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 _ { c } \simeq 1.03 kpc .
The dark-to-luminous mass ratio is ( M _ { dm } / M _ { \star } ) | _ { R _ { e } } \simeq 9.6 within the effective radius R _ { e } \simeq 0.62 kpc and ( M _ { dm } / M _ { \star } ) | _ { 3 { 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 } ] ) \simeq 18.34 and \log _ { 10 } ( D [ GeV cm ^ { -2 } ] ) \simeq 18.55 , 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 .