Evolution of Cosmic Voids: Structure, Galaxies, and Dynamics

Abstract

We investigate the structural, photometric, and dynamical evolution of cosmic voids and their galaxy populations from $z=2.09$ to the present, focusing on void size as a key evolutionary parameter. Using void catalogs from four Millennium Simulation snapshots and SDSS data at $z<0.04$, we perform a unified analysis of void demographics, galaxy properties, and internal kinematics. Our analysis reveals clear evidence that cosmic voids exhibit a significant evolutionary trend of becoming progressively emptier toward low redshift, accompanied by a marked decline in the brightness and clustering of their galaxy populations. The void galaxy luminosity function evolves significantly: $M^{*}$ fades and $α$ flattens with time, with large voids hosting brighter, more rapidly evolving galaxies than small voids. Stacked density profiles exhibit a universal shape when scaled by void radius, deepening and building more pronounced walls toward $z=0$. Galaxy spatial distributions reveal persistent size-dependent segregation, with galaxies in large voids lying farther from the center and more strongly clustered. Dynamical analysis of simulations shows coherent outward flows in all voids, with amplitudes decreasing toward $z=0$, providing a physical basis for observed redshift-space distortions. Comparison with SDSS broadly confirms these evolutionary trends but uncovers a non-zero central galaxy population in observed voids -- absent in $Λ$CDM predictions -- that may challenge current galaxy formation models in extreme underdensities. Future comparisons with additional simulations and deeper high-redshift surveys will provide stronger tests of $Λ$CDM in the most underdense regions.

Figures (7)

• Figure 1: Statistical overview of our void catalogs: distributions of void galaxy counts, effective radii, and density contrasts at four simulation redshifts ($z=0.0,\,0.51,\,1.01,\,2.09$) together with the observational sample at $z\sim0$.
• Figure 2: Top: mean number of galaxies per void as a function of void effective radius $R_{v}$. Bottom: mean density contrast $\langle\delta_{v}\rangle$ versus $R_{v}$. Points denote bin-averaged values and vertical bars indicate the standard error of the mean ($\pm 1\sigma$). Note that $\delta_{v}$ is computed relative to the sample background density ($\rho_{b}\sim 0.011$) for SDSS and ($\rho_{b}\sim 0.039$) for the simulation); this difference contributes to the apparent offset between the datasets.
• Figure 3: Left: Galaxy luminosity functions for void galaxies in the Small, Large, and All samples across four simulation redshift bins, with the SDSS $z\!\sim\!0$ measurements overplotted for comparison. Right: Redshift evolution of the best-fit Schechter parameters $M^*$ and $\alpha$ for the simulated samples, highlighting systematic trends with void size and the offset between simulations and observations at $z\!\sim\!0$.
• Figure 4: A statistical overview of our void catalog, showing the distributions of void effective radius, density contrast, and galaxy count across four simulation snapshots ($z = 0.0$, $0.5$, $1.0$, and $2.0$). For comparison, the corresponding SDSS measurements at $z\!\sim\!0$ are overplotted to provide an observational benchmark.
• Figure 5: Mean values of the center--distance and mean--distance parameters for galaxies residing in small and large voids. The curves show the results from four simulation snapshots, while the $z\!\sim\!0$ observational measurements are overplotted for comparison. Error bars represent the $1\sigma$ standard deviation of each distribution.