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 \alpha-\beta relation. The first (phase-space density v.s. radius) has been analysed through several different simulations, however the second (\alpha-\beta 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 \alpha-\beta relation. 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 \alpha_0 = -0.8, and outer anisotropy of approximately \beta_\infinity = 0.5.Comment: 4 pages, 1 figure, to appear in the XXIst IAP Colloquium "Mass Profiles and Shapes of Cosmological Structures", Paris 4-9 July 2005, France, (Eds.) G. Mamon, F. Combes, C. Deffayet, B. Fort, EAS Publications Serie