Velocity distributions in clusters of galaxies

We employ a high-resolution dissipationless N-body simulation of a galaxy cluster to investigate the impact of subhalo selection on the resulting velocity distributions. Applying a lower limit on the present bound mass of subhaloes leads to high subhalo velocity dispersions compared to the diffuse dark matter (positive velocity bias) and to a considerable deviation from a Gaussian velocity distribution (kurtosis similar to -0.6). However, if subhaloes are required to exceed a minimal mass before accretion on to the host, the velocity bias becomes negligible and the velocity distribution is close to Gaussian (kurtosis similar to -0.15). Recently, it has been shown that the latter criterion results in subhalo samples that agree well with the observed number-density profiles of galaxies in clusters. Therefore, we argue that the velocity distributions of galaxies in clusters are essentially unbiased. The comparison of the galaxy velocity distribution and the sound speed, derived from scaling relations of X-ray observations, results in an average Mach number of 1.24. Altogether 65 per cent of the galaxies move supersonically and 8 per cent have Mach numbers larger than 2 with respect to the intracluster gas.