Confrontation of top-hat spherical collapse against dark halos from cosmological <i>N</i>-body simulations

<jats:title>Abstract</jats:title> <jats:p>The top-hat spherical collapse model (TSC) is one of the most fundamental analytical frameworks to describe the non-linear growth of cosmic structure. TSC has motivated, and been widely applied in, various investigations even in the current era of precision cosmology. While numerous studies exist to examine its validity against numerical simulations in a statistical fashion, there are few analyses which compare the TSC dynamics in an individual object-wise basis, which is what we attempt in the present paper. We extract 100 halos at z = 0 from a cosmological N-body simulation according to the conventional TSC criterion for the spherical over-density. Then we trace back their spherical counterparts at earlier epochs. Just prior to the turn-around epoch of the halos, their dynamics are well approximated by TSC, but their turn-around epochs are systematically delayed and the virial radii are larger by ∼20% on average relative to the TSC predictions. We find that this systematic deviation can mainly be ascribed to the non-uniformity/inhomogeneity of dark matter density profiles and the non-zero velocity dispersions, both of which are neglected in TSC. In particular, the inside-out collapse and shell-crossing of dark matter halos play an important role in generating the significant velocity dispersion. The implications of the present result are briefly discussed.</jats:p>