Spatial correlation function and pairwise velocity dispersion of galaxies: CDM models versus the Las Campanas Survey

Abstract

We show, with the help of large N-body simulations, that the real-space two-point correlation function and pairwise velocity dispersion of galaxies can both be measured reliably from the Las Campanas Redshift Survey. The real-space correlation function is well fitted by the power law $ξ(r)=(r_0/r)^γ$ with $r_0=(5.06\pm0.12)\mpc$ and $γ=1.862\pm 0.034$, and the pairwise velocity dispersion at $1\mpc$ is $(570\pm 80)\kms$. A detailed comparison between these observational results and the predictions of current CDM cosmogonies is carried out. We construct 60 mock samples for each theoretical model from a large set of high resolution N-body simulations, which allows us to include various observational selection effects in the analyses and to use exactly the same methods for both real and theoretical samples. We demonstrate that such a procedure is essential in the comparison between models and observations. The observed two-point correlation function is significantly flatter than the mass correlation function in current CDM models on scales $\la 1\mpc$. The observed pairwise velocity dispersion is also lower than that of dark matter particles in these models. We propose a simple antibias model to explain these discrepancies. This model assumes that the number of galaxies per unit dark matter mass, $N/M$, decreases with the mass of dark haloes. The predictions of CDM models with $σ_8Ω_0^{0.6}\sim 0.4$-0.5 and $Ω_0 h\sim 0.2$ are in agreement with the observational results, if the trend of $N/M$ with $M$ is at the level already observed for rich clusters of galaxies. Thus CDM models with cluster-abundance normalization are consistent with the observed correlation function and pairwise velocity dispersion of galaxies. A high level of velocity bias is not required in these models.