Properties of the Lowest Metallicity Galaxies Over the Redshift Range z = 0.2 to z = 1

Low-metallicity galaxies may provide key insights into the evolutionary history of galaxies. Galaxies with strong emission lines and high equivalent widths (rest-frame EW(H-beta)>30 A) are ideal candidates for the lowest metallicity galaxies to z ~ 1. Using a Keck/DEIMOS spectral database of about 18,000 galaxies between z = 0.2 and z = 1, we search for such extreme emission-line galaxies with the goal of determining their metallicities. Using the robust direct Te method, we identify 8 new extremely metal-poor galaxies (XMPGs) with 12 + log O/H<7.65, including one at 6.949 +/- 0.091, making it the lowest metallicity galaxy reported to date at these redshifts. We also improve upon the metallicities for two other XMPGs from previous work. We investigate the evolution of H-beta using both instantaneous and continuous starburst models, finding that XMPGs are best characterized by continuous starburst models. Finally, we study the dependence on age of the build-up of metals and the emission-line strength.


INTRODUCTION
Low-redshift (z 1), low-metallicity galaxies could be the best analogs of small, star-forming galaxies (SFGs) at high redshifts (z 6). Such low-redshift galaxies may give insights into the properties of early SFGs, which may be responsible for reionizing the universe. Izotov et al. (2021) found that the properties of low-metallicity, compact SFGs with high equivalent widths (EWs) of the Hβ emission line are similar to the properties of highredshift SFGs.
Here we use a different approach to the problem, which is more analogous to choosing objects out of the SDSS spectroscopic sample but at considerably fainter magnitudes. We work with an archival sample of galaxies with spectra from Keck/DEIMOS, selecting those with high EW 0 (Hβ) and redshifts z = 0.2-1. Our main goal is to obtain a significant sample of XMPGs with strong [OIII]λ4363 detection where we can use the "direct T e method" (e.g., Seaton 1975;Pagel et al. 1992;Pilyu-gin & Thuan 2005;Yin et al. 2006;Izotov et al. 2006;Kakazu et al. 2007;Liang et al. 2007;Hu et al. 2009).
We organize the paper as follows: In Section 2, we describe the spectroscopic observations. In Section 3, we present our EW and flux measurements, our electron temperature determinations, our metal abundance measurements, and our error analysis. In Section 4, we give our final XMPG catalog and discuss our results. We give a summary in Section 5. We use a standard H 0 = 70 km s −1 Mpc −1 , Ω m = 0.3, Ω Λ = 0.7 cosmology throughout the paper.

SPECTROSCOPIC OBSERVATIONS
During the last ∼ 20 years, our team obtained spectroscopy of galaxies in a number of well-studied fields (e.g., GOODS, COSMOS, SSA22, the North Ecliptic Pole, etc.) for a variety of projects (e.g., Cowie et al. 2004Cowie et al. , 2016Kakazu et al. 2007;Barger et al. 2008Barger et al. , 2012Wold et al. 2014Wold et al. , 2017Rosenwasser et al. 2022) using the Deep Extragalactic Imaging Multi-Object Spectrograph (DEIMOS; Faber et al. 2003) on the Keck II 10 m telescope. The observational set-up of the ZD600 line mm −1 grating blazed at 7500Å and a 1 slit gives a spectral resolution of ∼ 4.5Å and a wavelength coverage of 5300Å. However, for an individual spectrum, the specific wavelength range is dependent on the slit position with respect to the center of the mask along the dispersion direction. The spectra have an average central wavelength of 7200Å.
The observations were not generally taken at parallactic angle, since the position angle was determined by the mask orientation. Each ∼60 minute exposure was broken into three 20 minute subsets, with the objects dithered along the slit by 1. 5 in each direction. The spectra were reduced and extracted using the procedures described in Cowie et al. (1996). In Figure 1, we show an example spectrum to illustrate the quality of the DEIMOS spectra obtained.
In Figure 2, we present the redshift distribution for our sample. There are two peaks that correspond to narrowband filter selection at z = 0.63 and z = 0.83. A substantial fraction of the objects, about 45%, are in these two peaks.
We note in passing that there are no signs of lensing in the sample. We do not see multiple emission lines in the spectra, and the objects are generally isolated. Since we are not concerned with luminosities and masses here, lensing would not affect our analysis.

EW Measurements
To determine the metallicities of our sample, we measure the EWs of the emission lines of interest in each spectrum: [OII]λ3727, [OIII]λ4363, [OIII]λ5007, and [NII]λ6583, as well as Hγ, Hβ, and Hα. We use EWs instead of emission line fluxes to avoid introducing biases from spectral flux calibrations. A challenge with determining EWs is measuring the continua of the spectra. We carefully inspected the spectra of all the sources with very weak continua to make sure that the continua are plausible. However, since we are primarily concerned with local line ratios, a continuum measurement is not critical to the metallicity determination. To measure the EWs, we simultaneously fit Gaussian functions to neighboring emission lines of interest, and we divide the integrated area under each fitted Gaussian by the median continuum level near each line. To convert these observed-frame EWs to rest-frame EWs, we divide by (1 + z).
When fitting Hβ and the [OIII]λλ4959, 5007 doublet, we enforce a 3:1 internal ratio for the doublet and require that all three lines have the same line width. We fit a single redshift and assume that the FWHM is the same for all three lines. We fit the lines simultaneously using four free parameters (z, FWHM, and the amplitudes of the [OIII]λ5007 and Hβ lines). We use the same procedure to fit simultaneously the Hα line and the [NII]λλ6548, 6583 doublet. We also use similar procedures to fit two Gaussian functions, with a single FWHM and redshift, to the Hγ and [OIII]λ4363 lines, as well as to the [OII]λλ3729, 3727 doublet. We do not account for stellar absorption in the Balmer lines. Given the strength of the emission lines in EELGs, the effects of stellar absorption are extremely small.
By fitting multiple Gaussians simultaneously rather than individual lines independently, we increase the fidelity of the fits to weaker emission features. For example, [OIII]λ4363 is a relatively weak line compared to the neighboring Hγ line. However, by simultaneously fitting Hγ and [OIII]λ4363, we can infer the line center and line width from the stronger Hγ line, thereby improving the fit to the weaker [OIII]λ4363 line. In Figure 3, we show     > 2σ detections in [OIII]λ4363, and most sources have a very strong detection.
In Figure 5, we show a Baldwin, Phillips, & Terlevich (BPT) diagram (Baldwin et al. 1981) for the lower redshift sources in our sample that have Hα measurements. We require S/N > 20 in Hα to choose sources where we can make a robust measurement of [NII]/Hα. We compare with the locus determined by the SDSS spectral sample. The figure demonstrates that our EW measurements are robust and that we have a spectral sample of SFGs that follow the BPT track. Although Figure 5 is limited to lower redshift sources due to the spectral coverage of [NII] and Hα, our higher redshift sources also do not show active galactic nucleus (AGN) signatures, such as [NeV]λ3426. This suggests relatively little AGN contamination in the higher redshift part of the sample.

Flux Determinations
To convert the [OIII]λ5007 to [OIII]λ4363 EW ratio to a flux ratio, we use the relation We assume the extinction in the sources is low and fix the flux ratio of Hγ to Hβ at the Balmer decrement value of 0.47 (e.g., Osterbrock 1989). We also assume the continuum is flat between adjacent lines. We may also compute flux ratios by assuming a shape for the underlying continuum. In Figure 6, we plot EW 0 (Hγ) versus EW 0 (Hβ) for sources with Hβ S/N > 20. There is a near linear relation. Assuming the underlying continuum is flat in f ν gives a median flux ratio for Hγ to Hβ of 0.465, consistent with the Balmer decrement, which is shown by the red line. We use this method to compute the flux ratio of the combined [OII]λλ3729, 3727 doublet to the Hβ line. We consider this method more uncertain than the Balmer decrement method, which we use for the other line ratios.

Electron Temperature and Oxygen Abundance Determinations
In the T e method, the metallicities of galaxies are deduced from the flux ratio of the [OIII]λλ4959, 5007 doublet to the [OIII]λ4363 thermal line. We follow the prescription of Izotov et al. (2006) and use their Equations 1 and 2 to determine the electron temperatures.
Using the T e method also allows ion abundances for galaxies to be derived directly from the strength of the emission lines, specifically O/H. Izotov et al. (2006) empirically fit relations to an electron temperature range for common galactic emission lines. This results in a large number of ionic abundance relations, including the desired O + and O 2+ relations for this work (their Equations 3 and 5). To obtain the total abundance of Oxygen for each galaxy, these two equations must be added together. Note that there is typically little change in the total metallicity when adding O + to O 2+ , as O 2+ is the strongly dominant ionization state of Oxygen in these galaxies. This means any uncertainties in our conversion of the EW ratio to flux ratio for [OII]λ3727/Hβ are less important.

Error Analysis
We first calculated the errors on the multi-Gaussian continuum fits. For each group of simultaneously fit emission lines, we shifted the positions of the fitted lines along the spectra in regular intervals, refitting the emission lines at each interval and calculating EWs. We then took the standard deviations of these EW measures as the 1σ error bounds on the EWs of the lines. We used this method in order to properly sample the systemic, non-uniform noise in the spectra resulting from sky subtraction procedures.
To propagate the measurement errors we used a Monte Carlo technique, as analytical propagation would be needlessly complex. In this technique, we evaluated the Oxygen abundance 10, 000 times, using values drawn randomly from normal distributions for the EWs of [OIII]λλλ5007,4959,4363 Hβ, Hγ, and [OII]λ3727, centered at the measured values, and with standard deviations corresponding to the 1σ errors on each value. We used the standard deviation of the distribution of total abundance for each galaxy as the 1σ error on the abundance of that galaxy. A general overview of the above error propagation procedure can be found in Andrae (2010).

DISCUSSION
Following the procedures in Section 3, we determined the 12+log O/H abundance for each galaxy in our sample with S/N > 20 in the Hβ line and detected above a 1σ threshold in [OIII]λ4363. In Table 1, we summarize the 10 XMPGs found in this way. The two lowest metallicities are 12+log O/H = 6.949±0.091 and 7.208±0.061 at EW 0 (Hβ) of 169 ± 5Å and 264 ± 4.69Å, respectively. In Figure 7, we show the triple Gaussian fits to Hβ, [OIII]λ4959, and [OIII]λ5007 and the double Gaussian fits to Hγ and [OIII]λ4363 for these two galaxies. We show the spectra of the remaining XMPGs in the Appendix, along with z-band images of the four XMPGs in the SSA22 field using newly reduced Subaru Hyper Suprime-Cam imaging (B. Radzom et al. 2022, in preparation).
A majority of our objects have been identified in previous work. However, our present spectroscopic observations are significantly improved over those observations and allow for the detection of the [OIII]λ4363Å line. Thus, our metallicity measurements for most of the objects are new. Two of our objects had previous metallicity measurements determined by Kakazu et al. (2007). In one case (2 h 40 m 35.56 s , −1 • 35 37.1 ), the present 5 hr exposure is comparable to the 4 hr exposure used in Kakazu et al. (2007). In the other case (22 h 19 m 06.30 s , +0 • 47 21.6 ), the present 7 hr exposure is considerably longer than the 1 hr exposure used in Kakazu et al. (2007), and the errors are correspondingly lower. We include in Table 1, if available, the original source identification and the original metallicity determination. Note-Right ascension is given in hours, minutes, and seconds, and declination is given in degrees, arcminutes, and arcseconds. † Identified in Kakazu et al. (2007). † † Objects with direct Te metallicity determinations in Kakazu et al. (2007). In Figure 8 we show 12+log O/H abundance versus EW 0 (Hβ). Those galaxies not detected above 1σ in [OIII]λ4363 are shown at a nominal (high) value of 10. In examining the figure, a relation can be seen between 12+log O/H and EW 0 (Hβ). Specifically, as EW 0 (Hβ) increases, the metallicity decreases with a median metallicity of 8.39 for sources with EW 0 = 50−100Å and 8.07 for sources with EW 0 > 100Å. For the EW 0 ≥ 100Å region, a Pearson's correlation test gives a linear correlation factor (r-value) of −0.51 and a probability value of 0.02 for an uncorrelated system to produce the same r-value.
A simple linear fit between the O abundances and log EW 0 (Hβ) gives the relation 12 + log(O/H) = 12.810 ± 0.101 − 2.233 ± 0.061 × log EW 0 (Hβ)Å (2) for galaxies with EW 0 ≥ 100Å (black curve). We determined the errors on the fit by performing a Monte Carlo simulation based on the uncertainties in the EW 0 (Hβ) and metallicity of the dataset. We show the 1σ distribution of the resulting set of fits in green shading in Figure 8. The minimum EW 0 (Hβ) requirement ensures the fitted relation accurately represents the higher EW 0 (Hβ) lower metallicity region, which has been under-constrained in past XMPG surveys. This relation underlines the effectiveness of searching for XMPGs in samples of high-EW emission-line galaxies. To highlight the high-EW sample we focus on subsequently, we plot the data points at EW 0 (Hβ) < 100Å with fainter symbols, and we plot a vertical line at EW 0 (Hβ) = 100Å.
We are interested in the relationships between EW 0 (Hβ), metallicity, and galaxy age (t) at EW 0 (Hβ) ≥ 100Å; specifically, the EW 0 (Hβ) evolution and the changes in metallicity as a function of galaxy age. By galaxy age, we mean the time since the onset of the currently dominant star formation episode. This does not preclude there being older underlying populations in the galaxy. To determine these relationships, we must first assume a star formation model.
We constructed instantaneous and continuous starburst models using the program Starburst99 (Leitherer et al. 1999;Vázquez & Leitherer 2005;Leitherer et al. 2010Leitherer et al. , 2014. We left the initial parameters for each Starburst99 model unchanged. We show the models in Figure 9. In Figure 8, we see that the instantaneous starburst model, where the EW(Hβ) drops very rapidly with time, is a poor fit to our data at EW 0 (Hβ)≥ 100Å; thus, we focus our attention on the continuous starburst model. Specifically, we fit a power law to the continuous star-burst model for t > 10 7 yr, which gives the relation log t(yr) = 12.956 − 2.700 × log EW(Hβ) . (3) In addition to our assumption that our galaxies are undergoing continuous starburst, we assume that (1) the oxygen abundance increases linearly with time, and (2) the hydrogen abundance remains constant throughout time. With these assumptions, we obtain the following relation between metallicity and age: or, combining with Equation 3, 12 + log O/H = δ + 12.956 − 2.700 × log EW 0 (Hβ) , (5) where δ is a single fitted parameter, which is a measure of the yield. We overplot Equation 5 on the distribution of galaxy metallicities for δ =0.93, which we chose to match the EW 0 (Hβ) ≥ 100Å points (red curve). The blue curve is the instantaneous starburst model with the δ offset set to an arbitrary value. This curve is too flat to provide a fit to the data at EW 0 (Hβ) ≥ 100Å. The continuous starburst model shows reasonable agreement with the EW 0 (Hβ) ≥ 100Å data, but it over-predicts the EW 0 (Hβ) < 100Å data, suggesting that the effective yield or the specific star formation rate is dropping with time. However, Figure 8 supports the main point, which is that there is a clear relation between EW 0 (Hβ), age, and metallicity for EW 0 (Hβ) ≥ 100Åand that young XMPGs are undergoing star formation rates that are closer to continuous rather than instantaneous. Thus, for a galaxy with a measured EW 0 (Hβ)≥ 100Å, we can estimate the galaxy's age and the galaxy's metal abundance using Equations 3 and 5.
The models we test here do not exhaust the full range of possible parameter space of Starburst99, and thus do not cover the full scope of star formation histories. Nonetheless, the continuous starburst model fits our high-EW sample well. The relation between EW 0 (Hβ) and metallicity is present due to the underlying relation of the two with the age of the galaxy.
In summary, we show that for EW 0 (Hβ)≥ 100Å, EW 0 (Hβ) is a good proxy for galaxy age and metallicity, and XMPGs are best modeled by continuous starburst models.

SUMMARY
In this study, we discovered 8 new galaxies below the XMPG threshold of 12 + log O/H = 7.65 and improved upon metallicity measurements from Kakazu  2007) for two more. Our lowest metallicity galaxy has 12+log O/H = 6.949±0.091. We compared metallicity and EW 0 (Hβ) for our spectral sample and found that at EW 0 (Hβ)≥ 100Å, there is a clear relation between the two, which we interpret as being a consequence of a near continuous star formation rate in the galaxy. For these sources, EW 0 (Hβ) is an adequate proxy for galaxy age and metallicity.
With the spectroscopic sample sizes continually increasing, we expect to find even lower metallicity galaxies, which will help determine if there is a minimum galaxy metallicity in a given redshift range. . EW0(Hβ) vs. metallicity for our sample with S/N cuts of Hβ ≥ 20 and [OIII]λ4363 ≥ 1. Data that met the S/N cut of Hβ ≥ 20 but not [OIII] λ4363 ≥ 1 are plotted at a nominal value of 10. Prior EW0(Hβ) vs. metallicity plots suffered from a lack of galaxies populating the region where EW0(Hβ) exceeded 100Å, and thus the overall shape of the relation was under-constrained. Here we see that as the rest-frame EW increases, the metallicity decreases. The black vertical dotted line shows the low metallicity threshold of 12+log (O/H)= 7.65, which is 1/10th of the solar metallicity. The black solid curve represents a linear fit of 12 + log(O/H) = 12.810 ± 0.101 − 2.233 ± 0.061 × log EW0(Hβ)Å. We show the 1σ distribution of the Monte Carlo simulation fits in green shading. The metallicity abundance error and EW0(Hβ) error were determined from the procedures presented in Section 3.4. Also shown are the continuous (red curve) and instantaneous (blue curve) starburst models from Starburst99. We plot the data points at EW0(Hβ) < 100Å with fainter symbols and change each starburst model curve to dotted. We plot the XMPG sample as a different symbol to differentiate between our high metallicity and low metallicity sample. There is agreement between the metallicity and EW0(Hβ) relation and the continuous starburst model at high EWs, which underlines the dependence of metallicity and EW0(Hβ) on age.    Table 1 and starting with the third source, along with their triple Gaussian fits. Right: Emission lines Hγ and [OIII]λ4363 for the same galaxies, along with their double Gaussian fits. A 5-point median smoothing has been applied.