arXiv subjects

A. L. Melott

Publications and source records attributed to A. L. Melott.

25 records · Page 2Linked to original sources

arXiv1994

Optimized Lagrangian Approximations for Modelling Large--Scale Structure at Non--Linear Stages

We report on a series of tests of Newtonian Lagrangian perturbation schemes using N--body simulations for various power--spectra with scale--independent indices in the range $-3$ to $+1$. The models have been evolved deeply into the non--linear regime of structure formation in order to probe the dynamical and statistical performance of the Lagrangian perturbation schemes (whose first--order solution contains as a subset the celebrated ``Zel'dovich--approximation'' (hereafter ZA). These tests reveal properties of the approximations at stages beyond the obvious validity of perturbation theory. Recently, another series of tests of different analytical and semi--numerical approximations for large--scale structure was conducted with the result that ZA displays the best dynamical performance in comparison with the N--body simulations, if the initial data were smoothed before evolving the model, i.e., a truncated form of ZA (TZA). We show in this Letter that the excellent performance of TZA can be further improved by going to second order in the Lagrangian perturbation approach. The truncated second--order Lagrangian scheme provides a useful improvement over TZA especially for negative power indices, which suggests it will be very useful for modelling standard scenarios such as ``Cold--'', ``Hot--'' and ``Mixed--Dark--Matter''.

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arXiv1994

Testing Higher--Order Lagrangian Perturbation Theory Against Numerical Simulations -- 2. Hierarchical Models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann--Lema\^ıtre cosmogonies investigated and solved up to the third order in the series of papers by Buchert (1989, 1992, 1993), Buchert \& Ehlers (1993), Buchert (1994), Ehlers \& Buchert (1994), is compared with numerical simulations. In this paper we study the dynamics of hierarchical models as a second step. In the first step (Buchert, Melott and Weiß 1994) we analyzed the performance of the Lagrangian schemes for pancake models, i.e., models which initially have a truncated power spectrum. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non--linear regime............We find that for spectra with negative power--index the second--order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low--order statistics like the power--spectrum. In cases with much small--scale power the gain from the higher--order schemes is small, but still measurable. However, in contrast to the results found for pancake models, where the higher--order schemes get worse than TZA at late non--linear stages and on small scales, we here find that the second--order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these

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arXiv1993

Optimizing the Zel'dovich Approximation

We have recently learned that the Zeldovich 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 we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that the ``truncated Zel'dovich approximation" (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear ($σ\sim 3$) regimes. TZA sets Fourier amplitudes equal to zero for {\it all} wavenumbers greater than $k_{n\ell}$, where $k_{n\ell}$ marks the transition to the nonlinear regime. Here, we study crosscorrelation of generalized TZA with a group of $n$--body simulations for three shapes of window function: sharp $k$--truncation (as in CMS), tophat in coordinate space, or a Gaussian. We also study the crosscorrelation as a function of initial scale within each window type. We find $k$--truncation, which was so much better than other things tried in CMS, is the {it worst} of these three window shapes. We find that a Gaussian window $e^{-k^2/2k_G^2}$ applied to the intial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation all cases we studied. The optimum choice of $k_G$ for the Gaussian window is (spectrum-- dependent) 1--1.5 times $k_{n\ell}$, with $k_{n\ell}$ defined by (3). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, phase agreement with the $n$--body simulation is better for the Gaussian window. We ascribe Gaussian window success to its superior treatment of phase evolution.

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arXiv1993

Quantitative Analysis of Voids in Percolating Structures in Two-Dimensional N-Body Simulations

We present in this paper a quantitative method for defining void size in large-scale structure based on percolation threshold density. Beginning with two-dimensional gravitational clustering simulations smoothed to the threshold of nonlinearity, we perform percolation analysis to determine the large scale structure. The resulting objective definition of voids has a natural scaling property, is topologically interesting, and can be applied immediately to redshift surveys.

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arXiv1993

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 Universe

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arXiv1993

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 $σ\approx 2$). 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 $n=-1$) using cross-correlation statistics employed in

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arXiv1993

Higher Order Moments of the Matter Distribution in Scale--Free Cosmological Simulations with Large Dynamic Range

We calculate reduced moments $\overline ξ_q$ of the matter density fluctuations, up to order $q=5$, from counts in cells produced by Particle--Mesh numerical simulations with scale--free Gaussian initial conditions. We use power--law spectra $P(k) \propto k^n$ with indices $n=-3,~-2,~-1,~0,~1$. Due to the supposed absence of characteristic times or scales in our models, all quantities are expected to depend on a single scaling variable. For each model, the moments at all times can be expressed in terms of the variance $\overline ξ_2$, alone. We look for agreement with the hierarchical scaling ansatz, according to which $\overline ξ_q \propto \overline ξ_2^{~q-1}$. For $n\leq -2$ models we find strong deviations from the hierarchy, which are mostly due to the presence of boundary problems in the simulations. A small, residual signal of deviation from the hierarchical scaling is however also found in $n \geq -1$ models. For the first time, due to our large dynamic range and careful checks of scaling and shot--noise effects, we are able to detect evolution away from the perturbation theory result.

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