  In this paper we reconsider a series expansion for a dark matter distribution
function in the spherically symmetric anisotropic limit. We show here that the
expansion may be renormalized so that the series does converge in time to an
estimate of the steady state distribution function in the central regions.
Subsequently we use this distribution function to discuss the nature of the
central equilibrium and, by invoking stationarity of Boltzmann's H function as
a measure of (thermodynamic) relaxation, we calculate the adiabatic variation
in the local logarithmic slope of the mass density. Similarly the pseudo
(phase-space) density variation with radius is calculated. These are compared
to empirical fitting functions. There is general agreement on the inner part of
the logarithmic slope of the density and of the inner profile of the
pseudo-density power law, but coincident continuity with the outer power-laws
is not yet achieved. Finally some suggestions are made regarding the actual
microphysics acting during the non-equilibrium approach to relaxation. In
particular a cascade regime is identified.
