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 (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 √ 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.

Voronoi Tessellations and the Cosmic Web: Spatial Patterns and Clustering across the Universe

“…This finding is in line with studies based on cluster samples of rich clusters or selected on the basis of their X-ray emission [9,2]. They do indeed show a trend of an increasing clustering strength as the clusters are richer (≈ massive).…”

Groups of galaxies

“…[6], [7] and [8]). Plotting the correlation lenght, r 0 , as a function of the mean inter-group separation of the different mass/luminosity classes, a nice agreement is found between the results obtained for galaxy groups and those obtained for clusters by [9]. Both groups and clusters are in the same hierarchy of distribution and this result can be compared with predictions of theories of galaxy formation and used to constrain them.…”

LSST Science Book, Version 2.0

“…Points with error bars show a compilation of literature bias values for z = 1.7 colorselected galaxies (A05a, Adelberger et al 2005b), z = 2.1 color selected galaxies (A05b, Adelberger et al 2005a), z ∼ 3 Lyman break galaxies (A05a; F08, Francke et al 2008; L06, Lee et al 2006), and z > 4 Lyman break galaxies (Ou04, Ouchi et al 2004). Also shown are z ∼ 1 galaxies separated by color (C08, Coil et al 2008), z ∼ 0 galaxies labeled by their optical luminosity, from and rich galaxy clusters from Bahcall et al (2003).…”