Spatial Correlation Function and Pairwise Velocity Dispersion of Galaxies: Cold Dark Matter Models versus the Las Campanas Survey

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Abstract
We show, with the help of large N-body simulations, that both the real-space two-point correlation function and pairwise velocity dispersion of galaxies can be measured reliably from the Las Campanas Redshift Survey. The real-space correlation function is well fitted by the power law ξ(r) = (r0/r)γ with r0 = (5.06 ± 0.12) h-1 Mpc and γ = 1.862 ± 0.034, and the pairwise velocity dispersion at 1 h-1 Mpc is 570 ± 80 km s-1. A detailed comparison between these observational results and the predictions of current cold dark matter (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 1 h-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 σ8 Ω0.60~0.4-0.5 and Γ ~ 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 Γ ~ 0.2 and 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.

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