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Collisional Evolution of Galaxy Clusters and the Growth of Common Halos

We investigated the dynamical evolution of clusters of galaxies in virial equilibrium using Fokker-Planck models and self-consistent N-body models. In particular, we focused on the growth of a common halo, which is a cluster-wide halo formed by matter stripped from galaxies, and the development of a 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 were also taken into account in the Fokker-Planck models. We find that the results of the Fokker-Planck models are in excellent agreement with those of the N-body models regarding the growth of the common halo mass and the evolution of the cluster density profiles. In the central region of the cluster, a shallow density cusp, approximated by $ρ(r) \propto r^{-α}$ ($α\sim$ 1), develops. This shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness, $α$, weakly depends on the relative importance of the tidal stripping. When the effect of stripping is important, the central velocity dispersion decreases as the central density increases and, consequently, a shallow ($α<2$) 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 a steep ($α>2$) cusp left. We conclude from our consideration of the origin of the cusp demonstrated here that shallow cusps should develop in real galaxy clusters.