Filamentary superclustering in a universe dominated by cold dark matter

The formation of large-scale filamentary structure in a universe dominated by cold dark matter (CDM) is examined using high-resolution N-body simulations. A measure of the filamentary nature of superclustering is provided by the relative orientations of neighboring clusters of galaxies. When all cluster pairs are considered, there is a clear tendency for the major axes of neighboring clusters to be aligned with one another over scales up to ∼10-15h^-2 Mpc. When the sample is restricted to only those clusters that reside in superclusters, however, significant alignments are found for separations up to ∼30h^-2 Mpc or more. The strength and extent of cluster alignments are found to be insensitive to the degree of biasing, while the abundance of rich clusters depends strongly on the bias factor. The cluster alignments survive even after strong nonlinear clustering has developed on small scales, and thus can provide a useful indicator of filamentary structure on very large scales today. Despite the fact that the standard CDM model has relatively little power on large scales compared with other competing models, it is found to be capable of producing large-scale alignments as strong as are observed. Other properties of superclusters in the CDM model, such as their sizes and the fraction of rich clusters which are supercluster members, also appear to be consistent with observations.