The Correlation Function of Galaxy Clusters and Detection of Baryon Acoustic Oscillations

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 D_v (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 Ω _m 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.