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.