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 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.
