3-POINT FUNCTIONS OF CLUSTERS IN THE BUBBLE UNIVERSE

We study, by numerical simulations, the three-point correlation functions, zeta, of clusters in the bubble universe. The clusters are identified as `knots' where three shells intersect. The shells are distributed randomly in space and have a power-law radius distributions. Compared with Paper I (Jing), this paper takes the shell mergers and cluster mergers into account. These modifications greatly improve the power-law models by reproducing the observed three-point functions of Abell clusters. Our results indicate that the bubble models are able to produce the observed hierarchical form of zeta. The three-point function, after being expressed in the hierarchical form, does not significantly depend on details of the models.