Hierarchical Pancaking: Why the Zel'dovich 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 characteristic of the Zel’dovich Approximation (ZA) and also appear in hierarchical N-body simulations. We find that we can predict the orientation and position of N-body simulation objects rather well, with decreasing accuracy for increasing large-$k$ (small scale) power in the initial conditions. We examined an N-body simulation with initial power spectrum $P(k)\propto k^3$, and found that a modified version of ZA based on the smoothed initial potential worked well in this extreme 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 considerably as the simulation evolves. We show that the nonlinear gravitational potential strongly resembles the smoothed initial potential. This explains why ZA with smoothed initial conditions reproduces large-scale structure so well, and probably why our Universe has a coherent large-scale structure.