Abstract
We propose a physically motivated definition of superclusters as the largest structures that will remain gravitationally bound as they separate at an exponentially increasing rate in the dark-energy-dominated future of the Universe. Using the spherical collapse model, we were able to analytically determine the condition by which a spherical shell will eventually stop its expansion, becoming the outer limit of a gravitationally bound structure. In particular for the present universe, this criterion states that only shells containing a mean density of 2.36 times the critical density (ρ_c), will eventually stop growing. We tested our criterion using N-body simulations, showing that it gives a good estimate of the external limit of bound structure, and accordingly overestimating its bound mass. The model also showed to give a good estimation of radial velocities up to deep inside the core of the structure. Using this information, we generated a method to estimate the critical shell of structures as seen in redshift space. This method relies in great amount on its calibration using numerical simulations. We applied our method to a large redshift catalog of the Shapley Supercluster, the largest such structure in the nearby Universe (z≤ 0.13), in order to estimate its size and mass. We found that its critical radius is nearly 15h^{-1}Mpc and its mass nearly 7×10^{15}h^{-1}M_{sun}, in good agreement with other studies of the area.
