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Register a new userAction-based distribution functions for spheroidal galaxy components
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Lorenzo Posti
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We present an approach to the design of distribution functions that depend on the phase-space coordinates through the action integrals. The approach makes it easy to construct a dynamical model of a given stellar component. We illustrate the approach by deriving distribution functions that self-consistently generate several popular stellar systems, including the Hernquist, Jaffe, and Navarro, Frenk and White models. We focus on non-rotating spherical systems, but extension to flattened and rotating systems is trivial. Our distribution functions are easily added to each other and to previously published distribution functions for discs to create self-consistent multi-component galaxies. The models this approach makes possible should prove valuable both for the interpretation of observational data and for exploring the non-equilibrium dynamics of galaxies via N-body simulation.
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A new family of self-consistent DF-based models of stellar systems is explored. The stellar component of the models is described by a distribution function (DF) depending on the action integrals, previously used to model the Fornax dwarf spheroidal galaxy (dSph). The stellar component may cohabit with either a dark halo, also described by a DF, or with a massive central black hole. In all cases we solve for the models self-consistent potential. Focussing on spherically symmetric models, we show how the stellar observables vary with the anisotropy prescribed by the DF, with the dominance and nature of the dark halo, and with the mass of the black hole. We show that precise fits to the observed surface brightness profiles of four globular clusters can be obtained for a wide range of prescribed velocity anisotropies. We also obtain precise fits to the observed projected densities of four dSphs. Finally, we present a three-component model of the Scupltor dSph with distinct DFs for the red and blue horizontal branch stars and the dark matter halo.
In the Gaia era, understanding the effects of perturbations of the Galactic disc is of major importance in the context of dynamical modelling. In this theoretical paper, we extend previous work in which, making use of the epicyclic approximation, the linearized Boltzmann equation had been used to explicitly compute, away from resonances, the perturbed distribution function of a Galactic thin disc population in the presence of a non-axisymmetric perturbation of constant amplitude. Here we improve this theoretical framework in two distinct ways in the new code that we present. First, we use better estimates for the action-angle variables away from quasi-circular orbits, computed from the AGAMA software, and we present an efficient routine to numerically re-express any perturbing potential in these coordinates with an accuracy well below the percent level. The use of more accurate action estimates allows us to identify resonances such as the outer 1:1 bar resonance at larger azimuthal velocities than the outer Lindblad resonance, and to extend our previous theoretical results well above the Galactic plane, where we explicitly show how they differ from the epicyclic approximation. In particular, the displacement of resonances in velocity space as a function of height can in principle constrain the 3D structure of the Galactic potential. Second, we allow the perturbation to be time-dependent, thereby allowing us to model the effect of transient spiral arms or of a growing bar. The theoretical framework and tools presented here will be useful for a thorough analytical dynamical modelling of the complex velocity distribution of disc stars as measured by past and upcoming Gaia data releases.
We present new dynamical models of dwarf spheroidal galaxies (dSphs) in which both the stellar component and the dark halo are described by analytic distribution functions that depend on the action integrals. In their most general form these distribution functions can represent axisymmetric and possibly rotating stellar systems. Here, as a first application, we model the Fornax dSph, limiting ourselves, for simplicity, to the non rotating, spherical case. The models are compared with state-of-the-art spectroscopic and photometric observations of Fornax, exploiting the knowledge of the line-of-sight velocity distribution of the models and accounting for the foreground contamination from the Milky Way. The model that best fits the structural and kinematic properties of Fornax has a cored dark halo, with core size $r_{rm c}simeq1.03$ kpc. The dark-to-luminous mass ratio is $(M_{rm dm}/M_{star})|_{R_{rm eff}}simeq9.6$ within the effective radius $R_{rm eff} simeq 0.62,$kpc and $(M_{rm dm}/M_{star})|_{3 {rm kpc}} simeq 144$ within 3 kpc. The stellar velocity distribution is isotropic almost over the full radial range covered by the spectroscopic data and slightly radially anisotropic in the outskirts of the stellar distribution. The dark-matter annihilation $J$-factor and decay $D$-factor are, respectively, $log_{10}(J$ $[$GeV$^2$ cm$^{-5}])simeq18.34$ and $log_{10}(D$ $[$GeV cm$^{-2}])simeq18.55$, for integration angle $theta = 0.5^{circ}$. This cored halo model of Fornax is preferred, with high statistical significance, to both models with a Navarro, Frenk and White dark halo and simple mass-follows-light models.
We report the discovery of NGC 253-dw2, a dwarf spheroidal (dSph) galaxy candidate undergoing tidal disruption around a nearby spiral galaxy, NGC 253 in the Sculptor group: the first such event identified beyond the Local Group. The dwarf was found using small-aperture amateur telescopes, and followed up with Suprime-Cam on the 8 m Subaru Telescope in order to resolve its brightest stars. Using g- and R_c-band photometry, we detect a red giant branch consistent with an old, metal-poor stellar population at a distance of ~ 3.5 Mpc. From the distribution of likely member stars, we infer a highly elongated shape with a semi-major axis half-light radius of (2 +/- 0.4) kpc. Star counts also yield a luminosity estimate of ~ 2x10^6 L_Sun,V (M_V ~ -10.7). The morphological properties of NGC 253-dw2 mark it as distinct from normal dSphs and imply ongoing disruption at a projected distance of ~ 50 kpc from the main galaxy. Our observations support the hierarchical paradigm wherein massive galaxies continously accrete less massive ones, and provide a new case study for dSph infall and dissolution dynamics. We also note the continued efficacy of small telescopes for making big discoveries.
We estimate the 3D density profile of the Galactic dark matter (DM) halo within $r lesssim 30$ kpc from the Galactic centre by using the astrometric data for halo RR Lyrae stars from Gaia DR2. We model both the stellar halo distribution function and the Galactic potential, fully taking into account the survey selection function, the observational errors, and the missing line-of-sight velocity data for RR Lyrae stars. With a Bayesian MCMC method, we infer the model parameters, including the density flattening of the DM halo $q$, which is assumed to be constant as a function of radius. We find that 99% of the posterior distribution of $q$ is located at $q>0.963$, which strongly disfavours a flattened DM halo. We cannot draw any conclusions as to whether the Galactic DM halo at $r lesssim 30$ kpc is prolate, because we restrict ourselves to axisymmetric oblate halo models with $qleq1$. Our result is inconsistent with predictions from cosmological hydrodynamical simulations that advocate more oblate ($langle{q}rangle sim0.8 pm 0.15$) DM halos within $sim 15%$ of the virial radius for Milky-Way-sized galaxies. An alternative possibility, based on our validation tests with a cosmological simulation, is that the true value $q$ of the Galactic halo could be consistent with cosmological simulations but that disequilibrium in the Milky Way potential is inflating our measurement of $q$ by 0.1-0.2. As a by-product of our analysis, our model constrains the DM density in the Solar neighbourhood to be $rho_{mathrm{DM},odot} = (9.01^{+0.18}_{-0.20})times10^{-3}M_odot mathrm{pc}^{-3} = 0.342^{+0.007}_{-0.007}$ $;mathrm{GeV} mathrm{cm}^{-3}$.
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