Self-Similar Dynamical Relaxation of Dark Matter Halos in an Expanding Universe

TL;DR

This paper develops advanced models of spherical collapse in an expanding universe to explain the structure of dark matter halos, revealing self-similar profiles that match simulations and linking halo structure to growth history.

Contribution

It introduces a novel self-similar solution framework incorporating dynamical relaxation effects, improving understanding of dark matter halo profiles and their formation history.

Findings

Profiles agree with N-body simulations at probed radii

Inner regions show universal density and phase-space profiles

Outer regions are influenced by slow accretion and cosmological variance

Abstract

We investigate the structure of cold dark matter halos using advanced models of spherical collapse and accretion in an expanding Universe. These base on solving time-dependent equations for the moments of the phase-space distribution function in the fluid approximation; our approach includes non-radial random motions, and most importantly, an advanced treatment of both dynamical relaxation effects that takes place in the infalling matter: phase-mixing associated to shell crossing, and collective collisions related to physical clumpiness. We find self-similar solutions for the spherically-averaged profiles of mass density rho(r), pseudo phase-space density Q(r) and anisotropy parameter beta(r). These profiles agree with the outcomes of state-of-the-art N-body simulations in the radial range currently probed by the latter; at smaller radii, we provide specific predictions. In the perspective provided by our self-similar solutions we link the halo structure to its two-stage growth history, and propose the following picture. During the early fast collapse of the inner region dominated by a few merging clumps, efficient dynamical relaxation plays a key role in producing a closely universal mass density and pseudo phase-space density profiles; in particular, these are found to depend only weakly on the detailed shape of the initial perturbation and the related collapse times. The subsequent inside-out growth of the outer regions feeds on the slow accretion of many small clumps and diffuse matter; thus the outskirts are only mildly affected by dynamical relaxation but are more sensitive to asymmetries and cosmological variance.