Weakly nonlinear Gaussian fluctuations and the edgeworth expansion

Abstract

view Abstract Citations (148) References (57) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Weakly Nonlinear Gaussian Fluctuations and the Edgeworth Expansion Juszkiewicz, Roman ; Weinberg, David H. ; Amsterdamski, Piotr ; Chodorowski, Michal ; Bouchet, Francois Abstract We use new analytical results and a series of N-body experiments to study the dynamics of weakly nonlinear clustering in an Einstein-de Sitter universe. The initial density fluctuations are assumed to be Gaussian with power spectra of the form P(k) is proportional to k^n^, with n = - 1 and n = 0. We focus on two spatially smoothed random fields: the mass density contrast, δ, and the peculiar velocity divergence, θ, with variances <δ^2^> = σ^2^ and <θ^2^> = σtheta^2^. Using perturbation theory, valid for σ < 1 and σtheta_ < 1, we calculate the evolution of the 1-point probability distribution functions (PDFs) of δ and θ. We expand the PDF in Hermite polynomials and powers of σ, using the so-called Edgeworth series. When σ < 1, the simulations and perturbation theory agree precisely, demonstrating that the N-body method yields accurate results for the density field in the regime of weakly nonlinear clustering. The skewness and kurtosis of the density field stay remarkably close to the values predicted by perturbation theory even when σ = 2. For σ < 1, the Edgeworth expansion properly describes the positive and negative tails of the PDF within ~1/σ standard deviations from zero. We show analytically that "biased" galaxy formation preserves the relation <δ^3^> is proportional to <δ^2^>^2^ predicted by second-order perturbation theory, provided that the galaxy density is a local function of the underlying mass density. Our results should be useful in the analysis of large-scale density and velocity fields, allowing one to derive constraints on the nature of primordial fluctuations, the value of the cosmological density parameter, and the physical processes that govern galaxy formation. Publication: The Astrophysical Journal Pub Date: March 1995 DOI: 10.1086/175420 arXiv: arXiv:astro-ph/9308012 Bibcode: 1995ApJ...442...39J Keywords: Cosmology; Galactic Clusters; Galactic Evolution; Gravitation; Many Body Problem; Nonlinearity; Space Density; Variations; Kurtosis; Normal Density Functions; Perturbation Theory; Power Spectra; Probability Distribution Functions; Skewness; Astrophysics; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; COSMOLOGY: THEORY; GALAXIES: CLUSTERING; METHODS: ANALYTICAL; METHODS: NUMERICAL; Astrophysics E-Print: Tex + epsf, 29 pages incl. 10 eps figures, subm. to ApJ, IAS preprint full text sources arXiv | ADS |