Modelling non-linear effects in the redshift space two-point correlation function and its implications for the pairwise velocity dispersion

Abstract

The anisotropies in the galaxy two-point correlation function measured from redshift survey exhibits deviations from the predictions of the linear theory of redshift space distortion on scales as large as 20 h -1 Mpc where we expect linear theory to hold in real space. Any attempt at analysing the anisotropies in the redshift correlation function and determining the linear distortion parameter β requires these deviations to be correctly modelled and taken into account. These deviations are usually attributed to galaxy random motions and these are incorporated in the analysis through a phenomenological model in which the linear redshift correlation is convolved with the random pairwise velocity distribution function along the line of sight. We show that a substantial fraction of the deviations arise from non-linear effects in the mapping from real to redshift space caused by the coherent flows. Models that incorporate this effect provide as good a fit to N-body results as the phenomenological model which only includes the effect of random motions. We find that the pairwise velocity dispersions predicted by all of the models that we have considered are in excess of the values determined directly from the N-body simulations. This indicates a shortcoming in our understanding of the statistical properties of peculiar velocities and their relation to redshift distortion.