Skewed exponential pairwise velocities from Gaussian initial conditions

Abstract

Using an Eulerian perturbative calculation, we show that the distribution of relative pairwise velocities which arises from gravitational instability of Gaussian density fluctuations has asymmetric (skewed) exponential tails. The negative skewness is induced by the negative mean streaming velocity of pairs (the infall prevails over expansion), while the exponential tails arise because the relative pairwise velocity is a number, not volume weighted statistic. The derived probability distribution is compared with N-body simulations and shown to provide a reasonable fit.