Previrialization: Perturbative and N-body results

We present a series of N-body experiments which confirm the reality of the previrialization effect. We use also a weakly nonlinear perturbative approach to study the phenomenon. These two approaches agree when the rms density contrast, sigma, is small; more surprisingly, they remain in agreement when sigma approximate to 1. When the slope of the initial power spectrum is n > -1, nonlinear tidal interactions slow down the growth of density fluctuations, and the magnitude of the suppression increases when n (i.e., the relative amount of small-scale power) is increased. For n < -1, we see an opposite effect: the fluctuations grow more rapidly than in linear theory. The transition occurs at n = -1 when the weakly nonlinear correction to sigma is close to zero and the growth rate is close to linear. Our results resolve recent controversy between two N-body studies of previrialization. Peebles assumed n = 0 and found strong evidence in support of previrialization, while Evrard & Crone, who assumed n = -1, reached opposite conclusions. As we show here, the initial conditions with n = -1 are rather special because the nonlinear effects nearly cancel out for that particular spectrum. In addition to our calculations for scale-free initial spectra, we show results for a more realistic spectrum of Peacock & Dodds. Its slope near the scale usually adopted for normalization is close to -1, so sigma is close to linear. Our results retroactively justify linear normalization at 8 h(-1) Mpc while also demonstrating the danger and limitations of this practice.