In view of recent and forthcoming surveys of distant clusters of galaxies, we investigate cluster evolution for a suite of N-body simulations. We examine Einstein-deSitter, open (Ω=0.2) and flat, low density (Ω=0.2 λ=0.8) models with power-law initial density distribution P∝Kn, n=-2,-1, and 0. We emphasize the effects of force resolution and the subtleties of cluster identification. We develop a physical picture of the evolution of velocity dispersions of individual clusters as a function of redshift. By studying simulated clusters individually we show that mergers and accretions change dispersions in a characteristic way. Dispersions reach their maximum (an increase of ∼20%) when the accreted object first swings into the center of the cluster; at this time the distribution of matter does not necessarily exhibit obvious substructure. For all the clusters in a particular simulation, the scatter in σ(script M sign) is about 10%, consistent with that predicted from merger activity. Although the abundance of cluster masses in the models is not consistent with Press-Schechter theory, the sense and degree of evolution is. Over the entire mass range in our simulations, the abundance of collapsed objects increases with time. Dispersions as a function of mass, on the other hand, decrease with time, consistent with spherical theory. For most models, the velocity dispersion function produced by these effects reflects a cluster population which increases with time and a group population which deceases with time. We predict, therefore, that redshift observations of distant groups will yield larger abundances than at z=0.0. To use n(>σ) to distinguish among cosmological models a volume of ≳2×106h-3 Mpc must be simulated. We extend our analysis to x-ray luminosities in order to compare our models with already existing data. Unbiased Einstein-deSitter models produce too many clusters to be consistent with the data. None of our other models is ruled out by either the observed local abundances or the observed evolution. To check consistency with the models further, one could compare x-ray and optical observations of a single sample of distant galaxies. Over the range of dispersions in our simulations (about 300-1200 km/s for a flat, unbiased model) our optical evolution is negligible, while for the same sample there are significantly more low-Lx clusters (Lx≲5×1044 erg/s) at z∼0.3 than at the present time. © 1995 American Astronomical Society.
