The velocity anisotropy - density slope relation

Details The velocity anisotropy - density slope relation The velocity anisotropy - density slope relation

2005-10-21

arxiv.org/abs/astro-ph/0510656v1

JCAP 0605:014,2006

Astronomy and Astrophysics

Astrophysics

15 pages, 7 figures

Scientific paper

10.1088/1475-7516/2006/05/014

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 already 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. We find strong indication that the relation is indeed an attractor. 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 \beta_0 = 0, central density slope of \alpha_0 = -0.8, and outer anisotropy of \beta_\infty = 0.5.

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