Distribution Functions for Cuspy Dark Matter Density Profiles

Various analytic expressions have been proposed for the density profile of dark matter halos. We consider six of these expressions for which the density profile has a power-law falloff ρ~r^-3 at large radii and a power-law cusp ρ~r^-γ (γ=0, 1/2, 1, 3/2) at small radii. The phase-space distribution function for these models is calculated assuming spherical symmetry and either an isotropic velocity dispersion tensor or an anisotropic dispersion tensor of the type proposed by Osipkov and Merritt. The differential energy distribution for these models is also derived. Several applications are discussed, including the analysis of dark matter search experiments and the study of halo formation in a cosmological setting. Analytic fitting formulae for some of the models are provided.