Searching for the Lowest-metallicity Galaxies in the Local Universe

To identify candidate low-metallicity BCDs, we conducted a query for objects in SDSS Data Release 12 (DR12) with photometric colors similar to those of currently known low-metallicity systems, including Leo P and I Zwicky 18. This color selection criteria will be biased toward finding BCDs at low redshift, corresponding to the colors of Leo P and I Zwicky 18; our color selection criteria does not account for the redshift evolution of BCD colors, which is the goal of a future work (K. Tirimba et al. 2018, in preparation). We require that the objects lie outside of the galactic plane, i.e., have Galactic latitudes b > +25 deg and b < −25 deg, have r-band magnitudes r ≤ 21.5, and fall within the following color cuts:

$$\begin{eqnarray*}&&\,0.2\leqslant u-g\leqslant 0.6\\ &&-0.2\leqslant g-r\leqslant 0.2\\ &&\,-0.7\leqslant r-i\leqslant -0.1\\ &&-0.4\mbox{--}2\,{z}_{\mathrm{error}}\leqslant i-z\leqslant 0.1.\end{eqnarray*}$$

Here, the magnitudes are given as inverse hyperbolic sine magnitudes ("asinh" magnitudes; Lupton et al. 1999). The 2z_error term ensures a 2σ lower bound on objects with a poorly constrained z-band magnitude. We also require the SDSS g-band fiber magnitude to be less than the z-band fiber magnitude to exclude H ii regions in redder galaxies from the query results. Finally, we require that the objects be extended, i.e., classified as a galaxy in SDSS. This query returned a total of 2505 candidate objects. Our full query is presented in Appendix.

To create a list of candidate objects best fit for observation, we individually examined the SDSS imaging of the 2505 objects from the photometric query. This procedure eliminated objects misclassified as individual galaxies, such as stars or star-forming regions located in the spiral arms of larger galaxies, and predisposes our candidate list toward systems in isolated environments. We also eliminated objects with existing SDSS spectra. The remaining candidate galaxies that appeared to have a bright knot surrounded by a dimmer, more diffuse region were chosen as ideal systems for follow-up spectroscopic observations, with the assumption that active star-forming H ii regions would appear as bright "knots" in SDSS imaging and would be the most likely to yield easily detectable emission lines. The surrounding diffuse region is assumed to be indicative of the remaining stellar population in the system. This selection criteria was not quantified, but is similar to the "single knot" morphological description as presented in Morales-Luis et al. (2011).

Our morphological selection criteria condensed the candidate list down to 236 objects. To date, we have observed 154 of the selected candidate BCDs, with the 154 objects having RAs best fit for our scheduled observing nights. The candidate systems we have targeted so far are shown in SDSS color–color space in Figure 1. A subset of these BCDs in SDSS imaging are shown in Figure 2.

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Spectroscopic observations of 135 candidate BCDs were made using the Kast spectrograph on the Shane 3 m telescope at Lick Observatory over 22 nights during semesters 2015B, 2016A, and 2016B. Eighty-five of the observed candidates yielded emission-line detections, and 78 of the 85 have confident emission-line measurements reported here.

The Kast spectrograph has separate blue and red channels, which our observational setup utilized simultaneously. Observations made prior to 2016 October 6 were obtained using the d55 dichroic, with the Fairchild 2k × 2k CCD detector on the blue side, and the Reticon 400 × 1200 CCD detector on the red side. Thereafter, the d57 dichroic was used, along with a Hamamatsu 1024 × 4096 CCD detector on the red side. The pixel scale on the Reticon is 078 per pixel, and 043 per pixel on the Fairchild and Hamamatsu devices. On the blue side, the 600/4310 grism with a dispersion of 1.02 Å pix⁻¹ was used, while on the red side, the 1200/5000 grating with a dispersion of 0.65 Å pix⁻¹ was used. This instrument setup covers ∼3300–5500 Å and ∼5800–7300 Å, with the instrument at FWHM resolutions of 6.4 Å and 2.7 Å, in the blue and red, respectively. This allows for sufficient coverage and spectral resolution of all emission lines of interest. Specifically, we are able to resolve the [N ii] doublet from Hα. However, we note that the [O ii] doublet is not resolved with this setup.

All targets were observed using a 2'' slit and at the approximate parallactic angle to mitigate the effects of atmospheric diffraction. Total exposure times range from 3 × 1200 s to 3 × 1800 s for our objects. Spectrophotometric standard stars were observed at the beginning and end of each night for flux calibration. Spectra of the Hg-Cd and He arc lamps on the blue side and the Ne arc lamp on the red side were obtained at the beginning of each night for wavelength calibrations. Bias frames and dome flats were also obtained to correct for the detector bias level and pixel-to-pixel variations, respectively. The right ascension and declination measured redshift, estimated distance, g-band magnitude, u − g color, and gas-phase oxygen abundance of a selection of observed and confirmed emission-line systems are reported in Table 1; the full sample of observed systems is available online.

Table 1.  Observational and Measured Properties of our BCD Sample, Observed at Lick and Keck Observatory

Target Name	R.A.	Decl.	Observations	z	Distance	mg	u − g	12 + log(O/H)
	(J2000)	(J2000)			(Mpc)
J0000+3052A	00h00m3145	+30°52'0930	Keck+LRIS	0.0151	67.6	19.84 ± 0.02	0.65	7.72 ± 0.01
J0000+3052B	00h00m3231	+30°52'1662	Keck+LRIS	0.0153	68.5	19.55 ± 0.02	0.43	7.63 ± 0.02
J0003+3339	00h03m5108	+33°39'2963	Shane+Kast	0.0211	94.7	19.57 ± 0.03	0.33	7.91 ± 0.03
J0018+2345	00h18m5932	+23°45'4032	Shane+Kast	0.0154	68.8	19.24 ± 0.02	0.26	7.18 ± 0.03
J0033–0934	00h33m5579	−09°34'3220	Shane+Kast	0.0121	54.2	17.97 ± 0.01	0.55	7.84 ± 0.23
J0035–0448	00h35m3964	−04°48'4093	Shane+Kast	0.0169	75.9	19.58 ± 0.02	0.53	7.64 ± 0.02
J0039+0120	00h39m3030	+01°20'2161	Shane+Kast	0.0147	66.0	19.88 ± 0.03	0.52	7.78 ± 0.03
J0048+3159	00h48m5531	+31°59'0205	Shane+Kast	0.0153	68.5	19.05 ± 0.03	0.31	8.45 ± 0.02
J0105+1243	01h05m2495	+12°43'3871	Shane+Kast	0.0142	63.4	19.77 ± 0.04	0.43	7.64 ± 0.05
J0118+3512	01h18m4000	+35°12'5700	Keck+LRIS	0.0165	73.9	19.23 ± 0.02	0.27	7.58 ± 0.01

Note. Distances reported in this table are luminosity distances, assuming a Planck cosmology (Planck Collaboration et al. 2016). All metallicity estimates for systems observed on Shane+Kast are determined using the R and S calibration methods, with the reported metallicity being the average of the R and S methods. All BCDs observed using Keck+LRIS have direct metallicity calculations, except for J0743+4807, J0812+4836, and J0834+5905. In these cases, we do not significantly detect the [O iii] λ4363 Å line, and adopt an upper limit to the [O iii] λ4363 Å emission-line flux equivalent to three times the error in the measured line flux at that wavelength. This results in a lower limit on their metallicities. The asterisk (*) in the Observations column indicates that observations were made first using Lick+Kast, with follow-up made using Keck+LRIS. For such systems, the derived values reported here are measurements from the Keck+LRIS observations. Values for the full sample of BCDs are available online.

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

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Spectroscopic observations of 29 candidate BCDs were made using the Low Resolution Imaging Spectrometer (LRIS) at the W.M. Keck Observatory over a three-night program during semesters 2015B and 2016A. Thirteen observations made using LRIS were emission-line galaxies previously observed using the Kast spectrograph, with the remaining objects having only LRIS data. Similar to the Kast spectrograph, LRIS has separate blue and red channels. Our setup utilized the 600/4000 grism on the blue side, which provides a dispersion of 0.63 Å pix⁻¹. On the red side, the 600/7500 grating provides a dispersion of 0.8 Å pix⁻¹. Using the D560 dichroic, the full wavelength coverage achieved with this instrument setup is ∼3200–8600 Å, with the blue side covering ∼3200–5600 Å and the red side covering ∼5400–8600 Å. The blue and red channels have FWHM resolutions of 2.6 Å and 3.1 Å respectively. We note that while the separate blue and red arms overlap in wavelength coverage, data near the region of overlap can be compromised due to the dichroic.

All targets were observed using a 07 slit using the atmospheric dispersion corrector on LRIS for total exposure times ranging from 3 × 1200 s to 3 × 1800 s. Bias frames and dome flats were obtained at the beginning of the night, along with spectra of the Hg, Cd, and Zn arc lamps on the blue side, and Ne, Ar, Kr arc lamps and red side for wavelength calibration. Photometric standard stars were observed at the beginning and end of each night for flux calibration. Observed and derived physical properties of a sample of BCDs observed using Keck+LRIS are reported in Table 1. For systems observed both at Lick and Keck, we present properties derived from observations made using Keck+LRIS and note the systems with an asterisk. The full sample of observed systems is available online.

The 2D raw images were individually bias subtracted, flat-field corrected, cleaned for cosmic rays, sky-subtracted, extracted, wavelength calibrated, and flux calibrated using PYPIT, a Python-based spectroscopic data reduction package.³ PYPIT applies a boxcar extraction to extract a 1D spectrum of the object. Multiple exposures on a single candidate BCD were combined by weighting each frame by the inverse variance at each pixel. The reduced and combined spectra of seven BCDs observed at Lick Observatory are shown in Figure 3.

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Emission-line fluxes were measured using the Absorption LIne Software (ALIS⁴ ; see Cooke et al. 2014 for details of the software), which performs spectral line fitting using χ² minimization. For integrated flux measurements, each emission-line is fit with a Gaussian model simultaneously with the surrounding continuum, which is modeled with a first order Legendre polynomial. In this procedure, the error in the continuum measurement is folded into the integrated flux errors. We assume that the FWHM of all emission lines are set by instrumental broadening, therefore all emission lines have the same FWHM. The integrated flux measurements of our observed systems are available online.

The measured emission-line fluxes are corrected for reddening and underlying stellar absorption using the χ² minimization approach described below and found in Appendix A of Olive & Skillman (2001):⁵

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{\lambda }\displaystyle \frac{{({X}_{R}(\lambda )-{X}_{T}(\lambda ))}^{2}}{{\sigma }_{{X}_{R}}^{2}(\lambda )},\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray}&&{X}_{R}(\lambda )=\displaystyle \frac{I(\lambda )}{I({\rm{H}}\beta )}=\displaystyle \frac{{X}_{A}(\lambda )}{{X}_{A}({\rm{H}}\beta ){10}^{f(\lambda )c({\rm{H}}\beta )}},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{X}_{A}(\lambda )=F(\lambda )\left(\displaystyle \frac{W(\lambda )+\,{a}_{{\rm{H}}{\rm{I}}}}{W(\lambda )}\right).\end{eqnarray} \tag{ 3 }$$

Here, X_T(λ) is the theoretical value of the Balmer line ratio at wavelength λ of consideration to Hβ, f(λ) is the reddening function, normalized at Hβ, c(Hβ) is the reddening, W(λ) is the equivalent width of the line, and a_{H i} is the equivalent width of the underlying stellar absorption at Hβ, both given in Angstroms. Minimizing the value of χ² allows for the determination of the best values of c(Hβ) and a_{H i}.

We note that the underlying stellar absorption is wavelength dependent. While we report the value of a_{H i} at Hβ, the best solution for the χ² minimization is the parameter that fits all Balmer line ratios used in the analysis, where the correction to each Balmer line ratio is applied as a_{H i} times a multiplicative coefficient that accounts for the wavelength dependence of underlying stellar absorption. The multiplicative coefficients we applied are given in Equation 5.1 of Aver et al. (2010), and we refer readers to Section 5 of Aver et al. (2010) for a more detailed discussion on the wavelength dependence of underlying stellar absorption.

There is some uncertainty in the relative flux calibration across the separate blue and red channels on Kast and on LRIS; Hα is therefore not included in this calculation. Instead, we rely on all detected higher-order Balmer lines when solving for the reddening and underlying stellar absorption. We include Hβ through H9 in this calculation, and exclude H and H8 due to blends with [Ne iii] and He i, respectively. We note that the uncertainty in flux scales across the separate channels does not affect direct metallicity measurements, since all relevant emission lines for direct measurements fall on the blue detector.

Throughout the procedure, we assume Balmer line ratios corresponding to a T_e = 10,000 K gas for our Kast observations, and Balmer line ratios for measured temperatures are adopted for LRIS observations. The underlying stellar absorption in our systems range from ≲1 Å–4.5 Å, and the amount of reddening ranges from c(Hβ) ∼ 0.001–0.5. The measured emission-line intensities for a few systems are shown in Table 2; the emission-line intensities for our full sample of BCDs are available online.

Table 2.  Measured Emission-line Intensities for a sample of observed BCDs

			Target Name
Ion	J0000+3052A	J0000+3052B	J0003+3339	J0018+2345	J0033−0934
[O ii] λ3727+3729	0.6249 ± 0.0064	1.413 ± 0.011	1.532 ± 0.040	0.799 ± 0.044	1.378 ± 0.052
H11 λ3771	0.0785 ± 0.0030	⋯	⋯	⋯	⋯
H10 λ3798	0.0256 ± 0.0048	⋯	⋯	⋯	⋯
H9 λ3835	0.1187 ± 0.0048	0.1140 ± 0.0082	0.120 ± 0.022	0.088 ± 0.035	0.109 ± 0.032
[Ne iii] λ3868	0.2528 ± 0.0046	0.2025 ± 0.0042	0.372 ± 0.022	0.157 ± 0.030	0.099 ± 0.050
H8+He i λ3889	0.2006 ± 0.0053	0.2202 ± 0.0088	0.260 ± 0.020	0.204 ± 0.032	0.196 ± 0.039
H+[Ne iii] λ3968	0.2120 ± 0.0055	0.2093 ± 0.0088	0.172 ± 0.022	0.228 ± 0.034	0.120 ± 0.048
Hδ λ4101	0.2518 ± 0.0051	0.2681 ± 0.0080	0.255 ± 0.018	0.262 ± 0.031	0.238 ± 0.041
Hγ λ4340	0.4289 ± 0.0052	0.4437 ± 0.0074	0.468 ± 0.022	0.458 ± 0.030	0.514 ± 0.046
[O iii] λ4363	0.0861 ± 0.0023	0.0518 ± 0.0025	⋯	⋯	⋯
He i λ4472	0.0309 ± 0.0020	0.0244 ± 0.0024	⋯	⋯	⋯
Hβ λ4861	1.0000 ± 0.0049	1.0000 ± 0.0065	1.000 ± 0.020	1.000 ± 0.027	1.000 ± 0.043
He i λ4922	0.0056 ± 0.0018	⋯	⋯	⋯	⋯
[O iii] λ4959	1.4318 ± 0.0053	0.8482 ± 0.0042	1.504 ± 0.021	0.612 ± 0.023	1.070 ± 0.045
[O iii] λ5007	4.337 ± 0.011	2.5839 ± 0.0077	4.796 ± 0.032	1.806 ± 0.034	2.393 ± 0.077
He i λ5015	0.0291 ± 0.0021	0.0240 ± 0.0025	⋯	⋯	⋯
He i λ5876	⋯	0.0532 ± 0.0093	⋯	⋯	⋯
[N ii] λ6548	⋯	0.0296 ± 0.0077	0.0211 ± 0.0063	0.0060 ± 0.0017	⋯
[Hα λ6563	2.786 ± 0.047	2.785 ± 0.049	2.860 ± 0.058	2.860 ± 0.047	2.86 ± 0.15
[N ii] λ6584	0.0163 ± 0.0047	0.0724 ± 0.0086	0.0634 ± 0.0010	0.01798 ± 0.00029	⋯
He i λ6678	0.0284 ± 0.0046	⋯	⋯	⋯	⋯
[S ii] λ6717	0.0653 ± 0.0049	0.137 ± 0.010	0.176 ± 0.021	0.0775 ± 0.0053	0.076 ± 0.098
[S ii] λ6731	0.0436 ± 0.0063	0.100 ± 0.012	0.090 ± 0.027	0.0564 ± 0.0077	0.222 ± 0.099
He i λ7065	0.0037 ± 0.0052	0.021 ± 0.011	⋯	⋯	⋯
F(Hβ) (×10−17 erg s−1 cm−2)	181.91 ± 0.89	220.0 ± 1.4	140.7 ± 2.8	172.0 ± 4.6	206.1 ± 8.8
EW(Hβ) (Å)	96.0 ± 1.3	47.51 ± 0.44	169 ± 27	66.4 ± 5.5	43.5 ± 4.4
c(Hβ)	0.001	0.001	0.056	0.001	0.501
EW(aH i) (Å)	4.50	3.44	4.43	3.52	2.47

Note. Measured emission-line fluxes, corrected for underlying stellar absorption and internal reddening, for some objects of our BCD sample. The equivalent width of the underlying stellar absorption is reported at Hβ. Emission-line intensities for the full sample of BCDs are available online.

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

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Our sample of observed BCDs consists of six systems confirmed or predicted to have metallicities in the lowest-metallicity regime, with gas-phase oxygen abundance 12+log(O/H) ≲ 7.20, or Z ≲ 0.03 Z_⊙. These systems are listed in Table 3 with their metallicities and the method by which we obtained a measurement of their gas-phase oxygen abundance. We are able to obtain an empirical estimate of the metallicity using the R and S methods on systems observed using Shane+Kast, or obtain a direct measurement of the metallicity using the temperature-sensitive oxygen line at [O iii] λ4363 Å on systems observed using Keck+LRIS. The following sections describe these methods in more detail.

4.2.1. Lick Data

The temperature-sensitive oxygen line at [O iii] λ4363 Å, which is necessary for a direct abundance measurement, is typically not detected in our sample of BCDs observed using the Kast spectrograph, owing to the lower S/N of those spectra. We therefore rely on empirical methods to estimate the metallicity of our candidate BCDs with 3 m observations. We adopt two separate methods for determining the oxygen abundance in H ii regions, each using the intensities, I, of three strong emission lines, as presented by Pilyugin & Grebel (2016). The R calibration uses the intensities of R₂, R₃, and N₂ and the S calibration uses the intensities of S₂, R₃, and N₂, where the standard notations are:

$$\begin{eqnarray}{R}_{2} & = & {I}_{[{\rm{O}}{\rm{II}}]}\lambda \lambda 3727,3729/{I}_{{\rm{H}}\beta }\\ {N}_{2} & = & {I}_{[{\rm{N}}{\rm{II}}]}\lambda \lambda 6548,6583/{I}_{{\rm{H}}\beta }\\ {S}_{2} & = & {I}_{[{\rm{S}}{\rm{II}}]}\lambda \lambda 6717,6731/{I}_{{\rm{H}}\beta }\\ {R}_{3} & = & {I}_{[{\rm{O}}{\rm{III}}]}\lambda \lambda 4959,5007/{I}_{{\rm{H}}\beta }.\end{eqnarray} \tag{ 4 }$$

The R and S calibrations are bifurcated; the oxygen abundance is estimated from either the lower or the upper branch depending on the value of log(N₂). The lower branch is used for H ii regions with log(N₂) < −0.6:

$$\begin{eqnarray}12+\mathrm{log}{({\rm{O}}/{\rm{H}})}_{R,L} & = & 7.932+0.944\,\mathrm{log}({R}_{3}/{R}_{2})\\ & & +0.695\mathrm{log}\,{N}_{2}+(0.970\\ & & -0.291\mathrm{log}({R}_{3}/{R}_{2})-0.019\,\mathrm{log}\,{N}_{2})\\ & & \times \mathrm{log}\,{R}_{2},\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}12+\mathrm{log}{({\rm{O}}/{\rm{H}})}_{S,L} & = & 8.072+0.789\,\mathrm{log}({R}_{3}/{S}_{2})\\ & & +0.726\mathrm{log}\,{N}_{2}+(1.069\\ & & -0.170\mathrm{log}({R}_{3}/{S}_{2})+0.022\,\mathrm{log}\,{N}_{2})\\ & & \times \mathrm{log}\,{S}_{2}.\end{eqnarray} \tag{ 6 }$$

The upper branch is applicable for H ii regions with logN₂ ≥ −0.6:

$$\begin{eqnarray}12+\mathrm{log}{({\rm{O}}/{\rm{H}})}_{R,U} & = & 8.589+0.022\,\mathrm{log}({R}_{3}/{R}_{2})\\ & & +0.399\mathrm{log}\,{N}_{2}+(-0.137\\ & & +0.164\mathrm{log}({R}_{3}/{R}_{2})+0.589\mathrm{log}\,{N}_{2})\\ & & \times \mathrm{log}\,{R}_{2},\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}12+\mathrm{log}{({\rm{O}}/{\rm{H}})}_{S,U} & = & 8.424+0.030\mathrm{log}({R}_{3}/{S}_{2})\\ & & +0.751\mathrm{log}\,{N}_{2}+(-0.349\\ & & +0.182\mathrm{log}({R}_{3}/{S}_{2})+0.508\mathrm{log}\,{N}_{2})\\ & & \times \mathrm{log}\,{S}_{2}.\end{eqnarray} \tag{ 8 }$$

For systems where we do not detect the weaker metal lines, [N ii] and/or [S ii], we adopt a 3σ upper limit on their fluxes to estimate their metallicities. The reported metallicity of each galaxy in our BCD sample is based on the mean oxygen abundance derived from the R and S calibrations. We note that the separate R and S metallicity estimates are often in good agreement with one another, with the mean and standard deviation of the absolute value difference between the two methods, ∣12 + log(O/H)_R − 12 + log(O/H)_S∣, being 0.055 ± 0.179. Resulting values are listed in Table 1, with the full sample available online.

4.2.2. Keck Data

The data acquired using LRIS at Keck Observatory are of much higher S/N and allow for both density- and temperature-sensitive emission lines to be detected. All calculations of the electron density, electron temperature, ionic abundances, and resulting metallicities were made using PyNeb (Luridiana et al. 2015).⁶

We significantly detect the [S ii] λλ6717,6731 Å doublet in all LRIS observations and use the ratio of the two lines to calculate the electron density. However, consistent with the expected electron density of an H ii region, the measured electron densities occupy the low-density regime, where the ratio of the [S ii] lines is less sensitive to the true electron density. Therefore, in all calculations of the metallicity, we assume a value of n_e = 100 cm⁻³ in our ionic abundance estimates, which is consistent with both the density as determined by the [S ii] λλ6717,6731 Å lines and the expected range of densities in H ii regions, 10² ≤ n_e (cm⁻³) ≤ 10⁴ (Osterbrock 1989).

We assume a two-zone photoionization model of the H ii region in these BCDs and calculate the corresponding temperatures of the separate high and low ionization zones. The ratio of the [O iii] λ4363 Å line to the [O iii] λ5007 Å line allows for a determination of the temperature of the high ionization zone (T_e [O iii]). We note that the temperature-sensitive oxygen line at [O iii] λ4363 Å is detected in most of our LRIS observations, however, we adopt a 3σ upper limit on the measured emission-line flux at [O iii] λ4363 Å when we do not significantly detect the line. This measurement allows for an estimate of the electron temperature and therefore a direct measurement of the gas-phase oxygen abundance. Because we do not detect the [O ii] λλ7320,7330 Å or the [N ii] λ5755 Å lines necessary for a direct measurement of the temperature in the low ionization zone (T_e [O ii]), we adopt the formulation relating the two temperatures presented by Pagel et al. (1992):

$$\begin{eqnarray}&&{t}_{e}^{-1}\,[{\rm{O}}\,{\rm{II}}]=0.5(\,{t}_{e}^{-1}\,[{\rm{O}}\,{\rm{III}}]\,+\,0.8)\end{eqnarray} \tag{ 9 }$$

where t_e = T_e/10⁴ K. Because this relation is derived from modeling of photoionized regions, we perturb the calculated low ionization zone temperature by ≤±500 K to account for the systematic uncertainty in the conversion, where 500 K is the 1σ uncertainty from the spread in the models.

The two-zone photoionization model of the H ii region also assumes that the total oxygen abundance is the sum of the singly and doubly ionized states:

$$\begin{eqnarray}&&\displaystyle \frac{{\rm{O}}}{{\rm{H}}}=\displaystyle \frac{{{\rm{O}}}^{+}}{{{\rm{H}}}^{+}}\,+\,\displaystyle \frac{{{\rm{O}}}^{++}}{{{\rm{H}}}^{+}}.\end{eqnarray} \tag{ 10 }$$

The measurements of electron density, electron temperature, ionic abundances, and oxygen abundances of our Keck BCD sample are presented in Table 4. This Keck BCD sample will appear in full, i.e., their spectra and further analysis, in a forthcoming work.

Table 4.  Physical and Chemical Properties of the BCDs Observed with Keck

Target Name	ne([S ii])	Te([O iii])	Te([O ii])	O++/H+	O+/H+	12 + log(O/H)
	(cm−3)	(K)	(K)	(×10−6)	(×10−6)
J0000+3052A	${120}_{-65}^{+115}$	15130 ± 190	13671 ± 78	45.2 ± 1.4	7.01 ± 0.17	7.72 ± 0.01
J0000+3052B	${150}_{-76}^{+140}$	15190 ± 350	13670 ± 140	26.7 ± 1.5	15.86 ± 0.58	7.63 ± 0.02
J0118+3512	${116}_{-42}^{+46}$	15500 ± 190	14000 ± 76	29.27 ± 0.84	8.50 ± 0.18	7.58 ± 0.01
J0140+2951	${18}_{-11}^{+16}$	12200 ± 29	11856 ± 15	88.39 ± 0.71	22.97 ± 0.22	8.05 ± 0.00
J0201+0919	${74}_{-40}^{+70}$	14730 ± 440	13850 ± 190	39.8 ± 3.1	11.29 ± 0.53	7.71 ± 0.03
J0220+2044A	${135}_{-71}^{+91}$	15900 ± 440	13540 ± 170	25.2 ± 1.6	8.65 ± 0.38	7.53 ± 0.03
J0220+2044B	⋯	17500 ± 1100	15060 ± 380	20.5 ± 3.0	3.98 ± 0.37	7.39 ± 0.06
J0452–0541	${42}_{-28}^{+39}$	15490 ± 410	13570 ± 160	27.2 ± 1.7	16.01 ± 0.66	7.64 ± 0.02
J0743+4807	${81}_{-55}^{+80}$	9500 ± 1600	10200 ± 1100	≥250	≥90	≥8.34
J0812+4836	${70}_{-35}^{+71}$	17200 ± 4000	14500 ± 1600	≥11	≥17	≥7.35
J0834+5905	${350}_{-190}^{+390}$	21000 ± 3100	15480 ± 980	≥7.7	≥7.8	≥7.17
KJ5	${170}_{-90}^{+118}$	11570 ± 560	11670 ± 300	68.0 ± 11.0	12.5 ± 1.3	7.90 ± 0.06
KJ5B	${125}_{-68}^{+100}$	14030 ± 390	13310 ± 180	40.7 ± 3.1	10.57 ± 0.51	7.71 ± 0.03
J0943+3326	${330}_{-150}^{+320}$	16500 ± 1300	14700 ± 500	10.4 ± 2.1	4.06 ± 0.47	7.16 ± 0.07
Little Cub	${32}_{-17}^{+34}$	18600 ± 2200	14680 ± 720	5.1 ± 1.5	9.1 ± 1.6	7.13 ± 0.08
KJ97	${48}_{-24}^{+44}$	11880 ± 310	12450 ± 160	72.2 ± 5.9	28.7 ± 1.4	8.00 ± 0.03
KJ29	${900}_{-390}^{+640}$	14270 ± 340	13370 ± 150	29.2 ± 1.9	12.72 ± 0.49	7.62 ± 0.02
KJ2	${450}_{-240}^{+450}$	17550 ± 150	14907 ± 52	24.40 ± 0.48	2.466 ± 0.042	7.43 ± 0.01
J1414–0208	${112}_{-66}^{+100}$	14700 ± 1400	13520 ± 610	19.1 ± 5.6	13.5 ± 2.3	7.50 ± 0.09
J1425+4441	${180}_{-100}^{+180}$	15070 ± 960	13320 ± 400	18.2 ± 3.0	13.5 ± 1.4	7.50 ± 0.06
J1655+6337	⋯	16620 ± 160	13914 ± 59	21.90 ± 0.49	5.169 ± 0.093	7.43 ± 0.01
J1705+3527	${83}_{-44}^{+52}$	15510 ± 130	13453 ± 54	37.69 ± 0.77	7.69 ± 0.14	7.66 ± 0.01
J1732+4452	${297}_{-78}^{+92}$	15200 ± 240	14146 ± 98	32.9 ± 1.3	8.94 ± 0.23	7.62 ± 0.02
J1757+6454	${69}_{-34}^{+41}$	14480 ± 190	13451 ± 81	39.1 ± 1.4	13.67 ± 0.34	7.72 ± 0.01
J2030–1343	${25}_{-15}^{+21}$	13890 ± 140	13446 ± 64	55.9 ± 1.6	13.54 ± 0.26	7.84 ± 0.01
J2213+1722	${29}_{-17}^{+25}$	15420 ± 140	13400 ± 58	30.18 ± 0.67	10.20 ± 0.18	7.61 ± 0.01
J2230–0531	${77}_{-36}^{+40}$	14860 ± 170	13845 ± 72	32.49 ± 1.00	8.79 ± 0.18	7.62 ± 0.01
J2319+1616	${137}_{-39}^{+39}$	10617 ± 23	11628 ± 13	106.82 ± 0.80	44.79 ± 0.42	8.18 ± 0.00
J2339+3230	${15.3}_{-9.1}^{+20.7}$	13990 ± 240	13470 ± 110	50.7 ± 2.3	12.17 ± 0.36	7.80 ± 0.02

Note. Measurements of the electron density, electron temperature, ionic abundances, and element abundances of our sample observed with Keck+LRIS. All calculations are made using PyNeb. Calculations of the electron temperature and abundances assume an electron density of n_e = 100 cm⁻³, due to the density insensitivity of the [S ii] λ6716/λ6731 line in the low-density regime. All systems have direct metallicity estimates, except for J0743+4807, J0812+4836, and J0834+5905, where we do not significantly detect the [O iii] λ4363 Å line and adopt an upper limit to the [O iii] λ4363 Å emission-line flux equivalent to three times the error of the measured line at that wavelength. In these cases, the resulting ionic abundances and metallicities are lower limits. The objects prefixed with KJ were also observed by James et al. (2017). J0943+3326 is also known in the literature as AGC198691 (Hirschauer et al. 2016). Our survey independently identified this system as a candidate metal-poor galaxy, and the values reported here reflect our measurements.

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4.2.3. R and S Calibration versus Direct Metallicity Measurements

Our sample contains 13 BCDs for which we obtained both Kast and LRIS spectra. Using these systems, we consider the reliability of the R and S calibration methods in providing a reasonable estimate of the metallicity of the system measured via the direct method. In the upper panel of Figure 4, we show the direct metallicity measurements versus R and S calibration estimates of the metallicity for the 13 systems, along with the idealized one-to-one scenario where the calibration method exactly predicts the direct metallicity. We calculate the 12 + log(O/H)_direct − 12 + log(O/H)_R&S of these 13 BCDs, shown in the lower panel. The mean and standard deviation of the difference between the two metallicities is 0.010 ±0.284 dex.

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The R and S calibration methods presented by Pilyugin & Grebel (2016) were derived using a compilation of 313 H ii regions with direct metallicity measurements. Their sample has a mean oxygen abundance of 12 + log(O/H) ∼ 8.0, and only a small fraction of their sample occupied the low-metallicity regime at 12 + log(O/H) ≤ 7.65, which may cause the resulting relations to be less well calibrated at the low-metallicity regime. In our sample of 13 BCDs, the two systems that occupy the lowest-metallicity regime at 12 + log(O/H)_direct ≲ 7.20 had metallicities significantly underestimated using the R and S calibration, 12 + log(O/H)_R&S ∼ 6.60. While it is possible that some of the systems in our sample with 12 + log(O/H)_R&S ≤7.0 have underestimated metallicities, there is a monotonic trend in that the systems predicted to be of the lowest metallicities using the R and S calibrations remain as the lowest-metallicity systems of our sample. This bolsters our confidence in being able to identify the lowest-metallicity systems from the strong line R and S calibration methods for follow-up observations and direct metallicity measurements.

We show a redshift distribution of our full sample of BCDs in Figure 5. Using these measured redshifts, we calculate the luminosity distance (d_L) to each system using astropy's cosmology subpackage, assuming the built in Planck15 cosmology (Planck Collaboration et al. 2016). The values are reported for a subsample in Table 5 and available in its entirety online. However, these distance measurements are not well constrained with our available data given the local velocity field. For comparison, we include an additional estimate of the distance using the Mould et al. (2000) flow model, which corrects for the local velocity field. We note that flow model estimates can be highly uncertain for nearby galaxies, and more reliable distance measurements would require additional data, such as photometry of the tip of the red giant branch (TRGB).

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Nevertheless, for completeness, we adopt the luminosity distances and calculate distance-dependent properties for each system and list these values in Table 5, with the caveat that these quantities depend on the somewhat uncertain distance estimates. The reported Hα luminosity of each system, L(Hα), is calculated using our observed Hα fluxes combined with the assumed distance determined above:

$$\begin{eqnarray}&&L({\rm{H}}\alpha )=F({\rm{H}}\alpha )\,4\pi {d}_{L}^{2}.\end{eqnarray} \tag{ 11 }$$

The resulting star formation rate (SFR) is calculated using the Kennicutt relation between L(Hα) and SFR:

$$\begin{eqnarray}&&\mathrm{SFR}=7.9\,\times {10}^{-42}\,L({\rm{H}}\alpha ),\end{eqnarray} \tag{ 12 }$$

where the SFR is in units of M_⊙ year⁻¹ and L(Hα) in erg s⁻¹. We then divide this SFR by a factor of 1.8, which corrects for the flattening of the stellar initial mass function (IMF) below 1 M_⊙ for a Chabrier (2003) IMF, instead of the power law Salpeter IMF adopted by Kennicutt (1998).

We note that the Kennicutt (1998) calibration between L(Hα) and the SFR is based on measurements of more metal-rich systems than the BCDs considered in this sample, which adds uncertainty in the calculation of a SFR from L(Hα). In particular, massive O and B stars in low-metallicity environments are likely more efficient at ionizing their surroundings than their metal-rich counterparts, meaning that the presented SFR may be an overestimate of the true SFR of the galaxy. It is also possible that in some of our BCDs, the IMF is not well sampled, which would also lead to a deviation from the Kennicutt (1998) relation.

We present estimates of the stellar mass of each BCD using the stellar mass-to-light (M/L) ratios presented in Bell et al. (2003). We adopt the calibrations using the r- and i-band magnitudes, specifically the i-band coefficients and r − i color, given below. The observed photometry of these BCDs is likely to be influenced by the strong emission lines from the H ii region, in addition to the light of the young O and B stars. We therefore select the bands that are least likely to be contaminated by the star-forming event:

$$\begin{eqnarray}&&{\mathrm{log}}_{10}\left(\displaystyle \frac{M}{L}\right)=0.006\,+(1.114\,\times (r-i)).\end{eqnarray} \tag{ 13 }$$

A small sample of the resulting stellar mass estimates is given in Table 5 and in full online.

The luminosity–metallicity (L–Z) relation is thought to be a consequence of the more fundamental relation between a galaxy's mass and its chemical abundance, known as the mass–metallicity (M–Z) relation. At the low-mass and low-luminosity end of the relation, galaxies are more inefficient in chemically enhancing their gas and in retaining heavy metals (Guseva et al. 2009). Berg et al. (2012) presented a study of low-luminosity galaxies with accurate distances made via the TRGB method or Cepheid observations and direct abundance measurements with the [O iii] λ 4363 Å line. Their sample showed a small scatter in the relationship between the observed luminosity and oxygen abundance, shown as the orange dashed line in Figure 6 and given by:

$$\begin{eqnarray}&&12\,+\,\mathrm{log}({\rm{O}}/{\rm{H}})=(6.27\,\pm \,0.21)+(-0.11\,\pm \,0.01){M}_{B}.\end{eqnarray} \tag{ 14 }$$

Here, M_B is the B-band luminosity. This relationship from the Berg et al. (2012) sample has a dispersion of σ = 0.15.

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It has been suggested that significant deviations from the L–Z relation may be due to abnormal processes in the chemical evolutionary history of the galaxy and may indicate recent infall processes or disruptions that led to the observed low metallicity. Ekta & Chengalur (2010) noted that outliers of the L–Z relation with H i observations tend to have disrupted morphologies, suggesting that these galaxies have undergone recent or current interactions. The observed metal-poor nature of these systems is credited to the mixing of previously enhanced, more metal-rich gas with newly accreted, nearly pristine gas. Tidal interactions mix the gas and these systems are thus observed to lie below the L–Z relation, i.e., have a lower metallicity than predicted by the relation, given their luminosity.

Using the empirical ${ugri}-{{UBVR}}_{c}$ transformations presented in Cook et al. (2014), we convert the observed SDSS magnitudes of our BCDs into absolute B-band luminosities:

$$\begin{eqnarray}&&B-i=(1.27\,\pm \,0.03)(g-i)+(0.16\,\pm \,0.01).\end{eqnarray} \tag{ 15 }$$

We plot the resulting absolute B-band luminosity of our BCDs versus the oxygen abundance (L–Z relation) in Figure 6, and compare our results with the Berg et al. (2012) sample of nearby dwarf galaxies and a selection of other known low-metallicity galaxies. We note that the mean residual of our sample of BCDs from the Berg et al. (2012) L–Z relation given in Equation (14) is 0.271; however, this is weighted by a bias toward systems that lie below the L–Z relation.

A significant fraction of our BCD sample appears to be outliers of the L–Z relation derived by Berg et al. (2012). If the L–Z relation from Berg et al. (2012) is representative of regular star-forming regions, i.e., chemical enrichment is a result of star formation and subsequent feedback and enrichment from the stellar population, and deviations from this relation indicate interactions with the surrounding media, such as the inflow and accretion of pristine gas from the IGM, then it seems that there exists a larger fraction of BCDs in our sample that are experiencing recent star formation and observed to have a low metallicity due to the accretion of metal-poor gas. This is in contrast with systems that are low metallicity simply because they have processed little of their reservoir of gas into stars since the formation of the galaxy, due to inefficient star formation.

We note that even with our sample of BCDs that have direct abundances, our distance measurements contribute a large source of uncertainty in M_B, as discussed in Section 4.3. For BCDs with metallicities based on the R and S calibration methods, we must also consider the accuracy of these methods in predicting the true metallicity of a system. Therefore, in addition to the distance uncertainties, there also exists an uncertainty in the metallicity for systems that currently only afford metallicity estimates made via strong emission lines.

Furthermore, the B-band flux is dominated by the light of massive O and B stars, likely on the specific population of O and B stars present. This makes the observed B-band luminosity more sensitive to the recent or ongoing star formation and less sensitive to the stellar mass and integrated star formation history of the galaxy (Salzer et al. 2005). The sensitivity of the B-band luminosity to the star formation event could shift the observed luminosity of a system to a higher luminosity than what is expected given its metallicity. Additionally, the B band is also more susceptible to absorption effects than longer wavelength bands.

To make more definite conclusions about our systems and how well they follow or deviate from the Berg et al. (2012) L–Z relation, we would require direct abundance measurements and accurate distance measurements. Alternatively, supplementary infrared imaging, which is a better proxy of galaxy mass than the B band, on the sample of metal-poor BCDs could provide a more fundamental L–Z analysis.

The stellar mass (M_*) and the metallicity of a galaxy are considered to be fundamental physical properties of galaxies and are correlated such that more massive galaxies are observed to have higher metallicities. This correlation is given by the mass–metallicity (M–Z) relation (Mannucci et al. 2010; Berg et al. 2012; Izotov et al. 2015; Hirschauer et al. 2018). It is unclear whether the M–Z relation arises because more massive galaxies form fractionally more stars than their low-mass counterparts leading to higher metal yields (Köppen et al. 2007), or whether galaxies of all masses form similar fractions of stars from their gas, but low-mass galaxies subsequently lose a larger fraction of metal-enriched gas due to their shallower galactic potentials (Larson 1974; Tremonti et al. 2004).

While there exists evidence for various origins of the M–Z relation, both the stellar mass and metallicity track the evolution of galaxies; the stellar mass indicates the amount of gas in a galaxy trapped in the form of stars, and the metallicity of a galaxy indicates the reprocessing of gas by stars as well as any transfer of gas from the galaxy to its surrounding environment (Tremonti et al. 2004). Understanding the origin of the M–Z relation would provide insight into the timing and efficiency of how galaxies process their gas into stars, which is relevant in models of the chemical evolution of galaxies over all ranges of galaxy mass and redshift.

Obtaining the stellar mass of a galaxy is challenging, and as a result, the luminosity of a galaxy is often adopted as a proxy of its mass. This relation is analyzed in the form of the L–Z relation, as discussed previously in Section 5.1. In this Section, we analyze the M–Z relation in the context of our BCDs, using stellar mass estimates of our BCD sample described in Section 4.4. We compare our BCDs to the Berg et al. (2012) M–Z relation, which is:

$$\begin{eqnarray}12+\mathrm{log}({\rm{O}}/{\rm{H}}) & = & (5.61\pm 0.24)\\ & & +(0.29\pm 0.03)\mathrm{log}({M}_{* }).\end{eqnarray} \tag{ 16 }$$

We note that Berg et al. (2012) estimate stellar masses for their sample of low-luminosity galaxies using a combination of optical and infrared luminosities and colors: the 4.5 μm luminosity, K − [4.5] color, and B − K color. We direct readers to Section 6.4 of Berg et al. (2012) for further details. Their resulting relation has a dispersion of σ = 0.15, comparable to the dispersion in their L–Z relation. Our BCDs in stellar mass versus gas-phase oxygen abundance space (M–Z relation) are presented in Figure 7, along with a selection of other known low-metallicity galaxies.

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In addition to the uncertainty in metallicity estimates made via the R and S calibration methods, we must also consider that even with BCDs that afford a direct metallicity measurement; we are only able to determine the metallicity of the H ii region ionized by the current star formation event. Due to the massive young stars, these H ii regions may be self-enriched (Kunth & Sargent 1986). More generally, H ii regions are a poor representation of BCDs as a whole, as the bulk of baryons are found in the gaseous interstellar medium of these systems. It is therefore unlikely that our metallicities are representative of the true global metallicity (James et al. 2014). Furthermore, galaxies that have formed a substantial fraction (i.e., >10%) of their stars in a recent star formation episode often have M/L ratios that deviate from typical M/L ratios. Although we have taken caution to use SDSS bands least likely to be contaminated by the ongoing or recent star formation event, even NIR stellar M/L ratios can vary, depending on factors such as star formation rate and metallicity (Bell & de Jong 2001).

Overall, however, our sample of BCDs, particularly those with direct abundance measurements, follow the Berg et al. (2012) M–Z relation slightly more closely than they do the L–Z relation, with a mean residual from Equation (16) of 0.264. This supports existing studies that the M–Z relation is the more fundamental of the two relations.

With the advent of numerous photometric surveys, our presented method of identifying candidate low-metallicity galaxies via photometry alone can be adapted to query the data products of forthcoming astronomical surveys to further increase the number of local galaxies with metallicities less than 12 + log(O/H) ≤ 7.65. Multiple ongoing surveys such as Pan-STARRS, the Dark Energy Survey (DES), and the Dark Energy Camera Legacy Survey (DECaLs) can each supplement the photometric search for low-metallicity systems and offer the following advantages: both Pan-STARRS and DES will survey larger areas of the sky than covered by SDSS, and in particular, the DES footprint will scan the southern hemisphere, providing photometric information of sky regions not covered by current surveys. DECaLS will reach fainter magnitudes and potentially uncover low-metallicity systems in our local universe that are currently below the detection limit of SDSS. Additionally, these surveys can extend the search for low-metallicity systems to somewhat higher redshifts. As shown in Figure 5, our BCD sample has a mean redshift of z = 0.016 and reaches a maximum redshift of z = 0.052. Oncoming surveys that reach higher redshifts can therefore cover a much greater volume (i.e., a survey that can reach twice as far as current limits would probe eight times the current volume).

However, searching for low-metallicity galaxies in either Pan-STARRS, DES, or DECaLS is complicated by the lack of u-band photometry, particularly because the most metal-poor systems currently known in the local universe appear to cluster around a tight u − g color space, as shown in Figure 1. Our current SDSS query parameters will require modification to efficiently pick out the same objects in their various color–color spaces—grizy in Pan-STARRS, grizY in DES, and grz in DECaLS. We note that the Canada France Imaging Survey (CFIS; Ibata et al. 2017) offers u-band photometry and an overlap in footprint with the DES, allowing the two to be used in conjunction. Finally, by extending the search for low-metallicity dwarf galaxies to a larger volume, the change in photometric colors as we move into higher redshifts must also be taken into account.