The stellar population of metal-poor galaxies at z ≈ 0.8 and the evolution of the mass–metallicity relation Free

ABSTRACT

We present results from deep Spitzer/Infrared Array Camera (IRAC) observations of 28 metal-poor, strongly star-forming galaxies selected from the DEEP2 Galaxy Survey. By modelling infrared and optical photometry, we derive stellar masses and other stellar properties. We determine that these metal-poor galaxies have low stellar masses, M_⋆ ≈ 10^8.1–10^9.5 M_⊙. Combined with the Balmer-derived star formation rates (SFRs), these galaxies have average inverse SFR/M_⋆ of ≈100 Myr. The evolution of stellar mass–gas metallicity relation to z ≈ 0.8 is measured by combining the modelled masses with previously obtained spectroscopic measurements of metallicity from [O iii] λ4363 detections. Here, we include measurements for 79 galaxies from the Metal Abundances across Cosmic Time Survey. Our mass–metallicity relation is lower at a given stellar mass than at z = 0.1 by 0.27 dex. This demonstrates a strong evolution in the mass–metallicity relation, |$(1+z)^{-1.45^{+0.61}_{-0.76}}$|⁠. We find that the shape of the z ≈ 0.8 mass-metallicity relation, a steep rise in metallicity at low stellar masses, transitioning to a plateau at higher masses, is consistent with z ∼ 0.1 studies. We also compare the evolution in metallicity between z ≈ 0.8 and z ∼ 0.1 against recent strong-line diagnostic studies at intermediate redshifts and find good agreement. Specifically, we find that lower mass galaxies (4 × 10⁸ M_⊙) built up their metal content 1.6 times more rapidly than higher mass galaxies (10¹⁰ M_⊙). Finally, we examine whether the mass–metallicity relation has a secondary dependence on SFR, and statistically concluded that there is no strong secondary dependence for z ≈ 0.8 low-mass galaxies.

1 INTRODUCTION

One key observable for understanding galaxy evolution is the chemical content of the interstellar gas and how it evolves. Specifically, comparisons of the gas-phase heavy-element abundances (i.e. ‘metallicity’) against the stellar mass enable us to understand how baryons behave in galaxies (Tremonti et al. 2004). The chemical enrichment of galaxies is first driven by star formation. As massive stars age, they produce heavy elements in their cores which are released via supernova winds into the interstellar medium when these stars reach their end stage. This chemical enrichment process is regulated by the cosmic accretion of more chemically pristine gas (e.g. Davé, Oppenheimer & Finlator 2011; Lilly et al. 2013).

The most reliable chemical abundance measurements are derived from the electron temperature (T_e) method (Aller 1984; Izotov et al. 2006). This method uses the emission-line flux ratio of [O iii] λ4363 to [O iii] λλ4959,5007. However, reliable measurements of [O iii] λ4363 are difficult to obtain in metal-rich and even harder to detect in high-z galaxies. Currently, there are 172 intermediate-redshift galaxies with robust (S/N ≥3) T_e-based metallicities (e.g. Hoyos et al. 2005; Hu et al. 2009; Atek et al. 2011; Amorín et al. 2014, 2015; Jones, Martin & Cooper 2015; Ly et al. 2014, 2015b, 2016a).

Due to the difficulty in obtaining temperature-based metallicities, previous studies have been primarily limited to using strong nebular emission lines (e.g. Pagel et al. 1979; Pettini & Pagel 2004) to measure the evolution of the mass–metallicity (M_⋆–Z) relation (e.g. Erb et al. 2006; Liu et al. 2008; Maiolino et al. 2008; Lamareille et al. 2009; Thuan, Pilyugin & Zinchenko 2010; Hunt et al. 2012; Nakajima et al. 2012; Wuyts et al. 2012; Yabe et al. 2012, 2014, 2015; Yates, Kauffmann & Guo 2012; Belli et al. 2013; Guaita et al. 2013; Henry et al. 2013; Cullen et al. 2014; Maier et al. 2014; Salim et al. 2014; Troncoso et al. 2014; Whitaker et al. 2014; Zahid et al. 2014; de los Reyes et al. 2015; Sanders et al. 2015, and references therein). A number of mass–metallicity studies have used the T_e method, but mostly in the local Universe with stacked spectra (e.g. Andrews & Martini 2013, hereafter AM13). In addition, robust stellar mass measurements at z ≳ 1 require deep infrared observations.

To address the lack of reliable T_e-based metallicity and stellar mass measurements at z ≈ 0.8, we present new infrared measurements from the Spitzer Space Telescope (hereafter Spitzer, Werner et al. 2004) for 28 z ≈ 0.8 [O iii] λ4363-detected galaxies identified by Ly et al. (2015b) from the DEEP2 survey (Newman et al. 2013).

The primary objectives of this study are: (1) measure the stellar population (i.e. stellar mass, stellar age, SFR) of these metal-poor galaxies; (2) determine the relationship between stellar mass and gas metallicity at z ≈ 0.8 for low-mass galaxies; and (3) explore the possible relationship between SFR, stellar mass, and gas metallicity. The oxygen abundances for these galaxies have been determined using the T_e method by Ly et al. (2015b). Currently, the stellar masses of these galaxies are poorly constrained with existing optical data, 1900–5000 Å rest-frame. Spitzer/IRAC (Fazio et al. 2004) observations, which sample red-ward of 1.6 |$\hbox{$\mu $m}$|⁠, are necessary for reliable stellar mass constraints.

This paper is outlined as follows. In Section 2, we discuss the DEEP2 sample, the Spitzer data for this study, and the Metal Abundance across Cosmic Time (⁠|$\mathcal {MACT}$|⁠) survey (Ly et al. 2016a). The latter is used to extend our analyses towards lower stellar masses relative to the DEEP2 sample. In Section 3, we describe our approach for estimating stellar masses and other stellar population properties from spectral energy distribution (SED) modelling. In Section 4, we present our main results on the stellar population for these low-metallicity galaxies, our M_⋆–Z relation, the evolution of the M_⋆–Z relation, its dependence on SFR, and the selection function of our study. We summarize our results in Section 5.

Throughout this paper, we adopt a flat cosmology with Ω_Λ  = 0.728, Ω_M  = 0.272, and H₀  = 70.4 km s⁻¹ Mpc⁻¹ (WMAP7; Komatsu et al. 2011).¹ We note that adopting Ω_Λ  = 0.7, Ω_M  = 0.3, and H₀  = 70 km s⁻¹Mpc⁻¹ would decrease stellar masses by 0.007 dex at z = 0.8. Magnitudes are reported on the AB system (Oke 1974).

2 THE SAMPLES

2.1 DEEP2 survey

In this study, we use the sample of 28 z ≈ 0.8 galaxies identified by Ly et al. (2015b) to have spectroscopic detections of [O iii] λ4363. Here, we briefly summarize the sample and refer readers to Ly et al. (2015b) for more details. From the fourth data release² of the DEEP2 Galaxy Redshift Survey (≈3 deg² surveyed area), 37 396 sources were selected with reliable spectroscopic redshifts. Of those, only sources with rest-frame spectral coverage of 3720–5010 Å were considered, limiting the sample to 4 140 galaxies. The emission lines of these galaxies were then fitted with Gaussian profiles, following the approach of Ly et al. (2014). Using emission-line fluxes, galaxies were selected with [O iii] λ4363 and [O iii] λ5007 detections at S/N ≥ 3 and S/N ≥ 100, respectively. Of the remaining galaxies, 26 were removed primarily due to OH night skyline contamination. This reduced the sample to 28 [O iii] λ4363-detected galaxies at z = 0.710–0.856, with a median (average) redshift of 0.774 (0.773).

2.1.1 Spitzer/IRAC data

Of the 28 DEEP2 galaxies, 19 galaxies had no previous Spitzer data, or the existing data were too shallow for stellar mass estimates. In order to derive robust stellar masses, we observe these 19 galaxies at 3.6 |$\mu$|m with the Spitzer/IRAC (Prop. No. 12104; Ly et al. 2015a). For DEEP2 galaxies #01–07, 10, and 26, see Table 1, existing Spitzer 3.6 and 4.5 |$\mu$|m data were obtained through the Spitzer Heritage Archive.³ We illustrate the Spitzer/IRAC 3.6 and 4.5 |$\mu$|m data in Fig. 1. The total integration times are listed in Table 1. The median (mean) total integration times were 52.5 (52.54) min for 3.6 |$\mu$|m and 47 (75.7) min for 4.5 |$\mu$|m.

2.2 |$\mathcal {MACT}$| survey

To increase the sample size and extend towards lower stellar masses (M_⋆ ≲ 3 × 10⁹ M_⊙; DEEP2 is a magnitude-limited survey, R < 24.1), we include the [O iii] λ4363-based samples from the |$\mathcal {MACT}$| survey in our mass–metallicity relation analysis. Here, we briefly summarize the |$\mathcal {MACT}$| sample and refer readers to Ly et al. (2016a) for more details.

The survey targeted ≈1900 emission-line galaxies of the Subaru Deep Field (≈0.25 deg² surveyed area; Kashikawa et al. 2004) that had excess flux in the narrow-band and/or intermediate-band filters (Ly et al. 2007). Using Keck and MMT, deep rest-frame optical spectra were obtained. The |$\mathcal {MACT}$| survey consists of two sub-samples, those with detections of the [O iii] λ4363 line at S/N ≥ 3 (N = 29 at z ≥ 0.5) and those with upper limits on [O iii] λ4363 (N = 50; z ≥ 0.5). For the latter, Ly et al. (2016a) required that [O iii] λ5007 was detected at S/N ≥ 100 and [O iii] λ4363 at S/N < 3. We refer to these two sub-samples collectively as the |$\mathcal {MACT}$| sample.

The stellar masses for the |$\mathcal {MACT}$| galaxies were determined with the Fitting and Assessment of Stellar Templates (fast; Kriek et al. 2009) code using the following photometric data: (1) FUV and NUV imaging from GALEX (Martin et al. 2005); (2) U-band imaging from Kitt Peak National Observatory (KPNO) Mayall telescope using MOSAIC (Sawyer et al. 2010); (3) BVR_Ci′z′z_bz_r imaging from the Subaru telescope with Suprime-Cam (Miyazaki et al. 2002); (4) H-band imaging from KPNO Mayall telescope using NEWFIRM (Probst et al. 2008); and (5) J- and K-band imaging from UKIRT using WFCAM (Casali et al. 2007). Further discussion of the photometric data for |$\mathcal {MACT}$| is provided in Ly et al. (2011) and Ly et al. (2016a). Together, the DEEP2 and |$\mathcal {MACT}$| galaxies are at z = 0.578 to z = 0.955 with a median (mean) redshift of 0.789 (0.763).

3 DERIVED MEASUREMENTS

3.1 Infrared photometry

Using the MOsaicker and Point source EXtractor (mopex, vers. 18.5.6; Makovoz & Marleau 2005), designed specifically to analyse Spitzer data, we performed aperture photometry to obtain the stellar continuum emission from the DEEP2 [O iii] λ4363-detected galaxies. We executed mopex mostly with default parameters with the following differences: not executing the fit_radius module, using a background-subtracted image for the point source probability (psp), adopting one aperture with a radius of 1|${^{\prime\prime}_{.}}$|8, and the values listed in Table 2 for the signal-to-noise ratio (SNR) in the select_conditions constraint.⁴ We then applied aperture corrections to obtain total photometric fluxes and calculated the background rms flux to estimate the uncertainty in the Spitzer images.

3.1.1 Total Spitzer fluxes

The aperture corrections for the Spitzer/IRAC 3.6 and 4.5 |$\mu$|m photometry were determined as follows:

First, we identified bright stars in each image (within a radius of 6 arcmin from the [O iii] λ4363-detected galaxy) using the coordinates of stars from the SDSS and cross-matched them against the Spitzermopex catalogues. Stars were then rejected if they were (1) within 12 arcsec of the edge of the image, (2) within 7 arcsec of another object identified by mopex, or (3) if the mopex flux was below 400 |$\mu$|Jy in a circular aperture (1|${^{\prime\prime}_{.}}$|8, radius). These restrictions were used to limit our calculations to bright isolated stars. Fluxes were then calculated using a circular aperture ranging from a radius of 1 pixel (0|${^{\prime\prime}_{.}}$|6) to 9 pixels (5|${^{\prime\prime}_{.}}$|4). The latter was chosen to include as much starlight as possible while excluding the light of other sources. The aperture corrections were then derived from the ratio of the 9- to 3-pixel fluxes. Outliers contaminated by nearby sources were removed iteratively using a sigma-clipping approach (σ = 2.5). The aperture correction, given in Table 1, is the mean from sigma clipping and has been applied to the IRAC fluxes in Table 1. If there were four or fewer stars within the search area after the restrictions, the aperture correction was set to the average correction (1.62 for both bands) of the remaining images. The 3.6 (4.5) |$\mu$|m aperture corrections range from 1.47 to 1.79 (1.50 to 1.68).

3.1.2 Measurements uncertainties

To determine the uncertainty in the IRAC 3.6 and 4.5 |$\mu$|m detections, we computed the background rms flux in the Spitzer images. This was done by measuring the flux within randomly placed apertures throughout an image that has been masked for sources and then fitting the distribution of fluxes to obtain the Gaussian width. The python package photutils.detect was used to construct a segmentation map to identify and mask pixels containing source emission. Here we required four contiguous pixels above a threshold value of 1.5σ. We then used photutils.aperture_photometry to measure the flux within a photutils.CircularAperture of three pixels (1|${^{\prime\prime}_{.}}$|8, radius) for 12 000 random positions across the masked image (typically ∼7000 positions were not affected by emission from sources). The distribution of background fluxes was then constructed and mirroring of the lower half relative to the median or peak (whichever was lower) was performed.⁵ For 3.6 |$\mu$|m data, the 3σ flux limits range between 0.42 and 1.49 |$\mu$|Jy, with a median and mean of 0.91 and 0.93 |$\mu$|Jy, respectively. For 4.5 |$\mu$|m data, 3σ flux limits range between 0.51 and 1.87 |$\mu$|Jy with a median (mean) of 0.72 (1.01) |$\mu$|Jy. These limits are provided in Table 1.

Additionally, we visually inspected the Spitzer images to determine if the galaxy was detected and not blended with neighbouring sources. If the galaxy was not detected, we use the 3σ background flux limit around the galaxy. If the galaxy was contaminated, we do not report a flux. Of the 28 galaxies, 21 were detected at 3.6 |$\mu$|m, one was not detected, and six suffered contamination from nearby sources. Among the nine galaxies with 4.5 |$\mu$|m data, four were detected, two were not detected, and three were confused with nearby sources.

3.2 Stellar masses

To estimate the stellar masses of DEEP2 [O iii] λ4363-detected galaxies, we combine Spitzer measurements with optical and near-infrared data, to model the SED of each galaxy. We describe below the photometric data (Section 3.2.1), the adopted SED models (Section 3.2.2), assumptions in our SED fitting (Section 3.2.3), and stellar mass comparisons (Section 3.2.4).

3.2.1 Optical and near-infrared data

The optical and near-infrared data, provided in Table 3, include Canada–France–Hawaii Telescope (CFHT) BRI photometry from Coil et al. (2004), ugriz from Matthews et al. (2013),⁶JHK_s for DEEP2 #01 from the NEWFIRM Medium-Band Survey (Whitaker et al. 2011), and K_s photometry for DEEP2 #04 from Bundy et al. (2006).

These photometric data have been corrected for nebular emission lines from optical spectroscopy using the technique described in Ly et al. (2015b) and Ly et al. (2016a). For our sample, this correction can be significant due to the strong Hβ + [O iii] emission such that it can over correct redder optical band(s), such as z-band. To avoid this overcorrection, we perform the SED modelling excluding the affected band(s).

3.2.2 SED modelling

In addition, we assumed a stellar metallicity of 0.02, a power-law dust attenuation with a slope of –0.7 (Charlot & Fall 2000), and an old-to-young stellar population reduction factor in A_V of 0.44. We did not include an active galactic nuclei (AGNs) model or the 2175 Å bump in the fitting, and the nebular component is excluded (see Section 3.2.1). The models also included a separation age between young and old stars of 10 Myr (default value for cigale). We defer discussions on our choices in SSP models and star formation histories to Section   3.2.3.

Physical parameters. The modelled parameters are listed in Table 4. Here we provide a brief discussion of the physical stellar population parameters and refer readers to Noll et al. (2009) for more information. The t_age parameter is the age of the oldest stars in the galaxy. The values for τ_main and t_age were chosen to allow for a wide range (star forming to passive) of possible star formation histories. The A_V parameter measures the V-band attenuation for the young stellar population used in the dust attenuation model. The values for A_V were chosen to allow for a broad range of possible attenuation corrections, from zero reddening to three magnitudes.

Using these adopted parameters, cigale created thousands of models for each galaxy and determined the best-fitting model using a Bayesian-like approach. A Bayesian methodology provides robust estimates on the physical properties, their associated uncertainties, and accounts for degeneracies between parameters by weighting each model by their χ² (Boquien et al. 2019). The results of the SED modelling are summarized in Table 5. We illustrate in Fig. 2 the SED-fitting result from cigale for one of our galaxies, DEEP2 #18.

We note that the SED results for DEEP2 #04 and #14 are not used. The SED models for these galaxies are not well constrained due to their limited photometric data set. DEEP2 #04 is a very bright galaxy that its optical measurements are not available in the DEEP2 catalogues. DEEP2 #14 was not detected by Spitzer/IRAC, thus limiting its photometric data set to three bands (BRI) and an upper limit at 3.6 |$\mu$|m. The upper limit is far below the BRI photometry, causing a poor fit (⁠|$\chi ^2_\nu = 5.7$|⁠).

3.2.3 Explanations for assumptions in SED fitting

There are two reasons why we chose the BC03 SSP model. First, it is more commonly used for galaxy evolution studies, which enable direct comparisons to earlier studies. Specifically, we will later compare our work against the local M_⋆–Z relation of AM13, which used stellar masses determined with the BC03 SSP model (Kauffmann et al. 2003).

Secondly, BC03 is the more conservative choice, as cigale only supports the BC03 and Maraston (2005, hereafter M05) SSP models. M05 was one of the first SSP models to include the thermally pulsating asymptotic giant branch (TP-AGB) phase. TP-AGB stars heavily affect the SED of galaxies at stellar ages of about 1 to 3 Gyr. Its effects are still debated (e.g. Kriek et al. 2010; Capozzi et al. 2016, and references therein); we refer readers to Conroy, Gunn & White (2009), which discussed differences in physical properties for these models.

We note that this age range is generally older than the ages of our galaxies, given our emission-line selection, thus TP-AGB stars are not expected to have a significant effect in our modelling. This is supported by the fact that stellar masses, which we derived with the M05 SSP, are only systematically lower by a median (mean) value of 0.14 (0.13) dex compared to BC03 (assuming a Salpeter (1955) IMF for both models).

A delayed τ star formation history is well-suited for young galaxies with ages < τ and is commonly used for both star-forming and quiescent galaxies at high redshifts (e.g. Papovich et al. 2011; Pacifici et al. 2013; Lee et al. 2015, 2018; Estrada-Carpenter et al. 2019). Furthermore, with our limited photometric data set, other star formation histories, such as those with episodic bursts, have more degrees of freedom to constrain.

3.2.4 Stellar mass comparisons

In panel (a) of Fig. 3, we examine how the new Spitzer/IRAC observations constrain the masses of the 28 galaxies. Here, we illustrate the masses derived from cigale including and excluding the new Spitzer/IRAC observations. As illustrated, the stellar masses estimated with or without the new observations are consistent for most of the galaxies with a dispersion below 0.1 dex. This suggests that the other galaxies without Spitzer measurements have robust stellar mass estimates from mostly optical data. In panel (b) of Fig. 3, we compare stellar masses calculated from cigale and a different SED fitting code, fast (Kriek et al. 2009). These fast estimates were derived by Ly et al. (2015b). To compare directly, we do not include the new Spitzer/IRAC 3.6 and 4.5 |$\hbox{$\mu $m}$| observations. While there are differences between the fast and cigale estimates, there is generally good agreement with a dispersion of 0.27 dex. The good agreement between cigale and fast indicates that we are able to conduct our M_⋆–Z analysis with the DEEP2 and |$\mathcal {MACT}$| samples.

In addition, we compare our stellar mass estimates against those obtained from modelling DEEP2 optical spectra (hereafter C17 Comparat et al. 2017). Here we briefly summarize the sample and modelling, and refer readers to C17 for more details. From the fourth DEEP2 data release, ≈23 000 unique galaxy spectra were selected with a redshift between 0.7 and 1.2. SED models were created using the firefly fitting code (Wilkinson et al. 2017), which uses a Maraston & Strömbäck (2011) SSP, three different stellar libraries, and three different IMFs. In the below comparisons, we adopt a Salpeter (1955) IMF for all stellar mass estimates, and use the C17 estimates that adopted the STELIB stellar library (Le Borgne et al. 2003).

Out of our 28 DEEP2 galaxies, 27 were modelled by C17 (DEEP2 #15 was not modelled). For BC03, we find that C17 stellar masses were higher by a median (mean) value of 0.47 (0.44) dex. For M05, C17 stellar masses were again higher by a median (mean) value of 0.62 (0.56) dex. The higher stellar masses measured by C17 is possibly due to the inability to constrain the Balmer stellar absorption lines. Specifically C17 masked regions affected by nebular emission lines, which included the Balmer lines. The best fits revealed significant stellar absorption, which was not seen from double Gaussian fitting by Ly et al. (2015b). We note that the average stellar mass uncertainty from C17 is 0.62 dex. This uncertainty is larger than that obtained from modelling broad-band optical and infrared data (0.17 dex). One of the factors contributing to the larger uncertainty is that obtaining significant detection of the continuum with spectroscopy is more difficult for these low-mass galaxies.

3.3 T_e-based oxygen abundances

Both [O iii] λ4363 and [O iii] λ5007 are collisionally excited emission lines where their flux ratio is dependent on the free electron kinetic temperature of the ionized gas, T_e. The cooling of the gas is controlled by collisional excitation of ionized atoms, such as single and doubly ionized oxygen, and radiation from these excited states. However, for metal-poor gas, cooling is difficult with the lack of ionized metals. Thus, the electron temperature of the gas is high and results in more collisions to the excited doubly-ionized oxygen state that produces the [O iii] λ4363 emission (Aller 1984). The gas-phase metallicity for our galaxies was determined by Ly et al. (2015b) by following previous direct metallicity studies and using the empirical relations of Izotov et al. (2006). Here, we briefly summarize the approach, and we refer readers to Ly et al. (2014) for more details. The electron temperature is determined from the flux ratio of [O iii] λλ4959,5007 against [O iii] λ4363. Using T_e and two emission-line flux ratios, [O ii] λλ3726,3729/Hβ and [O iii] λλ4959,5007/Hβ, the oxygen-to-hydrogen ratio (O/H) can be determined. A standard two-zone temperature model with T_e(O⁺)  = 0.7T_e(O⁺⁺)  + 3000 K was adopted (AM13). The median, mean, and dispersion in metallicity for the DEEP2 galaxies are 12 + log (O/H) = 8.17, 8.1, and 0.26, respectively.

4 RESULTS

We describe below the stellar population of these low-metallicity galaxies (Section 4.1), measurements of the M_⋆–Z relation (Section 4.2), comparisons to previous studies (Section 4.3), dependence on SFR for the M_⋆–Z relation (Section 4.4), and the selection function of our study (Section 4.5).

4.1 Stellar population

The 28 galaxies in our sample were originally classified as low-mass galaxies based on their optical photometry. However, infrared data are needed to observe the low-mass stars in these galaxies. Using the 3.6 |$\hbox{$\mu $m}$| (and 4.5 |$\hbox{$\mu $m}$| where available) photometry from Spitzer/IRAC and existing optical data, our SED models have confirmed that the 28 galaxies have low masses, with stellar masses between log (M_⋆/M_⊙) = 8.08 and 9.50 with a median (mean) of 8.72 (8.69). The good agreement in stellar mass measurements with and without Spitzer infrared data, as illustrated in Fig. 3(b), suggests that there is no evidence for an old (≳1 Gyr) population of low-mass stars in these galaxies. This result is driven primarily by the low luminosities observed at rest-frame 2 μm.

We note that we considered bottom-heavier IMFs by running cigale with a Salpeter (1955) IMF. As expected, the masses with the Salpeter (1955) IMF are systematically higher by 0.22 dex. While the stellar masses are higher, the results still support the lack of a significant old population of low-mass stars in these galaxies.

For our sample, we have spectroscopic measurements of Hβ and higher order Balmer lines (e.g. Hγ, Hδ). These measurements allow us to measure the SFRs using the Hβ luminosity corrected for dust attenuation using the Hγ/Hβ Balmer decrement (Ly et al. 2015b). Combining the Balmer-derived SFRs with derived stellar masses, the specific SFR (sSFR ≡ SFR/M_⋆) for these galaxies range from log (sSFR/yr⁻¹)  = –8.79 to –6.62 with a median and mean of –8.1 and –8.0, respectively.

4.2 M_⋆–Z relation

Our best fit of the M_⋆–Z relation illustrates that there is a strong evolution between z ∼ 0.1 and z ≈ 0.8. At a given stellar mass, the z ≈ 0.8 M_⋆–Z relation is lower than the relation from AM13 on average by 0.27 dex. This evolution follows |$(1+z)^{-1.45^{+0.61}_{-0.76}}$|⁠. The overall shape of the M_⋆–Z relation between AM13 and our results is similar, comprising of a steep rise in metallicity at low stellar masses then transitioning to a plateau at high stellar masses. Additionally, the overall shape of the M_⋆–Z relation is consistent with the relation found by Ly et al. (2016b).

4.3 Comparison with previous z ≈ 0.8 M_⋆–Z studies

Recent studies, such as Zahid et al. (2013, hereafter Z13) and Guo et al. (2016), have measured the evolution of the M_⋆–Z relation at intermediate redshifts. In these studies, strong-line metallicity diagnostics were used to determine chemical abundances. Specifically, Z13 used the Kobulnicky & Kewley (2004, hereafter KK04) calibration. Utilizing this calibration on our DEEP2 sample would yield metallicities that are 0.5–1 dex higher than those determined with the T_e method. This suggests that the local KK04 calibration is not valid for metal-poor galaxies at z ≈ 0.8. The use of different metallicity diagnostics inhibits a direct comparison against our results. However, relative comparisons against z ≈ 0.1 measurements using the same metallicity diagnostics can be examined.⁸

In Z13, a sample of 1254 galaxies at 0.75 < z < 0.82 was selected from the third data release⁹ of the DEEP2 Galaxy Redshift Survey. Here, we briefly summarize the sample and refer readers to Z13 for more details. Among the ∼50 000 spectra, galaxies were selected with [O ii] λ3727 and Hβ detections at S/N > 3. In addition, 17 X-ray galaxies were removed to limit AGN contamination. Stellar masses were determined from BRI-band photometry, and average Balmer stellar absorption was corrected for each of the selected galaxies.

In Fig. 6, we illustrate the evolution in metallicity as a function of stellar mass between z ≈ 0.1 and z ≈ 0.8 for Z13. Additionally, we extrapolate Z13 results to lower stellar masses using a linear fit, ΔZ ∝ 0.13 log (M_⋆/M_⊙), and compare it to the average evolution in metallicity of our samples (DEEP2, |$\mathcal {MACT}$|⁠, and DEEP2 + |$\mathcal {MACT}$|⁠). Here we take the average metallicity of our samples due to a limited sample size and the effects of the selection function at high masses (see Section 4.5). As shown in the figure, our evolution in metallicity is in good agreement with the extrapolated evolution of Z13 towards lower stellar masses. The difference in ΔZ between Z13 and our study is expected, because we are sampling two different stellar populations. For reference, Z13 galaxies are higher mass galaxies with stellar masses between log (M_⋆/M_⊙)  = 9.25 and 10.5, while our low-mass galaxies range from log (M_⋆/M_⊙)  = 8.08 to 9.50. As illustrated in Fig. 6, high-mass galaxies have accumulated most of their metallicity before z ≈ 0.8. Between z ≈ 0.8 and z ≈ 0.1, the chemical evolution for Z13 is low, ranging from ΔZ  = –0.21 to –0.08 dex. On the contrary, low-mass galaxies appear to undergo significant metal enrichment, with our samples (DEEP2, |$\mathcal {MACT}$|⁠, and DEEP2 + |$\mathcal {MACT}$|⁠) at ΔZ  = –0.29, –0.30, and –0.29 dex, respectively. Thus, a dwarf galaxy of M_⋆ ≈ 4 × 10⁸ M_⊙ at z ≈ 0.8 undergoes 1.6 times more enrichment than a massive galaxy of M_⋆ ≈ 10¹⁰ M_⊙ at the same redshift.

As a further test, we can directly compare our evolution in the M_⋆–Z relation to Ly et al. (2016b). We determined that the M_⋆–Z relation follows a |$(1+z)^{-1.45^{+0.61}_{-0.76}}$| evolution, such that metallicity is lower by ≈0.27 dex at z ≈ 0.8 compared to z = 0.1. This evolution is in agreement, within measurement uncertainties, of Ly et al. (2016b): |$(1+z)^{-2.32^{+0.52}_{-0.26}}$|⁠. We note that the higher dependence measured by Ly et al. (2016b) is due to a higher (i.e. more enriched) M_⋆–Z relation at z ≈ 0.07 than AM13.

4.4 SFR dependence

The idea that the M_⋆–Z relation has a secondary dependence on the SFR has been proposed by a number of observational and theoretical studies (e.g. Ellison et al. 2008; Lara-López et al. 2010; Mannucci et al. 2010; Davé et al. 2011; Lilly et al. 2013; Salim et al. 2014). Specifically, it has been suggested that higher SFRs can account for the lower metal abundances at higher redshifts, such that the M_⋆–Z relation is part of a larger non-evolving metallicity relation. To test this idea, we follow the approach of adopting a non-parametric method of projecting the M_⋆–Z–SFR relation on to 2D spaces. This was first implemented by Salim et al. (2014) and later applied to higher redshifts by Salim et al. (2015) and Ly et al. (2016b).

First, we consider how the M_⋆–Z relation depends on sSFR, which we illustrate in the left-hand panel of Fig. A1. The M_⋆–Z relation is divided into two sSFR bins, at the median of our DEEP2 + |$\mathcal {MACT}$| galaxies. Average measurements from composite spectra of AM13 are overlaid as grey squares. For reference, the local M_⋆–Z relation of AM13 is shown by the grey line. At a given stellar mass, the left-hand panel of Fig. A1 suggests that the metallicity for z ≈ 0.8 low-mass galaxies does not decrease as the (s)SFR increases.

Next, we consider how the metallicity and sSFR depend on mass. This is illustrated in the right-hand panel of Fig. A1. The galaxies are divided into two stellar mass bins, at the median of our samples. Galaxies from AM13 are overlaid as grey squares. In each stellar mass bin, the galaxies from AM13 demonstrate that there is a moderate negative correlation between metallicity and sSFR, as expected. However, the metallicities of the DEEP2 + |$\mathcal {MACT}$| galaxies do not decrease as the sSFRs increase. In the lower mass bin, there are a number of low-sSFR and low-metallicity¹⁰ galaxies (12 + log (O/H) ∼ 7.5), which go against what is predicted by Mannucci et al. (2010).

Our best fit yields t = −2.04 and p = 0.046 for a linear regression t-test. Thus, it suggests that we cannot rule out the null hypothesis (i.e. no correlation) at >95 per cent confidence. We note that a t-test of AM13 sSFR–Z relation with our DEEP2 + |$\mathcal {MACT}$| data yields t = 25.5 with p < 10⁻⁵ (>4σ). This suggests that we are able to rule out a strong sSFR–Z dependence.

In summary, we conclude that the M_⋆–Z relation at z ≈ 0.8 does not have a significant secondary dependence on SFR such that galaxies with higher sSFR have reduced metallicity. As illustrated in Figs A1 and A2, in each of the three projections, our galaxies display either a mild dependence or no dependence. Our result is in agreement with previous studies that have found a moderate or no SFR dependence of the M_⋆–Z relation (e.g. Pérez-Montero et al. 2013; de los Reyes et al. 2015; Salim et al. 2015; Guo et al. 2016; Sánchez et al. 2017). However, several studies have found a strong SFR dependence for galaxies in the local Universe (Lara-López et al. 2010; Lilly et al. 2013; Salim et al. 2014), and for high redshift galaxies, studies have found a similar trend but offset from the local relation (i.e. there is redshift dependence; Zahid et al. 2014; Salim et al. 2015).

4.5 [O iii] λ4363 selection function

The requirement to detect [O iii] λ4363 in our spectroscopic study leads to a concern of selection bias for our samples. Here, we briefly outline the effects on our results. We refer readers to Ly et al. (2016b) for an in-depth analysis.

The detection of the [O iii] λ4363 line is dependent on a combination of (1) the electron temperature/metallicity of the gas (Nicholls et al. 2014), and (2) the dust-corrected SFRs which determine the absolute strengths of the emission-line fluxes. At high SFRs, [O iii] λ4363 is detectable for a wide range of metallicities. As SFR decreases, only metal-poor galaxies can be detected in an emission-line flux-limited survey. The effects of the [O iii] λ4363 selection function is illustrated in the right-hand panel of Fig. A2 where sSFR decreases as metallicity increases, but at a lower rate than AM13. The difference in the slopes is the result of two factors at high and low metallicities. First, there is a selection towards metal-rich galaxies with high SFRs because those with low SFRs will not have [O iii] λ4363 detections and will fall below the flux limit cuts adopted by Ly et al. (2015b). Secondly, the DEEP2 + |$\mathcal {MACT}$| sample is lacking low-metallicity, high-sSFR galaxies. Unlike their metal-rich counterparts, these galaxies have detectable [O iii] λ4363 measurements.

5 CONCLUSIONS

We present new Spitzer/IRAC 3.6 |$\hbox{$\mu $m}$| (4.5 |$\hbox{$\mu $m}$| where available) photometry for 28 metal-poor strongly star-forming galaxies at z ≈ 0.8 from the DEEP2 Survey. These new measurements were necessary to better constrain the stellar masses of these galaxies by observing the light from low-mass stars. Our SED modelling of 0.35–3.6(4.5) |$\mu$|m data confirmed that these galaxies have low stellar masses, M_⋆ ≈ 10^8.1–10^9.5M_⊙.

Combining these stellar masses with metal abundances derived from the electron temperature method, and measurements from the |$\mathcal {MACT}$| survey, we determined that the M_⋆–Z relation evolves towards lower metallicity by ≈0.27 dex between z ≈ 0.8 and z = 0.1: ∝ |$(1+z)^{-1.45^{+0.61}_{-0.76}}$|⁠. Our evolution is in agreement within measurement uncertainties of Ly et al. (2016b): |$\propto (1+z)^{-2.32^{+0.52}_{-0.26}}$|⁠. We compared the evolution in metallicity from z ≈ 0.8 to z ≈ 0.1 against recent studies at intermediate redshifts. Specifically, we find good agreement with those reported by Z13 when extrapolated towards lower stellar masses. This suggests that lower mass galaxies (4 × 10⁸ M_⊙) chemically enriched their interstellar contents 1.6 times more rapidly than high mass galaxies (10¹⁰ M_⊙). Additionally, we measured the shape of the M_⋆–Z relation at z ≈ 0.8, which is consistent with the shape of local relation (AM13). Finally, we considered whether the M_⋆–Z relation has a secondary dependence on specific SFR. We determined an sSFR–Z relation of: |$\log ({\rm sSFR}) = -6.69^{+0.68}_{-0.76} - (0.17^{+0.09}_{-0.08}) \cdot [12+\log ({\rm O/H})]$|⁠. A linear t-test determined that we cannot rule out no dependence at >95 per cent confidence. However, a strong dependence, as determined for local galaxies (AM13), can be ruled out at >4σ confidence.

ACKNOWLEDGEMENTS

We thank the anonymous referee for providing constructive feedback that improved the paper. This work is based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory (JPL), California Institute of Technology (Caltech) under a contract with the National Aeronautics and Space Administration (NASA). Support for this work was provided by NASA through an award issued by JPL/Caltech under grant NNN12AA01C, and through a NASA traineeship grant awarded to the Arizona/NASA Space Grant Consortium. This research made use of astropy,¹¹ a community-developed core python package for Astronomy (Astropy Collaboration 2013). This research has made use of the NASA's Infrared Processing and Analysis Center (IPAC) Infrared Science Archive, which is funded by NASA and operated by the Caltech. This study makes use of data from the NEWFIRM Medium-Band Survey, a multi-wavelength survey conducted with the NEWFIRM instrument at the Kitt Peak National Observatory, supported in part by the National Science Foundation (NSF) and NASA.

Footnotes

REFERENCES

APPENDIX A: MASS–METALLICITY–SFR PLOTS

In this appendix, we provide different projections of the mass–metallicity–SFR relation. Fig. A1 compares gas metallicity against stellar mass (left-hand panel) and sSFR (right-hand panel). Here, binning was performed along sSFR and stellar mass, respectively. In Fig. A2, we illustrate SFR as a function of stellar mass in different metallicity bins (left-hand panel), and how the sSFR depends on metallicity (right-hand panel).