Evolution of the phase-space density in dark matter halos

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 approximate to 1.9 and stays remarkably stable over the Hubble time. Expressing the phase-space density by the NFW parameters, Q(r) Q(s)(r/R-s)(-beta), the evolution of Q is determined by Q(s). We have found that the effective mass surface density within R-s, Sigma(s) equivalent to rho R-s(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) proportional to R-s(-5/2) and Q(r) proportional to Sigma(-1/2)(s) R-s(-5/2)(r/R-s)(-beta). 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 Rs to increase and Q(s) to decrease discontinuously while keeping Q(s) x R-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.