Collisional Evolution of Galaxy Clusters and the Growth of Common Halos

We investigate the dynamical evolution of clusters of galaxies in virial equilibrium by using Fokker-Planck models and self-consistent N-body models. In particular, we focus on the growth of the common halo, which is a cluster-wide halo formed by the matter stripped from galaxies, and the development of the central density cusp. The Fokker-Planck models include the effects of two-body gravitational encounters both between galaxies and between galaxies and common halo particles. The effects of tidal mass stripping from the galaxies due to close galaxy--galaxy encounters and accompanying dissipation of the orbital kinetic energies of the galaxies are also taken into account in the Fokker-Planck models. We find that the Fokker-Planck models are in very good agreement with the N-body models with respect to the growth of the common halo mass and the evolution of cluster density profiles. In the central region of the cluster, a shallow density cusp approximated by $\rho (r) \propto r^{-\alpha}$ ($\alpha \sim$ 1) develops. This shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness $\alpha$ weakly depends on the relative importance of tidal stripping. When the effect of stripping is important, the central velocity dispersion decreases as the central density increases, and consequently a shallow ($\alpha <2$) cusp is formed. In the limit of no stripping, usual gravothermal core collapse occurs, i.e. the central velocity dispersion increases as the central density increases with leaving a steep ($\alpha >2$) cusp. Under the conditions of real galaxy clusters, shallow cusps develop