A universal density slope - velocity anisotropy relation

Abstract
One can solve the Jeans equation analytically for equilibrated dark matter structures, once given two pieces of input from numerical simulations. These inputs are 1) a connection between phase-space density and radius, and 2) a connection between velocity anisotropy and density slope, the relation. The first (phase-space density vs. radius) has been analysed through several different simulations, however the second ( relation) has not been quantified yet. We perform a large set of numerical experiments in order to quantify the slope and zero-point of the relation. This allows us to conclude that equilibrated dark matter structures indeed have zero central velocity anisotropy, central density slope of , and outer anisotropy of approximately .