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= 20.7+4.0−3.8h−1 Mpc with γ= 1.6+0.4−0.4 and r0= 9.7+1.2−1.2 with γ= 2.0+0.7−0.5h−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≃Ω0.6m/b0 and the cluster bias at the present time. For the Λ cold dark matter case we find β= 0.2+0.029−0.016, which is in agreement with the results based on large-scale cluster motions.
Highlights
Galaxy clusters occupy a special position in the hierarchy of cosmic structure formation, being the largest gravitationally collapsed objects in the universe
The traditional indicator of clustering, the cluster two-point correlation function, is a fundamental statistical test for the study of the cluster distribution and is relatively straightforward to measure from observational data
Many authors based on optical and X-ray data have shown that the large scale clustering pattern of galaxy clusters is well described by a power law, ξ(r) = (r◦/r)γ, with γ = 1.6 − 2
Summary
Galaxy clusters occupy a special position in the hierarchy of cosmic structure formation, being the largest gravitationally collapsed objects in the universe. They appear to be ideal tools for testing theories of structure formation as well as studying large-scale structure. The traditional indicator of clustering, the cluster two-point correlation function, is a fundamental statistical test for the study of the cluster distribution and is relatively straightforward to measure from observational data. In this paper we utilize the recently completed SDSS CE cluster catalog (Goto et al 2002) in order: (i) to study the two point correlation function in redshift space and (ii) to calculate the relative cluster bias at the present time comparing the observational results with those derived from three flat cosmological models with dark energy (quintessence).
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