3-POINT CORRELATION-FUNCTIONS AND THE HIERARCHICAL-CLUSTERING ANSATZ IN LOW-DENSITY COLD DARK MATTER UNIVERSES

Three-point correlation functions zeta123 in low-density unbiased cold dark matter universes are examined over the range 10(-2) < zeta123 < 10(5), using cosmological N-body simulation data. Although there exists a weak dependence on the configuration of the triplets (r1, r2, r3), the models are found to reproduce an observed relation, zeta123 = Q[xi(r1)xi(r2) + xi(r2)xi(r3) + xi(r3)xi(r1)], in an averaged sense, where xi(r) denotes a two-point correlation function. The amplitudes Q, averaged over all triplets of galaxies, are 1.2-1.4, in good agreement both with the observed value and with other model-dependent estimates. In particular, the relation holds equally well both in linear and in nonlinear regimes of fluctuations with the same value of Q. The three-point correlation function of clusters in these models does not show noticeably stronger enhancement of the amplitude relative to that of galaxies. This is in marked contrast to the case of two-point correlation functions of clusters whose amplitude is larger than those of galaxies, and would constrain attempts to account for the origin of cluster correlations on the basis of a biasing theory.