Patterns in nonlinear gravitational clustering: a numerical investigation

Abstract

The nonlinear clustering of dark matter particles in an expanding universe is usually studied by N-body simulations. One can gain some insight into this complex problem if simple relations between physical quantities in the linear and nonlinear regimes can be extracted from the results of N-body simulations. Hamilton and coworkers and Nityananda & Padmanabhan have made an attempt in this direction by relating the mean relative pair velocities to the mean correlation function in a useful manner. We investigate this relation and other closely related issues in detail for six different power spectra: power laws with spectral indexes n = -2 and -1; cold dark matter (CDM) and hot dark matter models with density parameter Ω = t1 a CDM model including a cosmological constant (Α) with Ω_CDM = 0.4 and Ω_Α = 0.6; and an n = -1 model with Ω = 0.1. We find the following: (t) Power-law spectra lead to self-similar evolution in an Ω = 1 universe. (2) Stable clustering does not hold in an Ω = 1 universe to the extent that our simulations can ascertain. (3) Stable clustering is a better approximation in the case of an Ω < 1 universe in which structure formation freezes out at some low redshift. (4) The relation between the dimensionless pair velocity and the mean correlation function, ξ^-, is only approximately independent of the shape of the power spectrum. At the nonlinear end, the asymptotic value of the dimensionless pair velocity decreases with increasing small-scale power because the stable clustering assumption is not universally true. (5) The relation between the evolved ξ^- and the linear regime ξ^- is also not universal but shows a weak spectrum dependence. We present simple theoretical arguments for these conclusions.