142 research outputs found
Testing Higher-Order Lagrangian Perturbation Theory Against Numerical Simulations - 1. Pancake Models
We present results showing an improvement of the accuracy of perturbation
theory as applied to cosmological structure formation for a useful range of
quasilinear scales. The Lagrangian theory of gravitational instability of an
Einstein-de Sitter dust cosmogony investigated and solved up to the third order
in the series of papers by Buchert (1989, 1992, 1993a), Buchert \& Ehlers
(1993), Buchert (1993b), Ehlers \& Buchert (1993), is compared with numerical
simulations. In this paper we study the dynamics of pancake models as a first
step. In previous work (Coles \etal 1993, Melott \etal 1993, Melott 1993) the
accuracy of several analytical approximations for the modeling of large-scale
structure in the mildly non-linear regime was analyzed in the same way,
allowing for direct comparison of the accuracy of various approximations. In
particular, the ``Zel'dovich approximation'' (Zel'dovich 1970, 1973, hereafter
ZA) as a subclass of the first-order Lagrangian perturbation solutions was
found to provide an excellent approximation to the density field in the mildly
non-linear regime (i.e. up to a linear r.m.s. density contrast of ). The performance of ZA in hierarchical clustering models can be
greatly improved by truncating the initial power spectrum (smoothing the
initial data). We here explore whether this approximation can be further
improved with higher-order corrections in the displacement mapping from
homogeneity. We study a single pancake model (truncated power-spectrum with
power-index ) using cross-correlation statistics employed inComment: TeX, 18 pages excl.figures; contact [email protected] ;
[email protected] . submitted to Astron. & Astrophy
A Test of the Adhesion Approximation for Gravitational Clustering
We quantitatively compare a particle implementation of the adhesion
approximation to fully non--linear, numerical nbody simulations. Our primary
tool, cross--correlation of nbody simulations with the adhesion approximation,
indicates good agreement, better than that found by the same test performed
with the Zel'dovich approximation (hereafter ZA). However, the
cross--correlation is not as good as that of the truncated Zel'dovich
approximation (TZA), obtained by applying the Zel'dovich approximation after
smoothing the initial density field with a Gaussian filter. We confirm that the
adhesion approximation produces an excessively filamentary distribution.
Relative to the nbody results, we also find that: (a) the power spectrum
obtained from the adhesion approximation is more accurate than that from ZA or
TZA, (b) the error in the phase angle of Fourier components is worse than that
from TZA, and (c) the mass distribution function is more accurate than that
from ZA or TZA. It appears that adhesion performs well statistically, but that
TZA is more accurate dynamically, in the sense of moving mass to the right
place.
Subject Heading: Galaxies, formation, clustering--large--scale structure of
the UniverseComment: TeX, 7 pages excluding figures (contact
[email protected]). submitted to Ap
The Bull's-Eye Effect as a Probe of
We compare the statistical properties of structures normal and transverse to
the line of sight which appear in theoretical N-body simulations of structure
formation, and seem also to be present in observational data from redshift
surveys. We present a statistic which can quantify this effect in a
conceptually different way from standard analyses of distortions of the
power-spectrum or correlation function. From tests with --body experiments,
we argue that this statistic represents a new and potentially powerful
diagnostic of the cosmological density parameter, .Comment: Minor revisions; final version accepted for publication in ApJ
Letters. Latex, 16 pages, including 3 figures. Higher resolution versions of
figures, including supplementary figures not included in the manuscript, are
available at: ftp://kusmos.phsx.ukans.edu/preprints/melott/omeg
Scaling in Gravitational Clustering, 2D and 3D Dynamics
Perturbation Theory (PT) applied to a cosmological density field with
Gaussian initial fluctuations suggests a specific hierarchy for the correlation
functions when the variance is small. In particular quantitative predictions
have been made for the moments and the shape of the one-point probability
distribution function (PDF) of the top-hat smoothed density. In this paper we
perform a series of systematic checks of these predictions against N-body
computations both in 2D and 3D with a wide range of featureless power spectra.
In agreement with previous studies, we found that the reconstructed PDF-s work
remarkably well down to very low probabilities, even when the variance
approaches unity. Our results for 2D reproduce the features for the 3D
dynamics. In particular we found that the PT predictions are more accurate for
spectra with less power on small scales. The nonlinear regime has been explored
with various tools, PDF-s, moments and Void Probability Function (VPF). These
studies have been done with unprecedented dynamical range, especially for the
2D case, allowing in particular more robust determinations of the asymptotic
behaviour of the VPF. We have also introduced a new method to determine the
moments based on the factorial moments. Results using this method and taking
into account the finite volume effects are presented.Comment: 13 pages, Latex file, 9 Postscript Figure
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