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The velocity anisotropy - density slope relation

Steen H. Hansen·Joachim Stadel
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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 already 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. 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 β_0 = 0, central density slope of α_0 = -0.8, and outer anisotropy of β_\infty = 0.5.

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Steen H. Hansen, Joachim Stadel. 2005-10-21. The velocity anisotropy - density slope relation. https://doi.org/10.1088/1475-7516%2F2006%2F05%2F014

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