Clustering of 3D Spatial Points Using Maximum Likelihood Estimator over Voronoi Tessellations: Study of the Galaxy Distribution in Redshift Space

Abstract

This paper describes an algorithm based on the 2D approach of Allard & Fraley that uses Voronoi tessellation and a non-parametric maximum likelihood estimator. We have designed a 3D version of this algorithm which detects multiple clusters of points immersed in background noise; its application to the detection of galaxy clusters in redshift space, using the astronomical database of the 2-degree Field Galaxy Redshift Survey, is presented and discussed. Adopting as a benchmark a particular set of catalogued clusters of galaxies, we find that the proposed algorithm recognizes the location of ~ 67% of the clusters. Three variants of the algorithm were assessed to deal with the elongation of the clusters in the radial direction of observation introduced by the astronomical distance indicator; their merits and limitations are discussed. We address separately the detection of the galaxy cluster location and the detection of galaxy cluster members, both of them having an anisotropic space as their search domain. In the case of detection of galaxy cluster members, a second stage of detection was incorporated in order to improve the results.