The formation and evolution of large- and superlarge-scale structure in the Universe .2. N-body simulations

We present a detailed study of the evolution of large-scale structure in N-body simulations using both the theory of Doroshkevich et al. (Paper I) and the new 'core-sampling' analysis of Buryak, Doroshkevich & Fong. The Zel'dovich approximation shows that under gravitational instability, the velocity held of the initial perturbations in the Universe induces a random network structure, traced by the 'ridges' of dark matter (DM) Zel'dovich pancakes or sheet-like structures. The approximate analytic solution of Paper I shows that the mean free path or mean separation of DM pancakes is similar to 5 h(-1) Mpc. Hence this is a characteristic scale of large-scale structure (LSS) as opposed to the similar to 50-100 h(-1) Mpc scale of superlarge-scale structure (SLSS). The 'modulation' of the network structure by the gravitational potential produces on SLSS scales DM underdense regions, which are predicted to correspond to the 'voids' seen in the observed galaxy distribution. Our aims in this paper are to explore the usefulness of our 'core-sampling' analysis for a quantitative 'empirical' description of the evolution of structure in N-body simulations, and to lest the theory of Paper I by comparing its prediction with the 'core-sampling measurement' of the mean free path between DM LSS elements in an N-body simulation. Six simulations in all are used, and 'measurements' are made at several different epochs for each simulation. For such DM particle catalogues, we need also to introduce a heuristic model for the mass function of LSS elements in a core sample, involving a new parameter, f(sm), the fraction of mass in 'supermassive' clumps, which then measures the degree of structure evolution in a simulation. The results show agreement between theory and the 'core sample' measured estimates for the characteristic scales of LSS in simulations. In particular, the theory accurately predicts the time dependence of the evolution of these scales. We demonstrate the dependence of the formation and evolution of structure on the computational box size of a Simulation, and we discuss the consequences for small box sizes, such as those currently used in the study of galaxy formation. We also discuss the complementary nature of, in particular, the correlation function approach with 'core-sampling' and comment on the relationship of the results with observations.