The correlation function of galaxy clusters and detection of baryon acoustic oscillations

Abstract

We calculate the correlation function of 13,904 galaxy clusters of z ≤ 0.4 selected from the cluster catalog of Wen et al. The correlation function can be fitted with a power-law model ξ(r) = (r/R 0) -γ on the scales of 10 h -1 Mpc ≤ r ≤ 50 h -1 Mpc, with a larger correlation length of R 0 = 18.84 ± 0.27 h -1 Mpc for clusters with a richness of R ≥ 15 and a smaller length of R 0 = 16.15 ± 0.13 h -1 Mpc for clusters with a richness of R ≥ 5. The power-law index of γ = 2.1 is found to be almost the same for all cluster subsamples. A pronounced baryon acoustic oscillations (BAO) peak is detected at r ∼ 110 h -1 Mpc with a significance of ∼ 1.9σ. By analyzing the correlation function in the range of 20 h -1 Mpc ≤ r ≤ 200 h -1 Mpc, we find that the constraints on distance parameters are Dv (z m = 0.276) = 1077 ± 55(1σ) Mpc and h = 0.73 ± 0.039(1σ), which are consistent with the cosmology derived from Wilkinson Microwave Anisotropy Probe (WMAP) seven-year data. However, the BAO signal from the cluster sample is stronger than expected and leads to a rather low matter density Ωm h 2 = 0.093 ± 0.0077(1σ), which deviates from the WMAP7 result by more than 3σ. The correlation function of the GMBCG cluster sample is also calculated and our detection of the BAO feature is confirmed. © © 2012. The American Astronomical Society. All rights reserved.