The Richness‐dependent Cluster Correlation Function: Early Sloan Digital Sky Survey Data

Abstract

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 LCDM model (Ωm≃0.3, h ≃0.7), and is inconsistent with the considerably weaker correlations predicted by Ωm = 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. Subject headings: cosmology:observations–cosmology:theory–cosmological parameters– dark matter–galaxies:clusters: general–large-scale structure of universe 1