CLUSTERING OF GALAXY CLUSTERS .2. RARE EVENTS IN THE CLUSTER DISTRIBUTION

We analyze subsamples of the Abell and ACO cluster catalogs, which are nearly complete, in order to study the large-scale structure traced by rich clusters. We use a variety of statistical techniques, minimal spanning trees, percolation, void probability functions, and cluster alignments, and we compare our findings with that expected from an ensemble of simulated cluster catalogs having the same selection functions and low-order clustering as the real data. The simulations have been built applying the Zel'dovich algorithm to a delta(k) spectrum Gaussian distributed with zero mean and random phases. The power spectrum is chosen so that the perturbed particle distribution has the same two-point correlation function as the real clusters. In this way we can test the reproducibility of the real data statistics in our simulations. We find that the minimal spanning tree distribution reveals features which are not reproduced in our simulations at a greater than or similar to 3 sigma level. Similarly, not reproduced are the shapes of many superclusters, found by a friends of-friends algorithm. These discrepancies are not alleviated when increasing the clustering strength or the large scale power in the simulations. We suggest that the real cluster distribution might be described by a statistic more complicated that a simple Gaussian.