An Excessive Core Collapse in Nbody Cosmological simulations

The particle mass used in cosmology N-body simulations is close to $10^{8}M_{\odot}$, which is about $10^{65}$ times larger than the GeV scale expected in particle physics. However, self-gravity interacting particle systems made up of different particles mass have different statistical and dynamical properties. Here we demonstrate that, due to this particle mass difference, the nowaday cosmology N-body simulations can have introduced an excessive core collapse process, especially for the low mass halos at high redshift. Such dynamical effect introduces an excessive cuspy center for these small halos, and it implies a possible connection to the so called "small scale crisis" for CDM models. Our results show that there exist a physical limit in cosmological simulations, by using about $10^3$ particles to describe smallest halos, and we provide a simple suggestion based on it to relieve those effects from the bias.