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

We calculate the correlation function of 13,904 galaxy clusters of z \leq 0.4 selected from the cluster catalog of Wen, Han & Liu. The correlation function can be fitted with a power-law model \xi(r)=(r/R_0)^{\gamma} on the scales of 10h^(-1)Mpc \leq r \leq 50h^(-1)Mpc, with a larger correlation length of R_0=18.84\pm0.27 h^(-1)Mpc for clusters with a richness of R \geq 15 and a smaller length of R_0=16.15 \pm 0.13 h^(-1)Mpc for clusters with a richness of R \geq 5. The power law index of \gamma=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 ~ 1.9\sigma. By analyzing the correlation function in the range of 20 h^(-1)Mpc \leq r \leq 200 h^(-1)Mpc, we find the constraints on distance parameters are D_v(0.276)=1077\pm55(1\sigma) Mpc and h=0.73 \pm 0.039 (1\sigma), which are consistent with the WMAP 7-year cosmology. However, the BAO signal from the cluster sample is stronger than expected and leads to a rather low matter density \Omega_m h^2=0.093\pm0.0077 (1\sigma), which deviates from the WMAP 7-year result by more than 3 \sigma. The correlation function of the GMBCG cluster sample is also calculated and our detection of the BAO feature is confirmed.