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

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.