January 22, 2003

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Publications in Astronomy/AstroPhysics dealing with Shape, by :

• Coles, Peter et al.:
  • Voronoi Cosmology, 1991.
• Icke, Vincent et al.:
  • Fragmenting the Universe. I. Statistics of Two-Dimensional Voronoi Foams, 1987.
  • The Galaxy Distribution as a Voronoi Foam, 1991.
• Ramella, M. et al. :
  • Finding galaxy clusters using Voronoi tessellations, 2001.

BibTeX references.

The Voronoi Universe

When an infinite gaseous medium collapses under its own gravity, the regions that happen to be a little less dense than average contract a little faster that the Universe expands. The regions that are less dense than average expand somewhat faster than the rest of the Universe. Thus, matter flows away from the low-density regions and towards the zones of higher density. In a paper in 1984, I proved that this means that the low-density regions become more and more spherical, even as they occupy more and more volume. Together with my colleague Rien van de Weygaert, we proved that this implies that self-gravitating matter assumes a very special mathematical form: a Voronoi tessellation.

Web-link

We present an objective and automated procedure for detecting clusters of galaxies in imaging galaxy surveys. Our Voronoi Galaxy Cluster Finder (VGCF) uses galaxy positions and magnitudes to find clusters and determine their main features: size, richness and contrast above the background. The VGCF uses the Voronoi tessellation to evaluate the local density and to identify clusters as significative density fluctuations above the background. The significance threshold needs to be set by the user, but experimenting with different choices is very easy since it does not require a whole new run of the algorithm. The VGCF is non-parametric and does not smooth the data. As a consequence, clusters are identified irrespective of their shape and their identification is only slightly affected by border effects and by holes in the galaxy distribution on the sky. The algorithm is fast, and automatically assigns members to structures. A test run of the VGCF on the PDCS field centered at alpha = 36h26m and delta = +29 deg. 52´(J2000) produces 37 clusters. Of these clusters, 12 are VGCF counterparts of the 13 PDCS clusters detected at the 3 sigma level and with estimated redshifts from z=0.2 to z=0.6. Of the remaining 25 systems, 2 are PDCS clusters with confidence level < 3 sigma and redshift z <= 0.6. Inspection of the 23 new VGCF clusters indicates that several of these clusters may have been missed by the matched filter algorithm for one or more of the following reasons: a) they are very poor, b) they are extremely elongated, c) they lie too close to a rich and/or low redshift cluster.

Keywords: cosmology: large-scale structure of Universe -- galaxies: clusters: general -- galaxies: statistics.

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