The Distribution Function of the Phase Sum as a Signature of Phase Correlations Induced by Nonlinear Gravitational Clustering

Abstract

We explore a signature of phase correlations in Fourier modes of dark matter density fields induced by nonlinear gravitational clustering. We compute the distribution function of the phase sum of the Fourier modes, theta_k1+theta_k2+theta_k3, for triangle wavevectors satisfying k1+k2+k3=0, and compare with the analytic prediction in perturbation theory recently derived by one of us. Using a series of cosmological N-body simulations, we extensively examine the time evolution and the dependence on the configuration of triangles and the sampling volume. Overall we find that the numerical results are remarkably consistent with the analytic formula from the perturbation theory. Interestingly the validity of the perturbation theory at a scale k is determined by P(k)/V_samp, the ratio of the power spectrum P(k) and the sampling volume V_samp, not by k^3P(k) as in the case of the conventional cosmological perturbation theory. Consequently this statistics of phase correlations is sensitive to the size of the sampling volume itself. This feature does not show up in more conventional cosmological statistics including the one-point density distribution function and the two-point correlation functions except as a sample-to-sample variation. Similarly if the sampling volume size V_samp is fixed, the stronger phase correlation emerges first at the wavevector where P(k) becomes largest, i.e., in linear regimes according to the standard cosmological perturbation theory, while the distribution of the phase sum stays fairly uniform in nonlinear regimes. The above feature can be naturally understood from the corresponding density structures in real space as we discuss in detail.