The cluster correlation function: Consistent results from an automated survey

The recently reported results of cluster correlations obtained from an automated survey of galaxy clusters (APM) are shown to be consistent with the Bahcall-Soneira richness-dependent cluster correlation function, and with the universal dimensionless cluster correlation. In agreement with these previously formulated relations, the APM clusters exhibit less strong clustering than the rich Abell clusters, as expected from their lower richness (N ≳ 20 galaxies) and higher number density (2.4 × 10^-5 h³ Mpc^-3) than the richer (N ≳ 50 galaxies) and rarer (0.6 × 10^-5 h³ Mpc^-3) Abell clusters. The predicted correlation length for the APM clusters based on their number density and richness is 14 h^-1 Mpc, compared with the observed value of 13 ± 1.4 h^-1 Mpc. The consistency between the new APM result and the Abell cluster correlations also indicates that projection effects do not significantly affect the cluster correlations and their implied large-scale structure.