The Nonlinear Evolution of the Bispectrum in Scale‐freeN‐Body Simulations

We have accurately measured the bispectrum for four scale-free models of structure formation with spectral indices of n = 1,0, -1, and -2. The measurements are based on a new method that can effectively eliminate alias and numerical artifacts and reliably extend the analysis into the strongly nonlinear regime. This work makes use of a set of state-of-the-art N-body simulations that have significantly increased the resolution range compared with previous studies on the subject. With these measured results, we demonstrate that the measured bispectrum depends on the shape and size of the k-triangle even in the strongly nonlinear regime. It increases with wavenumber and decreases with the spectral index. These results are in contrast with the hypothesis that the reduced bispectrum is a constant in the strongly nonlinear regime. We also show that the fitting formula of Scoccimarro and Frieman does not describe our simulation results well (with a typical error of about 40%). In the end, we present a new fitting formula for the reduced bispectrum that is valid for -2 ≤ n ≤ 0, with a typical error of only 10%. © 2005. The American Astronomical Society. All rights reserved.