Previrialization: Perturbative and N-Body Results

Abstract

We present a series of N-body experiments which confirm the reality of the previrialization effect. We also use weakly nonlinear perturbative approach to study the phenomenon. These two approaches agree when the rms density contrast, $σ$, is small; more surprisingly, they remain in agreement when $σ\approx 1$. 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 $σ$ 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 (1990) assumed $n=0$ and found strong evidence in support of previrialization, while Evrard \& Crone (1992), 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 (1994). Its slope near the scale usually adopted for normalization is close to $-1$, so $σ$ 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.