The kinematics of dense clusters of galaxies. III. Comparison with cosmological models

We compare the combined distribution of 31 group and 25 cluster velocity dispersions [Zabludoff et al., AJ, 106, 1301 (1993)] with the ensemble of 32 models for the formation and evolution of large-scale structure examined by Weinberg & Cole [MNRAS, 259, 652 (1992)]. The models include Gaussian and non-Gaussian initial fluctuations, different power law spectra (n=-1, n=0, n=-2, "pancake"), flat (Ω=1) and open (Ω=0.2) cosmologies, and unbiased (b₈=1) and biased (b₈=2) galaxy formation. The set of initial conditions we test, although limited, samples enough parameter space to indicate which general classes of models are consistent with the data. The two Gaussian, n=-1 models which best approximate the standard and open Cold Dark Matter (CDM) models do not match the observed distribution of velocity dispersions; models with b₈=2 and Ω=1 ("standard") or b₈=1 and Ω=0.2 ("open") predict too large a ratio of low to high velocity dispersion systems. A "COBE-normalized" CDM model with b₈=1 and Ω=1 produces clusters with velocity dispersions higher than those measured. All three models overestimate the total abundance of systems.