A Cascade Model for Nonlinear Structure Formation

Tzi-Hong Chiueh

《Chinese Journal of Physics》 32卷4期 (1994/08) Pp. 319-332

並列摘要

A model that describes how the statistical nature of the dynamical evolution of large-scale nonlinear structures is presented. Under the premises that self-similar cascades are the norm for the nonlinear evolution of gravitation, the probability distribution function (PDF) of the matter density fluctuations is derived. Such statistics is obtained by considering the fact that the cascades of mass are fluctuating in space and time, i.e., intermittency, and as a result the PDF of the density obeys a log-normal statistics on every length scale. The PDF changes with the scales, and the way by which it depends on the scale is determined by the direction of mass cascades. This model predicts quantitatively as to how the variance of the PDF should depend on the scale r for both the top-down and bottom-up cascade processes.The dependence of the PDF on different scales can affect the density two-point correlation ξ(r) in a definitive manner, in that the density correlation has a flatter power law for the top-down cascades than for the bottom-up cascades. To pin down the issue of cascade direction, I construct a calibration density correlation function, for which no intermittency effects are taken into account, and it has a scaling ξ(r) α r^(-2). With the observed galaxy correlation ξggαr^(-1.77), it is hence concluded from this model that the large-scale evolution is a top-down process, provided that galaxies trace the matter. If so, this model further predicts that the variance of the log-normal density PDF should scale with log(L/r)^(-1), where L is the largest scale at which the cascade begins.This model can also predict the scaling of the peculiar velocity, given the measured density two-point correlation. It yields that δυrms(r) αr^(-0.11), consistent with the observed velocity dispersion ~r^(-0.13±0.04).