PRECOLLAPSE SCALE-INVARIANCE IN GRAVITATIONAL-INSTABILITY

We numerically and analytically investigate the transition to the very nonlinear regime during the gravitational collapse of collisionless matter in an OMEGA = 1 expanding universe. It is found numerically that the formation of halos from isolated and smooth initial overdensities leads to the progressive establishment, complete at the collapse time, of a power-law density profile. The evolutions from various types of initial perturbations are shown to all produce such power laws. The slope are different, but the scale invariance itself appears quite generic. We then derive an analytical approximation based on a perturbative expansion whose first-order term is the well-known "Zeldovich approximation." This new approximation which we explicitly work out in a particular case, is found to be in perfect agreement with the numerical simulations up to density contrasts delta less-than-or-similar-to 50 (instead of delta less-than-or-similar-to 5 for the "Zeldovich approximation"). The establishment of a power-law density profile at collapse is thus confirmed analytically. It is crucial to not that the scale invariance pointed out is obtained before shell-crossing; it prepares the system for a self-similar evolution after the collapse. This work thus completes previous semianalytic studies of self-similar solutions which lacked such a natural starting point.