Shapefinders: A new shape diagnostic for large scale structure

Details Shapefinders: A new shape diagnostic for large scale structure Shapefinders: A new shape diagnostic for large scale structure

1998-01-07

arxiv.org/abs/astro-ph/9801053v1

Astrophys.J.495:L5-L8,1998

Astronomy and Astrophysics

Astrophysics

Latex (8 pages with aaspp.sty) requires \usepackage{graphicx}). To appear in ApJ Lett

Scientific paper

10.1086/311214

We construct a set of shape-finders which determine shapes of compact surfaces (iso-density surfaces in galaxy surveys or N-body simulations) without fitting them to ellipsoidal configurations as done earlier. The new indicators arise from simple, geometrical considerations and are derived from fundamental properties of a surface such as its volume, surface area, integrated mean curvature and connectivity characterized by the Genus. These `Shapefinders' could be used to diagnose the presence of filaments, pancakes and ribbons in large scale structure. Their lower-dimensional generalization may be useful for the study of two-dimensional distributions such as temperature maps of the Cosmic Microwave Background.

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