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 α-βrelation. The first (phase-space density v.s. radius) has been analysed through several different simulations, however the second (α-βrelation) has not been quantified yet. We perform a large set of numerical experiments in order to quantify the slope and zero-point of the α-βrelation. When combined with the assumption of phase-space being a power-law in radius this allows us to conclude that equilibrated dark matter structures indeed have zero central velocity anisotropy, central density slope of α_0 = -0.8, and outer anisotropy of approximately β_\infinity = 0.5.