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 results relative to the use of new statistical tools using the 3D isotropic undecimated wavelet transform, the 3D ridgelet transform and the 3D beamlet transform. We show that such multiscale methods produce a new way to measure in a coherent and statistically reliable way the degree of clustering, filamentarity, sheetedness, and voidedness of a datasetComment: 26 pages, 20 figures. Submitted to EURASIP Journal on Applied Signal Processing (special issue on "Applications of Signal Processing in Astrophysics and Cosmology"

The Multiscale Morphology Filter: Identifying and Extracting Spatial Patterns in the Galaxy Distribution

We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without prejudice as to their size or shape. The method is ideally suited for extracting catalogues of clusters, walls, and filaments from samples of galaxies in redshift surveys or from particles in cosmological N-body simulations: it makes no prior assumptions about the scale or shape of the structures.}Comment: Replacement with higher resolution figures. 28 pages, 17 figures. For Full Resolution Version see: http://www.astro.rug.nl/~weygaert/tim1publication/miguelmmf.pd

Weak Lensing Mass Reconstruction using Wavelets

This paper presents a new method for the reconstruction of weak lensing mass maps. It uses the multiscale entropy concept, which is based on wavelets, and the False Discovery Rate which allows us to derive robust detection levels in wavelet space. We show that this new restoration approach outperforms several standard techniques currently used for weak shear mass reconstruction. This method can also be used to separate E and B modes in the shear field, and thus test for the presence of residual systematic effects. We concentrate on large blind cosmic shear surveys, and illustrate our results using simulated shear maps derived from N-Body Lambda-CDM simulations with added noise corresponding to both ground-based and space-based observations.Comment: Accepted manuscript with all figures can be downloaded at: http://jstarck.free.fr/aa_wlens05.pdf and software can be downloaded at http://jstarck.free.fr/mrlens.htm

More than just halo mass: Modelling how the red galaxy fraction depends on multiscale density in a HOD framework

The fraction of galaxies with red colours depends sensitively on environment, and on the way in which environment is measured. To distinguish competing theories for the quenching of star formation, a robust and complete description of environment is required, to be applied to a large sample of galaxies. The environment of galaxies can be described using the density field of neighbours on multiple scales - the multiscale density field. We are using the Millennium simulation and a simple HOD prescription which describes the multiscale density field of Sloan Digital Sky Survey DR7 galaxies to investigate the dependence of the fraction of red galaxies on the environment. Using a volume limited sample where we have sufficient galaxies in narrow density bins, we have more dynamic range in halo mass and density for satellite galaxies than for central galaxies. Therefore we model the red fraction of central galaxies as a constant while we use a functional form to describe the red fraction of satellites as a function of halo mass which allows us to distinguish a sharp from a gradual transition. While it is clear that the data can only be explained by a gradual transition, an analysis of the multiscale density field on different scales suggests that colour segregation within the haloes is needed to explain the results. We also rule out a sharp transition for central galaxies, within the halo mass range sampled.Comment: 24 pages, 21 figures, accepted for publication by MNRA

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 cosmological $\Lambda$CDM 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 them 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 linear 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 $M \sim 10^{14}$ M$_{\odot}$ h$^{-1}$ have on average two connecting filaments, while clusters with $M \geq 10^{15}$ M$_{\odot}$ h$^{-1}$ have on average five connecting filaments. iv).- Density profiles indicate that the typical width of filaments is 2\Mpch. 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 ${\gamma}\approx -1$, corresponding to an isothermal density profile.Comment: 28 pages, 22 figures, accepted for publication in MNRAS. For a high-res version see http://www.astro.rug.nl/~weygaert/webmorph_mmf.pd

Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web

We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic. The richer information content of Betti numbers goes along the availability of fast algorithms to compute them. For continuous density fields, we determine the scale-dependence of Betti numbers by invoking the cosmologically familiar filtration of sublevel or superlevel sets defined by density thresholds. For the discrete galaxy distribution, however, the analysis is based on the alpha shapes of the particles. These simplicial complexes constitute an ordered sequence of nested subsets of the Delaunay tessellation, a filtration defined by the scale parameter, $\alpha$. As they are homotopy equivalent to the sublevel sets of the distance field, they are an excellent tool for assessing the topological structure of a discrete point distribution. In order to develop an intuitive understanding for the behavior of Betti numbers as a function of $\alpha$, and their relation to the morphological patterns in the Cosmic Web, we first study them within the context of simple heuristic Voronoi clustering models. Subsequently, we address the topology of structures emerging in the standard LCDM scenario and in cosmological scenarios with alternative dark energy content. The evolution and scale-dependence of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic Web and yields a promising measure of cosmological parameters. We also discuss the expected Betti numbers as a function of the density threshold for superlevel sets of a Gaussian random field.Comment: 42 pages, 14 figure

Multi-scale morphology of the galaxy distribution

Many statistical methods have been proposed in the last years for analyzing 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 (MF) taking into account these border effects. Then we 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 (MMF) to the 2dF Galaxy Redshift Survey data. The MMF clearly indicates an evolution of morphology with scale. We also compare the 2dF real catalog with mock catalogs and found that Lambda-CDM simulations roughly fit the data, except at the finest scale.Comment: 17 pages, 19 figures, accepted for publication in MNRA

Multiscale magnetic underdense regions on the solar surface: Granular and Mesogranular scales

The Sun is a non-equilibrium dissipative system subjected to an energy flow which originates in its core. Convective overshooting motions create temperature and velocity structures which show a temporal and spatial evolution. As a result, photospheric structures are generally considered to be the direct manifestation of convective plasma motions. The plasma flows on the photosphere govern the motion of single magnetic elements. These elements are arranged in typical patterns which are observed as a variety of multiscale magnetic patterns. High resolution magnetograms of quiet solar surface revealed the presence of magnetic underdense regions in the solar photosphere, commonly called voids, which may be considered a signature of the underlying convective structure. The analysis of such patterns paves the way for the investigation of all turbulent convective scales from granular to global. In order to address the question of magnetic structures driven by turbulent convection at granular and mesogranular scales we used a "voids" detection method. The computed voids distribution shows an exponential behavior at scales between 2 and 10 Mm and the absence of features at 5-10 Mm mesogranular scales. The absence of preferred scales of organization in the 2-10 Mm range supports the multiscale nature of flows on the solar surface and the absence of a mesogranular convective scale

A multiscale approach to environment and its influence on the colour distribution of galaxies

We present a multiscale approach to measurements of galaxy density, applied to a volume-limited sample constructed from SDSS DR5. We populate a rich parameter space by obtaining independent measurements of density on different scales for each galaxy, avoiding the implicit assumptions involved, e.g., in the construction of group catalogues. As the first application of this method, we study how the bimodality in galaxy colour distribution (u-r) depends on multiscale density. The u-r galaxy colour distribution is described as the sum of two gaussians (red and blue) with five parameters: the fraction of red galaxies (f_r) and the position and width of the red and blue peaks (mu_r, mu_b, sigma_r and sigma_b). Galaxies mostly react to their smallest scale (< 0.5 Mpc) environments: in denser environments red galaxies are more common (larger f_r), redder (larger mu_r) and with a narrower distribution (smaller sigma_r), while blue galaxies are redder (larger mu_b) but with a broader distribution (larger sigma_b). There are residual correlations of f_r and mu_b with 0.5 - 1 Mpc scale density, which imply that total or partial truncation of star formation can relate to a galaxy's environment on these scales. Beyond 1 Mpc (0.5 Mpc for mu_r) there are no positive correlations with density. However f_r (mu_r) anti-correlates with density on >2 (1) Mpc scales at fixed density on smaller scales. We examine these trends qualitatively in the context of the halo model, utilizing the properties of haloes within which the galaxies are embedded, derived by Yang et al, 2007 and applied to a group catalogue. This yields an excellent description of the trends with multiscale density, including the anti-correlations on large scales, which map the region of accretion onto massive haloes. Thus we conclude that galaxies become red only once they have been accreted onto haloes of a certain mass.Comment: 22 pages, 14 figures. Accepted for publication in MNRAS