Cosmic structure has formed as a result of gravitational amplification of primordial density fluctuations together with the action of other physical processes (adiabatic gas dynamics, radiative cooling, photoionization and recombination, radiative transfer). These complex nonlinear processes, acting over a wide range of length scales (from kiloparsecs to tens of megaparsecs), make this a difficult problem for computation. During the last two decades, significant progress has been made in developing numerical methods and statistical tools for analyzing simulations and data. Combined with observational advances, numerical simulations have led to the demise of several formerly popular models and to an improved understanding of galaxy clusters, quasistellar object (QSO) absorption line systems, and other phenomena. This review summarizes these advances.

http://risa.stanford.edu/articles/Simulations-EdBertARAA98.pdf

Simulations of structure formation in the universe

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.

Evolution of the cosmic web

Voids are the most prominent feature of the large-scale structure of the universe. Still, their incorporation into quantitative analysis of it has been relatively recent, owing essentially to the lack of an objective tool to identify the voids and to quantify them. To overcome this, we present here the VOID FINDER algorithm, a novel tool for objectively quantifying voids in the galaxy distribution. The algorithm first classifies galaxies as either wall galaxies or field galaxies. Then, it identifies voids in the wall-galaxy distribution. Voids are defined as continuous volumes that do not contain any wall galaxies. The voids must be thicker than an adjustable limit, which is refined in successive iterations. In this way, we identify the same regions that would be recognized as voids by the eye. Small breaches in the walls are ignored, avoiding artificial connections between neighboring voids. We test the algorithm using Voronoi tesselations. By appropriate scaling of the parameters with the selection function, we apply it to two redshift surveys, the dense SSRS2 and the full-sky IRAS 1.2 Jy. Both surveys show similar properties: ~50% of the volume is filled by voids. The voids have a scale of at least 40 h-1 Mpc and an average -0.9 underdensity. Faint galaxies do not fill the voids, but they do populate them more than bright ones. These results suggest that both optically and IRAS-selected galaxies delineate the same large-scale structure. Comparison with the recovered mass distribution further suggests that the observed voids in the galaxy distribution correspond well to underdense regions in the mass distribution. This confirms the gravitational origin of the voids.

http://iopscience.iop.org/article/10.1086/304973/pdf

Voids in the Large-Scale Structure

Past surveys have revealed that the large-scale distribution of galaxies in the universe is far from random: it is highly structured over a vast range of scales. Surveys being currently undertaken and being planned for the next decades will provide a wealth of information about this structure. The ultimate goal must be not only to describe galaxy clustering as it is now, but also to explain how this arose as a consequence of evolutionary processes acting on the initial conditions that we see in the cosmic microwave background anisotropy data. In order to achieve this we need to build mathematically quantifiable descriptions of cosmic structure. Identifying where scaling laws apply and the nature of those scaling laws is an important part of understanding which physical mechanisms have been responsible for the organization of clusters of galaxies, superclusters, and the voids between them. Finding where these scaling laws are broken is equally important since this indicates the transition to different underlying physics. In describing scaling laws it is helpful to make analogies with fractals, mathematical constructs that can possess a wide variety of scaling properties. We must beware, however, of saying that the universe is a fractal on some range of scales: it merely exhibits a specific kind of fractal-like behavior on those scales. The richness of fractal scaling behavior is an important supplement to the usual battery of statistical descriptors. This article reviews the history of how we have learned about the structure of the universe and presents the data and methodologies that are relevant to an understanding of any scaling properties that structure may have. The ultimate goal is to have a complete understanding of how that structure emerged. We are getting close!

/pdf/scaling-laws-in-the-distribution-of-galaxies-2j7mbr1swi.pdf

Scaling laws in the distribution of galaxies

The universe appears from recent observational results to be a highly structured but also highly disordered medium. This accounts for the difficulties with a conventional statistical approach. Since the statistics of disordered media is an increasingly well-studied field in physics, it is tempting to try to adapt its methods for the study of the universe (the use of correlation functions also resulted from the adaptation of techniques from a very different field to astrophysics). This is already the case for the fractal analysis, which, mainly developed in microscopic statistics, is increasingly used in astrophysics. I suggest a new approach, also derived from the study of disordered media, both from the study of percolation clusters and from the dynamics of so-called “cluster aggregation” gelification models. This approach is briefly presented. Its main interest lies in two points. First, it suggests an analysis able to characterize features of unconventional statistics (those that seem to be present in the galaxy distribution and which conventional indicators are unable to take into account). It appears alsoa priori very convenient for a synthetic approach, since it can be related to the other indicators used up to now: the link with the void probability function is very straightforward. The connexion with fractals can be said to be contained in the method, since the objects defined during this analysis are themselves fractal: different kinds of fractal dimensions are very easy to extract from the analysis. The link with the percolation studies is also very natural since the method is adapted from the study of percolation clusters. It is also expected that the information concerning the topology is contained in this approach; this seems natural since the method is very sensitive to the topology of the distribution and posses some common characteristics with the topology analysis already developed by Gottet al. (1986). The quantitative relations remain however to be calculated. Additionally, this approach concerns the variation of clustering properties of galaxy groups and clusters with their richness. Although such studies have been made for various cases (like comparison of the correlation functions between galaxies and clusters, or between clusters of different richness classes), the analysis presented here deals with it in a more systematic and synthetic way.

Statistics of the galaxy distribution

It is shown that the clustering structures in the observed universe and in numerical simulations are not well represented by a homogeneous measure on a fractal. It is proposed that a good description of these clustering structures is given by multifractals - fractals having more than one scaling index. The multifractal characteristics of a data sample and a numerical simulation of an axion-dominated universe are evaluated. The clustering structures revealed by the multifractal analysis are quite similar, both showing a variation of dimensionality from 1 to 3 over similar ranges of scales. The multifractal description provides a natural way of scaling the numerical models to the data. If a bias is applied to the simulation, the result is a distribution of points that has almost constant dimension, 1.5, on all scales. This reduction of the distribution of dimensionality by biasing may be a problem for theories that invoke naive biasing schemes. 17 references.

Vincent J. Martinez

Papers

Multifractal Description of the Large-Scale Structure of the Universe

The minimal spanning tree as an estimator for generalized dimensions