CLUSTER CORRELATIONS FROM N-POINT CORRELATION AMPLITUDES

We show, by using a new technique, how the much-debated cluster correlation function is directly related to the higher order galaxy correlations. We adopt mathematical techniques from biased galaxy formation: here the biasing simulates the detection of the clusters, rather than their dynamical formation. A simple, analytical example is given. As a practical application of our simplified model, we also present a novel method to determine the amplitudes of the irreducible N-point correlation functions in the gravitational clustering hierarchy. We use the corrected Lick catalog to obtain values of q(N) up to N = 8, considerably beyond previous attempts. The catalog, obtained from the Lick sample, has amplifications similar to the rich clusters, and the galaxy-"cluster" cross-correlation is close to the geometric mean of the galaxy and cluster autocorrelations.