"DIRECT" GAS-PHASE METALLICITIES, STELLAR PROPERTIES, AND LOCAL ENVIRONMENTS OF EMISSION-LINE GALAXIES AT REDSHIFTS BELOW 0.90

To select NB and IA excess emitters due to the presence of nebular emission line(s), we use the standard color excess selection, where photometric fluxes from these filters are compared against those for adjacent broad-band filters that sample the continuum. Since the technique has been extensively used, we briefly summarize it below, referring readers to Fujita et al. (2003) and Ly et al. (2011a). We summarize our excess emitter sample in Table 1.

The measured continuum adjacent to the line is determined by the two broad-band filters closest to the narrow bandpass. For NB921 and NB973, we start with the z'-band. Since the central wavelengths of these filters are redder than what the z' filter measures, we correct for such differences using the i'–z' color (Ly et al. 2012a, 2012b). The remaining filters use a flux-weighted combination of either the V- and R_C-band (IA598), the R_C- and i'-band (NB704, NB711, and IA679), or the i'- and z'-band (NB816):

$$\begin{equation} f_{\rm cont} = \epsilon f_{\rm blue} + (1-\epsilon) f_{\rm red}, \end{equation} \tag{ 1 }$$

where f_blue and f_red are the flux density in erg s⁻¹ cm⁻² Hz⁻¹ for the bluer and redder broad-band filters, respectively (e.g., i' and z' for NB816), and = 0.45 (IA598), 0.5 (NB704, NB711), 0.75 (IA679), and 0.6 (NB816).

Photometric measurements for broad-band data are obtained by running SExtractor (Bertin & Arnouts 1996) in "dual-image" mode, where the respective NB or IA image is used as the "detection" image. This works well because all broad-band, IA, and NB mosaicked images have very similar seeing, so that excess colors are determined within the same physical scale of the galaxies. For the extraction of fluxes and selection of sources, we use a 2'' diameter circular aperture. For comparison, the 3σ sensitivities for the V, R_C, i', and z' data are between 26.27 and 27.53 mag, which are generally deeper than the NB and IA imaging.

We also exclude sources which fall in regions affected by poor coverage and contamination by bright foreground stars. The unmasked regions cover 870.4 arcmin² for all filters with the exception of NB973, which covers 788.7 arcmin². The latter is smaller due to higher systematic noise in one of the 10 CCDs, which we mask to avoid significant spurious detections. In total, 123,123, 97,632, 133,273, 119,541, 84,786, 118,097, and 139,585 sources are detected in the unmasked regions of the NB704, NB711, NB816, NB921, NB973, IA598, and IA679 mosaics, respectively. Among these sources, 1695, 1480, 1602, 2361, 1243, 641, and 790 are identified as NB or IA excess emitters.

In certain circumstances, our sources are selected by more than one filter. This is due to some fortuitous redshift overlap of our NB/IA filters, such that different emission lines (e.g., Hα and [O iii]) are detectable at the same redshift (see Figure 1). Accounting for duplicate galaxies, the complete SDF ELG sample consists of 9264 galaxies, mostly at z = 0.01 to z = 1.62, with some at higher redshift due to Lyα emission. We note that the sample presented in this paper supersedes our earlier multi-NB studies. Previously, we had selected ELGs in four NB filters and examined the evolution of the Hα, [O iii], and [O ii] luminosity functions (L07). A fifth NB filter (NB973) was later included, and that filter allowed us to study dust attenuation at z = 0.4–0.5 (Ly et al. 2012a) and stellar properties out to z = 1.5–1.6 (Ly et al. 2012b).

The primary results of this paper are based on optical spectroscopy taken over the past several years, with Keck's Deep Imaging Multi-Object Spectrograph (DEIMOS; Faber et al. 2003) and MMT's Hectospec (Fabricant et al. 2005). In total, we obtained 945 optical spectra for 870 ELGs, and successfully detected emission lines to determine redshift for 713 galaxies or 82% of the targeted sample. These spectra were initially obtained to confirm that the NB technique efficiently identified ELGs. A summary of the spectroscopically confirmed excess emitters is provided in Table 1.

The majority (61%) of our spectroscopic sample was obtained from Hectospec. These spectra were obtained between 2008 March 13 and 2008 April 14, utilizing the 270 mm⁻¹ grating blazed at 5200 Å to yield spectral coverage of 3650–9200 Å. The combination of this grating with a fiber diameter of 15 yields a spectral resolution of ≈6 Å.

The typical seeing for these observations was between 07 and 14, and the data were obtained at airmasses below 1.35, with 95% (77%) of the data below 1.3 (1.2). Four different fiber configurations were used, with on-source integrations varying between four and six 20 minute exposures, which is sufficient for cosmic ray rejection. The MMT spectra were reduced following standard procedures with the iraf Hectospec Reduction Software.¹² Since no order-blocking filter was used, the spectra at wavelengths longward of 8200 Å have a significant amount of contaminating second-order light (up to 30% for the relatively blue flux standard stars). The flux calibration in the far-red is therefore unreliable, and we do not use it.

The Keck/DEIMOS observations were obtained in 2004, 2008, and 2009. The 2004 spectroscopic observations have been discussed in Kashikawa et al. (2006) and L07, and the more recent data have been discussed in Kashikawa et al. (2011). In brief, we constructed 13 slit-masks with 1'' slit widths. This typically corresponds to a spectral resolution of R ∼ 3600 at 8500 Å, and spectral dispersion of 0.47 Å pixel⁻¹. The 830 line mm⁻¹ grating and GG495 order-cut filter were used in all DEIMOS observations. This set-up resulted in a spectral coverage of ≈5000 Å–1 μm; however the coverage varied along the dispersion axis of the slit mask. The typical seeing for these observations was 05–10 in 2004 and 07–11 for 2008–2009, with integration times of 2–3 hr. Almost all (86%) of the DEIMOS spectra were obtained at low airmasses (⩽1.3), with the remaining data taken at an airmass of 1.35.

2.2.1. Flux Calibration

Because [O iii] λ4363 is more likely to be detected in higher temperature gas, a common concern is whether these galaxies harbor low-ionization nuclear emitting regions (LINERs; Heckman 1980), where the gas may be shock-heated. To determine if any of our galaxies are LINERs, the preferred method is to use the [O i] λ6300 emission line. Unfortunately, this is redshifted out of our spectral coverage for the majority of our galaxies. Instead, we use a variety of emission-line flux ratios, including [O ii]/[O iii], [O iii]/Hβ, and [O ii]/[Ne iii] λ3869, to determine if any of our galaxies could be a LINER. Four galaxies (MMT 02, 03, 06, and 12) have [O ii]/[O iii] ratios that are similar to or above unity (0.82–2.2), which is a cautionary LINER flag. Upon comparing our emission-line fluxes to SDSS DR7 LINERs, we find that only MMT 03 is arguably a LINER. The three remaining galaxies have too low (high) of an [O ii]/[O iii] ([O iii]/Hβ) ratio by at least 0.4 dex. Further independent evidence supporting the idea that MMT 03 is a LINER is its stellar mass. As we will later show (Section 4.4), it is our most massive galaxy. In general, LINERs are primarily found in more massive galaxies (e.g., 94% of SDSS DR7 LINERs are above a stellar mass of 10¹⁰ M_☉).

Another possibility to consider is that some of our galaxies might harbor an active galactic nucleus (AGN). Supporting evidence would include very high ionization lines (e.g., [Ne v] λ3425, He ii λ4686), although these lines have also been seen in some local blue compact dwarf galaxies (Izotov et al. 2012b). A search for [Ne v] and He ii yielded non-detections, arguing that our sample is free of Seyfert galaxies. In addition, our two galaxies (MMT 10 and 11) with coverage of [N ii] λ6583 have [N ii]/Hα ratios of 0.02 and 0.04, which places them in the star-forming region of the "BPT" diagram (Baldwin et al. 1981). While [N ii] is not available for the remaining 18 galaxies, we are able to use an analogous diagnostic tool called the "Mass-Extinction" diagram ("MEx"; Juneau et al. 2011). We illustrate in Figure 4 our sample against star-forming galaxies selected using the BPT diagram¹⁴ from the SDSS MPA-JHU DR7 sample.¹⁵ We find that all of our galaxies lie in the star-forming domain. Compared to local galaxies of similar stellar masses, our ELGs all show a higher [O iii]/Hβ flux ratio by ≈0.2–0.5 dex. We find that for more typical ELGs (i.e., those that lack [O iii] λ4363 detections) in our spectroscopic sample, the [O iii]/Hβ ratios are similarly higher than in SDSS. This holds for more massive galaxies with M_⋆ ∼10¹⁰ M_☉. We overlay the range of the full sample as a purple shaded region in Figure 4. We later discuss this result for higher ionization in Section 5.4, and discuss selection effects associated with our sample in Section 5.2.

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To correct the emission-line fluxes for dust attenuation, we use Balmer decrement measurements obtained from a combination of our spectroscopy and NB imaging. Since our ELGs possess high EWs, 12, 18, and 20 galaxies have Hδ, Hγ, and Hβ detected at ≳5σ, respectively. In addition, Hα measurements are available for five galaxies. Two of them (MMT 10 and MMT 11) are at lower redshifts, allowing us to use their spectroscopic Hα measurements. For the other 3 galaxies (MMT 04, 06, 11), the NB Hα flux is determined using the following equation:

$$\begin{equation} F_{{\rm H}\alpha } = \Delta {\rm NB} \frac{f_{\lambda ,{\rm NB}} - f_{\lambda ,{\rm BB}}}{1-(\Delta {\rm NB}/\Delta {\rm BB})} f_{\rm corr}, \end{equation} \tag{ 6 }$$

where f_{λ, NB} and f_{λ, BB} are the flux density in erg s⁻¹ cm⁻² Å⁻¹ for the NB and broad-band, Δ's are the respective FWHM of the filters (Δz' = 956 Å), and f_corr is the correction for the non-tophat shape of the NB filter when the redshifted Hα emission is in the filter's wing. Using filter throughputs and spectroscopic redshifts, we are able to determine f_corr. We note that for four galaxies (MMT 03, 07, 13, and 14), the NB fluxes are not reliable for Balmer decrement determinations. In particular, MMT 03 suffers from significant [N ii] contamination in the NB921 filter as a LINER candidate. For the other three sources, the Hα line falls in the wing of the NB921 or NB973 filter where precise filter response corrections cannot be made.

A significant problem encountered with using Balmer decrements to determine dust attenuation is the underlying stellar absorption. In three galaxies (MMT 03, MMT 04, and Keck 3), the spectra are of high S/N to sufficiently detect the continuum and fit and remove the stellar absorption or use iraf's splot command to re-measure the continuum from the absorption trough. For MMT 03 (Keck 3), we determine corrections of EW_abs(Hδ) = 2.7 Å (1.6 Å), EW_abs(Hγ) = 1.9 Å (2.5 Å), and EW_abs(Hβ) = 1.6 Å (0.0 Å). While for MMT 04, we measure EW_abs(Hδ) = 3.9 Å and EW_abs(Hγ) = 2.5 Å.

For the remaining galaxies, the S/N of our spectra are not sufficient to model the stellar absorption. To correct these galaxies, we adopt EW_abs(Hδ) = 2 Å and EW_abs(Hγ) = 1 Å. We assume no stellar absorption for Hβ and Hα, which is reasonable since the measured rest-frame emission-line EWs are significantly large (Hβ: median of 60 Å, average of 95 Å).

With these corrections for stellar absorption, we illustrate the Balmer decrements in Figure 5. In addition, we report in Table 4 the absorption-corrected Balmer decrements, and the determined or assumed EW for stellar absorption.

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Table 4. Balmer Decrement Measurements and Derived Reddening

ID	Hα/Hβ	Hγ/Hβ	EW(Hδ)	EW(Hγ)	EW(Hβ)	Source	E(B − V)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
MMT 01	...	...a	2.0	1.0	0.0	...	0.24$^{+0.21}_{-0.21}$
MMT 02	...	0.41$^{+0.03}_{-0.04}$	2.0	1.0	0.0	Hγ/Hβ	0.25$^{+0.20}_{-0.22}$
MMT 03	...b	0.39$^{+0.04}_{-0.04}$	2.7	1.9	1.6	Hγ/Hβ	0.35$^{+0.26}_{-0.24}$
MMT 04	3.98$^{+0.04}_{-0.03}$c	0.47$^{+0.01}_{-0.01}$	3.9	2.5	0.0	Hγ/Hβ	0.00$^{+0.05}_{-0.04}$d
MMT 05	...	0.49$^{+0.05}_{-0.04}$	2.0	1.0	0.0	Hγ/Hβ	0.00$^{+0.21}_{-0.21}$d
MMT 06	4.51$^{+0.16}_{-0.18}$	0.37$^{+0.06}_{-0.05}$	2.0	1.0	0.0	Hα/Hβ	0.39$^{+0.04}_{-0.03}$
MMT 07	...c	0.48$^{+0.02}_{-0.02}$	2.0	1.0	0.0	...	0.24$^{+0.21}_{-0.21}$
MMT 08	...	0.38$^{+0.05}_{-0.05}$	2.0	1.0	0.0	Hγ/Hβ	0.42$^{+0.43}_{-0.45}$
MMT 09	4.45$^{+0.45}_{-0.44}$	0.36$^{+0.10}_{-0.10}$	2.0	1.0	4.4	Hα/Hβ	0.38$^{+0.09}_{-0.10}$
MMT 10	3.26$^{+0.08}_{-0.11}$	0.47$^{+0.04}_{-0.04}$	2.0	1.0	0.0	Hα/Hβ	0.11$^{+0.02}_{-0.02}$
MMT 11	3.59$^{+0.12}_{-0.12}$	0.41$^{+0.03}_{-0.02}$	2.0	1.0	0.0	Hα/Hβ	0.19$^{+0.03}_{-0.03}$
MMT 12	...	0.37$^{+0.07}_{-0.11}$	2.0	1.0	0.0	Hγ/Hβ	0.51$^{+0.72}_{-0.46}$
MMT 13	...c	0.43$^{+0.05}_{-0.05}$	2.0	1.0	0.0	Hγ/Hβ	0.17$^{+0.26}_{-0.24}$
MMT 14	...c	0.46$^{+0.01}_{-0.01}$	2.0	1.0	0.0	Hγ/Hβ	0.03$^{+0.03}_{-0.03}$
Keck 1	...	0.38$^{+0.01}_{-0.01}$	2.0	1.0	0.0	Hγ/Hβ	0.41$^{+0.07}_{-0.07}$
Keck 2	...	...a	2.0	1.0	0.0	...	0.00e
Keck 3	...	0.35$^{+0.01}_{-0.01}$	1.6	2.6	0.0	Hγ/Hβ	0.62$^{+0.04}_{-0.04}$
Keck 4	...	0.53$^{+0.01}_{-0.01}$	2.0	1.0	0.0	Hγ/Hβ	0.00$^{+0.07}_{-0.07}$d
Keck 5	...	...a	2.0	1.0	0.0	...	0.24$^{+0.21}_{-0.21}$
Keck 6	...	...f	2.0	1.0	0.0	...	0.24$^{+0.21}_{-0.21}$

Notes. Uncertainties are reported at the 68% CL. Stellar absorption line corrections are reported in Columns 4–6. ^aHβ is affected by a weak OH sky-line. ^bThe NB921 flux is contaminated by significant [N ii] emission because this source is a LINER. ^cThe Hα emission falls at the very edge of NB921 or NB973 filter, and therefore extinction determinations are unreliable using Hα/Hβ. ^dNegative reddening was seen. We adopt E(B − V) = 0.0. ^eThe Hγ and Hδ fluxes suggests no reddening. ^fHγ is affected by an OH sky-line.

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Under the assumption that the hydrogen nebular emission originates from an optically thick ionization-bounded H ii region obeying Case B recombination, the intrinsic Balmer flux ratios are: (Hα/Hβ)₀ = 2.86, (Hγ/Hβ)₀ = 0.468, and (Hδ/Hβ)₀ = 0.259 for T_e = 10⁴ K and electron density of n_e = 100 cm⁻³ (see Section 4.2 for further discussion). We note that these values differ by less than 5% for T_e = 2 × 10⁴ K. Dust absorption alters these observed ratios:

$$\begin{equation} \frac{({\rm H}n/{\rm H}\beta)_{\rm obs}}{({\rm H}n/{\rm H}\beta)_0} = 10^{-0.4E(B-V)[k({\rm H}n)-k({\rm H}\beta)]}, \end{equation} \tag{ 7 }$$

where E(B − V) is the nebular color excess, and k(λ) ≡ A(λ)/E(B − V) is the reddening curve at λ. The latter is dependent on the dust reddening "law." We illustrate in Figure 5 the observed Balmer decrements under the Calzetti et al. (2000, hereafter C00) dust reddening formalism with k(Hα) = 3.33, k(Hβ) = 4.60, k(Hγ) = 5.12, and k(Hδ) = 5.39. We find that our Balmer decrements are consistent with the C00 dust reddening formula. For the remainder of our paper, all dust-corrected measurements adopt C00 reddening.

Our color excesses, which are tabulated in Table 4, are determined using either Hα/Hβ (06, 09–11) or Hγ/Hβ (MMT 02–05, 08, 12–14, and Keck 1, 3, and 4). We do not use Hδ/Hβ, since it is not well measured for the majority of our galaxies. However, the E(B − V) estimates from Hδ/Hβ are consistent with Hγ/Hβ, as indicated in Figure 5. In three galaxies (MMT 04, MMT 05, and Keck 4), the Hγ/Hβ ratios suggest negative reddening, so we adopt E(B − V) = 0.0. For four of our galaxies (MMT 01, 07, 5–6), the dust reddening could not be determined from Balmer decrements. For these galaxies, we assume E(B − V) = 0.24 ± 0.21 mag (A(Hα) ≈ 0.8 ± 0.7 mag), which is the average of our sample,¹⁶ and is similar to typical reddening found for local galaxies (A(Hα) = 0.8–1.1; Kennicutt 1998a). This also agrees with what we found for ELGs at z ≈ 0.4 (Ly et al. 2012a).

For Keck 2, the Hβ line unfortunately fell at the edge of a CCD gap, so the Hβ flux is not fully measured. However, the Hγ and Hδ lines are robustly detected (19 and 9σ). Assuming Case B recombination and no reddening, the Hγ/Hβ and Hδ/Hβ Balmer decrements yielded Hβ fluxes of 2.54 × 10⁻¹⁷ and 2.87 × 10⁻¹⁷ erg s⁻¹ cm⁻², respectively. This excellent agreement in predicted Hβ fluxes suggests that very little reddening is present in this galaxy. We assume E(B − V) = 0.0.

To determine the gas-phase metallicity for our galaxies, we use the empirical relations of Izotov et al. (2006b). This follows the approach of most direct metallicity studies. The first equation estimates T_e([O iii]) using the nebular-to-auroral [O iii] flux ratio:

$$\begin{equation} \log {\left(\frac{[{\rm O}\,\scriptsize{III}]\,\lambda \lambda 4959,5007}{[{\rm O}\,\scriptsize{III}]\,\lambda 4363}\right)} = \frac{1.432}{t_3}+\log {C_T}, \end{equation} \tag{ 8 }$$

where t₃ = T_e([O iii])/10⁴ K,

$$\begin{equation} C_T = \left(8.44-1.09t_3+0.5t_3^2-0.08t_3^3 \right)\frac{1+0.0004x}{1+0.044x}, \end{equation} \tag{ 9 }$$

and $x = 10^{-4}n_e t_3^{-0.5}$. For the majority of our galaxies, the [S ii] λλ6717, 6732 doublet, an estimator for n_e, is redshifted out of our spectral coverage. For one of our galaxies, MMT 10, both [S ii] lines are weakly detected. The λ6717/λ6732 flux ratio of ≈1.1 corresponds to n_e ≈ 400 cm⁻³ (assuming T_e = 10⁴ K). In addition, DEIMOS has the spectral resolution to separate [O ii] λλ3726, 3729. The λ3729/λ3726 flux ratios vary between 0.87 and 1.35, which correspond to n_e = 70–600 cm⁻³. To determine T_e, we assume n_e = 100 cm⁻³. We note that C_T is only affected by n_e in the high density regime (n_e ≳ 10⁴ cm⁻³), and therefore assuming n_e = 10, 100, or 10³ cm⁻³ yields nearly identical T_e.

We correct the nebular-to-auroral [O iii] flux ratio for dust attenuation using our dust attenuation prescriptions (see Section 4.1). Correcting for dust attenuation increases estimates of T_e, since dust extincts shorter wavelengths (e.g., 4363 Å) more than longer wavelengths (e.g., 5007 Å).

In addition, it has been known that (1) T_e determinations using various direct metallicity prescriptions, including Izotov et al. (2006b); and (2) strong-line metallicity diagnostics do not yield consistent results (Kewley & Ellison 2008). These discrepancies have been recently explored, and it is believed that outdated effective collision strengths for the various O⁺⁺ excitation states, and a non-equilibrium distribution of the electron energies result in overestimation of the electron temperature (Nicholls et al. 2012, 2013). Those authors provided applicable corrections for each method. We adopt their corrections, which correspond roughly to a 5% reduction for T_e estimates using the Izotov et al. (2006b) approach.

For the very strong ELGs we are studying, our [O iii] measurements have a very large dynamic range. The strongest [O iii] λ4363 line is as much as 0.089 of the [O iii] flux (MMT 03), while the weakest is 0.007 (Keck 3). We find that the average and median λ4363/λ5007 flux ratio for our sample are both 0.037. The derived electron temperatures for our galaxy sample, also have a wide range, from 10⁴ K to 4.5 × 10⁴ K. Among our 19 galaxies, 11 have T_e estimates of 10⁴–2.1 × 10⁴ K, which are similar to those measured in local galaxies.¹⁷ The large tail toward high T_e yields an average log (T_e/K) that is higher than the average of local galaxies by 0.15 dex.

Other higher redshift studies have measured high T_e in star-forming galaxies. For example, Yuan & Kewley (2009) detected [O iii] λ4363 in a lensed z = 1.7 galaxy and measured T_e ≈2.35 × 10⁴ K, and Hu et al. (2009) have also measured large [O iii] λ4363/λ5007 flux ratios in a few ELGs. The higher values of T_e are not well-determined, and have a large tail (0.2–0.3 dex) toward lower temperatures. This is likely the case for other published measurements, as Yuan & Kewley (2009) yielded a 3σ detection of [O iii] λ4363, and the measurement uncertainties of Hu et al. (2009) result in a significant tail toward low T_e.

MMT 03 has the most extreme T_e value, but as we mentioned in Section 3.1, it is a LINER with shock-heated, rather than photo-ionized gas producing most of its emission-line spectrum. Other galaxies with high T_e (≳ 2.5 × 10⁴ K) are MMT 06, 08, 09, 12, Keck 5, and 6. To examine if these temperatures are reasonable, we generate low-metallicity models with CLOUDY (Ferland et al. 1998). In our modeling, we input Starburst99 (Leitherer et al. 1999) SEDs that adopt Geneva stellar evolution models with five stellar metallicities between Z/Z_☉ = 0.05 and 2.0. Coupling the stellar and gas metallicity, we find that the highest plausible T_e([O iii]) temperature is ≈25,000 K for Z/Z_☉ = 0.02–0.03.¹⁸ Given this upper limit, we fix the dust-corrected T_e([O iii]) to not exceed this temperature for these six galaxies. We note that without this T_e offset, the resulting oxygen metallicity will be lower by 0.1–0.4 dex for these six galaxies.

The T_e measurements for all 20 objects are shown in Figure 6. Throughout this paper, we generate realizations of the emission-line fluxes to construct probability distribution functions (PDFs) for all observed and derived measurements. This is critical, as the distributions are non-Gaussian in the domain of low S/N (≲5), and it allows us to propagate our measurement uncertainties, including E(B − V).

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To determine the ionic abundances of oxygen, we use two emission-line flux ratios, [O ii] λλ3726+3729/Hβ and [O iii] λλ4959+5007/Hβ:

$$\begin{eqnarray} 12+\log {\left(\frac{{\rm O}^+}{{\rm H}^+}\right)} &=& \log {\left(\frac{[{\rm O}\,\scriptsize{II}]}{{\rm H}\beta }\right)} + 5.961 + \frac{1.676}{t_2}- 0.4\log {t_2}\nonumber\\ && - 0.034t_2+\log {(1+1.35x)} \end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray} 12+\log {\left(\frac{{\rm O}^{++}}{{\rm H}^+}\right)} &=& \log {\left(\frac{[{\rm O}\,\scriptsize{III}]}{{\rm H}\beta }\right)} + 6.200+ \frac{1.251}{t_3}\nonumber\\ &&- 0.55\log {t_3} - 0.014t_3. \qquad \end{eqnarray} \tag{ 11 }$$

Here, t₂ refers to the singly ionized oxygen electron temperature, T_e([O ii]). For our metallicity estimation, we adopt a standard two-zone temperature model with t₂ ≡ T_e([O ii])/10⁴ K = −0.577 + t₃(2.065 − 0.498t₃) (Izotov et al. 2006b). In computing O⁺/H⁺, we also correct the [O ii]/Hβ ratio for dust attenuation. We do not correct O⁺⁺/H⁺ since the effects are negligible (e.g., the [O iii]/Hβ ratio changes by less than 0.02 dex for A(Hα) = 1 mag).

Since the most abundant ions of oxygen in H ii regions are O⁺ and O⁺⁺, we can determine the oxygen abundances as

$$\begin{equation} \frac{\rm O}{\rm H} = \left(\frac{\rm O^+}{\rm H^+}\right) + \left(\frac{\rm O^{++}}{\rm H^+}\right). \end{equation} \tag{ 12 }$$

In Table 5, we provide observed and de-reddened flux ratios, estimates of T_e([O iii]), log (O⁺/H⁺), log (O⁺⁺/H⁺), and 12 + log (O/H) for our sample, and 95% confidence uncertainties (i.e., two standard deviations). In addition, we illustrate our PDFs of 12 + log (O/H) in Figure 7. Our three most metal-poor galaxies are MMT 13, Keck 2 and 6 with 12 + log (O/H) = 7.53$^{+0.52}_{-0.33}$, 7.54$^{+0.27}_{-0.22}$, and 7.24$^{+0.45}_{-0.30}$, respectively. For our sample of 19 star-forming galaxies, 4 of them can be classified as an XMPG as their metallicity is below 12 + log (O/H) = 7.65.

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Table 5. Emission-line Ratios, Electron Temperatures, and Gas-Phase Metallicities

ID	$\log {\left(\frac{[{\rm O}\,\scriptsize{III}]}{[{\rm O}\,\scriptsize{III}]\ \lambda 4363}\right)}$		log (Te/K)		$\log {\left(\frac{[{\rm O}\,\scriptsize{II}]}{{\rm H}\beta }\right)}$		$\log {\left(\frac{[{\rm O}\,\scriptsize{III}]}{{\rm H}\beta }\right)}$	$\log {\left(\frac{{\rm O}^+}{{\rm H}^+}\right)}$		$\log {\left(\frac{{\rm O}^{++}}{{\rm H}^+}\right)}$	$12+\log {\left(\frac{{\rm O}}{{\rm H}}\right)}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
MMT 01	1.52$^{+0.24}_{-0.17}$	1.46$^{+0.23}_{-0.21}$	4.32$^{+0.12}_{-0.13}$	4.37$^{+0.16}_{-0.15}$	+0.06$^{+0.09}_{-0.08}$	+0.18$^{+0.20}_{-0.17}$	0.89$^{+0.08}_{-0.07}$	−4.99$^{+0.50}_{-0.34}$	−4.84$^{+0.54}_{-0.39}$	−4.61$^{+0.29}_{-0.30}$	7.60$^{+0.37}_{-0.26}$	7.59$^{+0.40}_{-0.33}$
MMT 02	1.61$^{+0.40}_{-0.24}$	1.55$^{+0.39}_{-0.28}$	4.27$^{+0.16}_{-0.18}$	4.31$^{+0.22}_{-0.21}$	+0.50$^{+0.04}_{-0.04}$	+0.62$^{+0.29}_{-0.17}$	0.64$^{+0.04}_{-0.04}$	−4.54$^{+0.70}_{-0.44}$	−4.43$^{+0.74}_{-0.49}$	−4.74$^{+0.47}_{-0.38}$	7.71$^{+0.60}_{-0.42}$	7.74$^{+0.64}_{-0.43}$
MMT 03	1.17$^{+0.24}_{-0.21}$	1.09$^{+0.29}_{-0.27}$	4.60$^{+0.10}_{-0.22}$	4.65$^{+0.09}_{-0.20}$	+0.56$^{+0.05}_{-0.04}$	+0.74$^{+0.21}_{-0.20}$	0.34$^{+0.05}_{-0.05}$	...a	...a	...a	...a	...a
MMT 04	1.95$^{+0.14}_{-0.12}$	1.95$^{+0.14}_{-0.13}$	4.11$^{+0.05}_{-0.05}$	4.11$^{+0.05}_{-0.05}$	+0.36$^{+0.01}_{-0.01}$	+0.36$^{+0.03}_{-0.01}$	0.77$^{+0.01}_{-0.01}$	−4.37$^{+0.20}_{-0.18}$	−4.37$^{+0.21}_{-0.17}$	−4.12$^{+0.15}_{-0.15}$	8.07$^{+0.17}_{-0.15}$	8.07$^{+0.17}_{-0.16}$
MMT 05	1.66$^{+0.19}_{-0.17}$	1.66$^{+0.19}_{-0.16}$	4.24$^{+0.08}_{-0.12}$	4.24$^{+0.10}_{-0.12}$	−0.27$^{+0.09}_{-0.10}$	−0.27$^{+0.15}_{-0.10}$	0.92$^{+0.03}_{-0.03}$	−5.27$^{+0.36}_{-0.27}$	−5.27$^{+0.38}_{-0.25}$	−4.32$^{+0.22}_{-0.24}$	7.72$^{+0.26}_{-0.20}$	7.72$^{+0.26}_{-0.24}$
MMT 06	1.42$^{+0.41}_{-0.25}$	1.32$^{+0.41}_{-0.25}$	4.32$^{+0.22}_{-0.33}$	4.40$^{+0.19}_{-0.38}$	+0.54$^{+0.06}_{-0.05}$	+0.73$^{+0.07}_{-0.06}$	0.54$^{+0.05}_{-0.05}$	−4.52$^{+0.89}_{-0.46}$	−4.24$^{+1.16}_{-0.51}$	−5.01$^{+0.72}_{-0.27}$	7.65$^{+0.81}_{-0.46}$	7.83$^{+1.11}_{-0.39}$
MMT 07	1.84$^{+0.11}_{-0.08}$	1.78$^{+0.12}_{-0.13}$	4.15$^{+0.04}_{-0.05}$	4.18$^{+0.07}_{-0.06}$	−0.02$^{+0.01}_{-0.02}$	+0.10$^{+0.17}_{-0.13}$	0.87$^{+0.01}_{-0.01}$	−4.87$^{+0.17}_{-0.13}$	−4.81$^{+0.19}_{-0.15}$	−4.23$^{+0.16}_{-0.18}$	7.92$^{+0.13}_{-0.12}$	7.87$^{+0.16}_{-0.15}$
MMT 08	1.37$^{+0.31}_{-0.24}$	1.26$^{+0.41}_{-0.33}$	4.31$^{+0.22}_{-0.35}$	4.40$^{+0.20}_{-0.45}$	+0.40$^{+0.09}_{-0.10}$	+0.61$^{+0.36}_{-0.27}$	0.58$^{+0.10}_{-0.10}$	−4.65$^{+0.79}_{-0.49}$	−4.36$^{+1.08}_{-0.43}$	−4.97$^{+0.61}_{-0.29}$	7.58$^{+0.70}_{-0.46}$	7.74$^{+0.99}_{-0.36}$
MMT 09	1.43$^{+0.29}_{-0.22}$	1.34$^{+0.29}_{-0.26}$	4.32$^{+0.19}_{-0.28}$	4.40$^{+0.20}_{-0.26}$	+0.39$^{+0.10}_{-0.09}$	+0.58$^{+0.13}_{-0.12}$	0.76$^{+0.09}_{-0.09}$	−4.66$^{+0.64}_{-0.51}$	−4.39$^{+0.79}_{-0.47}$	−4.79$^{+0.42}_{-0.33}$	7.65$^{+0.55}_{-0.42}$	7.76$^{+0.72}_{-0.43}$
MMT 10	1.75$^{+0.33}_{-0.21}$	1.72$^{+0.33}_{-0.21}$	4.20$^{+0.10}_{-0.14}$	4.21$^{+0.11}_{-0.15}$	+0.09$^{+0.04}_{-0.04}$	+0.14$^{+0.04}_{-0.06}$	0.82$^{+0.02}_{-0.02}$	−4.85$^{+0.51}_{-0.32}$	−4.82$^{+0.47}_{-0.32}$	−4.35$^{+0.38}_{-0.30}$	7.80$^{+0.41}_{-0.25}$	7.78$^{+0.46}_{-0.33}$
MMT 11	1.85$^{+0.21}_{-0.15}$	1.80$^{+0.21}_{-0.16}$	4.15$^{+0.08}_{-0.08}$	4.17$^{+0.08}_{-0.09}$	+0.29$^{+0.03}_{-0.03}$	+0.39$^{+0.04}_{-0.03}$	0.82$^{+0.02}_{-0.02}$	−4.55$^{+0.29}_{-0.27}$	−4.50$^{+0.31}_{-0.27}$	−4.24$^{+0.27}_{-0.20}$	7.97$^{+0.26}_{-0.21}$	7.95$^{+0.30}_{-0.22}$
MMT 12	1.45$^{+0.42}_{-0.24}$	1.32$^{+0.54}_{-0.44}$	4.29$^{+0.21}_{-0.29}$	4.40$^{+0.24}_{-0.46}$	+0.58$^{+0.14}_{-0.12}$	+0.84$^{+0.60}_{-0.36}$	0.81$^{+0.13}_{-0.12}$	−4.46$^{+0.90}_{-0.46}$	−4.13$^{+1.24}_{-0.42}$	−4.74$^{+0.80}_{-0.42}$	7.80$^{+0.78}_{-0.43}$	7.96$^{+1.14}_{-0.46}$
MMT 13	1.57$^{+0.37}_{-0.20}$	1.52$^{+0.31}_{-0.27}$	4.30$^{+0.15}_{-0.20}$	4.32$^{+0.19}_{-0.23}$	−0.02$^{+0.08}_{-0.08}$	+0.07$^{+0.23}_{-0.16}$	0.78$^{+0.03}_{-0.04}$	−5.06$^{+0.57}_{-0.46}$	−4.98$^{+0.69}_{-0.45}$	−4.64$^{+0.43}_{-0.34}$	7.54$^{+0.52}_{-0.30}$	7.53$^{+0.52}_{-0.33}$
MMT 14	2.22$^{+0.12}_{-0.10}$	2.21$^{+0.15}_{-0.11}$	4.01$^{+0.03}_{-0.04}$	4.01$^{+0.04}_{-0.04}$	+0.25$^{+0.01}_{-0.01}$	+0.27$^{+0.03}_{-0.02}$	0.79$^{+0.01}_{-0.01}$	−4.11$^{+0.20}_{-0.15}$	−4.10$^{+0.17}_{-0.13}$	−3.80$^{+0.16}_{-0.10}$	8.38$^{+0.16}_{-0.12}$	8.37$^{+0.17}_{-0.11}$
Keck 1	1.92$^{+0.08}_{-0.08}$	1.81$^{+0.09}_{-0.09}$	4.12$^{+0.03}_{-0.03}$	4.17$^{+0.04}_{-0.04}$	−0.22$^{+0.03}_{-0.03}$	−0.02$^{+0.06}_{-0.08}$	0.90$^{+0.01}_{-0.01}$	−4.99$^{+0.13}_{-0.12}$	−4.89$^{+0.14}_{-0.13}$	−4.16$^{+0.10}_{-0.09}$	8.01$^{+0.09}_{-0.08}$	7.91$^{+0.12}_{-0.10}$
Keck 2	1.44$^{+0.15}_{-0.13}$	1.44$^{+0.15}_{-0.13}$	4.38$^{+0.09}_{-0.11}$	4.38$^{+0.09}_{-0.11}$	+0.14$^{+0.04}_{-0.04}$	+0.14$^{+0.04}_{-0.04}$	0.84$^{+0.02}_{-0.02}$	−4.86$^{+0.36}_{-0.30}$	−4.86$^{+0.36}_{-0.30}$	−4.68$^{+0.20}_{-0.19}$	7.54$^{+0.27}_{-0.22}$	7.54$^{+0.27}_{-0.22}$
Keck 3	2.30$^{+0.21}_{-0.18}$	2.14$^{+0.22}_{-0.16}$	3.98$^{+0.05}_{-0.06}$	4.03$^{+0.06}_{-0.08}$	+0.35$^{+0.01}_{-0.01}$	+0.66$^{+0.04}_{-0.04}$	0.68$^{+0.01}_{-0.01}$	−3.90$^{+0.33}_{-0.23}$	−3.82$^{+0.28}_{-0.23}$	−4.00$^{+0.26}_{-0.18}$	8.44$^{+0.29}_{-0.22}$	8.40$^{+0.31}_{-0.22}$
Keck 4	2.02$^{+0.29}_{-0.23}$	2.02$^{+0.29}_{-0.23}$	4.08$^{+0.09}_{-0.11}$	4.08$^{+0.09}_{-0.11}$	+0.27$^{+0.02}_{-0.02}$	+0.27$^{+0.02}_{-0.02}$	0.68$^{+0.01}_{-0.01}$	−4.37$^{+0.46}_{-0.34}$	−4.37$^{+0.46}_{-0.34}$	−4.13$^{+0.36}_{-0.26}$	8.07$^{+0.41}_{-0.29}$	8.07$^{+0.41}_{-0.29}$
Keck 5	1.16$^{+0.35}_{-0.24}$	1.10$^{+0.37}_{-0.25}$	4.36$^{+0.16}_{-0.77}$	4.40$^{+0.14}_{-0.76}$	+0.24$^{+0.05}_{-0.05}$	+0.36$^{+0.22}_{-0.16}$	0.88$^{+0.03}_{-0.04}$	−4.79$^{+1.04}_{-0.28}$	−4.61$^{+1.10}_{-0.33}$	−4.67$^{+0.60}_{-0.15}$	7.61$^{+0.86}_{-0.26}$	7.66$^{+0.90}_{-0.19}$
Keck 6	1.41$^{+0.24}_{-0.18}$	1.35$^{+0.32}_{-0.23}$	4.35$^{+0.16}_{-0.24}$	4.40$^{+0.17}_{-0.27}$	−1.14$^{+0.51}_{-0.83}$b	−1.02$^{+0.59}_{-0.94}$b	0.77$^{+0.03}_{-0.03}$	−6.18$^{+0.99}_{-1.02}$b	−5.99$^{+1.06}_{-1.03}$b	−4.78$^{+0.39}_{-0.29}$	7.32$^{+0.47}_{-0.25}$b	7.24$^{+0.45}_{-0.30}$b

Notes. Columns 3, 5, 7, 10, and 13 include dust attenuation corrections (see Section 4.1). Errors are reported at the 95% C.L. ^aThis source is likely a LINER, so metallicity determinations are not trustworthy (see Section 3.1). ^bThe 1σ upper limit of the [O ii] flux is adopted.

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In addition to gas-phase metallicity determinations, our extensive data allow us to determine dust-corrected SFRs using the hydrogen recombination lines, which are sensitive to the shortest timescale of star formation, ≲10 Myr (i.e., an instantaneous SFR estimate).

Assuming a Chabrier (2003, hereafter Chabrier) initial mass function (IMF) with minimum and maximum masses of 0.1 and 100 M_☉, and solar metallicity (Kennicutt 1998a),¹⁹ the SFR can be determined from the dust-corrected Hα luminosity as

$$\begin{equation} {\rm SFR}(M_{\odot }\, {\rm yr}^{-1}) = 4.4\times 10^{-42} L({\rm erg\,s}^{-1}). \end{equation} \tag{ 13 }$$

Similarly, SFRs can be determined from Hβ by first correcting for dust reddening (A(Hβ) = 4.60 E(B − V)), and then adopting the intrinsic Case B flux ratio, (Hα/Hβ)₀ = 2.86.

Our SFR estimates are summarized in Table 6 and illustrated in Figure 8. We find that our galaxies have dust-corrected SFRs of 0.04–64 M_☉ yr⁻¹ with an average (median) of 8.1 (2.3) M_☉ yr⁻¹.

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Table 6. Luminosities, Stellar Properties, and Star Formation Rates

ID	MB	$\log {\left[\frac{{\rm SFR}({\rm H}\alpha)}{M_{\odot }/{\rm yr}}\right]}$		$\log {\left[\frac{{\rm SFR}({\rm H}\beta)}{M_{\odot }/{\rm yr}}\right]}$		log (M⋆/M☉)a		log (tage/yr)a		AVa
		Obs.	De-red.	Obs.	De-red.	0.2 Z☉	Z☉	0.2 Z☉	Z☉	0.2 Z☉	Z☉
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
MMT 01	−18.67	...	...	+0.32	+0.76$^{+0.38}_{-0.38}$	7.99$^{+0.08}_{-0.06}$	8.23$^{+0.08}_{-0.33}$	7.40$^{+0.17}_{-0.29}$	8.10$^{+0.24}_{-0.98}$	0.6$^{+0.1}_{-0.1}$	0.3$^{+0.5}_{-0.2}$
MMT 02	−19.28	...	...	−0.29	+0.17$^{+0.37}_{-0.41}$	9.00$^{+0.07}_{-0.20}$	9.23$^{+0.01}_{-0.09}$	8.60$^{+0.22}_{-0.93}$	9.00$^{+0.12}_{-0.29}$	0.9$^{+0.3}_{-0.1}$	0.7$^{+0.2}_{-0.1}$
MMT 03b	−20.15	+0.35	+0.81$^{+0.35}_{-0.32}$	...	...	9.40$^{+0.11}_{-0.17}$	9.59$^{+0.09}_{-0.04}$	8.50$^{+0.30}_{-0.80}$	8.90$^{+0.24}_{-0.20}$	1.1$^{+0.2}_{-0.2}$	0.9$^{+0.1}_{-0.1}$
MMT 04	−19.07	+0.32	+0.32$^{+0.06}_{-0.06}$	...	...	8.44$^{+0.02}_{-0.05}$	8.60$^{+0.08}_{-0.11}$	7.50$^{+0.35}_{-0.10}$	8.20$^{+0.32}_{-0.50}$	0.7$^{+0.2}_{-0.3}$	0.6$^{+0.1}_{-0.3}$
MMT 05	...	...	...	−0.34	−0.34$^{+0.39}_{-0.38}$	...	...	...	...	...	...
MMT 06	−18.83	−0.15	+0.37$^{+0.05}_{-0.05}$	...	...	8.74$^{+0.12}_{-0.16}$	9.01$^{+0.02}_{-0.09}$	8.40$^{+0.40}_{-0.71}$	9.00$^{+0.12}_{-0.24}$	0.9$^{+0.2}_{-0.2}$	0.6$^{+0.1}_{-0.1}$
MMT 07	−17.61	−0.00c	+0.32$^{+0.27}_{-0.27}$c	...	...	7.66$^{+0.00}_{-0.00}$	7.62$^{+0.00}_{-0.00}$	7.40$^{+0.00}_{-0.00}$	7.40$^{+0.00}_{-0.00}$	0.5$^{+0.0}_{-0.0}$	0.4$^{+0.0}_{-0.0}$
MMT 08	−20.13	...	...	+0.38	+1.15$^{+0.79}_{-0.84}$	9.27$^{+0.06}_{-0.42}$	9.35$^{+0.11}_{-0.00}$	8.20$^{+0.29}_{-1.20}$	8.30$^{+0.42}_{-0.14}$	1.2$^{+0.4}_{-0.4}$	0.8$^{+0.3}_{-0.0}$
MMT 09	−19.50	+0.06	+0.56$^{+0.12}_{-0.13}$	...	...	8.93$^{+0.08}_{-0.14}$	9.14$^{+0.09}_{-0.02}$	8.50$^{+0.34}_{-0.80}$	8.90$^{+0.29}_{-0.12}$	0.7$^{+0.1}_{-0.2}$	0.5$^{+0.1}_{-0.2}$
MMT 10	−14.57	−1.52	−1.37$^{+0.02}_{-0.03}$	...	...	6.72$^{+0.09}_{-0.03}$	7.01$^{+0.33}_{-0.04}$	7.10$^{+0.31}_{-0.10}$	7.80$^{+1.28}_{-0.04}$	1.6$^{+0.1}_{-0.2}$	0.7$^{+0.2}_{-0.3}$
MMT 11	−17.28	−0.52	−0.26$^{+0.04}_{-0.03}$	...	...	7.86$^{+0.09}_{-0.11}$	8.09$^{+0.18}_{-0.08}$	7.80$^{+0.39}_{-0.52}$	8.50$^{+0.54}_{-0.44}$	0.9$^{+0.3}_{-0.4}$	0.6$^{+0.2}_{-0.3}$
MMT 12	−19.92	...	...	+0.14	+1.08$^{+1.33}_{-0.84}$	8.94$^{+0.08}_{-0.09}$	9.11$^{+0.09}_{-0.09}$	8.10$^{+0.42}_{-0.44}$	8.60$^{+0.22}_{-0.39}$	0.6$^{+0.3}_{-0.4}$	0.5$^{+0.1}_{-0.2}$
MMT 13	−17.52	−0.11c	+0.12$^{+0.35}_{-0.31}$c	...	...	7.39$^{+0.01}_{-0.09}$	7.28$^{+0.32}_{-0.09}$	7.30$^{+0.10}_{-0.10}$	7.10$^{+0.96}_{-0.10}$	0.3$^{+0.1}_{-0.0}$	0.5$^{+0.1}_{-0.5}$
MMT 14	−20.25	+1.26c	+1.30$^{+0.04}_{-0.04}$c	...	...	8.65$^{+0.04}_{-0.06}$	8.49$^{+0.01}_{-0.03}$	7.30$^{+0.12}_{-0.08}$	7.10$^{+0.05}_{-0.10}$	0.6$^{+0.0}_{-0.1}$	0.7$^{+0.1}_{-0.1}$
Keck 1	−18.08	...	...	+0.52	+1.28$^{+0.14}_{-0.13}$	7.57$^{+0.00}_{-0.11}$	7.39$^{+0.00}_{-0.07}$	7.30$^{+0.07}_{-0.08}$	7.00$^{+0.04}_{-0.00}$	0.0$^{+0.1}_{-0.0}$	0.2$^{+0.0}_{-0.1}$
Keck 2	−18.38	...	...	−0.29	−0.29	7.95$^{+0.18}_{-0.19}$	8.29$^{+0.05}_{-0.14}$	7.30$^{+0.67}_{-0.30}$	8.30$^{+0.21}_{-0.60}$	0.9$^{+0.1}_{-0.3}$	0.4$^{+0.2}_{-0.4}$
Keck 3	−21.12	...	...	+0.67	+1.81$^{+0.08}_{-0.07}$	9.42$^{+0.03}_{-0.06}$	9.46$^{+0.01}_{-0.05}$	7.50$^{+0.41}_{-0.17}$	7.70$^{+0.12}_{-0.06}$	1.0$^{+0.3}_{-0.8}$	0.6$^{+0.0}_{-0.3}$
Keck 4	−19.45	...	...	+0.55	+0.55$^{+0.12}_{-0.12}$	8.60$^{+0.04}_{-0.15}$	8.47$^{+0.05}_{-0.09}$	7.30$^{+0.28}_{-0.23}$	7.10$^{+0.21}_{-0.10}$	1.0$^{+0.1}_{-0.1}$	1.2$^{+0.1}_{-0.1}$
Keck 5	−18.05	...	...	−0.35	+0.09$^{+0.38}_{-0.38}$	8.23$^{+0.18}_{-0.14}$	8.47$^{+0.18}_{-0.12}$	8.70$^{+0.44}_{-0.64}$	9.10$^{+0.20}_{-0.38}$	0.2$^{+0.4}_{-0.2}$	0.0$^{+0.2}_{-0.0}$
Keck 6	−17.16	...	...	−0.42	+0.02$^{+0.38}_{-0.38}$	7.52$^{+0.11}_{-0.15}$	7.45$^{+0.06}_{-0.07}$	7.30$^{+0.18}_{-0.30}$	7.00$^{+0.10}_{-0.00}$	1.1$^{+0.2}_{-0.2}$	1.3$^{+0.1}_{-0.1}$

Notes. All values assume a Chabrier IMF, and where applicable, dust attenuation follows C00 formalism. Sixty eight percent confidence measurement uncertainties are reported. ^aOne-fifth solar metallicity results are given Columns 7, 9, and 11 while those obtained with solar metallicity models are provided in Columns 8, 10, and 12. ^bThis source is likely a LINER, so SFR estimates are not trustworthy. ^cSince the Hα line falls at the edges of the filters, these Hα SFRs are affected by accurate tracing of the NB filter profiles.

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One significant advantage of studying low-mass galaxies in the SDF is the ultra-deep imaging in 24 bands from the UV to the IR, which allows us to characterize their stellar properties. The SDF is imaged with: (1) Galaxy Evolution Explorer (GALEX; Martin et al. 2005) in both the FUV and NUV bands²⁰; (2) KPNO's Mayall telescope using MOSAIC in U; (3) Subaru telescope with Suprime-Cam in 14 bands (BVR_Ci'z'z_bz_r, and the five NB and two IA filters as mentioned previously); (4) KPNO's Mayall telescope using NEWFIRM (Probst et al. 2008) in J and H, (5) UKIRT using WFCAM in K, and (6) Spitzer Space Telescope in the four IRAC bands (3.6 μm, 4.5 μm, 5.8 μm, and 8.0 μm). As discussed in Ly et al. (2011b), a more complete photometric catalog from SExtractor was constructed from an ultra-deep mosaic that consisted of stacked optical and near-IR images with a normalization that takes into account the rms (i.e., χ² stacking).

Upon cross-referencing our 20 galaxies with the complete photometric sample, all but one of them have direct matches. The missing source (MMT 05) was confused with a nearby bright extended galaxy. We exclude MMT 05 in our stellar population analyses. For the remaining 19 galaxies, aperture photometry measurements in 15 bands from the FUV to K are used to construct their complete broad-band SEDs. There are two modifications that we make to these measurements.

First, since all our galaxies are virtually point sources for GALEX, we obtain more accurate photometry in the FUV and NUV bands by PSF-fitting with daophot (Stetson 1987). Our examination of the residuals for each source suggests that the PSF-fitting is extremely successful, and that these galaxies are not affected by contamination of nearby sources. Among the Keck sample, we note that only Keck 2 is detected in the FUV. The lack of FUV detections is un-surprising, since the Lyman continuum break occurs redward of the filter for the remaining five Keck sources. Also, Keck 6 is not detected in the NUV because of its intrinsic faintness. Because the MMT [O iii] λ4363 galaxies are brighter with z ≲ 0.65, they are all detected in the NUV and FUV bands, allowing for robust UV SFR determinations.

Second, since our galaxies all have very high emission-line EWs, we correct the broad-band photometry for the contribution from nebular emission lines, using emission-line measurements from our spectroscopy and NB imaging. Here we generate a spectrum for each galaxy with zero continuum and emission lines located at the redshifted wavelengths for [O ii], [Ne iii], Hβ, [O iii], Hα, and higher order Balmer lines. These spectra are then convolved with the filter bandpasses to determine excess fluxes, and then are removed from the broad-band photometry. The correction for emission lines to SEDs has been recently explored in other higher redshift studies where high-sSFR galaxies are more prominent at z ≳ 1 (Atek et al. 2011; Pirzkal et al. 2013). For two galaxies (MMT 10 and MMT 11), the redshifts are low enough to have spectroscopic detections of Hα. For a subset of MMT galaxies (03, 04, 06, 07, 09, 13, and 14), we use the NB921 or NB973 excess fluxes for Hα flux estimates. However, for galaxies at z ⩾ 0.5 and 0.43 ≲ z ≲ 0.47, Hα is redshifted into the near-IR or not available from optical spectroscopy. To correct Hα in these galaxies (Keck 1–6, MMT 1, 2, 8, and 12), we use spectroscopic information for Hβ, but with the assumption that Hα is three times stronger. Of course, higher dust reddening will yield stronger Hα corrections, so we are adopting a minimum correction of A(Hα) = 0.14 mag.

Both our observed SEDs and those corrected for nebular emission lines are tabulated in Table 7, and representative examples are shown in Figure 9. The black circles show the original broad-band photometry, while the blue circles show the corrected continuum fluxes after removal of emission lines. These three examples illustrate how the SEDs change when the emission-line corrections are small, average, and among the largest.

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Both the original and corrected SEDs were fitted with stellar population synthesis models (Bruzual & Charlot 2003) with the Fitting and Assessment of Synthetic Templates (Kriek et al. 2009) code. We use exponentially declining star formation histories (SFHs; i.e., τ models) similar to previous fitting by us and many other groups (Ly et al. 2011b). We have chosen this SFH for its simplicity, since broad-band data are generally unable to distinguish against more complicated SFHs (e.g., a constant SFR with a recent burst, which may be more representable for our galaxies). As we later find, these fits adopting an exponentially declining SFH are consistent with the data with nearly unity $\chi ^2_{\nu }$ values. Also, the primary purpose of our SED modeling is to obtain stellar masses of our galaxies. This is best traced from the rest-frame optical light from the older stellar population. Thus the inclusion of a recent burst does not significantly alter stellar mass estimates.

In these models, we continue to adopt C00 reddening, and inter-galactic medium attenuation following Madau (1995). The only differences are that we adopt a Chabrier IMF, allow for an extremely short burst model, τ = 10⁷ yr, and use stellar atmospheres with one-fifth (Z = 0.004) solar abundances. The latter is motivated by the fact that our galaxies are extremely metal-poor. In addition we considered solar abundance (Z = 0.02) for completeness. We find that for the majority of our galaxies, the Z = 0.004 models yield similar results to Z = 0.02 models. For consistency with our metallicity determinations, we adopt the SED fitting results with Z = 0.004 models.

We find that with the emission-line corrections, the SED fits are improved with lower χ² values by a factor 1.1–10.4 in the Z = 0.004 models with an average (median) improvement of 3.3 (2.1). In general, the results of fitting the SEDs with emission-line corrections yielded lower stellar masses by 0.1 dex and younger ages by 0.1 dex on average. However, these differences vary from one source to another. In particular, our analyses also reveal a moderate correlation between [O iii] EW and the difference in stellar mass determinations, which others have reported (Atek et al. 2011).

Our SED-fitting results are summarized in Table 6. We find that these galaxies typically are low-mass systems (median of 3 × 10⁸ M_☉, average of 2 × 10⁸ M_☉). However, there is dispersion in the mass distribution (extending from 5 × 10⁶ to 3 × 10⁹ M_☉). The estimated light-weighted stellar ages of log (t_age/yr) = 7.1–8.7 dex (average: 7.75 dex) suggest that these galaxies have undergone most of their star formation in the recent past.

We compare the de-reddened SFRs estimated from SED fitting against the Balmer-derived de-reddened SFRs and find good agreement, albeit with large uncertainties. We also compare the dust reddening determinations from SED fitting and Balmer decrements and find a weak correlation. With large uncertainties in determining reddening with both methods, it is not possible for us to investigate any difference between nebular and stellar reddening. The weak correlation is consistent with E(B − V)_gas ≈ 1.5E(B − V)_star. This result is similar to what we found for a larger sample of ELGs in Ly et al. (2012a).

Finally, we combine our dust-corrected SFRs (Section 4.3) and stellar mass determinations to illustrate our galaxies on the SFR–M_⋆ plane in Figure 8. Relative to their stellar mass, we find that our ELGs are all undergoing strong star formation. In particular, the sSFRs are between 10⁻⁹ yr⁻¹ and 7 × 10⁻⁷ yr⁻¹ with an average of 10⁻⁸ yr⁻¹. This is 2.0–3.0 dex higher than the so called "main sequence" of star formation for z ∼ 0 SDSS galaxies (Mannucci et al. 2010) and low-luminosity local galaxies (Berg et al. 2012). Extrapolating the main sequence of Noeske et al. (2007) toward lower stellar mass, we find that the sSFR of our ELGs are ≈0.5–1.0 dex higher than "typical" galaxies at z ∼ 0.45–0.85, but they are consistent with Noeske et al.'s (2007) sample at the 1σ level. We emphasize that the inverse of the sSFRs, is consistent with the stellar ages derived from SED fitting.

With the strong nebular emission lines seen in our galaxies, the nebular continuum from free–free, free–bound, and two-photon emissions can be important (see, e.g., Izotov et al. 2011). To estimate the contribution toward the total light, at rest-frame optical wavelengths, we generate spectral synthesis models from Starburst99. In our models we assume a constant SFH, a Kroupa (2001) IMF,²¹ Geneva stellar evolutionary models, and Z/Z_☉ = 0.05. For EW₀(Hβ) = 45 Å (the median of our sample), we estimate that the nebular continuum is responsible for ≲10% of the total optical/IR light, and thus the stellar masses (sSFRs) that we have reported are ≲0.05 dex overestimated (underestimated). We note that this correction can be as large as 20%–50% (0.1–0.3 dex) in galaxies (Keck 1, MMT 07) with EW₀(Hβ) of ≈250–400 Å. However, these corrections for only two galaxies do not significantly alter our MZR.

Utilizing our deep NB/IA images, we constructed postage stamps that contain only the emission-line excess flux, by differencing the NB/IA images with adjacent broad-band images (as previously discussed in Section 2.1). For proper removal of the continuum, we normalize the images by their respective zeropoints. We find that the majority (14 of 20) of our sample has between 1 and 4 NB/IA excess emitters within a projected radius of ≈100 kpc. The closest separation is 12 kpc with an average projected distance of 48 kpc.

To ensure that these nearby NB/IA excess sources are real, we conducted two checks. First, we examine if any of these nearby galaxies are also classified as an NB/IA excess emitter in our source catalogs. We find that more than half of them (16 of 34) are NB/IA excess emitters. Upon further inspection, we find that those that are missed did not satisfy our NB/IA excess selections because they have low emission-line EW or are faint, but many could also lie at the same redshift as our [O iii] λ4363 galaxies. Second, some of our galaxies are identified as an excess emitter in two or more filters (e.g., NB704 and NB921). This is due to multiple emission lines falling in these filters. We find that in these four galaxies, six of the nearby excess emitters are also detected in two or three filters. This result strongly suggests that these nearby NB/IA excess emitters surrounding our [O iii] λ4363-selected galaxies are physically real, and at a similar redshift.

While our sample size is small, the presence of nearby (≲100 kpc) companions in 70% of our galaxies suggests that this is unlikely to be a coincidence. To confirm this, we examine how frequent nearby emission-line companions are using our sample of 401 z = 0.4 Hα emitters, which has been previously discussed in Ly et al. (2012a). We determine the projected distance to the nearest Hα emitter, and find that the average of this distance is ≈350 kpc (median is ≈280 kpc). Furthermore we find only 49 of 401 (12%) Hα emitters have a companion that is within 100 kpc. This low percentage suggests that Hα emitters, while clustered, are infrequently found with a nearby satellite. An identical analysis with 715 z = 0.84 [O iii] emitters yielded similar numbers.

Three plausible explanations for the significant excess of nearby companions are that galaxy–galaxy interactions can: (1) stimulate a "starburst," (2) tidally strip out metal-rich gas into the CGM, or (3) cause accretion of metal-poor gas from the outskirts of the galaxy.

In the first case, the intense star formation can trigger strong winds that can entrain metal-rich gas into the CGM. If so, this would explain why these galaxies are identified to be extremely metal-deficient. Our measurements of SFR and masses (see Figure 8) suggest that the current SFR could form most of the stellar population in ∼100 Myr (average), supporting this hypothesis. Since our [O iii] λ4363 sample is inhomogenous (i.e., selection in different NB/IA filters), a more detailed study is warranted from the complete NB/IA sample. Forthcoming work will examine further these nearby companions and any correlation seen with the properties of the central galaxies.

In the case of "tidal disruption," one would expect to see evidence of gas stripping, in the form of tidal tails and asymmetric morphologies. An examination of our NB/IA-excess images reveal no tidal tails or any "bridge" between our targeted sources and a nearby companion. We do notice that the light distribution is asymmetric in half of our galaxies; however, the seeing-limited resolution of our data makes it difficult to interpret such results. Higher resolution imaging with Hubble Space Telescope (HST) is needed to quantitatively measure the morphological properties of these galaxies and detect any tidal tail features.

One of our galaxies (Keck 05) fortuitously has HST/WFC3 broad-band near-IR imaging (Jiang et al. 2013). Keck 05 is in fact two galaxies that are separated along the NE–SW direction by 09 (projected distance of 6.9 kpc at z = 0.84) with the nebular emission coming from the SW component. Our examination of the HST imaging reveals that the NE galaxy is diffuse along the P.A. toward the SW component. More careful analysis is needed to understand Keck 05 and its nearby companion, and as we emphasized, HST imaging for a larger fraction of our [O iii]-A sample is required to examine the possibility of tidal disruption for the case of low metallicities in our galaxies. We note however that this scenario is unlikely to result in low metallicity in the centers of these galaxies, as these dynamical effects are expected to have a stronger impact on the gas that is external to the galaxy, which is relatively more metal-poor, than the metal-rich gas that is located closer to the center.

Another contrasting possibility is that the interaction with the nearby galaxy induces gravitational torques that drive metal-deficient gas from the outskirts of galaxies into the centers (e.g., Mihos & Hernquist 1996). Support for this idea has been seen in local interacting galaxies where the radial metallicity gradient is unusually flat (Kewley et al. 2006; Rupke et al. 2010). This would explain (1) the deficiency of metals, (2) the excess of nearby galaxies, and (3) the high SFRs and SFR surface densities (see Section 4.6) in our galaxies.

Our data do not decisively distinguish between these models without dynamical information. In particular, IFU spectroscopy of the ionized gas would reveal the presence of inflowing or outflowing gas.

In addition to subtracting of the continuum to identify nearby companions, the NB/IA excess flux images allow us to determine their SFR surface density, Σ_SFR. These images are first converted to an emission-line luminosity, then integrated across the galaxy to determine a total Hα or Hβ observed luminosity, and finally corrected for dust attenuation (Section 4.1). Six of our galaxies (MMT 04, 06, 07, 09–11) have NB imaging or spectroscopy that observes Hα. In addition, three other galaxies (MMT 13, 14, and Keck 4) have Hβ measurements. The remaining galaxies (MMT 01, 02, 08, 12, Keck 1, 2, and 5) are [O iii]-selected. To obtain an estimate of the Hβ luminosity for the latter galaxies, we use the integrated [O iii]/Hβ ratio from our spectroscopy (see Table 3). Finally to obtain the Hα luminosities, we scale the de-reddened Hβ measurements by a factor of 2.86. We integrate the source flux over a region that is π(FWHM/2)², which is converted to physical distance using the angular diameter distance (1'' = 5.4 kpc at z = 0.4 and 7.8 kpc at z = 0.85). This measured area is larger due to the degradation from seeing. To correct for it, we determine the effective FWHM in quadrature: ${\rm FWHM}_{\rm eff}^2 = {\rm FWHM}^2-{\rm FWHM}_{\rm seeing}^2$. Due to the slightly extended nature of our galaxies, this correction to the area is typically a factor of two or less. We find a wide dispersion in the Σ_SFR between 0.005 and 5 M_☉ yr⁻¹ kpc⁻² with an average (median) of 0.5 (0.04) M_☉ yr⁻¹ kpc⁻². Compared to local galaxies (Kennicutt 1998b), our Σ_SFR's are on average an order of magnitude higher than normal spirals, and at the low end of IR-selected circumnuclear starbursts.

By construction, the 20 galaxies presented in this paper were selected to be extreme. First, our SDF follow-up spectroscopy concentrated on ELGs identified from our NB/IA imaging. Then in this paper we have selected only a few percent of these spectra, where the lines were strong enough to include detectable [O iii] λ4363. Half of our galaxies were solely targeted because of the strength of their [O iii] λλ4959, 5007 doublet (see Table 1). This favors emission from more highly ionized gas. Although the [O iii] λ4363 line is occasionally seen in LINERs, we only found one of them based on various emission-line ratios (see Section 3.1). The remaining 19 are all extreme starburst galaxies, which tend to be overlooked by traditional broad-band photometric selections. Aside from deep NB imaging, the only other windows on galaxy evolution which provides access to many extreme SFR galaxies are extensive spectroscopy with as little pre-selection as possible, preferably none (such as slitless spectroscopy; Atek et al. 2010) or selecting galaxies with unusual colors (Cardamone et al. 2009; van der Wel et al. 2011).

Thus these 20 galaxies lie far above the established correlation of SFR with stellar mass. In other words, their sSFR is between two and three orders of magnitude larger than the average observed in the local universe, or even than what is "normal" for galaxies at z = 0.4–0.9. These [O iii] λ4363-detected galaxies are extremely rare in the local universe, making up only 0.05% of those with SDSS spectra.

Since sSFR is the inverse of the star production time-scale, continuing at their high observed SFRs, our extreme galaxies would produce their entire stellar contents in only 1%–10% of the time it takes in normal galaxies. This strongly suggests that we are observing them in a highly atypical evolutionary phase, which could last 100 Myr or even less. If this is a phase that most galaxies pass through occasionally, then the "duty cycle" of this extreme burst of star formation would be only ∼1%–10%.

The NB technique has two observable limitations: (1) a minimum EW excess at the bright end (≲24 mag), and (2) an emission-line flux limit at the faint end. In the former case, our selections are limited to galaxies with rest-frame EWs of EW₀([O iii]) = 11–17 Å (z = 0.4–0.85) and EW₀(Hα) ≈ 20 Å (z = 0.24–0.40). With a 2.5σ emission-line flux limit of approximately 4.5 × 10⁻¹⁸ erg s⁻¹ cm⁻², the luminosity limit corresponds to 3 × 10³⁹ and 2 × 10⁴⁰ erg s⁻¹ at z = 0.40 and z = 0.84, respectively. These EW and luminosity limits are illustrated in Figure 3, and are compared to the ELGs in the SDSS. It can be seen that our NB imaging cannot detect the [O iii] emission from many SDSS galaxies, simply because of the lower EWs. For example, only 16% of the full SDSS galaxy sample would be identified as NB704 excess emitters at z = 0.40. However, this fraction increases to 90% for ELGs with moderate line strengths, EW₀([O iii]) ≳ 11 Å. For Hα, the majority (62%) of the SDSS would be detected at z = 0.4 with our NB921 imaging, and almost all (96%) of galaxies with EW₀(Hα) ≳ 22 Å. Thus, our NB survey is biased against weak emission lines. We note that the lower success of detecting [O iii] in SDSS ELGs at z = 0.4 compared to Hα is due to the higher metallicities in local galaxies. In metal-rich systems (i.e., lower T_e), O⁺ is a more effective coolant for the interstellar medium (ISM) than O⁺⁺, resulting in flux ratios of [O ii]/Hα ≈0.5 and [O iii]/Hα ≈0.1. Thus, our [O iii] NB selection is less sensitive to metal-rich galaxies.

In addition to our general NB selection, the primary restriction for our sample is an [O iii] λ4363 detection. First, this limits the sample toward high-EW galaxies, which generally have high sSFRs. Second, the detection alone will further bias our sample against moderately metal-poor galaxies (12 + log (O/H) ≈8.0). For example, in our spectroscopic survey, we have identified an additional ∼20 galaxies that possess strong [O iii] emission (EW₀ ≳ 50 Å). These galaxies, however, have very weak detections of [O iii] λ4363 (1–3σ).

While an [O iii] λ4363 detection restricts our ELG sample, we find that our 20 galaxies have many similarities to our more general ELG sample at z ≈ 0.4–1. For example, the median (average) stellar mass of our spectroscopic sample of over 200 galaxies is log (M_⋆/M_☉) = 8.9 (8.7). These values are moderately higher (0.4 dex) than our [O iii]-A sample. Also, as illustrated in Figure 4, our [O iii]-A sample shows similar [O iii]/Hβ ratios, which is a measure of the ionization. This demonstrates that ELGs selected from NB surveys at z = 0.4–1 all have higher ionization by ≈0.2–0.5 dex compared to local SDSS galaxies with similar stellar masses.

The SDSS has found rare populations of strongly star-forming galaxies called "green peas" (Cardamone et al. 2009) and "luminous compact galaxies" (LCGs; Izotov et al. 2011). The former population was identified by unusual optical colors due to significant contribution of very strong nebular emission lines ([O iii] and Hβ) in the r-band (hence they appear "green"). Ancillary data indicated that these luminous (r ≲ 20.5) galaxies are at z ≈ 0.1–0.35, have stellar masses of ∼10^8.5–10¹⁰ M_☉ and SFRs of ∼10 M_☉ yr⁻¹, are relatively metal-rich 12 + log (O/H) ∼ 8.7,²² and are very rare (2 deg⁻²). Because of the unusual color selection, selection effects are significant for this sample.

Analogously, LCGs were identified from the SDSS DR7 spectroscopic sample to have EW(Hβ) ≳ 50 Å, at least 2σ detections of [O iii] λ4363, and appear compact or unresolved in the SDSS images. These galaxies have redshifts of z = 0.02–0.63 (most of them are at z ≲ 0.35), median stellar masses of ∼10⁹ M_☉, median SFRs of ∼4 M_☉ yr⁻¹, and oxygen abundance of 12 + log (O/H) ≈ 8.2. Since it is believed that green peas are a subset of LCGs (Izotov et al. 2011), we will only compare our sample against the LCG population.

LCGs show many similarities and differences to our galaxies with [O iii] λ4363 detections. First, both samples occupy a distinct region in BPT and MEx diagnostics diagrams with large [O iii]/Hβ and low [N ii]/Hα (or stellar mass). While LCGs have low stellar masses and high sSFRs, they are on average ∼0.5 dex more massive than our sample and with lower sSFR by ∼0.5 dex. These LCGs can be found with stellar masses above 10¹⁰ M_☉, while our most massive galaxy has M_⋆ ≈3 × 10⁹ M_☉. In addition, these galaxies are relatively metal-rich by ∼0.4–0.5 dex compared to our sample. Also, 90% of our [O iii]-A sample is found above z = 0.4, while the majority of LCGs are identified at z ≲ 0.35. Therefore, while LCGs are low-mass, metal-poor galaxies, our [O iii]-A sample appears to be an extension of LCGs toward lower masses, lower metallicity, and higher redshift. These differences might suggest that metal-poor ELGs identified with deep NB imaging may evolve into LCGs. Finally, in terms of surface density, it is estimated that there are ≈20 LCGs per deg². The SDF has already detected [O iii] λ4363 in 20 galaxies over 0.25 deg², and more of them are expected to be found (see Section 5.6). The higher surface density is because our survey extends toward lower mass galaxies, which are more common, and because higher sSFR are seen for galaxies at higher redshift (see Section 5.6).

While these metal-poor galaxies are rare, there have been numerous efforts to identify them. Here, we compare our sample to previous [O iii] λ4363 studies. Two of the first studies that probed a large number of low-mass galaxies in the local universe were Lee et al. (2004) and Lee et al. (2006). First, Lee et al. (2004) identified and detected [O iii] λ4363 for 24 local galaxies from the KPNO International Spectroscopic Survey. These galaxies, spanning M_B = −15 and −19, were pre-selected to have gas-phase metallicities (determined from strong-line methods) to be below 12 + log (O/H) = 8.2. The sample provided the first measurement of the MZR using the "direct" method. Targeting 25 dwarf irregular galaxies, Lee et al. (2006) extended the MZR toward lower stellar masses. Since then, more extensive spectroscopy has been conducted targeting low-luminosity galaxies within 11 Mpc (Berg et al. 2012), and mining the SDSS (Brown et al. 2008; Izotov et al. 2006b, 2012a).

In addition, a few other studies have succeeded at extending the search toward higher redshift, where the redshift evolution of the MZR implies that more metal-poor galaxies should be found in the early universe. Hoyos et al. (2005) was the first study to detect [O iii] λ4363 in 17 ∼L_⋆ galaxies at z = 0.51–0.86 with gas metallicity ranging from 12 + log (O/H) = 7.8–8.3. These galaxies were selected from the DEEP2 Survey (Davis et al. 2003) and TKRS (Wirth et al. 2004), which are luminosity-limited to I = 24.5 and R = 24.3 mag, respectively. Then Kakazu et al. (2007) conducted follow-up spectroscopy of ultra-strong ELGs selected from NB imaging. While some level of detection for [O iii] λ4363 was available in 17 galaxies, only six had ⩾ 3σ[O iii] λ4363 detection.²³ The rest were too weak, with a median detection of ≈2σ. Among those with robust detections (⩾3σ), their most metal-poor galaxy has 12 + log (O/H) = $7.36^{+0.22}_{-0.18}$ (1σ). They have since extended their [O iii] λ4363 sample to a total of 31 galaxies at z = 0.40–0.85 (Hu et al. 2009). About three-fourths (23/31) of their sample are detected above 3σ with nine galaxies above 5σ. Their most metal-poor galaxies having 12 + log (O/H) = 6.97±0.17 and 7.25 ± 0.03 (1σ).

In addition, Atek et al. (2011) identified a sample of high-EW ELGs at z = 0.35–2.3 from space-based grism spectroscopy. With higher spectral resolution follow-up observations, they detected [O iii] λ4363 to determine a gas-phase metallicity of 12 + log (O/H) = 7.5 ± 0.1 for a galaxy at z = 0.7.

For a complete comparison, we compile available information for these studies. For the Berg et al. (2012) sample, dust-corrected Hα SFRs are determined from the Hα luminosities reported in Kennicutt et al. (2008), adopting the extinction determinations of Lee et al. (2009), and assuming a Chabrier IMF. We also correct their reported stellar masses from a Salpeter to Chabrier IMF. For the Hoyos et al. (2005) sample, we limit their sample to the seven galaxies where the [O ii] line is observed. Stellar masses for their sample were obtained from Bundy et al. (2006), where a simple cross-matching of sources yielded only one match. SFRs reported by Brown et al. (2008) and Lee et al. (2004) are also corrected from a Salpeter to Chabrier IMF. For the samples of Kakazu et al. (2007) and Hu et al. (2009), we are only able to report the redshifts and gas-phase metallicity for the former. In their final sample, only metal abundances and luminosities are immediately available.

Since the rest-frame B-band absolute magnitude, M_B, is commonly reported, we compute it for our galaxies using our emission-line corrected SED. The M_B magnitudes are determined as

$$\begin{equation} M_B = B + 2.5\log {(1+z)} + 5.0\log {(d_L/{\rm 10\,pc})}, \end{equation} \tag{ 14 }$$

where B is the apparent magnitude at 4450 Å determined from interpolating between adjacent broad-band filters. These magnitudes are reported in Table 6.

In Figure 10, we illustrate the redshifts, SFRs, stellar masses, sSFRs, and M_B's for [O iii] λ4363-detected galaxies. Our sample surveys a redshift domain that is similar to the studies of Hoyos et al. (2005) and Hu et al. (2009). In addition, our galaxies span M_B between −17 and −21 (excluding MMT 10, our lowest redshift galaxy), and have SFRs that are similar to local dwarf irregulars and z ∼ 1 L_⋆ galaxies.

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Comparing our metallicities against their masses or luminosities, we find that half of our sample follows the M_B–Z or M_⋆–Z relation of local and higher redshift galaxies. The remaining galaxies are located systematically below these relations by 0.2–0.3 dex. These galaxies have lower significance detections (3.1–3.6σ) of [O iii] λ4363. So while they deviate from these relations, the are consistent within the 95% measurement uncertainties. Deeper follow-up spectroscopy is needed to determine if these galaxies are extremely metal-poor or just moderately metal-poor.

Our three most metal-deficient galaxies are MMT 13 (z = 0.47), Keck 2 (z = 0.62) and Keck 6 (z = 0.82) with 12 + log (O/H) = 7.53$^{+0.52}_{-0.33}$, 7.54$^{+0.27}_{-0.22}$, and 7.24$^{+0.45}_{-0.30}$, respectively. While these galaxies have similar metallicities (within the errors) to the most metal-deficient galaxies in the local universe, I Zw 18 and SBS0335 (see Figure 10), there are some notable differences seen in their emission-line fluxes.

First, I Zw 18 and SBS0335 have [O iii]/Hβ ([O iii]/[O ii]) ratios of 2.2 and 3.2 (9.8 and 15.5), respectively. Keck 6, which has a more robust detection (4.3σ) of [O iii] λ4363, has a higher [O iii]/Hβ ratio by a factor of 1.3–2, but similar to what is seen for green peas and LCGs (see Section 5.3). Second, the [O ii] line is not detected, yielding an observed [O iii]/[O ii] ratio of ≳80. This non-detection is due to the high ionization and low metallicity of the ISM. In these circumstances, the excitation energies shift nearly completely toward O⁺⁺, resulting in extremely low [O ii] emission. For Keck 6, estimates using the strong-line R₂₃ and O₃₂ flux ratios also suggest that the metallicity of this galaxy is very low: 12 + log (O/H) = 7.65, using the Kobulnicky & Kewley (2004) calibration²⁴ with a high ionization parameter, log (q/cm s⁻¹) ≳ 8.8 (log (U) ≳ −1.7).

These galaxies are rare, but other studies have found them. For example, Kakazu et al. (2007) identified a few galaxies where [O ii] is undetectable but very high S/N detections of [O iii] exist. There are also cases where both lines are detected, yielding [O iii]/[O ii] flux ratios of ≈10–60. In addition, rest-frame optical spectroscopy of Lyα emitters at z = 2.2 have measured high [O iii]/[O ii] ratios (Nakajima et al. 2013), which yield high ionization parameter estimates.

Furthermore, several studies have shown that high-z star-forming galaxies are offset from local star-forming galaxies in the BPT diagram with systematically higher [O iii]/Hβ ratios (e.g., Hainline et al. 2009; Rigby et al. 2011). A recent comparison between theoretical models and emission-line measurements of z = 0.5–2.6 galaxies by Kewley et al. (2013) suggests that the ISM conditions at higher redshifts are far more extreme with high ionization and density. These conditions are more analogous to those seen in dense, clumpy H ii regions of local starburst galaxies. As illustrated in Figure 4, our [O iii]-A sample is offset by 0.2–0.5 dex in [O iii]/Hβ from the average of local galaxies with the same stellar mass. In addition we find high electron densities of n_e = 70–600 cm⁻³. These observables suggest that XMPGs at z = 0.4–1 are similar to typical z ≳ 1 galaxies, and can be used as a powerful tool for studying the ISM conditions in the early stages of galaxy formation.

It has been well established that the metal abundance of galaxies correlates with their stellar mass (e.g., Tremonti et al. 2004). The presence of such a correlation and the lack of significant scatter have provided a key constraint in modeling the evolution of galaxies. For example, the shape of the MZR, which shows a turnover in the metallicity at high masses and a steep decline at lower masses, can be explained by a simple model where massive star formation enriches the ISM through stellar feedback. However, such enrichment can drive metals beyond the ISM in low-mass galaxies, and thus lowering their effective metallicity (e.g., Davé et al. 2011).

Studies in the past have been mostly limited to more massive galaxies (≳10⁹ M_☉), and therefore whether the MZR extends toward lower masses or not is unclear with existing limited samples. In Figure 11(a), we illustrate the MZR of AM13, which stacked SDSS spectra to detect [O iii] λ4363 and determine metallicity using the same method for easier comparison. Here, the MZR is fitted with a logarithmic functional form devised by Moustakas et al. (2011):

$$\begin{equation} 12+\log ({\rm O/H})= 12+\log ({\rm O/H})_{\rm asm}-\log {\left[1+\left(\frac{M_{\rm TO}}{M_{\star }}\right)^{\gamma }\right]}, \end{equation} \tag{ 15 }$$

where 12 + log (O/H)_asm is the asymptotic metallicity at high masses, M_TO is the turnover mass, and γ controls the slope of the MZR at low masses.

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We note that while there are other determinations of the MZR using different strong-line diagnostics that do not require spectra stacking, there are nearly 1 dex differences in metallicity determinations using the same dataset (Kewley & Ellison 2008). For this reason, we chose to use measurements obtained with the same method. Since AM13 used a different T_e([O ii])–T_e([O iii]) relation to determine O⁺/H⁺, we adopt the same relation, t₂ = 0.7t₃ + 0.1,²⁵ for direct comparisons. We note that this difference only raises metallicity on average by 0.05 dex, with ≈0.2 dex as the largest correction.

We find that 9 of our 19 galaxies follow the local T_e-based MZR to within ±2σ. However, it appears that our entire sample has systematically lower metallicities at all masses. This may be the result of selection effects, since more metal-rich galaxies are less likely to have [O iii] λ4363 detections.

Recently, some have argued that the MZR is in fact a projection of a more "fundamental" plane between stellar mass, metallicity, and SFR (i.e., M_⋆–Z–SFR relation; Lara-López et al. 2010). One such projection, called the "fundamental metallicity relation" (FMR; Mannucci et al. 2010), suggests that galaxies with higher sSFR have lower metallicities compared to those at similar stellar masses. Efforts to describe the FMR have defined a plane in which a tighter correlation exists, by considering a combination of stellar mass and SFR:

$$\begin{equation} \mu _{\alpha } = \log {\left(\frac{M_{\star }}{M_{\odot }}\right)} - \alpha \log {\left(\frac{{\rm SFR}}{M_{\odot }\,{\rm yr}^{-1}}\right)}, \end{equation} \tag{ 16 }$$

where α is the coefficient that minimizes the scatter against metallicity. We illustrate the AM13's determination (α = 0.66) in Figure 11(b). A comparison against our sample reveals again that roughly half of our galaxies follow the FMR; however, the rest of our metallicities fall below it. Even more interesting, some of our galaxies (i.e., Keck 1, 3, and MMT 14), which followed the MZR are no longer within +2σ of the T_e-based FMR. In these galaxies, the [O iii] λ4363 detections are robust (S/N = 11.1, 4.6, and 7.6, respectively), and their SFRs are high. If anything, we see a positive or flat correlation between metallicity and sSFR (see Figure 10(b)), contrary to what is expected from the FMR. This might suggest that an M_⋆–Z–SFR relation as seen for local galaxies may not hold in low-mass galaxies at z = 0.4–0.9, and that there is a larger scatter compared to z ∼ 0.

With a statistically meaningful sample of [O iii] λ4363 detections, we can infer the space density of XMPGs from the largest emission-line sample at intermediate redshifts. As illustrated in Figure 3, we find that our [O iii] λ4363 sample has rest-frame EWs of EW₀(Hα) ≳ 100 Å and EW₀([O iii]) ≳ 50 Å. Limiting galaxies to these EWs, we find a number density at z ∼ 0.45 of 4.5 × 10⁻³ Mpc⁻³ for Hα and 5.1 × 10⁻³ Mpc⁻³ for [O iii]. Our spectroscopic follow-up sampled a broadly representative range, reaching down to EW₀ = 20 Å, and targeted about ≈25% of the high-EW galaxies. Among these spectra, 16% and 11% of the Hα-selected and [O iii]-selected galaxies yielded [O iii] λ4363 detections, respectively. Extending these statistics to the full high-EW sample, we estimate that the expected number density of galaxies with [O iii] λ4363 detections at z = 0.3–0.65 is 7 × 10⁻⁴ Mpc⁻³ for Hα-selected galaxies and 6 × 10⁻⁴ Mpc⁻³ for [O iii]-selected galaxies. This corresponds to a surface density of one per 13 arcmin² (Hα; z = 0.3–0.5) and one per 8 arcmin² ([O iii]; z = 0.3–0.65). About one-fifth of these galaxies will have 12 + log (O/H) ⩽ 7.65.

The higher rate of XMPGs (≈1%) among star-forming galaxies at high redshift compared to the local universe (recall 1 in 1700 SDSS galaxies are XMPGs) could be a reflection of galaxy evolution. In particular, several lines of evidence have shown that the SFRs and the sSFR's are an order magnitude higher at z ≳ 1 than the local universe (e.g., Noeske et al. 2007; Ly et al. 2011a, 2012b; Lee et al. 2012). Future surveys at z ≳ 1 with JWST and "WFIRST" should find many more XMPGs simply because: (1) the M_⋆–Z relation evolves toward lower metallicity at high redshift (see, e.g., Erb et al. 2006); and (2) the epoch of where the SFR density peaked (Hopkins 2004; L07), and where most of the mass assembly occurred (Dickinson et al. 2003; Rudnick et al. 2003), is at z ∼ 1–3.

Morales-Luis et al. (2011) reported that the number density of XMPGs in the local universe from the SDSS is ≈1.3 × 10⁻⁴ Mpc⁻³, which is similar to what we find in our study. This comparison would suggest that no evolution is seen in the number density of XMPGs. However, we caution against making such a comparison since the local estimate is highly uncertain due to a statistically small sample that suffers from incompleteness and complex selection functions.