Correlation Length of X‐Ray–Brightest Abell Clusters

We compute the cluster auto-correlation function \ξcc(r) of an X-ray flux limited sample of Abell clusters (XBACs, \{ebe}). For the total XBACs sample we find a power-law fit \ξcc=(r/r₀)\γ with r₀=21.1 Mpc h⁻¹and \γ =-1.9 consistent with the results of R \≥ 1 Abell clusters. We also analyze \ξcc(r) for subsamples defined by different X-ray luminosity thresholds where we find a weak tendency of larger values of r₀ with increasing X-ray luminosity although with a low statistical significance. In the different subsamples analyzed we find 21 < r₀ < 35 Mpc h⁻¹ and -1.9< \γ < -1.6. Our analysis suggests that cluster X-ray luminosities may be used for a reliable confrontation of cluster spatial distribution properties in models and observations.