Relaxed Dark Matter Halos

TL;DR

This paper develops a renormalized series expansion for dark matter distribution functions in spherical halos, analyzing their relaxation and density profiles, and compares theoretical predictions with empirical data.

Contribution

It introduces a renormalized series method to estimate steady state dark matter distributions and explores their thermodynamic relaxation and density profile behaviors.

Findings

Inner density slope agrees with empirical fits

Pseudo-density profile matches observed power laws

Identifies a cascade regime in non-equilibrium relaxation

Abstract

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.