HIGH-ORDER CORRELATIONS OF RICH GALAXY CLUSTERS

We analyze the two-dimensional all-sky distribution of rich Abell and ACO galaxy dusters by using counts in cells and measuring the high-order area-averaged angular correlation functions. Confirming previous results, we find a well-defined hierarchical relation between the two- and three-point correlation functions, remarkably constant with scale. In the angular range 2 degrees less than or equal to theta less than or equal to 4 degrees, the southern sample, limited at b(II) less than or equal to -40 degrees 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 three-dimensional coefficients S-J, where S-J = <(xi)over bar>(J)/<(xi)over bar>(J-1)(2), are similar to those measured for the galaxy distribution, and consistent with theoretical predictions. These results are confirmed to the fourth-order by our analysis of a three-dimensional sample of Abell and ACO clusters. Assuming that selection effects and/or the absence of a cluster fair sample are the reason for the difference between the two galactic hemispheres, and between Abell and ACO dusters, 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 nonlinear.