Void Galaxies Follow a Distinct Evolutionary Path in the Environmental COntext Catalog

The ECO catalog, a survey of ∼13,000 "local" galaxies with z ≤ 0.023, is the sample considered for this work (see Moffett et al. 2015 for original survey catalog description and Eckert et al. (2016) for updated catalog photometry and galaxy properties). ECO was constructed to act as a "context survey" for the RESOLVE) survey (S. J. Kannappan et al. in preparation; Eckert et al. 2015; Stark et al. 2016) in order to calibrate the effects of cosmic variance in large-scale structure. The goal of RESOLVE is to survey and study the stellar mass, baryonic mass, gas-to-stellar mass ratio, star formation, and dynamical mass of galaxies in a volume-limited census in the local universe by combining photometric and spectroscopic data spanning multiple wavelength regimes.

The ECO region spans a R.A. range between 130.05 and 237.45°, a decl. range between −1 and 49.85°, and a line-of-sight velocity range between 2530 and 7470 km s⁻¹. The region encompassed by ECO on-sky lies where the Updated Zwicky Catalog (Falco et al. 1999) and Sloan Digital Sky Survey (SDSS; York et al. 2000) redshifts overlap. The ECO region encloses the A-semester of the RESOLVE survey and incorporates redshifts from the RESOLVE, HyperLEDA (Paturel et al. 2003), Galaxy and Mass Assembly Survey (GAMA) (Driver et al. 2011), 2dF (Colless et al. 2001), and 6dF (Jones et al. 2009) surveys. The majority of ECO galaxies are present in SDSS, while ∼7% of galaxies are added to the final catalog from other sources. We use a volume-limited sample that is complete in absolute magnitude (12,698 galaxies with M_r  < −17.33) in order to define environment metrics, however, we use a volume-limited sample complete in baryonic mass for our analysis. The ECO galaxy sample is complete in stellar mass at M_* > 10^9.1 M_⊙, having 7448 objects with stellar masses above this limit and complete in baryonic mass at M_b  > 10^9.3 M_⊙ (Moffett et al. 2015), having 9526 objects with baryonic masses above this limit. We decided to use a baryonic-mass complete sample for this analysis because we are specifically interested in examining how environment affects the baryonic properties of void galaxies. Throughout the analysis we assume H₀ = 70 km s⁻¹ Mpc⁻¹, and we calculate distances using D = cz/H₀.

For the analysis presented in this paper, we wish to examine properties such as color, gas-to-stellar mass ratio, baryonic, and stellar mass, and fractional stellar mass growth rate (FSMGR). Galaxy properties and photometric data are described by Moffett et al. (2015) and Eckert et al. (2016) for the ECO catalog and by Eckert et al. (2015) for the RESOLVE catalog. ECO stellar masses and colors are derived via spectral energy distribution (SED) fitting (see Kannappan et al. 2013, for a description of the SED fitting procedure). The colors we use here are corrected for internal extinction and have k-corrections implicitly included.

Morphological classifications for ECO are determined from a combination of by-eye classifications and a method that exploits the relation between magnitude and the μ_Δ metric described in Kannappan et al. (2013), which combines the overall surface mass density with a surface mass density contrast. We refer the reader to Moffett et al. (2015) for a full description of how morphologies are derived for all galaxies in ECO.

The FSMGR quantity, described in Kannappan et al. (2013), is a property similar to the specific star formation rate (sSFR) of a galaxy. The FSMGR quantity is defined as FSMGR  ≡ M_<Gyr/M_>Gyr, where M_<Gyr is the stellar mass of a galaxy that has formed in the previous gigayear, and M_>Gyr is the stellar mass that formed prior to the last gigayear. The sSFR of a galaxy, on the other hand, has the total stellar mass in the denominator meaning its numeric value can never exceed a value of 1, unlike the FSMGR, which can reach values of up to ∼10 for highly star-forming galaxies.

In ECO, H i data exist for ∼44 % of all galaxies. H i data, and therefore H i gas masses, for ECO galaxies are obtained from the RESOLVE survey (Stark et al. 2016) and the public Arecibo Legacy Fast ALFA (ALFALFA) α.40 catalog (Haynes et al. 2011). We consider an H i detection to be robust if it is not confused (i.e., there are no nearby neighbors that could contaminate or confuse the detection) and if it has a signal-to-noise ratio (S/N) greater than 4. For ECO galaxies lacking robust H i detections, we resort to indirect methods to obtain the gas masses. The gas-to-stellar mass ratio of an ECO galaxy can be determined from a photometric gas fraction (PGF) relation calibrated with the RESOLVE survey (see Eckert et al. 2015 for a full description of the PGF technique).

The PGF technique takes advantage of the relation between galaxy color and the M_HI/M_* gas fraction (Kannappan 2004). For a galaxy's given color, a probability distribution of gas-to-stellar mass ratios can be made. We use these probability distributions to determine the predicted gas and baryonic masses of galaxies. To derive the predicted H i mass, we implement the (u − J) and b/a color calibration from Eckert et al. (2015) and obtain gas-to-stellar mass ratio distributions for each galaxy. The median of a galaxy's gas-to-stellar mass ratio probability distribution is used to assign a value of M_HI/M_* to that galaxy, and the predicted H i mass is then derived from that value using the stellar mass from SED fitting. We multiply all H i gas masses, real or predicted, by a factor of 1.4 to account for helium. Therefore, all values of gas mass presented in this paper are given by M_gas = 1.4 × M_HI.

We compute baryonic masses by adding M_* to M_gas, where M_gas is computed from either the PGF technique or H i data, depending on the strength of the H i detection. We can compare a galaxy's predicted baryonic mass to its real baryonic mass if the galaxy has an H i detection either from the RESOLVE or ALFALFA surveys. The RESOLVE H i masses are obtained via 21 cm data (Stark et al. 2016), and the RESOLVE-A region is only 78% complete in H i when counting strong, unconfused detections (i.e., detections that have an S/N > 4 and do not appear contaminated by nearby sources). We show the comparison between real and predicted baryonic masses in Figure 1. The error introduced by using a predicted baryonic mass diminishes toward higher masses, as the more massive galaxies are quenched and have baryonic masses that are dominated by the stellar mass. We measure the scatter to be ∼0.23 dex at lower baryonic masses (10^9.3 M_⊙ < M_b,real < 10^10.3 M_⊙) and ∼0.09 at higher baryonic masses (M_b,real > 10^10.3 M_⊙).

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For the analysis described in this paper, we use an Nth nearest neighbor metric to measure the local galaxy density. We adopt N = 3 when estimating densities with the Nth nearest neighbor method. We also performed the analysis using N = 3, 4, 5,  and 10, however, there were no major variations in the results of the analysis. In order to achieve robust statistics for our analysis, we assign void status to the 10% of galaxies with lowest local density. We discuss this choice of method for selecting void galaxies in detail below.

2.4.1. Redshift Distortion Corrections

2.4.2. Void Classification

In order to designate void status for a given galaxy, we need a way to quantify each galaxy's local density in ECO. We initially experimented with the publicly available void-finding algorithm ZOnes Bordering On Voidness (ZOBOV) (Neyrinck 2008) to find voids, but found that edge effects and having a low galaxy density often returned large spurious voids. The ZOBOV algorithm uses Voronoi tessellations to estimate local densities for galaxies and uses those densities to find density depressions in the sample volume. Because ZOBOV is designed to measure a void's shape and size, it includes galaxies living along the void border in its void definition. The problem with galaxies bordering the voids in ZOBOV is that those galaxies also border clusters and filaments, and often have relatively high local densities. We illustrate this in Figure 2, which shows void galaxies found by ZOBOV. In order to exclude the void borders from our void definition, we decided to apply a density cut to the galaxies located inside the ZOBOV voids in order to create a better void sample. Since the majority of galaxies with low Voronoi densities also live in ZOBOV voids, the void sample remains essentially the same if one applies a density cut to the Voronoi densities of the entire sample of galaxies instead of just the ZOBOV void galaxies. For comparison purposes, we also estimate densities for galaxies using Nth nearest neighbor distances (adopting N = 3) and, in both cases, we define void galaxies as the 10% of galaxies having the lowest density, which yields a statistically significant void sample.

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Figure 3 directly compares the two methods for estimating density. The comparison reveals that some galaxies can have a low Voronoi density while having a high Nth nearest neighbor density, while the opposite does not hold for galaxies with low Nth nearest neighbor densities. A galaxy can be falsely classified as a void galaxy through the Voronoi tessellation method if that galaxy lives on the border of a cluster or filament because its Voronoi cell will extend into the void, thus having a large volume and a low corresponding density. In contrast, the Nth nearest neighbor density of such a border galaxy will be high. In Figures 2 and 4, we show void galaxies chosen from both methods. In Figure 2, we show void galaxies in the top 10% most statistically significant voids identified by ZOBOV. We clarify that this figure includes all galaxies in a given ZOBOV void region, as opposed to the void galaxies chosen by our lowest tenth percentile density cut. Even in the most statistically significant voids, it appears by-eye that many of the ZOBOV void galaxies live in high-density regions. This is especially evident in the top right three panels of Figure 2. In Figure 4 we show the entire void and non-void galaxy sample chosen by our Nth nearest neighbor metric. It is evident in Figure 4 that void galaxies chosen via our Nth nearest neighbor method appear to avoid regions of high density, as opposed to void galaxies identified by ZOBOV.

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Given these results, we select the Nth nearest neighbor metric (with N = 3) to define our void sample. We note that our void definition recovers galaxies that can either be completely isolated or exist in groups of two or three, and a few of the void galaxies even appear to be arranged in thin filamentary-like structures known as tendrils (see Beygu et al. 2013; Alpaslan et al. 2014). Although we choose our void definition based on N = 3, the majority (>90%) of our void galaxies exist in FoF groups of N = 1.

The threshold for selecting void galaxies for this analysis is exactly the lowest 10% of galaxies ranked in density, selected from the entire sample of 12,698 ECO galaxies above the luminosity completeness limit (M_r  < −17.33). This corresponds to a third nearest neighbor density ρ_void of less than 0.02 galaxies Mpc⁻³ for the void galaxy sample. The mean third nearest neighbor distance density $\bar{\rho }$ of the entire ECO volume is 0.76 galaxies Mpc⁻³, meaning the density contrast for the void sample is δ < −0.97, where $\delta =\rho /\bar{\rho }-1$.

We do not account for edge effects in this study, however, it is important to assess the impact this has on our analysis. To address this, we create a "buffered" subsample of ECO data inside the R.A., decl. and line-of-sight velocity limits listed in Section 2.1 for all of ECO and rerun our void-finding algorithm. The buffered region we create is the same as that from Moffett et al. (2015), which was specifically designed to mitigate edge effects that arise when computing galaxy environment metrics. The subsample of ECO data we create is 2.4° smaller in R.A., leaving a buffer of 1.2 degrees from each edge in R.A., 2° smaller in decl., leaving a buffer of 1° from each edge in decl., and 940 km s⁻¹ shorter in line-of-sight velocity distances, corresponding to a line-of-sight velocity range of 3000–7000 km s⁻¹. These limits were chosen to ensure that the ECO subsample has a buffer region of at least 1 Mpc in all directions, with an additional allowance of ∼5.7 Mpc in the line-of-sight velocity distances to compensate for group peculiar velocities that extend up to 400 km s⁻¹ (Moffett et al. 2015).

The subsample of ECO data we create has a total of 9,359 galaxies complete in absolute magnitude (M_r  < −17.33) and a total of 936 void galaxies above this limit, corresponding to the lowest 10% of galaxy densities. Of these 936 void galaxies in the buffered subsample of ECO, 877 (93.6%) are in the original (full) ECO sample. We find that the results of this paper do not change when we perform our analysis on the buffered subsample of void galaxies. We therefore decide to keep our original sample of 1270 void galaxies, for this analysis.

In Figure 5 we show the baryonic mass distribution of the void and non-void galaxy sample. The samples have different mass distributions, with void galaxies being less massive on average than non-void galaxies. Our results show that void galaxies rarely have masses greater than 10^10.6 M_⊙. The void galaxy distribution has an excess in baryonic masses below 10^9.8 M_⊙ and a deficiency in masses above  ∼10¹⁰ M_⊙ when compared to the baryonic mass distribution of all ECO galaxies. While not shown here, we find a similar trend when comparing the stellar mass distributions of the void and non-void galaxy samples.

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In Figure 6 we examine normalized histograms of void and non-void galaxy properties in ECO and RESOLVE. We show the RESOLVE-A semester catalog data in the top panels as it has real H i masses derived from 21 cm data and compare that with ECO data in the bottom panels. We impose a cut of decl. > 5° in ECO for this figure only so that the top panels contain and display independent information.

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The histograms show that the ECO void galaxies are bluer, more star-forming, and more gas-rich than their non-void counterparts. RESOLVE shows qualitatively similar results, though they are much noisier due to the smaller size of that sample. We perform an Anderson–Darling (AD) k-sample test between the void and non-void galaxy property distributions for each panel shown in Figure 6 using the scipy.stats package from the SciPy library (Virtanen et al. 2020). We show the results of the test in Table 1 and note that p-values are capped at values of 0.001 and 0.25, so p-values above (below) 0.25 (0.001) are only quoted as lower or upper limits. The results of the AD test show that the differences between void and non-void galaxy properties are statistically significant. The two left panels of Figure 6 comparing (u − r)^e colors between void and non-void galaxies can be compared to Figure 3 of Hoyle et al. (2012), which shows that void galaxies are statistically bluer than non-void galaxies. These results are not surprising, since void galaxies are less massive and there are well-established correlations between mass, color, and gas content, with lower mass galaxies having higher gas fractions (Kannappan 2004), higher specific star formation rates (Bauer et al. 2005), and bluer colors (Dressler 1980; Baldry et al. 2004; Hoyle et al. 2012). The interesting question is whether these differences persist at fixed mass.

Table 1. Test Statistics and p-values of the AD k-Sample Test Performed between the Void and Non-void Galaxy Property Distributions Shown in Figure 6

RESOLVE-A
Galaxy property	AD statistic	p-value
(u − r)e	5.95	0.002
$\mathrm{log}(\mathrm{FSMGR})$	4.15	0.007
$\mathrm{log}({M}_{\mathrm{gas}}/{M}_{* })$	3.91	0.009
ECO
Galaxy property	AD statistic	p-value
(u − r)e	99.19	≤0.001
$\mathrm{log}(\mathrm{FSMGR})$	107.23	≤0.001
$\mathrm{log}({M}_{\mathrm{gas}}/{M}_{* })$	104.58	≤0.001

Note. Results are shown for both the ECO and RESOLVE-A semester samples.

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We move on to investigate how the properties of void galaxies differ from non-void galaxies when controlling for mass. Referring again to Figure 6, we compute histograms for a sample of non-void galaxies that have the same baryonic mass distribution as the void sample. To generate these histograms, we first determine the baryonic mass distributions of the void and non-void samples (shown in Figure 5). We then randomly sample from the non-void galaxies with a probability that is proportional to the ratio of the mass distributions in order to build a sample of non-void galaxies with a mass distribution identical to that of the void galaxies. During the random sampling, we check to make sure that a galaxy is not sampled twice. This process is then repeated 1000 times so that we end up with 1000 samples of non-void galaxies with a void-like mass distribution. The property distributions are all averaged together to generate the green histograms shown in Figure 6.

We find that differences between void and non-void galaxies persist when controlling for mass. The void galaxy sample is bluer, more gas-rich, and has a higher FSMGR when compared to the mass-matched non-void galaxy sample, despite having the same mass distribution. We note that the difference between the void (blue histograms) and mass-matched non-void (green histograms) galaxy samples is due to environment, while the difference between the mass-matched non-void (green histograms) and unaltered non-void (red histograms) samples is due to baryonic mass. We find that the mass-matched non-void histograms in ECO and RESOLVE-A decrease with respect to the void histograms, in fixed bins, by a factor of ∼0.2–0.5 at bluer colors, higher FSMGRs, and higher gas fractions. The mass-matched non-void histograms increase with respect to the void histograms, in fixed bins, by a factor of ∼1–3 at redder colors, lower FSMGRs, and lower gas fractions. As in Section 3.1, we perform an AD k-sample test between the void and mass-matched non-void galaxy property distributions for each panel in Figure 6 and present the results of the tests in Table 2. The results of the test show that the quantitative differences between void and non-void galaxy property distributions remain statistically significant in ECO, even when controlling for mass. These differences are less statistically significant in RESOLVE-A, though this could likely be an effect due to the low number of void galaxies (<100) in RESOLVE-A.

Table 2. Test Statistics and p-values of the AD k-Sample Test Performed between the Void and Mass-matched Non-void Galaxy Property Distributions Shown in Figure 6

RESOLVE-A
Galaxy property	AD statistic	p-value
(u − r)e	3.02	0.019
$\mathrm{log}(\mathrm{FSMGR})$	1.37	0.088
$\mathrm{log}({M}_{\mathrm{gas}}/{M}_{* })$	0.96	0.13
ECO
Galaxy property	AD statistic	p-value
(u − r)e	43.52	≤0.001
$\mathrm{log}(\mathrm{FSMGR})$	46.47	≤0.001
$\mathrm{log}({M}_{\mathrm{gas}}/{M}_{* })$	41.85	≤0.001

Note. Results are shown for both the ECO and RESOLVE-A semester samples.

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In Figure 7 we use an alternative method for controlling the mass distribution of void and non-void galaxies that lets us determine how galaxy properties depend on environment. We bin both samples in stellar and baryonic mass and compare the mean of log(FSMGR), (u − r)^e , and $\mathrm{log}\left({M}_{\mathrm{gas}}/{M}_{* }\right)$ for void and non-void galaxies in each bin. Error bars are 1σ confidence intervals made from a bootstrap resampling inside each bin. To compute the error from a bootstrap method, we resample (i.e., draw randomly from) the distribution inside each bin of mass x times, where x is the number of objects inside that bin, build a sample from the random draws and compute the mean. We draw objects with replacement so the same object in a given bin can be sampled more than once. We do this 1000 times and make a distribution of the mean values inside each bin and take the 16th and 84th percentiles of this distribution as the error. We find that void galaxies are bluer, more star-forming, and more gas-rich across almost all bins of baryonic mass. We find similar trends when controlling for the stellar mass, across all stellar mass bins.

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In order to assess the statistical significance of the comparisons shown in Figure 7, we perform a multivariate test for equal distributions based on nearest neighbors using the yaImpute package (Crookston & Finley 2007) in R (R Core Team 2018). Following the procedure in Section 10.3 of Rizzo (2019), we compute the third nearest neighbor test statistic, T_n,3, between void and non-void galaxies for the mass ranges shown in Figure 7 ($\mathrm{log}({M}_{b}/{M}_{\odot })=9.3-10.9$ for left panels, $\mathrm{log}({M}_{* }/{M}_{\odot })=9.1-10.5$ for right panels). We normalize the data, such that each variable has a value between 0 and 1, before computing T_n,3 and then perform a bootstrap of the T_n,3 test statistic to obtain a p-value. The p-value of each test is shown in the panels of Figure 7.

We find higher p-values (p > 0.05) for comparisons between the void and non-void galaxy samples complete in stellar mass, indicating that the differences between the stellar-mass complete samples may not be as statistically significant as the differences between the baryonic-mass complete samples. The difference in sample sizes is important to note, however, as there are 895 total void galaxies being tested in the left panels of Figure 7, 857 of which are centrals, while there are 522 total void galaxies being tested in the right panels of Figure 7. Similarly, there are 8288 non-void galaxies and 5718 non-void galaxy centrals being tested in the left panels of Figure 7, while there are 5821 total non-void galaxies being tested in the right panels of Figure 7. We note that these numbers vary from what is listed in Table 3 because we do not show the highest mass bins in Figure 7 due to very low (<10) sample sizes for the void galaxies. The difference in sample sizes inevitably leads to higher p-values for the void and non-void galaxy samples being tested in the right panels of Figure 7.

Table 3. Number of Satellites versus Centrals in the ECO Baryonic-mass and Stellar-mass Complete Void and Non-void Galaxy Samples

Sample	$\mathrm{log}({M}_{b}/{M}_{\odot })\gt 9.3$	$\mathrm{log}({M}_{* }/{M}_{\odot })\gt 9.1$
Void centrals	863	533
Void satellites	38	20
Non-void centrals	5999	4622
Non-void satellites	2626	2273

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Part of the differences observed between void and non-void galaxies at fixed mass can be attributed to contributions from satellite galaxies in the non-void populations. For this reason, we quantify how much the satellite population contributes to the differences we see between void and non-void galaxies at fixed mass in Figure 7. In the left-hand panels in Figure 7, we show the mean color, FSMGR, and gas fraction of group centrals for both void and non-void galaxies at fixed baryonic mass. We also compute the T_n,3 test statistic described above for void and non-void galaxy centrals and show the corresponding p-values in the left panels of Figure 7. For reference, we show the number of centrals and satellites in the baryonic and stellar mass complete void and non-void galaxy samples in Table 3. The mean of void galaxy group centrals hardly changes, due to the fact that more than 90% of all void galaxies exist inside N = 1 groups. The mean of non-void centrals at fixed baryonic mass, however, appears bluer, more star-forming, and more gas-rich than the mean of all non-void galaxies, especially at lower masses. We note that the p-values of the T_n,3 test statistic for void and non-void galaxy centrals indicate that the differences between void and non-void galaxies remain statistically significant among the population of centrals. Lower mass non-void galaxies can exist as satellites in large groups and clusters, and those satellites can be expected to have redder colors, lower FSMGRs, and gas fractions than galaxies outside of clusters of the same mass as they have been quenched through some of the environmental processes that take place in groups and clusters. Nevertheless, this satellite effect does not explain away all of the differences between void and non-void galaxies. Differences persist even when considering central galaxies alone.

In order to shed light on why void and non-void galaxies have different properties at fixed mass, we examine some of the property distributions inside each of the baryonic mass bins from Figure 7. In Figures 8 and 9, we examine the color and gas fractions of void and non-void galaxies inside different bins of baryonic mass. We make clear that the samples here are not mass matched as was done for Figure 6, given the narrow range of mass (${\rm{\Delta }}\mathrm{log}({M}_{b}/{M}_{\odot })=0.2$) in which the void and non-void galaxy properties are being compared for these figures. We perform an AD k-sample test between the void and non-void galaxy population inside each bin of mass in Figures 8 and 9 and present the p-value in every panel. We remind the reader that the AD p-values are capped below values of 0.001 and above values of 0.25 in scipy.stats. Although we report a high (>0.05) p-value in the panel of Figure 8 where $\mathrm{log}({M}_{b}/{M}_{\odot })=10.5-10.7$, and the panels of Figure 9 where $\mathrm{log}({M}_{b}/{M}_{\odot })=9.7-9.9$, 10.3–10.5, and 10.5–10.7 we note that sample sizes can affect the reported p-values of these comparisons.

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When we investigate the color distribution of void and non-void galaxies inside different bins of baryonic mass (see Figure 8), we see that at low masses there appears to be a lack of red-sequence galaxies inside of voids. Although a red sequence begins to emerge at higher masses, the voids consistently host a slightly bluer population of galaxies and appear to have a deficit in red-sequence galaxies when compared to the non-void population. The number of void galaxies begins to drop significantly past $\mathrm{log}({M}_{b}/{M}_{\odot })\gt 10.5$, thus reducing the statistical significance of these results, especially at the highest masses. A similar result holds for gas mass fraction (see Figure 9), where void galaxies show a significantly weaker gas-poor peak and a correspondingly stronger gas-rich peak than non-void galaxies. We note that the comparison of color for void and non-void galaxies in Figure 8 agrees qualitatively with Figure 4 of Hoyle et al. (2012), which shows that void galaxies are bluer than non-void galaxies at fixed magnitude.

So far, we have seen that void galaxies are bluer, more star-forming, and more gas-rich than galaxies with higher local densities, and that this is due to more than just the lower mass distribution in voids. In this section we additionally control for morphology in order to determine whether the differences we see between void and non-void galaxies inside a single bin of baryonic mass can be attributed to differences in the morphological distributions. Because voids tend to be occupied by late-type galaxies with lower masses than higher density regions, we control for morphology in order to determine if the differences we see in color, FSMGR, and gas fraction can be attributed to the larger number of bluer late types that exist in low-density regions.

In Table 4 we list the number of late types and early types in our void and non-void samples above the baryonic mass completeness limit, as well as the percentage of the total population for each sample. We note that 83% of void galaxies are late types, whereas 73% of the non-void galaxies are late types. One might normally expect to find more early-type galaxies inside the non-void environments, however, ECO and RESOLVE are both dominated by dwarf galaxies and late-type fractions are universally higher at low galaxy mass (Conselice 2006). We remind the reader that ECO and RESOLVE were both designed to explore the low-mass galaxy regime with volume-limited samples reaching down to mass limits of ∼10⁹ M_⊙. In addition, our non-void definition also includes galaxies in regions of average density explaining why the non-void sample is still dominated by late types. Nonetheless, since there is a higher fraction of late-type galaxies inside voids than non-voids, it is interesting to control for morphology to determine if the differences we see between the void and non-void galaxies can be attributed to the difference in morphological distributions.

In Figure 10, we control for both morphology and mass to determine if the void galaxies are intrinsically different from the non-void galaxies. We find that, even at fixed mass and morphology, void galaxies are different from their non-void counterparts. The late types appear very similar to each other, but void late types are still bluer, more gas-rich, and more star-forming than non-void late types. Early-type galaxies, however, show much larger variations in color, FSMGR, and the gas fraction between the void and non-void populations at fixed baryonic mass, suggesting that the properties of early-type galaxies correlate far more with environment than the properties of late-type galaxies.

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As described for Figure 7, we perform a test for equal distributions using the T_n,3 statistic for void and non-void galaxy late types and early types and report the p-value in each panel of Figure 10. We find high p-values (p > 0.05) for most of these tests, indicating that these comparisons may not be statistically significant. However, we note again that sample sizes could play a role, especially in the case of early-type galaxies as there are only 148 total void early-type galaxies and 2262 non-void early-type galaxies.

Our results show that, although morphology correlates highly with color, star formation, and gas-to-stellar mass ratio, environment still plays a role in the observed properties of galaxies at fixed mass and morphology. We controlled for the mass of late types and still found discrepancies between these properties, even at higher masses where the error introduced by using a predicted baryonic mass diminishes. The early-type population of void galaxies appears to differ significantly from that of the non-void population at fixed mass. This result is consistent with previous results suggesting that early types in low-density environments evolve differently from the massive red and dead early types commonly found in clusters, with low-density environments favoring bluer, lower mass early types with recent star formation driven by gas-rich mergers or gas inflows (Kannappan et al. 2009; Stark et al. 2013; Moffett et al. 2015; Lopes et al. 2016).

CAM (Hearin & Watson 2013) is an extension of the subhalo abundance matching (SHAM) method (Kravtsov et al. 2004; Vale & Ostriker 2004; Conroy et al. 2006) for assigning observed galaxy properties to dark matter halo properties. While SHAM only connects a single mass-like galaxy property, like stellar mass, to a single mass-like halo property, like maximum circular velocity, CAM allows for two or more halo properties to influence how galaxy properties are assigned in the SHAM algorithm. For example, CAM has been used to study the dependence of star formation rate on halo formation history (e.g., Hearin & Watson 2013; Hearin et al. 2014; Paranjape et al. 2015; Watson et al. 2015; Saito et al. 2016). Here we briefly describe our implementation of CAM.

For our fiducial mocks we assign baryonic mass to (sub)halos based on the value of V_peak, where V_peak is defined as the maximum value that the maximum circular velocity, ${V}_{\max }$, attains during the entire assembly history of the (sub)halo. We define ${V}_{\max }\equiv \mathrm{Max}\left\{\sqrt{{GM}(\lt r)/r}\right\}$, where M(<r) is the mass of the halo enclosed inside some radius r, as the maximum circular velocity of a test particle orbiting the halo's gravitational potential well. It is well established that using V_peak for matching in SHAM-based methods results in galaxy clustering statistics in closer agreement with observations compared to other (sub)halo properties (e.g., Reddick et al. 2013; Lehmann et al. 2017), although see Campbell et al. (2018) for some caveats. While the simplest form of SHAM assumes a monotonic relationship between galaxy mass and V_peak, there is significant evidence for some scatter,  ∼0.1– 0.3 dex in stellar mass at fixed halo mass (e.g., More et al. 2009; Yang et al. 2009). Given this, we add a constant level of scatter of ∼0.15 dex at fixed V_peak using the deconvolution method of Behroozi et al. (2010) with a publicly available implementation. ¹⁰

Once baryonic mass is assigned, in order to assign galaxy color, mock galaxies are probabilistically binned in 0.1 dex bins of baryonic mass using the utils.fuzzy_digitize function in Halotools (Hearin et al. 2017). Within each bin, the observed u − r colors of ECO galaxies are used to define a probability distribution: P_ECO(u − r∣M_b ). If there are N galaxies inside a baryonic mass bin M_b , then the galaxy colors are drawn randomly N times from the distribution P_ECO(u − r∣M_b ) and the draws are rank ordered. The (sub)halos inside each bin of baryonic mass are also rank ordered by an age parameter, the 100 Myr accretion rate (i.e., the mass that the halo has accreted in the previous 100 Myr). The u − r colors are then assigned to mock galaxies such that redder colors are tied to galaxies that live in (sub)halos with higher values of the 100 Myr accretion rate. The algorithm that assigns colors to mock galaxies also assumes a monotonic relation between u − r and the 100 Myr accretion rate at fixed baryonic mass, so it is necessary to introduce some scatter. We introduce scatter by degrading the rank order correlation following the method described in Appendix D in Campbell et al. (2018).

We create eleven mocks with varying levels of scatter between the u − r and 100 Myr accretion rate relation. One mock assumes a correlation coefficient of 0.0, meaning that for that mock the u − r color is not tied to the 100 Myr accretion rate. The other 10 mocks have correlation coefficients ranging from −0.1 to −1.0, in steps of 0.1, assigned to the relation between u − r color and 100 Myr accretion rate. The mock with a correlation coefficient of −1.0 assumes a monotonic relation between u − r and the 100 Myr accretion rate. By tying galaxy color to a secondary halo property other than mass, we are explicitly building galaxy assembly bias into our mocks. Moreover, the correlation coefficient for this relation encodes the strength of assembly bias, with a value of 0.0 corresponding to no assembly bias and a value of −1.0 corresponding to maximum assembly bias. As we will show, the amount of scatter that works best for this model to match the data adopts a correlation coefficient of ρ ∼ −0.6 between the u − r and 100 Myr accretion rate parameters (see Figure 11).

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Once the baryonic mass and u − r color have been assigned to a (sub)halo, we assign other galaxy properties, such as the gas fraction and FSMGR, by identifying an ECO galaxy with similar M_b and u − r as the halo and adopting its other properties. This process results in a mock galaxy distribution that preserves the joint distribution of galaxy properties.

We also experiment with different matching parameters in the models by abundance matching different galaxy properties to V_peak and the 100 Myr accretion rate of the dark matter halos, we discuss these results toward the end of this section.

We use the Vishnu cosmological N-body simulation that adopts a 130 h⁻¹ Mpc box size and a dark matter particle mass of 3.215 × 10⁷ h⁻¹ M_⊙ (see Johnson et al. 2019 for a detailed description of the simulation and halo catalogs) to construct our mock catalogs. We populate the simulation using the CAM mock population framework in Halotools (Hearin et al. 2017), as described above. We then extract four independent mock ECO galaxy catalogs from the 130 Mpc h⁻¹ simulation box. For each mock galaxy catalog, we choose a new location for the observer and we place galaxies in redshift space by using the positions and peculiar velocities of their (sub)halo with respect to the observer. We then make identical geometrical cuts in R.A., decl., and redshift as those in the ECO sample in redshift space, in order to preserve the same geometry as the ECO sample. We make sure to separate the four mock catalogs from each other by at least 10 Mpc h⁻¹, thus making them truly independent.

As a result of this procedure, each of the four mock catalogs has the same geometry, similar number density of galaxies, similar overall clustering, and the same joint distributions of observed properties as the ECO sample. Furthermore, galaxy baryonic mass directly correlates with dark matter halo mass, color directly correlates with halo mass accretion rate at fixed mass, and other observed properties like the FSMGR or gas fraction inherit indirect correlations with halo mass and accretion rate through their correlations with baryonic mass and color.

It is worth mentioning here that the size of our simulation box may not be large enough to properly model the formation of large cosmic voids. Nadathur et al. (2017) demonstrated that the "potential fluctuations associated with voids extend over scales of 200–300 Mpc h⁻¹." Although we have not shown what impact this consideration could have on our results, we believe it is safe to ignore as our void galaxies are defined by local density rather than large-scale structure. Furthermore, the simulation box is large enough to carve out four independent ECO mock catalogs of densities similar to that of the real ECO catalog, so we believe the simulation box is more than adequate for this type of study.

In Figure 11, we show our models with different varying levels of scatter between halo accretion rate and galaxy color at fixed baryonic mass and include the ECO data points from Figure 7. We show the results for three models in particular: model 1 which assumes a correlation coefficient of 0.0 to the relation between color and the 100 Myr accretion rate at fixed baryonic mass, model 2 which assumes a correlation coefficient of the −0.6 between color and the accretion rate at fixed baryonic mass, and model 3 which assumes a monotonic relation between color and accretion rate (i.e., correlation coefficient is −1.0) at fixed baryonic mass. We find that model 2 matches the data fairly well for both the non-void and void galaxies. Although the mocks are constructed such that the colors of void and non-void galaxies are tied to the halo accretion rate at fixed mass, it is interesting to see in the lower two panels of Figure 11 that the observed FSMGR and gas fractions trends at fixed mass also hold up in the mock catalogs, which is attributed to the high correlation that exists between color, FSMGR, and gas fractions. The model with a correlation coefficient of 0.0 represents a simple abundance matching of baryonic mass to V_peak and assumes no additional correlation between color and the 100 Myr accretion rate (i.e., no galaxy assembly bias). This model cannot reproduce the observed differences between void and non-void ECO galaxy properties. Galaxy assembly bias is thus required to explain the ECO results, at least in the family of models we consider.

Our resulting mock catalogs also do a fairly good job of matching the data when we abundance match stellar mass to V_peak and correlate M_gas/M_* to the 100 Myr accretion. When we abundance match the FSMGR to the 100 Myr accretion rate, the model matches the data, but only when the correlation is weak. It should not be surprising that the gas fraction and (u − r)^e parameters both work in the model when matched to the 100 Myr accretion rate because the M_gas/M_* for this sample is predicted from color via the PGF technique. The models fail, at all variations with scatter, when we match the luminosity to V_peak and/or match the FSMGR to the 100 Myr accretion rate. While we cannot confirm that the evolution of galaxies is determined solely by assembly bias, as we do not analyze simulations that include the baryonic physics present in different environments, we do show that the void and non-void galaxy trends at fixed mass are recovered in mock catalogs constructed through conditional abundance matching when certain galaxy parameters are abundance matched to the right (sub)halo mass and age parameters.

Our results are in general agreement with observational results that have found enhanced specific star formation rates in underdense regions (Grogin & Geller 1999, 2000; Rojas et al. 2004; Meyer et al. 2007). More recently, Ricciardelli et al. (2014) showed that specific star formation rates are higher in void galaxies, and that this is due to more than just the difference in mass distributions among different environments. Our results are also in agreement with those of Hoyle et al. (2012) who found that void galaxies are statistically bluer than non-void galaxies, even at fixed magnitude.

In comparison with theory, Patiri et al. (2006) used a semi-analytic model to study the ratio of blue and red galaxies in void and non-void regions, where the void sample is selected from maximal, non-overlapping spheres with a radius larger than 10 h⁻¹ Mpc and devoid of bright of galaxies. The results of their simulation agree with their observed results: the color distribution of galaxies is bimodal in both void and non-void regions, however, the ratio of blue to red galaxies is higher in voids (although this is more pronounced in the simulation than in the observation). They then controlled for color and found that the sSFR of void galaxies is similar to that of non-void galaxies in their simulation. They concluded that galaxy properties are not affected by environment at fixed color.

Kreckel et al. (2011) used a hydrodynamical simulation to study the environmental dependence of galaxies in voids. They predicted the trends we observe, but only at faint luminosities. Their void galaxy sample is defined by a large underdense region with a diameter of  ∼30 h⁻¹ Mpc residing at the center of their simulation box. They found that their void galaxies are bluer and more star forming at fixed luminosity for faint galaxies (M_r  > −16), but at higher luminosities (M_r  < −18) they find no difference between the void and non-void galaxies. Although we do not directly control for luminosity, we show at fixed baryonic mass that there is a difference between void and non-void galaxies well above the completeness limit of M_b  = 10^9.3 M_⊙, and most of these galaxies have luminosities brighter than M_r  = − 18.

More recent work by Tonnesen & Cen (2015) used a hydrodynamical simulation to analyze stellar and halo mass growth in an overdense and underdense region of a simulation box (on scales of ∼20 Mpc). Their simulation produced halos with earlier formation times in overdense regions. First, they found that the stellar-to-halo mass ratio depends on a large-scale environment and not just halo mass. They also found that the specific star formation of z = 0 galaxies is higher in the underdense region of their simulation box when compared to galaxies in the overdense region. Their work suggests that environment, in addition to halo mass, should be considered when assigning stellar masses to halos.

We examine nearest neighbor distances for void galaxies in order to investigate whether there is a merging population of void galaxies that could explain the presence of void early types. If we consider that possible mergers occur in galaxies that have a nearest neighbor at <100 kpc, we find that an extremely small fraction (<1%) of void galaxies look like candidates for mergers that will later become early types. Given the larger fraction of void galaxies that are considered early types, we can interpret this in several ways. One possible explanation could be that the early types we see do not arise as a consequence of merging or other interactive transformation processes, thus challenging assumptions about how early types form in the universe.

Observational and theoretical studies of blue early types do suggest the likelihood, especially in low-density environments, of formation in gas-rich mergers, but gas accretion may also be important (Bekki 2008; Kannappan et al. 2009; Stark et al. 2013; Verbeke et al. 2014). Another possible explanation for the low number of merger candidates relative to early types could be that the timescale on which galaxies live in a pre-merger state is far outlived by the lifetime of the post-merger remnant, consistent with a post-merger disk regrowth scenario (Kannappan et al. 2009; Stark et al. 2013; Moffett et al. 2015). Finally, we note that our analysis includes only galaxies brighter than M_r  = −17.33 and above the baryonic mass completeness limit, so does not rule out current interactions between the void early-type galaxies in our sample and neighboring galaxies whose masses and luminosities fall below our completeness limit.