Relaxing and virializing a dark matter halo

Navarro, Frenk & White have suggested that the density profiles of simulate d dark matter haloes have a 'universal' shape, so that a given halo can be characterized by a single free parameter which fixes its mass. In this pape r we revisit the spherical infall model in the hope of recognizing in detai l the existence and origin of any such universality. A system of particles is followed from linear perturbation, through first shell crossing, then th rough an accretion or infall phase, and finally to virialization. During th e accretion phase, the system relaxes through a combination of phase mixing , phase-space instability, and moderate violent relaxation. It is driven qu ickly, by the flow of mass through its surface, toward self-similar evoluti on. The selfsimilar solution plays its usual role of intermediate attractor , and can be recognized from a virial-type theorem in scaled variables and from our numerical simulations. The transition to final equilibrium state o nce infall has ceased is relatively gentle, an observation which leads to a n approximate form for the distribution function of the final object. The i nfall phase fixes the density profile in intermediate regions of the halo t o be close to r(-2). We make contact with the standard hierarchical cluster ing scenario and explain how modifications of the self-similar infall model might lead to density profiles in agreement with those found in cosmologic al simulations.