Abstract
One can solve the Jeans equation analytically for equilibrated dark matterstructures once two pieces of input from numerical simulations have beenobtained. These inputs are (1) a connection between phase-space density andradius, and (2) a connection between velocity anisotropy and density slope, theα–β relation. The first (phase-space density versus radius) has already beenanalysed through several different simulations, however the second(α–β relation) has not been quantified yet. We perform a large set of numericalexperiments in order to quantify the slope and zero-point of theα–β relation. We find a strong indication that the relation is indeed an attractor. When combinedwith the assumption of phase-space being a power-law in radius, this allows us to concludethat equilibrated dark matter structures indeed have zero central velocity anisotropyβ0 ≈ 0, a centraldensity slope of α0 ≈ −0.8, and outer anisotropy of .
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