Vicent J. Martinez

Detection of cosmic filaments using the Candy model

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.

Scaling Laws in the Distribution of Galaxies

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!

Filaments in observed and mock galaxy catalogues

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.

Reliability of the Detection of the Baryon Acoustic Peak

The correlation function of the distribution of matter in the universe shows, at large scales, baryon acoustic oscillations, which were imprinted prior to recombination. This feature was first detected in the correlation function of the luminous red galaxies of the Sloan Digital Sky Survey (SDSS). Recently, the final release (DR7) of the SDSS has been made available, and the useful volume is about two times bigger than in the old sample. We present here, for the first time, the redshift-space correlation function of this sample at large scales together with that for one shallower, but denser volume-limited subsample drawn from the Two-Degree Field Redshift Survey. We test the reliability of the detection of the acoustic peak at about 100 h ?1 Mpc and the behavior of the correlation function at larger scales by means of careful estimation of errors. We confirm the presence of the peak in the latest data although broader than in previous detections.

Comparing Estimators of the Galaxy Correlation Function

We present a systematic comparison of some of the usual estimators of the two-point correlation function, some of them currently used in cosmology, others extensively employed in the field of the statistical analysis of point processes. At small scales it is known that the correlation function follows reasonably well a power-law expression ξ(r) ∝ r-γ. The accurate determination of the exponent γ (the order of the pole) depends on the estimator used for ξ(r); on the other hand, its behavior at large scales gives information on a possible trend to homogeneity. We study the concept, the possible bias, the dependence on random samples, and the errors of each estimator. Errors are computed by means of artificial catalogs of Cox processes for which the analytical expression of the correlation function is known. We also introduce a new method for extracting simulated galaxy samples from cosmological simulations.

Morphology of the Galaxy Distribution from Wavelet Denoising

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 hot spots. 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 provides us with a unique and more accurate morphological description.

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 us to distinguish clustered (i.e., correlated) from regular (i.e., anticorrelated) point distributions. We outline the theoretical foundations of the method, perform tests with a Matern cluster process as an idealized 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 (or in this case reject) viable models of cosmic structure formation.

Multiscale morphology of the galaxy distribution

Many statistical methods have been proposed in the last years for analysing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex observational sample volumes. In this paper, we first show how to calculate the Minkowski Functionals (MFs) taking into account these border effects. We then present a multiscale extension of the MF which gives us more information about how the galaxies are spatially distributed. A range of examples using Gaussian random fields illustrate the results. . Finally, we have applied the Multiscale Minkowski Functionals (MMFs) to the 2dF Galaxy Redshift Survey data. The MMF clearly indicates an evolution of morphology with scale. We also compare the 2dF real catalogue with mock catalogues and found that A cold dark matter simulations roughly fit the data, except at the finest scale.

Multiscaling Properties of Large-Scale Structure in the Universe

The large-scale distribution of galaxies and galaxy clusters in the universe can be described in the mathematical language of multifractal sets. A particularly significant aspect of this description is that it furnishes a natural explanation for the observed differences in clustering properties of objects of different density in terms of multiscaling, the generic consequence of the application of a local density threshold to a multifractal set. The multiscaling hypothesis suggests ways of improving upon the traditional statistical measures of clustering pattern (correlation functions) and exploring further the connection between clustering pattern and dynamics.

Analysis of the spatial distribution of galaxies by multiscale methods

Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy distribution and discriminate the different cosmological models. We present in this paper multiscale geometric transforms sensitive to clusters, sheets, and walls: the 3D isotropic undecimated wavelet transform, the 3D ridgelet transform, and the 3D beamlet transform. We show that statistical properties of transform coefficients measure in a coherent and statistically reliable way, the degree of clustering, filamentarity, sheetedness, and voidedness of a data set.