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 $z\le 0.5$ 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 $\mathrm{\Lambda }$CDM model curve, we find $D_v(z=0.331)r_d^{fid}\mathrm{/}{r}_d=1261.5\pm 48$~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.