Nonlinear Approximations to Gravitational Instability: A Comparison in the Quasilinear Regime
Abstract
We compare different nonlinear approximations to gravitational clustering in the weakly nonlinear regime, using as a comparative statistic the evolution of nonGaussianity which can be characterised by a set of numbers $S_p$ describing connected moments of the density field at the lowest order in $<\delta^2>$: $<\delta^n>_c \simeq S_n<\delta^2>^{n1}$. Generalizing earlier work by Bernardeau (1992) we develop an ansatz to evaluate all $S_p$ in a given approximation by means of a generating function which can be shown to satisfy the equations of motion of a homogeneous spherical density enhancement in that approximation. On the basis of the values of we show that approximations formulated in Lagrangian space (such as the Zeldovich approximation and its extensions) are considerably more accurate than those formulated in Eulerian space such as the Frozen Flow and Linear Potential approximations. In particular we find that the $n$th order Lagrangian perturbation approximation correctly reproduces the first $n+1$ parameters $S_n$. We also evaluate the density probability distribution function for the different approximations in the quasilinear regime and compare our results with an exact analytic treatment in the case of the Zeldovich approximation.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 1994
 DOI:
 10.1086/174925
 arXiv:
 arXiv:astroph/9402065
 Bibcode:
 1994ApJ...436..517M
 Keywords:

 Approximation;
 Cosmology;
 Galactic Clusters;
 Galactic Evolution;
 Gravitation Theory;
 Gravitational Effects;
 Universe;
 Density Distribution;
 Distribution Functions;
 Nonlinearity;
 Perturbation Theory;
 Astrophysics;
 COSMOLOGY: LARGESCALE STRUCTURE OF UNIVERSE;
 COSMOLOGY: THEORY;
 GALAXIES: CLUSTERING;
 Astrophysics
 EPrint:
 21 pages, 1 figure, Latex