Relaxation and tidal stripping in rich clusters of galaxies. I - Evolution of the mass distribution
A set of differential equations is derived which describes the evolution of a rich cluster of galaxies over relaxation time scales. Two physical processes are included. Exchange of orbital kinetic energy between galaxies of different masses, due to gravitational two-body encounters, is computed from the isotropic, orbit-averaged Fokker-Planck equation. Tidal stripping of galaxies with massive halos is approximated by the cross sections of Richstone. The fraction of cluster mass in the "background" is allowed to increase with time as the galaxies are stripped. The equations are integrated numerically, starting from a Schechter distribution of galaxy masses. Unless most of the virial mass is initially in the background, tidal stripping tends to obscure the effects of mass segregation by rapidly depleting the cluster core of massive galaxies. The final core mass distribution is qualitatively similar in both cases to that of a cD galaxy, in that it contains a central mass of low velocity dispersion surrounded by a high velocity dispersion envelope.