Galaxies in N-body simulations: Overcoming the overmerging problem

We present analysis of the evolution of dark matter halos in dense environm ents of groups and clusters in dissipationless cosmological simulations. Th e premature destruction of halos in such environments, known as "the overme rging," reduces the predictive power of N-body simulations and makes diffic ult any comparison between models and observations. We analyze the possible processes that cause the overmerging and assess the extent to which this p roblem can be cured with current computer resources and codes. Using both a nalytic 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 reach ed before: similar to 1-3 kpc and 10(8)-10(9) M., respectively. We use the high-resolution Adaptive Refinement Tree (ART) N-body code to run cosmologi cal simulations with particle mass approximate to 2 x 10(8) h(-1) M. and sp atial resolution approximate to 1-2 h(-1) kpc and show that in these simula tions the halos do survive in regions that would appear overmerged with low er force resolution. Nevertheless, the halo identification in very dense en vironments remains a challenge even with resolution this high. We present t wo new halo-finding algorithms developed to identify both isolated and sate llite halos that are stable (existed at previous moments) and gravitational ly bound. To illustrate the use of the satellite halos that survive the ove rmerging, we present a series of halo statistics, which can be compared wit h those of observed galaxies. Particularly, we find that, on average, halos in groups have the same velocity dispersion as the dark matter particles; i.e., they do not exhibit significant velocity bias. The small-scale (100 k pc to 1 Mpc) halo correlation function in both models is well described by the power law xi proportional to r(-1.7) and is in good agreement with obse rvations. It is slightly antibiased (b approximate to 0.7-0.9) relative to the dark matter. To test other galaxy statistics, we use the maximum of the halo rotation velocity and the Tully-Fisher relation to assign luminosity to the halos. For two cosmological models, a flat model with the cosmologic al constant and Omega(0) = 1 - Omega(Lambda) = 0.3, h = 0.7 and a model wit h a mixture of cold and hot dark matter and Omega(0) = 1.0, Omega(v) = 0.2, h = 0.5, we construct luminosity functions and evaluate mass-to-light rati os in groups. Both models produce luminosity functions and mass-to-light ra tios (similar to 200-400) that are in reasonable agreement with observation s. The latter implies that the mass-to-light ratio in galaxy groups (at lea st for M-vir less than or similar to 3 x 10(13) h(-1) M. analyzed here) is not a good indicator of Omega(0).