Influence of the Void Environment on Chemical Abundances in Dwarf Galaxies and Implications for Connecting Star Formation and Halo Mass

We use the Direct T_e method described in Izotov et al. (2006) to estimate the gas-phase abundances of oxygen, nitrogen, and neon in our sample of dwarf galaxies, because this method is often regarded as the most accurate estimate of element abundances. It can be difficult to use due to the nature of the [O iii] λ4363 auroral line (for a more detailed discussion, see Douglass & Vogeley 2017a). Since the strength of [O iii] λ4363 is inversely proportional to the metallicity of a galaxy, it is best suited for low-redshift, low-metallicity galaxies. At metallicities $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ ≳ 8.5, [O iii] λ4363 becomes too weak to detect in the SDSS spectra. With the mass–metallicity (MZ) relation by Tremonti et al. (2004), this metallicity limit corresponds to a maximum stellar mass of

$$\begin{eqnarray*}12+\mathrm{log}\left(\displaystyle \frac{{\rm{O}}}{{\rm{H}}}\right) & = & 8.5\\ & = & -1.492+1.847(\mathrm{log}{M}_{* })\\ & & -\ 0.08026{(\mathrm{log}{M}_{* })}^{2}\\ \mathrm{log}\left(\displaystyle \frac{{M}_{* }}{{M}_{\odot }}\right) & = & 8.696.\end{eqnarray*}$$

The MZ relation by Andrews & Martini (2013) estimates that this maximum metallicity translates to a maximum stellar mass of

$$\begin{eqnarray*}12+\mathrm{log}\left(\displaystyle \frac{{\rm{O}}}{{\rm{H}}}\right) & = & 12+\mathrm{log}{\left(\displaystyle \frac{{\rm{O}}}{{\rm{H}}}\right)}_{\mathrm{asm}}-\mathrm{log}\left(1+{\left(\displaystyle \frac{{M}_{{TO}}}{{M}_{* }}\right)}^{\gamma }\right)\\ 8.5 & = & 8.798-\mathrm{log}\left(1+{\left(\displaystyle \frac{{10}^{8.901}}{{M}_{* }}\right)}^{0.640}\right)\\ {M}_{* } & = & 8.138\times {10}^{8}{M}_{\odot }\\ \mathrm{log}\left(\displaystyle \frac{{M}_{* }}{{M}_{\odot }}\right) & = & 8.911.\end{eqnarray*}$$

Even though it is dangerous to compare metallicity values calculated with different methods, both of these upper limits on the galaxy stellar masses correspond to the maximum mass of a dwarf galaxy ($\mathrm{log}({M}_{* }/{M}_{\odot })\approx 9$). Therefore, we can expect to estimate the chemical abundances of only dwarf galaxies in SDSS DR7 with the Direct T_e method (of course, there are exceptions to this; see Izotov et al. 2015, for example). Higher resolution spectra are necessary to probe higher-mass, higher-metallicity galaxies.

After solving for the temperature of the gas, we can calculate the amount of each element present in each of the ionization stages. The total gas-phase oxygen abundance is equal to the sum of the abundances of each of the ionized populations:

$$\begin{eqnarray}&&\displaystyle \frac{{\rm{O}}}{{\rm{H}}}=\displaystyle \frac{{{\rm{O}}}^{++}}{{{\rm{H}}}^{+}}+\displaystyle \frac{{{\rm{O}}}^{+}}{{{\rm{H}}}^{+}}.\end{eqnarray} \tag{ 1 }$$

We use an ionization correction factor (ICF) to account for the missing stages of neon and nitrogen, since we can observe these elements in only one of their main ionization stages. The total abundance for a particular element X is

$$\begin{eqnarray}&&\displaystyle \frac{X}{{\rm{H}}}=\displaystyle \sum _{i}{\mathrm{ICF}}_{i}\displaystyle \frac{{X}^{i}}{{\rm{H}}}.\end{eqnarray} \tag{ 2 }$$

For nitrogen, we employ the ICFs used in Douglass & Vogeley (2017b). We use the ICFs in Izotov et al. (2006) for neon.

We derive an ICF for oxygen to overcome some limitations on the observations of dwarf galaxies in SDSS to bolster our sample size. Because we are studying dwarf galaxies, the [O ii] λ3727 doublet necessary for estimating the abundance of O⁺ is only available for objects within the redshift range 0.02 < z < 0.03 (see Section 3.1 and Douglass & Vogeley 2017a for more details). To be able to study SDSS galaxies at redshifts less than 0.02, we need to find an alternate way to estimate the abundance of O⁺. While it is theoretically possible to estimate the O⁺ abundance from the [O ii] λλ7320, 7331 emission line doublet, Izotov et al. (2006) show that the resulting abundances are not very accurate because [O ii] λλ7320, 7331 is extremely weak. Another possibility is to use an ICF to approximate the missing ionization stage, as outlined in Section 2.1 for the nitrogen abundance. Because the [O ii] λ3727 emission line is commonly available for analysis, the oxygen abundance can be found with Equation (1). To construct an ICF for oxygen appropriate for our entire dwarf galaxy sample to include those with non-observed [O ii] λ3727, we compare $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ to 12 + logO⁺⁺/H⁺, as calculated by the Direct T_e method for the star-forming dwarf galaxies in SDSS from Douglass & Vogeley (2017a).

The scatter seen in Figure 1 is a result of the ionization parameter. A good proxy for the ionization parameter is found with the ratio of two different ionization stages of the same element; [O iii] λ5007/[O ii] λ3727 is traditionally used (Kewley & Dopita 2002). However, if the flux of [O ii] λ3727 is unknown, we must find an alternate proxy for the ionization ratio. Both oxygen and sulfur are alpha elements, so the relative amounts of them should remain fairly constant. Therefore, we find that replacing [O ii] λ3727 with [S ii] λ6717, 6731 produces a suitable proxy for the ionization parameter (L. Kewley, 2018, private communication).

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We fit a polynomial model to the data that incorporates both 12 + logO⁺⁺/H and the ratio of [O iii] λ5007 to [S ii] λλ6717, 6731, defined as

$$\begin{eqnarray}&&12+\mathrm{log}\,{\rm{O}}/{\rm{H}}=b+{a}_{1}x+{a}_{2}y+{a}_{3}{xy}+{a}_{4}{y}^{2},\end{eqnarray} \tag{ 3 }$$

where x = 12 + log O⁺⁺/H⁺, y = [O iii] λ5007/[S ii] λλ6717, 6731, a₁ = 0.82 ± 0.072, a₂ = −0.3 ± 0.15, a₃ = 0.03 ± 0.019, a₄ = 0.0006 ± 0.00032, and b = 1.9 ± 0.55 for star-forming dwarf galaxies.

For those star-forming dwarf galaxies for which [O ii] λ3727 is not observed in the SDSS spectra, we use the coefficients for the star-forming dwarf galaxies with Equation (3) to calculate the total oxygen abundance in the galaxy based on the amount of doubly ionized oxygen found in Equation (4) of Douglass & Vogeley (2017a).

We employ most of the same requirements for our sample as in Douglass & Vogeley (2017a, 2017b). All galaxies must have

• 1.  
  M_r > −17 (dwarf galaxies);
• 2.  
  a minimum 5σ detection of Hβ;
• 3.  
  a minimum 1σ detection of [O iii] λ4363;
• 4.  
  a flux > 0 for [O ii] λ3727, [O iii] λλ4959, 5007, and [N ii] λλ6548, 6584;
• 5.  
  T([O iii]) < 2 × 10⁴ K;
• 6.  
  a star-forming BPT classification by Brinchmann et al. (2004).

For those galaxies with a redshift z ≳ 0.02, we use the oii_flux value from the MPA-JHU catalog in place of their [O ii] λλ3726, 3729 flux measurement. See Douglass & Vogeley (2017a) for further details on each of these requirements.

We require the estimated electron temperature T([O iii]) < 2 × 10⁴ K for a few reasons. Nicholls et al. (2014) explain that temperatures above this value estimated from the direct method as prescribed by Izotov et al. (2006) are not reliable because the data used to derive these equations do not extend beyond 2 × 10⁴ K. Physically, one does not typically find H ii regions with temperatures higher than 2 × 10⁴ K because the equilibrium temperature between photoelectric heating and cooling due to recombination, free–free emission, and collisionally excited line radiation is often below this temperature. However, some extremely metal-deficient galaxies are found with temperatures higher than 2 × 10⁴ K (Guseva et al. 2017, for example); by eliminating these metal-poor galaxies, we are introducing a sample bias. We examine the significance of this bias in Section 4.3.

The large-scale environment of the galaxies is determined using the void catalog compiled by Pan et al. (2012), which was constructed using galaxies in the SDSS DR7 catalog. The VoidFinder algorithm of Hoyle & Vogeley (2002; based on the algorithm described by El-Ad & Piran 1997) removes all isolated galaxies (defined as having the third nearest neighbor more than 7 h⁻¹ Mpc away), using only galaxies with absolute magnitudes M_r < −20. After applying a grid to the remaining galaxies, spheres are grown from all cells containing no galaxies until it encounters four galaxies on its surface. A sphere must have a minimum 10 h⁻¹ Mpc radius to be classified as a void (or part of one). If two spheres overlap by more than 50%, they are considered part of the same void. See Hoyle & Vogeley (2002) for a more detailed description of the VoidFinder algorithm. Those galaxies that fall within these void spheres are classified as voids. Galaxies that lie outside the spheres are classified as wall galaxies. Because we cannot identify the center of any void within 5 h⁻¹ Mpc of the edge of the survey, we classify those galaxies within this border region as "Uncertain."

Of the ∼800,000 galaxies with spectra available in SDSS DR7, 9519 are dwarf galaxies. Applying the spectroscopic cuts, our sample includes 993 void dwarf galaxies and 759 wall dwarf galaxies.

The abundances estimated using the direct T_e method for our dwarf galaxy sample are listed in Table 1. Also included are other significant characteristics and identification for the galaxies, including their large-scale environmental classification.

Table 1.  Analyzed Dwarf Galaxies

Indexa	R.A.	Decl.	Redshift	$12+\mathrm{log}\left(\tfrac{{\rm{O}}}{{\rm{H}}}\right)$		$12+\mathrm{log}\left(\tfrac{{\rm{N}}}{{\rm{H}}}\right)$		$12+\mathrm{log}\left(\tfrac{\mathrm{Ne}}{{\rm{H}}}\right)$		$\mathrm{log}\left(\tfrac{{\rm{N}}}{{\rm{O}}}\right)$		$\mathrm{log}\left(\tfrac{\mathrm{Ne}}{{\rm{O}}}\right)$		Void/Wall
40726	11h25m5210	−00°39'4176	0.0187	8.15	±0.09	6.72	±0.06	7.44	±0.12	−1.43	±0.11	−0.71	±0.15	Wall
41257	12h41m1241	−00°45'2455	0.0113	8.16	±0.24	6.96	±0.16	7.35	±0.31	−1.20	±0.29	−0.81	±0.40	Wall
42296	14h39m5003	−00°42'2285	0.0060	7.93	±0.12	6.72	±0.08	7.30	±0.16	−1.21	±0.14	−0.63	±0.20	Wall
42829	15h40m1850	−00°48'4504	0.0125	8.10	±0.36	6.92	±0.25	7.41	±0.48	−1.18	±0.43	−0.68	±0.60	Wall
44522	11h47m0073	−00°17'3922	0.0049	8.10	±0.25	6.91	±0.17	7.53	±0.33	−1.19	±0.30	−0.58	±0.42	Wall

Notes. Five of the 1561 dwarf galaxies analyzed from SDSS DR7. The flux values for all required emission lines can be found in the MPA-JHU value-added catalog. Abundance values are calculated using the direct T_e method and the O⁺ approximation defined in Section 2.2, with error estimates via a Monte-Carlo method. The void catalog of Pan et al. (2012) is used to classify the galaxies as either Void or Wall. If a galaxy is located too close to the boundary of the SDSS survey to identify whether or not it is inside a void, it is labeled as uncertain.

^aKIAS-VAGC galaxy index number.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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4.1.1. Oxygen, Nitrogen, and Neon Abundances

The distributions of oxygen, nitrogen, and neon abundances for dwarf galaxies as a function of large-scale environment are shown in Figures 2–4, respectively. All three histograms show a slight shift between voids and walls in the chemical abundances of dwarf galaxies. A two-sample Kolmogorov–Smirnov (K-S) test quantifies this observation: a test statistic of 0.05 for oxygen, 0.07 for nitrogen, and 0.07 for neon are produced, corresponding to a probability of 26%, 5.8%, and 5.5%, respectively, that a test statistic greater than or equal to that observed will be measured if the void sample was drawn from the wall sample. The cumulative distribution function (CDF) for each of these elements can be seen on the right in Figures 2–4; they show that void dwarf galaxies have roughly the same oxygen abundances, slightly higher neon abundances, and slightly lower nitrogen abundances than dwarf galaxies in more dense regions. The K-S test quantifies the visual interpretation of these figures that the distribution of oxygen is not significantly different for star-forming dwarf galaxies in voids and walls, while the distributions of nitrogen and neon abundances do differ slightly.

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The average and median values of the dwarf galaxy abundances also indicate either a slight shift or no shift as a result of the large-scale environment. The average oxygen abundance for void dwarf galaxies is 8.03 ± 0.009 and the median is 8.04, and the average oxygen abundance for wall dwarf galaxies is 8.02 ± 0.010 with a median value of 8.03. This implies that there is no significant difference in the oxygen abundances between void and wall dwarf galaxies (average shift of 0.01 ± 0.013; median shift of 0.01). The average nitrogen abundance for void dwarf galaxies is only 6.66 ± 0.006 with a median of 6.68, while the wall dwarf galaxies have an average nitrogen abundance of 6.69 ± 0.007 and a median of 6.68. The void dwarf galaxies have slightly lower nitrogen abundances by about 5% (an average shift of 0.02 ± 0.009 and a median shift of 0.00) relative to wall dwarf galaxies. In contrast, the average neon abundance for void dwarf galaxies is 7.26 ± 0.012 and the median is 7.30, while the average neon abundance for wall dwarf galaxies is 7.22 ± 0.014 with a median value of 7.28. The void dwarf galaxies have slightly higher neon abundances by about 10% (an average shift of 0.04 ± 0.019; a median shift of 0.02) relative to the wall dwarf galaxies. A tabular version of this analysis can be found in Table 2.

Table 2.  Abundance Statistics

Environment	Average	Median	Average Shifta	Median Shifta	p-value	K-S Test Statistic
$12+\mathrm{log}({\rm{O}}/{\rm{H}})$
Void	8.03 ± 0.009	8.04	−0.01 ± 0.013	−0.01	0.259	0.0513
Wall	8.02 ± 0.010	8.03
$12+\mathrm{log}({\rm{N}}/{\rm{H}})$
Void	6.66 ± 0.006	6.68	0.02 ± 0.009	0.00	0.0575	0.0677
Wall	6.69 ± 0.007	6.68
$12+\mathrm{log}(\mathrm{Ne}/{\rm{H}})$
Void	7.26 ± 0.012	7.30	−0.04 ± 0.019	−0.02	0.0554	0.0681
Wall	7.22 ± 0.014	7.28
$\mathrm{log}({\rm{N}}/{\rm{O}})$
Void	−1.36 ± 0.011	−1.38	0.03 ± 0.016	0.03	0.00364	0.0902
Wall	−1.33 ± 0.012	−1.36
$\mathrm{log}(\mathrm{Ne}/{\rm{O}})$
Void	−0.77 ± 0.015	−0.74	−0.02 ± 0.023	−0.01	0.0199	0.0772
Wall	−0.79 ± 0.018	−0.75

Notes. Statistics on the gas-phase oxygen, nitrogen, neon, nitrogen relative to oxygen, and neon relative to oxygen abundances in dwarf void and wall galaxies. Combined with the histograms in Figures 2–6, these results indicate an influence on the chemical evolution of galaxies by the large-scale environment, especially on the relative abundance of nitrogen to oxygen. Void galaxies have slightly higher neon abundances and slightly lower nitrogen abundances and N/O ratios than wall galaxies. There is no significant shift in the oxygen abundance or the Ne/O ratio between void and wall dwarf galaxies.

^aWall/Void (Positive shifts indicate that the wall values are greater than the void values; negative shifts indicate that the void values are greater than the wall values.)

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4.1.2. Ratio of Nitrogen, Neon to Oxygen

The ratio of nitrogen to oxygen is also important to investigate, as it communicates the nucleosynthesis history of the galaxies. As seen in Figure 5, the N/O abundance ratio indicates a slight large-scale environmental influence on the chemical evolution of dwarf galaxies—void dwarf galaxies have slightly lower N/O ratios than dwarf galaxies in denser regions. This difference is quantified in the K-S test: the test returned a probability of only 0.4% that a test statistic greater than or equal to 0.09 will be measured if the void sample was drawn from the wall sample. The distribution of N/O abundance ratios for void dwarf galaxies is lower by about 7% (an average shift of 0.03 ± 0.016 and a median shift of 0.03) relative to the distribution of N/O ratios in wall dwarf galaxies.

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In contrast, the ratio of neon to oxygen serves as a diagnostic of the accuracy of the abundance estimates. Because neon and oxygen are both synthesized via α processes in the same mass stars, they should always be produced in the same fixed ratio, assuming that the ratio f the IMF-averaged Ne and O yields does not depend on stellar metallicities. Even if the void environment influences the chemical evolution of dwarf galaxies, there should exist only a minor (if any) shift in the Ne/O ratio. As can be seen in Figure 6, there is very little difference in the distributions of the Ne/O ratio between the two populations. The K-S test quantifies this difference: the test returns a probability of 2% that a test statistic greater than or equal to 0.077 will be measured if the void sample was drawn from the wall sample. Unlike the shifts measured in the distributions of nitrogen, neon, and N/O, the average shift of 0.02 ± 0.023 in the Ne/O abundance ratio is within the uncertainty of the shift. As physically expected, the void environment has almost no influence on the relative synthesis of neon and oxygen in star-forming dwarf galaxies.

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Uncertainties in the computed abundances are estimated using a Monte-Carlo method. Using the measured line fluxes and scaled uncertainty estimates, we calculate 100,000 abundance estimates. For each abundance estimate, a new positive "fake" line flux is drawn from a normal distribution. We use the standard deviation in these sets of 100,000 calculated abundance values for the error in our abundance estimate. See Douglass & Vogeley (2017a) for a more in-depth description of this process.

Many physical properties of galaxies exhibit a radial dependence (Bell & de Jong 2000). As a result, abundance estimates can depend on where the spectroscopic fiber is placed on the galaxy. The estimated abundance will not necessarily be representative of a global abundance value if not all of the galaxy's light is contained within the fiber. Belfiore et al. (2017) show that both the metallicity and N/O ratio gradients are relatively flat for lower mass galaxies (log(M/M_⊙) = 9) and steepen with increasing stellar mass. In SDSS DR7, the spectroscopic fiber diameter is 3''; this corresponds to a minimum physical diameter of 1.31 h⁻¹ kpc at a redshift z < 0.03. For most of the dwarf galaxies in this study, this contains the majority of their angular size. Assuming the abundance gradients remain flat for dwarf galaxies, as suggested by the results of Belfiore et al. (2017), then our estimates of the gas-phase chemical abundances for our sample of dwarf galaxies are independent of the location of the spectral fiber on the galaxies' surfaces.

The selection criteria outlined in Section 3.1 limit our sample to only star-forming dwarf galaxies. As a result, this is not a representative sample of the entire dwarf galaxy population. We are only able to discuss the influence of the large-scale environment on star-forming dwarf galaxies in this study. Unfortunately, it is impossible to estimate the chemical abundances of red dwarf galaxies with the direct T_e method because the UV photons from young stars are needed to excite the interstellar gas. In addition, our temperature requirement eliminates extremely metal-poor galaxies. To examine the influence of this bias on our results, we repeat the analysis with a maximum allowed temperature of 2.5 × 10⁴ and 3 × 10⁴ K (the maximum allowed temperature in the work by Douglass & Vogeley 2017a, 2017b). The resulting shifts in each abundance ratio are listed in Table 3. There is no difference in the measured shifts seen with temperature cutoffs of 3 × 10⁴ and 2.5 × 10⁴ K, but a significant number of low-metallicity galaxies are removed from the sample when we require temperatures no higher than 2 × 10⁴ K. While we still see shifts in the various abundance distributions, their statistical significance is reduced.

Table 3.  Effect of Maximum Temperature on Abundance Shifts

Max T[O iii]	$12+\mathrm{log}({\rm{O}}/{\rm{H}})$	$\mathrm{log}({\rm{N}}/{\rm{O}})$	$\mathrm{log}(\mathrm{Ne}/{\rm{O}})$
2 × 104 K	−0.01 ± 0.013 (2%)	0.03 ± 0.016 (7%)	−0.02 ± 0.023 (5%)
2.5 × 104 K	−0.02 ± 0.013 (5%)	0.04 ± 0.016 (10%)	−0.03 ± 0.023 (7%)
3 × 104 K	−0.02 ± 0.013 (5%)	0.04 ± 0.016 (10%)	−0.03 ± 0.023 (7%)

Note. Magnitude of the average shifts between the void and wall dwarf galaxies, with samples limited by the maximum temperature listed on the left. Positive shifts indicate that the wall values are greater than the void values; negative shifts indicate that the void values are greater than the wall values. These shifts change very little with the different maximum temperatures, so the bias toward higher metallicities introduced with the maximum allowed temperature of 2 × 10⁴ K reduces the significance of our results.

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While no estimates of the nitrogen or N/O abundances have been made on a large selection of the SDSS galaxies, we can compare our oxygen abundance estimates to the metallicity values measured by Tremonti et al. (2004). While we both use data from the MPA-JHU value-added catalog, Tremonti et al. (2004) employs an empirical method to calculate the metallicity that is based on calibrated relationships between direct T_e methods and strong-line ratios. The results of this comparison are shown in Figure 7. While the majority of our abundance estimates agree reasonably well with the values calculated by Tremonti et al. (2004), it is also clear that our estimates often predict abundances lower than those previously published. This is especially true for the low-metallicity regime ($12+\mathrm{log}({\rm{O}}/{\rm{H}})$ < 7.6). Methods that are based on calibrations rarely use low-metallicity galaxies in their source for calibrating. As a result, empirical methods will often overestimate the abundance values, especially in the low-metallicity regime. Kennicutt et al. (2003) show that strong-line methods (methods which make extreme use of the strong emission lines) can overestimate the metallicity abundances by as much as 0.3 dex. Therefore, we are not surprised at the apparent lack of correlation between our oxygen abundance estimates and those of Tremonti et al. (2004).

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Studying how the N/O ratio depends on the metallicity (gas-phase oxygen abundance) probes the nucleosynthetic production of nitrogen in stars within the galaxies. It is believed that nitrogen can be produced as both a primary and secondary element, depending on the initial metallicity of the stars. If there are enough of the heavy elements available when the stars are created (oxygen, carbon, etc.), then the CNO cycle can commence much earlier in the star's lifetime, resulting in a higher production of nitrogen than if the star is originally created with very few heavy elements. If this is the case, then we should see no relationship between the N/O ratio and the oxygen abundance below a certain metallicity value (the primary nitrogen production phase); above this threshold metallicity, the N/O value should increase linearly with the oxygen abundance (the secondary nitrogen production phase).

As we see in Figure 8, there is no evidence of a secondary nitrogen production phase in our sample of dwarf galaxies. This is in contrast with the evidence of secondary nitrogen production seen in Figure 11 of Section 4.7; the source of this discrepancy is unclear. The relationship between metallicity and the N/O ratio instead shows a large scatter, where the N/O ratio is roughly independent of the metallicity. This relationship between the N/O ratio and metallicity has been observed many times (e.g., Garnett 1990; Vila Costas & Edmunds 1993; Thuan et al. 1995; Izotov & Thuan 1999; Henry et al. 2000; Pilyugin et al. 2002; Lee et al. 2004; Pilyugin et al. 2004; Nava et al. 2006; van Zee & Haynes 2006; Pérez-Montero & Contini 2009; Amorín et al. 2010; Berg et al. 2012; Sánchez Almeida et al. 2016), and it has been interpreted to represent the production of primary nitrogen. As listed in Table 2, we find that the void dwarf galaxies have a median N/O value of −1.38 and the wall dwarf galaxies have a median N/O value of −1.36. These values fall within the previously reported N/O ratio averages for the plateau.

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Also shown in Figure 8 are local linear regressions of the void (red) and wall (black) dwarf galaxy samples. The local linear regressions in this and the following figures are calculated at each point using a window containing 50% of the nearest data. These non-parametric approximations successfully represent the central trend of the data, but they exaggerate the sparse scatter in the tails. Here they exhibit a slight negative correlation between the N/O ratio and the oxygen abundance. This would indicate a constant value of nitrogen being synthesized in the galaxies, independent of the amount of oxygen being produced. A negative correlation similar to this was also observed by Andrews & Martini (2013) and Douglass & Vogeley (2017b). In a footnote, Andrews & Martini (2013) note that they measure a slope of −0.21 for their stellar mass-binned galaxies with metallicities $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ < 8.5, while Douglass & Vogeley (2017b) find a slope of −0.38 ± 0.078 for dwarf galaxies. Linear fits to the local linear regressions find slopes of −0.254 ± 0.0029 and −0.36 ± 0.010 for the void and wall dwarf galaxies, respectively. We attribute these negative correlations to the significant scatter in the distributions and do not believe them to be physically relevant.

Similar evidence of the nitrogen production phases can also be observed when looking at the relationship between the nitrogen and oxygen abundances relative to hydrogen. Figure 9 depicts a positive relationship between the nitrogen and oxygen abundances. Linear fits to the central segments of the local linear regressions of the void and wall dwarf galaxy samples exhibit slopes of 0.746 ± 0.0029 and 0.70 ± 0.034, respectively, larger than the slope of 0.62 ± 0.078 found by Douglass & Vogeley (2017b). These slopes indicate that nitrogen is produced at a slower rate than oxygen in dwarf galaxies. A nitrogen plateau in Figure 8 would manifest itself as a relationship between the N/H and O/H ratios (shown in Figure 9) with a linear slope of 1. Secondary nitrogen production, a positive relationship in Figure 8, would correspond to a relationship between N/H and O/H in Figure 9 with a slope greater than 1.

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The slopes of the local linear regressions in both Figures 8 and 9 show that there is no significant difference in the abundance ratio relationships between void dwarf galaxies and dwarf galaxies in denser regions. This supports the results found by Douglass & Vogeley (2017b), and Vincenzo & Kobayashi (2018). The large-scale environment does not appear to have an influence in the nucleosynthesis of nitrogen in dwarf galaxies.

To serve as a diagnostic for the abundance estimates, we also look at the relationship between the metallicity and the Ne/O ratio. Because both neon and oxygen are synthesized in α processes, their relative abundance should not depend on a galaxy's metallicity. As Figure 10 shows, there is no significant relationship between the oxygen abundance and the Ne/O ratio. This matches the results of Kobulnicky & Skillman (1996), Izotov & Thuan (1999), Lee et al. (2004), Izotov et al. (2006), van Zee & Haynes (2006), and Pérez-Montero et al. (2007). We note an increase in the scatter of this relationship with decreasing metallicity, which the local linear regressions shown in Figure 10 emphasize. Since both the [O iii] λ4363 and the [Ne iii] λ3869 emission lines are relatively weak, the quality of their detection decreases with the metallicity and therefore increases the scatter in this relationship. The local linear regressions of the void and wall dwarf galaxies in Figure 10 do not show a difference in the abundance ratio relationship between void dwarf galaxies and dwarf galaxies in denser regions. As expected from stellar nucleosynthesis, the void environment does not appear to influence the relative abundances of α-process particles in dwarf galaxies.

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Expanding on the mass–metallicity relation investigated in Douglass & Vogeley (2017a), we look at the correlation between stellar mass and the oxygen abundance in our now substantially larger sample of dwarf galaxies. The mass–metallicity relation for our dwarf galaxies can be seen in the left panel of Figure 11. We also include those galaxies from the MPA-JHU catalog with metallicity estimates from Tremonti et al. (2004) to place our sample in context. The majority of our dwarf galaxies follow the expected mass–metallicity trend. There is no discernible influence from the large-scale environment on the mass–metallicity relation for dwarf galaxies.

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We also look at the N/O ratio as a function of stellar mass (Figure 11, right panel). Similar to the O/H–N/O relation studied in Section 4.5, the N/O ratio is predicted to be constant below some critical mass; above this, the N/O ratio should increase linearly with the stellar mass. Unlike the relation seen in Figure 8, we see both the N/O plateau and the positive correlation on the right in Figure 11. To better investigate the influence of the void environment on the relationship between the stellar mass and the N/O ratio, we include local linear regressions of the two dwarf galaxy populations in Figure 11. We observe a difference in this relation as a function of the large-scale environment: piecewise linear functions fit to the local linear regressions reveal that the critical mass for void galaxies is around $\mathrm{log}({M}_{* }/{M}_{\odot })\sim 7.7$, while the galaxies in denser regions exhibit a critical mass of ∼7.8. This difference suggests that void galaxies begin to synthesize secondary nitrogen at lower stellar masses than galaxies in more dense regions, consistent with the statistically insignificant shift seen in Figure 2, where void dwarf galaxies may have slightly higher oxygen abundances than dwarf galaxies in more dense environments.

In addition to looking at the stellar mass, we also investigate the relationship between the amount of neutral hydrogen and the gas-phase chemical abundances in our sample of star-forming dwarf galaxies. As shown in Moorman et al. (2014), void galaxies typically have lower H i masses than galaxies in more dense regions, consistent with the overall shift of the luminosity or stellar mass function to lower luminosity or mass in voids. In the fixed range of luminosity of our dwarf galaxy sample, as Figure 12 shows, our sample of void dwarf galaxies has higher H i masses than the dwarf galaxies in denser regions. The gas in the void environment is cooler than that found in denser regions (due to less events like shock heating, etc.), which permits void galaxies to have higher H i masses for a given stellar mass. Therefore, because we are fixing the stellar mass in our sample of galaxies (by only studying dwarf galaxies), we should find that the void dwarf galaxies have higher H i masses than for those dwarf galaxies in denser environments.

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The H i mass–metallicity and H i mass–N/O relations can be seen in Figure 13, extending the results of Bothwell et al. (2013) down to $\mathrm{log}({M}_{* }/{M}_{\odot })\approx 6$. Unlike the correlation between the stellar mass and the chemical abundances, there is very little correlation between the abundances and the H i mass. There is no significant relationship between the H i mass and the metallicity of a galaxy—the correlation coefficient for the dwarf galaxies shown in the upper left panel of Figure 13 is only 0.07 ± 0.046. This is not surprising, as our sample of star-forming dwarf galaxies probes the low-metallicity range of the MZ relation where there is no strong relationship between the metallicity and stellar mass. We also see no significant relationship between a dwarf galaxy's H i mass and its N/O ratio; the correlation coefficient for the galaxies shown in the upper right panel of Figure 13 is only 0.06 ± 0.046.

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Due to the time delay in the production of nitrogen relative to oxygen, we expect the N/O ratio to decrease with increasing H i mass, since more evolved galaxies have higher N/O ratios and will have used up most of their neutral hydrogen. Bothwell et al. (2013) demonstrates the existence of this relationship at a fixed stellar mass. The first row of Figure 13 shows little, if any, relationship between the H i mass and the chemical abundances. However, the bottom row of Figure 13 shows that there is an inverse relationship between the chemical abundance and the H i mass for fixed stellar mass (indicated by the colors of the points).

The gas-phase chemical abundance is expected to have a positive correlation with a galaxy's color. Older galaxies have had more time to convert their gas into heavier elements through star formation, increasing their metallicities. The color–metallicity and color–N/O relations for our sample of star-forming dwarf galaxies can be seen in Figures 14 and 15. As we see, bluer galaxies have lower O/H and N/O ratios when we look at both the u − r and g − r colors.

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The presence of a relationship between the N/O ratio and the color of a galaxy can indicate a time delay between the release of nitrogen and oxygen (van Zee & Haynes 2006; Berg et al. 2012). If higher-mass stars are the main source of oxygen, then the oxygen will be released on a shorter timescale than nitrogen for a given star formation episode (since higher-mass stars turn off the main sequence earlier than the intermediate-mass stars that synthesize nitrogen). Therefore, the amount of nitrogen relative to oxygen should increase as the hotter, more massive stars burn out and the galaxy becomes redder. This trend can be seen in the star-forming dwarf galaxies on the right of Figures 14 and 15, matching the trends seen in Douglass & Vogeley (2017b), van Zee & Haynes (2006), and Berg et al. (2012).

There does not appear to be any influence from the large-scale environment on the relationship between the color and chemical abundances for star-forming dwarf galaxies. There is no obvious difference between the void and wall dwarf galaxies in the left-hand panels of Figures 14 and 15, when we concentrate on the oxygen abundance as a function of color. To help discern any influence from the environment on the N/O ratio as a function of color, we show the local linear regressions on the right-hand plots of Figures 14 and 15. The shift toward higher N/O ratios seen in the wall bins in both figures is the same shift identified in the histograms in Figure 5. Any variation in the color–abundance relationship between the void and wall populations except a vertical shift would be evidence of the large-scale environment influencing the relationship. The scatter of the redder galaxies prohibits us from being able to make any assertions about differences in the slopes of these local linear regressions.

There is thought to be a fundamental relationship between the stellar mass, star formation rate (SFR), and metallicity of a galaxy (Lara-López et al. 2010; Mannucci et al. 2010; Andrews & Martini 2013); the metallicity of a galaxy should increase with stellar mass and decrease as a function of the SFR. Henry et al. (2013) observe an inverse relationship between the metallicity and SFR of low-mass galaxies. However, as was seen in Douglass & Vogeley (2017a), Figure 16 shows very little correlation between the SFR and metallicity or N/O ratio of the star-forming dwarf galaxies. When we separate the dwarf galaxies by their large-scale environment, we see no difference in the correlation coefficients between the two environments; there is no discernible influence on the relationship between the SFR and the chemical abundances by the large-scale environment.

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We also inspect the relationship between the sSFR and the gas-phase chemical abundances in star-forming dwarf galaxies. As shown in Figure 17, there is a stronger correlation between the sSFR of a dwarf galaxy and its metallicity and N/O ratio. The left-hand panel of Figure 17 shows the relationship between the gas-phase oxygen abundance and the sSFR for star-forming dwarf galaxies; to place our results in context, we also include (gray stars) those dwarf galaxies in SDSS DR7 for which Tremonti et al. (2004) was able to estimate metallicities. In the metallicity regime we are able to probe ($12+\mathrm{log}({\rm{O}}/{\rm{H}})\leqslant 8.5$), the star-forming dwarf galaxies display relatively little relationship between their sSFR and metallicity.

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As we see on the right in Figure 17, though, there is a strong anti-correlation between the sSFR and N/O ratio for the star-forming dwarf galaxies. Galaxies with higher sSFRs may be producing more massive stars than galaxies with lower sSFRs. If oxygen is produced in more massive stars than those which produce nitrogen, then the galaxies with higher sSFRs will produce more oxygen earlier than those galaxies with lower sSFRs. Increasing the gas-phase oxygen abundance relative to nitrogen will decrease the N/O ratio in these galaxies with higher sSFRs. Therefore, an anti-correlation between the sSFR and N/O ratio is further evidence that oxygen is produced in higher-mass stars than those which synthesize nitrogen. A large-scale environmental influence on the relationship between the sSFR and the N/O ratio would manifest as a difference in the slopes of the local linear regressions. With the influence of the scatter on these approximations, it is apparent that there is no significant influence from the large-scale environment on the relationship between N/O and sSFR.

We posit that if the shift toward slightly higher metallicities in the star-forming void dwarf galaxies was significant, it would be due to a large-scale environmental effect on the ratio of a galaxy's dark matter halo mass to stellar mass (M_DM/M_*). Goldberg & Vogeley (2004) show that gravitational clustering within a void proceeds as if in a very low-density universe, where the growth of gravitationally bound dark matter halos ends relatively early. Afterwards, there is relatively little interaction between the void galaxies because of the lower density and faster local Hubble expansion. Simulations by Jung et al. (2014) and Tonnesen & Cen (2015) show that, for a fixed dark matter halo mass, the stellar masses of central galaxies located in voids are smaller than those of central galaxies living in denser regions. The ΛCDM cosmology predicts that galaxies formed in voids will be retarded in their star formation when compared to those in denser environments. Therefore, void dwarf galaxies could have higher M_DM/M_* ratios than dwarf galaxies in denser regions. Indeed, Tojeiro et al. (2017) find that the ratio of stellar mass to halo mass increases with the large-scale environmental density.

If this were the case, then the potential well and virial radius of the void galaxies would be large enough to retain more of the heavy elements that are blown from the ISM to the CGM of a galaxy (e.g., from a supernova). The simulation results of Tonnesen & Cen (2015) find that, for central galaxies with halo masses between 10¹¹ and 10^12.9, void galaxies have ∼10% larger ratios of dark matter halo mass to stellar mass compared with wall galaxies at z = 0. In wall galaxies, more of these heavy elements can escape the dwarf galaxy, while in void galaxies they are confined to the CGM and eventually fall back onto the galaxy's ISM. If star-forming void dwarf galaxies are able to retain more oxygen relative to their hydrogen abundance, then they will reach the critical value of O/H for secondary nitrogen production (via the CNO cycle) earlier than the star-forming wall dwarf galaxies, for a given stellar mass. We see evidence of this in Figure 11, where the N/O plateau for the void dwarf galaxies exists for stellar masses $\mathrm{log}({M}_{* }/{M}_{\odot })\lesssim 7.7$. In contrast, the N/O plateau for the wall dwarf galaxies exists for stellar masses $\mathrm{log}({M}_{* }/{M}_{\odot })\lesssim 7.8$.

If void dwarf galaxies have higher M_DM/M_* ratios than dwarf galaxies in denser environments, we would expect to see an environmental influence on other characteristics of these galaxies. First, the ratio of neutral hydrogen mass to stellar mass of the dwarf galaxies would be higher in star-forming void galaxies than star-forming wall galaxies, under the assumption that neutral hydrogen traces dark matter. We see this effect both in Figure 9 of Moorman et al. (2016) and in Figure 12. Second, the H i mass function should shift less from wall to void galaxies than the shift seen in the luminosity function. Indeed, Moorman et al. (2016) finds a shift of characteristic H i mass by a factor of 1.4 in the H i mass function, while Hoyle et al. (2005) measures a shift by a factor of 2.5 in luminosity in the luminosity function between these two environments. The fact that we find an insignificant shift in the metallicity of dwarf galaxies between the void and denser environments indicates that the difference in the M_DM/M_* ratios between the two environments is not that significant (or it does not have much affect on the chemical composition of a galaxy's ISM).

As we see in Figure 5, star-forming void dwarf galaxies have a lower N/O ratio than wall dwarf galaxies. This strengthens the preliminary results found in Douglass & Vogeley (2017b) and the simulation results of Cen (2011), indicating that void galaxies are retarded in their star formation and that cosmic downsizing might depend on the large-scale environment. As suggested by van Zee & Haynes (2006), a galaxy with a declining SFR at late times (a wall galaxy) will have a higher N/O ratio than a galaxy with a constant SFR (a void galaxy); the ongoing star formation in the void galaxies will release more oxygen into the ISM, decreasing their N/O ratio relative to the galaxies with declining SFRs. This concept is supported by the color–N/O diagram in Figures 14 and 15, where the bluer galaxies have lower N/O ratios. The correlations between color and the N/O ratio found in van Zee & Haynes (2006), Berg et al. (2012), Douglass & Vogeley (2017b), and this work are a result of declining SFRs (van Zee & Haynes 2006). The average lower N/O ratios that we see in star-forming void dwarf galaxies may be observational evidence that cosmic downsizing is environmentally dependent.

Previous studies have either hypothesized (Pustilnik et al. 2006, 2011a, 2013) or concluded (Filho et al. 2015; Sánchez Almeida et al. 2016) that low-metallicity objects preferentially reside in low-density environments. Douglass & Vogeley (2017a) find that, out of 135 dwarf galaxies studied, there is no difference in the fraction of low-metallicity dwarf galaxies that reside in voids and denser regions. Of the 1722 dwarf galaxies we analyze, 82 have extremely low metallicity values ($12+\mathrm{log}({\rm{O}}/{\rm{H}})$ ≤ 7.6). Of these 82 low-metallicity dwarf galaxies, 46 are found in voids (approximately 5% of the star-forming void dwarf galaxy population studied) and 36 are located in denser regions (5% of the star-forming wall dwarf galaxy population studied). These population fractions do not support the existence of a special population of extremely metal-poor dwarf galaxies in voids.

We find that these 82 extremely metal-poor galaxies have comparably lower nitrogen abundances when compared to the total star-forming dwarf galaxy population studied. From Figures 14 and 15, it is apparent that these extremely metal-poor star-forming dwarf galaxies cover the entire color range of dwarf galaxies in this study. Figure 16 also shows that the sSFRs and sSFRs conform with the observed relationship between the N/O ratio and the sSFR.

One possible interpretation of these extremely metal-poor dwarf galaxies is that they are green pea galaxies. A class of luminous compact galaxies, Cardamone et al. (2009) identified these objects to be star-bursting galaxies at higher redshifts. (Their color is a result of unusually large [O iii] λ5007 emission line fluxes redshifted into the r-band of SDSS.) These galaxies are found to have low metallicities for their stellar mass; their N/O ratios are high for their estimated metallicities. They typically have sSFRs between 10⁻⁷ and 10⁻⁹ yr⁻¹ (Izotov et al. 2011). While some of the extremely metal-poor galaxies we identify also have high N/O ratios for their metallicities, they have sSFRs between 10⁻¹⁰ and 10⁻⁸ yr⁻¹, so only some of them might be green pea galaxies.

The few extremely metal-poor galaxies with high N/O ratios could be H ii regions contaminated by shock waves. As described by Peimbert et al. (1991), shock waves will increase the intensities of auroral lines. Since we estimate the temperature of the H ii regions with the ratio of [O iii] λ4363 to [O iii] λλ4959, 5007, this would result in an overestimation of the temperature and an underestimate of the oxygen abundance. The nitrogen abundance would also be underestimated, but to a lesser extent (as it is less sensitive to the electron temperature); this combination results in an overestimate of the N/O ratio. We would see evidence of shock waves dominating the spectra of these galaxies in the BPT diagram; because each of these galaxies resides in the star-forming region of the BPT diagram, shock waves are an unlikely explanation for those extremely metal-poor dwarf galaxies with high N/O ratios.