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 deg 2 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, r 0 - d , that best describes the observations and the LCDM prediction is r 0 ≃ 2.6 (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.