An analytic distribution function for a mass-less cored stellar system in a cuspy dark-matter halo

We demonstrate the existence of a distribution function that can be used to represent spherical mass-less cored stellar systems having constant mildly tangential velocity anisotropy embedded in cuspy dark-matter halos. In particular, we derived analytically the functional form of the distribution function for a Plummer stellar sphere in a Hernquist dark halo for β0 = −0.5 and for different degrees of embedding. This particular example satisfies the condition that the central logarithmic slope of the light profile γ0 > 2β0. Our models have velocity dispersion profiles similar to those observed in nearby dwarf spheroidal galaxies. Hence they can be used to generate initial conditions for a variety of problems, including N-body simulations that may represent dwarf galaxies in the Local Group