Rien van de Weygaert

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 that is well-peaked about a characteristic void size that 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 that 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, the solution of the cloud-in-cloud problem, i.e. counting as clusters only those objects which are not embedded in larger clusters, requires the study of random walks crossing one barrier. We show that a similar formulation of void evolution requires the 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.

A cosmic watershed : the WVF void detection technique

On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the cosmic web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its complex morphological components. One of the most characteristic aspects is that of the dominant underdense voids, the product of a hierarchical process driven by the collapse of minor voids in addition to the merging of large ones. In this study we present an objective void finder technique which involves a minimum of assumptions about the scale, structure and shape of voids. Our void finding method, the watershed void finder (WVF), is based upon the watershed transform, a well-known technique for the segmentation of images. Importantly, the technique has the potential to trace the existing manifestations of a void hierarchy. The basic watershed transform is augmented by a variety of correction procedures to remove spurious structure resulting from sampling noise. This study contains a detailed description of the WVF. We demonstrate how it is able to trace and identify, relatively parameter free, voids and their surrounding (filamentary and planar) boundaries. We test the technique on a set of kinematic Voronoi models, heuristic spatial models for a cellular distribution of matter. Comparison of the WVF segmentations of low-noise and high-noise Voronoi models with the quantitatively known spatial characteristics of the intrinsic Voronoi tessellation shows that the size and shape of the voids are successfully retrieved. WVF manages to even reproduce the full void size distribution function.

Spin Alignment of Dark Matter Halos in Filaments and Walls

The MMF technique is used to segment the cosmic web as seen in a cosmological N-body simulation into wall-like and filament-like structures. We find that the spins and shapes of dark matter halos are significantly correlated with each other and with the orientation of their host structures. The shape orientation is such that the halo minor axes tend to lie perpendicular to the host structure, be it a wall or filament. The orientation of the halo spin vector is mass-dependent. Low-mass halos in walls and filaments have a tendency to have their spins oriented within the parent structure, while higher mass halos in filaments have spins that tend to lie perpendicular to the parent structure.

The Aspen–Amsterdam void finder comparison project

Despite a history that dates back at least a quarter of a century studies of voids in the large–scale structure of the Universe are bedevilled by a major problem: there exist a large number of quite different void–finding algorithms, a fact that has so far got in the way of groups comparing their results without worrying about whether such a comparison in fact makes sense. Because of the recent increased interest in voids, both in very large galaxy surveys and in detailed simulations of cosmic structure formation, this situation is very unfortunate. We here present the first systematic comparison study of thirteen different void finders constructed using particles, haloes, and semi– analytical model galaxies extracted from a subvolume of the Millennium simulation. The study includes many groups that have studied voids over the past decade. We show their results and discuss their differences and agreements. As it turns out, the basic results of the various methods agree very well with each other in that they all locate a major void near the centre of our volume. Voids have very underdense centres, reaching below 10 percent of the mean cosmic density. In addition, those void finders that allow for void galaxies show that those galaxies follow similar trends. For example, the overdensity of void galaxies brighter than mB = 20 is found to be smaller than about 0.8 by all our void finding algorithms.

Multiscale phenomenology of the cosmic web

We analyze the structure and connectivity of the distinct morphologies that define the Cosmic Web. With the help of our Multiscale Morphology Filter (MMF), we dissect the matter distribution of a cosmologicalCDM N-body computer simulation into cluster, filaments and walls. The MMF is ideally suited to adress both the anisotropic morphological character of filaments and sheets, as well as the multiscale nature of the hierarchically evolved cosmic matter distribution. The results of our study may be summarized as follows: i).- While all morphologies occupy a roughly well defined range in density, this alone is not sufficient to differentiate between t given their overlap. Environment defined only in terms of density fails to incorporate the intrinsic dynamics of each morphology. This plays an important role in both linear and non lin- ear interactions between haloes. ii).- Most of the mass in the Universe is concentrated in filaments, narrowly followed by clusters. In terms of volume, clusters only represent a minute fraction, and filaments not more than 9%. Walls are relatively inconspicous in terms of mass and volume. iii).- On average, massive clusters are connected to more filaments than low mass clusters. Clusters with M � 10 14 Mh −1 have on average two connecting filaments, while clusters with M > 10 15 Mh −1 have on average five connecting filaments. iv).- Density profiles indicate that the typical width of filaments is 2 h −1 Mpc. Walls have less well defined boundaries with widths between 5-8 Mpc h −1 . In their interior, filaments have a power-law density profile with slope � − 1, corresponding to an isothermal density profile.

Evolution of the cosmic web

The cosmic web is the largest scale manifestation of the anisotropic gravitational collapse of matter. It represents the transitional stage between linear and non-linear structures and contains easily accessible information about the early phases of structure formation processes. Here we investigate the characteristics and the time evolution of morphological components. Our analysis involves the application of the NEXUS Multiscale Morphology Filter technique, predominantly its NEXUS+ version, to high resolution and large volume cosmological simulations. We quantify the cosmic web components in terms of their mass and volume content, their density distribution and halo populations. We employ new analysis techniques to determine the spatial extent of filaments and sheets, like their total length and local width. This analysis identifies clusters and filaments as the most prominent components of the web. In contrast, while voids and sheets take most of the volume, they correspond to underdense environments and are devoid of group-sized and more massive haloes. At early times the cosmos is dominated by tenuous filaments and sheets, which, during subsequent evolution, merge together, such that the present-day web is dominated by fewer, but much more massive, structures. The analysis of the mass transport between environments clearly shows how matter flows from voids into walls, and then via filaments into cluster regions, which form the nodes of the cosmic web. We also study the properties of individual filamentary branches, to find long, almost straight, filaments extending to distances larger than 100 h-1 Mpc. These constitute the bridges between massive clusters, which seem to form along approximatively straight lines.

Velocity Fields and Alignments of Clusters in Gravitational Instability Scenarios

The structure and evolution of the outskirts of clusters in several gravitational instability scenarios are studied. By means of the Hoffman-Ribak constrained random field code we generate realizations of fluctuation fields containing protoclusters of a specified height and shape. The samples generated consist of 64 3 particles in a box with a size of 50 h -1 Mpc. By means of a P 3 M N-body code, using a 128 3 grid, the evolution of the resulting particle distribution is followed into the nonlinear regime. The protoclusters are 3σ 0 fluctuations [σ 0 =σ 0 (4 h -1 Mpc)] in a cold dark matter scenario and in two scale-free scenarios [P(k)∞k n , n=0 or -2], Ω 0 =1

NEXUS : tracing the cosmic web connection.

We introduce the NEXUS algorithm for the identification of cosmic web environments: clusters, filaments, walls and voids. This is a multiscale and automatic morphological analysis tool that identifies all the cosmic structures in a scale free way, without preference for a certain size or shape. We develop the NEXUS method to incorporate the density, tidal field, velocity divergence and velocity shear as tracers of the cosmic web. We also present the NEXUS+ procedure which, taking advantage of a novel filtering of the density in logarithmic space, is very successful at identifying the filament and wall environments in a robust and natural way. To assess the algorithms we apply them to an N-body simulation. We find that all methods correctly identify the most prominent filaments and walls, while there are differences in the detection of the more tenuous structures. In general, the structures traced by the density and tidal fields are clumpier and more rugged than those present in the velocity divergence and velocity shear fields. We find that the NEXUS+ method captures much better the filamentary and wall networks and is successful in detecting even the fainter structures. We also confirm the efficiency of our methods by examining the dark matter particle and halo distributions.

The Spine of the Cosmic Web

We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments, and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes the local adjacency properties of the boundaries between the watershed basins to trace the critical points in the density field and the separatrices defined by them. The separatrices are classified into walls and the spine, the network of filaments and nodes in the matter distribution. Testing the method with a heuristic Voronoi model yields outstanding results. Following the discussion of the test results, we apply the SpineWeb method to a set of cosmological N-body simulations. The latter illustrates the potential for studying the structure and dynamics of the Cosmic Web.

The darkness that shaped the void: dark energy and cosmic voids

We assess the sensitivity of void shapes to the nature of dark energy that was pointed out in recent studies and also investigate whether or not void shapes are useable as an observational probe in galaxy redshift surveys. Our focus is on the evolution of the mean void ellipticity and its underlying physical cause. To this end, we analyse the morphological properties of voids in five sets of cosmological N-body simulations, each with a different nature of dark energy. To address the question of whether galaxy redshift surveys yield sufficiently accurate void morphologies, voids in the dark matter distribution are compared to those in the halo population. Voids are identified using the parameter-free Watershed Void Finder. The effect of redshift distortions is investigated as well. The main conclusions of this study are as follows: (i) the statistically significant sensitivity of voids in the dark matter distribution is confirmed; (ii) the level of clustering as measured by s8(z) is identified as the main cause of differences in the mean void shape ; and (iii) in the halo and/or galaxy distribution, it is practically unfeasible to distinguish at a statistically significant level between the various cosmologies due to the sparsity and spatial bias of the sample.