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 subhalos 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 -0.6). However, if subhalos are required to exceed a minimal mass before accretion onto the host, the velocity bias becomes negligible and the velocity distribution is close to Gaussian (kurtosis -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 un-biased. 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% of the galaxies move supersonically and 8% have Mach numbers larger than 2 with respect to the intra cluster gas. 
A. Faltenbacher and J. Diemand