PHASE-SHIFTS IN GRAVITATIONALLY EVOLVING DENSITY FIELDS

We examine the phases of the Fourier components of an initially Gaussian density field to see how the phases are shifted away from their initial values as the field evolves gravitationally. The analytic expression for the phase shift, in second-order perturbation theory, is presented. To investigate the fully nonlinear regime, we ran two-dimensional N-body simulations. The power spectra used were of the form P(k) is-proportional-to k(n), with n = -1 and n = 0. The numerical results show that second-order perturbation theory soon breaks down when computing the phase shifts. As a function of the expansion factor, we find the wavenumber k-phi at which the mean magnitude of the phase shift is equal to pi/4. The wavenumber k-phi is proportional to the wavenumber k(w) at which the peculiar velocity goes nonlinear. For n = -1, k-phi almost-equal-to 0.2k(w); for n = 0, k-phi almost-equal-to 0.3k(w). The phases of the Fourier components are significantly shifted from their initial values at a scale on which their amplitudes are still in the linear stage of growth.