Gravitational instability in the strongly nonlinear regime: A study of various approximations

Abstract

We study the development of gravitational instability in the strongly non-linear regime. For this purpose we use a number of statistical indicators such as filamentary statistics, spectrum of overdense/underdense regions and the void probability function, each of which probes a particular aspect of gravitational clustering. We use these statistical indicators to discriminate between different approximations to gravitational instability which we test against N-body simulations. The approximations which we test are, the truncated Zel'dovich approximation (TZ), the adhesion model (AM), and the frozen flow (FF) and linear potential (LP) approximations. Of these we find that FF and LP break down relatively early, soon after the non-linear length scale exceeds $R_{\ast }$ -- the mean distance between peaks of the gravitational potential. The reason for this break down is easy to understand, particles in FF are constrained to follow the streamlines of the initial velocity field. Shell crossing is absent in this case and structure gradually freezes as particles begin to collect near minima of the gravitational potential. In LP particles follow the lines of force of the primordial potential, oscillating about its minima at late times when the non-linear length scale $k_{\mathrm{NL}}^{-1}\simeq R_{\ast }$. Unlike FF and LP the adhesion model (and to some extent TZ) continues to give accurate results even at late times when $k_{\mathrm{NL}}^{-1}\ge R_{\ast }$. This is because both AM and TZ use

arXiv commentmn.sty (Latex), 20 pages + 11 figures (not included: hardcopy available on request from [email protected]), Submitted to MNRAS, IUCAA-24/94

Cited by in corpus (22)

• Adhesive Gravitational Clustering
• The growth of structure in the intergalactic medium
• BEC dark matter, Zeldovich approximation and generalized Burgers equation
• The Zel'dovich-type approximation for an inhomogeneous universe in general relativity: second-order solutions
• Matter power spectrum from a Lagrangian-space regularization of perturbation theory
• Impact of shell crossing and scope of perturbative approaches in real and redshift space
• Modelling the IGM and the Lyalpha forest at high redshift from the dark matter distribution
• Morphology of Clusters and Superclusters in N-body simulations of Cosmological Gravitational Clustering
• Constraining the Power Spectrum using Clusters
• The fractal distribution of galaxies and the transition to homogeneity
• Hydrodynamic approach to the evolution of cosmological structures
• Zel'dovich approximation and General Relativity
• Recovering the Primordial Density Fluctuations: A comparison of methods
• Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion
• Large-Scale Structure of Short-Lived LymanαEmitters
• Modeling Gravitational Clustering without Computing Gravitational Force
• A formal analysis of two dimensional gravity
• An Eulerian Perturbation Approach to Large Scale Structures: Extending the Adhesion Approximation
• Weakly Nonlocal Hydrodynamics and the Origin of Viscosity in the Adhesion Model
• Velocity dispersion in N-body simulations of CDM models
• Numerical study of the cosmological velocity field as a function of density
• Non--Linear Evolution of Cosmological Perturbations