The peculiar velocity function of galaxy clusters

The peculiar velocity function of clusters of galaxies is determined using an accurate sample of cluster velocities based on Tully-Fisher distances of Sc galaxies. In contrast to previous results based on samples with considerably larger velocity uncertainties, the observed velocity function does not exhibit a tail of high peculiar velocity clusters. The results indicate a low probability of ≲5% of finding clusters with one-dimensional peculiar velocities greater than ∼ 600 km s^-1. The rms one-dimensional cluster peculiar velocity is 293 ± 28 km s^-1. The observed cluster velocity function is compared with expectations from different cosmological models. The absence of a high-velocity tail in the observed function is most consistent with a low-mass-density (Ω ∼ 0.3) COM model and is inconsistent at the ≳3 σ level with Ω = 1.0 CDM and HDM models. The rms one-dimensional cluster peculiar velocities in these models correspond, respectively, to 314, 516, and 632 km s^-1 (when convolved with the observational uncertainties). Comparison with the observed rms cluster velocity of 293 ± 28 km s^-1 further supports the low-density CDM model.