DETECTING STRUCTURE IN 2 DIMENSIONS COMBINING VORONOI TESSELLATION AND PERCOLATION

Conventional source-detection algorithms in high-energy astrophysics a nd other fields mostly use spherical or quadratic sliding windows of v arying size on two-dimensionally binned representations of spatial eve nt distributions in order to detect statistically significant event en hancements (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 eve n missed at all, as the calculations are governed by nonphysical param eters like the bin size and the window geometry rather than by the act ual data. The approach presented here does not introduce any artificia l bias but makes full use of the unbinned two-dimensional event distri bution. A Voronoi tessellation on a finite plane surface yields indivi dual densities, or fluxes, for every single event, the distribution of which allows the determination of the contribution from a random Pois sonian background field (noise). The application of a nonparainetric p ercolation to the tessellation cells exceeding this noise level leads directly to a source list which is free of any assumptions about the s ource geometry. High-density fluctuations from the random background f ield will still be included in this tentative source list but can be e asily eliminated, in most cases, by setting a lower threshold to the r equired number of events per source. Since no finite-size detection wi ndows or the like have been used, this analysis yields automatically s traightforward fluxes for every source finally accepted. The main disa dvantage of this approach is the considerable CPU time required for th e construction of the Voronoi tessellation-it is thus applicable only to either small fields or low-event density regions.