EAS Publications Series

Mass Profiles and Shapes of Cosmological Structures
G.A. Mamon, F. Combes, C. Deffayet and B. Fort (eds)
EAS Publications Series, 20 (2006) 33-36
DOI: 10.1051/eas:2006042

A universal density slope - velocity anisotropy relation

S.H. Hansen, B. Moore and J. Stadel

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 $\alpha-\beta$ relation. The first (phase-space density vs. 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. This allows us to conclude that equilibrated dark matter structures indeed have zero central velocity anisotropy, central density slope of $\alpha_0 \approx -0.8$ , and outer anisotropy of approximately $\beta_\infty \approx 0.5$ .