Detecting structure in two dimensions combining Voronoi tessellation and percolation.

Abstract

Conventional source-detection algorithms in high-energy astrophysics and other fields mostly use spherical or quadratic sliding windows of varying size on two-dimensionally binned representations of spatial event distributions in order to detect statistically significant event enhancements (sources) within a given field. While this is a reasonably reliable technique for nearly pointlike sources with good statistics, poor and extended sources are likely to be incorrectly assessed or even missed at all, as the calculations are governed by nonphysical parameters like the bin size and the window geometry rather than by the actual data. The approach presented here does not introduce any artificial bias but makes full use of the unbinned two-dimensional event distribution. A Voronoi tessellation on a finite plane surface yields individual densities, or fluxes, for every single event, the distribution of which allows the determination of the contribution from a random Poissonian background field (noise). The application of a nonparametric percolation to the tessellation cells exceeding this noise level leads directly to a source list which is free of any assumptions about the source geometry. High-density fluctuations from the random background field will still be included in this tentative source list but can be easily eliminated, in most cases, by setting a lower threshold to the required number of events per source. Since no finite-size detection windows or the like have been used, this analysis yields automatically straightforward fluxes for every source finally accepted. The main disadvantage of this approach is the considerable CPU time required for the construction of the Voronoi tessellation---it is thus applicable only to either small fields or low-event density regions.