Characterising superclusters with the galaxy cluster distribution

Superclusters are the largest, observed matter density structures in the Universe. Recently Chon et al.(2013) presented the first supercluster catalogue constructed with a well-defined selection function based on the X-ray flux-limited cluster survey, REFLEX II. For the construction of the sample we proposed a concept to find the large objects with a minimum overdensity such that most of their mass will collapse in the future. The main goal of the paper is to provide support for our concept using simulations that we can, on the basis of our observational sample of X-ray clusters, construct a supercluster sample defined by a certain minimum overdensity, and to test how superclusters trace the underlying dark matter distribution. Our results confirm that an overdensity in the number of clusters is tightly correlated with an overdensity of the dark matter distribution. This enables us to define superclusters such that most of the mass will collapse in the future and to get first-order mass estimates of superclusters on the basis of the properties of the member clusters. We also show that in this context the ratio of the cluster number density and dark matter mass density is consistent with the theoretically expected cluster bias. Our previous work provided evidence that superclusters are a special environment for density structures of the dark matter to grow differently from the field as characterised by the X-ray luminosity function. Here we confirm for the first time that this originates from a top-heavy mass function at high statistical significance provided by a Kolmogorov-Smirnov test. We also find in close agreement with observations that the superclusters occupy only a small volume of few percent while they contain more than half of the clusters in the present day Universe.