Cluster-Galaxy Correlations in Cold Dark Matter Models

We study the ability of COBE-normalized cold dark matter (CDM) models to reproduce observed properties of the distribution of galaxies and clusters using N-body numerical simulations. We analyze the galaxy-galaxy and cluster-galaxy two-point correlation functions, ξgg and ξcg, in open (Ω0 = 0.4, ΩΛ = 0, σ8 = 0.75) and flat (Ω0 = 0.3, ΩΛ = 0.7, σ8 = 1.05) CDM models, both of which reproduce the observed abundances of rich clusters of galaxies. To compare models with observations, we compute projected cross-correlation functions ωgg and ωcg to derive the corresponding ξgg and ξcg. We use target galaxies selected from the Las Campanas Redshift Survey, target clusters selected from the APM Cluster Survey, and tracer galaxies from the Edinburgh Durham Sky Survey catalog. We find that the open model is able to reproduce the observed ξgg, whereas the flat model needs antibias in order to fit the observations. Our estimate of ξcg for the APM cluster sample analyzed is consistent with a power law ξcg = (r/r0)γ with r0 = 10.0 ± 0.7 h-1 Mpc and γ ≃ -2.1. For the open and flat-antibiased CDM models explored we find the corresponding cluster-galaxy correlation lengths 6.5 ± 0.7 h-1 Mpc and 7.2 ± 0.5 h-1 Mpc, respectively, significantly lower than the observed value. Our results indicate that COBE-normalized CDM models are not able to reproduce the spatial cross-correlation of clusters and galaxies.