Redshift-space distortions with the halo occupation distribution - I. Numerical simulations

We show how redshift-space distortions of the galaxy correlation function or power spectrum can constrain the matter density parameter Omega m and the linear matter fluctuation amplitude sigma(8). We improve on previous treatments by adopting a fully non-linear description of galaxy clustering and bias, which allows us to achieve the accuracy demanded by larger galaxy redshift surveys and to break parameter degeneracies by combining large-scale and small-scale distortions. Given an observationally motivated choice of the initial power spectrum shape, we consider different combinations of Omega(m) and s8 and find parameters of the galaxy halo occupation distribution ( HOD) that yield nearly identical galaxy correlation functions in real space. We use these HOD parameters to populate the dark matter haloes of large N-body simulations, from which we measure redshift-space distortions on small and large scales. We include a velocity bias parameter alpha(v) that allows the velocity dispersions of satellite galaxies in haloes to be systematically higher or lower than those of dark matter. Large-scale distortions are determined by the parameter combination beta = Omega(0.6)(m)/b(g), where b(g) is the bias factor defined by the ratio of galaxy and matter correlation functions, in agreement with the linear theory prediction of parameter degeneracy. However, linear theory does not accurately describe the distortions themselves on scales accessible to our simulations. We provide fitting formulas to estimate beta from measurements of the redshift-space correlation function or power spectrum, and we show that these formulas are significantly more accurate than those in the existing literature. On small scales, the 'FOG' distortions at projected separations similar to 0.1 h(-1) Mpc depend on Omega(m)alpha(2)(v) but are independent of sigma(8), while at intermediate separations they depend on sigma(8) as well. One can thus use measurements of redshift-space distortions over a wide range of scales to separately determine Omega(m), sigma(8), and alpha(v).