Correlation length of X-ray brightest Abell clusters

Abstract

We compute the cluster auto-correlation function $\xi_{cc}(r)$ of an X-ray flux limited sample of Abell clusters (XBACs, \cite{ebe}). For the total XBACs sample we find a power-law fit $\xi_{cc}=(r/r_0)^{\gamma}$ with $r_0=21.1$ Mpc h$^{-1}$and $\gamma =-1.9$ consistent with the results of $R \ge 1 $ Abell clusters. We also analyze $\xi_{cc}(r)$ for subsamples defined by different X-ray luminosity thresholds where we find a weak tendency of larger values of $r_0$ with increasing X-ray luminosity although with a low statistical significance. In the different subsamples analyzed we find $21 < r_0 < 35 $ Mpc h$^{-1}$ and $-1.9< \gamma < -1.6$. Our analysis suggests that cluster X-ray luminosities may be used for a reliable confrontation of cluster spatial distribution properties in models and observations.