Uncertainties in the cluster-cluster correlation function

We apply the bootstrap resampling technique is applied to estimate sampling errors and significance levels of the two-point correlation functions determined for a subset of the CfA redshift survey of galaxies and a redshift sample of 104 Abell clusters. We also calculate the angular correlation function for a sample of 1664 Abell clusters. We find the standard errors in |ξ(r)| for the Abell data to be considerably larger than quoted ‘Poisson errors’. Our best estimate for the ratio of the correlation length of Abell clusters (richness class |R≥1|⁠, distance class |D≤4|⁠) to that of CfA galaxies is |4.2+1.4-1.0| (68 percentile error). The enhancement of cluster clustering over galaxy clustering is statistically significant in the presence of resampling errors. The uncertainties found do not include the effects of possible systematic biases in the galaxy and cluster catalogs and could be regarded as lower bounds on the true uncertainty range.