Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2010-06-14
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
13 pages, 7 figures, accepted paper ISVD2010, Quebec, Canada. IEEE CPS, ed. M.A. Mostafavi(extended version). For high-res ver
Scientific paper
We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determine the set of Betti numbers ($\beta_{\rm k},k=1,...,D$), which represent a complete characterization of the topology of a manifold. This forms a useful extension of the geometry and topology of the galaxy distribution by Minkowski functionals, of which three specify the geometrical structure of surfaces and one, the Euler characteristic, represents a key aspect of its topology. In order to develop an intuitive understanding for the relation between Betti numbers and the running $\alpha$ parameter of the alpha shapes, and thus in how far they may discriminate between different topologies, we study them within the context of simple heuristic Voronoi clustering models. These may be tuned to consist of a few or even only one specific morphological element of the Cosmic Web, ie. clusters, filaments or sheets.
de Weygaert Rien van
Eldering Bob
Kruithof Nico
Platen Erwin
Vegter Gert
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