The richness-dependent cluster correlation function: Early Sloan Digital Sky Survey data

The cluster correlation function and its richness dependence are determined from 1108 clusters of galaxies - the largest sample of clusters studied so far - found in 379 deg² of Sloan Digital Sky Survey early data. The results are compared with previous samples of optically and X-ray-selected clusters. The richness-dependent correlation function increases monotonically from an average correlation scale of ∼12 h^-1 Mpc for poor clusters to ∼25 h^-1 Mpc for the richer, more massive clusters with a mean separation of ∼90 h^-1 Mpc. X-ray-selected clusters suggest slightly stronger correlations than optically selected clusters (∼2 σ). The results are compared with large-scale cosmological simulations. The observed richness-dependent cluster correlation function is well represented by the standard flat Λ-dominated cold dark matter (LCDM) model (Ω_m ≃ 0.3., h ≃ 0.7) and is inconsistent with the considerably weaker correlations predicted by Ω _m = 1 models. An analytic relation for the correlation scale versus cluster mean separation, r₀-d, that best describes the observations and the LCDM prediction is r₀ ≃ 2.6√d (for d ≃ 20-90 h^-1 Mpc). Data from the complete Sloan Digital Sky Survey, when available, will greatly enhance the accuracy of the results and allow a more precise determination of cosmological parameters.