Action-based dynamical models of dwarf spheroidal galaxies: application
  to Fornax
  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.
