GRAVITATIONAL-INSTABILITY IN THE STRONGLY NONLINEAR REGIME - A STUDY OF VARIOUS APPROXIMATIONS

We study the development of gravitational instability in the strongly non-linear regime. For this purpose we use a number of statistical ind icators such as filamentary statistics, the spectrum of overdense/unde rdense regions and the void probability function, each of which probes a particular aspect of gravitational clustering. We use these statist ical indicators to discriminate between different approximations to gr avitational instability which we test against N-body simulations. The approximations that we test are the truncated Zel'dovich approximation (TZ), the adhesion approximation (AA), and the frozen flow (FF) and l inear potential (LP) approximations. Of these we find that FF and LP b reak down relatively early, soon after the non-linear length scale exc eeds R - the mean distance between peaks of the gravitational potenti al. The reason for this breakdown is easy to understand: particles in FF are constrained to follow the streamlines of the initial velocity f ield. Shell crossing is absent in this case and structure gradually fr eezes as particles begin to collect near minima of the gravitational p otential. In LP, particles follow the lines of force of the primordial potential, oscillating about its minima at late times when the non-li near length scale k(NL)(-1) similar or equal to R. Unlike FF and LP, the adhesion model (and to some extent TZ) continues to give accurate results even at late times when k(NL)(-1) greater than or equal to R This is because both AA and TZ use the presence of long-range modes in the gravitational potential to move particles. Thus, as long as the i nitial potential has sufficient long-range power to initiate large-sca le coherent motions, TZ and AA will remain approximately valid. In rel ation to AA, TZ suffers from a single major drawback - it underestimat es the presence of small clumps. Similarly, it predicts the right mean density in large voids but misses subcondensations within them. The r eason for this is clear: the artificial removal of power on scales sma ller than k(NL)(-1) in the initial potential in TZ, designed to preven t shell crossing, causes a substantial fraction of matter (which would have been clustered in N-body simulations) to lie within low-density regions at all epochs. On the other hand, TZ is very fast to implement and more accurately predicts the location of large objects at late ti mes; AA more correctly represents the subcondensations but does not al ways accurately predict their positions.