THE MASS–METALLICITY AND LUMINOSITY–METALLICITY RELATIONS FROM DEEP2 AT z ∼ 0.8

Our z ∼ 0.8 sample comes from the DEEP2 survey. The DEEP2 team used the DEIMOS (Faber et al. 2003) multi-object spectrograph on the Keck telescope to measure spectra for galaxies in four fields covering 3.5 deg² down to a limiting magnitude of R_AB = 24.1. The survey contains spectra for ∼50, 000 galaxies, the majority of which are in the redshift range 0.7 < z < 1.4. The relatively high-resolution (R ⩾ 5000) spectra cover the nominal spectral range 6500–9100 Å. For this study, we used the third data release¹ data and the one-dimensional spectra were obtained from the Horne extraction (Horne 1986).

BRI photometry was obtained by the DEEP2 team for these objects from imaging carried out using the CFH12K camera on the 3.6 m Canada–France–Hawaii Telescope (CFHT; Coil et al. 2004). For a subsample of the data, K_s-band photometry was available in addition to the BRI photometry. These data were obtained using the Wide Field Infrared Camera on the 5 m Hale telescope at Mt. Palomar (Bundy et al. 2006). All magnitudes in this study are in the AB system.

From the 46,337 unique objects in the survey, we begin by selecting 31,656 galaxies for which we have secure redshift determinations from the DEEP2 team (Q ⩾ 3, see the Web site for more details). For our determination of metallicity, we use the R₂₃ strong-line diagnostic, first calibrated by Pagel et al. (1979). We apply a more recent R₂₃ calibration based on the stellar population synthesis and photoionization model calibrations from Kewley & Dopita (2002), and updated in Kobulnicky & Kewley (2004). In the text, we refer to this calibration as KK04. The R₂₃ method is a parameterization of metallicity as a function of the ratio of the oxygen nebular emission ([O ii] λ3727 doublet, [O iii] λ4959, and [O iii] λ5007) to Hβ. The method is formally defined in Section 3.3. Given the nominal spectral range of the DEEP2 survey, we can sufficiently bracket the required emission lines within the 0.75 < z < 0.82 redshift range. Due to a varying object position on the slit mask, the actual spectral range varies from object to object and we require that the spectra cover the wavelength range of 3720–5020 Å, leaving us with 2738 galaxies. We were unable to measure the metallicity in 234 galaxies due to our inability to fit the oxygen or Hβ emission lines, leaving us with 2504 galaxies.

We calculate the R₂₃ ratios using the continuum-normalized flux (see the Appendix for full description). In the Appendix, we show that the pseudo-EW is equal, to within the errors, to the EW and refer to it hereafter as the EW. The errors on our EW and line ratio determination come from propagating the measurement uncertainties in the spectrum. In selecting galaxies for analysis, we require that the S/N Hβ>3, EW(Hβ)>4 Å, and the error in the R₂₃ line ratio be less than 2. At high metallicities, the line strength of the [O ii] and [O iii] line diminishes due to the effectiveness of line cooling of the H ii region. In order to avoid biasing our MZ relation to lower metallicities, we do not place a signal-to-noise ratio (S/N) cut on these lines. We normalize the line flux to the continuum by fitting a polynomial to the underlying continuum and dividing the spectrum by this fit. We require that the fit to the continuum be 1σ_c above zero, where σ_c is the standard deviation of the line-subtracted spectrum (see the Appendix for more detail). These cuts leave us with 1713 galaxies.

Strong-line methods of metallicity determination assume a star-forming population of galaxies and are not applicable to active galactic nuclei (AGNs). We identify all galaxies with log(R₂₃)>1 as AGNs and remove them from our sample (L. J. Kewley et al. 2011, in preparation). Furthermore, using the color separation for blue and red galaxies parameterized by Willmer et al. (2006) for the DEEP2 survey, Weiner et al. (2007) conclude that a very small fraction of blue galaxies have AGNs whereas at least half of the red galaxies with detectable emission lines show evidence of AGN emission. Similar to T04, we select the blue star-forming galaxies to analyze, as described in the following section. We remove the red galaxies from our sample and are left with 1631 blue emission-line galaxies. The first and second columns of Table 1 summarize our selection. The median for EW(Hβ), S/N Hβ, and σ_R23 of our selected sample is 12.1, 10.0, and 0.65, respectively.

Willmer et al. (2006) studied the red and blue galaxy luminosity functions by dividing the DEEP2 sample at the trough of the bimodal U − B color distribution. The U- and B-band absolute magnitudes are synthesized by relating the observed magnitudes to spectral energy distributions (SEDs) of nearby galaxies and inferring a rest-frame absolute magnitude from this SED. We follow a similar procedure and synthesize the U- and B-band absolute magnitudes using the filters of Buser (1978) and Ažusienis & Straižys (1969), respectively. The red and blue galaxy color division found by Willmer et al. (2006) is given by

$$\begin{equation} U-B = 1.0\hbox{--}0.032(M_{B} + 21.5). \end{equation} \tag{ 1 }$$

The color division has been converted to AB magnitudes using Table 1 of Willmer et al. (2006). In Columns 3 and 4 of Table 1, we examine the cuts from our selection with respect to the galaxy color.

The top left panel of Figure 1 shows the color–magnitude diagram and the solid red line is the color division given by Equation (1). The other three panels give the absolute B-band magnitude, stellar mass (derived in Section 3.1), and U − B color distribution, respectively. The black histogram gives the full sample of 4198 DEEP2 galaxies between 0.75 < z < 0.82. We refer to this sample as the DEEP2 Full sample. Using the U − B color division, we split the DEEP2 Full sample into subsamples of red and blue galaxies. The histograms of these subsamples are plotted in red and blue and we refer to these subsamples as the DEEP2 Red and DEEP2 Blue samples, respectively. The gray histogram is the distribution of our selected sample of 1631 galaxies described in Section 2.2 and we refer to this as our DEEP2 Selected sample. The median properties of these samples are given in Table 2.

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The absolute B-band magnitude distribution in the top right panel of Figure 1 shows a range of −19.0>M_B > − 23 for the DEEP2 Full sample. Faber et al. (2007) showed that luminosity functions derived for blue galaxies from the DEEP2 data have an M*_B = −21.15 in our selected redshift range. Our DEEP2 Selected sample consists of galaxies around the knee of the blue galaxy luminosity function (Schechter 1976) with ∼15% (245/1631) of our Galaxies brighter than M*_B. The bottom left panel of Figure 1 shows that the U − B color range is 0 < U − B < 1.5 for the DEEP2 Full sample. The color division between red and blue is at U − B ∼ 1 and the bimodal distribution is clearly highlighted by the well-separated peaks in the blue and red histograms. The bimodal color distribution separates red early-type galaxies from blue late-type star-forming galaxies (Strateva et al. 2001; Hogg et al. 2003; Baldry et al. 2004; Willmer et al. 2006). The mass distribution shown in the bottom right panel of Figure 1 reflects this bimodality, whereby the red galaxies in our sample are not only brighter, but more massive and separated from the lower mass blue galaxies.

By comparing the histograms and median properties in Figure 1, it is clear that the DEEP2 Red sample of galaxies is brighter and more massive than the DEEP2 Blue sample. However, when comparing the histograms and median properties of our DEEP2 Selected sample, which is comprised solely of blue galaxies, with the DEEP2 Blue sample, there is no selection bias toward the brighter or more massive galaxies as one may expect given the selection criteria. We conclude from the comparison of the properties of the DEEP2 Selected and DEEP2 Blue samples that our selected galaxies are representative of the population of blue star forming of galaxies in the DEEP2 survey at 0.75 < z < 0.8.

We estimate galaxy stellar masses by comparing photometry with stellar population synthesis models in order to determine the mass-to-light ratio (Bell et al. 2003; Fontana et al. 2004). We use the Le Phare² code developed by S. Arnouts and O. Ilbert to estimate the galactic stellar mass. Le Phare is a set of FORTRAN routines developed to determine the photometric redshifts of galaxies. If the redshift is known, it can be held fixed while other physical parameters of the galaxy are determined (i.e., stellar mass) by SED fitting.

The stellar templates of Bruzual & Charlot (2003) and an IMF described by Chabrier (2003) are used to synthesize magnitudes. The 27 models span three metallicities and seven exponentially decreasing star formation models (SFR ∝e^−t/τ) with τ = 0.1, 0.3, 1, 2, 3, 5, 10, 15, and 30 Gyr. We apply the extinction law of Calzetti et al. (2000) allowing E(B − V) to range from 0 to 0.6 and stellar population ages ranging from 0 to 13 Gyr. Ilbert et al. (2010) provide a more detailed description of how the physical parameters are estimated.

We are able to determine stellar masses using BRI and K_s-band data for 454 of our selected galaxies. The K-band survey of the DEEP2 fields covers 60% of the area so K-band photometry is not available for all galaxies in the survey (Bundy et al. 2006). In order to test for systematic variation in the stellar mass determination for the remaining sample of galaxies with only BRI photometry, we compare the stellar masses for our 454 galaxies determined with BRI and K_s-band data with stellar masses determined for the same galaxies with just the BRI bands. The left panel of Figure 2 shows the comparison. The x-axis is the mass determination from BRI band data and the y-axis is the mass determination from BRIK_s-band data. The dashed line is the one-to-one correspondence and the solid line is a linear bisector fit to the data.

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We perform a bootstrap linear fit by taking the bisector of the X versus Y and Y versus X regression using the routine boot_xyfit.pro from the IDL astronomy users library. Bootstrapping is a non-parametric statistical method of inferring errors whereby errors are calculated from the distribution of the fitted parameters for many fits to randomly selected subsample of the data. In order to minimize the covariance between the slope and intercept, we zero point the data by subtracting 10 from the logarithm of the stellar mass. The linear fit is given by

$$\begin{equation} X_{{\it BRIK}_s} = (-0.042\pm 0.006) - (1.00\pm 0.01) X_{\it BRI}, \end{equation} \tag{ 2 }$$

where $X_{\it BRI} = M_{\it BRI} - 10, X_{{\it BRIK}_s} = M_{{\it BRIK}_s} - 10,$ and M_BRI and $M_{{\it BRIK}_s}$ are the stellar masses determined by using three and four bands, respectively. The slope is consistent with unity. To first order, the absence of the K_S-band data results in only a ∼0.04 dex overestimate of the stellar mass.

The DEEP2 galaxies with K_s-band data from the full sample are generally brighter and more massive than our selected galaxies, while the color distribution is consistent with our selected sample. The K_s-band data for our selected sample span the full range of mass, color, and absolute B-band magnitude and the medians are 9.81, 0.68, and −20.7, respectively. To check for any systematic variations with galaxy properties, we fit half of the data that are below the median in mass, color, and magnitude, respectively, and find that the fits are all consistent within the errors. When K_s-band photometry is unavailable, we subtract 0.04 dex from the mass to correct for the systematic overestimate. After applying this correction, there is a 0.12 dex dispersion between the one-to-one correspondence of the two mass estimates.

We have redetermined the local MZ and LZ relations from ∼21, 000 galaxies in the SDSS data release 7 (see the Appendix). We compared our stellar mass determination using Le Phare with those determined by the MPA/JHU team from fitting the photometry and a Kroupa IMF (Kroupa 2001). Both methods use stellar population synthesis to fit the photometry and we expect the estimates to only vary by a constant offset. The right panel of Figure 2 shows this comparison. The dashed line is the one-to-one correspondence and the solid line is a bootstrap linear bisector fit to the data as described earlier. The linear fit is given by

$$\begin{equation} X_{\rm{LP}} = (0.198\pm 0.001) + (1.035\pm 0.003)X_{{\rm SDSS}}, \end{equation} \tag{ 3 }$$

where X_LP = M_LP − 10 and X_SDSS = M_SDSS − 10. M_LP and M_SDSS are the stellar masses determined using Le Phare and those provided by the MPA/JHU team, respectively. As before, to minimize the covariance of the slope and intercept, we zero point the data by subtracting 10 from the masses. The slope is near unity and to first order the estimates differ by only a constant offset of 0.198 dex (a factor of ∼1.6). Taking into account this constant offset, there is a 0.14 dex dispersion in the one-to-one correspondence between the two mass estimates.

For local galaxies it has been shown that the errors between photometric and dynamical mass are typically ∼0.2 dex (Drory et al. 2004). In this study, we observe galaxies at z ∼ 0.8 and therefore expect even greater errors in the photometric determination of mass. Moreover, Conroy et al. (2009) have shown that additional uncertainties in estimates of physical parameters from stellar population synthesis modeling result from the choice of IMF, dust model, and spectral libraries. However, the full impact of these effects on the absolute calibration of the physical parameters is still not well understood. Therefore, when investigating the evolution of the MZ relation, we take care to have a consistent relative calibration of the physical parameters between the samples. The absolute calibration remains uncertain.

When measuring EWs, it is necessary to make a correction for underlying stellar absorption in the Balmer lines. Kobulnicky & Phillips (2003) have estimated an average correction of 2 Å in the EW(Hβ) for the underlying Balmer absorption using 22 galaxies from the spectroscopic galaxy atlas of Kennicutt (1992). The galaxies in the Kennicutt atlas have a spectral resolution of 5–8 Å. We expect the effects of Balmer absorption to be greater in galaxy spectra with lower resolution because the flux of the narrow emission line is spread over a broader region of the absorption trough. Presumably for this reason, Cowie & Barger (2008) find a correction of 1 Å by stacking spectra observed using DEIMOS onboard Keck with a spectral resolution of 3.5 Å. The DEEP2 data have also been obtained using DEIMOS but with a smaller spectral resolution of 1.4 Å.

Unfortunately, the low S/N in our data does not allow us to investigate the Balmer absorption in individual galaxy spectra. However, the strength of the Balmer absorption is a function of the age of the stellar population and is therefore expected to correlate with physical parameters of the galaxy such as stellar mass. In order to investigate the effects of stellar absorption on our measurement, we stack our spectra in bins of stellar mass and examine the effect of the Balmer absorption on the EW(Hβ).

We stack our spectra into seven mass bins. We normalize each spectrum to the continuum by dividing by the median value of the continuum between 4800–4815 Å and 4900–4915 Å. We then stack ∼230 spectra in each mass bin by interpolating all spectra to have the same wavelength vector and take the median of the flux corresponding to each wavelength element. We get similar results if we take the mean rather than the median. The left panel of Figure 3 shows an example of a stacked spectrum. We see that the Hβ emission line sits on a broad absorption trough. The EW(Hβ) correction accounts for the integrated flux of the emission line (red curve) that lies below the continuum (blue curve) and would not be included when measuring the EW(Hβ) in lower S/N spectra due to the absorption (green curve). To obtain a correction, we measure the EW(Hβ) for the stacked spectrum and a corrected spectrum with the absorption removed. The right panel shows the correction to the EW(Hβ) as a function of stellar mass. The red line is a linear least-squares fit given by

$$\begin{equation} \rm{EW}_{{\rm corr}} = (1.01 \pm 0.05) + (0.38 \pm 0.08)x, \end{equation} \tag{ 4 }$$

where x = log(M_*) − 10. EW_corr is the amount added to the EW(Hβ) to correct for underlying absorption. We emphasize that the correction given by Equation (4) is sensitive to the fitting procedure. A different method (using a smaller continuum window, for example) may yield a different correction. The median correction to the EW(Hβ) in our sample is 0.9. We note that this correction does not significantly affect our derived MZ relation owing to the fact that the median correction of 0.9 Å is small compared to the median EW(Hβ) of 12.1 Å. This small correction translates to a median increase of 0.04 dex in metallicity.

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We perform a simple test in order to assess the effect of varying the spectral resolution on the Balmer absorption correction. We convolve our stacked spectra with Gaussians of varying widths. We find that the Balmer correction is sensitive to the spectral resolution. The correction increases with smaller spectral resolution and the slope of the correction with respect to stellar mass flattens. We speculate that the larger correction found by Kobulnicky & Phillips (2003) may be attributed to the lower spectral resolution of their data. In a future study, using higher quality data we hope to quantitatively establish the magnitude of this effect.

We use the strong-line diagnostics of KK04 as presented in KE08 in order to obtain an estimate of galaxy gas-phase metallicities. The diagnostics are based on the Kewley & Dopita (2002) R₂₃ theoretical calibrations. In both diagnostics, the metallicity is determined using the R₂₃ and O₃₂ ratios. We calculate these ratios from our EWs such that

$$\begin{equation} R_{23} = \frac{\rm{EW}([{\rm O}\,\mathsc {ii}]) + \rm{EW}([{\rm O}\,\mathsc {iii}])}{\rm{EW}(\rm H{\beta })} \end{equation} \tag{ 5 }$$

and

$$\begin{equation} O_{32} = \frac{\rm{EW}([{\rm O}\,\mathsc {iii}])}{\rm{EW}([{\rm O}\,\mathsc {ii}])}, \end{equation} \tag{ 6 }$$

where EW([O ii]) is for the [O ii] doublet and EW([O iii]) is taken to be 1.33 × EW([O iii] λ5007). We have used the assumption that the ratio of the fluxes of [O iii] λ5007 to [O iii] λ4959 is 3 (Osterbrock 1989). We have fitted the [O iii] λ4959 line because the widths of the Hβ, [O iii] λ4959, and [O iii] λ5007 line fits are tied in order to increase the S/N of the fit, as described in the Appendix, but the S/N in the EW([O iii] λ5007) is higher and the EW([O iii] λ4959) is inferred from theoretical considerations for the metallicity determination.

We use Equations (A4) and (A6) given in the Appendix of KE08 to derive the ionization parameter and metallicity, respectively. The R₂₃ method for determining metallicities is known to be sensitive to the ionization parameter. The ionization parameter characterizes the ionization state of the gas and quantitatively represents the number of ionizing photons per second per unit area divided by the hydrogen density. The ionization parameter has the units of velocity and can be thought of as the maximum velocity of the ionization front through the nebula. The metallicity and ionization parameter are interdependent. In order to obtain a consistent measurement of the metallicity and ionization parameter an iterative scheme is used, the details of which are provided in the Appendix of KE08. Furthermore, all metallicities used in this study for comparison that are not explicitly calculated using the KK04 calibration are converted to be consistent using the conversions provided in KE08.

Figure 4 shows the R₂₃ (top) and O₃₂ (bottom) line ratios for our sample. The gray pluses are the individual measurements and the black filled circles are the data sorted into 15 mass bins of equal number of data points. The median values of the R₂₃ and O₃₂ line ratios are 5.1 and 0.6 and median errors are 0.6 and 0.06, respectively. Both the R₂₃ and O₃₂ line ratios are sensitive to the metallicity and the relation between stellar mass and the line ratios can be attributed to the relation between stellar mass and metallicity.

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Metallicity is not a monotonic function of R₂₃, but rather is doubly valued for a given ratio. A particular value of R₂₃ corresponds to two different metallicities, one on the higher metallicity branch and one on the lower metallicity branch. The peak of the R₂₃ ratio occurs at 12 + log(O/H) ≈ 8.4. This degeneracy is due to the fact that on the lower branch R₂₃ scales with metallicity because the intensity of the collisionally excited [O ii] and [O iii] lines scales with the abundance. On the upper branch, nebular cooling, which results from collisional excitation followed by photon emission, effectively cools the nebula decreasing the electron temperature leading to a decrease in the rate of collisional excitation of the [O ii] and [O iii] lines. In order to break this degeneracy, generally other line ratios such as [N ii]/H_α are used. However, in our sample, these lines are not observed and the metallicity is assumed to lie on the upper branch. This assumption breaks down at lower masses. Looking at the R₂₃ mass relation in Figure 4, a turnover appears to occur at about log(M_*) ∼ 9.2 and we revisit this issue in Section 4.

The top panel of Figure 5 shows stellar mass and metallicity measured for our sample of 1631 galaxies. The bottom panel shows binned data with a boxcar smoothing. In determining the metallicity, we have assumed that all galaxies fall on the upper branch of the KK04 metallicity diagnostic. T04 have shown that in the local universe the MZ relation extends down to a stellar mass of M_* = 10^8.5 M_☉ with no break in the slope. We work under the assumption that the MZ relation at z ∼ 0.8 extends to at least M_* ∼ 10⁹ M_☉ with no break in slope. Under this assumption, we interpret the break in the slope at M_* = 10^9.2 M_☉ observed in the bottom panel of Figure 5 to be caused by the misplacement of lower branch galaxies on the upper branch. This turnover mass is further evidenced by the R₂₃ ratio as a function of stellar mass seen in Figure 4. We take a lower mass limit, indicated by the vertical dashed line in the bottom panel of Figure 5, of M_* = 10^9.2 M_☉ to fit our MZ relation. We note that 283 of our 1631 galaxies fall below this limit, leaving us with 1348 galaxies from which we determine the MZ relation.

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We parameterize the MZ relation with a quadratic function of the form

$$\begin{equation} 12 + \log (\rm O/H) = A + Bx + Cx^2, \end{equation} \tag{ 7 }$$

where x = log(M_*) − 10. Our data and fit residuals are not normally distributed so we apply a standard non-parametric bootstrapping technique in determining the fit parameters and errors. One of the underlying assumptions of the bootstrapping method is that the observed distribution reasonably approximates the parent distribution. Under this assumption and the assumption of independence of the sample, properties determined from many independent random subsamples of the data should be normally distributed. We begin by randomly selecting, with replacement, 1348 galaxies from our sample of 1348 galaxies. Meaning, within a random subsample some data points may be selected more than once while others may not be selected at all. We then bin these randomly selected galaxies by sorting them into 15 equally populated mass bins. The mass and metallicity in each bin are determined by taking the median of the data in the bin. We perform a least-squares quadratic fit to the binned data using the routine poly_fit.pro in IDL. We randomly resample and fit the data 10,000 times and take the mean and standard deviation of this distribution of fitted parameters, which are normally distributed, as the fit parameters and errors for the MZ relation.

The MZ relation is best fitted by

$$\begin{equation} 12 + \log (\rm O/H) = 8.923 + 0.24 \, x - 0.06 \, x^2, \end{equation} \tag{ 8 }$$

with the 1σ errors in each of the parameters in Equation (8) given by σ_A = 0.007, σ_B = 0.01, and σ_C = 0.03. Figure 6 shows the DEEP2 MZ relation at z ∼ 0.8 compared to the local MZ relation from SDSS (see the Appendix). The black filled circles are the data sorted into 15 mass bins. Each bin contains ∼90 data points and the errors on the data are determined by randomly selecting ∼90 data points in each bin and taking the median of the subsample. We take the standard deviation of this distribution as the error in each bin. We note that this scatter characterizes the distribution of metallicities within each mass bin and therefore accounts for both measurement uncertainties and intrinsic scatter in the metallicity determination. The gray lines are the 16% and 84% percentile contours of the data. The large dispersion at the high-mass end is due to the large interval in mass covered by the highest mass bins.

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Overall, we find that the high-mass (M > 10^10.5 M_☉) DEEP2 galaxies have similar metallicities (within the errors of ±0.05 dex) to local galaxies at the same stellar mass. At lower masses (M < 10^10.5 M_☉), the DEEP2 galaxies have lower metallicities than the SDSS sample for a given stellar mass, up to a Δlog(O/H) ∼ 0.15 dex.

Figure 7 shows the LZ relation derived from the DEEP2 sample and the local sample from SDSS. Similar to the MZ relation, the LZ relation is determined for galaxies with M_* > 10^9.2 M_☉. The filled circles are the median metallicities in 15 luminosity bins. The solid curve is a linear fit to the binned data and is parameterized by the equation

$$\begin{equation} 12 + \log (\rm O/H) = (8.909 \pm 0.006) - (0.117 \pm 0.008)X_{B}, \end{equation} \tag{ 9 }$$

where X_B = M_B + 21. The errors in the fit and binned data of the LZ relation are derived in the same manner as for the MZ relation. The gray lines are the 16% and 84% percentile contours of the data. The dashed curve is the local LZ relation from SDSS taken from the Appendix of this paper. The fit made is over the full range of magnitudes (−21 < M_B < −18) of the local LZ relation. However, the local LZ relation appears to turn over at M_B < −20. The dot-dashed curve is a fit to the linear part of the local LZ relation with M_B > − 20. The slope of this fit and the DEEP2 LZ relation are consistent to within the errors. KK04 find that the slope of the LZ relation for z = 0.6–0.8 and z = 0.8–1.0 is −0.117 ± 0.017 and −0.134 ± 0.032, respectively. To within the errors, the slopes derived by KK04 agree with DEEP2 and local LZ relation slopes as well.

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We list and address some key assumptions made in this paper.

• 1.  
  All galaxies with M_* ⩾ 10^9.2 M_☉ are on the upper branch of the R₂₃ diagnostic. At the lower mass end of the DEEP2 MZ relation, the dispersion is small and consistent with the dispersion found in the local MZ relation (T04). This small dispersion suggests that at z ∼ 0.8, the vast majority of galaxies with M_* > 10^9.2 M_☉ are on the upper metallicity branch of the R₂₃ diagnostic. Additionally, T04 have observed a continuous slope down to M_* ∼ 10^8.5 M_☉. A breakdown of this assumption would result in the R₂₃ measure of metallicity in low-metallicity galaxies to be significantly overestimated (∼1 dex) resulting in a flattening of the MZ relation at lower masses. This flattening is observed to occur at M_* = 10^9.2 M_☉ and given the small dispersion, we hypothesize that misplacement on the upper branch is minor above this mass. Near-infrared spectroscopy to obtain additional line ratios for a representative subsample of DEEP2 galaxies is needed to test this hypothesis.
• 2.  
  Metals are instantaneously recycled. This approximation was first introduced by Schmidt (1963). The approximation is valid when metals produced in massive stars, such as oxygen, are considered and if the star formation rate (SFR) is not subject to extreme variations on short timescale (Pagel 1997). From their study of DEEP2 galaxies since z = 1.1, Noeske et al. (2007b) determine that the dominant form of evolution is a gradual decline in star formation.
• 3.  
  We have attempted to remove AGN using empirical limits on the R₂₃ ratio and the color bimodality. This removes most of the galaxies whose emission is dominated by AGN, but composite galaxies in our sample may be blue and not exceed the empirical R₂₃ limit. AGN contamination in composite galaxy spectra increases the R₂₃ ratio due to the high [O iii]/Hβ ratio. On the upper metallicity branch of the R₂₃ diagnostic, the metallicity is a monotonically decreasing function of R₂₃. Therefore, AGN contamination will lower the metallicity estimate. However, due to their relatively small numbers in the DEEP2 blue galaxy sample (Weiner et al. 2007) and the small dispersion in the MZ relation, AGN contamination is likely to play a minor role in the MZ relation (Lamareille et al. 2009). Near-infrared spectroscopy to obtain additional AGN-sensitive emission-line ratios is required to verify this assumption.
• 4.  
  Since its introduction by Salpeter (1955), the initial stellar mass function (IMF)—describing the mass distribution of stars at birth—has largely been taken to be universal and invariant. Indirect evidences for variations in the local IMF have been provided by the comparison of Hα emission to the far-ultraviolet flux (Meurer et al. 2009) and the Hα flux to broadband color index (Hoversten & Glazebrook 2008). Comparison of the rate of luminosity evolution to that of color evolution provides indirect observational evidence for a possible redshift evolution in the IMF (van Dokkum 2008). Furthermore, IMF variations have been cited as the possible cause of the MZ relation (Köppen et al. 2007). We work under the assumption that the IMF is universal.
• 5.  
  MZ and LZ relation studies assume that the absence of low surface brightness galaxies (LSBGs) does not significantly bias the determination of the MZ and LZ relations. Impey & Bothun (1997) point out that LSBGs will be absent in magnitude-limited surveys. However, by comparing photometry in overlapping fields where both CFHT and Hubble Space Telescope imaging is available, no galaxies brighter than the magnitude limit of R_AB = 24.1 are found to be lost due to low surface brightness (Simard et al. 2002; Willmer et al. 2006). Melbourne et al. (2007) come to similar conclusions regarding the loss of LSBGs from deep imaging in the GOODS-N field.

In many previous studies, luminosity has been taken as a proxy for mass (Kobulnicky & Koo 2000; Pettini et al. 2001; Garnett 2002; Kobulnicky et al. 2003; Kobulnicky & Kewley 2004; Maier et al. 2004; Shapley et al. 2004, 2005). However, it has been recognized that the evolution in the LZ relation cannot straightforwardly be attributed to metallicity evolution, but that luminosity evolution must also be considered. By comparing Figures 6 and 7, we see that the offset in metallicity in the MZ relation is significantly smaller than the offset in the LZ relation. Lamareille et al. (2009; among others) suggest that the differential evolution in the LZ and MZ relations results from an evolution in the mass-to-light ratio. They estimate the evolution such that

$$\begin{equation} \Delta M_{B} = a^{-1} \times [\Delta \log (\rm O/H)^M - \Delta \log (\rm O/H)^L], \end{equation} \tag{ 10 }$$

where a is the slope of the LZ relation and Δlog(O/H)^M and Δlog(O/H)^L are the differences in metallicity at a fixed stellar mass and fixed B-band magnitude in the MZ and LZ relations, respectively. Equation (10) assumes that the metallicity evolution is characterized by the MZ relation and that additional evolution inferred from the LZ relation is due to evolution of the luminosity.

We estimate the evolution of the B-band luminosity as a function of stellar mass from Equation (10). We take the difference between the local and DEEP2 LZ relation, Δlog(O/H)^L, to be the average difference between the binned DEEP2 data and the fit to the local LZ relation over all magnitudes (see Figure 7). Consequently, Δlog(O/H)^L = 0.20 ± 0.03 dex and a = −0.11. We take Δlog(O/H)^M to be the difference between the DEEP2 binned data and local MZ relation fit. The difference is parameterized by

$$\begin{equation} \Delta \log (\rm O/H)^M = (0.12\pm 0.01) - (0.08\pm 0.02)x, \end{equation} \tag{ 11 }$$

where x = log(M_*) − 10. Here we have performed a linear least-squares fit using poly_fit.pro and the errors are determined from the residuals of the fit and do not account for observational uncertainties.

Figure 8 shows the B-band luminosity evolution inferred from our comparison of the DEEP2 MZ and LZ relations. Combining Equations (10) and (11), we get

$$\begin{equation} \Delta M_{B} = (0.68\pm 0.06) + (0.7\pm 0.1){\rm x}, \end{equation} \tag{ 12 }$$

the B-band luminosity evolution of blue star-forming galaxies between z ∼ 0.8 and the local galaxy population as a function of stellar mass. This is shown in Figure 8 by the solid line.

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It has been shown that the luminosity functions of blue galaxies evolve with time (Ilbert et al. 2005; Blanton 2006; Willmer et al. 2006; Faber et al. 2007). These studies conclude that M*_B has dimmed by ∼1 mag since z ∼ 0.8, consistent with the evolution observed in our sample at the higher stellar mass end. A differential evolution in the B-band Tully–Fisher relation has also been observed since z ∼ 1 and is consistent with the observed luminosity evolution (Weiner et al. 2006). Noeske et al. (2007b) show that the star formation as a whole was higher at z ∼ 1 and that the SFR gradually declines with galaxies spending 67% of their lifetime since z = 1 with SFR that are within a factor of two of their average and 95% of their time within a factor of four. In an accompanying letter, Noeske et al. (2007a) find that initial onset and rate of decline in star formation are functions of redshift and galaxy mass with less massive galaxies having later initial onsets with a lower rate of decline and consider this an important component of downsizing (Cowie et al. 1996). The absolute B-band luminosity is a tracer of star formation and the observed differential evolution with respect to stellar mass shown in Figure 8 may be attributed to this type of downsizing.

There are considerable difficulties in making a comparison of the MZ relation owing to the varying quality and type of data and the different methodologies and sample selections. The systematic differences among strong-line metallicity calibrations have been investigated by KE08. They derived conversions that reach agreement among calibrations to within ±0.05 dex in metallicity. KE08 conclude that while absolute metallicity values are uncertain, relative metallicities (such as MZ relations) can be reliably compared, providing that the metallicities have been converted into the same base calibration.

Though offsets between different metallicity calibrations can now be removed, the systematic effects on differing measurements of stellar mass have yet to be fully explored. Moreover, comparisons between spectral and photometric methods have not been rigorously investigated and the systematic effects of the photometric bands used in determining stellar mass remain uncertain. These problems are further compounded by the fact that many of the selection criteria in these studies may be a function of redshift (i.e., S/N of flux or EW, minimum values of flux or EW, color, etc.) and therefore the samples from which the MZ relations are determined may not be comparable even if similar selections are used.

Several authors have investigated the MZ relation covering the redshift interval examined in this study (z = 0.75–0.82). Figure 9 compares our MZ relation (solid curve) with previously derived relations from Savaglio et al. (2005; dot-dashed), Cowie & Barger (2008; triple-dot-dashed), and Lamareille et al. (2009; long dashed line). All metallicities have been converted to the KK04 calibration using the conversions in KE08. We have attempted to make the stellar masses consistent with ours by converting all the determinations to the Chabrier IMF used in this study. The relations plotted only cover the stellar mass range over which they were determined.

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The first attempt to investigate the MZ relation at intermediate redshifts was made by Savaglio et al. (2005) using the Gemini Deep Deep Survey. This sample consists of 28 galaxies from the Gemini Deep Deep Survey with emission in [O ii], Hβ, and [O iii] at the 3σ level covering the redshift range of z = 0.40–0.98. This sample consists of galaxies designated as late (7/28) and intermediate type (21/28). This sample is augmented with 28 galaxies from the Canada France Redshift Survey (Lilly et al. 1995). The dot-dashed fit in Figure 9 is a linear bisector fit of the S05 mass and metallicity. Though Savaglio et al. establish an MZ relation at higher redshifts, the small sample size and selection in addition to the fitting method do not allow us to make a direct comparison with our determination.

Lamareille et al. (2009) study the evolution of the MZ relation by splitting their sample into three redshift ranges. They find that the most massive galaxies undergo the most evolution at z ∼ 0.8, implying that the slope of the MZ relation flattens out at higher redshifts. However, L09 do not find a strong Spearman rank correlation coefficient, thus hindering a rigorous statistical analysis. The relation shown in Figure 9 (long-dashed line) is a linear fit to average metallicities in four mass bins for ∼130 galaxies in the redshift range of z = 0.6–0.8. The galaxies are selected to have S/N>4 in the flux of the [O ii], Hβ, and [O iii] emission lines. The flattening of the slope at higher redshifts may possibly be a consequence of the S/N cut on the [O ii] and [O iii] lines. These cuts may be a function of redshift and bias against higher metallicity galaxies generally found at higher stellar masses. At lower masses, the MZ relation of L09 is in agreement with our determination.

Cowie & Barger (2008, hereafter C08) study the evolution of the MZ relation by splitting their sample into a low-z and mid-z redshift interval. The two intervals are 0.05 < z < 0.475 and 0.475 < z < 0.9 and have a median redshift of 0.44 and 0.75, respectively. The low-z and mid-z samples have 35 and 154 galaxies, respectively. They find that there is a 0.25 dex difference in the metallicity in the mid-z sample as compared with the local relation and that the metallicity increases by 0.13 dex between the mid-z and low-z sample. The triple-dot-dashed line in Figure 9 shows the mid-z relation.

A major source of discrepancy between our determination and C08 can be attributed to the fitting procedure. Figure 31 of C08 shows that the spread in metallicity becomes larger as metallicity decreases. This may result from the greater uncertainty in determining metallicity from the R₂₃ diagnostic which becomes less sensitive to metallicity around the R₂₃ local maximum (12 + log(O/H) ∼ 8.4; see C08, Figure 23; or KK04, Figure 7, for example). The relation is curved so symmetric errors in R₂₃ become asymmetric errors in metallicity. In a least-squares fit, the data are assumed to be normally distributed, however, in this case they are not and outliers exert greater influence in determining the best fit. Looking at Figure 63 of C08 shows that the median of the metallicity in four mass bins is systematically higher than the fitted relation. With the diamonds in Figure 9, we plot the median of the MZ relation for the mid-z sample sorted into three mass bins (L. Cowie 2010, private communication). We fit our relation to the median metallicity in 15 mass bins as described in Section 4. The MZ relation determined from the median of the C08 data is more comparable to our determination. Given the many uncertainties discussed in comparing the MZ relation, the agreement between the relation of L09, C08, and our determination from DEEP2 is promising.

Our MZ relation comparisons highlight the need for consistent sample selection and MZ relation fitting techniques when comparing MZ relations at the same or different redshifts.

Conventionally, when spectra are not flux calibrated, as is the case in most spectroscopic redshift surveys, EWs are utilized in determining the emission-line ratios used for inferring metallicity (Kobulnicky & Phillips 2003, hereafter KP03). The essential feature of EWs is the normalization of the line emission to the underlying continuum. Here we will discuss the algorithm developed to determine line ratios in a self-consistent manner.

We define F(x) as the flux vector of our spectra with x being the rest-frame wavelength vector corresponding to each resolution element. We mask out ±5σ_v of our rest-frame line center wavelengths (from NIST³) and fit a global continuum. Here we take σ_v to be a velocity dispersion of 150 km s⁻¹. We model the global continuum as

$$\begin{equation} C(x) = \displaystyle \sum _{i=1}^{39} c_{i} T_{i}(x) + \displaystyle \sum _{j=0}^2 p_{j}x^{j}, \end{equation} \tag{ A1 }$$

where T_i(x) are the model stellar spectra obtained from Bruzual & Charlot (2003). We perform a bounded value nonlinear least-squares fit using the MPFIT⁴ set of routines (Markwardt 2009) in IDL to obtain c_i and p_j with the constraint that c_i ⩾ 0. We obtain a continuum-normalized flux, such that

$$\begin{equation} N(x) = \frac{F(x)}{C(x)} - 1, \end{equation} \tag{ A2 }$$

and fit a three-parameter Gaussian, $A_{N} e^{- \frac{(x-x_{N})^2}{2 \sigma _{N}}}$ to all emission lines. A_N, x_N, and σ_N are the gain, line center, and sigma of the Gaussian, respectively, and are used as initial estimates for fits to the local flux. In all our fits to the DEEP2 data, we derive the errors on our parameters by propagating the measurement uncertainties in the spectrum.

We define L(x) as the local flux for each line. L(x) = F(x) in the range x_N − 25σ_N < x < x_N + 25σ_N and zero elsewhere. We perform a bounded value nonlinear least-squares fit to the local flux L(x) with a two-component model r(x), such that r(x) = p(x) + g(x), where

$$\begin{equation} p(x) = a + bx \end{equation} \tag{ A3 }$$

is a linear fit that models the underlying continuum and

$$\begin{equation} g(x) = \displaystyle \sum _{i=1}^n a_{i} e^{\frac{(x-x_{oi})^2}{2 \sigma ^2}} \end{equation} \tag{ A4 }$$

is a Gaussian that models the emission line, where a_L, x_oL, and σ_L are defined as the gain, center, and sigma of the Gaussian fit to L(x), respectively. We note that in the case of Hβ, due to possible underlying stellar absorption, we fit continuum between 4775–4815 Å and 4905–4945 Å. It should be noted that σ in Equation (A4) does not have a summation index. If n > 1, then the multiple Gaussians simultaneously fitted will have different a_L and x_oL but the same σ_L. The parameters of the Gaussian are constrained such that a_L ⩾ 0, x_oL can only vary by ±2 Å from the line centers obtained from NIST⁵ and 0 Å < σ_L < 10 Å. For the [O ii] λλ3726, 3728 doublet n = 2 and for all other lines n = 1. This enables us to fit the local continuum, p(x), to all lines separately, except in the case of the [O ii] doublet where we fit the continuum to both lines simultaneously.

We obtain a continuum-normalized local flux, R(x), such that

$$\begin{equation} R(x) = \frac{L(x)}{p(x)} - 1. \end{equation} \tag{ A5 }$$

We refit a model, g_R(x), of the form given in Equation (A4) with n = 3 for the H_β and [O iii] λλ4959, 5007 lines and n = 2 for the [O ii] λλ3726, 3728 doublet. These values of n for the two sets of lines ensure that the fitted σ will be the same for all lines in the set. We obtain a pseudo-EW for each line, EW_p, such that $\mathrm{EW}_{p} = a_{R}\sigma _{R} \sqrt{2 \pi }$, where a_R and σ_R are the parameters from the fit of g_R(x) to R(x).

It becomes problematic to measure an EW or pseudo-EW when the S/N is low in the underlying continuum. In this situation, the continuum is poorly measured and therefore a normalization to the continuum is prone to large errors. Before normalizing the local flux, L(x), to the continuum, p(x), we estimate the noise of the local continuum, σ_c, by taking the rms of C'(x), where C'(x) = L(x) − r(x). We require that p(x), in the region of the line x_o − 3σ_L < x < x_o + 3σ_L, be 1σ_c above zero. If this condition is not met, we do not normalize to the continuum but instead fit a function of the form given in Equation (A4) to D(x), where D(x) = L(x) − p(x). We then calculate a pseudo-EW from the parameters of the fit. In this study, a small fraction (∼1%) of our Galaxies have such a low S/N in the continuum and are excluded from the study.

In order to test the robustness of our fitting method, we compare our pseudo-EW and line ratios with published EWs and line ratios determined from calibrated fluxes from the Nearby Field Galaxies Survey (NFGS; Jansen et al. 2000). KP03 compare how well interactively determined EW ratios correspond to those determined from measured fluxes. We deredden the fluxes from NFGS sample as described in KP03 and use their results as a benchmark for comparison. Of the 198 galaxies in the survey, 118 have published fluxes. Of those 118, 104 galaxies have an S/N of at least 8 for [O ii] λλ3726, 3728, [O iii] λλ4959, 5007, and H_β emission lines. We remove two additional galaxies that have a good fit determined visually but poor agreement with ratios determined from calibrated fluxes, presumably due to the underlying continuum which is poorly measured, leaving us with a sample of 102 galaxies plotted in Figures 10 and 11.

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Figure 10 shows a direct comparison between the EWs determined by Jansen et al. (2000) and the pseudo-EW determined by our automated method. The rms dispersion from one-to-one agreement is 0.6, 4.0, and 0.7 Å with the mean value of the EW being 7.5, 28.0, and 15.3 Å for H_β, [O ii], and [O iii], respectively.

In order to justify the fact that the pseudo-EW can be used in inferring gas-phase metallicities, we need to establish agreement between the calibrated flux ratios and our pseudo-EW ratios. Figure 11 shows agreement in line ratios determined with our method as compared to those from calibrated fluxes with an rms dispersion from one-to-one agreement of 0.10, 0.06, 0.11, and 0.08 dex for the [O ii]/H_β, [O iii]/H_β, O₃₂ and R₂₃ ratios, respectively. Table 3 gives the rms deviation from one-to-one agreement between line ratios determined using the two different methods. The top row shows the rms deviation from KP03 and the bottom row shows the rms deviation for our automated method for our sample of 102 galaxies. The median absolute deviation between the EW and flux-calibrated metallicities is <0.01 dex. In this local sample, the errors from the statistical measurement uncertainties are about one half of those introduced by using EWs or our pseudo-EW in line ratio determinations. Because galaxies are fainter at higher redshift, we expect them to have larger measurement uncertainties, thereby making the errors from using EWs comparable or even less than the statistical measurement uncertainties.

The O₃₂ and R₂₃ ratios are of particular importance because of their use in inferring metallicities. Figure 11 and Table 3 demonstrate that our method for determining line ratios is comparable to those that use flux-calibrated ratios. Figure 12 shows a typical spectrum and fit used in this study from the DEEP2 survey. Our automated method has several advantages over interactive determination of EWs. (1) The method is automated so considerably faster than interactively determining EWs and much more practical when working with large samples. (2) The automated method yields results that are reproducible because it no longer requires the input of wavelength limits in determining EWs. (3) The measurement errors in flux, when available, can be propagated through to the determination of metallicity and therefore provide a much more robust estimate of the true errors in 12 + log[O/H]. (4) In data where a low S/N makes it difficult to distinguish between the line and the continuum, the automatic fit is less susceptible to confusion. (5) Low S/N spectra where the continuum is not detected, EWs cannot be determined. These cases are handled in a much more robust manner allowing us to measure a pseudo-EW even when EWs cannot be measured.

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The local MZ relation has been determined from the SDSS data by both T04 and KE08. T04 derive a galaxy averaged gas-phase metallicity by simultaneously fitting the most prominent emission lines with stellar population synthesis and photoionization models. KE08 determine the metallicity using several common strong-line diagnostics and calibrations and provide conversions between the various methods. Additionally, they investigate the effects of various AGN classification scheme and aperture covering fraction. The two determinations differ by as much as 0.3 dex when compared directly due mainly to the difference in methodology of determining metallicities. Converting to the same metallicity diagnostic using Table 3 from KE08 the difference decreases to <0.05 dex.

The different MZ relations found in the literature at various redshifts may not necessarily be directly comparable. The differences resulting from the various metallicity diagnostics and calibrations have ostensibly been resolved by KE08. It should be noted however that it still remains uncertain whether relations calibrated using local galaxy samples are valid at higher redshifts. Care must be taken when comparing samples as selections effects lead to non-trivial differences in the determination of the MZ relation. We attempt to manage some of the differences arising from selection bias and different diagnostics by redetermining the local MZ relation from the SDSS data release 7 (Abazajian et al. 2009, http://www.mpa-garching.mpg.de/SDSS/DR7/) using similar selection cuts and the same metallicity calibration as our DEEP2 data set.

The SDSS DR7 consists of ∼818, 000 galaxies spanning 0 < z < 0.7. The emission-line EWs and galaxy stellar masses are calculated by the MPA/JHU group and are publicly available on the SDSS DR7 website. The EWs have been corrected for stellar absorption. The ugriz fiber and C model magnitudes (recommended for galaxy photometry) are also provided. We determine the stellar masses by fitting the photometry to population synthesis models using the Le Phare code (see Section 3.1).

We select galaxies by constraining the redshift such that 0.04 < z < 0.1. The lower limit is imposed to minimize aperture effects. Furthermore, we follow the method of KE08 whereby we determine the g-band fiber covering fraction by comparing the fiber and model magnitudes. KE08 determine that a 20% covering fraction is insufficient to avoid aperture bias. We require a larger aperture fiber covering fraction of >30% in order to further reduce aperture effects. For the selected sample the median covering fraction is 38%. The upper redshift limit is imposed in order to minimize evolutionary effects and because the star-forming sample is found to be incomplete at higher redshifts (Kewley et al. 2006).

In order to minimize selection biases when comparing, we impose a similar selection criteria as applied to the DEEP2 sample. We require that SN Hβ>3, σ_r23 < 2, and EW(Hβ)>4 Å. The SDSS data have much broader spectral coverage. For all galaxies in our redshift range we use the star-forming galaxies defined by the Kewley et al. (2006) classification scheme. KE08 showed that MZ relation derived from the SDSS data using the log([N ii]/O[ii]) ratio is insensitive to the classification scheme used to identify and remove AGN. The selected SDSS data sample consists of ∼21, 000 galaxies. The median EW(Hβ) and S/N Hβ of our selected sample is 8.9 and 20.7, respectively.

Figure 13 shows the local MZ and LZ relations derived from the selected SDSS sample. The metallicities have been derived using the EWs as described in Section 3.3. We place galaxies on the lower R₂₃ branch when log([N ii]/O[ii]) < −1.2 (KE08). An insignificant fraction (25/21816) are on the lower branch. The fits to the relations use the same bootstrapping method described in Section 4. For the MZ relation, the data are binned in 30 equally populated mass bins. From the left panel of Figure 13 it can be seen that the lowest mass bin suggests a turnover in the relation. This may be a result of incompleteness, though this is difficult to establish from these data. Whatever the case, the lowest mass bin is excluded when fitting the MZ relation. The MZ relation is given by

$$\begin{eqnarray} 12 + \log (\rm O/H) &=& (9.051 \pm 0.001) + (0.151 \pm 0.004) \, {\rm x}\nonumber\\ && - (0.104 \pm 0.006) \, {\rm x}^2, \end{eqnarray} \tag{ A6 }$$

where x = log(M_*) − 10, the logarithm of the stellar mass in solar mass units zero pointed to reduce the covariance of the parameters by subtracting 10. The dashed line in the left panel of Figure 13 shows this fit.

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The LZ relation is determined by sorting the data into 30 equally populated luminosity bins. The relation is shown in the right panel of Figure 13. The dashed curve is a linear fit to the data and is parameterized by

$$\begin{equation} 12 + \log (\rm O/H) = (9.089\pm 0.003) - (0.0833 \pm 0.002)X_{B}, \end{equation} \tag{ A7 }$$

where X_B = M_B + 21. The data turn over at M_B ∼ −20, presumably due to the more fundamental turnover observed in the MZ relation at the higher masses. If we fit the LZ relation in the linear part of the relation, M_B > − 20, the fit is

$$\begin{equation} 12 + \log (\rm O/H) = (9.131\pm 0.006) - (0.105 \pm 0.003)X_{B}. \end{equation} \tag{ A8 }$$

This dot-dashed line in the right panel of Figure 13 shows this fit.