Evolution of Phase-Space Density in Dark Matter Halos

TL;DR

This paper investigates how the phase-space density profile of dark matter halos evolves through quiescent and violent phases, revealing invariances and scaling relations that govern their structural changes over cosmic time.

Contribution

It introduces a constrained simulation approach to study the evolution of phase-space density in dark matter halos, highlighting invariances and scaling laws during different evolutionary phases.

Findings

Phase-space density profile remains stable during quiescent phases.

Effective mass surface density within Rs remains constant during evolution.

Major mergers cause discontinuous changes in halo parameters while preserving certain invariants.

Abstract

The evolution of the phase-space density profile in dark matter (DM) halos is investigated by means of constrained simulations, designed to control the merging history of a given DM halo. Halos evolve through a series of quiescent phases of a slow accretion intermitted by violent events of major mergers. In the quiescent phases the density of the halo closely follows the NFW profile and the phase-space density profile, Q(r), is given by the Taylor & Navarro power law, r^{-beta}, where beta ~ 1.9 and stays remarkably stable over the Hubble time. Expressing the phase-space density by the NFW parameters, Q(r)=Qs (r/Rs)^{-beta}, the evolution of Q is determined by Qs. We have found that the effective mass surface density within Rs, Sigma_s = rhos Rs, remains constant throughout the evolution of a given DM halo along the main branch of its merging tree. This invariance entails that Qs ~ Rs^{-5/2} and Q(r) ~ Sigma_s^{-1/2} Rs^{-5/2} (r/ Rs)^{-beta}. It follows that the phase-space density remains constant, in the sense of Qs=const., in the quiescent phases and it decreases as Rs^{-5/2} in the violent ones. The physical origin of the NFW density profile and the phase-space density power law is still unknown. Yet, the numerical experiments show that halos recover these relations after the violent phases. The major mergers drive Rs to increase and Qs to decrease discontinuously while keeping Qs Rs^{5/2} = const. The virial equilibrium in the quiescent phases implies that a DM halos evolves along a sequence of NFW profiles with constant energy per unit volume (i.e., pressure) within Rs.