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 similar to12 h(-1) Mpc for poor clusters to similar to25 h(-1) Mpc for the richer, more massive clusters with a mean separation of similar to90 h(-1) Mpc. X-ray - selected clusters suggest slightly stronger correlations than optically selected clusters (similar to2 sigma). The results are compared with large-scale cosmological simulations. The observed richness-dependent cluster correlation function is well represented by the standard. at Lambda-dominated cold dark matter (LCDM) model (Omega(m) similar or equal to 0.3, h similar or equal to 0.7) and is inconsistent with the considerably weaker correlations predicted by Omega(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) similar or equal to 2.6rootd (for d similar or equal to 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.