Modelling the two-point correlation function of galaxy clusters in the Sloan Digital Sky Survey

Abstract

We study the clustering properties of the recently compiled Sloan Digital Sky Survey (SDSS) cluster catalogue using the two-point correlation function in redshift space. We divide the total SDSS sample into two richness subsamples, roughly corresponding to Abell R ≥ 0 and Automated Plate Measuring (APM) clusters, respectively. If the two-point correlations are modelled as a power law, ξ(r) = (r0/r)γ, then the best-fitting parameters for the two subsamples are r0 = 20.73.8+4.0 h-1 Mpc with γ = 1.6-0.4+0.4 and r0 = 9.7-1.2+1.2 with γ = 2.0-0.5+0.7 h-1 Mpc, respectively. Our results are consistent with the dependence of cluster richness on the cluster correlation length. Finally, comparing the SDSS cluster correlation function with predictions from three flat cosmological models (Ωm = 0.3) with dark energy (quintessence), we estimate the cluster redshift-space distortion parameter β ≃ Ωm0.6/b0 and the cluster bias at the present time. For the A cold dark matter case we find β= 0.2 -0.016+0.029, which is in agreement with the results based on large-scale cluster motions.