Modelling the redshift‐space distortion of galaxy clustering

We use a set of large, high‐resolution cosmological N ‐body simulations to examine the redshift‐space distortions of galaxy clustering on scales of order 10–200  h −1 Mpc. Galaxy redshift surveys currently in progress will, on completion, allow us to measure the quadrupole distortion in the 2‐point correlation function, ξ(σ, π), or its Fourier transform, the power spectrum P ( k , μ), to a high degree of accuracy. On these scales we typically find a positive quadrupole, as expected for coherent infall on to overdense regions and outflow from underdense regions, but the distortion is substantially weaker than that predicted by pure linear theory. We assess two models that may be regarded as refinements to linear theory, the Zel’dovich approximation and a dispersion model in which the non‐linear velocities generated by the formation of virialized groups and clusters are treated as random perturbations to the velocities predicted by linear theory. We find that neither provides an adequate physical description of the clustering pattern. If used to model redshift‐space distortions on scales for 10 < λ < 200  h −1 Mpc the estimated value of β [β =  f (Ω 0 ) /  b where f (Ω 0 ) ≈ Ω 0.6 0 and b is the galaxy bias parameter] is liable to systematic errors of the order of 10 per cent or more. We discuss how such systematics can be avoided by (i) development of a more complete model of redshift distortions and (ii) the direct use of galaxy catalogues generated from non‐linear N ‐body simulations.