Evolution of the Phase‐Space Density in Dark Matter Halos

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 ~β, where β≈1.9 and stays remarkably stable over the Hubble time. Expressing the phase-space density by the NFW parameters, Q(r) = Q s (r/Rs) - & beta , the evolution of Q is determined by Q s' We have found that the effective mass surface density within R s, Σ s = p s R s , remains constant throughout the evolution of a given DM halo along the main branch of its merging tree. This invariance entails that Q s ∝ 'σ ~1/2 R S ~5/2 (r/R s ) ~β . It follows that the phase-space density remains constant, in the sense of Q s = const., in the quiescent phases and it decreases as R s -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 R s to increase and Q s to decrease discontinuously while keeping Q s xR s 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 R s © 2007. The American Astronomical Society. All rights reserved.