The metallicity evolution of low mass galaxies: New constraints at intermediate redshift
Alaina Henry, Crystal L. Martin, Kristian Finlator, Alan Dressler
aa r X i v : . [ a s t r o - ph . C O ] A p r Draft version June 19, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE METALLICITY EVOLUTION OF LOW MASS GALAXIES: NEW CONSTRAINTS AT INTERMEDIATEREDSHIFT Alaina Henry , Crystal L. Martin , Kristian Finlator & Alan Dressler Draft version June 19, 2018
ABSTRACTWe present abundance measurements from 26 emission-line selected galaxies at z ∼ . − .
7. Byreaching stellar masses as low as 10 M ⊙ , these observations provide the first measurement of theintermediate redshift mass-metallicity (MZ) relation below 10 M ⊙ . For the portion of our sampleabove M > M ⊙ (8/26 galaxies), we find good agreement with previous measurements of theintermediate redshift MZ relation. Compared to the local relation, we measure an evolution thatcorresponds to a 0.12 dex decrease in oxygen abundances at intermediate redshifts. This resultconfirms the trend that metallicity evolution becomes more significant towards lower stellar masses,in keeping with a downsizing scenario where low mass galaxies evolve onto the local MZ relation at latercosmic times. We show that these galaxies follow the local fundamental metallicity relation, whereobjects with higher specific (mass-normalized) star formation rates (SFRs) have lower metallicities.Furthermore, we show that the galaxies in our sample lie on an extrapolation of the SFR-M ∗ relation(the star-forming main sequence). Leveraging the MZ relation and star-forming main sequence (andcombining our data with higher mass measurements from the literature), we test models that assumean equilibrium between mass inflow, outflow and star formation. We find that outflows are requiredto describe the data. By comparing different outflow prescriptions, we show that momentum drivenwinds can describe the MZ relation; however, this model under-predicts the amount of star formationin low mass galaxies. This disagreement may indicate that preventive feedback from gas-heating hasbeen overestimated, or it may signify a more fundamental deviation from the equilibrium assumption. INTRODUCTION
The balance between gaseous inflows, outflows, andstar formation is a critical frontier in our understandingof galaxy evolution. Feedback caused by stellar winds,supernovae, and supermassive black holes is often usedto explain a variety of observations, from luminosity andstellar mass functions, to the enrichment and reionizationof the intergalactic medium. However, a complete physi-cal picture of these feedback processes (i.e. Murray et al.2005; Hopkins et al. 2012) is still debated. Continuedefforts to provide new observational tests are essential.The correlation between galaxy stellar masses and gas-phase metallicities (the MZ relation) is one importantprobe of star formation feedback. The galactic out-flows that slow star formation, and the inflows that pro-mote it can also alter metallicities. On one hand, metalpoor material, when accreted onto a galaxy, can lowerthe metallicity. On the other hand, supernova drivenwinds may remove metal enriched material from galax-ies. It has been known for many years that modelswhich ignore inflows and outflows (i.e. closed-boxes), fail Some of the data presented herein were obtained at theW.M. Keck Observatory, which is operated as a scientificpartnership among the California Institute of Technology, theUniversity of California and the National Aeronautics and SpaceAdministration. The Observatory was made possible by thegenerous financial support of the W.M. Keck Foundation. Department of Physics, University of California, SantaBarbara, CA 93106 Astrophysics Science Division, Goddard Space Flight Cen-ter, Code 665, Greenbelt, MD 20771; [email protected] NASA Postdoctoral Program Fellow Hubble Fellow Carnegie Observatories, 813 Santa Barbara Street,Pasadena, CA 91101 to reproduce observed abundance patterns in galaxies(van den Bergh 1962). Indeed, in recent years, bothanalytical and numerical models have shown that out-flows (and sometimes gas accretion) are needed to ex-plain the MZ relation (Tremonti et al. 2004; Dalcanton2007; Brooks et al. 2007; Finlator & Dav´e 2008; Erb2008; Dav´e et al. 2011b, 2012; Peeples & Shankar 2011;Dayal et al. 2013; Lilly et al. 2013). However, to date,studies have not converged on the properties (rates, kine-matics, metal enrichment, halo mass dependence, andredshift evolution) of these gaseous flows.One avenue to better understand the physics thatgoverns the MZ relation is to study low mass galax-ies (e.g. Lee et al. 2006; Zhao et al. 2010; Wuyts et al.2012; Berg et al. 2012). In these systems, galacticwinds are especially effective at escaping the gravita-tional potential of their hosts, regulating star forma-tion and enabling enrichment of the intergalactic medium(Oppenheimer et al. 2009; Kirby et al. 2011). Hence, ob-servational constraints on low mass galaxies offer someof the most stringent tests of galaxy formation models.Outside the local universe, the MZ relation ispoorly constrained at stellar masses below 10 M ⊙ (and 10 M ⊙ for z > z ∼
1, these sur-veys are typically limited to R .
24. Hence, theseintermediate-redshift MZ relations have been derived for
M > M ⊙ (Lilly et al. 2003; Savaglio et al. 2005;Lamareille et al. 2009; Zahid et al. 2011; Cresci et al.2012; Moustakas et al. 2011). Nevertheless, in the caseof the Cosmic Origins Survey (COSMOS), the extensive Table 1
DEIMOS Followup Observation SummaryDate Mask Name Mask RA Mask Dec Mask PA Slit PA Slit Widths Exposure Time Seeing(J2000) (J2000) (degrees) (degrees) ( ′′ ) (hours) ( ′′ )27 January 2011 D 10:00:22.97 02:09:28.9 85 90 1.5 6.5 0.628 January 2011 F 10:01:11.46 02:10:27.4 106 90 1.5 6.3 0.822 January 2012 M 10:00:24.25 02:05:19.8 85 90 1.5 4.9 1.022/24 January 2012 L 10:00:22.56 02:15:29.8 13 0 1.2 5.3 0.923/24 January 2012 Q 10:00:28.96 02:20:05.1 95 90 1.5 6.8 1.0 Note . — Coordinates, position angles (PAs), exposure times, and seeing are given for each observed mask. On masks D, F,M, and Q, the slit PAs and slit-widths were matched to the IMACS venetian blind spectroscopic data (described in Dressler et al.2011a and Henry et al. 2012). For mask L, the slits were rotated 90 degrees relative to the search data. broad and intermediate-band photometry allows reliablemass constraints an order of magnitude lower at inter-mediate redshifts. Therefore, spectroscopic followup offainter galaxies can significantly extend the intermediateredshift MZ relation.In this paper we use an emission line selected sampleto place new constraints on the low mass end of the MZrelation at z ∼ . − .
7. By drawing our sample pri-marily from the ultra-faint emission line objects that wehave previously identified with blind spectroscopy in theCOSMOS field (Martin et al. 2008; Dressler et al. 2011a;Henry et al. 2012), we obtain oxygen abundances forgalaxies with stellar masses of 10 M ⊙ . M . M ⊙ .In this manner, we provide the first constraints on thelow mass evolution of the MZ relation, reaching stellarmasses that are comparable to the limiting mass of localSDSS samples.This paper is organized as follows: in § § § § § §
7. In this paper weuse AB magnitudes, a Chabrier (2003) initial mass func-tion, and a ΛCDM cosmology with Ω M = 0.3, Ω Λ = 0 . H = 70 km s − Mpc − . Throughout the text we re-port measurements of doublet lines: [O II ] λλ , III ] λλ , II ]” and “[O III ]” to refer to both linesin the doublet, or, when appropriate, the sum of theirfluxes OBSERVATIONS
Target Selection & Followup Spectroscopy
The emission line galaxies in the present sample wereinitially identified as part of our multislit narrowbandspectroscopic survey. The observations are presentedin detail in Martin et al. (2008), Dressler et al. (2011a),and Henry et al. (2012). In brief, our design usesthe Inamori-Magellan Areal Camera and Spectrograph(IMACS; Dressler et al. 2011b) on the 6.5m MagellanBaade Telescope at Las Campans Observatory. We useda venetian blind slit mask, and narrowband filter cen-tered in the 8200˚A OH airglow free window. This method allows for the efficient selection of emission line galaxies,and reaches fluxes as low as 2.5 × − erg s − cm − –a factor of five fainter than narrowband imaging surveys(e. g. Kashikawa et al. 2011).Because of the faintness of the emission lines, andthe narrow bandpass in our search data, we use fol-lowup spectroscopy with DEIMOS (Faber et al. 2003)to identify the redshifts of the IMACS-detected galax-ies. The primary goal of these observations was toconfirm Ly α emitting galaxies and measure the faint-end slope of the Ly α luminosity function at z = 5 . z ∼ . − .
7, these followup observations con-tain the [O
III ] λλ , II ] λλ , β emission lines that comprise the R23 metallicity indica-tor (Pagel et al. 1979). Three classes of these objectswere included on followup slit-masks:1. Emission line galaxies for which continuum in thesearch data ruled out the Ly α identification werechosen as MZ targets. To obtain the best possiblespectrum, we searched the COSMOS photomet-ric redshift catalog (Ilbert et al. 2009) for nearbygalaxies ( < ′′ ) with z ∼ . − .
7, and shiftedthe slit-positions to coincide with these matches .In total, the final sample of 26 star forming galax-ies (described in §
3) contains 15 objects that meetthese criteria.2. Additionally, galaxies were drawn from the [O
III ]+ H β narrowband excess catalog which we derivedin Dressler et al. (2011a). The present star-formingsample contains 11 objects that were selected inthis way.3. Finally, we also detect R23 from ultra-faint emis-sion lines which we originally considered Ly α can-didates, but, upon the followup observations de-scribed below, we determined that the discoveryline was [O III ] λ III ] λ β . Sixgalaxies with measurable R23 fall under this clas-sification.In practice, the objects described in Because the COMSOS photometric redshifts include narrow-band photometry and use templates that include emission lines,the photometric redshifts are often very close to the spectroscopicredshifts for the emission-line selected galaxies in our survey. λ rest ( ◦ A) −200204060803720 3740 F λ / F ([ O III ] ) + C o n s t a n t Figure 1.
The spectra of 34 galaxies with complete coverage of the R23 metallicity indicator ([O
III ]+ [O II ]/ H β ; Pagel et al. 1979) areshown. The spectra of 26 objects that comprise our MZ sample are shown in black, and are sorted by stellar mass with higher masses atthe top (the same as their appearance in Tables 2 and 3). The two AGN candidates are shown in grey at the top, and also continue themass-ordered scheme. The Class 3 objects with ambiguous optical counterparts are shown at the bottom (in grey) in the same order astheir appearance in the tables. All spectra are normalized by their flux in [OIII] λ β and [O II ] emission. The strong “absorption” trough near 4845 ˚A in one object (980802) is a detector artifact. focus on the former two classes. For completeness, inTables 2 and 3 we list the subset of these objects whereR23 could be measured; however, we do not considerthem further in this paper.The DEIMOS observations of these followup slit-maskswere carried out in January 2011 and January 2012. Asummary of observations for each followup mask is givenin Table 1. In four of the five masks, we used slit-widthsand PAs that were matched to the search data (1.5 ′′ wideand 90 ◦ east of north). On mask L, in order to betterlocate objects detected through blind spectroscopy, weused a slit orientation which is orthogonal to the venetianblind search slits. This method also allowed for narrowerslits (1.2 ′′ ). All observations were carried out using thethe GG495 blocking filter with 830G grating. Under thisconfiguration, we achieved a spectral resolution of 3.7 ˚A(2.9 ˚A) for a source that fills the 1.5 ′′ (1.2 ′′ ) slit. Thegrating angle was chosen to give a central wavelength of7270 ˚A, with blue coverage down to 5500˚A for most slits.The DEIMOS spectra were reduced using the DEEP2DEIMOS data reduction pipeline (Cooper et al. 2012),with an updated optical model for the 830G grating (P.Capak, private communication). The data were flux cal-ibrated using observations of several spectrophotometricstandard stars, taken through a 1.5 ′′ slit at the parallac-tic angle. The stars used were G191B2B, GD50, Feige66, Feige 67, and Hz 44 (Massey & Gronwall 1990; Oke1990), and the data for each was taken from the ESOspectrophotometric standard star database. Sensitivityfunctions derived from these stars differ systematicallybetween observations, with offsets up to 30%. After shift-ing the lower sensitivity functions to match the highestone, the observations agree at the 2-3% level, indicatingan excellent relative calibration.Finally, we have verified that the effects of differentialatmospheric refraction have a negligible impact on ourmeasured line flux ratios. In order to quantify possibledifferential slit losses, we calculate the component of theatmospheric refraction that falls perpendicular to the slitin each observation (frame) of each mask. The worst caseoccurs on mask L, where the slits are narrowest and theslit-PA was the furthest from parallactic. For these data,the refraction (perpendicular to the slit) between 6000 ˚A(near [O II ]) and 8000 ˚A (near [O III ] and H β ) rangesfrom 0.04 to 0 . ′′
33 (Fillipenko 1982). Therefore, since theguiding was done in the R-band (in between the observedwavelengths of the emission lines), we estimate the slit-losses on the red and blue parts of our spectra differ byno more than 4% (for 1 ′′ seeing). In most frames, theeffect is even smaller, so we conclude that no systematiccorrection is needed to interpret our emission line ratios. COSMOS Imaging Data
In order to derive stellar masses ( § Spitzer /IRAC bands.Furthermore, our SED fits are improved by the inclu-sion of intermediate-band imaging, and updated Sub-aru/SuprimeCam z ′ -band data (from observations made with the new, fully depleted, red-efficient CCDs). Sincethe optical and near-infrared photometry are performedin 3 ′′ apertures on data with homogenized PSFs (1.5 ′′ FWHM), we apply a point source aperture correction of-0.28 magnitudes to all optical and near-infrared bands.For the IRAC data we use 3.8 ′′ diameter apertures, andapply point source aperture corrections of -0.29, -0.33,-0.51, and -0.59 magnitudes to bands one through four.No aperture corrections are applied to the GALEX data,as these magnitudes were derived from fits to the PSF.Finally, we note that the recommended zero point off-sets have been applied (Capak et al. 2007; Ilbert et al.2009), and a Galactic foreground extinction correctionis made using the Cardelli et al. (1989) extinction curvewith E(B-V) = 0.019. ANALYSIS
Emission Line Measurements
In total, we identify 47 galaxies at z ∼ . − .
7; ofthese 34 have complete coverage of the R23 ([O
III ]+[O II ]/ H β ; Pagel et al. 1979) metallicity indicator. Theirspectra are shown in Figure 1. The remaining 13 galaxiesat these redshifts either have essential lines lost in theOH airglow spectrum, or are class § z ∼ . − . II ], the twodoublet components are fit simultaneously. As an exam-ple, Figure 2 shows a typical spectrum and the Gaussianfits to the emission lines.To facilitate a correction for H β stellar absorption, wealso measure emission line equivalent widths. Because itcan be difficult to assess the uncertainty on the contin-uum flux density when it is measured spectroscopically,we compare two methods. On one hand, we measure theequivalent widths directly from the spectra. In 25/28 ob-jects in our sample, we detect continuum, although it issometimes weak. As a second method, we compare theemission line fluxes from the DEIMOS data to the contin-uum under the emission line from the SED fit (describedbelow). After accounting for a systematic offset (becausethe emission line fluxes are subject to slit losses but theSED fits use total fluxes), the equivalent widths mea-sured by these different techniques agree to within 50%.We adopt this level of uncertainty on the H β equivalentwidths.Finally, having measured the fluxes and equivalentwidths of our emission lines, we apply a correction forthe stellar absorption. Because the stellar absorptioncomponent is much broader than the emission line, thiscorrection depends on the spectral resolution. At the res-olution of our data, the correction is approximately 1 ˚A (cid:0) rest ( (cid:1) A) F (cid:2) ( (cid:3) e r g s (cid:4) c m (cid:5) (cid:6) A (cid:7) ) (cid:8) rest ( (cid:9) A) (cid:10) rest ( (cid:11) A) (cid:12) rest ( (cid:13) A) Figure 2.
The DEIMOS spectrum of object 54.5+4-0.18 measures the R23 oxygen abundance indicator with high signal to noise. TheGaussian fits used to measure the emission line fluxes are shown in red. From left to right, the lines shown are [O II ] λλ , β ,[O III ] λ III ] λ in equivalent width (Cowie & Barger 2008; Zahid et al.2011). While the amount of absorption also dependsslightly on the age of the stellar population, the mainsource of uncertainty in this correction is from the ob-served H β emission equivalent width, as discussed above.We propagate this error in our H β fluxes and the metal-licities that we infer in § Stellar Masses, SFRs, and dust constraints fromSED fitting
Stellar masses are determined by fitting template stel-lar populations to the broad- and intermediate-bandphotometry described in §
2. For this task, we useFAST (Fitting and Assessment of Synthetic Templates;Kriek et al. 2009). The choice of population synthesistemplates can have an important impact on the proper-ties derived from SEDs, because the contribution fromthe (infrared-bright) thermally pulsing asymptotic giantbranch (TP-AGB) stars differs from model to model.The most widely used templates are Bruzual & Charlot(2003; BC03), Maraston (2005), and Charlot & Bruzual(2007; Bruzual 2007); the latter two options provide alarger contribution from TP-AGB stars (and correspond-ingly smaller masses). Nevertheless, the proper contri-bution from TP-AGB stars remains a subject of debate(Kriek et al. 2010; Conroy & Gunn 2010; Zibetti et al.2013). Therefore, in order to facilitate comparisons withthe literature, we derive stellar masses using the BC03models. We have verified that the Charlot & Bruzualand Maraston et al. models produce stellar masses thatare systematically smaller by approximately 0.1 dex.In order to assure accurate stellar population con-straints, it is also important to account for emission linecontribution to our SEDs. (The stellar synthesis tem-plates that we fit to the SEDs do not contain nebularfeatures. Failing to remove emission line contaminationcan result in incorrectly inferred ages and stellar masses;Schaerer & de Barros 2009; Atek et al. 2011.) We useour line fluxes to calculate the small contribution from[O II ] to the r -band, and [O III ] and H β to the i -band.For the galaxies in our sample, we find that 1-5% ofthe r − band light and 2-15% of the i − band light canbe attributed to emission lines. These contributions are subtracted from the r and i − band continuum flux den-sities. Emission from H α , on the other hand, falls be-tween the z ′ and J bands, so it does not contaminateany of the photometry in the present analysis. Finally,we consider emission line contamination to the interme-diate band photometry. In these cases, the correctionswill be larger and more uncertain. Therefore, we excludethe band at 624 nm that includes [O II ], and the band at827 nm that covers [O III ] and H β . The remaining tenintermediate bands should be relatively unaffected.The grid of stellar population parameters that we fitwith FAST include: a set of exponentially decliningstar formation histories with e-folding times, τ , rangingfrom 40 Myr to 10 Gyr; characteristic stellar populationages ranging from 50 Myr to the age of the universe at z ∼ . − .
7; and A V = 0 − §
4, the galaxies in our sample mostly have sub-solar to solar gas-phase metallicities. The derived stellarmasses, SFRs, and visual extinction values are given inTable 3. Because of the intermediate band photome-try, the dust extinction constraints exclude much of theallowed parameter space. Therefore we use the SED-derived dust constraints to correct our emission line ra-tios, including these uncertainties in our error budget. Inmaking this correction, we also account for the fact thatnebular extinction is 2.3 times higher than stellar extinc-tion on average (Calzetti et al. 2000; Cresci et al. 2012).While the precise relation between stellar and nebularextinction remains controversial (Cowie & Barger 2008;Cresci et al. 2012; Wofford et al. 2013), we adopt the“standard” Calzetti et al. (2000) relation to allow com-parison with other studies.In § II ], H β , and the SED fits. The re-sults, outlined in the Appendix, show that the agreementbetween the different diagnostics is good; systematic off-sets are smaller than 0.2 dex. This level of uncertainty log M/M (cid:14)(cid:15) (cid:16) (cid:17) (cid:18) l o g [ O III ] (cid:19) / H (cid:20) Figure 3.
The [O
III ] / H β ratio as a function of stellar masscan be used to identify AGN, similar to the [O III ]/ H β vs.[N II ]/ H α “BPT” diagram (Baldwin, Phillips, & Terlevich 1981;Juneau et al. 2011). Red point show our emission line selectedsample, while contours (with levels defined arbitrarily) show theSDSS data. The solid black lines show the demarcation betweenstar-forming galaxies (below and to the left), objects with activenuclei (above and to the right), and composite objects (the regionin between the black lines around 10 - 10 M ⊙ ). The two high-est mass objects in our sample, 55.5-3-0.60 and 73.5+5-0.54, falloutside of the z = 0 star-forming locus, so we identify them ascandidate AGN. does not affect our conclusions. Contamination from AGN
In order to measure the MZ relation of star-forminggalaxies, it is important to ensure that the observedemission lines do not originate from an active galac-tic nucleus (AGN). The typical approach for low red-shift galaxies is to use the [O
III ]/ H β and [N II ]/H α emission line ratios (the canonical BPT diagram;Baldwin, Phillips, & Terlevich 1981). However, for theredshift of our sample, H α and [N II ] fall at infraredwavelengths. Therefore, in lieu of followup spectroscopy,we turn to an alternate diagnostic: the Mass-Excitation(MEx) diagram (Juneau et al. 2011). This approach,shown in Figure 3, uses stellar mass as a proxy for theH α /[N II ] λ α /[N II ] λ CALCULATING OXYGEN ABUNDANCES
Interpreting metal abundance measurements requiresthat we account for systematic uncertainties. Dif- ferent methods for measuring strong oxygen abun-dances yield results which are offset by up to 0.7dex (Kewley & Ellison 2008; L´opez-S´anchez et al. 2012;Andrews & Martini 2013). On one hand, photoioniza-tion models that are used to derive theoretical cali-brations (i.e. Kewley & Dopita 2002) are often basedon simplistic assumptions about H II region geome-tries and ionizing spectra (van Zee et al. 2006). Onthe other hand, empirical methods, which correlateline ratios with H II region electron temperatures (i.e.Pettini & Pagel 2004; Pilyugin & Thuan 2005), gener-ally give lower metallicities than photoionization model-based calibrations (McGaugh 1991; Kewley & Dopita2002). Because electron temperature measurements maybe overestimated when temperature and density gradi-ents are present in H II regions, it is possible that theempirical calibrations are biased towards low metallici-ties (Peimbert & Costero 1969; Stasi´nska 2005). Alter-natively, Nicholls et al. (2012) have suggested that dis-crepancies between electron-temperature measurementsand theoretical strong-line estimates can be explained ifthe electrons in H II regions deviate from an equilibriumMaxwell-Boltzmann distribution.Ultimately, the differences between metallicity calibra-tions are still not fully understood, but the systematicoffsets can be accounted for using a set of transforma-tion equations given by Kewley & Ellison (2008). In thesections that follow (except for § § High-Metallicity or Low? Determining the Branchof R23
Metallicities derived from R23 can be degenerate, sincethis diagnostic is double valued. At high metallici-ties, the oxygen lines are weaker because cooling is ef-ficient and the H II regions have lower electron tem-peratures. On the other hand, at low metallicities, theoverall decrease in oxygen relative to hydrogen also im-prints a decrease in R23 with decreasing metallicity. The“turnover” metallicity that demarcates the transition be-tween the upper and lower branches of R23 depends onthe ionization parameter , and differs among the calibra-tions that are in the literature. For the typical ionizationparameters of our galaxies, and the KK04 calibration,the turnover metallicity is around 12+log(O/H) ∼ . ∼ . − . II ] λ II ] or [N II ] λ α ratios to first provide a metallicity estimatethat identifies the branch. However, this method is more The ionization parameter is defined as the ratio of the ionizingphoton density to the hydrogen density. It can be written as U = Q/ πr n H c , where Q is the ionizing photon rate, r is the radiusof the H II region, n is the hydrogen density, and c is the speed oflight. The parameterization q = U × c is also commonly found inthe literature. challenging at z > . II ] λλ , z >
2. The R23 diagnostic, onthe other hand, can be measured from the ground outto z ∼ II ] λλ , β -detectedgalaxies (0 . < z < .
85) from the PEARS Survey(Probing Evolution and Reionization Spectroscopically;Xia et al. 2012). In the upper left panel, we show thatR23 decreases with increasing stellar mass for most ofour sample. Furthermore, three of the four galaxies fromXia et al. follow the trends from our emission line se-lected sample. This diagnostic paints a clear picture: ifmetallicity decreases as a function of decreasing mass,most of the galaxies in our sample must fall on the up-per branch of the R23 indicator. The two lowest massgalaxies shown in Figure 4 (1217842 from our sample,and 246 from Xia et al.) hint at a possible turnover at M ∼ . − .
5, indicating that these galaxies may fall onthe lower branch of R23.Because it is not ideal to introduce a mass dependenceon our metallicity derivations, we explore other emis-sion line diagnostics in Figure 4. First, we compare tothe emission line ratios of [O
III ]/H β and log([O III ]/[O II ]) ≡ O32 as a function of stellar mass. These lineratios have been proposed to break the R23 degeneracyby Maiolino et al. (2008), with low metallicity solutionsbeing preferred when [O
III ]/H β> > . III ]/H β thresholds is object 246 from Xia et al.(2012).The inference of upper branch metallicities for 3/4 ofthe objects presented by Xia et al. (2012) contrasts withtheir lower branch assumption. These authors argued forlower metallicities because of the relatively high values of[O III ]/H β and O32 for most of their sample. However,comparison to the R23 vs mass plot (upper left) showsthat for at least three of these galaxies, higher metallic-ity solutions are more plausible. (Although the galaxiespresented by Xia et al. 2012 may prefer higher O32 andionization parameters than the remainder of our sample,metallicity is not a strong function of ionization parame-ter on the upper branch, so their galaxies still follow ourR23-stellar mass correlation.)Ultimately, caution is required when using [O III ]/H β and O32 to determine the branch of R23, because thesequantities are dependent on the ionization parameter.Observations of high-redshift galaxies show that theirline ratios are offset to high values of [O III ]/H β ata fixed [N II ]/H α (Shapley et al. 2005; Erb et al. 2006;Hainline et al. 2009). This offset is usually interpreted asevidence for a systematically high ionization parameter (Brinchmann et al. 2008), suggesting that some galax-ies deviate from the local metallicity vs. ionization pa-rameter correlation. In summary, attempting to breakthe R23 degeneracy using quantities that depend on theionization parameter could erroneously indicate lowerbranch solutions.In Figure 4, we also investigate the use of H β equivalentwidth to select low-metallicity galaxies. Kakazu et al.(2007) and Hu et al. (2009) have found that, for theiremission line selected sample, galaxies are likely to havevery low metallicities (indicated by detectable [O III ] λ β equivalent widths aremore than 30 ˚A (rest). However, 8/26 galaxies in oursample meet this criterion, and we do not detect [O III ] λ β equivalent width merely selectsagainst galaxies with M & . M ⊙ . As we show in § β equiv-alent widths and somewhat lower luminosities than thepresent sample of emission line objects. We infer that itis not straightforward to use H β equivalent width to dis-criminate between upper and lower branch metallicities.Guided by Figure 4 we conclude that, in the absenceof other metallicity diagnostics, the correlation betweenstellar mass and R23 is the preferred method to breakthe R23-degeneracy. This exercise shows that for z ∼ . − . . and 10 . M ⊙ . Therefore, we adopt upperbranch solutions above M = 10 . M ⊙ . The two lowestmass galaxies (1217842 from our sample and 246 fromXia et al. 2012) are less certain. For 1217842 we adopta metallicity in the turn around region (12 + log(O/H)= 8.4), with error bars denoting the upper bound of thehigh metallicity solution and the lower bound of the lowmetallicity solution. The lowest-mass object from Xia etal. ( β measurement could be in error becauseit is blended with [O III ] in their low resolution data.Followup spectroscopy can better constrain the metallic-ities of galaxies near the R23 turnaround by providingthe [N II ]/H α and [N II ]/[O II ] ratios (Kewley & Ellison2008). At present, however, the conclusions drawn inthe remainder of this work do not depend on these twogalaxies because their metallicity errors are large. Oxy-gen abundances for the entire sample are listed in Table3. Our inference of upper branch metallicities at M > . − . M ⊙ is inconsistent with results reported byZahid et al. (2011). In contrast to Figure 4, Zahid etal. find that the mean value of R23 turns over around M ∼ . M ⊙ for their z ∼ . M < . M ⊙ , and objects withR23 >
10 have been removed as candidate AGN. Thecoupling of these effects may bias the lowest mass bintowards lower mean values of R23, and mimic the effectof a turnover in the R23 vs mass correlation. We con-clude that on average, galaxies at z ∼ . − . M & . − . M ⊙ . At higherredshifts, where metallicity evolution is significant (i.e.Erb et al. 2006), we expect that the transition from the Log M/M (cid:21) L o g R This workXia et al. (2012)
Log M/M (cid:22) [ O III ] / H (cid:23) Log M/M (cid:24) E W ( H (cid:25) ) Log M/M (cid:26)(cid:27) (cid:28) O Figure 4.
Our measured values of R23 decrease with increasing stellar mass, implying that most of the galaxies in our sample fall on theupper branch of R23. This diagram is contrasted with three other diagnostics that have previously been used to identify whether galaxieshave low or high metallicities (Maiolino et al. 2008; Hu et al. 2009; Xia et al. 2012). These include the [O
III ] λλ , β flux ratio,the rest-frame equivalent width of H β , and the ratio O32 ≡ log ([O III ] λλ , II ] λλ , β EW of 352˚A (rest),object 246 from Xia et al. is not shown in the EW(H β ) panel. upper to lower branch of R23 will occur at higher stellarmasses. RESULTS
The Mass-Metallicity Relation
Figure 5 presents the MZ relation for our 26 star-forming galaxies, and compares it to both the local re-lation (Tremonti et al. 2004), and other intermediate-redshift measurements from the literature. In each case,we have taken care to (when necessary) convert stellarmasses to a Chabrier (2003) IMF (using multiplicativeconstants given in Savaglio et al. 2005; Cowie & Barger2008), and convert metallicities to a KK04 calibration(using equations given in Kewley & Ellison 2008). Inthe mass range 8 . ≤ M ⊙ ≤ .
0, our data give a medianvalue of 12 + log(O/H) = 8.63, with an RMS scatter of0.12 dex.The intermediate redshift MZ relation has beenmeasured for higher mass galaxies by several au-thors (Savaglio et al. 2005; Cowie & Barger 2008;Lamareille et al. 2009; Zahid et al. 2011). Among thehigher mass portion of our sample (
M > . M ⊙ ,where we can compare directly to previous results) thereis good agreement with all of the published MZ rela-tions. While the addition of our data does not distin- guish between these relations, we note that the Zahidet al. sample stands out as the largest (1350 galax-ies, as opposed to fewer than 100 galaxies in each ofthe others). These authors discuss the differences be-tween Savaglio et al. (2005), Cowie & Barger (2008), andLamareille et al. (2009). They conclude that sample se-lection effects and linear fits which are biased by out-liers may account for the differences among these works.While these effects are likely important, we also notethat different dust correction methods may be significant.On one hand, Zahid et al. (2011) and Lamareille et al.(2009) calculate R23 from equivalent widths, as they areless sensitive to dust extinction. Although this methodis subject to systematic uncertainties correlated withgalaxy colors, Liang et al. (2007) show that this effecthas a relatively weak impact on metallicity (-0.2 to 0.1dex). Cowie & Barger, on the other hand, take the ap-proach of determining dust extinction from SED fits.However, they do not assume a higher dust extinctionfor nebular compared to stellar light, as their lower red-shift sample suggests that these quantities are consis-tent. Comparatively, the dust correction adopted bySavaglio et al. (2005) is cruder; they use the same ex-tinction ( A V = 2 .
1) for all galaxies. If this correctionis accurate for the median of their sample, then at high(low) masses the dust correction will be underestimated
Log M/M ⊙ + l o g ( O / H ) z~0.65 (This work)z=0.6-0.9 (Xia et al. 2012)z~0.1 (Tremonti et al. 2004)z~0.8 (Zahid et al. 2011)z=0.5-0.7 Lamareille et al.(2009)z=0.475-0.9 (Cowie & Barger 2008)z=0.4-1.0 (Savaglio et al. 2005) Figure 5.
The addition of our 26 low mass galaxies constrains the low mass portion of the MZ relation at intermediate redshifts. Forcomparison, we have re-calculated the metallicities presented in Xia et al. (2012), assuming– contrary to these authors– that the threehighest mass objects have metallicities on the upper branch. Other studies are shown for comparison, and are (when necessary) convertedto a Chabrier (2003) initial mass function and a Kobulnicky & Kewley (2004) metallicity. The dashed and dotted grey lines that follow theTremonti et al. (2004) MZ relation show the 68 and 95% contours for the SDSS data. For reference, solar metallicity is 12 + log (O/H) =8.69 (Allende Prieto et al. 2001). −22−21−20−19−18−17−16 M B + l o g ( O / H ) This wo kXia et al. (2012)T emonti et al. (2004)Zahid et al. (2011)Hu et al. (2009)
Figure 6.
The luminosity metallicity relation for the present emis-sion line selected sample is compared to correlations from the litera-ture. Notably, we compare to the measurements of the ultra-strongemission line galaxies reported by Hu et al. (2009). Because thesegalaxies have detected [O
III ] λ (overestimated), and metallicities will be overestimated(underestimated). Qualitatively, this effect could explaintheir steeper MZ slope. Additionally, it is worth notingthat our data are inconsistent with an extrapolation of the Savaglio et al. relation. In the sections that follow,we take the results from Zahid et al. (2011) as the bestmeasurement of the high mass, intermediate-redshift MZrelation.The addition of our low mass data allows for new con-straints on the evolution of the MZ relation. In Figure5 we compare to the local relation measured from theSDSS (Tremonti et al. 2004). In the mass range 10 . ≤ M/M ⊙ ≤ . , we find a mean metallicity that is 0.12dex lower than the local relation (at M = 10 . M ⊙ ).This trend confirms that metallicity evolution is rela-tively slow from intermediate to low redshifts. Addition-ally, as our data are consistent with an extrapolation ofthe results from Zahid et al. (2011), we agree with theirfinding that metallicity evolution is more significant atlower masses than at higher masses. This trend is qual-itatively consistent with downsizing in the later phases( z ∼ − Table 2
Emission Line MeasurementsIMACS ID COSMOS ID RA Dec z F([O
III ] λ III ] λ β ) F([O II ] λ β )(J2000) (J2000) ˚A (rest)27.5+5-0.47 799604 10:00:11.314 +02:04:07.60 0.675 16 . ± . · · · . ± . . ± . . pm . · · · . ± . . ± . . ± . · · · . ± . . ± . . ± . · · · . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . a . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · · · · · · · . ± . . ± . . ± . · · · . ± . . ± . . ± . . ± . · · · · · · . ± . . ± . . ± . . ± . · · · · · · . ± . . ± . . ± . < . · · · · · · . ± . . ± . . ± . . ± . · · · Candidate AGN55.5-3-0.60 984577 10:01:01.126 +02:11:07.85 0.623 39 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . Note . — Emission line fluxes are in units of 10 − erg s − cm − . Equivalent widths and H β fluxes are given as measured (without applyingthe 1˚A stellar absorption correction.) Objects lacking an IMACS ID were selected strictly from the COSMOS narrowband (NB816) imaging, as wedescribed in §
2. The [O II ] flux is the sum of the λλ , III ] doublet lines fell on an OHsky line; in this situation, metallicities are derived by assuming a flux ratio of F([O
III ] λ III ] λ ≡ a This galaxy was drawn from our earlier (wider and shallower) survey first presented in Martin et al. (2008). cosmic times. Hence, extending observations to lowermasses at all redshifts will provide essential insights intothe physics of galaxy assembly and metal production.We compare our data to theoretical predictions for theMZ relation in § The Luminosity-Metallicity Relation
In Figure 6 we show the metallicity luminosity relationderived from our data. While the MZ relation may repre-sent a more fundamental correlation than the metallicity-luminosity relation, the latter allows comparison to stud-ies where stellar-mass measurements have not been pos-sible. Here, we focus on the ultra-strong emission line(USEL) sample presented by Kakazu et al. (2007) andHu et al. (2009). Like the galaxies in our sample, theUSELs lie at intermediate redshifts and are emission lineselected. However, the majority of the USELs are lowmetallicity galaxies with detected [O
III ] 4363 ˚A emis-sion. In Figure 6, we compare the metallicity-luminosityrelation of the USELs to our sample. In order to makea fair comparison, we have calculated the metallicities of the USELs using R23 and KK04, assuming lower-branch solutions. No correction for dust is applied, whichHu et al. (2009) argue is appropriate for these faint, lowmass objects. It is worth noting that, under these as-sumptions, the majority of USELS have 12 + log (O/H) > .
0, and would not be classified as extremely metalpoor galaxies (12 + log(O/H) < .
65 ; Kniazev et al.2003). However, this classification changes when directmethod metallicities are used: in this case, the oxygenabundances reported by Hu et al. (2009) are 0.03 - 0.74dex lower (0.4 dex on average).Figure 6 shows clearly that the USELs have lowermetallicities than the emission-line selected galaxies inthe present work. In fact, this trend is not surpris-ing. Because of the differing selections for the USELsand the present sample, the former have H β equiva-lent widths that are two times larger (on average) thanthe latter. This difference translates to higher specific(mass-normalized) SFRs for the USELs. One possibleexplanation is that more actively star-forming galaxieswill have B-band luminosities which are high for their1 Table 3
Derived PropertiesIMACS ID COSMOS ID M B U − B log M ∗ log SFR A V log R23 log O32 12+log(O/H) log q . +0 . − . . +0 . − . . +0 . − . . ± . − . ± .
16 8 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . ± . − . ± .
22 8 . +0 . − . . +0 . − . . +0 . − . − . +0 . − . . +0 . − . . ± . − . ± .
11 8 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . ± . − . ± .
19 8 . +0 . − . . +0 . − . . +0 . − . − . +0 . − . . +0 . − . . ± . − . ± .
05 8 . +0 . − . . +0 . − . . − . − . − . +0 . − . . +0 . − . . ± .
12 0 . ± .
04 8 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . ± .
05 0 . ± .
10 8 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . ± . − . ± .
07 8 . +0 . − . . +0 . − . · · · . +0 . − . . +0 . − . . +0 . − . . ± .
01 0 . ± .
02 8 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . ± . − . ± .
14 8 . +0 . − . . +0 . − . . +0 . − . − . +0 . − . . +0 . − . . ± . − . ± .
06 8 . +0 . − . . +0 . − . . +0 . − . − . +0 . − . . +0 . − . . ± . − . ± .
05 8 . +0 . − . . +0 . − . · · · . +0 . − . − . +0 . − . . +0 . − . . ± .
06 0 . ± .
06 8 . +0 . − . . +0 . − . · · · . +0 . − . . +0 . − . . +0 . − . . ± .
03 0 . ± .
08 8 . +0 . − . . +0 . − . · · · . +0 . − . − . +0 . − . . +0 . − . . ± . − . ± .
11 8 . +0 . − . . +0 . − . · · · . +0 . − . − . +0 . − . . +0 . − . . ± . − . ± .
07 8 . +0 . − . . +0 . − . . +0 . − . − . +0 . − . . +0 . − . . ± .
03 0 . ± .
07 8 . +0 . − . . +0 . − . · · · . +0 . − . − . +0 . − . . +0 . − . . ± .
04 0 . ± .
04 8 . +0 . − . . +0 . − . · · · . +0 . − . − . +0 . − . . +0 . − . . ± .
03 0 . ± .
07 8 . +0 . − . . +0 . − . · · · . +0 . − . − . +0 . − . . +0 . − . . ± .
04 0 . ± .
08 8 . +0 . − . . +0 . − . · · · . +0 . − . − . +0 . − . . +0 . − . . ± .
08 0 . ± .
04 8 . +0 . − . . +0 . − . . +0 . − . − . +0 . − . . +0 . − . . ± . − . ± .
14 8 . +0 . − . . +0 . − . . +0 . − . − . +0 . − . . +0 . − . . ± .
06 0 . ± .
02 8 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . ± . − . ± .
25 8 . +0 . − . . +0 . − . · · · . +0 . − . − . +0 . − . . +0 . − . . ± .
11 0 . ± .
13 8 . +0 . − . . +0 . − . · · · . +0 . − . − . +0 . − . . +0 . − . . ± .
16 0 . ± .
05 8 . +0 . − . . +0 . − . Objects with ambiguous counterparts in the COSMOS data52.5+8-0.69 · · · · · · · · · · · · · · · · · · . ± .
04 0 . ± . · · · · · · · · · · · · · · · · · · · · · · · · . ± . − . ± . · · · · · · · · · · · · · · · · · · · · · · · · . ± .
16 0 . ± . · · · · · · · · · · · · · · · · · · · · · · · · . ± .
03 0 . ± . · · · · · · · · · · · · · · · · · · · · · · · · . ± .
14 0 . ± . · · · · · · · · · · · · · · · · · · · · · · · · . ± .
13 1 . ± . · · · · · · Candidate AGN55.5-3-0.60 984577 -19.78 0.62 10 . +0 . − . . +0 . − . . +0 . − . · · · · · · · · · · · · . +0 . − . . +0 . − . . +0 . − . · · · · · · · · · · · · Note . — These quantities are derived from COSMOS imaging and our measured line ratios. Magnitudes and colors are in AB units and arederived by integrating the best-fitting SED under the appropriate bandpasses. Stellar masses and SFRs are given in solar units, and were derivedusing FAST (Kriek et al. 2009). For this derivation we used a Chabrier (2003) initial mass function and a Calzetti et al. (2000) extinction curve.The line ratios, metallicity, and ionization parameter ( q ) are derived, taking into account a 1˚A (equivalent width) correction to the H β fluxes, aswell as the dust correction and its associated uncertainty. Metallicities and ionization parameters are calculated using the Kobulnicky & Kewley(2004) calibration. A dust correction has not been applied to the objects have ambiguous optical counterparts in the COSMOS imaging survey. M ⊙ . THE FUNDAMENTAL METALLICITY RELATION
In the previous section, we showed that, for a fixed lu-minosity (and possibly mass), galaxies with higher equiv-alent width emission lines (i. e. the USELs) have lowermetallicities. This result supports the idea that star for-mation drives some of the scatter in the MZ relation,even out to intermediate redshifts. For local galaxiesat fixed stellar mass, objects with higher SFRs havelower metallicities than lower-SFR galaxies (Ellison et al.2008; Mannucci et al. 2010, 2011; Yates et al. 2012;Andrews & Martini 2013). Mannucci et al. (2010) de-scribe this relation as a plane, and refer to it as theFundamental Metallicity Relation (FMR). Remarkably,Mannucci et al. report that high-redshift galaxies alsolie on the plane (albeit at lower masses and higher SFRsthan most low-z galaxies), implying that the physicsgoverning the evolution of metal enrichment has notchanged over cosmic time. This finding has recentlybeen confirmed for a large sample of intermediate red-shift ( z ∼ .
6) galaxies from zCOSMOS (Cresci et al.2012). Nevertheless, tests for evolution of the FMR havenot yet been extended below M ∼ M ⊙ . Here, weprovide the first such test.In light of the significant differences between metallici-ties derived from various calibrations (Kewley & Ellison2008), it is essential that we use metallicities which arederived consistently with those in (Mannucci et al. 2010,2011; the latter work extends the initial analysis to lowermasses). These metallicities are based on the calibra-tion from Maiolino et al. (2008), which is semi-empirical.The high metallicities are derived from the photoion-ization models of Kewley & Dopita (2002), whereas thelower metallicities are constrained from direct T e mea-surements reported by Nagao et al. (2006). While theMaiolino et al. calibration of R23 does not include a de-pendence on the ionization parameter, in other calibra-tions (i.e. KK04) this dependence is weak on the upperbranch of R23, where the present sample lies. There-fore, for this section, we re-calculate the metallicities forour sample using the Maiolino et al. (2008) calibrationof R23.Figure 7 compares our galaxies to the z = 0 . + l o g ( O / H ) Log M/M ⊙ −0.4−0.20.00.20.4 ∆ L o g ( O / H ) -1.41 ≤ log SFR ≤ -0.42-0.36 ≤ log SFR ≤ 0.02 0.08 ≤ log SFR ≤ 1.23 −0.2 −0.1 0.0 0.1 0.2µ (Mean of (he Res duals) L i k e li h oo d Full SampleM < 10 M ⊙ M > 10 M ⊙ Figure 7.
The fundamental metallicity relation, derived using theMaiolino et al. (2008) metallicity calibration, shows that low massgalaxies with high SFRs have systematically lower metallicities.The galaxy 23.5+2-0.33, which strongly influences the weighted mean of the residuals (see text), is shown as an open green sym-bol.
Top-
The MZ relation is plotted, with galaxies color-codedin three bins of SFR. The curves show the local FMR reported byMannucci et al. (2011). FMR.
Bottom–
Residuals from the localFMR (data minus relation given in Equation 1) show increasedscatter towards low stellar masses, owing to larger measurementerrors for faint galaxies. (Note that residuals are calculated usingmeasured SFRs rather than the mean values where Equation 1 hasbeen evaluated for the top panel. As a result the residuals in thebottom panel do not exactly correspond to the differences betweenthe data and models in the top panel.)
Inset–
Likelihood functionsfor the mean of the residuals are shown for different subsets of thedata, including the full sample, low and high mass subsamples, andthe SFR divided subsamples. With one exception, the likelihoodfunctions shown here include the galaxy 23.5+2-0.33, which drivessome of the trends towards larger positive residuals (see text). Thethin green curve shows the effect of removing this outlier. the relation (Equation 2 from Mannucci et al. 2011):12 + log(O / H) = 8 .
90 + 0 . m − . s − . m +0 . ms − . s for µ . ≥ .
5= 8 .
93 + 0 . µ . −
10) for µ . < . , (1)where m = log( M ) − s = log(SFR), and µ =log( M ) − . z ∼ . − . >
0, so it is reasonable to question whetherthese galaxies deviate slightly from the FMR. There-fore, we calculate the mean of the residuals, µ = h ∆log(O/H) i , and its uncertainty by using a maximum likeli-hood estimation to account for the individual measure-3 Table 4
Residuals from the local FMRSample Mean of the Residuals, µ Full sample 0 . ± . M > . M ⊙ − . ± . M < . M ⊙ . ± . − . ≤ log SFR ≤ − .
42 0 . ± . − . ≤ log SFR ≤ .
02 0 . ± . . ≤ log SFR ≤ . − . ± . − . ± . − . ≤ log SFR ≤ .
02 0 . ± . M < . M ⊙ . ± . ment errors. Under this approach, the probability ofobserving a galaxy with a residual y i and error, σ i is p i = e − ( y i − µ ) / σ i . Then, for the full sample the likeli-hood function becomes L ( µ ) = Q p i . We evaluate thislikelihood function between − . < µ < .
4, taking themaximum and the 68% confidence intervals of L ( µ ) torepresent the mean and its error. This estimate is madefor the full sample, as well as low and high mass subsam-ples (divided at 10 . M ⊙ ) and the subsamples in threebins of SFR.In the inset panel of Figure 7, we show the likelihoodfunctions for the mean of the FMR residuals. These cal-culations indicate only insignificant deviations from thelocal FMR. In Table 4, we give the mean of the residualsand its uncertainty for the full sample and various sub-samples. At first glance, we see two weakly significantdeviations from the local plane: one among the lowermass ( M < . M ⊙ ) galaxies, and the other for thosewith intermediate SFRs (green points). However, uponcloser inspection we find that these trends arise solelybecause of one galaxy (23.5+2-0.33) with a metallicity3.4 σ above the fundamental plane. (Furthermore, thisgalaxy has a strong influence on our calculation not be-cause its residual is large, but rather because its errorsare small.) Without this galaxy, the deviation disappears(see the thin green curve in the inset of Figure 7), andthe mean of the residuals fall within 1.5 σ of zero for allof the subsamples listed in Table 4. Since any claimsof a deviation from the FMR should be based on morethan one object, we conclude that our data show no com-pelling evidence for evolution at 10 < M/M ⊙ < . .This result lends greater leverage to the finding that theFMR is not evolving for higher mass galaxies at theseredshifts (Cresci et al. 2012).It is also interesting to examine the scatter aboutthe FMR, as intrinsic scatter could indicate that thereare additional physical processes that influence gas-phase metallicities. For intermediate redshift galaxies,Cresci et al. (2012) report a scatter of 0.11 to 0.14 dexabout the FMR. Yet, in our sample, the scatter appearsto be larger at lower masses. We find an RMS of 0.2 dexbelow M < . M ⊙ . Assigning some galaxies to thelower branch of R23 does not reduce this scatter. Theamplitude of the residuals are larger (or the about thesame for a few galaxies) when the lower metallicity solu-tions are adopted. In order to disentangle intrinsic scat-ter from increased measurement errors in faint galaxies,we use a Monte Carlo simulation. First, we assume that there is no intrinsic scatter relative to the FMR. Then,focusing only on the galaxies with M < . M ⊙ , wegenerate 10,000 mock realizations of the FMR residuals,perturbing the data in Figure 7 by their uncertainties.We calculate the RMS about the FMR for each real-ization, and find a mean of 0.23 dex, in good agreementwith observations. This exercise implies that the amountof scatter that we observe can be entirely explained byour measurement errors. Therefore, we conclude thatthe intrinsic scatter about the FMR must be small. Re-peating the simulation with additional intrinsic scattershows allows us to place an upper limit on this scatter.We find that an intrinsic scatter of 0.16 dex produces anobserved RMS ≤ . z = 0 . CONSTRAINING GAS FLOWS WITH THEMASS-METALLICITY AND SFR-M ⋆ RELATIONS
As we introduced in §
1, the MZ relation is an im-portant measure of galaxy evolution. Galaxies are notclosed boxes; gas must be accreted from the IGM tofuel star formation (e.g. Erb 2008; Bouch´e et al. 2010),and galactic outflows are commonly observed at bothlow and high-redshift (e.g. Heckman et al. 1990; Martin2005; Henry et al. 2007; Soto et al. 2012; Kornei et al.2012; Erb et al. 2012). The MZ relation provides an in-dependent, albeit indirect, constraint on these gaseousflows. On one hand, the accretion of primordial gas willreduce the gas-phase metallicity in a galaxy. On theother hand, galactic winds can create a deviation fromthe closed-box model by lowering the gas fraction with-out changing the metallicity (Edmunds 1990; Dalcanton2007). Combining our data with the higher mass MZ re-lation provides an important increase in dynamic rangethat allows for more stringent constraints on models.Our emission line selection of galaxies does not stronglybias our sample or hamper our ability to test theoreticalmodels. In Figure 5 we show that our sample is consis-tent with the DEEP2 MZ relation reported by Zahid etal. (2011; at least in the limited mass range where ourdata overlap). This agreement can be understood, sincethe FMR dependence on the SFR is relatively weak. Forexample, if the SFRs of our galaxies were biased high bya factor of several, then (following the Mannucci et al.2011 FMR) an “unbiased” sample would have metallici-ties which are approximately 0.1 dex higher. An increasein metallicity this large is implausible, as it would imply alack of metallicity evolution inconsistent with other stud-ies. Likewise, it is worth pointing out that the high S/Nof the spectra shown in Figures 1 and 2 implies that oursample is not biased towards higher metallicities by arequirement for strong H β emission. The objects whichwere excluded due to low S/N all fell among the class § Log M h /M ⊙ L o g S F R / M ⊙ / r − + l o g ( O / H ) Log M/M ⊙ This workThis work, binnedDEEP2Momentum DrivenEnergy DrivenConstant WindNo Wind
Figure 8.
The SFR-M ∗ correlation (top) and MZ relation (bottom) constrain models from Dav´e et al. (2012). Large red squares showthe average mass, metallicity, and SFR for four mass bins: M > . M ⊙ , 10 . < M/M ⊙ < . , 10 . < M/M ⊙ < . and M < . M ⊙ . Error bars on the binned data represent the standard deviation of the mean. We combine our data with binned higher mass datafrom DEEP2: the z = 0 . − . ∗ correlation reported by Noeske et al. (2007; converted to a Chabrier 2003 IMF), and the z ∼ . χ for the union of ourdata and the Zahid et al. data. SFR-M ∗ models are not renormalized. The models are described in detail in § M ∗ − M halo relation from Moster et al. (2010). ∗ relation (i.e. the star-forming main sequence)in the top panel of Figure 8. This comparison demon-strates that our galaxies do not have extreme SFRs fortheir stellar masses. Rather, they lie on an extrapolationof the relation reported by Noeske et al. (2007). Oursample could only be significantly biased if the “true”SFR-M ∗ relation turns over and becomes steeper at lowstellar masses. While this trend is predicted to occurwhen photoionization heating suppresses star formationin low mass halos, it is not expected to be importantabove M halo & M ⊙ (Okamoto et al. 2008). Whilebeyond the scope of this paper, it is worth noting thatwe do not detect the flattening of the SFR-M ∗ relationat low masses which is reported by Pirzkal et al. (2012). Theoretical Framework
One set of models which have recently gained tractionare those that adopt an equilibrium between mass inflow( ˙ M in ), outflow ( ˙ M out ), and gas consumption via starformation ( ˙ M ∗ ; Bouch´e et al. 2010; Dutton et al. 2010;Finlator & Dav´e 2008; Dav´e et al. 2012). These modelsprovide a relatively simple interpretation of the FMR asa manifestation of stochastic star formation. When agalaxy accretes gas, its metallicity is diluted and its starformation increases. The increased star formation servesto consume the extra gas and return the galaxy to itsequilibrium. Likewise, a pause in gas accretion will lowerstar formation rates and increase gas-phase metallicitiesuntil accretion resumes. These models not only predict aMZ relation, but also the SFR-M ∗ relation that we haveshown in Figure 8. above. Therefore, in the remainderof this section we leverage the two relations to gain thebest possible constraints on the models.Quantitatively, we can express the equilibrium condi-tion as (reproducing Equation 1 from Dav´e et al. 2012):˙ M in = ˙ M out + ˙ M ∗ . (2)Following this assumption, Finlator & Dav´e (2008) andDav´e et al. (2012) show that SFRs and metallicities canbe written as: SF R = ζ ˙ M grav (1 + η )(1 − α z ) (3)and Z O = y η − α Z . (4)The quantities in Equations 3 and 4 are defined as fol-lows:1. Z O is taken to represent the mass fraction of oxygenin the ISM. This quantity is converted to the unitsof 12 + log(O/H) by taking log( Z O ) = log(O/H)+ log( × M O /M H ). M O and M H are the atomicmasses of oxygen and hydrogen.2. ˙ M grav is the cosmological baryonic accretion rate,taken from Dekel et al. (2009). Because this quan-tity (as well as others below) are expressed in termsof halo mass, we adopt the M ∗ − M halo relation fromMoster et al. (2010). 3. ζ is a quantity that represents preventive (ratherthan ejective) feedback from gas heating. Thereare multiple forms of preventive feedback, and theycombine multiplicatively. In the range of halo-masses where our objects lie, the most importantof these is gravitational heating from virial shockformation in accreted gas. Following Dav´e et al.(2012), we take the analytical form given byFaucher-Giguere et al. (2011): ζ grav ≈ . (cid:18) z (cid:19) . (cid:18) M halo M ⊙ (cid:19) − . . (5)At high masses star formation quenching associ-ated with supermassive black holes becomes impor-tant. While we do not aim to constrain quenching,we implement it following Dav´e et al. (2012): ζ quench = / (cid:18) M halo . M ⊙ (cid:19) ! − . . (6)The mass scale that we have adopted for ζ quench is for z = 0, and while it may be higher at earliercosmic times (Dekel et al. 2009), the exact scalingis unimportant in the present analysis. At the lowmass end, we take the photoionization feedback tobe unimportant; as mentioned above, it is not ex-pected to play a significant role at M halo & M ⊙ .Finally, Dav´e et al. (2012) do note that heating bygalactic winds may be important, but the physicsof this effect is poorly understood. As such, theyadopt an arbitrary parameterization of ζ winds toconsider its qualitative effects. As we will showbelow, this additional heating is not needed to re-produce the present data.4. y is the nucleosynthetic yield of oxygen, whichis between 0 . < y < .
021 (Finlator & Dav´e2008). Since metallicity calibrations are uncertain(Kewley & Ellison 2008), we take y as a free pa-rameter as we search for a normalization that bestmatches our observed MZ relation. Hence, ourcomparison to the MZ relation concerns its slope,but not the normalization.5. η is the mass loading factor, which is definedas the ratio of the outflow rate to the SFR: η = ˙ M out / ˙ M ∗ . In the comparison that follows,we adopt mass-loading factors that correspond(respectively) to momentum- and energy- drivenwinds (i.e. Murray et al. 2005; Finlator & Dav´e2008; Dav´e et al. 2011b; Peeples & Shankar 2011;Dav´e et al. 2012): η = ( M halo / M ⊙ ) − / (7) η = ( M halo / M ⊙ ) − / . (8)The normalizations of these η are taken fromDav´e et al. (2012). In addition to these two pa-rameterizations of η , we compare to the case of nowinds ( η = 0), also η = 1, where the mass loss rateis fixed to the SFR.6. Finally, the quantity α Z is the ratio of the metallic-ities of infalling gas and the ISM: Z in /Z ISM . The6 inclusion of α Z allows for enriched inflows (pos-sibly from previously ejected material now beingre-accreted from the galaxy halo). Additionally, itappears in the model for SFR as a simple way toquantify the recycling of enriched halo gas into theISM (i.e. an additional source of fuel for star for-mation). The parameterization of α z is taken frommomentum-driven wind simulations in Dav´e et al.(2011b, 2012): α Z = (0 . − . z )( M ∗ / M ⊙ ) . (9)(although they note that it is a “crude” parameter-ization). While we aim to test models beyond thosethat are momentum-driven, α z is not reported forthese simulations. Therefore we use this parame-terization for all of the models with winds. For theno wind case we consider α z = 0, since there can beno recycling of previously ejected material in thisscenario. We consider the effects of modifying α z in the discussion below. Comparison of equilibrium models tointermediate-redshift data
Figure 8 shows how the equilibrium models com-pare to the intermediate-redshift MZ and SFR-M ∗ re-lations. In order to get the best constraints on themodels, we combine our sample with binned DEEP2data representing the MZ relation for z ∼ . ∗ relation for z ∼ . − . χ (including uncertainties in both metallicity and mass )are y = 0 . , . , .
010 and 0.008 for the momentumdriven, energy driven, constant wind ( η = 1) and no wind( η = 0, α z = 0) models respectively. We next describehow each model compares to the data: No wind — Not surprisingly, equilibrium models that ex-clude outflows are unable to reproduce the data. Mostdrastically, when η = 0 and α z = 0, Equation 4 hasno mass dependence. Hence, the predicted MZ relationis implausibly flat, and the slope of SFR-M ∗ relation isalso too flat. Figure 8 shows that, without winds lowmass galaxies make too many stars (and metals), andare unable to get rid of the metals that they make. It isworth noting that α z is not strictly zero in the no-windsimulation (Dav´e et al. 2011a), since infalling gas can beenriched by other galaxies or could represent the accre-tion of a satellite galaxy. A non-zero α z would furtherincrease the SFR and amplify the disagreement betweenthe SFR-M ∗ data and the no-wind model. Constant Wind — A model where the mass-loss rate isequivalent to the SFR shows good agreement with theSFR-M ∗ relation at all stellar masses. However, thismodel predicts an MZ relation which is too flat at lowstellar masses. We take χ i = ( OH i − f ( M i )) / ( σ OH,i + f ′ ( M i ) σ M,i ), where f ( M i ) and f ′ ( M i ) are the model and its derivative evaluated at M i . χ is the sum over the i observations of χ i . Momentum Driven Wind — Of the models shown in Fig-ure 8, the momentum driven wind shows the best matchto the MZ data. However, the metallicities predicted bythis model turn up at higher masses, owing to the de-pendence on α z . Equation 4 shows that the predictedmetallicities diverge as α z approaches unity at highermasses. While the disagreement between the model anddata is only apparent in the highest mass bin, the upturnremains implausible. Locally, the MZ relation flattens tohigher masses (Tremonti et al. 2004), so the model shownin Figure 8 crosses the z ∼ . M ∼ . M ⊙ . This observation suggests that the mass scaling for α Z given by Dav´e et al. (2012) may be too steep at highmasses.In addition to the MZ relation, we compare themomentum-driven wind model to the SFR-M ∗ relationin the top panel of Figure 8. In this case, the modelslightly under-predicts the SFRs for the galaxies in thepresent study as well as for the lower mass DEEP2 mea-surements. This discrepancy between the data and mod-els at low masses is qualitatively similar to what is foundat higher masses and lower redshifts. Dav´e et al. (2011a)and Weinmann et al. (2012) find that both simulationsand semi-analytic models are unable to reproduce thepopulation of low mass galaxies with high specific SFRs.Given the uncertainty in α z , we next consider whethermodifying this variable can produce a momentum drivenwind model that is a good fit to both the MZ and SFR-M ∗ data. If we remove the mass-dependence of α z inEquation 9 ( α z ∝ M . ∗ ), the predicted SFR-M ∗ relationappears very similar to the constant wind model (a goodmatch to the data), but the predicted MZ relation (notshown) is far too flat. In summary, modifying α z doesnot improve the agreement between the data and themomentum driven wind model. Energy Driven Wind — The energy driven wind modelsshown in Figure 8 are too steep compared to both theMZ data and the SFR-M ∗ data. However, as we al-ready noted, some of this steepening of the MZ rela-tion occurs because α z may be too large at high masses.In fact, an energy driven wind model with α z ∝ M . ∗ and y = 0 .
022 appears very similar to the momentumdriven wind model shown in both the top and bottompanels. For this model, the MZ relation model reducesto a straight line that runs through all of the data, andSFRs are slightly under-predicted at low masses. Ul-timately, we cannot distinguish the momentum drivenmodel from an energy driven model with α z ∝ M . ∗ .However, we do note that this variable shows some massdependence in the momentum-driven wind simulations(Dav´e et al. 2011a,b), so it unlikely that this dependenceis non-existent for energy-driven winds. We thereforeconclude that energy-driven winds are unlikely to explainthe data.Recent simulations from Hopkins et al. (2012) havesuggested that outflows depend strongly on gas surfacedensity, so that winds from low density dwarf galaxiesare dominated by energy-driving from supernovae andstellar winds. More massive star-forming galaxies withhigher gas densities, on the other hand, are predicted toprefer momentum driven winds. The present data do notindicate a mass-dependent η ; Figure 8 shows no evidencefor steeper MZ and SFR-M ∗ slopes towards lower masses.7This analysis (and Figure 8) shows that there may bea tension between the data and the equilibrium model.On one hand, models which best match the MZ re-lation under-predict the amount of star formation inlow mass galaxies (and even intermediate masses probedby DEEP2). Likewise, models that best reproduce theSFR-M ∗ relation over-predict the metallicities of galax-ies. This trend can be understood as a generic prop-erty of the models, because both Equations 3 and 4 areproportional to (1 + η ) − (1 − α z ) − ; changes in thesemodel components alter the MZ and SFR-M ∗ relation inthe same manner . However, if preventive feedback fromgas heating has been overestimated ( ζ underestimated inEquations 3 and 5), then SFRs can be increased withoutmodifying the MZ relation. In fact, Dav´e et al. (2012)note that ζ grav is taken from simulations that do notinclude metal-line cooling (Faucher-Giguere et al. 2011),and raise the question of whether this effect is important.Alternatively, if ζ is correct, then the data may suggesta deviation from the equilibrium model.Ultimately, we conclude that this disagreement re-mains subtle. While we have argued that emission lineselection does not largely bias our results, we cannotrule out a small effect. As an example, if the SFRs pre-sented in Figure 8 are high by 0.1 dex, we would expectan unbiased sample to have an SFR- M ∗ relation thatagrees better with the momentum driven wind model atlow masses. Additionally, according to the FMR, SFRswhich are 0.1 dex lower should be accompanied by metal-licities which are around 0.03 dex higher, in even betteragreement with the momentum driven wind MZ relation.Even without emission-line selection bias, it is importantto recall that the [O II ], H β , and SED-based SFR indi-cators discussed in the Appendix differ systematically byup to 0.2 dex. However, modifying the SFR under thesescenarios can not satisfactorily bring the data in line withthe momentum-driven model. Even in the higher massdata alone, this model predicts a steeper SFR- M ∗ rela-tion than the DEEP2 result (Noeske et al. 2007); there-fore, the discrepancy which we have identified is apparentin a magnitude-limited sample. We conclude that H α fol-lowup spectroscopy of our sample (combined with a massselected control sample) can definitively assess the effectsof emission line selection, while simultaneously reducingerrors on dust, SFR, and metallicity. We leave this workas the subject of a future paper.Finally, it is worth pointing out that systematicuncertainties in our metallicity calibration cannot ex-plain the discrepancy between the data and models.Kewley & Ellison (2008) show that local (SDSS) MZrelations have similar low mass slopes under mostcalibrations. The Tremonti et al. (2004) calibrationand the direct-method electron temperature calibration(Andrews & Martini 2013) are two exceptions– both pro-duce MZ relations that are steeper than what we haveused here. Hence, if we calculated metallicities in thesame way as Tremonti et al. or by using electron temper-atures, the tension between the data and models wouldbe amplified. On the other hand, the calibrations re-ported by Pilyugin (2001) and Pilyugin & Thuan (2005)give MZ relations that are flatter than most. However,we note that they also have metallicities around 0.5-0.7dex lower than those from KK04. These lower metal-licities would introduce other difficulties, as they would require normalizing yields that fall below the plausiblerange indicated in Finlator & Dav´e (2008). CONCLUSIONS
In this work we have placed the first constraints on thelow mass, intermediate redshift MZ relation. By usingemission line selection in the COSMOS field, we are ableto efficiently identify and measure the metallicities from26 galaxies reaching masses of 10 M ⊙ at z ∼ .
65. Com-bined with previous measurements from magnitude lim-ited samples, these data extend our knowledge of the MZrelation to masses an order of magnitude smaller. Thislimit is comparable to the low mass limit of the local MZrelation determined from SDSS data. Therefore, for thefirst time we are able to measure the metallicity evolutionof intermediate redshift galaxies at
M < M ⊙ . Com-pared to the z ∼ . . < M/M ⊙ < . . We showthat this measurement is consistent with an MZ relationthat evolves more strongly at low stellar masses. We in-terpret this mass-dependent evolution as consistent withdownsizing trends, where higher mass objects have lessleverage to alter their gas-phase metallicities after mostof their stars have been assembled.An important development in our understanding ofmetallicity evolution is the discovery that the scatter inthe relation can be reduced by accounting for star forma-tion. This measurement was quantified as a plane, anddubbed the Fundamental Metallicity Relation (FMR) byMannucci et al. (2010). Using the present sample, wefind that a planar relation does indeed exist among lowmass, intermediate redshift galaxies. Consistent with thefindings of Mannucci et al., we see no evidence for evo-lution of the FMR, as our emission-line selected sam-ple falls in good agreement with their z ∼ . M < . M ⊙ .The MZ relation is an important probe of galaxy evolu-tion models, as accretion and galactic outflows modulatethe gas-phase metallicities of galaxies. Hence, compari-son to model predictions can help us to gain insight intogalaxy formation. We have combined our MZ relationwith the SFR-M ∗ correlation that is also measured fromour data, taking higher mass data from the literature(Noeske et al. 2007; Zahid et al. 2011). We compare tothe family of models outlined in Dav´e et al. (2012), whereit is assumed that galaxies prefer to maintain an equi-librium between inflows, outflows, and star formation(Finlator & Dav´e 2008; Bouch´e et al. 2010; Dutton et al.2010; Dav´e et al. 2012). We find that models which pre-dict the MZ relation may under-predict the SFRs of lowmass galaxies, and at the same time, models that pre-dict the SFRs of low mass galaxies tend to over-predicttheir metallicities. While this finding could represent abreakdown of the equilibrium model in low mass galax-ies, it could alternatively be an indication that feedbackfrom gas-heating has been overestimated in simulations(i.e. Faucher-Giguere et al. 2011). To solidify this re-8sult, we have begun H α and [N II ] spectroscopy to fol-lowup the present sample and simultaneously measure amass-selected control sample. These data will clarify theeffects of emission line selection and greatly reduce thestatistical uncertainties in our metallicity, dust, and SFRmeasurements.To conclude, these observations have provided a valu-able look at the metallicity evolution of low mass galaxiesoutside the local universe. We look forward to the physi-cal insights and new constraints that can be gained fromlarger samples and a better characterization of system-atic uncertainties.The authors thank Jane Rigby, Dawn Erb, Joey Wong,Amber Straughn, Evan Skillman, Molly Peeples, NicolasBouch´e, Brian Siana and Susan Kassin for insightful dis-cussions. We also wish to thank the anonymous refereefor helping to improve this manuscript. We are grate-ful to Esther Hu and Jabran Zahid for providing tabulardata, and Peter Capak and the COSMOS team for thehigh-level science products that made this project pos-sible. This research has made use of the NASA/IPACInfrared Science Archive, which is operated by the JetPropulsion Laboratory, California Institute of Technol-ogy, under contract with the National Aeronautics andSpace Administration. This work was supported by NSFgrants AST-0808161 and AST-1109288. The authors rec-ognize and acknowledge the very significant cultural roleand reverence that the summit of Mauna Kea has alwayshad within the indigenous Hawaiian community. We aremost fortunate to have the opportunity to conduct ob-servations from this mountain. REFERENCESAllende Prieto, C., Lambert, D. L., & Asplund, M. 2001, ApJ,557, L63Andrews, B. H., & Martini, P. 2013, ApJ, 765, 140Atek, H., Siana, B., Scarlata, C., et al. 2011, ApJ, 743, 121Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5Berg, D. A., Skillman, E. D., Marble, A. R., et al. 2012, ApJ, 754,98Bouche, N., Dekel, A., & Genzel, R., et al. 2010, ApJ, 718, 1001Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004,MNRAS, 351, 1151Brinchmann, J., Pettini, M., & Charlot, S. 2008, MNRAS, 385,769Brooks, A., Governato, F., Booth, C. M., et al. 2007, ApJ, 655,17LBruzual, G. & Charlot, S. 2003, MNRAS, 344, 1000Bruzual, G. 2007, ASPC, 374, 303Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682Capak, P., Aussel, H., Ajiki, M., et al. 2007, ApJS, 172, 99Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345,245Chabrier, G. 2003, PASP, 115, 763Conroy, C., & Gunn, J. E. 2010, ApJ, 172, 833Cooper, M. C., Newman, J. A., Davis, M., Finkbeiner, D. P.,Gerke, B. F. 2012, ASCL, 1203.003Cowie, L. L., & Barger, A. J. 2008, ApJ, 686, 72Cresci, G., Mannucci, F., Maiolino, R., et al. 2010, Nature, 467,811Cresci, G., Mannucci, F., Sommariva, V., et al. 2012, MNRAS,421, 262Dalcanton, J. J. 2007, ApJ, 658, 941Dav´e, R., Oppenheimer, B. D., & Finlator, K.,2011, MNRAS,415, 11Dav´e, R., Finlator, K., & Oppenheimer, B. D. 2011, MNRAS,416, 1354 Dav´e, R., Finlator, K., & Oppenheimer, B. D., 2012, MNRAS,421, 98Dayal, P., Ferrara, A., & Dunlop, J. S. 2013, MNRAS, 430, 2891Dekel, A., Birnboin, Y., Engel, G., et al. 2009, Nature, 457, 451Dressler, A., Martin, C. L., Henry, A., Sawicki, M., & McCarthy,P. 2011, ApJ, 740, 71Dressler, A., Bigelow, B., Hare, T., et al. 2011, PASP, 123, 288Dutton, A. A., van den Bosch, F. C., Dekel, A. 2010, MNRAS,405, 1690Edmunds, M. G. 1990, MNRAS, 246, 678Elbaz, D., Daddi, E., Le Borgne, D., et al. 2007, A&A, 468, 33Ellison, S., Patton, D. R., Simard, L., & McConnachie, A. W.2008, ApJ, 672, 107LErb, D. K., Shapley, A. E., Pettini, M., et al. 2006, ApJ, 644, 813Erb, D. K. 2008, ApJ, 674, 151Erb, D. K., Quider, A. M., Henry, A. L., & Martin, C. 2012, ApJ,759, 26Faber, S. M., Phillips, A. C., Kibrick, R.I., et al. 2003, SPIE,4841, 1657Faucher-Giguere, C. A., Keres, D., & Ma, C.-P. 2011, MNRAS,417, 2982Fillipenko, A. V. 1982, PASP, 94, 715Finlator, K., & Dav´e, R. 2008, MNRAS, 385, 2181Finlator, K., Oppenheimer, B. D., Dav´e, R. 2011, MNRAS, 410,1730Hainline, K. N., Shapley, A. E., Kornei, K. A., et al. 2009, ApJ,701, 52Heckman, T. M., Armus, L., & Miley, G. K. 1990, ApJS, 74, 833Henry, A. L., Martin, C. L., Dressler, A., Sawicki, M., &McCarthy, P. 2012, ApJ, 744, 149Henry, A. L., Turner, J. L., Beck, S. C., Crosthwaite, L. P., &Meier, D. S. 2007, AJ, 133, 757Hopkins, P. F., Quataert, E., & Murray, N. 2012, MNRAS, 421,3522Hu, E., Cowie, L. L., Kakazu, Y. & Barger, A. 2009, ApJ, 698,2014Ilbert, O., Capak, P., Salvato, M., et al. 2009, ApJ, 690, 1236Juneau, S., Dickinson, M., Alexander, D. M., & Salim, S. 2011,ApJ, 736, 104Kakazu, Y., Cowie, L. L., & Hu, E. M. 2007, ApJ, 668, 853Kashikawa, N., Shimasaku, K., Matsuda, Y., et al. 2011, ApJ,648, 7Kewley, L. J., & Dopita, M. A. 2002, ApJS, 142, 35Kewley, L. J., & Ellison, S. L. 2008, ApJ, 681, 1183Kennicutt, R. C., 1998, ARA&A, 36, 189Kirby, E. N., Martin, C. L., & Finlator, K. 2011, ApJ, 742, 25LKniazev, A. Y., Grebel, E. K., Hao, L., et al. 2003, ApJ, 593, 73LKobulnicky, H. A., & Kewley, L. J. 2004, ApJ, 617, 240Kornei, K. A., Shapley, A. E., Martin, C. L., et al. 2012, ApJ,758, 135Kriek, M., van Dokkum, P. G., Labb´e, I., et al. 2009, ApJ, 700,221Kriek, M., Labb´e, I., Conroy, C., et al. 2010, ApJ, 722, L64Kroupa, P. 2001, MNRAS, 322, 231Lamareille, F., Brinchmann, J., Contini, T., et al. 2009, A&A,495, 53Lara-L´opez, M. A., Cepa, J., Bongiovanni, A., et al. 2010, A&A,521, 53LLee, H., Skillman, E. D., Cannon, J. M., et al. 2006, ApJ, 647, 970Le F`evre, O., Vettolani, G., Paltani, S., et al. 2004, A&A, 428,1043Liang, Y. C., Hammer, F., & Yin, S. Y. 2007, A&A, 474, 807Lilly, S. J., Carollo, C. M., & Stockton, A. N. 2003, ApJ, 597, 730Lilly, S. J., Le F`evre, O., Renzini, A., et al. 2007, ApJS, 172, 70Lilly, S. J., Carollo, M. C., Pipino, A., Renzini, A., & Peng, Y.2013, arXiv:1303.5059L´opez-S´anchez, ´A. R. , Dopita, M. A., Kewley, L. J., et al. 2012,MNRAS, 426, 2630Ly, C., Malkan, M. A., Kashikawa, N., et al. 2007, ApJ, 657, 738Maiolino, R., et al. 2008, A&A, 488, 463Mannucci, F., Cresci, G., Maiolino, R., Marconi, A., & Gnerucci,A. 2010, MNRAS, 408, 2115Mannucci, F., Salvaterra, R., & Campisi, M. A. 2011, MNRAS,414, 1263Maraston, C. 2005, MNRAS, 362, 799 Martin, C. L., Sawicki, M., Dressler, A., & McCarthy, P. 2008,ApJ, 679, 942Martin, C. L. 2005, ApJ, 621, 227Massey, P., & Gronwall, C. 1990, ApJ, 358, 344McGaugh, S. 1991, ApJ, 380, 140Moster, B. P., Somerville, R. S., Maulbetsch, C., et al. L. 2010,ApJ, 710, 903Moustakas, J., Kennicutt, R. C., & Tremonti, C. A. 2006, ApJ,642, 775Moustakas, J., Zaritsky, D., Brown, M., et al. 2011,arXiv:1112.3300Murray, N., Quatert, E., & Thompson, T. A. 2005, ApJ, 618, 569Nagao, T., Maiolino, R., & Marconi, A., 2006, A&A, 459, 85Newman, J. A., Cooper, M. C., Davis, M., et al. 2012,arXiv:1203.3192Nicholls, D., Dopita, M. A., & Sutherland, R. S., ApJ, 2012, 752,148Noeske, K. G., Faber, S. M., Weiner, B. J., et al. 2007, ApJ, 660,L47Okamoto, T., Gao, L., Theuns, T. 2008, MNRAS, 390, 920Oke, J. B. 1990, AJ, 99, 1621Oppenheimer, B. D., Dav´e, R., & Finlator, K. 2009, MNRAS,396, 729Pagel, B. E. J., Edmunds, M. G., Blackwell, D. E., Chun, M. S.,& Smith, G. 1979, MNRAS, 189, 95Peeples, M. S., Pogge, R. W., & Stanek, K. Z. 2009, ApJ, 695, 259Peeples, M. S., & Shankar, F. 2011, MNRAS, 417, 2962Peimbert, M., & Costero, R. 1969, Bol. Obs. Ton. y Tac., 5, 3Pettini, M., & Pagel, B. E. J. 2004, MNRAS, 384, 59L Pilyugin, L. S. 2001, A&A, 374, 412Pilyugin, L. S., & Thuan, T. X. 2005, ApJ, 631, 231Pirzkal, N., Rothberg, B., Ly, C., et al. 2012, ApJ,arXiv:1208.5535Savaglio, S., Glazebrook, K., Le Borgne, D., et al. 2005, ApJ, 635,260Schaerer, D., & de Barros, S. 2009, A&A, 502, 423Shapley, A. E., Coil, A. L., Ma, C.-P., Bundy, K. 2005, ApJ, 635,1006Soto, K. T., Martin, C. L., Prescott, M. K. M., & Armus, L.2012, ApJ, 757, 86Stasi´nska, G. 2005, A&A, 434, 507Takahashi, M. I., Shioya, Y., Taniguchi, Y., et al. 2007, ApJS,172, 456Tremonti, C. A., Heckman, T. M., Kauffman, G., et al. 2004,ApJ, 613, 898van den Bergh, S. 1962, AJ, 67, 486van Zee, L., Skillman, E. D., & Haynes, M. P. 2006, ApJ, 637, 269Weinmann, S. M., Pasquali, A., Oppenheimer, B. D., et al. 2012,MNRAS, 426, 2797Wofford, A., Leitherer, C., & Salzer, J. 2013, ApJ, 765, 118Wuyts, E., Rigby, J. R., Sharon, K., & Gladders, M. D. 2012,ApJ, 755, 73Xia, L., Malhotra, S., Rhoads, J., et al. 2012, AJ, 144, 28Yates, R. M., Kauffman, G., & Guo, Q. 2012, MNRAS, 422, 215Zahid, H. J., Kewley, L. J., & Bresolin, F. 2011, ApJ, 730, 137Zhao, Y., Gao, Y., & Gu, Q. 2010, ApJ, 710, 663Zibetti, S. Gallazzi, A., Charlot, S. Pierini, D., & Pasquali, A.2013, MNRAS, 428, 1479APPENDIX
ASSESSING SFR MEASUREMENTS In § § β and [O II ]. For the H β method, we use the dust extinction from the SED fits, scaled up by a factor of 2.3to account for the difference between stellar and nebular extinction (Calzetti et al. 2000). We also correct the H β fluxesfor the small amount of stellar absorption, as discussed above. Next, the H β luminosities are converted to H α , assuminga Balmer decrement of 2.8. We then use the H α -SFR calibration given by Kennicutt (1998), scaled appropriately to aChabrier (2003) IMF. To derive SFRs from [O II ] luminosity, we use the calibration given by Moustakas et al. (2006),which includes an M B dependence, but does not require that the line measurement be corrected for dust.In order to make a direct comparison to the SED-derived SFRs, we must correct the emission line fluxes for both slitlosses and and extraction aperture losses. Rather than model these losses (which would not account for uncertainties inthe absolute flux calibration), we compare our data to narrowband imaging in COSMOS. First, we infer the emissionline flux from the narrowband (NB816) photometry, using the methods outlined in Ly et al. (2007) and Takahashi et al.(2007). Since the NB816 bandpass has a non-uniform throughput, we calculate a correction to this flux based on therelative throughput at the observed wavelengths of the emission lines. (This correction can be important, since it is notunusual that both of the [O III ] doublet lines are found away from the central wavelength of the NB816 filter.) Becausethe COSMOS catalog contains total magnitudes (under the reasonable assumption that the galaxies are unresolvedwith 1.5 ′′ FWHM spatial resolution), the line fluxes inferred from narrowband imaging are not subject to aperturelosses. For 17 galaxies in our sample with emission lines that are bright enough to be detected in the narrowbandimaging, we can infer the aperture losses by comparing these narrowband imaging fluxes to our spectroscopic fluxes. Wefind typical correction factors of 1.1-2.0, with a median of 1.4. We adopt this average correction to explore systematicdifferences between star formation indicators.Figure 9 compares the SFRs derived from the SEDs, H β , and [O II ]. In addition to the SED fits described in § τ as a free parameter; red points), we also make thecomparison for constant star-forming models (blue points). This exercise shows that the SFRs derived using differentmethods are correlated, so that we can easily distinguish the galaxies with high and low SFRs. However, Figure 9also shows that there are systematic shifts as large as 0.2 dex between the different estimators. Determining the mostaccurate star formation indicator is beyond the scope of this paper. Ultimately, a systematic uncertainty of 0.2 dexdoes not affect our conclusions. In §
6, we show that the scatter in the MZ relation is correlated with SFRs. As withthe local FMR, metallicity depends only weakly on the SFR, so that a 0.2 dex offset in SFR translates to a 0.03 dexshift in the metallicity predicted by the local FMR (Mannucci et al. 2010, 2011). This difference in metallicity is muchsmaller than the uncertainties on the FMR residuals shown in Figure 7. Likewise, in § ∗ relation toconstrain models. However, 0.2 dex of systematic uncertainty is small compared to the dynamic range of SFRs shownin Figure 8. An systematic offset is unlikely to alter our conclusions, as the SFR-M ∗ trends discussed in § Hβ SFR (M ⊙ yr −1 ) S E D S F R ( M ⊙ y r − ) Constant SFRτ models 0.1 1.0 10.0 100.0
SED SFR (M ⊙ yr −1 ) [ O II ] S F R ( M ⊙ y r − ) [OII] SFR (M ⊙ yr −1 ) H β S F R ( M ⊙ y r − ) Figure 9.
Star formation rates derived three different methods are compared. Blue points assume a constant star formation history, andthe red points assume exponentially declining SFRs ( τ models) discussed in § β -derived SFRs are corrected for dust extinctionusing these SED fits. (The center and right panels– where the SED-independent [O II ] SFRs are compared– show that the τ models tendtowards slightly less dust.) The [O II ] and H ββ