arXiv subjects

Thomas Buchert

Publications and source records attributed to Thomas Buchert.

105 records · Page 6Linked to original sources

arXiv1998

A global descriptor of spatial pattern interaction in the galaxy distribution

We present the function J as a morphological descriptor for point patterns formed by the distribution of galaxies in the Universe. This function was recently introduced in the field of spatial statistics, and is based on the nearest neighbor distribution and the void probability function. The J descriptor allows to distinguish clustered (i.e. correlated) from ``regular'' (i.e. anti-correlated) point distributions. We outline the theoretical foundations of the method, perform tests with a Matern cluster process as an idealised model of galaxy clustering, and apply the descriptor to galaxies and loose groups in the Perseus-Pisces Survey. A comparison with mock-samples extracted from a mixed dark matter simulation shows that the J descriptor can be profitably used to constrain (in this case reject) viable models of cosmic structure formation.

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arXiv1998

Modeling multi-stream flow in collisionless matter: approximations for large-scale structure beyond shell-crossing

The generally held view that a model of large-scale structure, formed by collisionless matter in the Universe, can be based on the matter model ``dust'' fails in the presence of multi-stream flow, i.e., velocity dispersion. We argue that models for large-scale structure should rather be constructed for a flow which describes the average motion of a multi-stream system. We present a clearcut reasoning how to approach the problem and derive an evolution equation for the mean peculiar-velocity relative to background solutions of Friedmann-Lema\^ıtre type. We consider restrictions of the nonlinear problem and show that the effect of velocity dispersion gives rise to an effective viscosity of non-dissipative gravitational origin. We discuss subcases which arise naturally from this approach: the ``sticky particle model'' and the ``adhesion approximation''. We also construct a novel approximation that features adhesive action in the multi-stream regime while conserving momentum, which was considered a drawback of the standard approximation based on Burger's equation. We finally argue that the assumptions made to obtain these models should be relaxed and we discuss how this can be achieved.

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arXiv1998

Fluctuations in the IRAS 1.2 Jy Catalogue

An analysis of the IRAS 1.2 Jy redshift catalogue with emphasis on the separate examination of northern and southern parts (in galactic coordinates) is performed using a complete set of morphological descriptors (Minkowski functionals), nearest neighbour distributions and the variance of the galaxy counts. We find large fluctuations in the clustering properties as seen in a large difference between the northern and southern parts of the catalogue on scales of 100Mpc/h. These fluctuations remain discernible even on the scale of 200Mpc/h. We also identify sparse sampling as a major source of ``apparent homogenization''. Tests on observational selection effects concerning luminosity, colour and redshift-space distortion support the significance of these large-scale fluctuations.

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arXiv1997

A fresh look at the adhesion approximation

I report on a systematic derivation of the phenomenological ``adhesion approximation'' from gravitational instability together with a brief evaluation of the related status of analytical modeling of large-scale structure.

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arXiv1997

Characterizing cluster morphology using vector-valued Minkowski functionals

The morphology of galaxy clusters is quantified using Minkowski functionals, especially the vector-valued ones, which contain directional information and are related to curvature centroids. The asymmetry of clusters and the amount of their substructure can be characterized in a unique way using these measures. -- We briefly introduce vector-valued Minkowski functionals (also known as Quermaßvectors) and suggest their application to cluster data in terms of a morphological characterization of excursion sets. Furthermore, we develop robust structure functions which describe the dynamical state of a cluster and study the evolution of clusters using numerical simulations.

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arXiv1997

Cosmic density and velocity fields in Lagrangian perturbation theory

A first- and second-order relation between cosmic density and peculiar-velocity fields is presented. The calculation is purely Lagrangian and it is derived using the second-order solutions of the Lagrange-Newton system obtained by Buchert & Ehlers. The procedure is applied to two particular solutions given generic initial conditions. In this approach, the continuity equation yields a relation between the over-density and peculiar-velocity fields that automatically satisfies Euler's equation because the orbits are derived from the Lagrange-Newton system. This scheme generalizes some results obtained by Nusser et al. (1991) in the context of the Zel'dovich approximation. As opposed to several other reconstruction schemes, in this approach it is not necessary to truncate the expansion of the Jacobian given by the continuity equation in order to calculate a first- or second-order expression for the density field. In these previous schemes, the density contrast given by (a) the continuity equation and (b) Euler's equation are mutually incompatible. This inconsistency arises as a consequence of an improper handling of Lagrangian and Eulerian coordinates in the analysis. Here, we take into account the fact that an exact calculation of the density is feasible in the Lagrangian picture and therefore an accurate and consistent description is obtained.

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arXiv1997

Averaging Inhomogeneous Cosmologies -- a Dialogue

The averaging problem for inhomogeneous cosmologies is discussed in the form of a disputation between two cosmologists, one of them (RED) advocating the standard model, the other (GREEN) advancing some arguments against it. Technical explanations of these arguments as well as the conclusions of this debate are given by BLUE.

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arXiv1997

The Significance of the Fluctuations in the IRAS 1.2 Jy Galaxy Catalogue

In an analysis of the IRAS 1.2 Jy redshift catalogue, with emphasis on the separate examination of northern and southern parts (in galactic coordinates), we found that the clustering of galaxies differs significantly between north and south, showing fluctuations in the clustering properties at least on scales of 100 Mpc/h (Kerscher et al. 1997, astro-ph/9704028). We give a brief description of our morphological method which is based on Minkowski functionals and show the results obtained from the IRAS 1.2 Jy galaxy catalogue. We discuss several error estimates and select different subsamples from the 1.2 Jy catalogue according to flux and colour and validate the results for the whole sample. Furthermore we look closer at the spatial origin of the fluctuation and we compare with optically selected galaxies from the CfA1 survey.

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arXiv1997

Beyond genus statistics: a unifying approach to the morphology of cosmic structure

The genus statistics of isodensity contours has become a well-established tool in cosmology. In this Letter we place the genus in the wider framework of a complete family of morphological descriptors. These are known as the Minkowski functionals, and we here apply them for the first time to isodensity contours of a continuous random field. By taking two equivalent approaches, one through differential geometry, the other through integral geometry, we derive two complementary formulae suitable for numerically calculating the Minkowski functionals. As an example we apply them to simulated Gaussian random fields and compare the outcome to the analytically known results, demonstrating that both are indeed well suited for numerical evaluation. The code used for calculating all Minkowski functionals is available from the authors.

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arXiv1996

Averaging inhomogeneous Newtonian cosmologies

Idealizing matter as a pressureless fluid and representing its motion by a peculiar--velocity field superimposed on a homogeneous and isotropic Hubble expansion, we apply (Lagrangian) spatial averaging on an arbitrary domain $\cal D$ to the (nonlinear) equations of Newtonian cosmology and derive an exact, general equation for the evolution of the (domain dependent) scale factor $a_{\cal D}(t)$. We consider the effect of inhomogeneities on the average expansion and discuss under which circumstances the standard description of the average motion in terms of Friedmann's equation holds. We find that this effect vanishes for spatially compact models if one averages over the whole space. For spatially infinite inhomogeneous models obeying the cosmological principle of large--scale isotropy and homogeneity, Friedmann models may provide an approximation to the average motion on the largest scales, whereas for hierarchical (Charlier--type) models the general expansion equation shows how inhomogeneities might appreciably affect the expansion at all scales. An averaged vorticity evolution law is also given. Since we employ spatial averaging, the problem of justifying ensemble averaging does not arise. A generalization of the expansion law to general relativity is straightforward for the case of irrotational flows and will be discussed. The effect may have important consequences for a variety of problems in large--scale structure modeling as well as for the interpretation of observations.

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arXiv1996

Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory

The ``Newtonian'' theory of spatially unbounded, self--gravitating, pressureless continua in Lagrangian form is reconsidered. Following a review of the pertinent kinematics, we present alternative formulations of the Lagrangian evolution equations and establish conditions for the equivalence of the Lagrangian and Eulerian representations. We then distinguish open models based on Euclidean space $\R^3$ from closed models based (without loss of generality) on a flat torus $\T^3$. Using a simple averaging method we show that the spatially averaged variables of an inhomogeneous toroidal model form a spatially homogeneous ``background'' model and that the averages of open models, if they exist at all, in general do not obey the dynamical laws of homogeneous models. We then specialize to those inhomogeneous toroidal models whose (unique) backgrounds have a Hubble flow, and derive Lagrangian evolution equations which govern the (conformally rescaled) displacement of the inhomogeneous flow with respect to its homogeneous background. Finally, we set up an iteration scheme and prove that the resulting equations have unique solutions at any order for given initial data, while for open models there exist infinitely many different solutions for given data.

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arXiv1995

The performance of Lagrangian perturbation schemes at high resolution

We present high--spatial resolution studies of the density field as predicted by Lagrangian perturbation approximations up to the third order. The first--order approximation is equivalent to the ``Zel'dovich approximation'' for the type of initial data analyzed. The study is performed for two simple models which allow studying of typical features of the clustering process in the early non--linear regime. We calculate the initial perturbation potentials as solutions of Poisson equations algebraically, and automate this calculation for a given initial random density field. The presented models may also be useful for other questions addressed to Lagrangian perturbation solutions and for the comparison of different approximation schemes. In an accompanying paper we investigate a detailed comparison with various N--body integrators using these models (Karakatsanis \& Buchert 1995). Results of the present paper include the following: 1. The collapse is accelerated significantly by the higher--order corrections confirming previous results by Moutarde \etal (1991); 2. the spatial structure of the density patterns predicted by the ``Zel'dovich approximation'' differs much from those predicted by the second-- and third--order Lagrangian approximations; 3. Second--order effects amount to internal substructures such as ``second generation'' --pancakes, --filaments and --clusters, as are also observed in N--body simulations; 4. The third--order effect gives rise to substructuring of the secondary mass--shells. The hierarchy of shell--crossing singularities that form features small high--density clumps at the intersections of caustics which we interprete as gravitational fragmentation.

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arXiv1995

Applications of Minkowski Functionals to the Statistical Analysis of Dark Matter Models

A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the large-scale structure in the Universe. These measures are sensitive to both, geometrical and topological properties of spatial patterns and appear to be very effective in discriminating different point processes. Moreover by the means of conditional subsampling, different building blocks of large-scale structures like sheets, filaments and clusters can be detected and extracted from a given distribution.

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arXiv1995

Optimizing Higher-Order Lagrangian Perturbation Theory for Standard CDM and BSI models

We investigate the performance of Lagrangian perturbation theory up to the second order for two scenarios of cosmological large-scale structure formation, SCDM (standard cold dark matter) and BSI (broken scale invariance). The latter model we study as a representative of COBE-normalized CDM models which fit the small-scale power of galaxy surveys. In this context we optimize the performance of the Lagrangian perturbation schemes by smoothing the small-scale fluctuations in the initial data. The results of the so obtained Lagrangian mappings are computed for a set of COBE-normalized SCDM and BSI initial data of different sizes and at different times. We compare these results against those obtained with a numerical PM-code. We find an excellent performance of the optimized Lagrangian schemes down to scales close to the correlation length. This is explained by the counterintuitive fact that nonlinearities in the model can produce more small-scale power, if initially such power is removed. The optimization scheme can be expressed in a way which is independent of the type of fluctuation spectrum and of the size of the simulations.

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arXiv1993

Lagrangian theory of gravitational instability of Friedman-Lemaitre cosmologies - generic third-order model for non-linear clustering

The Lagrangian perturbation theory on Friedman-Lemaitre cosmologies investigated and solved up to the second order in earlier papers (Buchert 1992, Buchert \& Ehlers 1993) is evaluated up to the third order. On its basis a model for non-linear clustering applicable to the modeling of large-scale structure in the Universe for generic initial conditions is formulated. A truncated model is proposed which represents the ``main body'' of the perturbation sequence in the early non-linear regime by neglecting all gravitational sources which describe interaction of the perturbations. However, I also give the irrotational solutions generated by the interaction terms to the third order, which induce vorticity in Lagrangian space. The consequences and applicability of the solutions are put into perspective. In particular, the model presented enables the study of previrialization effects in gravitational clustering and the onset of non-dissipative gravitational turbulence within the cluster environment.

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