  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.
