A detection of baryon acoustic oscillations from the distribution of galaxy clusters

We calculate the correlation function of 79,091 galaxy clusters in the redshift region of $z \leq 0.5$ selected from the WH15 cluster catalog. With a weight of cluster mass, a significant baryon acoustic oscillation (BAO) peak is detected on the correlation function with a significance of $3.7 \sigma$. By fitting the correlation function with a $\Lambda$CDM model curve, we find $D_v(z = 0.331) r_d^{fid}/r_d = 1261.5 \pm 48$~Mpc which is consistent with the Planck 2015 cosmology. We find that the correlation function of the higher mass sub-sample shows a higher amplitude at small scales of $r < 80~h^{-1}{\rm Mpc}$, which is consistent with our previous result. The 2D correlation function of this large sample of galaxy clusters shows a faint BAO ring with a significance of $1.8\sigma$, from which we find that the distance scale parameters on directions across and along the line-of-sight are $\alpha_{\sigma} = 1.02 \pm 0.06$ and $\alpha_{\pi} = 0.94 \pm 0.10$, respectively.