VEGA: Voids idEntification using Genetic Algorithm

TL;DR

VEGA addresses the lack of a universal, geometry-dependent void definition by integrating Voronoi tessellation and convex-hull volume estimation with a Genetic Algorithm that optimizes a three-component objective: background volume fraction $V_b$, mean neighbor distance $\bar{d}_{nn}$, and luminosity-density contrast $\delta_{L_{ch}}$. It introduces grid points treated as zero-luminosity tracers to regularize cell shapes and a background luminosity density that scales with grid spacing $d_G$, enabling robust identification of void-block cells and subsequent seed-based void construction. When tested on Millennium-based galaxy distributions and compared with the Aikio–Mahonen method, VEGA yields coherent void catalogs with meaningful density and shape statistics, demonstrating reliability across tracer distributions. This approach provides a flexible, non-strictly geometric void finder that can be applied to simulations and potentially observational data, contributing to multi-probe cosmological analyses and void-based cosmological tests.

Abstract

Cosmic voids are large, nearly empty regions that lie between the web of galaxies, filaments and walls, and are recognized for their extensive applications in the field of cosmology and astrophysics. Despite their significance, a universal definition of voids remains unsettled as various void-finding methods identify different types of voids, each differing in shape and density, based on the method that were used. In this paper, we present VEGA, a novel algorithm for void identification. VEGA utilizes Voronoi tessellation to divide the dataset space into spatial cells and applies the Convex Hull algorithm to estimate the volume of each cell. It then integrates Genetic Algorithm analysis with luminosity density contrast to filter out over-dense cells and retain the remaining ones, referred to as void block cells. These filtered cells form the basis for constructing the final void structures. VEGA operates on a grid of points, which increases the algorithm's spatial accessibility to the dataset and facilitates the identification of seed points around which the algorithm constructs the voids. To evaluate VEGA's performance, we applied both VEGA and the Aikio Mähönen method to the same test dataset. We compared the resulting void populations in terms of their luminosity and number density contrast, as well as their morphological features such as sphericity. This comparison demonstrated that the VEGA void finding method yields reliable results and can be effectively applied to various particle distributions.

Figures (3)

• Figure 1: The effect of adding grid points with different $d_G$ values is illustrated. The rows from top to bottom correspond to $d_G$ values of 5, 4, 3, and no grids respectively. (Left Column) A slice of the projected galaxy distribution is shown in red, with the added grid points displayed in blue. (Right Column) The impact of using grid points alongside galaxies on the Voronoi diagrams is shown. Hatched cells are those with one or more vertices located outside the dataset boundaries and are excluded from further analysis. Cells colored in gray represent marginal cells that are adjacent to the dataset boundary.
• Figure 2: Results of the Genetic Algorithm analysis are shown, with the rows from top to bottom corresponding to $d_{G}$ values of 5, 4, 3, and to the case without grids, respectively. (Left) column displays the Voronoi cells associated with galaxies and grid points. (Middle) column presents the GA results after post-processing corrections, where cells identified as void block cells are colored in grey. (Right) column illustrates the final void identified by VEGA, with the corresponding cells colored in grey. Galaxies are shown in red, and grid points in blue.
• Figure 3: (Left Panel) displays median trends and associated errors for void sphericity ($\Theta$) versus radius ($R_{\mathrm{void}}$). (Right Panel) shows the median trends and errors between luminosity density contrast ($\delta_{L}$) and number density contrast ($\delta_{N}$). Histograms of these parameters are displayed alongside the median plots. Results are presented for VEGA runs with varying grid spacings $d_{G}$, alongside the results obtained using the AM method.