Velocity Correlations of Galaxy Clusters

We determine the velocity correlation function, pairwise peculiar velocity di erence, and root-mean-square pairwise peculiar velocity dispersion of rich clusters of galaxies, as a function of pair separation, for three cosmological models: = 1 and = 0:3 CDM, and = 0:3 PBI models (all at and COBEnormalized). We nd that close cluster pairs, with separation r 10h 1Mpc, 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 5h 1Mpc scale ranges from 1700km s 1 for = 1 CDM, to 1000km s 1 for PBI, to 700km s 1 for = 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 200h 1Mpc, the cluster peculiar velocities are increasingly dominated by bulk and random motions; they are independent of cluster mass. The cluster velocity correlation function, which re ects the bulk motion minus the relative motion of pairs, is negative on small scales for = 1 and = 0:3 CDM, and positive for PBI; this indicates stronger pairwise motion than bulk motion on small scales for CDM, and relatively larger bulk motions for PBI. The cluster velocity correlation function is positive on very large scales, from r 10h 1Mpc to 200h 1Mpc, for all models. These positive correlations, which decrease monotonically with scale, indicate signi cant bulk motions of clusters up to 200h 1Mpc. 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. Cosmology: large-scale structure of Universe { Cosmology: theory { galaxies: clustering { galaxies: clusters of