The Galaxy Bias Profile of Cosmic Voids:A Comparison of Void Finders

TL;DR

This work investigates how the environmental modulation of individual galaxy bias $b_i$ inside cosmic voids depends on the void identification method. Using the IllustrisTNG $TNG300$ simulation at $z=0$, five void finders—sparkling, zobov, revolver-voxel, revolver-zobov, and popcorn—are applied to the same galaxy sample to derive $b_i$ profiles as a function of void-centric distance and of the normalized distance $R/R_{ m max}$. The study finds that the radial bias gradient is a robust feature across most finders, with density-threshold voids preferentially selecting anti-biased galaxies ($b_i<0$) and watershed voids including more high-bias boundary galaxies; relaxing the density threshold enhances the presence of strongly anti-biased tracers, especially for popcorn. Normalizing distances by $R_{ m max}$ reveals a broadly universal void-bias profile shape across definitions, supporting its use in void-based cosmological analyses and demonstrating that the observed environmental modulation of galaxy bias is intrinsic to void dynamics rather than an artifact of a particular void finder.

Abstract

Cosmic voids, the largest underdense regions in the Universe, provide unique laboratories for studying galaxy formation and constitute powerful probes of cosmology. Recent work has shown that individual galaxy bias (b_i), which quantifies how each galaxy traces the underlying dark matter field, exhibits a characteristic radial dependence within spherical voids, defining a void bias profile in which galaxies near void centers display systematically lower bias values. We investigate how the environmental modulation of individual galaxy bias depends on the adopted void-finding algorithm by comparing measurements across five distinct void definitions: spherical voids 'sparkling', watershed-based methods ('zobov' and 'revolver' in two modes), and free-form integrated-density voids ('popcorn'). We apply these complementary void-finding algorithms to the same galaxy sample drawn from the IllustrisTNG simulation (TNG300-1 at $z=0$) and compute individual galaxy bias profiles as a function of distance from void centers. We quantify the correlation between b_i and the membership of the void catalogs and explore how this relationship varies with the integrated underdensity threshold for density-based methods. We find that the radial gradient of individual bias within voids, generally increasing from negative values at the void centers to higher values at the boundaries, is robust across most void definitions. However, density-threshold methods preferentially select galaxies with b_i<0, while watershed methods without density constraints include substantial contamination from high-bias boundary galaxies. The correlation between negative bias and void membership is systematically strengthened as the integrated underdensity threshold becomes less restrictive, with popcorn achieving the highest purity in isolating anti-biased populations.

Figures (7)

• Figure 1: Comparison of the five void catalogs used in this work. The top panel shows the void size function for each voids catalog. The bottom panel shows the normalized distribution of the integrated density contrast, $\Delta$, for these same catalogs.
• Figure 2: Example slice of the TNG300 simulation box ($10h^{-1}{\rm Mpc} < z < 20h^{-1}{\rm Mpc}$) illustrating the galaxies belonging to voids (squares) and the boundaries that define them are colored by the five distinct void finders. Galaxy positions (scatter points) are color-coded by their individual large-scale galaxy bias, ranging from blue (lowest bias) to red (highest bias), like shows in the color bar.
• Figure 3: Comparison of the individual bias distribution in galaxies of the five void catalogs used in this work, as indicated in the key figure. The gray shaded region represent the $b_i$ distribution on the complete TNG300 galaxies catalog.
• Figure 4: Relationship between the distance $R$ of voids galaxies to their corresponding center and $\langle b_i \rangle$. Top panel: normalized distribution of $R$ for each void catalog. Bottom panel: $\langle b_i \rangle$ profile in function of $R$ for each void catalog.
• Figure 5: Relationship between the normalized distance $R/R_{\rm max}$ of voids galaxies to their corresponding center and $\langle b_i \rangle$, where $R_{\rm max}$ represents the highest distance of a tracer to the center of their host void. Top panel: normalized distribution of $R/R_{\rm max}$ for each void catalog. Bottom panel: $\langle b_i \rangle$ profile in function of $R/R_{\rm max}$ for each void catalog. The dotted lines show the linear fit corresponding to each sample.