arXiv subjects

Rien van de Weygaert

Publications and source records attributed to Rien van de Weygaert.

106 records · Page 6Linked to original sources

arXiv2003

A hierarchy of voids: Much ado about nothing

We present a model for the distribution of void sizes and its evolution in the context of hierarchical scenarios of gravitational structure formation. We find that at any cosmic epoch the voids have a size distribution which is well-peaked about a characteristic void size which evolves self-similarly in time. This is in distinct contrast to the distribution of virialized halo masses which does not have a small-scale cut-off. In our model, the fate of voids is ruled by two processes. The first process affects those voids which are embedded in larger underdense regions: the evolution is effectively one in which a larger void is made up by the mergers of smaller voids, and is analogous to how massive clusters form from the mergers of less massive progenitors. The second process is unique to voids, and occurs to voids which happen to be embedded within a larger scale overdensity: these voids get squeezed out of existence as the overdensity collapses around them. It is this second process which produces the cut-off at small scales. In the excursion set formulation of cluster abundance and evolution, solution of the cloud-in-cloud problem, i.e., counting as clusters only those objects which are not embedded in larger clusters, requires study of random walks crossing one barrier. We show that a similar formulation of void evolution requires study of a two-barrier problem: one barrier is required to account for voids-in-voids, and the other for voids-in-clouds. Thus, in our model, the void size distribution is a function of two parameters, one of which reflects the dynamics of void formation, and the other the formation of collapsed objects.

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arXiv2003

Void Hierarchy and Cosmic Structure

Within the context of hierarchical scenarios of gravitational structure formation we describe how an evolving hierarchy of voids evolves on the basis of {\em two} processes, the {\em void-in-void} process and the {\it void-in-cloud} process. The related analytical formulation in terms of a {\it two-barrier} excursion problem leads to a self-similarly evolving peaked void size distribution.

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arXiv2002

Froth across the Universe Dynamics and Stochastic Geometry of the Cosmic Foam

A review on the properties and dynamical origin and nature of the cosmic foam, the tenuous space-filling frothy network permeating the interior of the Universe. We discuss the properties of this striking and intriguing pattern, describing its observational appearance, and seeking to elucidate its dynamical origin and nature. An extensive discussion on the gravitational formation and dynamical evolution of weblike patterns puts particular emphasis on the formative role of the generic anisotropy of the cosmic gravitational force fields. These tidal fields play an essential role in shaping the pattern of the large scale cosmic matter distribution. Special attention is put on a geometrical and stochastic framework for a systematic evaluation of its fossil information content on the cosmic structure formation process. Its distinct geometric character and the stochastic nature provides the cosmic web with some unique and at first unexpected properties. The implications for galaxy clustering are discussed on the basis of its relevant branch of mathematics, stochastic geometry. Central within this context are Voronoi tessellations, which have been found to represent a surprisingly versatile model for spatial cellular distributions.

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arXiv2002

Report to Anaximander: A Dialogue on the Origin of the Cosmos in the Cradle of Western Civilization

The presentations in the 2nd Hellenic Cosmology Workshop covered a broad range of cosmological subjects. Following the analogy with the architectural masters of Ancient Greece, the contributions are presented in ``architectural'' sessions. The session on the ``Architects'' involves ``fundamental cosmology'', focussing on the topology and geometry of our Universe and the fundamental physical laws and processes at work in the first decisive moments of the (Very) Early Universe. Following these cosmic blueprints, the ``Constructors'' set out to present the ultimate realization of the cosmic framework. This concerns the search for the best available estimates of the parameters characterizing the Friedmann-Robertson-Walker metric. The specification of these cosmic measures paves the way for the ``Interior Decorators'' to take care of the cosmic ``Infrastructure''. This involves the patterns and morphology of Megaparsec scale cosmic structure and its emergence through gravitational instability, as well as aspects concerning the rise of galaxies through the complex interplay of gravitational, hydrodynamic, radiative, stellar and other dissipative processes.

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arXiv2002

The Cosmic Foam: Stochastic Geometry and Spatial Clustering Across the Universe

We stress the importance of stochastic geometry as a branch of mathematical statistics particularly suited to model and investigate nontrivial spatial patterns. One of its key concepts, Voronoi tessellations, represents a versatile and flexible mathematical model for foamlike patterns. Based on a seemingly simple definition, Voronoi tessellations define a wealthy stochastic network of interconnected anisotropic components, each of which can be identified with the various structural elements of the cosmic galaxy distribution. Here we describe results of an ongoing investigation of a variety of aspects of cosmologically relevant spatial distributions and statistics within the framework of Voronoi tessellations. Interesting is the recent finding of a profound scaling of both clustering strength and clustering extent for the distribution of tessellation nodes, representing galaxy clusters. It suggests a hitherto unexpected fundamental and profound property of foamlike geometries. In a sense, cellular networks may be the source of an intrinsic ``geometrically biased'' clustering.

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arXiv2000

Tessellation Reconstruction Techniques

The application of Voronoi and Delaunay tessellation based methods for reconstructing continuous fields from discretely sampled data sets is discussed. The succesfull operation as ``multidimensional interpolation'' method is corroborated through their ability to reproduce even intricate statistical aspects of the analytical predictions of perturbation theory of cosmic velocity field evolution. The newly developed and fully self-adaptive technique for density field estimation by means of Delaunay tessellations, basically exploiting their ``minimum triangulation'' quality, is shown to succesfully reproduce the morphology of the foamlike structure in N-body simulations of cosmic structure formation. The full hierarchy of structure is implicitly and directly reproduced at every spatial resolution scale present in the particle distribution, at the same time automatically and sharply rendering its characteristic anisotropic filamentary and wall-like features.

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arXiv1999

The Cosmic Foam and the Self-Similar Cluster Distribution

Voronoi Tessellations form an attractive and versatile geometrical asymptotic model for the foamlike cosmic distribution of matter and galaxies. In the Voronoi model the vertices are identified with clusters of galaxies. For a substantial range out to a scale in the order of the cellsize, their spatial two-point correlation function is a power-law with a slope $γ\approx 1.95$. This study presents recent results showing that subsets of vertices selected on the basis of their ``richness'', i.e. inflow volume, retain this power-law correlation behaviour. Interestingly, they do so with a ``clustering length'' $r_{\rm o}$ that is exactly linearly proportional to the average inter-vertex distance in the sample, thus forming a realization of the Szalay-Schramm prescription. For the geometry and structural patterns even more significant is the finding tessellation vertices display a similar linear increase for their correlation length $r_{\rm a}$, the coherence length at which $ξ(r_{\rm a})=0$. Such patterns therefore exhibit positive correlations out to distances considerably in excess of the cellsize. Most intriguing is the implication of self-similar scaling, while these results may be regarded as the presentation of a ``geometrical bias'' effect. A seemingly rigid structure appears to represent a flexible and useful geometric model for exploring the statistical and dynamical repercussions of the nontrivial cellular patterns in Megaparsec scale cosmic structure.

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arXiv1999

The Structure of the Local Universe and the Coldness of the Cosmic Flow

Unlike the substantial coherent bulk motion in which our local patch of the Cosmos is participating, the amplitude of the random motions around this large scale flow seems to be surprisingly low. Attempts to invoke global explanations to account for this coldness of the local cosmic velocity field have not yet been succesfull. Here we propose a different view on this cosmic dilemma, stressing the repercussions of our cosmic neighbourhood embodying a rather uncharacteristic region of the Cosmos. Suspended between two huge mass concentrations, the Great Attractor region and the Perseus-Pisces chain, we find ourselves in a region of relatively low density yet with a very strong tidal shear. By means of constrained realizations of our local Universe, based on Wiener-filtered reconstructions inferred from the Mark III catalogue of galaxy peculiar velocities, we show that indeed this configuration may induce locally cold regions. Hence, the coldness of the local flow may be a cosmic variance effect.

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arXiv1998

Cold Flows and Large Scale Tides

Several studies have indicated that the local cosmic velocity field is rather cold, in particular in the regions outside the massive, virialized clusters of galaxies. If our local cosmic environment is taken to be a representative volume of the Universe, the repercussion of this finding is that either we live in a low-$Ω$ Universe and/or that the galaxy distribution is a biased reflection of the underlying mass distribution. Otherwise, the pronounced nature of the observed galaxy distribution would be irreconcilable with the relatively quiet flow of the galaxies. Here we propose a different view on this cosmic dilemma, stressing the fact that our cosmic neighbourhood embodies a region of rather particular dynamical properties, and henceforth we are apt to infer flawed conclusions with respect to the global Universe. Suspended between two huge mass concentrations, the Great Attractor region and the Perseus-Pisces chain, we find ourselves in a region of relatively low density yet with a very strong tidal shear. This tidal field induces a local velocity field with a significant large-scale bulk flow but a low small-scale velocity dispersion. By means of constrained realizations of our local Universe, consisting of Wiener-filtered reconstructions inferred from the Mark III catalogue of galaxy peculiar velocities in combination with appropriate spectrally determined fluctuations, we study the implications for our local velocity field. We find that we live near a local peak in the distribution of the cosmic Mach number, $|v_{bulk}|/σ_v$, and that our local cosmic niche is located in the tail of the Mach number distribution function.

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arXiv1998

Large Scale Structure: Setting the Stage for the Galaxy Formation Saga

Over the past three decades the established view of a nearly homogeneuous, featureless Universe on scales larger than a few Megaparsec has been completely overhauled. In particular through the advent of ever larger galaxy redshift surveys we were revealed a galaxy distribution displaying an intriguing cellular pattern in which filamentary and wall-like structures, as well as huge regions devoid of galaxies, are amongst the most conspicuous morphological elements. In this contribution we will provide an overview of the present observational state of affairs concerning the distribution of galaxies and the structure traced out by the matter distribution in our Universe. In conjunction with the insight on the dynamics of the structure formation process obtained through the mapping of the peculiar velocities of galaxies in our local Universe and the information on the embryonic circumstances that prevailed at the epoch of Recombination yielded by the various Cosmic Microwave Background experiments, we seek to arrive at a more or less compelling theoretical framework of structure formation.The main aspects of this framework of the rise of structure through gravitational instability can probably be most readily appreciated through illustrative examples of various scenarios, as for instance provided by some current state-of-the-art N-body simulations. We will subsequently wrap up the observational and theoretical evidence for the emergence and evolution of structure in the Universe by sketching the stage for the ultimate Holy Grail of late 20th century astrophysics, understanding the saga of the formation of what arguably are the most prominent and at the same time intoxicatingly beautiful and intriguing denizens of our Cosmos, the {\it galaxies}.

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arXiv1998

Velocity Field Statistics and Tessellation Techniques: Unbiased Estimators of $Ω$

We describe two new -- stochastic-geometrical -- methods to obtain reliable velocity field statistics from N-body simulations and from any general density and velocity fluctuation field sampled at a discrete set of locations. These methods, the Voronoi tessellation method and Delaunay tessellation method, are based on the use of the Voronoi and Delaunay tessellations of the point distribution defined by the locations at which the velocity field is sampled. Adjusting themselves automatically to the density of sampling points, they represent the optimal estimator for volume-averaged quantities. They are therefore particularly suited for checking the validity of the predictions of quasi-linear analytical density and velocity field perturbation theory through the results of N-body simulations of structure formation. We illustrate the subsequent succesfull application of the two methods to estimate the bias-independent value of $Ω$ in the N-body simulations on the basis of the predictions of perturbation theory for the $Ω$-dependence of the moments and PDF of the velocity divergence in gravitational instability structure formation scenarios with Gaussian initial conditions. We will also shortly discuss practical and complicating issues involved in the obvious extension of the Voronoi and Delaunay method to the analysis of observational samples of galaxy peculiar velocities.

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arXiv1996

The Square Kilometer Array: new challenges for cosmology

The cosmological case for a next generation radio observatory, the Square Kilometer Array, is discussed and reviewed. An instrument like the SKA would be able to measure galaxy redshifts of normal late-type galaxies, via the 21 cm line of HI, out to redshifts of $\sim 3$. Not only would such very deep redshift surveys enable us to map the large scale galaxy distribution and probe the large scale structure of the universe out to previously unexplored scales, it would also allow for the first time to obtain direct observational data on the evolution of this structure. Other promising applications concern the mapping of the local velocity field of the universe, study of the formation and evolution of galaxies, and determining the global cosmological parameters $H_0$, $q_0$ and $Λ$ through the application of classical cosmological tests like source counts. Particularly emphasized is the redshift survey capability of the SKA. A review is given of the current knowledge of the galaxy distribution, starting from an inventarisation of nearby cosmic structures, through a discussion of how it all fits together in a coherent ``foamlike pattern''. After providing a short overview of the basics of theories of structure formation, a description is provided of different observational strategies to probe the structure of the universe out to larger depths, ranging from pencil-beam surveys and cluster surveys out to the new and ambitious complete and deep galaxy redshift surveys like the 2dF and the Sloan survey. It is argued that a survey with the SKA would be a natural and complementary follow-up. We finally conclude with a specification of the technical requirements for the SKA to make it into an instrument ideally suited for these purposes.

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arXiv1996

Tidal Fields and Structure Formation

The role of tidal shear in the formation of structure in the Universe is explored. To illustrate the possible and sometimes dramatic impact of tidal fields we focus on the evolution of voids. We firstly analyze the role of tidal fields both in the highly symmetric situation of an initially homogeneous ellipsoidal underdensity embedded in an artificially imposed tidal field. In addition, we present selfconsistent case studies consisting of N-body simulations that start from constrained Gaussian initial conditions in which the matter distribution is appropriately sculpted to yield an a priori specified tidal field. We conclude that voids may indeed be induced to collapse. Also, we present evidence for the strong relation between tidal fields and filaments in the mass distribution.

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arXiv1995

A new method for accurate velocity statistics estimation

We introduce two new methods to obtain reliable velocity field statistics from N-body simulations, or indeed from any general density and velocity fluctuation field sampled by discrete points. These methods, the {\it Voronoi tessellation method} and {\it Delaunay tessellation method}, are based on the use of the Voronoi and Delaunay tessellations of the point distribution defined by the locations at which the velocity field is sampled. In the Voronoi method the velocity is supposed to be uniform within the Voronoi polyhedra, whereas the Delaunay method constructs a velocity field by linear interpolation between the four velocities at the locations defining each Delaunay tetrahedron. The most important advantage of these methods is that they provide an optimal estimator for determining the statistics of volume-averaged quantities, as opposed to the available numerical methods that mainly concern mass-averaged quantities. As the major share of the related analytical work on velocity field statistics has focussed on volume-averaged quantities, the availability of appropriate numerical estimators is of crucial importance for checking the validity of the analytical perturbation calculations. In addition, it allows us to study the statistics of the velocity field in the highly nonlinear clustering regime. Although in most cases both the Voronoi and the Delaunay method lead to equally good velocity field estimates, the Delaunay method may be slightly preferable. In particular it performs considerably better at small radii. Note that it is more CPU-time intensive while its requirement for memory space is almost a factor 8 lower than the Voronoi method.

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arXiv1995

Constraining Peaks in Gaussian Primordial Density Fields: an Application of the Hoffman-Ribak Method

We develop an algorithm for setting up initial Gaussian random density and velocity fields containing one or more peaks or dips, in an arbitrary cosmological scenario. The intention is to generate appropriate initial conditions for cosmological N-body simulations that focus on the evolution of the progenitors of the present-day galaxies and clusters. The procedure is an application of the direct and accurate prescription of Hoffman & Ribak (1991) for generating constrained random fields. For each peak a total of 21 physical characteristics can be specified, including its scale, position, density Hessian, velocity, and velocity gradient. The velocity (or, equivalently, gravity) field constrants are based on a generalization of the formalism developed by Bardeen et al. (1986). The resulting density field is sculpted such that it induces the desired amount of net gravitational and tidal forces. We provide a detailed mathematical presentation of the formalism. Afterwards we provide analytical estimates of the likelihood of the imposed constraints. Amongst others, it is shown that the tidal field has a strong tendency to align itself along the principal axes of the mass tensor. The method is illustrated by means of some concrete examples. In addition to the illustration of constraint-field correlation functions and how they add up to the mean fields, followed by illustrations of the variance characteristics of field realizations, we concentrate in particular on the consequences of imposing gravitational field constraints (or, equivalent in the linear regime for growing mode fluctuations, peculiar velocity field constraints).

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arXiv1994

Shear Fields and the Evolution of Galactic-Scale Density Peaks

We present preliminary results of our investigation into the influence of shear fields on the evolution of galactic scale fluctuations in a primordial Gaussian random density field. Specifically, we study how the matter associated with a galaxy-scale peak evolves, to determine whether the shear can affect the peak's ability to form a virialized structure. We find that the evolution of the mass distribution in the immediate surroundings of $\geq 1σ$ initial density peaks is sensitive to the nature and magnitude of the shear. Its final fate and configuration spans a plethora of possibilities, ranging from accretion onto the peak to complete disruption. On the other hand, the mass defining the peak itself always tends to form a virialized object, though a given galaxy-scale peak need not necessarily form only one halo. Furthermore, galaxy-size halos need not necessarily be associated with initial galaxy-scale density peaks. Under certain conditions, the shear field is capable of breaking up a single primordial peak into two (and perhaps, more) distinct halos, or of promoting the growth of smaller-scale peaks into galaxy-size halos.

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