Abundances in “Green Pea” Star-forming Galaxies

Ionic abundances were calculated using a two-zone model, where the electron temperature determined from [O III] is applicable to the higher-ionization species (O⁺⁺, Ne⁺⁺, and S⁺⁺), and the electron temperature from [N II] or [O II] is applicable to the lower-ionization species (O⁺, N⁺, S⁺). Given the high ionization, a direct measurement of the electron temperature from [N II] or [O II] is not possible. However, a number of calibrated relationships exist for estimating T_e [N II] or T_e [O II] from T_e [O III] and other parameters. A10 use a relationship for T_e [O II] from Perez-Montero & Contini (2009, hereafter PMC09) that depends on T_e [O III] and the measured values of the electron density, in turn depending on measurements of the [S II] λ6717/λ6731 ratio. In many of the GP spectra, the red end has lower S/N and the [S II] lines are more difficult to measure accurately. Alternatively, Pilyugin (2007) proposes a relationship for T_e [O II] that depends on T_e [O III] and an excitation parameter, $P\equiv [\mathrm{O}\mathrm{III}]/([\mathrm{O}\mathrm{II}]+[\mathrm{O}\mathrm{III}])$. Values for T_e [O II] were calculated for every GP with a determination of T_e [O III] using that relationship. For comparison, a value for T_e [N II] was also calculated using a relationship from PMC09. In general, the differences between the derived T_e [O II] and T_e [N II] values are small. For the subsequent abundance analysis the T_e [O II] from the Pilyugin (2007) relationship was adopted for the low-ionization species.

Electron temperatures, densities, and ionic abundances were determined from the line intensities using the nebular package (Shaw & Dufour 1995). Total abundances were calculated from the ionic abundances by use of the traditional ionization correction factors (ICFs) (Peimbert & Costero 1969; Peimbert & Torres-Peimbert 1977).

The resulting O/H versus mass relation for the GPs is shown in Figure 1. A linear least-squares fit gives

$$\begin{array}{}\text{(1)}& \log \mathrm{O}/\mathrm{H}+12=(0.091\pm 0.068)\log \mathrm{M}+(7.26\pm 0.65);r=0.33.\end{array}$$

The error bars in log O/H + 12 derive from the uncertainties in the line-intensity measurements propagated through the electron temperature determination, the ionic abundances, and the ICFs. However, the spread in O/H at a given mass is larger. Intrinsic O/H variations at a given mass are likely. Additionally, systematic errors in the T_e -based method using forbidden lines, including the possibility of temperature fluctuations and inadequacies in the ICFs, generally result in uncertainties comparable with or larger than the errors resulting from the uncertainties in the strength of λ4363. Temperature variations in gaseous nebulae can bias the abundance determinations by 0.1–0.5 dex (Peimbert & Peimbert 2010). Yin et al. (2007) and López-Sánchez & Esteban (2010) propose that temperature fluctuations are a potentially important source of systematic error in T_e -based abundances in star-forming galaxies. In the few cases where abundances in Galactic or extragalactic H II regions can be determined from the much fainter recombination lines, the traditional T_e -based method gives systematically lower values by ∼0.2–0.3 dex (Esteban et al. 2009). This is often cited as the explanation for photoionization model-based strong-line methods, such as N2O2, giving higher absolute values of O/H compared with T_e -based strong-line methods (e.g., López-Sánchez & Esteban 2010).

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The mass-metallicity relation (eq. [1]) agrees within the errors with the results of I11 (see Table 4) and is also consistent with a linear fit to the results of A10, as estimated from their Figure 3, although their choice of a polynomial fit gives a somewhat different relation. It should be noted that I11 reestimated the galaxy masses for their subset of the C09 sample using a different treatment of the continuum. However, these data show no significant difference in the trend of O/H based on the choice of GP mass, so for the rest of this article, the C09 masses will be adopted to better enable comparisons with results from A10.

The average log O/H + 12 of 8.11 ± 0.13 is consistent with the findings of A10, 8.05 ± 0.14, noting that their average O/H includes GPs where the oxygen abundances were estimated from the N2 method. The average of the O/H values for the GP sample quoted by I11 is ∼8.11.

Any metallicity trend can be evaluated further by looking at Ne/H, which also shows an increase with mass (Fig. 2) and an average value of log Ne/H + 12 = 7.43 ± 0.18. A simple linear least-squares fit yields

$$\begin{array}{}\text{(2)}& \log \mathrm{Ne}/\mathrm{H}+12=(0.128\pm 0.091)\log \mathrm{M}+(6.22\pm 0.86);r=0.35,\end{array}$$

in agreement with the O/H trend within the errors. The trend of Ne/O with mass is shown in Figure 3 and is roughly constant with a formal fit:

$$\begin{array}{}\text{(3)}& \log \mathrm{Ne}/\mathrm{O}=(0.039\pm 0.033)\log \mathrm{M}-(1.05\pm 0.31);r=0.30.\end{array}$$

The average log Ne/O = -0.68 ± 0.06 is typical of H II regions and blue compact galaxies with log O/H + 12 < 8.5 (Milingo et al. 2010). The average log Ne/O value found by I11 for their sample of LCGs can be estimated from their Figure 7 as roughly -0.70. I11 find that Ne/O increases with increasing O/H in their LCGs, which they explain as resulting from oxygen being incorporated in grains. These Ne/O values also suggest a small trend with O/H.

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The S/H values are more uncertain, due to the weakness of λ6312 and the effect of the lower S/N in the region of the sulfur lines at λ6717 and λ6731. There are also probable inadequacies in the ICF to account for nonobserved stages of ionization. The degree of ionization of the GPs suggests that there should be significant sulfur in ionization stages higher than [S III]. The average value of log S/H + 12 = 6.83 ± 0.11 is slightly higher than is characteristic of H II regions and blue compact galaxies with O/H similar to the GPs (Milingo et al. 2010). The average value of log S/O = -1.25 ± 0.14. Infrared observations of [S IV] in the GPs would help to more accurately constrain the sulfur abundance. I11 found log S/O = -1.64 for their LCG sample.

T_e -based N/H determinations in 57 GPs average log N/H + 12 = 6.86 ± 0.19. The N/O versus O/H relation is shown in Figure 4 and is consistent with a constant log N/O ratio at a value of ∼-1.25 ± 0.16. The formal fit is

$$\begin{array}{}\text{(4)}& \log \mathrm{N}/\mathrm{O}=(-0.10\pm 0.32)(\log \mathrm{O}/\mathrm{H}+12)-(0.44\pm 2.6);r=0.08.\end{array}$$

The average log N/O agrees with the peak in the histogram in Figure 1 of A10; however, the lack of a trend in N/O with O/H is in contrast with the findings of A10. A10 found an N/O ratio that increased with O/H using a version of the N2S2 method for estimating N/O calibrated from SDSS SFGs with direct ionic abundance determinations. A possible explanation for the discrepancy is discussed in § 4.2. I11 found that N/O shows a significant spread for their entire sample of LCG and BCD galaxies, although they found no appreciable increase in N/O with O/H up to 12 + log O/H ∼ 8.4.

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He I λ5876 intensities were measured in 70 GPs. In a subset of nine, He II λ4686 was weak but measurable, enabling a determination of the helium abundance. He I λ6678 was measured in 23 of the GP spectra, but the line is systematically weaker than λ5876 and in the portion of the spectrum with consistently lower S/N. Consequently, He I λ6678 was not used in the helium abundance determination.

He⁺ abundances were determined from the intensities of λ5876 utilizing the calculations of Benjamin et al. (1999) and the formulation given by Peimbert & Peimbert (2000):

$$\begin{array}{}\text{(5)}& \mathrm{N}({\mathrm{He}}^{+})/\mathrm{N}({\mathrm{H}}^{+})=\{\mathrm{I}(\lambda 5876)/\mathrm{I}(\mathrm{H}\beta )\}0.735T_4^{0.230-6.3\times {10}^{-4}{N}_e}.\end{array}$$

T_e was assumed to be T_e [O III]. He⁺⁺ abundances were determined from the λ4686/Hβ line ratios and the recombination coefficients compiled by Storey & Hummer (1995). In some cases it was possible to calculate the radiation softness parameter, ζ = N(O⁺)N(S⁺⁺)/N(S⁺)N(O⁺⁺) (Vìlchez & Pagel 1988). In those objects, and by extension to all other GPs, ζ is small enough to justify assuming that the contribution of neutral helium is negligible. The resulting value of He/H is 0.091 ± 0.008, with the contribution of He⁺⁺ to the total helium abundance on the order of 1–2%.

A second estimate can be made using the intensity of He I λ5876 in all 70 objects using T_e [O III] where available and assuming 13,000 K otherwise, which is representative of the average T_e in the GPs. That result is He/H = 0.086 ± 0.013 assuming that the contribution of both neutral helium and He⁺⁺ is negligible. This corresponds to a helium abundance by mass, Y = 0.255 ± 0.027. For comparison, the helium abundance for NGC 346 in the Small Magellanic Cloud is Y = 0.2405 ± 0.0018 (Peimbert et al. 2000).

The line intensities were used to estimate O/H from N2O2, N2, and O3N2 and N/O from N2S2. For N2 and O3N2 the calibration of PP04 was adopted. The average O/H in the GPs lies at the lower limit of the range of validity for the O3N2 method (log O/H + 12 = 8.0–8.1). The behavior of O3N2 and choice of calibration for the N2 index will be discussed further in § 4.

The O/H values derived from N2O2 reproduce the results of C09 (correlation coefficient of 0.92), with a small systematic offset to lower O/H by 0.1–0.2 dex. Table 4 summarizes the mass-metallicity relations in the GPs derived from the different abundance estimating techniques, along with the relation of I11 for the GPs and for their complete sample of LCGs. All methods are in agreement within the errors, with the exception of N2O2. Although the N2O2 method is susceptible to errors in flux calibration or reddening correction, it is possible to demonstrate from these data that such errors are not responsible for the discrepancy between N2O2 and the other methods. A10 suggest that N2O2 overestimates O/H because the calibration fails to take into account the influence of the systematically higher N/O with O/H they find in the GPs. However, where N/O ratio is constant, as it is in the GPs (Fig. 4), N2O2 does not retain a metallicity sensitivity (Kewley & Dopita 2002; Kewley & Ellison 2008). The most straightforward explanation is that the metallicity in the GPs is below the range in O/H where N2O2 is applicable.

As Table 4 shows, O/H estimates from N2 and O3N2 show trends with mass in agreement with trends based on the direct method and with the results inferred from A10 and I11. One can conclude that N2 gives O/H abundances consistent with the direct method within the statistical errors. To examine that conclusion in more detail, Figure 5 shows the differences in O/H estimated by N2 compared with the direct method for the individual GPs. The residuals show scatter of ∼0.12 dex, but also a systematic difference in the sense that N2 somewhat overestimates O/H for log O/H + 12 <  ∼ 8.1 and underestimates O/H for log O/H + 12 >  ∼ 8.2.

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The GPs are predominantly of higher ionization and lower O/H than the objects on which the original calibrations were based. Empirical calibrations of N2, O3N2, and N2S2 have been generally based on some combination of Galactic and extragalactic H II regions plus H II galaxies. Additionally, the relevant line ratios are ionization-sensitive. Therefore, it is of interest to reevaluate the calibration of the strong-line methods. The calibrations based on GP T_e -based abundances are shown in Table 5, along with frequently utilized calibrations from the literature. PMC09 have investigated the dependence of N/O on the calibration of N2. The N/O ratios characteristic of the GPs lie in the region where that effect is small. In fact, the average N/O value for the GPs utilized in equation 13 of PMC09 gives essentially the same calibration as the one shown in Table 5, which lacks the N/O term.

The N2 calibration based on the GPs is most similar to the calibration of PP04 and more at variance with the calibrations of Denicoló et al. (2002), Yin et al. (2007), and PMC09. The N2S2 calibration based on GP data differs from that used by PMC09 and A10. The O3N2 calibration based on the GPs (log O/H + 12 = -0.27O3N2 + 8.67, not included in Table 5) has the appearance of agreement with that of PP04. However, it will be seen that the agreement is somewhat coincidental. Additional discussion of the different calibrations is included in § 4.

A10 used the N2S2 method, recalibrated using SDSS SFGs with T_e -based estimates of ionic abundances, to derive N/O in all the galaxies used in their analysis. The use of N2S2 has the advantage of minimizing the dependence of N/O on reddening correction or flux calibration. Utilizing these line-intensity measurements and the N2S2 calibration of PMC09 or as modified by A10 to calculate N/O values, a trend in N/O versus O/H can be reproduced with O/H determined from N2 only, or in combination with direct determinations where T_e is available. These trends have different slopes, but are both in agreement with the findings of A10 that N/O increases with O/H in a manner consistent with their Figure 7. Closer examination of the trend of N/O with O/H based on these measurements shows that the relationship is steeper for O/H estimated entirely from N2, decreases by utilization of T_e -based O/H where available supplemented with N2 estimates, and disappears altogether when only the T_e -based O/H is utilized. Using T_e -based abundances for both N and O where available, supplemented with N2 and N2S2 estimates otherwise, gives a shallower trend with slope ∼30% of the slope obtained from using N2S2 versus N2 only. However, limiting the sample to direct abundance determinations of both N and O, as discussed in § 3.1, shows that N/O is constant, consistent with the behavior of N/O in the I11 sample of LCGs. A possible explanation to reconcile the different results follows.

T_e -based abundances in the GPs confirm an average O/H and a mass-metallicity relation in agreement with the findings of I11 for their LCGs. Average abundances of O, N, Ne, and He are similar to abundances in Small Magellanic Cloud H II regions (Peimbert et al. 2000). The S estimate in the GPs is more susceptible to systematic errors, due to greater uncertainties in the relevant line ratios and the ICF. N/O is independent of O/H within the errors over the range of 7.9 < log O/H + 12 < 8.4.

Izotov & Thuan (1999) studied a sample of approximately 50 blue compact galaxies with 7.6 < log O/H + 12 <  ∼ 8.1 and determined log N/O = -1.46 ± 0.14 and log Ne/O = -0.72 ± 0.06. Estimates from Figure 7 of I11 for the LCGs with 7.9 < log O/H + 12 < 8.3 give log N/O ∼ -1.4 to -1.3 and log Ne/O ∼ -0.7. Values for the GPs are log N/O = -1.25 ± 0.16 and log Ne/O = -0.68 ± 0.06. Although the N/O ratio in the GPs is evidence of, at most, only modest N enrichment, a larger N/O ratio could result from nitrogen enhancement by Wolf-Rayet stars. A larger N/O ratio would also be expected if the GPs recently began the intense star-forming phase, perhaps for only a few million years, given the presence of Wolf-Rayet stars. In this delayed-release scenario a larger N/O ratio would be expected at the beginning of a starburst interval as the result of a preceding quiescent phase where nitrogen enrichment from 4–8 M_⊙ stars was occurring (Kobulnicky and Skillman 1999). In this model, the N/O ratio subsequently decreases as supernovae enhance O and other α-elements. I11 find that star formation must be occurring in bursts in the LCGs, with the bursting nature more pronounced in the LCGs with higher Hβ equivalent widths and lower masses, the subset most similar to the GPs.

If nitrogen enhancement were predominantly by Wolf-Rayet stars, there should be evidence of helium enrichment as well (Kobulnicky et al. 1997). The uncertainties in the He and N abundances in the individual GPs are large enough to mask a small trend. The average values of He/H and N/H for the GPs can be plotted on Figure 9 of Kobulnicky et al. (1997), which depicts He/H versus N/H for 60 low-metallicity galaxies. The result is inconclusive, as that one data point lies near the upper limits of both He/H and N/H, but still within the distribution of the low-metallicity galaxies.

Although A10 find that their results are consistent with the trend in O/H versus mass that they see in their sample of SDSS star-forming galaxies; the mass-metallicity relationship inferred from these measurements for the GPs is shallower over the range 8.5 < log M_⊙ < 10.5 than found in the galaxies studied by Tremonti et al. (2004). The criteria used to identify the original GPs suggest the possibility of a selection effect in the deduced mass-metallicity relation. The galaxy sample of Tremonti et al. (2004) includes a range in [O III]/Hβ, while the GPs were originally chosen by C09 based on strong [O III]. Consequently, the GPs constitute a sample with an artificial metallicity cutoff that is biased toward low metallicity. This could in turn result in a shallower mass-metallicity relationship for the GPs than is characteristic of the large sample of Tremonti et al. (2004) introduced solely by using strong [O III]/Hβ as the selection criterion. It is interesting that the mass-metallicity relation found by I11 for their 803 LCGs agrees with that found here for the GPs, even though the I11 sample was selected by Hβ equivalent width and not the strength of [O III], specifically to avoid biasing their sample to low-metallicity objects. However, one of their other selection criteria was the presence of measurable λ4363 necessary to enable the T_e -based abundance determinations. That criterion could also have the effect of selecting for lower-metallicity objects. I11 judged that not to be the case based on the argument that removing that constraint only increased their sample by ∼20%.

As shown in Table 4, N2 with the PP04 calibration produces a mass-metallicity relation consistent with the T_e -based relation. N2O2 does not, because O/H is outside the valid range for that method. The behavior of the O3N2 method will be discussed further subsequently. It remains to explain why the N/O trend with O/H based on the N2S2 method in combination with the direct plus N2 method gives a different result from the direct-only method. The following discussion shows that the behaviors of N2 and N2S2 are coupled in an unexpected way as the result of the relative uniformity of the emission-line spectra in the GP sample.

Combining the definitions of N2S2 and N2 with the published calibrations demonstrates that the two methods are not independent, at least in the GPs. A conversion relation between N/O (N2S2) and O/H (N2) can be derived from the calibration of PMC09 for N2S2 and PP04 for N2:

$$\begin{array}{}\text{(6)}& \log \mathrm{N}/{\mathrm{O}}_{\mathrm{N}2\mathrm{S}2}=2.22(\log \mathrm{O}/\mathrm{H}+12{)}_{\mathrm{N}2}-20.6-1.27\log ([\mathrm{S}\mathrm{II}]/\mathrm{H}\alpha ).\end{array}$$

In 51 of the 71 GPs with measured line intensities, the [S II]/Hβ ratios are between ∼0.25 and ∼0.50, reducing log N/O (N2S2) to a linear relation with O/H (N2) plus some amount of scatter. Consequently, if the N2 and N2S2 methods are utilized together, they will introduce a bias and N/O will show a trend with O/H based solely on the definitions of the indices and the calibrations. A similar conversion relation results by utilizing the N2 calibration of PMC09.

Figure 6 illustrates the specific case where N/O is obtained from N2S2 and O/H is determined solely by the N2 method. The solid line is the least-squares fit to the measurements in this article, which is consistent with the trend found by A10. The dashed lines represent the conversion relationship for [S II]/Hβ ratios of 0.10, 0.25, and 0.50. The observed variation in [S II]/Hβ flattens the trend compared with the slope of the conversion relation, but the net effect shows N/O increasing with O/H. As more objects are included with directly determined O/H, this trend moderates until it disappears when limiting the sample to only T_e -based O/H. N2S2 or N2 would still give valid results if used independently when T_e -based abundances are not possible, however, plotting N2S2 against N2 in the GPs leads to the appearance of a relationship different from the actual abundance trend.

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Similarly, the N2 and O3N2 methods are not independent in the GPs. The O3N2 method gives oxygen abundance estimates that are more tightly correlated with those from the N2 method (correlation coefficient of 0.99) than one might expect given the systematic uncertainty in the calibrations of O3N2 and N2 as shown in Table 1. Based on the definition of the indices and calibrated relationships from PP04, there is a conversion relationship:

$$\begin{array}{}\text{(7)}& 12+\log \mathrm{O}/{\mathrm{H}}_{\mathrm{N}2}=1.78(\log \mathrm{O}/\mathrm{H}+12{)}_{\mathrm{O}3\mathrm{N}2}-6.64+0.57\log (\lambda 5007/\mathrm{H}\beta ).\end{array}$$

The λ5007/Hβ ratio varies by just over a factor of 2 in the 71 GPs used in this study. As a result, in the GPs O3N2 and N2 are equivalent to within a roughly constant offset, with O3N2 giving a systematically lower estimate of O/H, which is the observed behavior. One consequence is that the agreement between the calibration of O3N2 based on the GP abundances and the calibration of PP04 is, to some extent, coincidental and derives from the GP-based calibration of N₂. These data cannot be used to imply that O3N2 should independently be assumed to be valid in this low-metallicity, high-ionization regime (O3N2 > 1.9, P > 0.80); although, López-Sánchez & Esteban (2010) find that O3N2 with the PP04 calibration is applicable for 7.70 < log O/H + 12 < 8.68 in their sample of star-forming galaxies, some of which were classified as Wolf-Rayet galaxies.

As expected, the higher ionization level in the GPs introduces additional systematic error into O/H and N/O estimates from the N2 and N2S2 methods, respectively. The presence of λ4686/Hβ plus strong [O III]/Hβ is more typical of planetary nebulae than H II region spectra, and the GPs generally occupy the locus of planetary nebulae on a Baldwin-Phillips-Terlevich (BPT; Baldwin, et al. 1981) plot of λ5007/Hβ versus λ3727/λ5007. Strong-line methods are not expected to work in planetary nebulae because of the higher effective temperatures (Stasińska 2002). Relaño et al. (2010) have found that the [N II]/Hα and [N II]/[O III] line ratios show variations as a function of ionization in NGC 595, the most luminous H II region in M33, which contains Wolf-Rayet stars. Yin et al. (2007) analyzed the N2 method and found the calibration to be ionization-dependent, with the slope of the relation becoming slightly flatter as the excitation parameter, P, increased. Table 5 includes the calibration based on 149 of their galaxies that had P > 0.80, which is also the average value for the excitation parameter in the GPs. The slope of the GP-based calibration of N2 is shallower than the slopes of the other calibrations in Table 5, with the exception of PP04, by greater than twice the statistical errors. The slope of the N2S2 calibration based on GP abundances is shallower by more than 3 times the statistical error compared with the slopes of the calibrations of PMC09 and A10.

At some point, ionization effects could invalidate these strong-line methods. To isolate the effect of even higher ionization on the behavior of the N2 and N2S2 methods, a cursory examination was made of emission-line strengths taken from the literature for approximately 50 SMC and LMC planetary nebulae, chosen with T_e -based abundances and O/H comparable with the GPs. No relationship was evident in N2 with O/H over the range of -2.5 < N2 < -0.3, although a trend exists between N2S2 and log N/O in the planetary nebulae, with a slope similar (within the errors) to the trend found in the GPs.

Table 6 lists three abundance-related parameters for several N2 calibrations over the range of the N2 index in the GPs (∼-1.8 < N2 < -0.8). Both the Yin et al. (2007) and PMC09 calibrations yield a wider range in O/H while, respectively, overestimating and underestimating the absolute O/H values. The PMC09 calibration utilizing the N/O term is included for completeness and was evaluated using N/O values for the individual GPs. The absolute value of ΔO/H (T_e - N2) is reduced, consistent with the findings of PMC09 that including the N/O dependence reduces the dispersion in the N2-based metallicity estimates, although this is a small effect in the GPs.

The calibration of PP04 gives the smallest average value of the residual compared with T_e -based O/H, comparable with the residual produced by the GP-based calibration. López-Sánchez & Esteban (2010) examined the N2 method with the PP04 calibration in their study of star-forming galaxies, including Wolf-Rayet galaxies, and found an absolute value of ΔO/H(N2 - T_e) = 0.12 ± 0.13. The PP04 calibration introduces the smallest systematic effect in the mass-metallicity relation for the GPs, giving a shallower slope within 10% of the T_e -based value, while the calibration of PMC09 gives a slope that is steeper than the T_e -based value by slightly more than ∼30%.

Table 7 shows the same abundance parameters for the different N2S2 calibrations applied to the GP line intensities. The greater slope of the calibrations based on H II regions and H II galaxies overestimates log N/O compared with T_e -based log N/O for values of N2S2 >  ∼ -0.4 and underestimates log N/O otherwise. The A10 calibration exhibits a larger amount of scatter than the calibration of PMC09; however, the residuals in log N/O estimates from each calibration are within the estimated error cited in Table 1.

It is not unexpected that the calibration of N2S2 would be different in the GPs. First, given the estimated error in the published calibrations, some variance could be expected solely because the GPs have a smaller range in both N2S2 and log N/O than the larger sample of objects on which the other calibrations are based. More importantly, however, the relation between N/O and [N II]/[S II] has an ionization dependence. PMC09 were motivated to use N2S2 for N/O estimates to minimize the effects of errors in reddening correction or flux calibration. To first order, the [N II]/[S II] line ratio would be sensitive to N⁺/S⁺ and, therefore, N/S, just as the [N II]/[O II] line ratio is sensitive to N⁺/O⁺ and, therefore, N/O. Since sulfur is also an α-element, N/O would scale with N/S. The ionization potentials of N⁺ and O⁺ are similar, a fact that constitutes the rationale for the ICF used to calculate the total nitrogen abundance. However, the ionization potential of O⁺ is more similar to S⁺⁺ than S⁺, again the basis for the traditional ICF used to calculate total sulfur abundance (Peimbert & Costero 1969). N/S and, therefore, N/O would not necessarily maintain the same relationship with [N II]/[S II] as ionization increases.

Based on this argument and as a consistency check, $[\mathrm{N}\mathrm{II}]/([\mathrm{S}\mathrm{II}]+[\mathrm{S}\mathrm{III}])$ should scale directly with N/O. There are 15 objects with both T_e -based abundances and a measurement of [S III] λ6312, so a calibration can be determined for this “N2S23” index, which would be expected to have a slope on the order of unity. The [S III] line is weak and the number of data points is limited, but the result is

$$\begin{array}{}\text{(8)}& \log \mathrm{N}/\mathrm{O}=(0.99\pm 0.30)\mathrm{N}2\mathrm{S}23-(0.95\pm 0.10),r=0.89.\end{array}$$

As ionization increases at a given N/S ratio, one would expect the fraction of S that is S⁺ to be less than the fraction of N that is N⁺. Therefore, the [N II]/[S II] ratio would overestimate N/S (and, equivalently, N/O), and the slope of the relation between N2S2 and N/O in the GPs would be expected to be less than unity, as is the case. Kewley & Dopita (2002) have previously noted that the [N II]/[S II] ratio is strongly dependent on ionization making it less useful than [N II]/[O II] for estimating O/H.

In summary, the N2 and N2S2 methods are still valid for star-forming galaxies ionized by Wolf-Rayet stars, although use of the calibrations based on GPs should give more accurate O/H and N/O estimates in galaxies with harder SEDs. There is evidence that the slope of both the N2 and N2S2 calibrations decreases as ionization increases in star-forming galaxies. The higher ionization exhibited by the GPs is sufficient to alter the calibration of these two strong-line methods, but is not high enough to invalidate them.

I11 concluded that oxygen abundances from strong-line methods should not be used in galaxy evolution studies without a careful analysis of the errors. The GP results confirm that care should be taken when applying strong-line methods to star-forming galaxies where ionization or metallicity is substantially different from the objects on which the calibrations are based. Caution may be warranted at either extreme of ionization seen in star-forming galaxies. Berg et al. (2011) find that the common strong-line methods, including N2 with the PP04 calibration, overestimate O/H in their study of four very low mass, low-ionization galaxies. However, Berg et al. (2011) were not able to determine T_e -based abundances, so O/H was estimated from comparison with photoionization models. Nevertheless, without information inferring a high level of ionization where the GP-based calibration would apply, the N2 method as calibrated by PP04 would still be recommended based on its ability to give reasonable O/H estimates over a wide range of ionization and absolute abundances.

Finally, looking for trends in N/O with O/H based solely on strong-line methods can lead to biased results, depending on the details of the spectra being analyzed. Using N2S2 with N2, given the relatively small range in the [S II]/Hβ ratio in the GPs, leads to the conclusion that nitrogen is enhanced with respect to oxygen at these low metallicities, which is not the case, as seen from the T_e -based abundances.