A universal density slope – velocity anisotropy relation

University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland

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 – β relation. The first (phase-space density vs. radius) has been analysed through several different simulations, however the second (α – β 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 α – β relation. This allows us to conclude that equilibrated dark matter structures indeed have zero central velocity anisotropy, central density slope of α₀ ≈ –0.8, and outer anisotropy of approximately β_∞ ≈ 0.5.