Peculiar velocities of galaxy clusters: a comparison of mixed dark matter and low-density cold dark matter

We determine the distribution of peculiar velocities of galaxy clusters in two competing cosmological scenarios: a spatially flat, low-density, cold dark matter universe with cosmological density parameter $$\Omega = 0.2$$ and a cosmological constant $$\Lambda = 3H_0^2(1 - \Omega)$$ (LCDM); and an $$\Omega = 1$$ universe containing a mixture of hot and cold dark matter (MDM). Although the spatial clustering properties of clusters in the two models are almost identical, the rms cluster peculiar velocities in the MDM universe are substantially higher. We compare the theoretical peculiar velocity distributions with observations and find that both models have difficulties in reproducing the observed distribution of cluster peculiar velocities. The reliable detection of several more clusters with peculiar velocities greater than $$1000\,{\rm km \ s}^{-1}$$ would be difficult to reconcile with the models, particularly LCDM.