arXiv subjects

T. Buchert

Publications and source records attributed to T. Buchert.

24 records · Page 2Linked to original sources

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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arXiv1994

High-Resolution Simulation of Deep Pencil Beam Surveys

We report on a recent paper (Weiß \& Buchert 1993), where we carry out pencil beam constructions in a high-resolution simulation of the large-scale structure of galaxies. As an example we present the results for the case of ``Hot-Dark-Matter" (HDM) initial conditions (with scale-free $n = 1$ power index on large scales and $Ω= 1$) as a representative of models with sufficient large-scale power. We use an analytic approximation for particle trajectories of a self-gravitating dust continuum and apply a local dynamical biasing of volume elements to identify luminous matter in the model. Using this method, we are able to resolve formally a simulation box of 1200h^-1 Mpc (e.g. for HDM initial conditions) down to the scale of galactic halos using $2160^3$ particles. Pencil beam probes are taken for a given epoch using the parameters of observed beams. In particular, our analysis concentrates on the detection of a quasi-periodicity in the beam probes. The simulation is designed for application to parameter studies which prepare future observational projects. We find that a large percentage of the beams shows quasi-periodicities with periods which cluster at a certain length scale. The periods found range between one and eight times the cutoff length in the initial fluctuation spectrum.

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arXiv1994

Higher--Order Lagrangian Perturbation Theory

Fundamental assumptions which form the basis of models for large-scale structure in the Universe are sketched in light of a Lagrangian description of inhomogeneities. This description is introduced for Newtonian self-gravitating flows. On its basis a Lagrangian perturbation approach is discussed and compared with the standard Eulerian theory of gravitational instability. The performance of Lagrangian perturbation solutions up to the third order is demonstrated in comparison with numerical N-body simulations. First results of this comparison are presented for large scales (PM-code) and for small scales (tree-code).

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arXiv1993

Robust Morphological Measures for Large-Scale Structure in the Universe

We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which includes the topological Euler characteristic and geometric descriptors to specify the content, shape and connectivity of spatial sets. The method is numerically robust even for small samples, independent of statistical assumptions, and yields global as well as local morphological information. We illustrate the method by applying it to a Poisson process, a `double-Poisson' process, and to the Abell catalogue of galaxy clusters.

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arXiv1993

Third-Order Lagrangian Perturbation Theory - Realization at High-Spatial Resolution

The Lagrangian theory of gravitational instability of homogeneous-isotropic Friedman-Lemaitre cosmogonies investigated and solved in the series of papers by Buchert (1989), (1992), Buchert & Ehlers (1993), Buchert (1993a,b), Ehlers & Buchert (1993), is illustrated. The third-order solution of this theory for generic initial conditions is presented and realized in a special case by employing methods of high-spatial resolution of the density field.

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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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