The three-point correlation functions of Abell clusters

Abstract

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 &gt;= 1 clusters can be represented by a scaling form ζ = Q(ξ_1<SUB>xi</SUB>_2_ + ξ_2<SUB>xi</SUB>_3_ + ξ_3<SUB>xi</SUB>_1_) and Q ~ 0.7,just as for galaxies. We also analyze R &gt;= 2 Abell clusters to determine the richness dependence of ζ, and we find that ζ of R &gt; 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 &gt;= 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.