VELOCITY CORRELATIONS OF GALAXY CLUSTERS

We determine the velocity correlation function, pairwise peculiar velo city difference, and rms pairwise peculiar velocity dispersion of rich clusters of galaxies, as a function of pair separation, for three cos mological models: Omega = 1 and Omega = 0.3 cold dark matter (CDM), an d Omega = 0.3 primeval baryonic isocurvature (PBI) models (all flat an d COBE-normalized). We find that close cluster pairs, with separation r less than or equal to 10 h(-1) Mpc, exhibit strong attractive peculi ar velocities in all models; the cluster pairwise velocities depend se nsitively on the model. The mean pairwise attractive velocity of clust ers on 5 h(-1) Mpc scale ranges from similar to 1700 km s(-1) for Omeg a = 1 CDM to similar to 1000 km s(-1) for PBI to similar to 700 km s(- 1) for Omega = 0.3 CDM. The small-scale pairwise velocities depend als o on cluster mass: richer, more massive clusters exhibit stronger attr active velocities than less massive clusters. On large scales, from si milar to 20 to 200 h(-1) Mpc, the cluster peculiar velocities are incr easingly dominated by bulk and random motions; they are independent of cluster mass. The cluster velocity correlation function is negative o n small scales for Omega = 1 and Omega = 0.3 CDM, indicating strong pa irwise motion relative to bulk motion on small scales; PBI exhibits re latively larger bulk motions. The cluster velocity correlation functio n is positive on very large scales, from r similar to 10 h(-1) Mpc to r similar to 200 h(-1) Mpc, for all models. These positive correlation s, which decrease monotonically with scale, indicate significant bulk motions of clusters up to similar to 200 h(-1) Mpc. The strong depende nce of the cluster velocity functions on models, especially at small s eparations, makes them useful tools in constraining cosmological model s when compared with observations.