  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 researches 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 to 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 counter-parts at
earlier epochs. Just prior to the turn-around epoch of the halos, their
dynamics is well approximated by TSC, but their turn-around epochs are
systematically delayed and the virial radii are larger by ~ 20 percent on
average relative to the TSC predictions. We find that this systematic deviation
is mainly 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.
