HIERARCHICAL PANCAKING - WHY THE ZELDOVICH APPROXIMATION DESCRIBES COHERENT LARGE-SCALE STRUCTURE IN N-BODY SIMULATIONS OF GRAVITATIONAL CLUSTERING

To explain the rich structure of voids, clusters, sheets and filaments apparent in the Universe, we present evidence for the convergence of the two classic approaches to gravitational clustering, the 'pancake' and 'hierarchical' pictures. We compare these two models by looking at agreement between individual structures - the 'pancakes' which are ch aracteristic of the Zel'dovich approximation (ZA) and also appear in h ierarchical N-body simulations. We find that we can predict the orient ation and position of N-body simulation objects rather well, with decr easing accuracy for increasing large-k (small-scale) power in the init ial conditions. We examine an N-body simulation with initial power spe ctrum P(k) proportional to k(3), and find that a modified version of t he ZA based on the smoothed initial potential works well in this extre me hierarchical case, implying that even here very low-amplitude long waves dominate over local clumps (although we can see the beginning of the breakdown expected for k(4)). In this case the correlation length of the initial potential is extremely small initially, but grows cons iderably as the simulation evolves. We show that the non-linear gravit ational potential strongly resembles the smoothed initial potential. T his explains why the ZA with smoothed initial conditions reproduces la rge-scale structure so well, and probably why our Universe has a coher ent large-scale structure.