Velocity correlations of galaxy clusters

We determine the velocity correlation function, pairwise peculiar velocity difference, and rms pairwise peculiar velocity dispersion of rich clusters of galaxies, as a function of pair separation, for three cosmological models: {OMEGA} = 1 and {OMEGA} = 0.3 cold dark matter (CDM), and {OMEGA} = 0.3 primeval baryonic isocurvature (PBI) models (all flat and COBE-normalized). We find that close cluster pairs, with separation r <= 10 h^-1^ Mpc, exhibit strong attractive peculiar velocities in all models; the cluster pairwise velocities depend sensitively on the model. The mean pairwise attractive velocity of clusters on 5 h^-1^ Mpc scale ranges from ~1700 km s^-1^ for {OMEGA} = 1 CDM to ~1000 km s^-1^ for PBI to ~700 km s^-1^ for {OMEGA} = 0.3 CDM. The small-scale pairwise velocities depend also on cluster mass: richer, more massive clusters exhibit stronger attractive velocities than less massive clusters. On large scales, from ~20 to 200 h^-1^ Mpc, the cluster peculiar velocities are increasingly dominated by bulk and random motions; they are independent of cluster mass. The cluster velocity correlation function is negative on small scales for {OMEGA} = 1 and {OMEGA} = 0.3 CDM, indicating strong pairwise motion relative to bulk motion on small scales; PBI exhibits relatively larger bulk motions. The cluster velocity correlation function is positive on very large scales, from r~10 h^-1^ Mpc to r~200 h^-1^ Mpc, for all models. These positive correlations, which decrease monotonically with scale, indicate significant bulk motions of clusters up to ~200 h^-1^ Mpc. The strong dependence of the cluster velocity functions on models, especially at small separations, makes them useful tools in constraining cosmological models when compared with observations.