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 filamentsapparent in the Universe, we present evidence for the convergence of the twoclassic approaches to gravitational clustering, the ``pancake'' and``hierarchical'' pictures. We compare these two models by looking at agreementbetween individual structures -- the ``pancakes'' which are characteristic ofthe Zel'dovich Approximation (ZA) and also appear in hierarchical N-bodysimulations. We find that we can predict the orientation and position of N-bodysimulation objects rather well, with decreasing accuracy for increasinglarge-$k$ (small scale) power in the initial conditions. We examined an N-bodysimulation with initial power spectrum $P(k) \propto k^3$, and found that amodified version of ZA based on the smoothed initial potential worked well inthis extreme hierarchical case, implying that even here very low-amplitude longwaves dominate over local clumps (although we can see the beginning of thebreakdown expected for $k^4$). In this case the correlation length of theinitial potential is extremely small initially, but grows considerably as thesimulation evolves. We show that the nonlinear gravitational potential stronglyresembles the smoothed initial potential. This explains why ZA with smoothedinitial conditions reproduces large-scale structure so well, and probably whyour Universe has a coherent large-scale structure.Comment: 17 pages of uuencoded postscript. There are 8 figures which are too large to post here. To receive the uuencoded figures by email (or hard copies by regular mail), please send email to: jenny@kusmos.phsx.ukans.edu. This is a revision of a paper posted earlier now in press at MNRA