Properties of Voids and Void Galaxies in the TNG300 Simulation

The large-scale structure of the Universe is an interconnected network of walls, sheets, filaments, and galaxy clusters, between which lie vast regions of near nothingness known as cosmic voids (see, e.g., Giovanelli & Haynes 1991). The origin of the "cosmic web" dates back to the early Universe during the epoch of inflation, when quantum fluctuations near the end of the inflationary period gave rise to slight anisotropies in the post-inflation matter density field. These anisotropies are observed in the cosmic microwave background (CMB), with regions that deviate by a few microkelvin from the average CMB temperature (see, e.g., Planck Collaboration et al. 2020), and they are responsible for the structure that is seen in the cosmic web today.

Perturbations in the density field are unstable. Regions that are overdense experience an inward gravitational force, causing them to increase in density as they collapse and accrete surrounding matter (Bertschinger 1998). The opposite is true for regions that are initially underdense. Matter in these regions experiences an outward gravitational force that attracts it toward nearby, higher-density regions. As matter streams out, these regions become more underdense, increasing the relative outward gravitational pull and causing them to expand even further. Since these expanding regions never become virialized, their growth can always be modeled by linear perturbation theory (see, e.g., Goldberg & Vogeley 2004). Primordial overdensities in the post-inflation matter density field evolved in a bottom-up, hierarchical fashion consistent with cold dark matter (CDM) theory (see, e.g., Liddle & Lyth 1993), forming halos, clusters, walls, and filaments. Conversely, primordial underdensities expanded, becoming the voids.

Voids have properties that make them interesting regions for performing various cosmological tests (Sheth & van de Weygaert 2004), and the interiors of mature voids can be described as low-density Friedmann–Lemaître–Robertson–Walker universes (see, e.g., Icke 1984; van de Weygaert & van Kampen 1993). This makes voids excellent laboratories for tests of the expansion rate and geometry of the Universe, the dark energy equation of state, and modified theories of gravity (see, e.g., Li et al. 2012; Clampitt et al. 2013; Gibbons et al. 2014; Cai et al. 2015; Pollina et al. 2016; Cai et al. 2017; Falck et al. 2018; Paillas et al. 2019). Furthermore, since voids are smaller than the mean-free path of neutrinos (Lesgourgues & Pastor 2006), voids can be used to constrain the sum of neutrino masses via tests that examine the ways in which neutrino properties affect the sizes and distributions of voids (see, e.g., Villaescusa-Navarro et al. 2013; Massara et al. 2015; Banerjee & Dalal 2016; Kreisch et al. 2019; Schuster et al. 2019; Contarini et al. 2021).

Voids are not completely devoid of internal structure, and even the most mature voids in the local Universe show substructure in the form of galaxies and diffuse filaments (Szomoru et al. 1996; El-Ad & Piran 1997; Hoyle & Vogeley 2004; Sheth & van de Weygaert 2004; Kreckel et al. 2012; Alpaslan et al. 2014). The dynamical structure within voids can have significant impact on cosmic flow patterns in the local Universe, with matter around the ridges of voids affecting the peculiar motions of galaxies around nearby walls and filaments (see, e.g., Bothun et al. 1992; van de Weygaert 2016; Vallés-Pérez et al. 2021; Bermejo et al. 2022).

Additionally, the fact that voids resemble low-density universes with large Hubble parameters (see, e.g., Icke 1984; Goldberg & Vogeley 2004) makes void galaxies interesting objects with which to test models of galaxy formation and evolution. From linear theory, it is known that dark matter halos in underdense regions of the Universe form later in the history of the Universe than do their counterparts in overdense regions (Liddle & Lyth 1993). Therefore, studying the physical properties of void galaxies in the local Universe has the potential to provide insight into an early epoch of galaxy evolution.

Furthermore, the degree to which the location of a galaxy within the cosmic web affects the evolution of the galaxy is an open question. Some studies have concluded that, due to their differing dynamical histories, void galaxies differ systematically from nonvoid field galaxies (see, e.g., Peebles 2001; Croton et al. 2005; Kreckel et al. 2012; Rodríguez Medrano et al. 2022; Rosas-Guevara et al. 2022). For example, when compared to observed galaxies in walls and filaments, some studies have found that void galaxies are, on average, bluer in color, have lower stellar masses, are richer in H i, have higher specific star formation rates, and have later morphological types (see, e.g., Rojas et al. 2004; Croton et al. 2005; Hoyle et al. 2012; Kreckel et al. 2012; Beygu et al. 2016; Douglass et al. 2018; Florez et al. 2021; Pandey et al. 2021; Rodríguez Medrano et al. 2022). However, other studies have found little to no difference between the stellar masses, gas content, star formation rates, chemical abundances, dark matter profiles, or metallicities of void versus nonvoid field galaxies (see, e.g., Szomoru et al. 1996; Patiri et al. 2006; Moorman et al. 2014; Liu et al. 2015; Douglass & Vogeley 2017; Douglass et al. 2019; Wegner et al. 2019; Domínguez-Gómez et al. 2022).

The properties of void and nonvoid galaxies have also been studied in recent magnetohydrodynamical (MHD) simulations of Lambda cold dark matter (ΛCDM) universes. In agreement with some observational studies, Rosas-Guevara et al. (2022) found that, compared to galaxies in denser environments, void galaxies in the EAGLE simulation (Schaye et al. 2015) have lower stellar mass fractions. In addition, Rosas-Guevara et al. (2022) found clear trends of galaxy properties as a function of the distances of galaxies from the nearest void center. In particular, star formation activity and H i gas density decreased with increasing void-centric distance, and stellar mass fraction increased with increasing void-centric distance. Similarly, in a study of galaxies in the HorizonAGN simulation (Dubois et al. 2016), Habouzit et al. (2020) found that low-stellar-mass galaxies with high star formation rates occur more frequently in the inner regions of voids than in denser regions of the cosmic web.

Another open question involves the degree to which the location of a galaxy within the cosmic web influences the formation of active galactic nuclei (AGNs). Some studies have concluded that the AGN fraction of galaxies is independent of the local matter density (e.g., Karhunen et al. 2014; Sabater et al. 2015; Amiri et al. 2019; Habouzit et al. 2020), while others have found a positive correlation with local matter density (e.g., Manzer & De Robertis 2014; Argudo-Fernández et al. 2018). Still other studies have concluded that there is a negative correlation between AGN fraction and the local matter density (e.g., Kauffmann et al. 2004; Constantin et al. 2008; Platen 2009; Lopes et al. 2017; Mishra et al. 2021; Ceccarelli et al. 2022).

The relatively isolated nature of void galaxies suggests that their growth and evolution do not depend strongly on merger-driven nuclear activity. For example, Ceccarelli et al. (2022) found that the growth channels for void galaxies and their central, supermassive black holes (SMBHs) differed from those of their nonvoid counterparts. Ceccarelli et al. (2022) attribute this to the fact that, compared to the SMBHs in their nonvoid galaxies, the SMBHs in their void galaxies had larger surrounding O iii reservoirs that fed into the central regions of the galaxies. In contrast, however, Habouzit et al. (2020) found that void galaxies and their SMBHs in the HorizonAGN simulation grow in a manner that is similar to that of galaxies in denser environments, where merger-driven nuclear activity is common. Understanding the discrepancies between these results could further our understanding of the various ways in which nuclear activity is triggered, as well as the effects that cosmic flow patterns and mergers have on AGNs.

Here, we investigate the properties of voids and void galaxies in the z = 0 snapshot of the TNG300 simulation (hereafter TNG300; Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018; Pillepich et al. 2018; Springel et al. 2018). TNG300 is a cosmological MHD simulation of a ΛCDM universe with sufficient spatial and mass resolution within a large volume to conduct statistical analyses of voids and void galaxies. Using TNG300, we construct the largest catalog of luminous void galaxies within a cosmological MHD simulation to date. We compare various physical properties (sizes, colors, star formation rates, luminosity functions, mass functions, metallicities, and nuclear activity) of the void galaxies to those of galaxies found in walls and filaments. In addition, we examine the degree to which location within the cosmic web (i.e., within voids and outside voids) affects AGN activity.

This paper is organized as follows. TNG300 and our void-finding algorithm are discussed in Section 2. In Section 3, we present the properties of the voids and the void galaxies, and we compare the properties of void galaxies to nonvoid field galaxies. A summary and discussion of our results is presented in Section 4. Throughout, we compute error bars using 10,000 bootstrap resamplings of the data. Error bars are omitted from figures when the error bars are comparable to or smaller than the sizes of the data points.

2.1.  TNG300

2.2. Void Finder

2.3. Field Galaxy Sample

Our investigation of galaxy properties focuses on field galaxies (i.e., galaxies that reside outside cluster environments), subdivided according to whether the galaxies reside within a void ("void galaxies") or outside a void ("nonvoid galaxies"). We define field galaxies to be all galaxies that are not contained within parent halos with masses ≥10¹⁴ h⁻¹ M_⊙, which eliminates cluster galaxies from the sample. We then use the void catalog from Section 2.2 to separate void galaxies from nonvoid galaxies. From this, our field galaxy sample consists of 75,220 void galaxies and 527,454 nonvoid galaxies.

As part of our analysis, we investigate the relative ages of void and nonvoid galaxies. Even in simulation space, determining the formation time of a galaxy is not simple. This is due to the hierarchical nature of structure formation, which results in many smaller overdensities merging to form a single galaxy. Here, we adopt two indicators of galaxy age: (i) the age of the oldest bound stellar particle, and (ii) the luminosity-weighted age. For both of these age indicators, we use the subhalo cutout provided by the TNG, which contains all particles that are identified by the SUBFIND algorithm as being bound to the halo. The formation times of stellar particles are given as scale factors in the simulation, and we convert these to lookback times using the Planck Collaboration et al. (2016) cosmological parameters and the astropy.cosmology package (Astropy Collaboration et al. 2013, 2018).

The age of the oldest bound stellar particle is a useful indicator of the age of a simulated galaxy, but it is not straightforward to use as a comparison to observed galaxies. In contrast, the luminosity-weighted age is a metric that can be compared to observations (see, e.g., Li et al. 2018). To obtain luminosity-weighted ages of the simulated galaxies, we use the following equation from Lu et al. (2020):

$$\begin{eqnarray}&&\langle x\rangle =\displaystyle \frac{{\sum }_{k=1}^{N}{L}_{k}{x}_{k}}{{\sum }_{k=1}^{N}{L}_{k}},\end{eqnarray} \tag{ 1 }$$

where x_k is the logarithm (base 10) of the formation age of the kth particle and L_k is the SDSS r-band luminosity of the kth particle. Above, the summation is computed over all stellar particles that are bound to the subhalo.

3.1. Void Properties

Using the 3D SVF algorithm, a total of 5078 voids were identified. The void radii span an order of magnitude, with the smallest voids having radii of r_v = 2.5 h⁻¹ Mpc and the largest void having a radius of r_v = 24.7 h⁻¹ Mpc. The median void radius is 4.4 h⁻¹ Mpc. In total, voids cover a volume of 168.3³ h⁻³ Mpc³, or 82% of the simulation box. The number of voids as a function of radius is shown in Figure 1, from which it is clear that the majority of voids have radii ≲10 h⁻¹ Mpc.

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The mean radial number density contrast of the voids is shown in Figure 2. Squares show the result obtained using the luminous galaxies ("luminous density contrast") and crosses show the result obtained using the dark matter particles ("dark matter density contrast"). For each void, the density contrast in concentric spherical shells of thickness δ r, centered on the void center, was calculated as

$$\begin{eqnarray}&&{\rm{\Delta }}=\displaystyle \frac{n(r)}{\bar{n}(r)}-1,\end{eqnarray} \tag{ 2 }$$

where n(r) is the number of galaxies or dark matter particles within the radial bin that ranges from $r-\tfrac{\delta r}{2}$ to $r+\tfrac{\delta r}{2}$, and $\bar{n}(r)$ is the average number density of galaxies or dark matter particles within the simulation box. In both cases (i.e., luminous density contrast and dark matter density contrast), the mean radial density profiles resemble reverse spherical top-hat distributions, which are expected for underdense regions in the local Universe (see, e.g., Icke 1984; Sheth & van de Weygaert 2004). These profiles are characterized by an underdense, flat interior that rises steeply above the mean density at the ridge of a void and slowly decreases to the mean density at large distances from the void center.

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From Figure 2, it is clear that mass does not directly trace light within the voids. Rather, the mean central density contrast obtained from the galaxies (Δ = −0.77 ± 0.04) is somewhat lower than the mean central density contrast of the dark matter (Δ = −0.64 ± 0.02), i.e., the centers of the voids are more "devoid" of galaxies than they are of dark matter. The opposite is true at the ridges of the voids where, on average, there is a higher concentration of galaxies than dark matter, with the mean dark matter density contrast reaching a maximum of 0.33 ± 0.02 at r = 1.25r_v and the mean luminous density contrast reaching a maximum contrast of 0.42 ± 0.02 at r = 1.4r_v .

Voids form in regions of space with differing background densities (i.e., as compared to the average density of the Universe). That is, some voids form in regions of space that have relatively high local background densities ("voids in clouds"), while others form in regions of space that have relatively low local background densities ("voids in voids"); see Sheth & van de Weygaert (2004) for a discussion of void hierarchy. In Figure 3, we use mean integrated number density profiles to explore the effects of the local background density on the density contrast. For legibility of the figure, the number density profiles for the dark matter particles are shown as spline fits. Following Sheth & van de Weygaert (2004), we define voids-in-voids to be those with an integrated galaxy density contrast <0 at r = 3r_v and voids-in-clouds to be those with an integrated galaxy density contrast >0 at r = 3r_v . To construct the mean integrated density profiles, the number density contrast of the galaxies (points) and the dark matter particles (lines) was computed in concentric spheres of radius r, centered on each void center, from which means were then computed.

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The mean integrated number density profiles obtained using all voids (blue line and blue circles in Figure 3) show the same trends as the mean differential number density profiles in Figure 2. On average, the central regions of the voids have a dark matter density contrast that is 65% ± 2% lower than the average dark matter density contrast in the simulation and a galaxy density contrast that is 77% ± 4% lower than the average galaxy density contrast in the simulation. At the ridges of the voids, the mean interior density contrast for the galaxies reaches a maximum that is 22% ± 1% higher than the average galaxy density contrast at r = 2.08r_v and the mean interior density contrast for the dark matter reaches a maximum that is 18% ± 2% higher than the average dark matter density contrast at r = 2.25r_v .

For radii r ≲ r_v , the local background density in which the voids are located has relatively little effect on the integrated number density profiles of the galaxies and the dark matter. For radii r > r_v , however, significant differences for the integrated number density profiles of voids-in-voids (black line and green diamonds) and voids-in-clouds (yellow line and red crosses) occur. In the case of voids-in-voids, galaxies largely trace the dark matter for r ≳ r_v . At the ridges of voids-in-voids, the mean interior density contrast remains less than the average in the simulation (i.e., the mean interior density contrast is –0.20 ± 0.01 at the ridges) and for radii 1.5r_v ≲ r ≲ 4r_v the mean interior density contrast of voids-in-voids remains approximately constant at a value of ∼ −0.2. In the case of voids-in-clouds, the galaxies trace the dark matter for a small range of radii (r_v ≲ r ≲ 1.2r_v ), but are more overdense than the dark matter for r ≳ 1.2r_v . At the ridges of voids-in-clouds, the integrated number densities of the galaxies and dark matter exceed the integrated number densities of the galaxies and dark matter in the full void sample by a factor of ∼3 and they remain significantly higher than than the average density out to distances as large as ∼4r_v .

3.2. Properties of Void and Nonvoid Galaxies

Below, we investigate the following properties of void and nonvoid galaxies: (i) the distribution of physical sizes, (ii) optical color–magnitude relationships, (iii) luminosity and stellar mass functions, (iv) ages, (v) stellar and gas chemical abundances, (vi) specific star formation rates, and (vii) relationships between stellar mass and SMBH mass, as well as AGN fraction.

3.2.1. Physical Sizes

The TNG300 subhalo catalog defines the photometric radii of the galaxies to be the radii at which the surface-brightness profiles drop below 20.7 mag arcsec⁻¹ in the K band. We use this definition to compute normalized probability distributions for the radii of void and nonvoid galaxies, the results of which are shown in Figure 4. From this figure, the majority of the galaxies in both populations have radii ≲5 h⁻¹ kpc, and the probability of a given galaxy having a radius ≲5 h⁻¹ kpc is the same for both void and nonvoid galaxies. For galaxy radii ≳5 h⁻¹ kpc, the distribution of void galaxy radii declines much more steeply than the distribution of nonvoid galaxy radii. As a result, the largest void galaxies have radii ∼11 h⁻¹ kpc, while the largest nonvoid galaxies have radii that are ∼2 times larger than the largest void galaxies.

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3.2.2. Optical Color–Magnitude Relationships

Figure 5 shows the relationship between the (g − r) optical color and the absolute SDSS r-band magnitude, M_r , for nonvoid galaxies (panel b) and void galaxies (panel d). From these, it is clear that both void and nonvoid galaxies have distributions that peak in two locations: (i) intrinsically bright, red galaxies, and (ii) intrinsically faint, blue galaxies. Red crosses in panels (b) and (d) of Figure 5 indicate the locations of the peaks, and show that the peaks occur in similar locations of the (g − r) versus M_r space for both void and nonvoid galaxies. Formally, the blue peak occurs at (M_r , g − r) = (−14.77, 0.59) for the void galaxies and at (M_r , g − r) = (−14.76, 0.64) for the nonvoid galaxies, i.e., the blue peaks occur at identical absolute magnitudes but slightly different colors, with the void galaxies being somewhat bluer than the nonvoid galaxies near the blue peaks. The red peak occurs at (M_r , g − r) = (−20.47, 0.77) for the void galaxies and at (M_r , g − r) = (−20.55, 0.77) for the nonvoid galaxies, i.e., the red peaks occur at essentially identical absolute magnitudes and colors for both populations of galaxies.

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Panels (a) and (c) in Figure 5 show normalized probability distributions for the absolute r-band magnitudes of the nonvoid and void galaxies, respectively. From this, it is clear that the distributions differ signficantly, and this will be reflected in the luminosity functions of void and nonvoid galaxies below. Panel (e) in Figure 5 shows normalized probability distributions for the (g − r) colors of void galaxies (diamonds) and nonvoid galaxies (circles). From this, it is clear that, while both types of galaxies have a broad distribution of optical colors, the distributions are substantially different and, in particular, there is a much higher concentration of red, nonvoid galaxies than red, void galaxies.

We further explore the differences between the optical color distributions for void and nonvoid galaxies in Figure 6, which shows the cumulative probability distributions of (g − r) values for void galaxies (diamonds) and nonvoid galaxies (circles). A two-sample Kolmogorov–Smirnov (KS) test performed on the two distributions in Figure 6 rejects the null hypothesis that both distributions are drawn from the same underlying distribution at a high confidence level (>99.9999%), indicating that the distribution of void galaxy colors is significantly different from that of nonvoid galaxies. In particular, void galaxies are typically bluer than nonvoid galaxies, with the median (g − r) color of void galaxies being 0.4205 ± 0.0007 and the median (g − r) color of nonvoid galaxies being 0.4881 ± 0.0003.

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3.2.3. Luminosity and Stellar Mass Functions

Next, we compute luminosity functions and stellar mass functions for void and nonvoid galaxies. Figure 7 shows the luminosity functions, computed in terms of SDSS r-band absolute magnitude (i.e., the number of galaxies per magnitude per unit volume). Lines in Figure 7 show the best-fitting Schechter luminosity functions (Schechter 1976) of the form

$$\begin{eqnarray}\begin{array}{rcl}{\rm{\Phi }}(M){dM} & = & 0.4\mathrm{ln}(10)\,{{\rm{\Phi }}}_{* }\,{\left[{10}^{0.4({M}_{* }-M)}\right]}^{(1+\alpha )}\\ & \times & \exp \left[-{10}^{0.4({M}_{* }-M)}\right]{dM},\end{array}\end{eqnarray} \tag{ 3 }$$

where M_* is the absolute magnitude of an L_* galaxy.

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Overall, the luminosity functions of both void and nonvoid galaxies are fitted reasonably well by Schechter functions, though some deviation is apparent (particularly at the extreme ends of the luminosity functions). The parameters of the best-fitting Schechter functions are ϕ_* = (1.9 ± 0.2) × 10⁻³ Mpc⁻³, M_* = −20.5 ± 0.1 and α = −1.17 ± 0.03 (nonvoid galaxies), and ϕ_* = (1.7 ± 0.2) × 10⁻³ Mpc⁻³, M_* = −21.1 ± 0.1 and α = −1.11 ± 0.02 (void galaxies). Within the formal errors, the luminosity functions have characteristic bright galaxy absolute magnitudes, M_*, that differ significantly, i.e., L_*,r nonvoid galaxies are intrinsically ∼70% brighter than L_*,r void galaxies. However, the faint-end slopes of the luminosity functions, α, are consistent within 2σ.

Results for the differential stellar mass functions (i.e., the number of galaxies per log stellar mass bin per unit volume) of void and nonvoid galaxies are shown in Figure 8. For stellar masses between 10^7.25 h⁻¹ M_⊙ and 10^10.25 h⁻¹ M_⊙, the mass functions exhibit roughly power-law behaviors, with the slope of the power law being substantially shallower for nonvoid galaxies than it is for void galaxies. Below stellar masses of 10^7.25 h⁻¹ M_⊙, both mass functions fall below the power law due to the finite resolution of the simulation, which leads to undercounting of the smallest galaxies. Above stellar masses of 10^10.25 h⁻¹ M_⊙, both mass functions decrease sharply due to the fact that high-mass galaxies are relatively rare objects. From the high-mass ends of the mass functions, however, it is clear that the sample of nonvoid galaxies has a larger fraction of high-mass galaxies than does the void galaxy sample. The combined differences in the mass functions result in the median stellar mass for the void galaxies being a factor of ∼2 smaller than the median stellar mass for the nonvoid galaxies: (1.58 ± 0.01) × 10⁸ h⁻¹ M_⊙ versus (3.08 ± 0.01) × 10⁸ h⁻¹ M_⊙.

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3.2.4. Ages

Next, we quantify the ages of the void and nonvoid galaxies using two metrics: (i) the oldest stellar particles within the subhalos, and (ii) the luminosity-weighted ages of the galaxies (see Equation (1)). From this, the median age of the oldest stellar particles bound to the subhalos in the void galaxies is 10.1033 ± 0.0001 Gyr and the median age of the oldest stellar particles bound to the subhalos in the nonvoid galaxies is 10.10685 ± 0.00003 Gyr, i.e., the oldest stellar particles bound to the subhalos in the void galaxies are ∼3.6 Myr years younger than the oldest stellar particles in the nonvoid galaxies. In comparison, the median luminosity-weighted age of the void galaxies is 9.217 ± 0.002 Gyr and the median luminosity-weighted age of the nonvoid galaxies is 9.3642 ± 0.0009 Gyr, i.e., when using luminosity-weighted ages, we find that the void galaxies are ∼147 Myr younger than the nonvoid galaxies. Both age indicators reveal that void galaxies are systematically younger than nonvoid galaxies, but the age difference between void and nonvoid galaxies is reflected less by the time at which the first stars formed (i.e., the ages of the oldest stellar particles) than it is by the overall star formation histories of the galaxies (i.e., the luminosity-weighted ages). That being said, the difference between the median luminosity-weighted ages of void and nonvoid galaxies is too small to be detected in modern surveys, which report typical dispersions for luminosity-weighted ages of galaxy populations between 0.15 and 0.30 dex (see, e.g., González Delgado et al. 2014; Scott et al. 2017; Li et al. 2018; Lu et al. 2020).

3.2.5. Stellar and Gas Chemical Abundances

Results for the stellar and gas chemical abundance ratios are shown in Figures 9 and 10, respectively. Here, we subdivide the galaxy samples using four distinct stellar mass bins, the boundaries of which are M_* = 10^7.40 h⁻¹ M_⊙, 10^8.15 h⁻¹ M_⊙, 10^8.90 h⁻¹ M_⊙, 10^9.65 h⁻¹ M_⊙, and 10^10.40 h⁻¹ M_⊙. These are indicated by vertical, dashed blue lines in Figure 8. The panels in Figures 9 and 10 are arranged vertically in order of increasing stellar mass, such that panels (a) and (e) include only galaxies in the first bin, panels (b) and (f) include only galaxies in the second bin, panels (c) and (g) include only galaxies in the third bin, and panels (d) and (h) include only galaxies in the fourth bin. The left panels of Figures 9 and 10 show the average stellar and gas chemical abundance ratios, respectively. The right panels of Figures 9 and 10 show the ratios of the corresponding data points for void and nonvoid galaxies from the left panels.

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From Figures 9 and 10, void galaxies have stellar and gas metal fractions that are systematically lower than those of nonvoid galaxies. This result holds true across all stellar mass bins, but the differences are more pronounced for galaxies with lower stellar masses than they are for galaxies with higher stellar masses. That is, in order of increasing stellar mass, the stellar metallicities of nonvoid galaxies exceed those of void galaxies by ∼20% (Figure 9(e)), ∼8% (Figure 9(f)), ∼6.5% (Figure 9(g)), and ∼2.5% (Figure 9(h)). A similar, but less pronounced, trend is shown by the gas metallicities, i.e., in order of increasing stellar mass, the gas metallicities of nonvoid galaxies exceed those of void galaxies by ∼7.5% (Figure 10(e)), ∼4.5% (Figures 10(f) and (g)), and ∼2% (Figure 10(h)).

3.2.6. Specific Star Formation Rates

Results for the relationships between stellar mass and specific star formation rate (sSFR) are shown in Figure 11(b) (nonvoid galaxies) and Figure 11(c) (void galaxies). Here, the sSFRs are instantaneous rates, derived from the sum of star formation rates in individual gas cells at z = 0. From Figures 11(b) and (c), it is clear that both void and nonvoid galaxies show a main sequence of star formation. Normalized 1D probability distributions for M_* and sSFR are also shown in Figure 11 (top panels and side panel, respectively). Red crosses at (8.38, −9.45) in Figure 11(b) and (8.25, −9.40) in Figure 11(d) indicate the peak densities, which were determined from the relative maxima in the top and side panels.

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Figure 12 shows the normalized cumulative probability distribution functions for the sSFR of void and nonvoid galaxies. A two-sample KS test shows that the two distributions are not drawn from the same underlying distribution (confidence level >99.9999%). The median sSFR for void galaxies is 21.8% ± 0.5% higher than it is for nonvoid galaxies (${5.015}_{-0.018}^{+0.021}\,\times {10}^{-10}\,{\mathrm{yr}}^{-1}$ versus ${4.116}_{-0.008}^{+0.008}\times {10}^{-10}\,{\mathrm{yr}}^{-1}$); hence, per unit stellar mass, the void galaxies have star formation rates that are higher than those of the nonvoid galaxies.

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3.2.7. Supermassive Black Holes and Fraction of Active Galactic Nuclei

Finally, we investigate the relationships between stellar mass and SMBH mass for TNG300 void and nonvoid galaxies, the results of which are shown in Figure 13 (black points). SMBHs are "seeded" into TNG subhalos once the subhalos pass a given mass threshold, and this seeding of SBMHs gives rise to unphysical artifacts in the stellar mass–SMBH mass relationship for SMBH with masses below ∼3 × 10⁶ h⁻¹ M_⊙ (i.e., due to recently seeded SMBHs having nearly identical masses, independent of the stellar mass of their host galaxy). Therefore, we focus our analysis below on galaxies for which the masses of the SMBHs are ≳3 × 10⁶ h⁻¹ M_⊙, which results in a sample of 107,527 nonvoid galaxies and 10,231 void galaxies. We further subdivide these particular galaxies according to whether or not their SMBHs are in an active state. To do this, we use the ratio of Bondi accretion rate to Eddington accretion rate as a measure of nuclear activity. Following Weinberger et al. (2017), we classify galaxies with ratios greater than 0.05 as "active." From this classification, we find 1330 void galaxies with SMBH masses ≳3 × 10⁶ h⁻¹ M_⊙ are in an active state (i.e., an AGN fraction of 13.0% ± 0.4%) and 11,269 nonvoid galaxies with SMBH masses ≳3 × 10⁶ h⁻¹ M_⊙ are in an active state (i.e., an AGN fraction of 10.5% ± 0.1%). That is, for TNG300 galaxies with SMBHs in the mass range that we consider, void galaxies have a somewhat higher (24% ± 4%) AGN fraction than do nonvoid galaxies. We also note that it is primarily intermediate-mass SMBHs that are in an active state, since there are few TNG300 AGNs with SMBH masses ≳10⁸ h⁻¹ M_⊙ or ≲10^6.3 h⁻¹ M_⊙.

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The top panels in Figure 13 show the relationships for galaxies with an inactive SMBH, while the bottom panels show the relationships for galaxies with an active SMBH. Results for nonvoid galaxies are shown in the left panels of Figure 13, and results for void galaxies are shown in the right panels. The observed relationships between stellar mass and SMBH mass from Reines & Volonteri (2015) are also shown in Figure 13 for comparison (red stars, inactive SMBH; green crosses, active SMBH). Observational results for galaxies with an inactive SMBH come from a sample of galaxies with dynamical black hole masses (Table 3 of Reines & Volonteri 2015), and observational results for galaxies with an active SMBH come from a sample of broad-line AGNs (Table 1 of Reines & Volonteri 2015).

From Figure 13, the relationship between SMBH mass and stellar mass for TNG galaxies with inactive black holes is in rough agreement with the observational results from Reines & Volonteri (2015). For galaxies with inactive black holes that have masses ≳10⁷ h⁻¹ M_⊙, there is a tighter relationship between SMBH mass and galaxy stellar mass in the TNG300 galaxies than there is for observed galaxies. In contrast to observed galaxies, there are no TNG300 nonvoid galaxies with inactive black holes with masses >2 × 10⁹ h⁻¹ M_⊙ and no TNG300 void galaxies with inactive black holes with masses >7 × 10⁸ h⁻¹ M_⊙. In the case of nonvoid galaxies, inactive SMBHs with masses >2 × 10⁹ h⁻¹ M_⊙ do exist in the TNG300 simulation, but all of these objects are located within galaxies that reside in large clusters of galaxies (and all of which were omitted from our sample since the focus of our investigation is the field galaxy population).

Similar to the galaxies with inactive SMBHs, TNG300 galaxies with active black holes show a much tighter relationship between stellar mass and SMBH mass than do the observed galaxies from Reines & Volonteri (2015). However, while the slope of the relationship is similar to that of observed galaxies with AGNs, the amplitude of the relationship for TNG300 galaxies with AGNs is significantly higher than it is for observed galaxies. As a result, at fixed stellar mass, the SMBHs in TNG300 active galaxies are a factor of ∼10 more massive than would be expected based on the best-fitting relationship from Reines & Volonteri (2015; i.e., red dashed lines in Figure 13).

Here, we have investigated the properties of voids and void galaxies in the z = 0 snapshot of the cosmological MHD simulation TNG300. The large volume and high spatial resolution of TNG300 makes it possible to study a substantial number of voids and void galaxies.

Voids were identified using a spherical void-finding algorithm that was applied to the TNG300 galaxy catalog (i.e., in analogy to observational studies of voids and void galaxies, here the voids were identified via underdensities in the distribution of luminous galaxies, not the distribution of dark matter mass or dark matter halos). From this, a total 5078 voids with radii that range from 2.5 h⁻¹ Mpc to 24.7 h⁻¹ Mpc were identified. The median radius of the TNG300 voids is 4.4 h⁻¹ Mpc, in good agreement with the typical sizes of voids that have been found in TNG300 (Dávila-Kurbán et al. 2023) and in previous simulations that have computational volumes similar to that of TNG300 (see, e.g., Paillas et al. 2017; Habouzit et al. 2020).

As expected (see, e.g., Sheth & van de Weygaert 2004), the radial underdensity profiles of the TNG300 voids follow a reverse spherical top-hat profile. This is the case whether luminous tracers of the underdensity (i.e., luminous galaxies) or dark matter particles are used to compute the profiles.

Recently, Schuster et al. (2023) performed an in-depth study of void profiles in the Magneticum suite of cosmological MHD simulations (see, e.g., Dolag et al. 2016 and Hirschmann et al. 2014 for other studies that have used Magneticum). ² The authors find the density profiles of isolated voids to be similar for various void sizes, spatial resolutions, and mass scales. Their stacked, isolated, dark matter void profiles are similar to ours, although our dark matter profile (see Figure 2) has a flatter interior out to r = r_v . However, since we do not investigate void profiles as functions of void shape or size, it is difficult to make direct comparisons. Regardless, the similarities to our galaxy number density profile corroborate their conclusion that the physical properties of voids are universal characteristics that are independent of tracer type and resolution.

Dávila-Kurbán et al. (2023) obtained integrated galaxy number density profiles for "voids-in-clouds" and "voids-in-voids" ("S-type" and "R-type" voids in their notation) in TNG300. To obtain their void catalog, Dávila-Kurbán et al. (2023) used the void-finding algorithm of Ruiz et al. (2015), a modified version of the void-finding algorithm that we employed, but with a few differences. Dávila-Kurbán et al. (2023) considered candidate void centers as Voronoi cells constructed in the subhalo field that had density contrasts <−0.8; Dávila-Kurbán et al. (2023) also adopted a stricter integrated underdensity contrast threshold of Δ_void ≤ −0.9 for their candidate voids. In addition, Dávila-Kurbán et al. (2023) did not allow for any overlap between voids; instead, they rejected all spheres that overlapped already established, larger voids. Because of this, Dávila-Kurbán et al. (2023) identify far fewer voids in TNG300 than we do here (82 voids versus 5078 voids), and the radii of their voids are restricted to a much narrower range than the radii of the voids in this work (7–11 h⁻¹ Mpc versus 2.5–24.7 h⁻¹ Mpc). Because of the differences in void-finding algorithms and size ranges of the resulting voids, we would expect some differences between our results and those of Dávila-Kurbán et al. (2023); and, indeed, this is the case when we compare the two catalogs of "voids-in-clouds." In particular, the ridges of profiles for "voids-in-clouds" in Dávila-Kurbán et al. (2023) only reach maxima up to ∼0.3, which is considerably lower than the maximum for our median profile (i.e., 0.6). However, the profiles of "voids-in-voids" in Dávila-Kurbán et al. (2023) are similar to the luminous profiles that we find for our "voids-in-voids."

In the observed Universe, Sánchez et al. (2017) provide 2D photometric galaxy number density profiles for voids in the Dark Energy Survey (DES; Flaugher 2005; Dark Energy Survey Collaboration et al. 2016). These voids were found with a circular void finder, and utilized projected density maps of various thicknesses. Much like our voids, the interiors of DES voids are nearly empty of galaxies. However, the DES voids do not have flat interiors and gradually increase in density out to the ridges of voids. It is unclear whether this is due to projection effects caused by using 2D spectroscopic slices.

Furthermore, several authors have provided void galaxy cross-correlation functions for large voids in various SDSS, SDSS Baryon Oscillation Spectroscopic Survey (BOSS; Dawson et al. 2013), and SDSS extended BOSS (eBOSS; Alam et al. 2021) data releases (see, e.g., Nadathur et al. 2019; Hamaus et al. 2020; Woodfinden et al. 2022). For instance, Nadathur et al. (2019) and Woodfinden et al. (2022) report voids with very empty and flat interiors (ξ₀ ∼ −1.0) out to around 20 h⁻¹ Mpc that reach maxima of ξ₀ ∼ 0.05 at ∼60R_v. In addition, Hamaus et al. (2020) report values of ξ₀ that rise from ∼−0.90 in the innermost regions to −0.55 by 0.5R_v and 0.2 at 1R_v. Thus, the innermost regions of our TNG300 voids appear to have a higher galaxy density than those in the observed Universe, but their profiles rise more gradually out to the effective radii of voids. Despite this, the ridges of TNG300 voids have a higher overdensity of galaxies not seen in the observed Universe.

In terms of the detectability of our voids, the small size of most of our voids means their average galaxy number density is orders of magnitudes larger than what is available in most current observational surveys. For instance, we report an average galaxy number density of TNG300 voids of 9.4 × 10⁻² h³ Mpc⁻³, whereas Mao et al. (2017) found an average galaxy number density of 3.6 × 10⁻⁴ h³ Mpc⁻³ in their SDSS BOSS Data Release 12 void member catalogs. Because of this, it is unlikely that the smaller voids we report would be detected in current-generation surveys.

We find that the TNG300 voids are more devoid of galaxies than they are of dark matter, and this result is independent of the local background density within which the voids are embedded (i.e., voids-in-voids versus voids-in-clouds). That is, within the voids, mass does not trace light. This result agrees with previous studies that have compared luminous tracers within voids to the underlying dark matter field (see, e.g., Ricciardelli et al. 2014; Pollina et al. 2017). In particular, Pollina et al. (2017) used the Magneticum suite to test the linearity of the bias of luminous tracers compared to the underlying dark matter field. There, the authors found a linear relationship between the density contrast of tracers and the density contrast of dark matter within voids when galaxies, clusters, or AGNs are used as tracers.

In addition, we note that previous work on the locations of satellite galaxies in the Illustris-1 (Vogelsberger et al. 2014a, 2014b; Genel et al. 2014; Sijacki et al. 2015) and TNG100 simulations have demonstrated that mass does not trace light in host-satellite systems (see, e.g., Brainerd 2018; McDonough & Brainerd 2022). Hence, the distribution of luminous galaxies in a ΛCDM universe is an unreliable tracer of the dark matter distribution in overdense regions of space. However, the linear bias between the galaxy and dark matter distributions in underdense regions still makes galaxies valuable probes of the density field within the linear regime of voids.

In TNG300, we identified a total of 75,220 void galaxies and 527,454 nonvoid field galaxies, and systematic differences between the void and nonvoid galaxies are clear. Compared to the nonvoid galaxies, the void galaxies are, on average, younger, bluer in color, less metal enriched, have lower stellar masses, and have smaller physical extents. The luminosity functions of both void and nonvoid galaxies exhibit similar faint-end slopes, but the luminosity of an L_* nonvoid galaxy is ∼70% greater than the luminosity of an L_* void galaxy, consistent with void galaxies being smaller and less massive than nonvoid galaxies on average. In addition, void galaxies have a somewhat higher sSFR than nonvoid galaxies and, in the case of galaxies with central SMBHs with masses ≳3 × 10⁶ h⁻¹ M_⊙, void galaxies have a somewhat higher AGN fraction than nonvoid galaxies. These results are in agreement with previous studies that find void galaxies to be bluer, lower in stellar mass, and less metal enriched than nonvoid galaxies (see, e.g., Rojas et al. 2004; Florez et al. 2021; Rosas-Guevara et al. 2022) and that concluded AGN fraction is not strongly dependent upon the local matter density of a galaxy (see, e.g., Carter et al. 2001; Karhunen et al. 2014; Habouzit et al. 2020).

The relationship between central SMBH mass and host-galaxy stellar mass was also investigated. In the case of TNG300 galaxies with inactive SMBHs, the SMBH mass–stellar mass relationships of void and nonvoid galaxies is in rough agreement with results obtained by Reines & Volonteri (2015) for observed galaxies. However, for galaxies with SMBH masses ≳10⁷ h⁻¹ M_⊙, the SMBH mass–stellar mass relationship is considerably tighter for TNG300 galaxies than it is for observed galaxies. A relationship between SMBH mass and stellar mass that is tighter for TNG300 galaxies than observed galaxies is also shown by void and nonvoid TNG300 galaxies with active central black holes. In both cases, the tightness of the relationship for simulated galaxies may simply be reflective of the relative ease with which both parameters can be obtained in simulation space. Lastly, while the slopes of the SMBH mass–stellar mass relationships for active TNG300 void and nonvoid galaxies agree well with those of observed galaxies, at fixed stellar mass the SMBHs in active TNG300 galaxies are ∼10 times more massive than would be expected based on the best-fitting relationship from Reines & Volonteri (2015).

The lower host-galaxy stellar masses and higher SMBH masses of TNG300 AGNs compared to those of Reines & Volonteri (2015) could be caused by several factors. For example, in TNG300, a SMBH of mass 6.2 × 10⁶ M_⊙ is seeded into any friends-of-friends halo whose mass exceeds 7.3 × 10¹⁰ M_⊙, which is based on the host–halo relationship of Di Matteo et al. (2008) and Sijacki et al. (2009). This initial mass could be too large, resulting in more massive SMBHs in TNG300 by z = 0.0. This would, however, also affect the relationships in the top panels of Figure 13. Another explanation could involve the AGN feedback models in TNG300, which describe how energy is injected into the galaxies and circumgalactic medium (CGM). Zinger et al. (2020) find the AGN feedback channel of TNG300 AGNs to be both highly "ejective" and "preventative." This means the AGN state is highly efficient at expelling star-forming gas from the galaxy and increasing the entropy of the CGM, which strongly quenches future star formation within the galaxy. Therefore, if the feedback injection is over-tuned, or if TNG300 galaxies spend too long in their "active" state, this could cause the host-galaxy stellar masses of TNG300 AGNs to be lower than those of Reines & Volonteri (2015).

Our results for the systematic differences between void and nonvoid galaxies in the TNG300 simulation are consistent with the expectation that the two populations of galaxies underwent somewhat different evolutionary paths, with nonvoid galaxies forming in regions of space that had both higher gas densities and higher galaxy densities than void galaxies. In a universe in which structure forms hierarchically, this naturally leads to nonvoid galaxies forming earlier than void galaxies (i.e., due to biased galaxy formation in which the highest peaks collapse first) and becoming larger on average than void galaxies (i.e., due to both a larger local reservoir of gas and a higher frequency of galaxy collisions outside the voids). Here, we have investigated void and nonvoid galaxy properties in a single simulation snapshot (corresponding to the present epoch) and, therefore, we cannot make definitive statements about the degree to which the evolutionary paths of the TNG300 void and nonvoid galaxies differed, and the ways in which those differences affected their physical properties at z = 0. Further work, concentrated on the details of the evolution of void and nonvoid galaxies over cosmic time, will be necessary to establish and quantify differences in the evolutionary paths and the resulting effects on the natures of the two populations of galaxies.

We are grateful to the anonymous reviewer for helpful comments and suggestions that improved the manuscript. This work was partially supported by National Science Foundation grant AST-2009397. The IllustrisTNG simulations were undertaken with compute time awarded by the Gauss Centre for Supercomputing (GCS) under GCS Large-Scale Projects GCS-ILLU and GCS-DWAR on the GCS share of the supercomputer Hazel Hen at the High Performance Computing Center Stuttgart (HLRS), as well as on the machines of the Max Planck Computing and Data Facility (MPCDF) in Garching, Germany. In addition, we are pleased to acknowledge that the computational work reported on in this paper was performed on the Shared Computing Cluster, which is administered by Boston University's Research Computing Services.