Dark matter distribution in dwarf spheroidal galaxies

We study the distribution of dark matter in dwarf spheroidal galaxies by modelling the moments of their line-of-sight velocity distributions. We discuss different dark matter density profiles, both cuspy and possessing flat density cores. The predictions are made in the framework of standard dynamical theory of two-component (stars and dark matter) spherical systems with different velocity distributions. We compare the predicted velocity dispersion profiles to observations in the case of Fornax and Draco dwarfs. For isotropic models the dark haloes with cores are found to fit the data better than those with cusps. Anisotropic models are studied by fitting two parameters, dark mass and velocity anisotropy, to the data. In this case all profiles yield good fits but the steeper the cusp of the profile, the more tangential is the velocity distribution required to fit the data. To resolve this well-known degeneracy of density profile versus velocity anisotropy we obtain predictions for the kurtosis of the line-of-sight velocity distribution for models found to provide best fits to the velocity dispersion profiles. It turns out that profiles with cores typically yield higher values of kurtosis which decrease more steeply with distance than the cuspy profiles, which will allow to discriminate between the profiles once the kurtosis measurements become available. We also show that with present quality of the data the alternative explanation of velocity dispersions in terms of Modified Newtonian Dynamics cannot yet be ruled out.