Delfin++: A Delaunay based algorithm for finding 3D polyhedral voids in galaxy surveys

Abstract

Delfin++ (Delaunay Edge Void Finder) is a simple and time-efficient algorithm, with a single input variable, designed to find cosmological voids within a 3-dimensional distribution of galaxies by characterizing them as polyhedral regions from a Delaunay tessellation. Two density metrics are defined and used to search for density minima and construct polyhedra that represent the underdense zones. A density threshold is used to define the limit above which a galaxy will not be considered part of a void. This threshold is commonly defined as 0.2n̄, where n̄ is the mean point density of the sample, whereas the values used in this work range from 0.2n̄ to 0.33n̄. The algorithm is applied to artificial data, with different density contrasts, as well as to galaxy data from SDSS DR10. The detected voids are compared with voids that have been produced through the application of vide. Our algorithm detects roundish underdense regions in the galaxy samples, with differences and overlaps compared to the vide algorithm’s results. Closer agreement is revealed when the edge length density metric is used over large galaxy samples, allowing for the detection of up to 90% of the largest vide voids. We measure ellipticities of Delfin++ detected voids and find that their distribution is shifted towards smaller values in comparison with vide’s distribution, and with predictions from an analytical model. The voids found with Delfin++ are not intended to generate a catalog, but rather represent a proof of concept of a simpler algorithm or with fewer rules for further calibration and future production of a final catalog. Delfin++ performance tests suggest that enhanced characterization of voids can be achieved through (i) choice of other density threshold values, and (ii) early recognition and rejection of deformed polyhedra induced by missing data.