Galaxies in N-body simulations: overcoming the overmerging problem

We present analysis of the evolution of dark matter halos in dense environments of groups and clusters in dissipationless cosmological simulations. The premature destruction of halos in such environments, known as the overmerging, reduces the predictive power of N-body simulations and makes difficult any comparison between models and observations. We analyze the possible processes that cause the overmerging and assess the extent to which this problem can be cured with current computer resources and codes. Using both analytic estimates and high resolution numerical simulations, we argue that the overmerging is mainly due to the lack of numerical resolution. We find that the force and mass resolution required for a simulated halo to survive in galaxy groups and clusters is extremely high and was almost never reached before: ~1-3 kpc and 10^8-10^9 Msun, respectively. We use the high-resolution Adaptive Refinement Tree (ART) N-body code to run cosmological simulations with the particle mass of \approx 2x10^8/h Msun} and the spatial resolution of \approx 1-2/h kpc, and show that in these simulations the halos do survive in regions that would appear overmerged with lower force resolution. Nevertheless, the halo identification in very dense environments remains a challenge even with the resolution this high. We present two new halo finding algorithms developed to identify both isolated and satellite halos that are stable (existed at previous moments) and gravitationally bound. To illustrate the use of the satellite halos that survive the overmerging, we present a series of halo statistics, that can be compared with those of observed galaxies. (Abridged)