The Correlation Function of Optically Selected Galaxy Clusters in the Sloan Digital Sky Survey

Abstract

We measure the two-point spatial correlation function for clusters selected from the photometric MaxBCG galaxy cluster catalog for the Sloan Digital Sky Survey (SDSS). We evaluate the correlation function for several cluster samples using different cuts in cluster richness. Fitting the results to power-laws, $ξ_{cc}(r) = (r/R_0)^{-γ}$, the estimated correlation length $R_0$ as a function of richness is broadly consistent with previous cluster observations and with expectations from N-body simulations. We study how the linear bias parameter scales with richness and compare our results to theoretical predictions. Since these measurements extend to very large scales, we also compare them to models that include the baryon acoustic oscillation feature and that account for the smoothing effects induced by errors in the cluster photometric redshift estimates. For the largest cluster sample, corresponding to a richness threshold of $\Ng\ge 10$, we find only weak evidence, of about $1.4-1.7σ$ significance, for the baryonic acoustic oscillation signature in the cluster correlation function.