High-Order Correlations of Rich Galaxy Clusters

We analyse the two{dimensional all{sky distribution of rich Abell and ACO galaxy clusters by using counts in cells and measuring the high{order area{averaged angular correlation functions. Con(cid:12)rming previous results, we (cid:12)nd a well de(cid:12)ned hierarchical relation between the two and three{point correlation functions, remarkably constant with scale. In the angular range 2 (cid:14) (cid:20) (cid:18) (cid:20) 4 (cid:14) , the southern sample, limited at bII (cid:20) (cid:0)40 (cid:14) and including both Abell and ACO clusters, shows a remarkable hierarchical behavior up to the sixth order, while northern Abell clusters give positive correlations in the same range only up to the fourth order. The inferred deprojected values of the 3{D coe(cid:14)cients SJ, where SJ = (cid:22) (cid:24)J= (cid:22) (cid:24) J(cid:0)1 2 , are similar to those measured for the galaxy distribution, and consistent with theoretical predictions. These results are con(cid:12)rmed to the 4th order by our analysis of a 3{D sample of Abell and ACO clusters. Assuming that selection e(cid:11)ects and / or the absence of a cluster fair sample are the reason of the di(cid:11)erence between the two galactic hemi-spheres, and between Abell and ACO clusters, our results indicate that the statistical properties of the cluster distribution originate from the underlying galaxy distribution and show that the biasing between clusters and galaxies is non{linear.