The Role of Dark Matter in the Dynamical Evolution of Galaxy Clusters in the Framework of the N-Body Problem

Numerical N-body studies of the dynamical evolution of a cluster of 1000 galaxies were carried out in order to investigate the role of dark matter in the formation of cD galaxies. Two models explicitly describing the darkmatter as a full-fledged component of the cluster having its own physical characteristics are constructed. These treat the dark matter as a continuous underlying substrate and as "grainy" matter. The ratio of the masses of the dark and luminous matter of the cluster is varied in the range 3-100. The observed logarithmic spectrum dN similar to dM/M is used as an initial mass spectrum for the galaxies. A comparative numerical analysis of the evolution of the mass spectrum, the dynamics of mergers of the cluster galaxies, and the evolution of the growth of the central, supermassive cD galaxy suggests that dynamical friction associated with dark matter accelerates the formation of the cD galaxy via the absorption of galaxies colliding with it. Taking into account a dark-matter "substrate" removes the formation of multiple mass-accumulation centers, and makes it easier to form a cD galaxy that accumulates 1-2% of the cluster mass within the Hubble time scale (3-8 billion years), consistent with observations.