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

We investigate the structure of cold dark matter halos using advanced models of spherical collapse and accretion in an expanding universe. These are based 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 take place in the infalling matter: phase-mixing associated with shell crossing and collective collisions related to physical clumpiness. We find self-similar solutions for the spherically averaged profiles of mass density ρ(r), pseudo phase-space density Q(r), and anisotropy parameter β(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 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.