Populating dark matter haloes with galaxies: comparing the 2dFGRS with mock galaxy redshift surveys

ABSTRACT In two recent papers, we developed a powerful technique to link the distribution of galaxies to that of dark matter haloes by considering halo occupation numbers as a function of galaxy luminosity and type. In this paper we use these distribution functions to populate dark matter haloes in high‐resolution N ‐body simulations of the standard ΛCDM cosmology with Ω m = 0.3, Ω Λ = 0.7 and σ 8 = 0.9 . Stacking simulation boxes of 100 h −1 Mpc and 300 h −1 Mpc with 512 3 particles each we construct mock galaxy redshift surveys out to a redshift of z = 0.2 with a numerical resolution that guarantees completeness down to 0.01 L *. We use these mock surveys to investigate various clustering statistics. The predicted two‐dimensional correlation function ξ( r p , π) reveals clear signatures of redshift space distortions. The projected correlation functions for galaxies with different luminosities and types, derived from ξ( r p , π) , match the observations well on scales larger than ∼3 h −1 Mpc. On smaller scales, however, the model overpredicts the clustering power by about a factor two. Modelling the ‘finger‐of‐God’ effect on small scales reveals that the standard ΛCDM model predicts pairwise velocity dispersions (PVD) that are ∼400 km s −1 too high at projected pair separations of ∼1 h −1 Mpc. A strong velocity bias in massive haloes, with b vel ≡σ gal /σ dm ∼ 0.6 (where σ gal and σ dm are the velocity dispersions of galaxies and dark matter particles, respectively) can reduce the predicted PVD to the observed level, but does not help to resolve the overprediction of clustering power on small scales. Consistent results can be obtained within the standard ΛCDM model only when the average mass‐to‐light ratio of clusters is of the order of 1000 (M/L) ⊙ in the B ‐band. Alternatively, as we show by a simple approximation, a ΛCDM model with σ 8 ≃ 0.75 may also reproduce the observational results. We discuss our results in light of the recent WMAP results and the constraints on σ 8 obtained independently from other observations.