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Register a new userVoronoi Tessellations and the Cosmic Web: Spatial Patterns and Clustering across the Universe
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Added by
Rien van de Weygaert
Publication date
2007
fields
Physics
and research's language is
English
Authors
Rien van de Weygaert
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The spatial cosmic matter distribution on scales of a few up to more than a hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi tessellations are a versatile and flexible mathematical model for such weblike spatial patterns. They would be the natural asymptotic result of an evolution in which low-density expanding void regions dictate the spatial organization of the Megaparsec Universe, while matter assembles in high-density filamentary and wall-like interstices between the voids. We describe the results of ongoing investigations of a variety of aspects of cosmologically relevant spatial distributions and statistics within the framework of Voronoi tessellations. Particularly enticing is the finding of a profound scaling of both clustering strength and clustering extent for the distribution of tessellation nodes, suggestive for the clustering properties of galaxy clusters. Cellular patterns may be the source of an intrinsic ``geometrically biased clustering.
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Voids form a prominent aspect of the Megaparsec distribution of galaxies and matter. Not only do they represent a key constituent of the Cosmic Web, they also are one of the cleanest probes and measures of global cosmological parameters. The shape and evolution of voids are highly sensitive to the nature of dark energy, while their substructure and galaxy population provides a direct key to the nature of dark matter. Also, the pristine environment of void interiors is an important testing ground for our understanding of environmental influences on galaxy formation and evolution. In this paper, we review the key aspects of the structure and dynamics of voids, with a particular focus on the hierarchical evolution of the void population. We demonstrate how the rich structural pattern of the Cosmic Web is related to the complex evolution and buildup of voids.
Nowadays, big data of digital media (including images, videos and 3D graphical models) are frequently modeled as low-dimensional manifold meshes embedded in a high-dimensional feature space. In this paper, we summarized our recent work on geodesic centroidal Voronoi tessellations(GCVTs), which are intrinsic geometric structures on manifold meshes. We show that GCVT can find a widely range of interesting applications in computer vision and graphics, due to the efficiency of search, location and indexing inherent in these intrinsic geometric structures. Then we present the challenging issues of how to build the combinatorial structures of GCVTs and establish their time and space complexities, including both theoretical and algorithmic results.
This work investigates the alignment of galactic spins with the cosmic web across cosmic time using the cosmological hydrodynamical simulation Horizon-AGN. The cosmic web structure is extracted via the persistent skeleton as implemented in the DISPERSE algorithm. It is found that the spin of low-mass galaxies is more likely to be aligned with the filaments of the cosmic web and to lie within the plane of the walls while more massive galaxies tend to have a spin perpendicular to the axis of the filaments and to the walls. The mass transition is detected with a significance of 9 sigmas. This galactic alignment is consistent with the alignment of the spin of dark haloes found in pure dark matter simulations and with predictions from (anisotropic) tidal torque theory. However, unlike haloes, the alignment of low-mass galaxies is weak and disappears at low redshifts while the orthogonal spin orientation of massive galaxies is strong and increases with time, probably as a result of mergers. At fixed mass, alignments are correlated with galaxy morphology: the high-redshift alignment is dominated by spiral galaxies while elliptical centrals are mainly responsible for the perpendicular signal. These predictions for spin alignments with respect to cosmic filaments and unprecendently walls are successfully compared with existing observations. The alignment of the shape of galaxies with the different components of the cosmic web is also investigated. A coherent and stronger signal is found in terms of shape at high mass. The two regimes probed in this work induce competing galactic alignment signals for weak lensing, with opposite redshift and luminosity evolution. Understanding the details of these intrinsic alignments will be key to exploit future major cosmic shear surveys like Euclid or LSST.
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.
For over twenty years, the term cosmic web has guided our understanding of the large-scale arrangement of matter in the cosmos, accurately evoking the concept of a network of galaxies linked by filaments. But the physical correspondence between the cosmic web and structural-engineering or textile spiderwebs is even deeper than previously known, and extends to origami tessellations as well. Here we explain that in a good structure-formation approximation known as the adhesion model, threads of the cosmic web form a spiderweb, i.e. can be strung up to be entirely in tension. The correspondence is exact if nodes sampling voids are included, and if structure is excluded within collapsed regions (walls, filaments and haloes), where dark-matter multistreaming and baryonic physics affect the structure. We also suggest how concepts arising from this link might be used to test cosmological models: for example, to test for large-scale anisotropy and rotational flows in the cosmos.
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