Optimizing the Zeldovich Approximation
Abstract
We have recently learned that the Zel'dovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work by Coles, Melott & Shandarin (hereafter CMS) the accuracy of several analytic approximations to gravitational clustering was studied in the mildly nonlinear regime. We found that what was called the `truncated Zel'dovich approximation' (TZA) was better than any other (except, in one case, the ordinary Zel'dovich approximation) over a wide range from linear to mildly nonlinear (σ ~ 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k_nl_, where k_nl_ marks the transition to the nonlinear regime. Here we study the crosscorrelation of generalized TZA with a group of Nbody simulations for three shapes of window function: sharp ktruncation (as in CMS), a tophat in coordinate space, and a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that ktruncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window exp (k^2^/2k_G_^2^) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved cross correlation in those cases that most needed improvement, e.g. those with more smallscale power in the initial conditions. The optimum choice of k_G_ for the Gaussian window is (somewhat spectrumdependent) 1 to 1.5 times k_nl_, where k_nl_ is defined by equation (3). Although all three windows produce similar power spectra and density distribution functions after application of the Zel'dovich approximation, the agreement of the phases of the Fourier components with the Nbody simulation is better for the Gaussian window. We therefore ascribe the success of the bestchoice Gaussian window to its superior treatment of phases in the nonlinear regime. We also report on the accuracy of particle positions and velocities
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 August 1994
 DOI:
 10.1093/mnras/269.3.626
 arXiv:
 arXiv:astroph/9312044
 Bibcode:
 1994MNRAS.269..626M
 Keywords:

 Astrophysics
 EPrint:
 Submitted to MNRAS. TeX file