CHAOS IV: Gas-phase Abundance Trends from the First Four CHAOS Galaxies

All CHAOS observations are obtained following a consistent methodology, but here we highlight details specific to new observations of NGC 3184. Optical spectra of NGC 3184 were obtained during 2012 March and 2013 January using the Multi-Object Double Spectrographs (MODS; Pogge et al. 2010) on the Large Binocular Telescope (LBT). The spectra were acquired with the MODS1 unit as the MODS2 spectrograph was not available at the time of the observations. We obtained simultaneous blue and red spectra using the G400L (400 lines mm⁻¹, R ≈ 1850) and G670L (250 lines mm⁻¹, R ≈ 2300) gratings, respectively. This setup provided broad spectral coverage extending from 3200 to 10,000 Å. Multiple fields were targeted in order to maximize the number of H ii regions with auroral-line detections, i.e., [S ii] λλ4068,4076, [O iii] λ4363, [N ii] λ5755, [S iii] λ6312, and [O ii] λλ7320,7330. Individual field masks, cut to target 17–25 H ii regions simultaneously, were observed for six exposures of 1200 s, or a total integration time of 2 hr per field.

Targeted H ii regions in NGC 3184, as well as alignment stars, were selected based on archival broadband and Hα imaging from the SINGS program (Kennicutt et al. 2003a; Muñoz-Mateos et al. 2009). Slits were cut to be 1'' wide by a minimum of ∼10'' long, to cover the extent of individual H ii regions, and extended to utilize extra space for the sky. Slits were placed on relatively bright H ii regions across the entirety of the disk with the goal of ensuring that both radial and azimuthal trends in the abundances could be investigated. The locations of the slits for each of the three MODS fields observed in NGC 3184 are shown in Figure 1.

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We refer to the locations of the observed H ii regions in NGC 3184 as offsets, in R.A. and decl., from the center of the galaxy (see Table A1 in Appendix A). The observations were obtained at relatively low airmass (≲1.2). Furthermore, slits were cut close to the median parallactic angle of the observing window for NGC 3184. The combination of low airmass and matching the parallactic angle minimizes flux lost due to differential atmospheric refraction between 3200 and 10,000 Å (Filippenko 1982).

We report the new observations of NGC 3184 in Appendix A, while details of previously reported observations can be found in B15 for NGC 628, C15 for NGC 5194, and C16 for NGC 5457. The adopted properties of these four galaxies are listed in Table 1. Note that for NGC 628, NGC 5194, and NGC 5457, we report properties of these galaxies as adopted by the original CHAOS studies. It may be of interest to some readers that since the time of the previous CHAOS studies, updated (and likely more accurate) distances have been measured for NGC 628 and NGC 5194 by McQuinn et al. (2017) and for NGC 5457 by Jang & Lee (2017) using the tip of the red giant branch method. While many absolute properties change with galaxy distance, the results presented here are concerned only with relative abundance trends versus R_e or R₂₅, and so they are not affected by the updated distances.

For a detailed description of the data reduction procedures, we refer the reader to B15. Here, we only note the primary points of our data processing. Spectra were reduced and analyzed using the beta-version of the MODS reduction pipeline⁶ , which runs within the XIDL⁷ reduction package. Given that the bright disks of CHAOS galaxies can complicate local sky subtraction, additional sky slits were cut in each mask that provided a basis for clean sky subtraction. Continuum subtraction was performed in each slit by scaling the continuum flux from the sky-slit to the local background continuum level. One-dimensional spectra were then corrected for atmospheric extinction and flux calibrated based on observations of flux-standard stars (Bohlin 2014). At least one flux standard was observed on each night science data were obtained. An example of a flux-calibrated spectrum is shown in Figure 2.

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We provide a more detailed description of the adopted continuum modeling and line-fitting procedures applied to the CHAOS observations in B15. Below, we only highlight the fundamental components of this process. We model the underlying continuum of our MODS1 spectra using the STARLIGHT⁸ spectral synthesis code (Fernandes et al. 2005) in conjunction with the models of Bruzual & Charlot (2003). Allowing for an additional nebular continuum, we fit each emission line with a Gaussian profile. We note that we have modeled blended lines (H7, H8, and H11–H14) in the Balmer series based on the measurements of unblended Balmer lines and the tabulated atomic ratios of Hummer & Storey (1987), assuming Case B recombination.

We correct the strength of emission features for line-of-sight reddening using the relative intensities of the four strongest Balmer lines (Hα/Hβ, Hγ/Hβ, Hδ/Hβ). We report the determined values of E(B − V) in Table A2 of Appendix A.⁹ We do not apply an ad hoc correction to account for Balmer absorption as the lines were fit simultaneously with the stellar population models. The stellar models contain stellar absorption with an equivalent width of ≈1–2 Å in the Hβ line. The uncertainty associated with each measurement is determined from measurements of the spectral variance, extracted from the two-dimensional variance image, uncertainty associated with the flux calibration, Poisson noise in the continuum, read noise, sky noise, flat-fielding calibration error, error in continuum placement, and error in the determination of the reddening. We also include a 2% uncertainty based on the precision of the adopted flux calibration standards (Oke 1990, see discussion in Berg et al. 2015).

A few emission features required extra care, such as the intrinsically faint auroral lines that are critical to this study. As has been done with the previous CHAOS galaxies, we inspected the lines by eye and measured the flux of each auroral line by hand in the extracted spectra to confirm the fit. In cases where these measurements were in disagreement, we adopted the by-hand measurement. This was most common for the [N ii] λ5755 line, which falls near the wavelength region affected by the dichroic cutoff of MODS and the "red bump" Wolf–Rayet carbon features. Additionally, we have updated our line-fitting code to include the [Fe ii] λ4360 emission feature, which may significantly contaminate [O iii] λ4363 line measurements at high metallicities (12 + log(O/H) > 8.4; Curti et al. 2017).

Finally, the [O ii] λλ3726,3729 doublet is blended for all observations due to the moderate resolution of MODS. However, two components are apparent in the doublet profile for the majority of spectra and are therefore modeled using two Gaussian profiles. The reported [O ii] λ3727 fluxes represent the total flux in the doublet.

The reddening-corrected emission-line intensities measured from H ii regions in NGC 628, NGC 5194, and NGC 5457 have been previously reported in B15, C15, and C16, respectively. For the NGC 3184 observations reported here, the reddening-corrected line intensities are listed in Table A2 of Appendix A.

The combined sensitivity and large wavelength coverage of CHAOS observations allows electron temperature and density measurements from multiple ions. The temperature-sensitive auroral-to-nebular line ratios most commonly observed in the CHAOS spectra are [S ii] λλ4068,4076/λλ6717,6731; [O iii] λ4363/λλ4959,5007; [N ii] λ5755/λλ6548,6584; [S iii] λ6312/λλ9069, 9532; and [O ii] λλ7320,7330/λλ3727,3729. To account for possible contamination by atmospheric absorption of the red [S iii] lines, we follow our practice in B15 of upward correcting the weaker of the two lines by the theoretical ratio of λ9532/λ9069 = 2.47. Assuming a three-zone ionization structure, these measurements probe the physical conditions throughout the nebula, and allow for the comparison of multiple measures in the low-ionization zone. We use the ratio of the [S ii] λλ6717,6731 emission lines as a sensitive probe of the nebular electron density in typical H ii regions (${10}^{1.5}\lt {n}_{e}({\mathrm{cm}}^{-3})\lt {10}^{3.5}$). In order to compare the first four CHAOS galaxies in a uniform, consistent manner, we recalculate the nebular temperatures and densities adopting the atomic data reported in Table 4 of B15 and using the observed temperature- and density-sensitive line ratios with the PyNeb package in python (Luridiana et al. 2012, 2015).

3.1.1. Temperature Relationships

It is common practice to use temperature–temperature (${T}_{e}-{T}_{e}$) relationships derived from photoionization models to infer the temperatures in unobserved ionization zones. The relationships of Garnett (1992, hereafter, G92) are a typical choice; however, significant updates in atomic data (especially for [S iii] and [O ii]; see Figure 4 in B15) have occurred since the time of that work and so new relationships are warranted.

In C16, we obtained temperature measurements from one or more auroral lines in 74 H ii regions in M101, the largest number in a single galaxy to date. These data used the updated atomic data recommended in B15 and provided a large data set of well-measured temperatures from multiple ions that allowed us to empirically determine new ${T}_{e}-{T}_{e}$ relationships:

$$\begin{eqnarray}&&{T}_{e}[{\rm{N}}\,{\rm{II}}]=(0.714\pm 0.142)\times {T}_{e}[{\rm{O}}\,{\rm{III}}]+(2.57\pm 1.25),\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{T}_{e}[{\rm{S}}\,{\rm{III}}]=(1.312\pm 0.075)\times {T}_{e}[{\rm{N}}\,{\rm{II}}]-(3.13\pm 0.58),\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{T}_{e}[{\rm{S}}\,{\rm{III}}]=(1.265\pm 0.140)\times {T}_{e}[{\rm{O}}\,{\rm{III}}]-(2.32\pm 1.35),\end{eqnarray} \tag{ 3 }$$

where temperatures are in units of 10⁴ K.

Using the combined data from the first four CHAOS galaxies, we compile a sample of 190 individual H ii regions with multiple auroral-line measurements. Of these regions, 175 have T_e[O iii], T_e[S iii], or T_e[N ii]. In Figure 3, we compare these data to the ${T}_{e}-{T}_{e}$ relationships of G92 (red dotted–dashed lines) and C16 (black dashed lines). For reference, the line of equality is shown as a dotted black line. We recognize that these are simple ${T}_{e}-{T}_{e}$ relationships; in the future, we will use the full CHAOS data set to explore more complicated ${T}_{e}-{T}_{e}$ relationships, for example, accounting for the effects of ionization discussed below.

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For each set of variables, we determine the best-fit ${T}_{e}-{T}_{e}$ relationship using a Bayesian linear regression. Specifically, we use the code python linmix,¹⁰ which is an implementation of the linear mixture model algorithm developed by Kelly (2007) to fit data with uncertainties on two variables, including explicit treatment of intrinsic scatter. Intrinsic scatter, σ_int., is due to real deviations in the physical properties of our sources that are not completely captured by the variables considered. By introducing an additional term representing the intrinsic scatter to the weighting of each data point in the fit, we can determine the median of the normally distributed intrinsic random scatter about the regression. The calculated total and intrinsic scatters, σ_tot. and σ_int. respectively, as well as the number of regions used in the fit, are presented in Figure 3.

The top two panels of Figure 3 compare temperature measurements that characterize the low-ionization zone. On the left, we use the 115 regions with both [N ii] and [O ii] measurements in our sample, and find a best fit of T_e[N ii] = [T_e[O ii]$-(1.203\pm 1.144)]/(1.004\pm 0.150)$. As expected, the overall trend follows a one-to-one relationship within the limits of the uncertainties but with both large total (σ_tot. = 1280 K) and intrinsic (σ_int. = 1150 K) scatters. While equal temperatures are expected from photoionization models, the data tend to be shifted toward higher T_e[O ii]. This is true for the majority of the sample, which is clustered within 1000–2000 K of the equality relationship, but especially for the more extreme outliers that offset up to roughly 5000 K.

We note that dielectronic recombination can contribute to the observed [O ii] emission, especially λλ7320,7330, in more metal-rich nebulae (e.g., Rubin 1986). The magnitude of the effect increases strongly with decreasing temperature (increasing metallicity) but depends on the electron density. To this end, Liu et al. (2001) showed that recombination can play an important role in exciting both the [O ii] λλ7320,7330 and [N ii] λ5754 auroral lines in the higher-density gas of planetary nebulae (>10³ cm⁻³). These authors showed that this effect leads to overestimated [O ii]- and [N ii]-derived electron temperature measurements. However, we show below that T_e[N ii] is well behaved with respect to T_e[S iii], which implies that the recombination contribution must be small at the low densities of our nebulae. Thus, our data are consistent with previous reports of systematically larger T_e[O ii] than T_e[N ii] measurements (e.g., Esteban et al. 2009; Pilyugin et al. 2009; Berg et al. 2015) that cannot be accounted for by recombination processes, and so we do not favor [O ii] as a reliable low-ionization zone temperature indicator. We reserve further analysis for the complete CHAOS sample, where we will revisit the reliability of [O ii] as a diagnostic and investigate the effects of sky contamination, recombination, and reddening.

In the top right panel of Figure 3, we compare [N ii] and [S ii] using the [S ii] temperatures presented in C16, plus newly derived values for NGC 628, NGC 5194, and NGC 3184, comprising a sample of 106 regions. As expected for two ions that probe similar low-ionization gas, the best fit is consistent with equality as T_e[N ii] = [T_e[S ii]$-(0.072\pm 1.392)]/(1.101\pm 0.180)$. Again, the intrinsic scatter accounts for the majority of the total scatter; however, the large deviations observed indicate that observational uncertainties still play a large role at high [S ii] temperatures.

In the middle two panels of Figure 3, we examine the relationship between the intermediate-ionization zone, characterized by [S iii], with both the high-ionization zone ([O iii]; left panel) and low-ionization zone ([N ii]; right panel). In the middle left panel, we find that the best fit to the T_e[O iii]–T_e[S iii] relationship is in good agreement with C16 but diverges from G92 for the hottest regions observed: T_e[S iii] = (1.795 ± 0.067) × T_e[O iii]−(8.167 ± 1.122). Previous studies have reported large discrepancies between T_e[O iii] and T_e[S iii] and significant scatter in their relationship (e.g., Hägele et al. 2006; Pérez-Montero et al. 2006; Binette et al. 2012; Berg et al. 2015). The T_e[O iii]–T_e[S iii] relationship for our sample of 59 regions is no exception, with a significant scatter of σ_tot. = 900 K that can be attributed almost entirely to intrinsic scatter (σ_int. = 860 K). Given the large number of outliers presented in both our sample and the literature, we reiterate and stress the finding of B15 that T_e[O iii] alone is less reliable than T_e[S iii] or T_e[N ii] for abundance calculations in metal-rich H ii regions.

Curti et al. (2017) cautioned of the potential contamination of the temperature-sensitive [O iii] λ4363 line by the neighboring [Fe ii] λ4360 line. This effect is especially prominent at abundances of 12 + log(O/H) > 8.4, where the [Fe ii] line increases in strength and the [O iii] λ4363 line becomes faint due to the decreasing H ii region temperature. Because Curti et al. (2017) used stacks of integrated galaxy light spectra in their study, the source of the [Fe ii] λ4360 emission is difficult to trace; however, as a precaution, we have added the Fe ii emission feature to our line-fitting code so that the [Fe ii] λ4360 and [O iii] λ4363 lines are simultaneously fit and deblended, and we have inspected the fits by eye (see Section 2.2). In fact, we do not measure T_e[O iii] in any very metal-rich H ii regions in CHAOS and so do not find any significant [Fe ii] contamination affecting our T_e[O iii] measurements. For instance, [Fe ii] λ4360 emission is seen in the blue inset window of the spectrum shown in Figure 2. However, [O iii] λ4363 was not strong enough to be identified as a detection and so the high-ionization zone temperature was inferred from T_e[S iii] and not affected by the [Fe ii] contamination.

In the middle right panel of Figure 3, we plot T_e[N ii] versus T_e[S iii]. Similar to the trend reported in B15, we find a very tight correlation, especially for the coolest, most metal-rich regions typical of CHAOS (with T_e < 10⁴ K). The best-fit line (blue) to the 90 regions is T_e[S iii] $=\,(1.522\pm 0.042)\times \,{T}_{e}$[N ii]–(4.576 ± 0.463), in agreement with the relationship of C16 (black dashed line) and about which the dispersion is quite small: ${\sigma }_{\mathrm{tot}.}=420$ K. The C16 relationship is also very similar to the G92 relationship, where differences (seen in both bottom panels) are likely due to changes in the adopted [S iii] atomic data.

Finally, we compare the low- and high-ionization zones in the bottom two panels of Figure 3. On the left, the relationship between the low-ionization zone T_e[N ii] and the high-ionization zone T_e[O iii] is reasonably well behaved, but it has too few data points to analyze further. On the other hand, the T_e[O ii]–T_e[O iii] plot shows a cloud of scattered points that is difficult to characterize.

Significant [O iii] λ4363, [N ii] λ5755, and/or [S iii] λ6312 detections are measured in 30 regions in NGC 3184, resulting in direct oxygen abundance measurements. The electron temperatures and densities characterizing each H ii region observed in NGC 3184 are reported in Table A3 in Appendix A.

3.1.2. Ionization-based Temperature Priorities

CHAOS has proven highly successful at measuring significant detections of both [N ii] λ5755 and [S iii] λ6312, demonstrating the utility of these lines in metal-rich H ii regions. Given the robust T_e[N ii]$-{T}_{e}$[S iii] relationship demonstrated for the 90 H ii regions with simultaneous detections, our results further endorse the recommendation of B15 to prioritize these two temperature indicators. However, it is interesting that the T_e[N ii]–T_e[S iii] relation shows a notable increase in dispersion for ${T}_{e}\gt {10}^{4}$ K, whereas the dispersion in the T_e[O iii]–T_e[S iii] relationship seems to settle down in that same T_e regime.

Recently, Yates et al. (2020) measured a large range of T_e[O iii]/T_e[O ii] ratios spanning significant temperature (and, due to its inverse dependence, metallicity) parameter space from a sample of 130 H ii regions and integrated-light galaxies. They postulate that deviations from equal temperatures are rooted in the ionization structure of the nebulae, where ${{\rm{O}}}^{++}$-dominated nebulae have cooler [O iii] temperatures and O⁺-dominated nebulae have cooler [O ii] temperatures. Because the relative flux of the [O iii] λ5007 and [O ii] λ3727 emission lines is dependent on the number of oxygen ions in the O⁺⁺ relative to O⁺ state, we can use the [O iii] λ5007/[O ii] λ3727 ratio as a proxy for O⁺⁺/O⁺ or the ionization structure.

In Figure 4, we reproduce the T_e[O iii]–T_e[S iii] and T_e[N ii]–T_e[S iii] relationships from Figure 3 but with the points color-coded by their reddening-corrected [O iii] λ5007/[O ii] λ3727 flux ratios. As expected, low-ionization H ii regions (low ${F}_{\lambda 5007}$/F_λ3727; dark blue/purple points) show the tightest correlation between the low- and intermediate-ionization zone temperatures (T_e[N ii] versus T_e[S iii]) and high-ionization H ii regions (high F_λ5007/F_λ3727; yellow points) show the tightest correlation between high- and intermediate-ionization zone temperatures (T_e[O iii] versus T_e[S iii]). Motivated by these dispersion-ionization correlations, we recommend simple, yet improved, ionization-based temperature priorities below.

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While few T_e[O iii] detections were found in the first CHAOS paper examining NGC 628, many more detections were added with the addition of NGC 5457, revealing the utility of T_e[O iii] at high T_e and high ionization (high F_λ5007/F_λ3727). Therefore, we prefer a T_e[O iii] measurement for high-ionization nebulae that are dominated by the O⁺⁺ zone and a T_e[N ii] measurement for low-ionization nebulae that are predominantly O⁺, where T_e[S iii] is used in the absence of a [N ii] λ5755 detection. In order to apply this rubric, we define a high- (low-) ionization nebula criterion of F_λ5007/F_λ3727 >  (<) 1.25. This division was chosen based on a statistical analysis of the T_e[O iii]-based oxygen abundance dispersion with F_λ5007/F_λ3727 using data from the C16 study of M101 and the Rosolowsky & Simon (2008) study of M33, where dispersion was minimized for F_λ5007/F_λ3727 > 1.25. The details of this analysis will be presented in D. A. Berg et al. (2020, in preparation).

We calculate absolute and relative abundances using the PyNeb package in python, assuming a five-level atom model (De Robertis et al. 1987), the atomic data reported in Table 4 of B15, and the temperatures determined from the [O iii], [S iii], and/or [N ii] measured temperatures in conjunction with ${T}_{e}-{T}_{e}$ scaling relationships. We showed in Section 3.1 that our electron temperature results for the first four CHAOS galaxies are consistent with the C16 ${T}_{e}-{T}_{e}$ relationships; therefore, we use Equations (1)–(3) to determine the temperatures of unmeasured ionization zones. Further, the dispersion in our measured ${T}_{e}-{T}_{e}$ relationships correlates with the average ionization of the nebulae, as represented by the ${{\rm{O}}}_{32}\,={F}_{\lambda 5007}/{F}_{\lambda 3727}$ ratio.

We adopt the ionization-based temperature prioritization depicted in Figure 5. Specifically, if all three ionic temperatures are measured and the average ionization of the nebula is relatively high (O₃₂ > 1.25), we prioritize T_e[N ii] for the low-ionization zone, T_e[S iii] for the intermediate-ionization zone, and T_e[O iii] for the high-ionization zone. If, instead, the average ionization of the H ii region is relatively low (O₃₂ < 1.25), we adopt the measured low- and intermediate-ionization zone temperatures as before but instead use T_e[S iii] in combination with Equation (3) to infer the high-ionization zone temperature. The justification of this choice is the large dispersions for high-ionization points in the ${T}_{e}-{T}_{e}$ relations shown in Figure 4, with the result that we have less confidence in λ4363 in this regime (see discussion in Section 4.2). In the absence of a measurement of the appropriate ionization-zone temperature, temperatures should be inferred from the next preferred ion measured (following the ordering in Figure 5) in combination with the ${T}_{e}-{T}_{e}$ relationships from Equations (1)–(3).

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While the ionization-based temperature prioritizations presented here offer an improvement to temperature-based abundance determinations, we note two caveats. First, it is best to have independent measurements of the temperature in each ionization zone to reduce the reliability on relationships from photoionization modeling. Second, there are inherent, systematic uncertainties remaining due to the nominal assumption that H ii region structures can be simply divided into three 1D ionization zones when the reality is much more complicated.

3.2.1. Oxygen Abundances

We adopt the ionization-based temperature prioritization recommended in Figure 5 in order to determine the abundances of the first four CHAOS galaxies in a uniform, homogeneous manner. Ionic abundances relative to hydrogen are calculated using:

$$\begin{eqnarray}&&\displaystyle \frac{N({X}^{i})}{N({{\rm{H}}}^{+})}=\displaystyle \frac{{I}_{\lambda (i)}}{{I}_{{\rm{H}}\beta }}\displaystyle \frac{{j}_{{\rm{H}}\beta }}{{j}_{\lambda (i)}},\end{eqnarray} \tag{ 4 }$$

where the emissivity coefficient, j_λ(i), is sensitive to the adopted temperature.

The total oxygen abundance is calculated as the sum of the O⁺/H⁺ and O⁺⁺/H⁺ ion fractions. While emission from O⁺³ is negligible in typical star-forming regions, some oxygen might be in O⁰ phase for the moderate-to-low ionization parameters characteristic of the CHAOS data (−2.5 < log U < −4.0; see, for example, Figure 5 in Berg et al. 2019). In the current work, we can estimate the typical contribution to the oxygen abundance by O⁰ emission using the [O i] λ6300 feature, which can be distinguished from the [O i] λ6300 night sky line at the distances of our sample and the resolution of MODS. For our sample, the average I([O i]λ6300)/I(Hβ) = 0.022, corresponding to an O⁰/(O⁰ + O⁺ +O⁺⁺) fraction of 3%. This means that, on average, the oxygen abundance may be underestimated by only ΔO/H < 0.02 dex due to missing O⁰/H⁺ contributes. Given that possible contributions from O⁰ are typically less significant than the uncertainties on the oxygen abundance measurements, O⁰/H⁺ is not included in our oxygen abundance determinations, consistent with previously published CHAOS data.

The total oxygen abundances for our NGC 3184 sample are reported in Table A3 of Appendix A, noting that neither O⁰ nor contributions from dust (also typically <0.1 dex; Peimbert & Peimbert 2010; Peña-Guerrero et al. 2012) are included. Additionally, given that the abundances reported in previous CHAOS works were not derived with a methodology consistent with Figure 5, we re-derive the abundances for NGC 628, NGC 5194, and NGC 5457 in order to compare our sample in a uniform manner. Since both NGC 628 and NGC 5194 were analyzed following the methodology laid out in B15 and both had very few [O iii] λ4363 detections, their results were not significantly modified. C16's study of NGC 5457, on the other hand, generally prioritized [O iii]-derived temperatures for the purpose of comparing to T_e[O iii]-based abundances in the literature. The total and relative abundances for NGC 628, NGC 5194, and NGC 5457 used in this work are report in Table B1 in Appendix B.

3.2.2. Nitrogen Abundances

3.2.3. Sulfur Abundances

3.2.4. Argon Abundances

In the case of argon, only the Ar⁺⁺ ionization state is observed in the majority of CHAOS optical spectra, but the ionization potentials of O⁺ (13.62–35.12 eV) and O⁺⁺ (35.12–54.94 ev) encompass portions of Ar⁺ (15.76–27.63 eV), Ar⁺⁺ (27.63–40.74 eV), and Ar⁺³ (40.74–59.81 eV). While ratios of sulfur and oxygen ions relative to Ar⁺⁺ have both been used individually in the past to trace unseen argon ions, C16 found that the low-ionization regions of the CHAOS NGC 5457 sample are not well represented by either. Instead, C16 corrected for the decrease in Ar⁺⁺/S⁺⁺ seen in low-ionization nebula by adopting a linear correction to Ar⁺⁺/S⁺⁺: log(Ar⁺⁺/S⁺⁺) = −1.049 × (O⁺/O) −0.022, for O⁺/O ≥ 0.6. For higher-ionization nebulae, Ar⁺⁺/S⁺⁺ was uncorrelated with O⁺/O and so a constant value of log(Ar⁺⁺/S⁺⁺) = −0.65 was assumed, similar to Kennicutt et al. (2003b).

The log(Ar⁺⁺/S⁺⁺) correction from C16 is shown in the top panel of Figure 6. The previously reported trend of decreasing Ar⁺⁺/S⁺⁺ with increasing O⁺/O is reproduced, but with more dispersion in the updated ionic abundances, especially for NGC 5457—the data it was derived for. We find that all four CHAOS galaxies follow just as well the Ar⁺⁺/O⁺⁺-based ICF of Thuan et al. (1995) over the full range in O⁺/O probed by the sample. Given that three of the galaxies seem to be systematically offset from the Ar⁺⁺/S⁺⁺ relation, we choose to apply the ICF(Ar) from Thuan et al. (1995), which has an uncertainty of 10%, to all four CHAOS galaxies. The differences between the updated ion fractions and those measured in C16 support the finding by Yates et al. (2020) and this work that ionization plays an important role in the temperature and metallicity determinations of an H ii region. We list the resulting Ar abundances in Table A3 of Appendix A.

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3.2.5. Neon Abundances

In the past, studies of radial abundance trends have used both a variety of methods to characterize abundance and to normalize the galactocentric radius to show significant variations in the gradients of different galaxies (e.g., Zaritsky & Kennicutt 1994; Moustakas et al. 2010). However, many of these studies have relied on abundance measurements in just a handful of H ii regions per galaxy. More recently, abundance trends have been studied in large numbers of H ii regions using IFU spectroscopy of individual galaxies. Using empirical oxygen abundances determined from CALIFA IFU spectra, Sánchez et al. (2014) found a universal O/H gradient with a characteristic slope of ${\alpha }_{{\rm{O}}/{\rm{H}}}=-0.10\pm 0.09$ dex/R_e over 0.3 < R_g/R_e < 2.0 for 306 galaxies, whereas Sánchez-Menguiano et al. (2016) report a shallower slope of α_O/H = −0.075 dex/R_e, with σ = 0.016 dex for 122 face-on spiral galaxies. However, the recent study of 102 spiral galaxies using VLT/MUSE IFU spectra by Sánchez-Menguiano et al. (2018) found a distribution of slopes with an average of α_O/H = −0.10 ± 0.03 dex/R_e. These authors find that radial gradients are steepest when the presence of an inner drop or an outer flattening is also detected in the radial profile and point to radial motions in shaping the abundance profiles.

While IFU studies have greatly expanded our understanding of abundance gradients, they have thus far relied on strong-line abundance calibrations and, therefore, have systematic uncertainties (e.g., see reviews from Kewley & Ellison 2008; Maiolino & Mannucci 2019). CHAOS now allows us to compare radial abundance trends using large numbers of direct abundance measurements in H ii regions. We display the O/H abundances derived in Section 3.2.1 for the four CHAOS galaxies in Figure 7 as a function of galactocentric radius. Because the locations of individual H ii regions are known with high precision relative to one another, we consider only the uncertainties associated with oxygen abundance here. We plot the galactocentric radius relative to the isophotal (R₂₅) and effective (R_e) radii of each galaxy in the top and middle panels of Figure 7, respectively. Because there is no visual evidence for an outer disk flattening in the O/H gradient in the coverage of the CHAOS sample, we characterize the O/H gradient in each galaxy with a single, Bayesian linear regression using the python linmix code (solid lines). Parameters of the resulting fits are given in Table 2.

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Table 2.  Linear Fits to CHAOS Gradients

y	x	Galaxy	# Reg.	Equation	σint.	σtot.
12 + log(O/H) (dex)	Rg (${R}_{25}^{-1}$)	NGC 0628	45	$y=(8.71\pm 0.06)-(0.40\pm 0.11)\times x$	0.12	0.13
		NGC 5194	28	$y=(8.75\pm 0.09)-(0.27\pm 0.15)\times x$	0.07	0.10
		NGC 5457	72	$y=(8.78\pm 0.04)-(0.90\pm 0.07)\times x$	0.10	0.11
		NGC 3184	30	$y=(8.74\pm 0.16)-(0.48\pm 0.28)\times x$	0.14	0.16
	Rg (${R}_{e}^{-1}$)	NGC 0628	45	$y=(8.70\pm 0.06)-(0.11\pm 0.03)\times x$	0.12	0.13
		NGC 5194	28	$y=(8.67\pm 0.08)-(0.07\pm 0.04)\times x$	0.07	0.10
		NGC 5457	72	$y=(8.75\pm 0.03)-(0.20\pm 0.02)\times x$	0.10	0.11
		NGC 3184	30	$y=(8.71\pm 0.15)-(0.18\pm 0.10)\times x$	0.14	0.16
12 + log(S/H) (dex)	Rg (${R}_{e}^{-1}$)	NGC 0628	45	$y=(7.60\pm 0.06)-(0.19\pm 0.03)\times x$	0.12	0.13
		NGC 5194	28	$y=(7.51\pm 0.11)-(0.10\pm 0.05)\times x$	0.07	0.12
		NGC 5457	72	$y=(7.40\pm 0.05)-(0.23\pm 0.03)\times x$	0.18	0.19
		NGC 3184	30	$y=(7.59\pm 0.15)-(0.34\pm 0.11)\times x$	0.11	0.13
log(N/O) (dex)	Rg (${R}_{25}^{-1}$)	NGC 0628	59	$y=(-0.64\pm 0.04)-(0.61\pm 0.06)\times x$	0.10	0.11
		NGC 5194	28	$y=(-0.34\pm 0.09)-(0.44\pm 0.16)\times x$	0.05	0.08
		NGC 5457	72	$y=(-0.73\pm 0.03)-(0.81\pm 0.06)\times x$	0.07	0.10
		NGC 3184	30	$y=(-0.30\pm 0.13)-(0.83\pm 0.22)\times x$	0.04	0.08
	Rg (${R}_{e}^{-1}$)	NGC 0628	59	$y=(-0.65\pm 0.03)-(0.18\pm 0.02)\times x$	0.10	0.11
		NGC 5194	28	$y=(-0.34\pm 0.09)-(0.12\pm 0.04)\times x$	0.05	0.08
		NGC 5457	72	$y=(-0.74\pm 0.03)-(0.18\pm 0.01)\times x$	0.08	0.10
		NGC 3184	30	$y=(-0.30\pm 0.12)-(0.35\pm 0.09)\times x$	0.05	0.08
log(N/O)${}_{\mathrm{prim}.}$ (dex)		NGC 0628	11	$y=-1.28$		0.13
		NGC 5194	4	$y=-0.71$		0.03
		NGC 5457	15	$y=-1.38$		0.13
		NGC 3184	0	$y=-$1.15		⋯
log(N/O)${}_{\sec .}$ (dex)	Rg (${R}_{e}^{-1}$)	NGC 0628	38	$y=(-0.43\pm 0.05)-(0.34\pm 0.04)\times x$	0.06	0.07
		NGC 5194	20	$y=(-0.27\pm 0.18)-(0.17\pm 0.11)\times x$	0.07	0.09
		NGC 5457	45	$y=(-0.58\pm 0.07)-(0.30\pm 0.05)\times x$	0.06	0.08
		NGC 3184	30	$y=(-0.30\pm 0.12)-(0.35\pm 0.09)\times x$	0.05	0.08
Scaled
log(N/O)${}_{\sec .}$ (dex)	Rg (${R}_{e}^{-1}$)	All Four	133	$y=(-0.15\pm 0.03)-(0.36\pm 0.02)\times x$	0.05	0.09
		NonInter.	113	$y=(-0.16\pm 0.03)-(0.34\pm 0.02)\times x$	0.05	0.08

Note. Linear fits to trends in abundance versus radius for the four CHAOS galaxies. The fits are determined using the Bayesian linear mixture model implemented in the linmix python code, which fits data with uncertainties on two variables, including explicit treatment of intrinsic scatter. The y and x variables are given in the first two columns, with the number of associated H ii regions used in the fit listed in Column 4. The resulting best fit is given in Column 5, with uncertainties on both the slope and y-intercept. Columns 6 and 7 list the intrinsic and total uncertainties, ${\sigma }_{\mathrm{tot}.}$ and ${\sigma }_{\mathrm{int}.}$. Note that the primary log(N/O) value given for NGC 3184 is italicized to indicate that this quantity is an estimated value from the extrapolated secondary fit, and not a measurement.

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Comparing the individual O/H gradients in Figure 7, there are apparent differences in both the O/H versus R_g/R₂₅ and O/H versus ${R}_{g}/{R}_{e}$ gradients in the top and middle panels, respectively. While the gradients align more closely when plotted versus the effective radius (R_e), the gradients of individual galaxies are still uniquely distinct. The four CHAOS galaxies have a range of slopes of $-0.20\lt {\alpha }_{{\rm{O}}/{\rm{H}}}$ (dex/R_e) < −0.07. Because the high-quality direct abundances of the CHAOS sample allow us to better constrain the unique gradient of an individual galaxy, we are seeing tangible gradient differences, even among just four galaxies, but within the dispersion seen for the large CALIFA samples of strong-line abundances. In this sense, the CHAOS data are demonstrating that O/H versus ${R}_{g}/{R}_{e}$ gradients are not uniformly behaved.

NGC 5194 presents the largest deviation from the typical CHAOS slope, where its nearly flat slope has been attributed to interactions with its companion, NGC 5195, resulting in radial migration and mixing of the interstellar gas (see discussion in C15). However, even when we only consider the three noninteracting spiral galaxies in our sample, we find tangible differences in the O/H abundance gradients and dispersions of individual CHAOS galaxies. The varying coefficients of the best-fit gradients characterizing the CHAOS galaxies (tabulated in Table 2) show that detailed direct abundance measurements reveal a range in the chemical evolution of individual galaxies.

Sulfur abundances can be an extremely useful tool, particularly in the absence of oxygen abundance information. Notably, sulfur abundances only require a limited wavelength coverage of ∼λ4850–λ9100 (but better if coverage extends to ∼λ9600) to ensure measurement of all the necessary inputs to a direct abundance: (i) reddening correction (from Hα/Hβ and the Paschen lines), (ii) density (from [S ii] λ6717/λ6731), (iii) temperature (from [S iii] λ6312/λ9069), (iv) S⁺ (from [S ii] λλ6717,6731), and (v) S⁺⁺ (from [S iii] λλ9069,9532). Surveys with limited blue-wavelength coverage (e.g., MUSE; Bacon et al. 2010) may therefore be able to take advantage of sulfur's utility and measure direct abundance trends in the absence of the blue oxygen lines.

Prompted by the importance of S as a temperature indicator, and the expectation of alpha elements that S and O abundances should trace one another, we explore the S/H gradients of the CHAOS galaxies in the bottom panel of Figure 7. As before, we fit Bayesian linear regression models and report the results in Table 2. The S/H and O/H gradients of our galaxies are all consistent within the uncertainties, with the interesting exception of NGC 628. These fits suggest that S/H abundances provide an alternative direct measurement of a galaxy's metallicity gradient. S/H abundances may also be easier to measure in moderate- to metal-rich H ii regions where [S iii] λ6312 is significantly detected more often than [O iii] λ4363. However, it is important to note that S/H abundances have the disadvantage of requiring an ICF for the unseen S⁺³ and, thus, are generally considered inferior to O/H abundances. Typically, in the CHAOS sample, the correction for S⁺³ is less than 20%, but it can get as high as 80%, so caution is warranted.

Why does sulfur seem to behave so well for the CHAOS sample? While the dominant observable ionic states of O in the CHAOS spectra, O⁺ and O⁺⁺, probe the full ionization range of H ii region nebulae, our data largely consist of moderate-ionization nebulae. Our regions have O⁺/O ionization fractions that are typical of the more metal-rich H ii regions in spiral galaxies, and this combination produces regions that both exhibit more moderate ionization and have cooler temperatures. Given this, it is perhaps not surprising that T_e[S iii] characterizes the CHAOS data so well. At the typically higher metallicities of the CHAOS regions, the nebula are generally lower-excitation and so have large S⁺⁺ fractions (i.e., S⁺⁺ is the dominant ionization zone). To be quantitative, given the excitation energy of [S iii] λ6312 (3.37 eV), a temperature of T_e ∼ 7000 K is required for 1% of the electrons to excite [S iii]. This temperature is well matched to the majority of our H ii regions, which have temperature measurements of 6000 K < T_e < 8000 K. On the other hand, the excitation energy of [O iii] λ4363 (5.35 eV) requires a much hotter nebular temperature of T_e ∼ 11,000 K for 1% of electrons to excite [O iii]. In these typically moderate-ionization nebula, not only is O⁺⁺ a sub-dominant ion, but the relatively low electron temperature of the gas will rarely excite to the upper level of O⁺⁺ from which λ4363 is emitted. In contrast, the observable ionic states of S in the CHAOS spectra (S⁺, S⁺⁺) probe the lower-ionization zones (≲35 eV) that are dominant in the majority of metal-rich H ii regions.

The N/O abundances for the four CHAOS galaxies are presented in Figure 8. Galactocentric radii are normalized to the isophotal radius, R₂₅, of each galaxy in the top panel and to the effective radius, R_e, in the bottom panel. Once again, we analyze gradients of galaxies by comparing their individual Bayesian linear regression fits (solid lines). Interestingly, when trends in N/O versus R_g/R₂₅ are considered as a single, linear relationship as was done with O/H in Section 4.2, all four galaxies appear to have similar gradients, only offset from one another. Additionally, as noted in previous CHAOS papers, the N/O relationships are more tightly ordered with radius than the O/H gradients, presented by smaller dispersions. On the other hand, when the N/O trends are normalized by their effective radius (bottom panel), three of the four galaxies (NGC 628, NGC 5457, and NGC 3184) shift to lie nearly on top of one another, while NGC 5194 emerges as an outlier once again.

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We further investigate the similarities of the CHAOS N/O gradients by comparing them over the same radial extent. Limited by the coverage of NGC 3184, we refit the N/O gradient of the R_g/R_e < 2.0 inner disks of the CHAOS galaxies with a Bayesian linear regression model and plot them as solid lines in the top left-hand panel of Figure 9. Now, three of the four galaxies have trends that run parallel to one another: all have very tight trends with slopes of α_N/O = −0.3 dex/R_e and dispersions of σ < 0.06 dex (see Table 2). Given that the inner disk radial gradients decline more steeply for N/O than O/H, these trends are indicative of secondary nitrogen.

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In order to isolate the secondary N/O trend of the CHAOS sample, we remove the offset between galaxies by subtracting their individual y-intercept offsets. The resulting scaled N/O versus O/H relationships are shown in the bottom left-hand panel of Figure 9, where a tight secondary N/O relationship emerges that characterizes the entire CHAOS sample well. Given the relatively flat gradient of NGC 5194 in the top left-hand panel of Figure 9, we fit the secondary N/O relationship excluding NGC 5194 (denoted by the semi-transparent green points) in the bottom left-hand panel of Figure 9. The Bayesian linear regression reports a slope of α_N/O = −0.33 dex/R_e, with a very small total dispersion of σ = 0.08 dex.

It is remarkable that a simple shift produces such a tight secondary N/O gradient for these three galaxies and indicates that a physical origin may be responsible. A common interpretation of N/O trends owes vertical offsets to differences in individual star formation histories (SFHs) that set the primary N/O plateau (e.g., Henry et al. 2000). Given the limited disk coverage of the CHAOS sample, it is difficult to determine the primary N/O plateau that is expected at large radii (low metallicity). However, we can explore the existing data in the outer disk as an illustrative exercise. Using NGC 5457 as our best and largest data set for exploring radial trends, we note that the N/O trend is approximately flat for R_g/R_e > 2.5, and so we adopt 2.0 < R_g/R_e < 2.5 as the transition from primary to secondary N production (gray-shaded band). In the upper right-hand panel of Figure 9, we fit a weighted average to the N/O values for R_g/R_e > 2.5. For NGC 3184, no N/O measurements exist for R_g/R_e > 2.5, and so a (toy-model) plateau was assumed based on the value of the extrapolated secondary relationship at the transition radius.

In the bottom right-hand Figure 9, we apply a second scaling method. We normalize the individual N/O relationships by their corresponding plateaus and once again see that a tight secondary N/O relationship emerges that characterizes the inner disk of the CHAOS sample well. Fitting a Bayesian linear regression to the three noninteracting galaxies, we find a slope of ${\alpha }_{{\rm{N}}/{\rm{O}}}=-0.34$ dex/R_e and σ = 0.08, equal to the slope determined using a y-intercept offset. Once again, we find remarkable consistency of the N/O gradient slopes, regardless of the offset method used, suggesting a universal N/O gradient. The agreement between the bottom two panels of Figure 9 may be indicative of a break near 2.0 < R_g/R_e < 2.5 and a transition to a flatter gradient for R_g/R_e > 2.5. We currently do not have sufficient data coverage of the outer CHAOS disks, but more radially extended data sets will be able to test this break/plateau prediction. Coefficients for the secondary N/O fits are tabulated in Table 2.

If the slope of N/O versus radius is simply dependent on metallicity, then a universal N/O gradient like the one depicted in Figure 9 can be interpreted as resulting directly from the nucleosynthetic yields of the stars producing it. In yield models, the integrated N yield is dominated by intermediate-mass stars and increases with increasing metallicity, while the oxygen yields from massive stars decrease with increasing metallicity. Further, the small observed scatter about this relationship could result from the fact that we are observing regions of star formation with differing average burst ages, and the majority of N is produced around 250 Myr after the burst onset, whereas the massive stars producing oxygen have main-sequence lifetimes of only a few Myr (see discussion in Section 7).

Beyond simple gradients in spiral galaxies, other patterns in the spatial distribution of metals in the ISM may be key to understanding the redistribution of recently synthesized products. While some processes happen on relatively short timescales, such as local oxygen production from massive stars (<30 Myr; Pipino & Matteucci 2009) and H ii region mixing on subkiloparsec scales (<100 Myr), the timescale for differential rotation to chemically homogenize an annulus of the ISM is much longer (∼1 Gyr; see, e.g., Kreckel et al. 2018). Further, the fate of metals after they are produced is unclear, as the spatial and temporal scales on which oxygen enriches the ISM are poorly known. Therefore, azimuthal inhomogeneities are expected and can inform us about asymmetric processes occurring in the disk.

Ho et al. (2017) studied the azimuthal variations in the oxygen abundance gradient of the nearby, strongly barred, spiral galaxy NGC 1365 as part of the TYPHOON program, finding O/H to be lower, on average, by 0.2 dex downstream from the spiral arms. Given the strong correlation with spiral pattern, these authors find that the observed abundance variations are due to the mixing and dilution processes driven by the spiral density waves. On the other hand, the TYPHOON program has also reported a much smaller magnitude of 0.06 dex azimuthal variations for the unbarred spiral galaxy NGC 2997 (Ho et al. 2018).

We test for azimuthal variations in the CHAOS sample by examining the offset in direct abundance from each galaxy's average gradient for O/H and N/O as a function of both radius and position angle within the disk. We find no evidence of systematic azimuthal variations in the direct abundance CHAOS sample of unbarred spiral galaxies explored here. However, while CHAOS observations span broad radial and azimuthal coverage, region selection is biased to the highest surface-brightness H ii regions and so may not include the faint inter-arm coverage needed to unveil these subtle trends.

A fundamental relationship of global galaxy evolution is the luminosity–metallicity relationship, which includes spiral disk galaxies (e.g., Garnett & Shields 1987; Vila-Costas & Edmunds 1993; Zaritsky & Kennicutt 1994). This relationship typically refers to the total or average metallicity of a galaxy, but what does this mean for the abundance gradients in individual spiral galaxies? While several recent studies support a characteristic oxygen abundance gradient for the main disk of spiral galaxies (e.g., Sánchez et al. 2014; Sánchez-Menguiano et al. 2018), Belfiore et al. (2017) reported an increasing oxygen abundance slope (dex/R_e) with stellar mass for Sloan Digital Sky Survey-IV MaNGA (Bundy et al. 2015) galaxies with M_⋆ < 10^10.5 M_⊙. However, in a study of 49 local star-forming galaxies, Ho et al. (2015) found that metallicity gradients expressed in terms of the isophotal radius (R₂₅) did not correlate with either stellar mass or luminosity but rather increase with decreasing total stellar mass when expressed in terms of dex kpc⁻¹ (see, also, Pilyugin et al. 2019). Alternatively, Pilyugin et al. (2019) concluded in their study of MaNGA galaxies that oxygen abundance is governed by a galaxy's rotational velocity. Despite these works, no clear evidence has emerged to conclusively determine the dependence of abundance gradients on basic galaxy properties or halo properties (e.g., rotational velocity).

Locally, the oxygen abundance trends of spiral galaxies have also been observed to correlate with stellar-mass surface density (e.g., McCall 1982; Edmunds & Pagel 1984; Ryder 1995; Garnett et al. 1997). In Figure 10, we examine the stellar-mass surface-density profiles for the CHAOS galaxies (see Appendix C for details). The left panel shows the typical trend of decreasing stellar-mass surface density as you move further out in the disk but with NGC 5194 having a slightly elevated density of stars compared to the others. In the middle and right panels, we plot the local surface mass–metallicity relationship for O/H and S/H, respectively. Similar to the global relationship (see, e.g., Tremonti et al. 2004), local metallicity measurements also increase with mass surface density and plateau at high mass values. This local trend is especially tight for the three noninteracting CHAOS galaxies.

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The metallicity–surface-density relationships in Figure 10 may reflect fundamental similarities in the evolution of non-barred, noninteracting spiral galaxies. For example, Ryder (1995) argues for a galaxy evolution model that includes self-regulating star formation, where energy injected into the ISM by newly formed stars inhibits further star formation. These models were able to successfully reproduce the observed correlations between surface brightness and star formation rate (SFR; Dopita & Ryder 1994) and surface mass density (e.g., Phillipps & Edmunds 1991; Ryder 1995; Garnett et al. 1997). The current work supports these ideas that stellar-mass, gas-mass, and SFR surface densities are fundamental and interdependent parameters that govern the chemical evolution of spiral galaxies. A more thorough investigation of the dependence of metallicity on local properties will be conducted in the future with the entire CHAOS sample.

In a simple closed-box model, assuming instantaneous recycling of stellar nucleosynthetic products and no gas flows, chemical evolution is solely a function of the gas fraction, μ_gas: $Z=y\cdot \mathrm{ln}({\mu }^{-1})$, where Z is the metallicity and y is the metal yield. Inverting this equation, one can measure the effective yield, y_eff, given the observed metallicity, Z_obs, and gas fraction:

$$\begin{eqnarray}&&{y}_{\mathrm{eff}}=\displaystyle \frac{{Z}_{\mathrm{obs}}}{\mathrm{ln}({\mu }_{\mathrm{gas}}^{-1})}.\end{eqnarray} \tag{ 5 }$$

In Figure 11, we plot the radially averaged inverse gas fraction trends for the CHAOS sample (see Appendix C for the sources of the gas distributions). While the inverse gas fractions steadily decrease with increasing radius for all four galaxies (left panel), plotting abundance versus inverse gas fractions reveals different effective yield trends (three right panels). Nonetheless, the trends appear to be the most ordered for O/H and S/H, with similar slopes among the three noninteracting galaxies. The less-ordered trends for N/H may then be revealing the effects of varying gas flows in each galaxy and the time effects of production in lower-mass stars. Further, this picture is consistent with the result from theoretical models based on stochastically forced diffusion that most scatter in observed abundance gradients (∼0.1 dex) is due to stellar feedback and gas velocity dispersion (Krumholz & Ting 2018).

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Following Equation (5), these plots of abundance versus the inverse gas fraction trace the effective yield of the relevant element. The true yield is a function of stellar nucleosynthesis, but the effective yield (slope of Z–ln(${\mu }_{\mathrm{gas}}^{-1}$) plots) will be altered from this value by gas inflows and outflows. In this context, the similar slopes in O/H and S/H versus ln(${\mu }_{\mathrm{gas}}^{-1}$) are indicative of a closed-box effective yield of both oxygen and sulfur, whereas the O/H and S/H trends of NGC 5194 diverge as expected for gas flows associated with interacting galaxies. According to Figure 11, the CHAOS galaxies generally follow slopes of (0.5–1.25) × 10⁻⁵ for sulfur and (1.5–2.0) × 10⁻⁴ for oxygen, which corresponds to y_eff(O) = 0.006–0.008 assuming Z = 0.02 Z_⊙ and 12 + log(O/H)_⊙ = 8.69 (Asplund et al. 2009). These y_eff(O) values are consistent with the range of effective oxygen yields measured for spiral galaxies by Garnett (2002), spanning 0.0033–0.017. We note that the effective yield values (Garnett 2002) found for NGC 628 and NGC 5194 are higher than our own, but this difference is largely accounted for by the offset in the measured abundance scales for these two galaxies.

Next, we turn our focus from abundance gradients to relative abundance trends with O/H metallicity. In Figure 12, we plot the relative abundances of α-elements. In descending panel order, we plot S/O, Ar/O, and Ne/O as a function of O/H (left side), where diamond points are color-coded according to galaxy.

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Stellar nucleosynthetic yields (e.g., Woosley & Weaver 1995) indicate that α-elements are predominantly produced on relatively short timescales by core-collapse supernovae (SNe; massive stars) explosions. The α-element ratios in Figure 12 are, therefore, expected to be constant, so we plot the variance-weighted mean α/O ratios of the CHAOS observations as black dashed lines in each panel. The average values are denoted in the upper left corners and can be compared to the solar values from Asplund et al. (2009; blue dotted line). The average CHAOS α/O values are generally greater than solar, but individual galaxies also show slight shifts from one another.

Relative to the constant relationship assumed in each panel of Figure 12, the CHAOS observations visually show significant scatter and may also deviate in a systematic way. C16 discovered a significant population of low-ionization (high O⁺/O) H ii regions in NGC 5457 with low Ne/O values. A deeper exploration of the α/O ratios in that work revealed a lack of previous observations in the low-ionization regime and challenges in finding an appropriate ICF to use.

Similar to C16, in Section 3.2.5, we found a large dispersion in the Ne⁺⁺/O⁺⁺ ratios of the CHAOS galaxies for low-ionization H ii regions. Additionally, many of these regions also exhibit exceptionally low values of log(Ar/Ne) (see Figure 6). This motivated us to apply a correction to the Ne/O abundances based on the offset in Ne/Ar from the average CHAOS value for low-ionization H ii regions (O⁺/O > 0.5). The updated Ne/O values, plotted in the bottom panel of Figure 12, show a smaller dispersion around the mean sample value but with a few significant NGC 5457 outliers. While the proposed correction removes the bifurcation in Ne/O at low ionization, it seems to over-correct the Ne/O abundance for the nebulae with discordantly low Ar/O abundances.

Following C16, we further examine the α/O dependence on ionization by plotting our α/O ratios for the four CHAOS galaxies versus O⁺/O in the right column of Figure 12. For both Ar and S, there seems to be a small residual systematic dependence on ionization that is not adequately corrected for by C16 or other traditional ICFs. In this case, the high-ionization H ii regions (O⁺/O < 0.5) have S/O and Ar/O ratios that are generally under- and over-predicted, respectively, relative to the average, while the low-ionization H ii regions (O⁺/O > 0.5) seem to be evenly dispersed about the mean. In general, no simple corrections to the ICFs are yet apparent. Instead, we will derive new ICFs for the CHAOS data using updated photoionization models in a future paper.

Historically, N/O enrichment has been studied as a function of total oxygen abundance owing to the relative ease of integrated-light galaxy observations. In this context, the observed scaling of nitrogen with oxygen has long been understood as a combination of primary nitrogen plus a linearly increasing fraction of secondary nitrogen that comes to dominate the total N/O relationship at intermediate metallicities (e.g., Vila-Costas & Edmunds 1993; van Zee & Haynes 2006; Berg et al. 2012). Note that the scatter of the N/O–O/H relationship reported in previous studies is often significantly larger than that of the CHAOS N/O radial gradients (e.g., van Zee & Haynes 2006; Berg et al. 2012).

In Figure 13, we plot the N/O versus O/H values (left panel) and the N/O versus S/H value (right panel) for the CHAOS galaxies. For comparison, we also plot the empirical stellar N/O–O/H relationship from Nicholls et al. (2017) and measured abundances for nearby metal-poor dwarf galaxies from Berg et al. (2019), which should compose a primary N plateau at low O/H and S/H values. Despite the tight N/O radial gradients observed for individual CHAOS galaxies (see Figure 9), large dispersion is seen in N/O when plotted versus O/H, similar to previous N/O–O/H studies. Guided by the stellar relationship (purple line), our data do follow the general trend of low N/O due to primary nitrogen at low oxygen abundances, followed by increasing N/O, presumably as secondary nitrogen becomes prominent, at larger O/H (12 + log(O/H) ≳ 8.2). A similar trend is seen for N/O–S/H. Yet, individual galaxies in our sample clearly occupy different regions on the N/O versus O/H and N/O versus S/H plots. Interestingly, the collective trend of the four galaxies appears to produce a stronger correlation between N/O with S/H than O/H. However, significant scatter is seen for each galaxy, and the dispersions for the N/O–S/H and N/O–O/H relationships are consistent for each galaxy.

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A schematic of nitrogen production for the CHAOS galaxies is shown in Figure 14. The radial gradient fits to the N/O, O/H, and S/H relationships are combined to produce the plotted N/O versus O/H relationship (middle panel) and N/O versus S/H (right panel) for each galaxy. The progressively increasing N/O values at smaller galactocentric distance correspond to increasing O/H abundance, as is expected for secondary N production. This results in parallel secondary N/O slopes for the N/O–S/H trends in Figure 14 and similar slopes in the N/O–O/H relationship for the three noninteracting galaxies. However, the individual relationships are distinct in two ways. First, each galaxy has a different primary plateau level, indicating large variations in their SFHs. Second, each galaxy has a different O/H transition value for when secondary N becomes important and turns the N/O curve upwards.

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Henry et al. (2000) found that chemical evolution models differing only by their assumed star formation efficiencies (SFEs) produced a range of primary N/O plateaus. We illustrate the effect of varying the SFE by over-plotting the Henry et al. (2000) constant SFR models, where efficiency has been varied by a factor of 25, on our N/O versus O/H data in Figure 14. For low SFRs, the buildup of oxygen is slow and on the order of the lag time before intermediate-mass stars begin ejecting nitrogen. This allows a high N/O plateau to be established at low oxygen abundances (darkest purple curve). On the other hand, high SFRs early in the SFH form a large number of massive stars that produce greater levels of oxygen ahead of N enrichment, establishing a lower plateau (lightest purple curve) and shifting the entire N/O–O/H trend in Figure 14 to the right toward greater O/H. In between these scenarios, continuous star formation with roughly 250 Myr between bursts will result in N and O increasing in lockstep, dependent on the elemental yields. The coupling of the N/O plateau with galaxy SFH is also reported by cosmological hydrodynamical simulations of individual regions within spatially resolved galaxies (Vincenzo & Kobayashi 2018). In these simulations, asymptotic giant branch (AGB) stars contribute significant N at low O/H, but the exact value of the primary N/O plateau will vary from galaxy to galaxy according to the relative contributions from SNe and AGB stars, as determined by their galaxy formation time and SFH.

On the left-hand side of Figure 14, we extend the highest N/O plateau from NGC 5194 (green) and the lowest N/O plateau from NGC 5457 (yellow). Based on the above discussion, for the low N/O plateau of NGC 5457, we can put forth an SFH scenario in which the SFE was high early in the galaxy's evolution, allowing oxygen to build up from many bursts of star formation before nitrogen was returned from longer-lived intermediate-mass stars. Due to the higher level of nucleosynthetic products from massive stars, contributions from secondary nitrogen production may dominate over primary nitrogen production at relatively low O/H and S/H values. On the other hand, the high N/O plateau of NGC 5194 could be due to an SFH in which low SFE at early times allows nitrogen production, although delayed, to keep pace with oxygen and sulfur production and enrich the ISM. Here, we assume low SFE to mean either constant, low SFRs or long quiescent periods between bursts. In this scenario, primary nitrogen production is the dominant mechanism until the galaxy reaches relatively high O/H. Note, however, that this is a very simplistic model where N/O is changing monotonically, in a hierarchical galaxy-building scenario that may not be true.

In summary, the primary N/O plateau sensitively probes the SFH of a galaxy, rather than being set by the ratio of N to O yields, and explains the large range of plateau levels observed for spiral galaxies. When this offset is accounted for, the N/O plateau then informs the primary N production yields, and the universal N/O gradient (see Figure 13) is a direct probe of the secondary N yields of intermediate-mass stars.

In Figure 13, we plotted the N/O–O/H trend of the CHAOS galaxies and found large observed scatter in N/O for a given O/H. Given the tight correlations measured for the CHAOS N/O radial gradients (see Table 2), this scatter seems to be real. Previous works have suggested that some of this scatter may be due to the time-dependent nature of N/O production (i.e., a N/O "clock"; Garnett 1990; Pilyugin 1999; Henry et al. 2006). A directly observable effect of an aging ionizing stellar population is an increasing fraction of low- to high-ionization gas in the H ii region (see, for example, how the shape of the ionizing continuum changes with age in Chisholm et al. 2019).

In Figure 15, we reproduce the N/O–O/H and N/O–S/H trends, color-coded by the O⁺/O ratio, or low-ionization fraction. Interestingly, the overall trend of increasing N/O seems to be ordered by ionization or age. In the bottom panels of Figure 15, we scale N/O (as was done in Section 4.3) by shifting the vertical offsets in order to remove differences in individual primary N/O plateaus and SFHs; yet, the overall trend of increasing N/O ordered by ionization remains. Nearly all of the CHAOS points now have N/O abundances that are lower relative to the scaled average stellar relationship of Nicholls et al. (2017), suggesting that the physics of a recent burst of star formation has the effect of shifting the N/O abundances downward, as expected for a recent injection of newly synthesized oxygen. The regions with the lowest N/O also have high ionization. However, the standard N/O clock assumes regions with high N/O ratios have experienced a burst of star formation followed by a long quiescent period that allowed their gas to be enriched with N from slow-evolving stars after a few 100 Myr. Given the fact that typical H ii regions are younger than ∼10 Myr, the simple delayed-release N clock hypothesis fails to explain our observed spread in N/O at a given O/H.

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Alternatively, Coziol et al. (1999) suggested that high N/O ratios in starburst nucleus galaxies could result if N production occurs from a different, older population of intermediate-mass stars, such as would result from a sequence of bursts of star formation. Similarly, Berg et al. (2019) used chemical evolution models of dwarf galaxies to show that N/O was elevated in regions experiencing an extended duration of star formation (continuous star formation) up to 0.4 Gyr. Then, the overall effect of observing a large sample of H ii regions with a range of luminosity-weighted average stellar population ages may be to produce the vertical spread in N/O at a given O/H seen in Figure 15.

Perhaps another reason for the increased scatter of the N/O–O/H trends relative to the N/O–R_g relationships is the possibility that N production is (or behaves as) a secondary function of the carbon abundance, rather than the typically assumed oxygen abundance (Henry et al. 2000). Recently, Groh et al. (2019) investigated grids of stellar models at very low metallicities and found that the ratio between nitrogen and carbon abundances (N/C) remains generally unchanged for nonrotating stellar models during their main-sequence phase. However, the N/C production can increase by as much as 10–20× in rotating models at the end of the main sequence. Thus, variations in stellar rotation speeds of different burst populations could result in significant effects on setting the low-metallicity stage. Additionally, Berg et al. (2019) showed that differential outflows of ISM gas can affect the primary C/O and N/O ratios. Since O and S are produced on different timescales than N, newly synthesized O and S may be preferentially lost in SNe winds, and these outflows may have a greater probability of escaping in the outer parts of the disk.

At higher metallicities, where the effects of stellar winds become more important, other authors have suggested that Wolf–Rayet stars can expel significant amounts of N resulting in local regions of N/O enrichment. For the CHAOS sample, however, we do not find any correlation in the N/O dispersion with the Wolf–Rayet features sometimes seen in the optical spectra.

Another hypothesis is that the dispersion in N/O could be explained if we are consistently underestimating the O/H abundance in low-ionization nebula. We have tested this hypothesis by looking at the offset in O/H abundance from the radial gradients relative to the secondary N/O radial gradient offsets and find some evidence of an anticorrelation, but it cannot explain all of the dispersion observed in N/O.

In summary, while we have observed a universal N/O gradient for the CHAOS galaxies that seems to be tied to the nucleosynthetic yields of N, we also observe a large dispersion when plotted relative to O/H. We have discussed several possible scenarios that could contribute to the N/O–O/H scatter, including extended star formation periods, differential outflows, and a secondary dependence on carbon abundance, but the importance of these contributions has not yet been determined. At this time, the source of the scatter in the N/O–O/H relationship remains an open question but with several promising possibilities for future study.

Owing to the well-studied nature of the galaxies in our sample, there exists a plethora of ancillary data to aid in this task. Specifically, we use HERACLES CO(2–1) line-integrated intensity (moment–0) maps (Leroy et al. 2009) to trace the molecular gas, THINGS H i 21 cm line-integrated intensity maps (Walter et al. 2008) to trace the atomic gas, Spitzer IRAC 3.6 μm images to trace stellar mass, and SFR surface-density maps created in the z = 0 Multiwavelength Galaxy Synthesis project (Z0MGS; Leroy et al. 2019).

The CO maps were converted into molecular gas surface-density maps by assuming a standard Galactic CO-to-H₂ conversion factor of ${\alpha }_{\mathrm{CO}}=4.35\,{M}_{\odot }\,{\mathrm{pc}}^{-2}{({\rm{K}}\mathrm{km}{{\rm{s}}}^{-1})}^{-1}$ (including heavy element contribution; Bolatto et al. 2013) and a CO(2–1)/(1–0) line ratio of ${R}_{21}=0.7$ (Leroy et al. 2013; Saintonge et al. 2017). For the atomic gas surface-density maps, H i intensities were converted using a standard conversion factor of $1.97\times {10}^{-2}\,{M}_{\odot }\,{\mathrm{pc}}^{-2}{({\rm{K}}\mathrm{km}{{\rm{s}}}^{-1})}^{-1}$, which includes heavy element contribution. The stellar-mass surface-density distributions adopted a conversion factor of $420\,{M}_{\odot }\,{\mathrm{pc}}^{-2}({\rm{M}}\,\mathrm{Jy}\,{\mathrm{sr}}^{-1})$, assuming a fixed mass-to-light ratio of ${Y}_{3.6}=0.6\,{M}_{\odot }/{L}_{\odot ,3.6}$ (Querejeta et al. 2015). For all galaxies except NGC 5457, we also have dust-corrected IRAC 3.6 μm images from S⁴G (Sheth et al. 2010; Querejeta et al. 2015). The same conversion factors were used for these maps. Finally, the SFR surface-density maps were derived by combining background-subtracted, astrometry-matched, and resolution-matched Galaxy Evolution Explorer FUV and Wide-field Infrared Survey Explorer (WISE) 24 μm images, and converting the measured broadband intensities to SFR surface density (Jarrett et al. 2013; Cluver et al. 2017).

Next, we built radial profiles from the mass and SFR surface-density maps. Using the galaxy parameters listed in Table 1, we determined the de-projected galactocentric radius for each pixel in each map. Pixels were then assigned to a series of radial bins each having a width of 15'', where the bin size was limited by the beam size of the Z0MGS SFR maps (all other maps have smaller beam sizes). Within each radial bin, we derived mean, median, and 16%–84% percentiles for each surface-density tracer. For molecular gas surface density in particular, we also estimated the error of the mean value based on the published moment–zero uncertainty maps (Leroy et al. 2009). The resulting derived molecular gas surface-density profiles have a signal-to-noise ratio (S/N) ≥ 3 in most of the bins; however, in cases with lower S/Ns, the 3σ upper limit was provided.

The Z0MGS WISE 1 maps (which trace stellar-mass distribution) were also used to derive the effective radii, R_e, used throughout this work. For this calculation, all foreground stars in the field of view were masked. All pixels were put into a series of radial bins, where masked pixels with ${R}_{g}\lt 0.4\times {R}_{25}$ and all pixels with ${R}_{g}\gt 0.4\times {R}_{25}$ were substituted for the median unmasked pixel value within the same radial bin. The resulting maps were then integrated out to $1.5\times {R}_{25}$ to determine each galaxy's integrated flux, and the equi-radius contour encompassing half of this integrated flux is the effective radius (see Table 1).

The derived mass surface densities for various galaxy components (i.e., stars, H i, H₂) are plotted in Figure C1 for the CHAOS sample. As expected for an interacting galaxy, the H₂ profile of NGC 5194 is different from the other three galaxies, as it both dominates the gas profile and makes up a larger fraction of the total galaxy mass. We find that the stellar- and gas-mass surface-density profiles of the other three noninteracting galaxies look similar, with H₂ more prominent in the inner $\sim 1{R}_{e}$ of the disk, H i dominating the outer disk, and the stellar mass roughly following the total gas mass (${M}_{\mathrm{gas}}={M}_{{\rm{H}}{\rm{I}}}+{M}_{{{\rm{H}}}_{2}}$) for ${R}_{g}/{R}_{e}\lt 2$.

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We show the total gas-mass surface-density profiles, which are dominated by the H₂ gas for most of the disk, versus both radius and elemental abundances (O, N, and S) in the left column of Figure C2. Interestingly, while we find the stellar-mass and gas-mass surface-density profiles of individual galaxies to be offset from one another when plotted versus their N/O profiles, the shift is minimal for the O/H and S/H trends. Since the decline of H₂ gas mass with radius corresponds to a decreasing SFR (as shown in the right column of Figure C2) and SFE, this could indicate that the H₂ mass surface density plays the leading role in the stellar and subsequent chemical evolution of these galaxies.

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Rosales-Ortega et al. (2012), using IFU spectroscopy from the PINGS (Rosales-Ortega et al. 2010) and CALIFA surveys, reported the first local mass–metallicity (M–Z) scaling relationship of H ii regions in spiral galaxies, with a secondary dependence on the equivalent width of Hα (a proxy from SFR). This local M–Z–EW(Hα) relationship is the logical product of inside-out disk growth and the dependence of SFR on mass. While the more widely known fundamental M–Z–SFR global relationship (Mannucci et al. 2010) has been explained by galaxy growth via the accretion of cold gas that is altered by feedback of gaseous inflows and outflows, the local M–Z–SFR relationship allows us to explore physical parameters that may be regulating the growth and chemical evolution within spiral disks.

The stellar-mass surface-density (${{\rm{\Sigma }}}_{{M}_{\odot }}$) radial profiles are reproduced for the four CHAOS galaxies in the first panel of Figure C3. We fit a polynomial to the ${{\rm{\Sigma }}}_{{M}_{\odot }}$–R_e (Figure C3) and ${{\rm{\Sigma }}}_{\mathrm{SFR}}$–R_e trend of each galaxy. These fits are then used to plot the stellar-mass surface densities corresponding to the observed O/H and N/O abundances of the CHAOS H ii regions. The ${{\rm{\Sigma }}}_{{M}_{\odot }}$–O/H and ${{\rm{\Sigma }}}_{{M}_{\odot }}$–N/O trends are plotted in the middle and right panels of Figure C3, respectively, and color-coded by SFR surface density (${{\rm{\Sigma }}}_{\mathrm{SFR}}$). Since SFR is known to depend on stellar mass, the vertical color gradient seen for the SFR in the ${{\rm{\Sigma }}}_{{M}_{\odot }}$–O/H is expected. However, in the ${{\rm{\Sigma }}}_{{M}_{\odot }}$–N/O relationship, not only is the scatter significantly reduced relative to the O/H trend, but SFR also appears to increase along the N/O gradient.

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The metallicity–surface-density relationship may reflect fundamental similarities in the evolution of non-barred, noninteracting spiral galaxies. For example, Ryder (1995) argues for a galaxy evolution model that includes self-regulating star formation, where energy injected into the ISM by newly formed stars inhibits further star formation. These models were able to successfully reproduce the observed correlations between surface brightness and SFR (Dopita & Ryder 1994) and surface mass density (e.g., Phillipps & Edmunds 1991; Ryder 1995; Garnett et al. 1997). The current work supports the idea that stellar-mass surface density is a fundamental parameter governing spiral-galaxy evolution and is particularly important for the relative timescales involved in N/O production.