Phase shifts in gravitationally evolving density fields

Computer Science – Numerical Analysis

Scientific paper

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Cosmology, Galactic Clusters, Many Body Problem, Perturbation Theory, Phase Shift, Space Density, Analytic Functions, Density Distribution, Numerical Analysis, Power Spectra

Scientific paper

The phases of the Fourier components of an initially Gaussian density field are examined 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, 2D N-body simulations were run. The power spectra used were of the form P(k) varies as k exp 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, the wavenumber k-phi at which the mean magnitude of the phase shift is equal to pi/4 is found. The wavenumber k-phi is proportional to the wavenumber kw at which the peculiar velocity goes nonlinear. For n = -1, k-phi is approximately equal to 0.2kw; for n = 0, k-phi is approximately equal to 0.3 kw. 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.

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