The Motions of Clusters and Groups of Galaxies
  The distributions of peculiar velocities of rich clusters and of groups of galaxies are investigated for different cosmological models and are compared with observations. Four cosmological models are studied: standard ($\Omega=1$) CDM, low-density ($\Omega=0.3$) CDM, HDM ($\Omega=1$), and PBI ($\Omega=0.3$), all COBE normalized. We find that rich clusters of galaxies exhibit a Maxwellian distribution of peculiar velocities in all models,as expected from a Gaussian initial density field. The cluster 3-D velocity distribution typically peaks at $v \sim 600$ km s$^{-1}$, and extends to high cluster velocities of $v \sim 2000$ km s$^{-1}$. The low-density CDM model exhibits somewhat lower velocities: it peaks at $\sim 400$ km s$^{-1}$, and extends to $\sim 1200$ km s$^{-1}$. Approximately 10\% ($\sim$1\% for low- density CDM) of all model rich clusters move with high peculiar velocities of $v \ge 10^3$ km s$^{-1}$. The highest velocity clusters frequently originate in dense superclusters. The model velocity distributions of groups and clusters of galaxies are compared with observations. The data exhibit a larger high-velocity tail, to $v_r \geq 2000$ km s$^{-1}$, than seen in the model simulations (except HDM). Due to the large observational uncertainties, however, the data are consistent at a $\sim 1$ to $3\sigma$ level with the model predictions and with a Gaussian initial density field. Accurate observations of cluster peculiar velocities, especially at the high-velocity tail, should provide powerful constraints on the cosmological models. 
Neta A. Bahcall, Mirt Gramann and Renyue Cen