$ shifts in $\Omega_m$ and $\sigma_8$, which bring Planck into much better agreement with WMAP9. Combining Planck without the $A_{\rm L}$-lensing contribution with CMASS yields similar results to WMAP9. We find $\sum m_{\nu} = 0.36\pm0.10\,$eV ($3.4\sigma$) when combining with~\citet{Beutler:2013b}, CFHTLenS, galaxy-galaxy lensing and further BAO constraints. This constraint is robust against various permutations of datasets (see Table~\ref{tab:para2} for details). We also investigated the Planck re-analysis of~\citet{Spergel:2013rxa}, finding that it yields results very similar to Planck with a slightly increased significance for a neutrino mass. While the preference for neutrino mass is driven mainly by the low redshift growth of structure constraints it is reassuring that the three growth of structure datasets included in this analysis (CMASS-RSD, CFHTLenS and galaxy-galaxy lensing) yield consistent results. Our constraints could be significantly improved by including cluster counts detected through the Sunyaev-Zeldovich effect. We chose, however, to not include these datasets, because of the significant systematic uncertainty of these measurements with respect to the treatment of the neutrino mass. In this paper we present many combinations of datasets and a natural question is, which of these presents the main result of this paper. When discussing the implications of our results in section~\ref{sec:particle}, we selected the constraint $\sum m_{\nu} = 0.35\pm0.10\,$eV, obtained with the Planck$-A_{\rm L}$ chain. However, we cannot conclusively put this forward as the fiducial result of our analysis, without having an explanation for the tension with the $A_{\rm L}$-lensing amplitude. The origin of the tension between the different components in the Planck dataset remains an open question, which we will hopefully learn more about with the next data release of Planck. A neutrino mass at this level would relieve the tension of current datasets with the clustering prediction of GR reported in~\citet{Beutler:2013b}. If we remove the $A_{\rm L}$-lensing contribution to Planck and combine with the $(D_V/r_s,F_{\rm AP},f\sigma_8)$ constraints of~\citet{Beutler:2013b} by varying the neutrino mass and the growth index $\gamma$ as free parameters, where $f(z) = \Omega_m^{\gamma}(z)$, we find $\gamma = 0.67\pm0.14$. This result is in $1\sigma$ agreement with the GR prediction of $\gamma^{\rm GR} = 0.55$. Similar results are obtained for WMAP9. If our result is confirmed by future, more precise cosmological measurements, it will have significant implications for particle physics and cosmology. The constraint $\sum m_{\nu} = 0.35\pm0.10\,$eV can be expressed as \begin{align} \Omega_{\nu}h^2 &= 0.0039\pm0.0011\;\;\;\;\; \text{or}\\ f_{\nu} &= 0.0315\pm0.0088. \end{align} The large value of $\sum m_{\nu}$ found in our analysis would be too large to allow for cosmological probes to distinguish between the inverted and the normal mass hierarchies just by the measurement of the sum of the masses. However, within the normal hierarchy we can predict $m_{\beta} = 0.117\pm0.031\,$eV, while for the inverted hierarchy we find $m_{\beta} = 0.123\pm0.032\,$eV. These masses are below the predicted detection limits of the KATRIN experiment (assuming a sensitivity of $m_{\beta} \sim 0.2\,$eV~\citealt{Wolf:2008hf}). The constraints presented in this paper will be further improved in the near future. Within the CMASS dataset the weakest point of the constraint is certainly the large uncertainty on $f\sigma_8$, which, however, is predicted to improve significantly with future datasets like the Dark Energy Spectroscopic Instrument (DESI)~\citep{Font-Ribera:2013rwa, Abazajian:2013oma}. Even the BOSS dataset could provide additional constraints on the neutrino mass using the characteristic scale-dependent damping of the power spectrum (see~\citealt{Zhao:2012xw} for such an attempt) which, however, requires refined simulations including massive neutrinos~\citep{Villaescusa-Navarro:2013pva}. | 14 | 3 | 1403.4599 |
1403 | 1403.6896_arXiv.txt | { The New Vacuum Solar Telescope (NVST) is a 1 meter vacuum solar telescope that aims to observe the fine structures on the Sun. The main tasks of NVST are high resolution imaging and spectral observations, including the measurements of solar magnetic field. NVST is the primary ground-based facility of Chinese solar community in this solar cycle. It is located by the Fuxian Lake of southwest China, where the seeing is good enough to perform high resolution observations. In this paper, we first introduce the general conditions of Fuxian Solar Observatory and the primary science cases of NVST. Then, the basic structures of this telescope and instruments are described in detail. Finally, some typical high resolution data of solar photosphere and chromosphere are also shown. | % \label{sect:intro} The New Vacuum Solar Telescope (NVST) is a vacuum solar telescope with 985 mm clear aperture. It is the primary observation facility of the Fuxian Solar Observatory (FSO). The location of FSO is \ensuremath{24^{\circ}}34\ensuremath{'}48\ensuremath{''}N and \ensuremath{102^{\circ}}57\ensuremath{'}01\ensuremath{''}E, the northeast side of the Fuxian Lake (Figure \ref{Fig1}), with the altitude of 1,720 m above the sea level. The average seeing (Fried parameter, r$_{0}$) of FSO obtained in the period from 1998 to 2000 was about 10 cm (Figure \ref{Fig2}). The sunshine duration of FSO is about 2,200 hours per year. The average wind velocity is 6 m s$^{-1}$, more than 75\% wind around FSO is from the lake and toward the telescope (\cite{lou01}). The weather parameters were measured by an automatic meteorological station. The seeing parameters include the scintillation and the Fried parameter, and were measured by the scintillometer and the Solar Differential Image Motion Monitor (SDIMM) that was first developed by the FSO team (\cite{liu01}; \cite{becker03}). \begin{figure} \centering \includegraphics[width=\textwidth, angle=0]{ms1719fig1.eps} \caption{Building (left), telescope and the wind screen (right) of NVST.} \label{Fig1} \end{figure} \begin{figure} \centering \includegraphics[width=\textwidth, angle=0]{ms1719fig2.eps} \caption{Variations curve of the seeing (r$_{0}$) at FSO in the period from September 1999 to September 2000.} \label{Fig2} \end{figure} The early science cases of NVST were focused on the spectrum observation because NVST was originally proposed mainly as the ground-based large scale spectrometer of the Chinese one meter Space Solar Telescope (\cite{deng09}). The original primary working mode of NVST is multi-bands spectrum observation, including the Stokes parameter measurement of the solar magnetic sensitive lines. The good seeing of FSO encourages the FSO team to expand the scientific goals to high resolution observations in order to cover more topics related to open and hot issues. Now, the scientific goals of the telescope include observing the Sun with very high spatial and spectral resolutions in the wavelength range from 0.3 to 2.5 micron; detecting small scale structures and the fine details in the evolution of the solar magnetic field and their coupling to the plasma; investigating the energy transfer, storage and release in the solar atmosphere, such as the corona heating, the triggering of the solar eruption, and the other key questions regarding solar activities. Now, as the primary optical and near infrared solar telescope of Chinese solar community (\cite{fang11}; \cite{wang13}), NVST is required to undertake more science and technology tasks, including the key experiments of the next generation solar telescopes (\cite{liu12}). In the next section, we are briefly describing the basic structure of NVST. The instrumentation of the telescope will be introduced in Section 3. We display some high resolution observational data obtained by NVST in Section 4. | \label{sect:suma} The observation data of NVST including images and movies have been opened at present (http://fso.ynao.ac.cn). As one of the current big solar telescopes in the world, NVST shows the expected power in the high resolution observations. Considering its location is just between Europe and America, NVST could combine with the other big solar telescopes (\cite{scha03}; \cite{schm12}; \cite{good12}) to form a global high resolution observation net. NVST is expected to contribute some original discovers in the near future, so it is necessary to equip more high-precision instruments, especially the instruments of magnetic-field measuring. | 14 | 3 | 1403.6896 |
1403 | 1403.6544_arXiv.txt | This paper investigates the conditions for producing rapid variations of solar energetic particle (SEP) intensity commonly known as ``dropouts''. In particular, we use numerical model simulations based on solving the focused transport equation in the 3-dimensional Parker interplanetary magnetic field to put constraints on the properties of particle transport coefficients both in the direction perpendicular and parallel to the magnetic field. Our calculations of the temporal intensity profile of 0.5 and 5 MeV protons at the Earth show that the perpendicular diffusion must be small enough while the parallel mean free path should be long in order to reproduce the phenomenon of SEP dropouts. When the parallel mean free path is a fraction of 1 AU and the observer is located at $1$ AU, the perpendicular to parallel diffusion ratio must be below $10^{-5}$, if we want to see the particle flux dropping by at least several times within three hours. When the observer is located at a larger solar radial distance, the perpendicular to parallel diffusion ratio for reproducing the dropouts should be even lower than that in the case of 1 AU distance. A shorter parallel mean free path or a larger radial distance from the source to observer will cause the particles to arrive later, making the effect of perpendicular diffusion more prominent and SEP dropouts disappear. All these effects require that the magnetic turbulence that resonates with the particles must be low everywhere in the inner heliosphere. | Solar Energetic Particles (SEPs) encounter small-scale irregularities during transport in the large scale interplanetary magnetic field. The particles are scattered by the irregularities whose scales are comparable to the particles' gyro radius. The parallel diffusion is produced by the pitch angle scattering, while the perpendicular diffusion is caused by crossing the local field line or following magnetic field lines randomly walking in space. Low-rigidity particles tend to follow more tightly along individual field lines, whereas high-rigidity particles can cross local field lines more easily. As a result, the perpendicular diffusion of lower rigidity particles is generally smaller than that of high-rigidity particles. The diffusion coefficients of SEPs depend on the magnetic turbulence in the solar wind. Jokipii (1966) was the first to use the Quasi-Linear Theory (QLT) to calculate particle diffusion coefficients from magnetic turbulence spectrum. But later it was found that the observed particle mean free paths are usually much larger than the QLT results derived from a slab magnetic turbulence \citep{Palmer82}. According to \cite{matthaeus1990evidence}, the slab model is not a good approximation to describe the Interplanetary Magnetic Field (IMF) turbulence because there is also a stronger two-dimensional (2D) component. \citet{BieberEA94} showed that with a ratio of turbulence energy between slab and 2D components, $E^{slab}:E^{2D}=20:80$, the QLT was able to derive a parallel mean free path much better in agreement with observations. However, the perpendicular diffusion remained a puzzle for many years. It is shown that the particles' perpendicular diffusion model of Field Line Random Walk (FLRW) based on QLT has difficulty to describe spacecraft observations and numerical simulations. Recently, the Non-Linear Guiding Center Theory (NLGC) \citep{Matthaeus2003ApJ...590L..53M} was developed to describe the perpendicular diffusion in magnetic turbulence. The perpendicular diffusion coefficient from the NLGC theory agrees quite satisfactorily with numerical simulations of particle transport in typical solar wind conditions. Observations by the ACE and Wind spacecraft show that there are rapid temporal structures in the time profiles of $ \sim 20 $ keV nucleon$^{-1}$ to $ \sim 5 $ MeV nucleon$^{-1}$ ions during impulsive SEP events. The phenomenon is commonly known as ``dropouts'' or ``cutoffs'' in some cases. In the dropouts, the particle intensities exhibit short time scale (about several hours) variations, whereas, the cutoffs are referred to as some special dropouts in which the intensities suddenly decrease without recovery. They do not seem to be associated with visible local magnetic field changes \citep{mazur2000interplanetary,Gosling2004Correlated,chollet2008multispacecraft,Droge2010}. Contrarily to the previous studies, by performing a detailed analysis of magnetic field topology during SEP events, \cite{trenchi2013solar,trenchi2013observations} identified magnetic structures associated with SEP dropouts. \cite{,trenchi2013solar} found that SEP dropouts are generally associated with magnetic boundaries which represent the borders between adjacent magnetic flux tubes while \cite{trenchi2013observations}, using the Grad-Shafranov reconstruction, identified flux ropes or current sheet associated with SEP maxima. The dropouts and cutoffs can be interpreted as a result of magnetic field lines that connect or disconnect the observer alternatively to the SEP source on the Sun. However, with perpendicular diffusion, particles can cross the field lines as they propagate in the interplanetary space. A strong enough perpendicular diffusion can efficiently diminish longitudinal gradients of fluxes. The dropouts and cutoffs provide a good chance for us to estimate the level of perpendicular diffusion in the interplanetary space. In an effort to interpret the SEP dropouts, \cite{giacalone2000small} did a simulation of test particle trajectory in a model with random-walking magnetic field lines using Newton-Lorentz equation to study SEPs dropouts. It was found that the phenomenon is consistent with random-walking magnetic field lines. In addition, it was found from their simulations that, particle perpendicular diffusion relative to the Parker spiral due to the field line random walk can be significant, and the ratio of perpendicular diffusion to the parallel one relative to the Parker spiral can be as large as $2\%$. However, their perpendicular diffusion coefficients relative to the background magnetic field (instead of Parker spiral) could still be very small, so dropouts can be obtained. Recently, using the same technique as in \cite{giacalone2000small}, \cite{Guo2013Small} found that in some condition, dropouts can be reproduced in the foot-point random motion model, but no dropout is seen in the slab + 2D model. In \cite{Droge2010}, the large scale magnetic field is assumed to be a Parker spiral, and the observer is located at $1$ AU equatorial plane. At the start the observer is connected to the source region, and leaves the region after some time due to the effect of co-rotation. Based on a numerical solution of the focused transport equation, they found that in order to reproduce cutoffs, the ${\kappa _ \bot }/{\kappa _\parallel }$ should be as small as a few times of ${10^{ - 5}}$. In the turbulence view, some other mechanisms \citep{ Ruffolo2003Trapping, Chuychai2005Suppressed, Chuychai2007Trapping, Kaghashvili2006Propagation, Seripienlert2010Dropouts} are also proposed to interpret the dropout phenomenon. In this work, we use a Fokker-Planck focused transport equation to calculate the transport of SEPs in three-dimensional Parker interplanetary magnetic field. We intend to put constraints on the conditions of the perpendicular and parallel diffusion coefficients for observing the SEP dropouts and cutoffs. In SECTION 2 we describe our SEP transport model. In SECTION 3 simulation results are presented. In SECTION 4 the simulation results are discussed, and conclusions based on our simulations are made. | By numerically solving the Fokker-Planck focused transport equation for $500$ keV and $5$ MeV protons, we have investigated the effect of the perpendicular diffusion coefficients on the dropouts and cutoffs when an observer is located at $1$ AU or $3$ AU in the ecliptic. SEPs are injected from a source near the Sun, and the source rotates with the Sun. The dropouts and cutoffs are caused by the magnetic flux tubes which are alternately filled with and devoid of ions past the spacecraft. In this paper, all the times between neighbouring valleys and peaks are less than $3$ hours, and the ratio $R_2$ between the second peak value and the second valley value are used to identify the dropouts. The dropout is defined to be present when $R_2$ is more than a significant factor, which is set to be 2. We list the values of $R_2$ in the cases of different magnetic field turbulence intensities in Table \ref{diffusionCoefficients}. Our simulations are performed for several different parallel mean free paths (${\lambda _\parallel } = $ $0.5$ AU, $0.087$ AU, $0.026$ AU at $1$ AU) with different assumption for the ratios of perpendicular diffusion coefficient to the parallel one. With a larger parallel mean free path, the onset time of SEP flux appears earlier, and more dropouts can be detected. Meanwhile, the flux increases more quickly, and the peak time is also earlier. This feature is closely related to the pitch angle distribution of particles arriving at the observer. Since the particles encounter fewer scatterings when they propagate in the interplanetary space with a larger parallel mean free path. Therefore, the distribution of pitch angle would be anisotropic for a longer time in this case. In order to reproduce the dropouts and cutoffs at 1 AU, the perpendicular diffusion has to be small: ${\kappa _ \bot }/{\kappa _\parallel } \lesssim 5 \times {10^{ - 5}}$ when observer is located at $1$ AU, while ${\kappa _ \bot }/{\kappa _\parallel } \lesssim 1 \times {10^{ - 5}}$ when observer is located at $3$ AU. In any case when the dropouts are reproduced, cutoffs can also be reproduced when the observer's flux tubes completely move out of the source region. If the observer is located at a larger radial distance (eg, $3$ AU in our simulation), it takes a longer time for the particles to propagate from the Sun to the observer, and perpendicular diffusion has more time to be effective. In order to reproduce the dropout at several AU, the ratio of ${\kappa _ \bot }/{\kappa _\parallel }$ should be lower than that in the cases of $1$ AU. As a result, our simulation also predicts that the dropout may disappear at larger radial distances, which can be checked by analysing data from Ulysses or other spacecraft at large distance. With a wider source, the observer can detect more dropouts. Other than this, the fluxes with a wider source show behaviors similar to those with a narrower source. As $a$ changes from $0$ to $12$, in the case of ${\kappa_\bot}/{\kappa_\parallel}=1\times{10^{-5}}$, the ratio $R_i$ is much larger in the case of $a=12$ than that in the case of $a=0$. However, in the cases of ${\kappa_\bot}/{\kappa_\parallel}=1\times{10^{-4}}$ and ${\kappa_\bot}/{\kappa_\parallel}=5\times{10^{-5}}$, the ratio $R_i$ does not change significantly as $a$ changes from $0$ to $12$. For $5$ MeV protons, the case of ${\lambda _\parallel } = 0.13$ AU has been analysed. Due to the higher particle speed and a typically larger parallel mean free path, the onset time appears earlier than for $500$ keV protons. As a result, more dropouts can be detected. In order to reproduce the dropouts and cutoffs, the ratio of the perpendicular diffusion coefficient to the parallel one should be smaller than $10^{-5}$, which is a little lower than that in the cases for $500$ keV protons. Different ${\kappa _ \bot }$ and ${\kappa _\parallel } $ are obtained by altering the parameters $A_1$ and $A_2$ in our simulations, respectively, where ${A_1}={\left({\delta{B_{slab}}}\right)^2}/({{{B_0}}^2}\cdot l_{slab})$, and ${A_2}={\left({\delta{B_{2D}}}\right)^2}/{\left({{B_{0}}}\right)^2}\cdot{l_{2D}}$. In Table \ref{diffusionCoefficients}, we list all coefficients in the diffusion formulae which are used in our simulations with $\lambda_\parallel$ equal to $0.5$ AU, $0.087$ AU, $0.026$ AU for $500$ keV protons and $0.13$ AU for $5$ MeV protons at $1$ AU. In this table, we assume a slab turbulence correlation length $l_{slab}=0.03$ AU, and 2D correlation length $l_{2D}=0.003$ AU. As we can see, the ${\left({\delta{B_{slab}}/{B_0}}\right)^2}$ is much larger than ${\left({\delta{B_{2D}}/{B_0}}\right)^2}$ in all cases. This result is consistent with the observation \citep{Tan2014Correlation}. However, we should note that the exact values of ${\left({\delta {B_{slab}}/{B_0}}\right)^2}$, ${\left({\delta{B_{2D}}/{B_0}}\right)^2}$, $l_{slab}$ and $l_{2D}$ cannot be well determined. For example, we can assume slab turbulence correlation length $l_{slab}=0.003$ AU instead, and ${\lambda _\parallel } = 0.5$ AU, $0.087$ AU, and $0.026$ AU for $500$ keV protons given ${\left({\delta{B_{slab}}/{B_0}}\right)^2}=0.05$, $0.3$, and $1$, respectively. In our results we need a very small $\delta B_{2D}/\delta B_{slab}$ to get a small perpendicular diffusion coefficients from the NLGC theory. However, the NLGC results with a small $\delta B_{2D}/\delta B_{slab}$ are much larger than simulation results \citep[e.g.,][]{Qin07}. Although $\delta B_{2D}/\delta B_{slab}$ must be small to get the small perpendicular diffusion coefficients, the actual value of $\delta B_{2D}/\delta B_{slab}$ needed according to simulations \citep{Qin07} is not as extremely small as that shown in Table \ref{diffusionCoefficients} from NLGC theory. In \cite{Droge2010}, the cutoffs can be reproduced for a ratio of ${\kappa _ \bot }/{\kappa _\parallel }$ a few times $10^{-5}$. This ratio is similar to what we deduced from our simulations. The basic difference between this simulation and the one in \cite{Droge2010} is that we reproduced the dropouts and cutoffs simultaneously, while their simulation only reproduced the cutoffs. We believe that the cutoffs are only a special type of dropout in which the intensity suddenly decreases without recovery. In \cite{giacalone2000small} and \cite{Guo2013Small}, perpendicular diffusion coefficients relative to the background magnetic field (instead of Parker spiral) needed to be very small for reproducing the dropouts. That is consistent with our results. It should be noted that in our model, the large scale magnetic field is assumed to be a Parker spiral so that the Fokker-Planck focused transport equation can be solved efficiently with our stochastic method. In reality, the magnetic field lines with randomly walking foot-point do not have an azimuthal symmetry. However the large-scale geometry of interplanetary magnetic field and the behaviours of particle transport in it are not much different from those with a Parker magnetic field. The only difference is a slight shift of SEP source location relative to the magnetic field line passing through the observation at 1 AU. Some special sets of turbulence parameters are needed in our simulations to produce small perpendicular diffusion coefficients in order to produce the dropouts and cutoffs. For example, turbulence dominated by a slab component leads to very small perpendicular diffusion coefficients. In the future, it will be interesting for us to study solar wind turbulence geometry from spacecraft observations when SEP dropouts and cutoffs occur. | 14 | 3 | 1403.6544 |
1403 | 1403.6128_arXiv.txt | { We present homogeneous and accurate iron abundances for 42 Galactic Cepheids based on high–spectral resolution (R$\sim$ 38,000) high signal-to-noise ratio (SNR $\geq$ 100) optical spectra collected with UVES at VLT (128 spectra). The above abundances were complemented with high--quality iron abundances provided either by our group (86) or available in the literature. We paid attention in deriving a common metallicity scale and ended up with a sample of 450 Cepheids. We also estimated for the entire sample accurate individual distances by using homogeneous near-infrared photometry and the reddening free Period-Wesenheit relations. The new metallicity gradient is linear over a broad range of Galactocentric distances ($\Rg \sim$5--19 kpc) and agrees quite well with similar estimates available in the literature (-0.060$\pm$0.002 dex/kpc). We also uncover evidence which suggests that the residuals of the metallicity gradient are tightly correlated with candidate Cepheid Groups (CGs). The candidate CGs have been identified as spatial overdensities of Cepheids located across the thin disk. They account for a significant fraction of the residual fluctuations, and in turn for the large intrinsic dispersion of the metallicity gradient. We performed a detailed comparison with metallicity gradients based on different tracers: OB stars and open clusters. We found very similar metallicity gradients for ages younger than 3 Gyrs, while for older ages we found a shallower slope and an increase in the intrinsic spread. The above findings rely on homogeneous age, metallicity and distance scales. Finally we found, by using a large sample of Galactic and Magellanic Cepheids for which are available accurate iron abundances, that the dependence of the luminosity amplitude on metallicity is vanishing. } | Recent findings concerning the metallicity gradient across the Galactic thin disk, based on high spectral resolution, high signal-to-noise spectra and on stellar tracers for which we can provide accurate individual Galactocentric distances, are disclosing a new interesting scenario. The iron gradients traced by stellar populations younger than a few hundred of Myrs show a well defined trend when moving from the inner to the outer disc regions. The iron abundances in the innermost disc regions ($R_G\sim$5 kpc) are well above solar \citep[\feh $\sim$0.4,][hereinafter G13]{Andrievsky2002,Pedicelli2009,Luck2011a,Luck2011b,Genovali2013} while in the outer disk ($R_G\sim$15 kpc) they are significantly more metal--poor \citep[\feh $\sim$-0.2/-0.5,][]{Andrievsky2004,Yong2006,Lemasle2008}. However, the young stellar populations in the two innermost Galactic regions showing ongoing star formation activity --the Bar and the Nuclear Bulge-- attain solar iron abundances. Thus suggesting that the above regions are experiencing different chemical enrichment histories \citep{Bono2013}. The use of high-quality data and homogeneous analysis of large sample of classical Cepheids and young massive main sequence stars provided the opportunity to overcome some of the systematics affecting early estimates of the metallicity gradient. However, current findings still rely on several assumptions that might introduce systematic errors. i) Distances -- Cepheids are very solid primary distance indicators, but they only trace young stellar populations. The use of red clump stars is very promising, since they are ubiquitous in the innermost Galactic regions. However, their individual distances might be affected by larger uncertainties, since we are dealing with stellar populations covering a broad range in ages and in metal abundances \citep{Girardi2001,Salaris2002}. ii) Gradients -- Recent spectroscopic investigations indicate that the use of homogeneous and accurate iron abundances decreases the spread along the radial gradient (G13). This means that they can be adopted to investigate the fine structure of the metallicity distribution \citep{Lepine2011} and the possible occurrence of gaps and/or of changes in the slope \citep{Lepine2013}. iii) Ages -- The central helium burning phases of intermediate--mass ($M\sim$3.5--10 $M_\odot$) stars take place along the so--called blue loops. During these phases an increase in stellar masses causes a steady increase in the mean luminosity. These are the reasons why classical Cepheids do obey to a Period-Age relation. However, the ages covered by Cepheids is quite limited ($\approx$20--400 Myr). Most of the current chemical evolution models do predict a steady decrease in slope of the metallicity gradient as a function of age \citep{Portinari2000,Cescutti2007,Minchev2013}. However, we still lack firm estimates of this effect since homogeneous estimates of distance, age and chemical composition for a large sample of intermediate and old open clusters \citep{Salaris2004,Carraro2007b,Yong2012} are still missing. In this investigation we provide new accurate and homogeneous iron abundance estimates for 42 Galactic Cepheids based on high spectral resolution, high signal-to-noise ratio (\snr) spectra acquired with UVES at VLT. The total sample includes estimates for 75 Cepheids (74 Classical Cepheids and one Type II Cepheid --DD Vel-- that will be discussed in a forthcoming paper), whose abundances were partially published in \cite{Genovali2013}. Moreover, we also analyzed three high spectral resolution spectra for the Cepheids --TV CMa, RU Sct, X Sct-- collected with NARVAL at the T\'elescope Bernard Lyot (TBL)\footnote{Based on observations collected with TBL (USR5026) operated by OMP \& INSU under programme ID L072N06 (PI: B. Lemasle).} that we adopted to double check current iron abundance estimates. We also added a new estimate of the FEROS spectrum for the Cepheid CE Pup whose metallicity was already available in the literature \citep{Luck2011a}. The above iron abundances were complemented with similar estimates provided either by our group \citep[][53 Cepheids]{Lemasle2007,Lemasle2008,Romaniello2008} or available in the literature \citep[][322 Cepheids]{Yong2006,Luck2011a,Luck2011b}. We ended up with a sample of 450 Classical Cepheids i.e. the 73\% of the entire sample of known Galactic Cepheids according to the Classical Cepheids list in the GCVS (candidate Cepheids are excluded from this estimate). For the entire sample, we estimated homogeneous distances based on reddening-free near infrared Period--Wesenheit relations \citep{Inno2013}. This is the eighth paper of a series devoted to chemical composition of Galactic and Magellanic Cepheids (see the reference list). The name of the project is DIsk Optical and Near infrared Young Stellar Object Spectroscopy (DIONYSOS). The structure of the paper is the following. In \S 2 we present the spectroscopic data sets adopted in the current investigation and the method adopted to estimate the iron abundances. The photometric data and the individual distances are discussed in \S 3, together with a detailed analysis of the errors affecting Cepheid distances. \S 4 deals with the metallicity gradient, while in \S 5 we investigate the dependence of the metallicity gradient on stellar age. In this section the metallicity gradient is compared with the metallicity gradients based on younger tracers (OB stars) and with intermediate-age tracers (open clusters). In \S 6 we address in detail the fine structure of the metallicity gradient and perform a thorough analysis of the Cepheid radial distribution across the Galactic disk. \S 7 deals with the longstanding open problem concerning the dependence of the luminosity amplitude on the metallicity, while in \S 8 we summarize the results and briefly outline the future developments of this project. | We performed accurate new measurements of iron abundances for 42 Galactic Cepheids using high-resolution, high-\snr \ UVES, NARVAL and FEROS spectra. The iron abundance, for eleven Cepheids located in the inner disk, is based on multi-epoch spectra (from four to six) and their intrinsic uncertainty is smaller when compared with other Cepheids at super-solar iron content. Current sample was complemented with Cepheid iron abundances based on high--resolution spectra provided either by our group \citep{Lemasle2007,Lemasle2008,Romaniello2008,Genovali2013} or available in literature \citep{Luck2011a,Luck2011b}. We ended up with a sample of 450 Cepheids. To improve the accuracy on the metallicity distribution across the disk, we estimated homogeneous and reddening-free distances by using near-infrared Period--Wesenheit relations for the entire sample. The main findings of the current iron abundance analysis are given in more detail in the following. \begin{itemize} \item[$\bullet$] We found that the metallicity gradient, based on current spectroscopic measurements, is linear with a slope of -0.051$\pm$0.003 dex/kpc, in agreement with recent studies by \cite{Luck2011a} and \cite{Luck2011b}. The metallicity gradient based both on our and on literature iron abundances shows a similar slope: -0.060 $\pm$ 0.002 dex/kpc. Current estimates agrees quite well with the chemical evolution model for the thin disc recently provided by \cite{Minchev2013}. In particular, they found that the iron gradient is -0.061 dex/kpc for Galactocentric distances ranging from 5 to 12 kpc and -0.057 dex/kpc for Galactocentric distances ranging from 6 to 11 kpc. The predicted slopes become marginally shallower if they account for stellar radial migrations. \item[$\bullet$] We estimated the metallicity gradient by selecting the Cepheids in our sample with a distance above the Galactic plane smaller than 300 pc and we found that it is, within the errors, quite similar: -0.052$\pm$0.004 dex/kpc. The same outcome applies to the the gradient based on the entire sample, and indeed we found: -0.055$\pm$0.002 dex/kpc. We also found that the spread in iron in the outer disk ($R_G \ge13$ kpc) decreases by more than a factor of two (0.13 vs 0.17 dex) if we adopt the subsample located closer to the Galactic plane. \item[$\bullet$] We also confirm that classical Cepheids in the inner disk ($\Rg$ $\sim$5.5--6.0 kpc), just beyond the position of the Galactic Bar corotation resonance \citep{Gerhard2011}, attain super-solar (\feh$\sim$0.4) iron abundances. This result supports similar findings by G13 and by \cite{Andrievsky2002,Pedicelli2010,Luck2011b}. There is preliminary evidence that the iron abundance in the innermost Galactic regions (Nuclear Bulge, Galactic Bar) is more metal--poor than predicted by chemical evolution models (\cite{Minchev2013}). Indeed recent spectroscopic iron abundances of young stars (red supergiants, luminous blue variables, Wolf--Rayet, O-type stars) indicate either solar or sub--solar abundances \citep{Davies2009a,Davies2009b,Origlia2013}. On the other hand, chemical evolution models suggest in the same regions iron abundances larger than \feh$\sim$0.8 \citep{Minchev2013}. The above evidence indicate that objects located inside the corotation resonance of the bar experienced a different chemical enrichment history when compared with Cepheids located just beyond this limit. \item[$\bullet$] The new homogeneous Cepheid metallicity distribution is characterized by a smaller intrinsic dispersion when compared with similar estimates available in the literature. We found evidence of a steady increase in the abundance dispersion when moving in the outer disk ($\Rg$ > 14 kpc). Current data do no allow us to constrain whether this effect is the aftermath of outward stellar migrators as recently suggested by \cite{Minchev2012} or the consequence of the infall of the Sagittarius dwarf galaxy producing a flared outer disk as suggested by \cite{Purcell2011}. \item[$\bullet$] To investigate the fine structure of the metallicity in the disk, we searched for Cepheids groups following the approach suggested by \cite{Ivanov2008}. We found ten candidate Cepheids Groups, i.e. physical aggregation of stars whose mean residual metallicity agrees quite well with the trend of the metallicity residuals as a function of the Galactocentric distance. The presence of the CGs appears to be the main culprit of the fluctuations in the metallicity residuals and of the azimuthal effects on the radial gradient. This suggests that members of CGs experienced a very similar chemical enrichment history. Most of the CGs are located close to spiral arms (Sagittarius-Carina and Perseus arms) according to a simple logarithmic spiral model provided by \cite{Vallee2005}. The above findings indicate that the occurrence of CGs with sizes ranging from OB association/young cluster to star complexes/superassociations appear to be largely responsible for the intrinsic spread of the iron metallicity gradient. Moreover, the association of the metallicity residuals with candidate CGs supports the results by \cite{Sofue2013} concerning the association of a local minimum in the Galactic rotational curve at $\Rg\sim$=9.5 kpc with the Perseus arm. \item[$\bullet$] We also found that the mean periods of the Cepheids hosted in candidate CGs with negative iron residuals have, on average, slightly longer periods and larger intrinsic dispersions when compared with the candidate CGs showing a positive iron residual. Thus suggesting a common star formation episode within each candidate CG. The evidence of possible abundance inhomogeneities in the Galactic disk dates back to \cite[][and references therein]{Efremov1995} who suggested that the different star complexes might have different star formation histories and different interactions with the intergalactic medium. It is clear that the abundance information (iron and $\alpha$--elements) will provide a new spin to the analysis of their evolutionary and pulsation properties. \item[$\bullet$] To constrain the impact of age on iron abundance gradient, we compared the Cepheid iron gradient with those based on OCs. Spectroscopic metallicities and homogeneous distances and age were collected for OCs spanning a large range in age. The OC gradient based on clusters younger than 3 Gyrs agrees quite well with the Cepheid gradient. \item[$\bullet$] The comparison between Cepheids and OCs older than 3 Gyrs is more complex. Indeed, we found that old OCs display a clear flattening in iron abundance for $R_G\ge15$ kpc. This result supports similar findings available in the literature e.g. \cite{Carraro2007b}, \cite{Bragaglia2008}, \cite{Magrini2009,Magrini2010}, \cite{Jacobson2011a,Jacobson2011b}, \cite{Yong2012}. Moreover, old OCs located between the solar circle and $\Rg\sim$12 kpc seem to show a dichotomic distribution. The difference is of the order of several tenths of dex and might be due to a selection bias affecting the azimuthal distribution. However, the comparison of Cepheids iron abundances with similar abundances for old OCs further support the evidence that the metallicity gradient does depend on age for ages larger than $\sim$3 Gyrs. \item[$\bullet$] We investigate the possible occurrence of a metallicity effect on the pulsational amplitude by using a large sample of fundamental Galactic and Magellanic Cepheids \citep{Luck1992,Luck1998,Romaniello2008} with accurate iron abundances. The comparison of low, medium, and high metallicity subsamples indicate that luminosity amplitudes are, within current uncertainties, independent of iron abundance. \end{itemize} Classical Cepheids appear to be solid young stellar tracers to constrain the recent chemical enrichment of the Galactic thin disk. Current sample of Galactic Cepheids is smaller when compared with similar tracers (OB stars, HII regions, red clump stars, open clusters). However, their distances, ages and abundances can be firmly estimated. They are ubiquitous in young star forming regions and the recent identification of classical Cepheids both in the Nuclear Bulge and in the Galactic Bar \citep{Matsunaga2011b,Matsunaga2013} will provide the opportunity to use the same stellar tracer to constrain the change in iron abundance across the corotation resonance. This also means the opportunity to constrain whether the high star formation rate of the innermost Galactic regions is driven by a disk instability that is dragging material from the inner disk into these regions \citep{Freeman2013,Ness2013a,Ness2013b}. Classical Cepheids are also excellent tracers to constrain the speed of the spiral arm pattern by fitting a kinematic model to the observed Cepheid kinematics \citep{Fernandez2001,Lepine2001}. The Cepheid kinematics is time consuming, since a proper coverage of the radial velocity curves does require spectroscopic time series data. The use of template radial velocity curves significantly decreases the number of measurements required for an accurate estimate of the center of mass radial velocity \citep{Metzger1998}. However, we still lack accurate radial velocity curve templates covering the entire period range. Current observational scenario appears to be even more appealing in the outer disk, since we are still facing a "Cepheid desert" for Galactocentric distances larger than $\sim$18 kpc. New identification and characterization of Cepheids at least in the first and in the second quadrant are urgently needed to properly trace the outskirts of the Galactic disk. | 14 | 3 | 1403.6128 |
1403 | 1403.0404_arXiv.txt | We present the {\em \underline{Ch}asing the \underline{I}dentifi\underline{c}ation of \underline{A}SCA \underline{G}alactic \underline{O}bjects} (\chic) survey, which is designed to identify the unknown X-ray sources discovered during the \asca\ Galactic Plane Survey (AGPS). Little is known about most of the AGPS sources, especially those that emit primarily in hard X-rays ($2-10$ keV) within the $F_{x} \sim 10^{-13} \mathrm{~to~} 10^{-11}$ \erg\ X-ray flux range. In ChIcAGO, the subarcsecond localization capabilities of \cxo\ have been combined with a detailed multi-wavelength follow-up program, with the ultimate goal of classifying the $>100$ unidentified sources in the AGPS. Overall to date, 93 unidentified AGPS sources have been observed with \cxo\ as part of the \chic\ survey. A total of 253 X-ray point sources have been detected in these \cxo\ observations within $3'$ of the original \asca\ positions. We have identified infrared and optical counterparts to the majority of these sources, using both new observations and catalogs from existing Galactic plane surveys. X-ray and infrared population statistics for the X-ray point sources detected in the \cxo\ observations reveal that the primary populations of Galactic plane X-ray sources that emit in the $F_{x} \sim 10^{-13} \mathrm{~to~} 10^{-11}$ \erg\ flux range are active stellar coronae, massive stars with strong stellar winds that are possibly in colliding-wind binaries, X-ray binaries, and magnetars. There is also a fifth population that is still unidentified but, based on its X-ray and infrared properties, likely comprise partly of Galactic sources and partly of active galactic nuclei. | From 1996 to 1999, the \textit{Advanced Satellite for Cosmology and Astrophysics} (\asca) performed the \asca\ Galactic plane survey (AGPS), which was designed to study 40 deg$^{2}$ of the X-ray sky, over the Galactic coordinates $|l| \lesssim 45^{\circ}$ and $|b| \lesssim 0^{\circ}.4$, in the $0.7-10$ keV energy range \citep{sugizaki01}. This survey resulted in a catalog of 163 discrete X-ray sources with X-ray fluxes between $F_{x} \sim 10^{-13} \mathrm{~and~} 10^{-11}$ \erg, many of which are much harder and more absorbed than any other X-ray source previously detected in the Galactic plane. While the AGPS yielded the first ever \ns\ distribution of hard ($2-10$ keV) Galactic plane X-ray sources, \asca's limited spatial resolution ($3'$) and large positional uncertainty ($1'$) left $>100$ of the AGPS sources unidentified. Even in the era of the \textit{Chandra X-ray Observatory} and the \textit{XMM-Newton} telescope, a substantial fraction of the AGPS source catalog, and therefore a large fraction of the Galactic plane X-ray population, still remain unidentified. For the last few years, new and archival multi-wavelength data have been used to improve the general understanding of the Galactic X-ray sources detected in the AGPS. Recent work has demonstrated that unidentified \asca\ sources represent a whole range of unusual objects. For example \citet{gelfand07} used new and archival \cxo\ and \xmm\ observations to identify the AGPS source \object[AX J1550.8-5418]{AX J155052--5418} (also known as \object[PSR J1550-5418]{1E 1547.0--5408}) as a magnetar sitting at the center of a faint and small, previously unidentified, radio supernova remnant (SNR) called G327.24--0.13. Investigations of archival \xmm\ data allowed \citet{kaplan07} to identify the AGPS source \object[AX J1835.4-0737]{AX J183528--0737} as a likely symbiotic X-ray binary (SyXB) comprising of a late-type giant or supergiant and a neutron star (NS) with a 112s pulse period. \citet{gaensler08} identified the AGPS source \object[AX J1721.0-3726]{AX J172105--3726} as the X-ray emission associated with the radio \object[SNR G350.1-00.3]{SNR G350.1--0.3}. The \xmm\ X-ray spectrum, combined with the presence of non-thermal, polarized, radio emission, showed G350.1--0.3 to be a very young and luminous SNR. A central compact object was also resolved in these X-ray observations and identified as a NS. \xmm\ \citep{funk07} and \cxo\ \citep{lemiere09} observations have demonstrated that the AGPS source \object[AX J1640.7-4632]{AX J164042--4632} is an X-ray pulsar wind nebula (PWN) located at the center of the radio \object[SNR G338.3-00.0]{SNR G338.3--0.0}. \cxo\ results, discussed in \citet{anderson11}, have revealed that two AGPS sources, \object[AX J1632.8-4746]{AX J163252--4746} and \object[AX J1847.6-0156]{AX J184738--0156}, are massive stars in colliding wind binaries (CWBs). New \cxo, \xmm, and ATCA observations have also been used to identify the AGPS source \object[PSR J1622-4950]{AX J162246--4946} as the radio and X-ray emitting magnetar, \object[PSR J1622-4950]{PSR J1622--4950}, and have exposed the likely X-ray transient nature of this source \citep{anderson12}. These identifications over the last 8 years have therefore demonstrated that many of the unidentified AGPS sources are unusual and rare Galactic plane X-ray objects. The most comprehensive X-ray survey to-date, in terms of area coverage, was performed by the \textit{ROSAT} X-ray Satellite \citep[for example see][]{voges99}, which mapped the soft X-ray source population ($0.1-2.4$ keV) down to a flux sensitivity of a few $10^{-13}$ \erg. Projects that focused on the \textit{ROSAT} data covering the Galactic plane \citep[e.g. the ROSAT Galactic Plane Survey;][]{motch97,motch98} demonstrated that stars and AGN dominate the soft X-ray sky. However, performing a similar Galactic plane survey to include those sources with energies up to $10$ keV, sensitive to the $F_{x} \sim 10^{-13} \mathrm{~to~} \sim10^{-11}$ \erg\ flux range, would be impractical to achieve with the current X-ray telescopes \cxo\ and \xmm\ due to their limited fields of view. Astronomers have therefore had to rely upon characterizing the distribution of the harder X-ray source populations within much smaller regions of the Galactic plane \citep[e.g.][]{hands04,ebisawa05,grindlay05}. For example, \citet{motch10} used the XGPS \citep{hands04} to determine the contributions of active stellar coronae and accreting X-ray source populations in the Galactic plane for $F_{x} \lesssim 10^{-12}$ \erg. The Chandra Multiwavelength Plane survey \citep[ChaMPlane;][]{grindlay05} has now surveyed 7 deg$^{2}$ of the Galactic plane and bulge with \cxo\ \citep{vandenberg12}, identifying the contributions of magnetic cataclysmic variables (CVs) to the Galactic ridge X-ray emission \citep{hong12b}. The key to obtaining a complete understanding of the Galactic plane X-ray source populations, from $0.3-10$ keV, that make up the $F_{x} \sim 10^{-13} \mathrm{~to~} 10^{-11}$ \erg\ X-ray flux range is to identify the unidentified AGPS sources, as \asca\ covered a much larger area of the Galactic plane ($\sim40$ deg$^{2}$) than other X-ray surveys \citep[for example the XGPS and ChaMPlane;][]{hands04,motch10,grindlay05,vandenberg12}. In order to identify the AGPS sources, the {\em \underline{Ch}asing the \underline{I}dentifi\underline{c}ation of \underline{A}SCA \underline{G}alactic \underline{O}bjects} (\chic) survey was conceived. In this survey the subarcsecond capabilities of \cxo\ are used to localize the unidentified AGPS sources listed by \citet{sugizaki01}. Once the positions of these sources have been determined, an extensive multi-wavelength program is activated, which is aimed at determining the identities of the sources and the nature of their X-ray emission. In this paper, we present the results of \cxo\ observations of 93 unidentified AGPS sources, along with the multi-wavelength follow-up that has allowed the identification of optical, infrared and radio counterparts. Section 2 explains the \cxo\ observing strategy employed to localize the unidentified AGPS sources. To begin the identification process, we automated the \cxo\ data analysis and preliminary multi-wavelength follow-up, which involves comparisons with existing optical, near-infrared (NIR) and infrared (IR) surveys. X-ray spectral modeling using ``quantile analysis'' \citep{hong04} and \citet{cash79} statistics, and further multi-wavelength observations in the optical, infrared and radio bands required to ultimately classify each source, are also described. Section 3 details the results of each AGPS position observed with \cxo. These results include details on the individual X-ray sources detected, the parameters of their likely X-ray spectral shapes, and the names and magnitudes of their infrared, optical and radio counterparts. The possibility of short term variability or periodicity is also explored. In Section 4, we discuss the AGPS sources that have been identified through a visual inspection of radio Galactic plane surveys. The X-ray fluxes and NIR and IR magnitudes of the remaining unidentified sources, reported in Section 3, are then used to conduct X-ray and infrared population statistics. Resulting flux and color-color diagrams allow the identification of likely Galactic plane X-ray populations with infrared counterparts. This analysis is followed by a discussion of particularly interesting individual sources that have been identified as a result of this work. The final part of this section includes a tabulated summary of all the 163 AGPS sources along with their confirmed identifications (obtained from the literature and the present paper) or their tentative identifications that are based on our \chic\ survey statistical results. In Section 5 we summarize the results from this paper, with a particular focus on our statistical findings. | The main aim of the \chic\ survey is to identify the Galactic plane X-ray source populations that make up the $F_{x} \sim 10^{-13} \mathrm{~to~} 10^{-11}$ \erg\ flux range. To achieve this we have used new observations from the \cxo\ X-ray telescope, along with extensive multi-wavelength follow-up, to identify sources from the \asca\ Galactic Plane Survey \citep{sugizaki01}. We have reported observations of the \asca\ positions of 93 unidentified AGPS sources with \cxo, from which a total of 253 X-ray point sources, termed ``\chic\ sources'', have been detected. Through visual inspection of Galactic plane radio surveys, we have found 5 \chic\ sources within supernova remnants that have no cataloged optical or infrared counterparts. These sources could potentially be compact objects associated with their surrounding SNRs. Further radio analysis has also demonstrated that the \chic\ sources detected in the \cxo\ observations of the AGPS sources AX J144519--5949, AX J151005--5824, AX J154905--5420, \object[AX J1622.1-5005]{AX J162208--5005}, AX J194310+2318, AX J194332+2323, and AX J195006+2628 are all coincident with H {\sc ii} regions. Table~\ref{Tab11} demonstrates that the range of luminosities, which are calculated using kinematic distances to the H {\sc ii} regions, are consistent with the luminosities we expect from flaring PMS stars, massive stars, and CWBs. We therefore identify the $54$ separate \chic\ sources seen in these \cxo\ observations as young and massive stars within H {\sc ii} regions. Of the 93 \cxo-observed AGPS fields, 62 have one or more sources with $>20$ X-ray counts, resulting in the detailed study of 74 \chic\ sources in this paper. The multi-wavelength follow-up of these \chic\ sources demonstrates the need for \cxo's subarcsecond localization capabilities to correctly identify likely infrared and optical counterparts. The main focus of this paper has been on those unidentified \chic\ sources with $>20$ X-ray counts and with near-infrared or infrared counterparts. This has allowed us to perform population statistics to identify some of the likely objects that make up the $F_{x} \sim 10^{-13} \mathrm{~to~} 10^{-11}$ \erg\ Galactic plane X-ray source populations. We have developed a new statistical diagnostic for identifying likely populations of X-ray emitting sources using $K$-band fluxes and upper-limits (see Figure~\ref{Fig8}). The unidentified \chic\ sources in Region i of Figure~\ref{Fig8} have soft X-ray emission and low X-ray-to-infrared flux ratios, making them consistent with many of the archival and identified \chic\ stars. Their X-ray-to-infrared flux ratios are also similar to the COUP stars (see Figure~\ref{Fig7}), which are predominantly PMS stars. The majority of the Region i sources also fall within the general stellar locus that is expected in Figures~\ref{Fig9a} and \ref{Fig9b} \citep{hadfield07}. They are therefore likely to be active stellar coronae, which is consistent with the main soft X-ray populations expected in the Galactic plane \citep{hong05}, or PMS stars. Many of the \chic\ sources in Region ii of Figure~\ref{Fig8} have infrared colors similar to known Wolf-Rayet stars, as demonstrated in Figure~\ref{Fig9}, which indicate the presence of excess infrared emission resulting from strong, dense stellar winds. These sources are therefore likely to be massive stars generating X-rays through instability-driven wind shocks or even colliding winds in CWBs \citep[for example see][]{anderson11}. Only two unidentified \chic\ sources are located within Region iii of Figure~\ref{Fig8}, along with the archival high-mass and symbiotic X-ray binaries (and AGN). As such X-ray binaries (XRBs) are rare, only a few unidentified \chic\ sources are expected to fall within this group. This result therefore demonstrates that Figure~\ref{Fig8} may be a very useful diagnostic for identifying XRBs. Region vi contains four identified magnetars and a candidate LMXB. Even though there are likely two different source populations in Region vi, Figure~\ref{Fig8} demonstrates that hard X-ray sources ($E_{50}>1.3$ keV), with an X-ray-to-infrared flux ratio $F_{x}/F_{Ks} > 10^{2}$, are very rare and interesting Galactic X-ray sources. The population of \chic\ sources in Region iv of Figure~\ref{Fig8} remains unidentified. Based on their position relative to the identified AGN in Figure~\ref{Fig7} and they high $N_{H}$ values compared to the Galactic column density, we suggest that the 4 \chic\ sources ChI J181116--1828\_2, ChI J181213--1842\_7, ChI J190749+0803\_1, and ChI J194152+2251\_2 could be background AGN. The remaining 8 unidentified Region iv \chic\ sources have far lower $N_{H}$ values than the Galactic column densities indicating that they could be located in our own Galaxy. Optical and infrared spectroscopic follow-up is required to identify the true nature of this population. With further source identifications, a full \ns\ model of the hard ($2-10$ keV) Galactic plane X-ray populations between $F_{x} \sim 10^{-13} \mathrm{~and~} 10^{-11}$ \erg\ will be able to be constructed. This \ns\ will be more complete than those constructed from previous X-ray surveys in the same flux range, as it will be representative of 40 deg$^{2}$ of the Galactic plane. It will also show individual contributions from different Galactic X-ray source populations including non-accretion powered sources such as CWBs, SNRs, PWNe, and magnetars, which have not been a focus of previous work. Using the \ns\ distribution and distance estimates, it will then be possible to construct luminosity functions and three-dimensional spatial distributions of each class of X-ray source in the Galactic plane. \appendix | 14 | 3 | 1403.0404 |
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