Masses of rich clusters of galaxies as a test of the biased cold dark matter theory

We present a survey of the suite of constraints needed to test the ability of the biased cold dark matter theory to account for the mass concentrations observed in rich clusters of galaxies. Of particular importance are the choice of the galaxy clustering length, r₀_, and the bias parameter, b, that measures the relation between r₀_ and the corresponding statistic for the mass distribution. Formation of high mass concentrations in clusters and production of large-scale flows are promoted by decreasing b and increasing r₀_; dynamical mass estimates tend to prefer the opposite direction. Another important factor is the rate of nonlinear development of a primeval mass fluctuation into a system, such as a rich cluster, that is much denser than the background. We have attempted to place limits on the uncertainties in these factors that are conservative at each step in the interpretation of observations and theory, that is, favorable but not overly generous for the cold dark matter theory. We find that no values r₀_ and b are concordant with all available constraints. The choice b ~ 1. 5 and hr₀_ ~ 4 Mpc is least problematic, requiring violation of two otherwise apparently reasonable conditions, one from the statistics of Abell clusters, the other from several dynamical mass estimates of systems of galaxies. If hr₀_ proves to be appreciably larger than 4 Mpc, the discordance will be even more serious.