Density Profiles of Collisionless Equilibria. II. Anisotropic Spherical Systems

It has long been realized that the dark matter halos that form in cosmological N-body simulations are characterized by density profiles ρ(r) that, when suitably scaled, have similar shapes. In addition, combining the density and velocity dispersion profiles σ(r), both of which have decidedly non-power-law shapes, leads to a quantity ρ/σ3 that is a power law in radius over 3 orders of magnitude in radius. Halos' velocity anisotropy profiles β(r) vary from isotropic near their centers to quite radially anisotropic near the virial radius. Finally, there appears to be a nearly linear correlation between β and the logarithmic density slope γ for a wide variety of halos. This work is part of a continuing investigation of the above interrelationships and their origins using analytical and semianalytical techniques. Our findings suggest that the nearly linear β-γ relationship is not just another expression of scale-free ρ/σ3 behavior. We also note that simultaneously reproducing density and anisotropy profiles like those found in simulations requires β(r) and γ(r) to have similar shapes, leading to nearly linear β-γ correlations. This work suggests that the β-γ and power-law ρ/σ3 relations have distinct physical origins.