On the definition of superclusters

To obtain a physically well-motivated definition of superclusters, we proposed in our previous work to select superclusters with an overdensity criterion that selects only those objects that will collapse in the future, including those that are at a turn-around in the present epoch. In this paper we present numerical values for these criteria for a range of standard cosmological models. We express these criteria in terms of a density ratio or, alternatively, as an infall velocity and show that these two criteria give almost identical results. To better illustrate the implications of this definition, we applied our criteria to some prominent structures in the local Universe, the Local supercluster, Shapley supercluster, and the recently reported Laniakea supercluster to understand their future evolution. We find that for the Local and Shapley superclusters, only the central regions will collapse in the future, while Laniakea does not constitute a significant overdensity and will disperse in the future. Finally, we suggest that those superclusters that will survive the accelerating cosmic expansion and collapse in the future be called "superstes-clusters", where "superstes" means survivor in Latin, to distinguish them from traditional superclusters.