Confrontation of Top-Hat Spherical Collapse against Dark Halos from Cosmological N-Body Simulations

TL;DR

This study compares the top-hat spherical collapse model's predictions with individual dark matter halos from N-body simulations, revealing systematic deviations due to inhomogeneity and velocity dispersions.

Contribution

It provides an object-wise analysis of TSC against simulated halos, highlighting the causes of deviations and refining understanding of halo dynamics.

Findings

TSC approximates halo dynamics near turn-around epoch

Turn-around occurs later and halos are larger than TSC predictions

Inhomogeneity and velocity dispersion cause deviations from TSC

Abstract

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.