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.
