Pattern in Nonlinear Gravatational 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 et al. (1991) and Nityananda and Padmanabhan (1994) 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 the case of six different power spectra: power laws with spectral indexes $n=-2,-1$, cold dark matter (CDM), and hot dark matter models with density parameter $\Omega =1$; CDM including a cosmological constant ($\Lambda$) with ${\Omega }_{CDM}=0.4$, ${\Omega }_{\Lambda }=0.6$; and $n=-1$ model with $\Omega =0.1$. We find that: (i) Power law spectra lead to self-similar evolution in an $\Omega =1$ universe. (ii) Stable clustering does not hold in an $\Omega =1$ universe to the extent our simulations can ascertain. (iii) Stable clustering is a better approximation in the case of $\Omega <1$ universe in which structure formation freezes out at some low redshift. (iv) The relation between dimensionless pair velocity and the mean correlation function, $\bar{\xi }$, 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. (v) The relation between the evolved $\bar{\xi }$ and the linear regime $\bar{\xi }$ is also not universal but shows a weak spectrum dependence. We present simple theoretical arguments for these conclusions.

Princeton Univ Obs, in press ApJ (Aug 1, 1996) Figures (revised) also available from ftp://astro.princeton.edu/cen/SCALING

Cited by in corpus (38)

• Stable clustering, the halo model and nonlinear cosmological power spectra
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Dark Energy and Gravity
• Cosmological Model Predictions for Weak Lensing: Linear and Nonlinear Regimes
• Loop Corrections in Non-Linear Cosmological Perturbation Theory II. Two-point Statistics and Self-Similarity
• Information content of the non-linear matter power spectrum
• The Statistics of Weak Lensing at Small Angular Scales: Probability Distribution Function
• Self-Similar Evolution of Gravitational Clustering: N-Body Simulations of the n=-2 Spectrum
• Statistics of Weak Lensing at Small Angular Scales: Analytical Predictions for Lower Order Moments
• Comments on the size of the simulation box in cosmological N-Body simulations
• Effects of the size of cosmological N-Body simulations on physical quantities -- I: Mass Function
• Why Does Gravity Ignore the Vacuum Energy?
• The Omega Dependence of the Evolution of xi(r)
• Probing The Gravity Induced Bias with Weak Lensing: Test of Analytical results Against Simulations
• Quantifying resolution in cosmological N-body simulations using self-similarity
• Scaling laws in gravitational clustering for counts-in-cells and mass functions
• Error Estimates for Measurements of Cosmic Shear
• Nonlinear Gravitational Clustering: dreams of a paradigm
• Halo collapse: virialization by shear and rotation in dynamical dark-energy models. Effects on weak-lensing peaks
• Effects of the size of cosmological N-Body simulations on physical quantities - III: Skewness
• The Adaptive TreePM: An Adaptive Resolution Code for Cosmological N-body Simulations
• Exponents of non-linear clustering in scale-free one dimensional cosmological simulations
• Scaling Relations for Gravitational Collapse in Two Dimensions
• A critique of scaling behaviour in non-linear structure formation scenarios
• Cosmic Statistics through Weak Lenses
• Power transfer in nonlinear gravitational clustering and asymptotic universality
• Gravitational collapse in an expanding background and the role of substructure II: Excess power at small scales and its effect of collapse of structures at larger scales
• A Modified TreePM Code
• A Simple Method for Computing the Non-Linear Mass Correlation Function with Implications for Stable Clustering
• Stable clustering and the resolution of dissipationless cosmological N-body simulations
• Gravitational Collapse in an Expanding Universe: Scaling Relations for Two-Dimensional Collapse Revisited
• Tidal virialization of dark matter haloes with clustering dark energy
• Gravitational clustering in a D-dimensional Universe
• An Optimally Weighted Estimator of the Linear Power Spectrum Disentangling the Growth of Density Perturbations Across Galaxy Surveys
• Self-similarity and stable clustering in a family of scale-free cosmologies
• Challenges in Non-Linear Gravitational Clustering
• Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure
• Testing growth rate dependence in cosmological perturbation theory using scale-free models