A statistical study of the 3-point correlation functions of Abell clusters
Yipeng Jing, Jialu Zhang · 1989
We estimate the 3-point spatial correlation functions for four subsamples of Abell clusters with richness R≥1 as well as for the whole northern sample of R≥2 Abell clusters. Our preliminary results show that the 3-point correlation functions of Abell clusters can be expressed by the scaling form: ζ=Q (ξ_1ξ_2+ξ_2ξ_3+ξ_3ξ_1), and Q remains almost a constant≈0.65 and is independent of the cluster richness. This value of Q is very close to the estimated constant Q_g of the 3-point correlation functions of galaxies, which means that from galaxies to R≥2 Abell clusters, their 3-point correlation functions share the same universal scaling form although they span three magnitudes. This universal form would be of great value for understanding the large-scale structures of the universe.