Modelling peculiar velocities of dark matter haloes

We present a simple model that accurately describes various statistical properties of peculiar velocities of dark matter haloes. We pay particular attention to the following two effects. First, the evolution of the halo peculiar velocity depends on the local matter density, instead of the global density. Secondly, dark matter haloes are biased tracers of the underlying mass distribution, thus haloes tend to be located preferentially at high density regions. For the former, we develop an empirical model calibrated with N -body simulations while, for the latter, we use a conventional halo bias model based on the extended Press-Schechter model combined with an empirical lognormal probability distribution function of the mass density distribution. We find that, compared with linear theory, the present model significantly improves the accuracy of predictions of statistical properties of the halo peculiar velocity field including the velocity dispersion, the probability distribution function, and the pairwise velocity dispersion at large separations. Thus, our model predictions may be useful in analysing future observations of the peculiar velocities of galaxy clusters.