THE 3-POINT CORRELATION-FUNCTION OF RICH CLUSTERS - THE RELIABILITY OF DETERMINATIONS FROM SMALL SAMPLES

We investigate to what extent small 3D samples of rich clusters can be expected to constrain the form of the three-point correlation function of such clusters. We generate artificial cluster catalogues (from an underlying lognormal field) in such a way that the clusters should possess a three-point function obeying the Kirkwood superposition relationship. We find that, with the presently available size of cluster samples, we are unable to put tight constraints upon the form of the three-point correlation function. In particular, we cannot strongly rule out the existence of a 'triplet' contribution to the cluster correlation function (which appears in the Kirkwood superposition formula). This has important implications for theories in which clusters are biased tracers of the large-scale mass distribution, because these theories predict a triplet term.