Correlation Functions of the APM Clusters of Galaxies

TL;DR

This study analyzes the correlation functions of APM galaxy clusters, revealing higher amplitudes and a stronger richness dependence than previously reported, with results consistent across different methods.

Contribution

The paper provides new measurements of the APM cluster correlation function showing stronger amplitude and richness dependence than earlier findings.

Findings

Correlation length increases with richness limit.

Correlation function amplitude is higher than previous reports.

Results are robust against methodological variations.

Abstract

We have found that the two-point correlation function of the APM clusters of galaxies has an amplitude much higher than that claimed by the APM group. As the richness limit increases from R = 53 to 80, the correlation length increases from 17.5 to 28.9 h^{-1}Mpc. This indicates that the richness dependence of the APM cluster correlation function is also much stronger than what the APM group has reported. The richness dependence can be represented by a fitting formula r_0 = 0.53 d_c + 0.01, which is consistent with the Bahcall's formula r_0 = 0.4 d_c. We have tried to find the possible reason for discrepancies. However, our estimates for the APM cluster correlation function are found to be robust against variation of the method of calculation and of sample definition.