The Voronoi tessellation method in astronomy

The Voronoi tessellation is a natural way of space segmentation, which has many applications in various fields of science and technology, as well as in social sciences and visual art. The varieties of the Voronoi tessellation methods are commonly used in computational fluid dynamics, computational geometry, geolocation and logistics, game dev programming, cartography, engineering, liquid crystal electronic technology, machine learning, etc. The very innovative results were obtained in astronomy, namely for a large-scale galaxy distribution and cosmic web pattern, for revealing the quasi-periodicity in a pencil-beam survey, for a description of constraints on the isotropic cosmic microwave background and the explosion scenario likely supernova events, for image processing, adaptive smoothing, segmentation, for signal-to-noise ratio balancing, for spectrography data analysis as well as in the moving-mesh cosmology simulation. We briefly describe these results, paying more attention to the practical application of the Voronoi tessellation related to the spatial large-scale galaxy distribution.Comment: 24 pages, 6 figures, accepted to Intelligent Astrophysics, Eds. I. Zelinka, D. Baron, M. Bresci

Cosmic voids detection without density measurements

Cosmic voids are effective cosmological probes to discriminate among competing world models. Their identification is generally based on density or geometry criteria that, because of their very nature, are prone to shot noise. We propose two void finders that are based on dynamical criterion to select voids in Lagrangian coordinates and minimise the impact of sparse sampling. The first approach exploits the Zel'dovich approximation to trace back in time the orbits of galaxies located in voids and their surroundings, the second uses the observed galaxy-galaxy correlation function to relax the objects' spatial distribution to homogeneity and isotropy. In both cases voids are defined as regions of the negative velocity divergence, that can be regarded as sinks of the back-in-time streamlines of the mass tracers. To assess the performance of our methods we used a dark matter halo mock catalogue CoDECS, and compared the results with those obtained with the ZOBOV void finder. We find that the void divergence profiles are less scattered than the density ones and, therefore, their stacking constitutes a more accurate cosmological probe. The significance of the divergence signal in the central part of voids obtained from both our finders is 60% higher than for overdensity profiles in the ZOBOV case. The ellipticity of the stacked void measured in the divergence field is closer to unity, as expected, than what is found when using halo positions. Therefore our void finders are complementary to the existing methods, that should contribute to improve the accuracy of void-based cosmological tests.Comment: 12 pages, 18 figures, accepted for publication in MNRA

Low-Density Structures in the Local Universe. II. Nearby Cosmic Voids

We present the results of the search for spherical volumes containing no galaxies with luminosities brighter than the Magellanic Clouds in the Local Supercluster and its vicinity. Within a distance of 40 Mpc from us, 89 cosmic voids were discovered with the diameters of 24 to 12 Mpc, containing no galaxies with absolute magnitudes brighter than M_K < -18.4. A list of these voids and the sky distribution maps are given. It was found that 93% of spherical voids overlap, forming three more extended percolated voids (hypervoids). The largest of them, HV1, has 56 initial spherical cells and extends in a horseshoe shape, enveloping the Local Volume and the Virgo cluster. The Local Void (Tully, 1988) in the Hercules-Aquila region is the closest part of the HV1. Another hypervoid, HV2, contains 22 spherical voids in the Eridanus constellation, and the third compact hypervoid (HV3) comprises 6 spherical cells in the Bootes. The total volume of these voids incorporates about 30% of the Local Universe. Among 2906 dwarf galaxies excluded from the original sample (n = 10502) in the search for spherical volumes, only 68 are located in the voids we have discovered. They are characterized by late morphological types (85% are Ir, Im, BCD, Sm), absolute magnitudes M_B ranging from -13.0 to -16.7, moderate star formation rates (log SSFR ~ -10 M_sun/(yr*L_sun) and gas reserves per luminosity unit twice to three times larger than in the other dwarf galaxies located in normal environments. The dwarf population of the voids shows a certain tendency to sit shallow near the surfaces of cosmic voids

Cosmic voids detection without density measurements

Cosmic voids are effective cosmological probes to discriminate among competing world models. Their identification is generally based on density or geometry criteria that, because of their very nature, are prone to shot noise. We propose two void finders that are based on dynamical criterion to select voids in Lagrangian coordinates and minimize the impact of sparse sampling. The first approach exploits the Zel'dovich approximation to trace back in time the orbits of galaxies located in voids and their surroundings; the second uses the observed galaxy-galaxy correlation function to relax the objects' spatial distribution to homogeneity and isotropy. In both cases voids are defined as regions of the negative velocity divergence, which can be regarded as sinks of the back-in-time streamlines of the mass tracers. To assess the performance of our methods we used a dark matter halo mock catalogue CODECS, and compared the results with those obtained with the ZOBOV void finder. We find that the void divergence profiles are less scattered than the density ones and, therefore, their stacking constitutes a more accurate cosmological probe. The significance of the divergence signal in the central part of voids obtained from both our finders is 60 per cent higher than for overdensity profiles in the ZOBOV case. The ellipticity of the stacked void measured in the divergence field is closer to unity, as expected, than what is found when using halo positions. Therefore, our void finders are complementary to the existing methods, which should contribute to improve the accuracy of void-based cosmological tests