Self-Similar Evolution of Gravitational Clustering: N-Body Simulations of the n=-2 Spectrum

Abstract

The power spectrum P(k)\propto k^n with n=-2 is close to the shape of the measured galaxy spectrum on small scales. Unfortunately this spectrum has proven rather difficult to simulate. Further, 2-dimensional simulations have suggested a breakdown of self-similar scaling for spectra with n<-1 due to divergent contributions from the coupling of long wave modes. This paper is the second (numerical) part of our investigation into the nonlinear gravitational clustering of scale-free spectra. Using high-resolution N-body simulations we find that the n=-2 power spectrum, as well as trajectories of the amplitude and phase of Fourier modes, display self-similar scaling. The evolution of the phase shift does show a different scaling at late times, but this was shown analytically to arise from the purely kinematical effect of bulk flows. Thus our analytical and N-body results verify that self-similarity in gravitational clustering holds for -3<n<1. The N-body spectrum is also compared with analytic fitting formulae, which are found to slightly underestimate the power in the nonlinear regime. The asymptotic shape of the spectrum at high-k is a power law with the same slope as predicted by the stable clustering hypothesis.