Enn Saar

Galaxy number or luminosity density serves as a basis for many structure classification algorithms. Several methods are used to estimate this density. Among them kernel methods have probably the best statistical properties and allow also to estimate the local sample errors of the estimate. We introduce a kernel density estimator with an adaptive data-driven anisotropic kernel, describe its properties and demonstrate the wealth of additional information it gives us about the local properties of the galaxy distribution.

Context. The main feature of the spatial large-scale galaxy distribution is an intricate network of galaxy filaments. Although many attempts have been made to quantify this network, there is no unique and satisfactory recipe for that yet. Aims. The present paper compares the filaments in the real data and in the numerical models, to see if our best models reproduce statistically the filamentary network of galaxies. Methods. We apply an object point process with interactions (the Bisous process) to trace and describe the filamentary network both in the observed samples (the 2dFGRS catalogue) and in the numerical models that have been prepared to mimic the data. We compare the networks. Results. We find that the properties of filaments in numerical models (mock samples) have a large variance. A few mock samples display filaments that resemble the observed filaments, but usually the model filaments are much shorter and do not form an extended network. Conclusions. We conclude that although we can build numerical models that are similar to observations in many respects, they may fail yet to explain the filamentary structure seen in the data. The Bisous-built filaments are a good test for such a structure.

Context. The main feature of the spatial large-scale galaxy distribution is an intricate network of galaxy filaments. Although many attempts have been made to quantify this network, there is no unique and satisfactory recipe for that yet. Aims. The present paper compares the filaments in the real data and in the numerical models, to see if our best models reproduce statistically the filamentary network of galaxies. Methods. We apply an object point process with interactions (the Bisous process) to trace and describe the filamentary network both in the observed samples (the 2dFGRS catalogue) and in the numerical models that have been prepared to mimic the data.We compare the networks. Results. We find that the properties of filaments in numerical models (mock samples) have a large variance. A few mock samples display filaments that resemble the observed filaments, but usually the model filaments are much shorter and do not form an extended network. Conclusions. We conclude that although we can build numerical models that are similar to observations in many respects, they may fail yet to explain the filamentary structure seen in the data. The Bisous-built filaments are a good test for such a structure.

The lecture introduces a trous wavelet transforms, explains how to estimate the spatial density for galaxy distributions, and, finally, how to describe the morphology of cosmological density fields. An example application of these methods to the 2dFGRS gives unexpected results.

We have developed a method based on wavelets to obtain the true underlying smooth density from a point distribution. The goal has been to reconstruct the density field in an optimal way ensuring that the morphology of the reconstructed field reflects the true underlying morphology of the point field which, as the galaxy distribution, has a genuinely multiscale structure, with near-singular behavior on sheets, filaments and hotspots. If the discrete distributions are smoothed using Gaussian filters, the morphological properties tend to be closer to those expected for a Gaussian field. The use of wavelet denoising provide us with a unique and more accurate morphological description.

We have developed a method based on wavelets to obtain the true underlying smooth density from a point distribution. The goal has been to reconstruct the density field in an optimal way ensuring that the morphology of the reconstructed field reflects the true underlying morphology of the point field which, as the galaxy distribution, has a genuinely multiscale structure, with near-singular behavior on sheets, filaments and hotspots. If the discrete distributions are smoothed using Gaussian filters, the morphological properties tend to be closer to those expected for a Gaussian field. The use of wavelet denoising provide us with a unique and more accurate morphological description.

We propose to apply a marked point process to automatically delineate filaments of the large-scale structure in redshift catalogues. We illustrate the feasibility of the idea on an example of simulated catalogues, describe the procedure, and characterize the results. We find the distribution of the length of the filaments, and suggest how to use this approach to obtain other statistical characteristics of filamentary networks.

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!

Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. 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. To describe cosmic structures, we need to build mathematically quantifiable descriptions of 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, superclusters of galaxies 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 we are helped by making 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. We exploit the richness of fractal scaling behavior merely as an important supplement to the usual battery of statistical descriptors. We review the history of how we have learned about the structure of the Universe and present the data and methodologies that are relevant to the question of discovering and understanding 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!