The three-point correlation functions of Abell clusters
Yipeng Jing, Jialu Zhang · The Astrophysical Journal · 1989
The three-point angular as well as spatial correlation functions are determined for the statistical catalog of Abell clusters. The separate estimations (both angular and spatial) for the northern sample, the southern sample, and the total sample consistently show that the three-point correlation function of R >= 1 clusters can be represented by a scaling form ζ = Q(ξ_1xi_2_ + ξ_2xi_3_ + ξ_3xi_1_) and Q ~ 0.7,just as for galaxies. We also analyze R >= 2 Abell clusters to determine the richness dependence of ζ, and we find that ζ of R > 2 clusters can be well represented by the scaling form and Q is almost independent of richness. Together with the three-point correlation functions of galaxies, our results indicate that from galaxies to R >= 2 Abell clusters, their three-point correlation functions possess a universal scaling form, although they span three magnitudes. This universal form would be of great value in understanding the origin and evolution of the large-scale structure of the universe.