3-POINT CORRELATION-FUNCTION OF GALAXY CLUSTERS IN COSMOLOGICAL MODELS - A STRONG DEPENDENCE ON TRIANGLE SHAPES

In this paper, we use large P(3)M N-body simulations to study the thre e-point correlation function zeta of clusters in two theoretical model s. The first model (LCDM) is a low-density flat model of Omega(0) = 0. 3, Lambda(0) = 0.7 and h = 0.75, and the second model (PIM) is an Eins tein-de Sitter model with its linear power spectrum obtained from obse rvations. We find that the scaled function Q(r, u, v), which is define d as the ratio of zeta(r, ru, ru + rv) to the hierarchical sum xi(r)xi (ru) + xi(ru)xi(ru + rv) + xi(ru + rv)xi(r) (where xi is the two-point correlation function of clusters), depends weakly on r and u, but ver y strongly on v. Q(r, u, v) is about 0.2 at v = 0.1 and 1.8 at v = 0.9 . A model of Q(r, u, v) = Theta 10(1.3v2) can fit the data of zeta ver y nicely with Theta approximate to 0.14. This model is found to be uni versal for the LCDM clusters and for the PIM clusters. Furthermore, Q( r, u, v) is found to be insensitive to the cluster richness. We compar e our N-body results with simple analytical theories of cluster format ion, like the peak theories or the local maxima theories. We find that these theories do not provide an adequate description for the three-p oint function of clusters. We also examine the observational data of r presently available, and do not find any contradiction between the ob servations and our model predictions. The v-dependence of q in a proje cted catalogue of clusters is shown to be much weaker than the v-depen dence of Q found in the three-dimensional case. This is probably the r eason why the v-dependence of Q has not been found in an angular corre lation function analysis of the Abell catalogue. The v-dependence foun d in this paper might be an important feature of clusters formed in th e Gaussian gravitational instability theories. Therefore it would be i mportant to search for the v-dependence of Q in redshift samples of ri ch clusters.