Correlation length of X-ray-brightest Abell clusters

We compute the cluster autocorrelation function xi(cc)(r) of an X-ray flux-limited sample of Abell clusters (XBACs). 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 greater than or equal to 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 Mpc h(-1) < 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.