Velocity Correlations of Galaxy Clusters

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Abstract
We determine the velocity correlation function, pairwise peculiar velocity difference, and root-mean-square 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 CDM, and Omega=0.3 PBI models (all flat and COBE-normalized). We find that close cluster pairs, with separation r<10Mpc/h, 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 5Mpc/h scale ranges from 1700 km/s for Omega=1 CDM, to 1000 km/s for PBI, to 700 km/s 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 200Mpc/h, the cluster peculiar velocities are increasingly dominated by bulk and random motions; they are independent of cluster mass. The cluster velocity correlation function, which reflects the bulk motion minus the relative motion of pairs, is negative on small scales for Omega=1 and Omega=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 10 to 200Mpc/h, for all models. These positive correlations, which decrease monotonically with scale, indicate significant bulk motions of clusters up to 200Mpc/h. 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.

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