Robustness of cosmic void statistics: insights from SDSS DR7 and the ELUCID simulation

Abstract

We present a systematic analysis of the statistical properties of cosmic voids using galaxies from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and subhaloes from the ELUCID constrained simulation. By comparing voids identified in redshift space, real space, and reconstructed volumes, we assess the impact of redshift-space distortions (RSD) and tracer bias. Using the \texttt{VAST} toolkit, we apply both the geometry-based \texttt{VoidFinder} algorithm and watershed-based methods. We find that void properties are not equally robust. The three-dimensional morphology of voids, quantified by their sphericity and triaxiality, remains stable across different reconstructions and tracer selections. In contrast, void size distributions and radial density profiles depend strongly on the identification algorithm, with watershed-based methods systematically producing larger voids and higher compensation walls than \texttt{VoidFinder}. Using the full ELUCID simulation box, we show that tracer bias mainly affects void density profiles, with noticeable changes only for the most massive subhaloes ($>10^{11.5}\,h^{-1}{\rm M}_\odot$). The agreement between SDSS observations, the ELUCID reconstruction, and the full simulation box demonstrates the high fidelity of constrained simulations and reveals a clear hierarchy in the robustness of void statistics.

Figures (10)

• Figure 1: Illustration of the volume-limited sample selection for SDSS galaxies. The rectangular region in the redshift--absolute magnitude plane defines the sample boundaries: $0.01 \le z \le 0.12$ and $^{0.1}M_r - 5 \log h < -20.09$. The vertical line at $z=0.12$ represents the redshift completeness limit corresponding to the chosen luminosity threshold.
• Figure 2: Distribution of void effective radii $r_{\mathrm{e}}$ identified with VoidFinder (left) and REVOLVER (right) for SDSS DR7 galaxies (real and redshift space) and ELUCID simulation subhaloes in the reconstructed volume. The top panels show number counts, while the bottom panels show the corresponding probability density functions (PDFs). The mean radius $\langle r_{\rm e} \rangle$ for each sample is indicated in the bottom panels with its standard error of the mean.
• Figure 3: Comparison of the PDFs of void effective radii measured in the full ELUCID simulation box and in the reconstructed volume. The reconstructed volume reproduces the geometry and volume of the observational sample, while the full simulation box represents the entire computational domain.
• Figure 4: Dependence of void effective radii on subhalo mass in the full ELUCID simulation box. The top panels show differential number counts, while the bottom panels show the PDFs of void effective radii $r_{\mathrm{e}}$. Left and right columns correspond to results from VoidFinder and REVOLVER, respectively. Four subhalo mass bins are shown (see legends), each containing an equal number of haloes.
• Figure 5: Comparison of void sphericity ($s$, left panels) and triaxiality ($T$, right panels) measured with three different watershed-based algorithms. The rows from top to bottom correspond to the REVOLVER, VIDE, and ZOBOV methods, respectively. Within each panel, the distributions are compared across three samples: SDSS redshift space, SDSS real space, and the reconstructed volume, shown as solid, dashed, and dash-dotted lines. All voids satisfy a radius cut of $r_{\mathrm{e}} \geq 10\,h^{-1}\,\mathrm{Mpc}$.