Optical and X-ray clusters as tracers of the supercluster-void network.: I.: Superclusters of Abell and X-ray clusters

We study the distribution of Abell and X-ray-selected clusters of galaxies and derive selection functions of these cluster samples. We find that selection functions and percolation properties of Abell clusters of richness class R = 0 and R greater than or equal to 1 are similar; the percolation of X-ray clusters occurs at the same dimensionless radius as the percolation of Abell clusters. We present a new catalog of superclusters of Abell clusters out to a redshift of z(lim) = 0.13, a catalog of X-ray clusters located in superclusters deter mined by Abell clusters, and a list of additional superclusters of X-ray clusters. We investigate the distribution of X-ray-selected clusters of galaxies with respect to superclusters determined by Abell clusters of galaxies and show that the distribution of X-ray clusters follows the supercluster-void network determined by Abell clusters. We find that X-ray clusters are more strongly clustered than other clusters: the fraction of X-ray clusters is higher in rich superclusters, and the fraction of isolated X-ray clusters is lower than the fraction of isolated Abell clusters. Poor, non-Abell X-ray clusters follow the supercluster-void network as well: these clusters are embedded in superclusters determined by Abell clusters and populate filaments between them.