Galaxy And Mass Assembly (GAMA): The inferred mass--metallicity relation from z=0 to 3.5 via forensic SED fitting
Sabine Bellstedt, Aaron S. G. Robotham, Simon P. Driver, Jessica E. Thorne, Luke J. M. Davies, Benne W. Holwerda, Andrew M. Hopkins, Maritza A. Lara-Lopez, ?ngel R. López-Sánchez, Steven Phillipps
MMNRAS , 1– ?? (2019) Preprint 24 February 2021 Compiled using MNRAS L A TEX style file v3.0
Galaxy And Mass Assembly (GAMA): The inferredmass–metallicity relation from z = Sabine Bellstedt, (cid:63) Aaron S. G. Robotham, , Simon P. Driver, Jessica E. Thorne, Luke J. M. Davies, Benne W. Holwerda, Andrew M. Hopkins, Maritza A. Lara-Lopez, ´Angel R. L´opez-S´anchez, , , Steven Phillipps ICRAR, The University of Western Australia, 7 Fairway, Crawley WA 6009, Australia ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D) Department of Physics and Astronomy, University of Louisville, Natural Science 102, Louisville KY 40292, USA Australian Astronomical Optics, Macquarie University, 105 Delhi Rd, North Ryde, NSW 2113, Australia Armagh Observatory and Planetarium, College Hill, Armagh, BT61 9DG, UK Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia Astrophysics Group, School of Physics, University of Bristol, Bristol BS8 1TL, UK
ABSTRACT
We analyse the metallicity histories of ∼ z < .
06 modelled by the SED-fitting code
ProSpect using an evolving metallicity implementation. These metallicity histories, in combinationwith the associated star formation histories, allow us to analyse the inferred gas-phase mass–metallicity relation.Furthermore, we extract the mass–metallicity relation at a sequence of epochs in cosmic history, to track the evolvingmass–metallicity relation with time. Through comparison with observations of gas-phase metallicity over a largerange of redshifts, we show that, remarkably, our forensic SED analysis has produced an evolving mass–metallicityrelationship that is consistent with observations at all epochs. We additionally analyse the three dimensional mass–metallicity–SFR space, showing that galaxies occupy a clearly defined plane. This plane is shown to be subtlyevolving, displaying an increased tilt with time caused by general enrichment, and also the slowing down of starformation with cosmic time. This evolution is most apparent at lookback times greater than 7 Gyr. The trends inmetallicity recovered in this work highlight that the evolving metallicity implementation used within the SED fittingcode
ProSpect produces reasonable metallicity results over the history of a galaxy. This is expected to provide asignificant improvement to the accuracy of the SED fitting outputs.
Key words: galaxies: elliptical and lenticular, cD – galaxies: evolution
An analysis of the chemically enriched nature of galaxies,referred to as their metallicity, has become a commonlyused tool to study the evolution of galaxy populations. Therelation between galaxy metallicity and luminosity wasreadily highlighted in the past (McClure & van den Bergh1968; Rubin et al. 1984), showing that more luminousgalaxies tend to have higher metallicities. It has beendetermined, however, that the scatter in themass–metallicity is lower than the scatter in theluminosity–metallicity (L-Z) relation (Berg et al. 2012), anindication that it is stellar mass that is more fundamentallylinked than luminosity to a galaxy’s metallicity. Thegas-phase mass–metallicity relation (MZR), has since been (cid:63)
Email: [email protected] studied in great detail for dwarf galaxies (Lequeux et al.1979; L´opez-S´anchez 2010; Berg et al. 2012; Calabr`o et al.2017; McQuinn et al. 2020), large statistical samples ofgalaxies (Tremonti et al. 2004; Lara-L´opez et al. 2013c;Curti et al. 2020), galaxies that fall below the MZR(Peeples et al. 2009), and integral field data (S´anchez et al.2013, 2019a) etc, to understand why this relation exists,and what its implications are for galaxy evolution.One of the earliest explanations for this relation camefrom Larson (1974), who pointed towards gas loss as ameans of suppressing metallicity in lower-mass galaxies. Thegas fraction of a galaxy does seem to impact its position inthe MZR, with galaxies deficient in gas tending to havehigher metallicities (Hughes et al. 2013; Lara-Lopez et al.2013a; Zahid et al. 2014a; Brown et al. 2018). Notably,however, the environment of a galaxy seems to have little orno effect on its position in the MZR, as shown both by © a r X i v : . [ a s t r o - ph . GA ] F e b Bellstedt et al.
Mouhcine et al. (2007) with an analysis of large-scaleenvironment. Hughes et al. (2013) also investigated the roleof the local environment on the MZR, concluding that anyenvironmental trends that could be observed, were likely asecond-order effect.Another key element to interpreting the MZR isunderstanding how it has evolved with time. Many studieshave devoted their attention to the measurement ofmetallicities in galaxies at high redshifts (including Erbet al. 2006; Mannucci et al. 2010; Henry et al. 2013b; Yabeet al. 2014; Ly et al. 2016; Huang et al. 2019; Weldon et al.2020; Sanders et al. 2020) in order to characterise how theshape and normalisation of the MZR have evolved withtime. These studies have shown that the normalisation ofthe MZR was lower at earlier times, with a similar shape.In a study of the stellar populations in spiral galaxies,Bell & de Jong (2000) established that the metallicities ofgalaxies were dependent on both mass and surface density,where the star formation histories of galaxies were driven bytheir surface densities. This pointed toward a connectionbetween metallicity and star formation rate (SFR). Ellisonet al. (2008) showed that, at a given stellar mass, themetallicity of a galaxy was higher for galaxies with a lowerSFR. Analysis of the SFRs of galaxies across the MZRrevealed that the MZR was actually a projection of thethree dimensional mass–metallicity–SFR relation (forexample Mannucci et al. 2010; Lara-L´opez et al. 2010; Yateset al. 2012; Lara-L´opez et al. 2013c; Brown et al. 2016,2018; Curti et al. 2020). We now understand that the statusof chemical enrichment of a galaxy is fundamentally linkedto the star formation rate, and the build-up of stellar mass.Observational measurements of gas-phase metallicities ingalaxies are typically conducted via measurements ofnebular emission lines (for example Savaglio et al. 2005; Erbet al. 2006; Yabe et al. 2014; Huang et al. 2019; Sanderset al. 2020). Depending on which lines are detected for anindividual galaxy (typically O iii and O ii , but also lines likeN ii , S ii and S iii , in addition to H α and H β ), variousparameters can be derived which, with the combination ofcarefully pre-determined calibrations (such as thosepresented by, for example Pettini & Pagel 2004; Kobulnicky& Kewley 2004; Bian et al. 2018) can be converted into agas-phase metallicity value. The impact of both thestrong-line parameters and the metallicity calibrations is anextensive field of research, as there are significantsystematic differences between the various implementations,as highlighted by Kewley & Ellison (2008) andL´opez-S´anchez & Esteban (2010). Consequently, whenconducting an analysis of the evolution in the MZR ortrends with SFR, stellar mass, gas fractions andenvironment, the underlying measurement systematics mustbe carefully considered and accounted for.Not only can the signatures of a galaxy’s gas-phasemetallicity be found in the strength of its nebular emissionlines, but the optical range of the SED is also sensitive tovariations in the galaxy’s gas-phase metallicity. Inparticular, variations in the history of a galaxy’s gas-phasemetallicity can also influence the SED (as demonstrated byThorne et al. in prep.). With careful modelling, andsufficiently accurate photometric measurements, it istherefore possible to model the metallicity of a galaxy usingSED fitting. Historically, the metallicity evolution implementation within SED fitting codes has beensimplified, with the focus of most methods instead beingplaced on the parametrisation of a galaxy’s star formationhistory. As shown in recent work that uses the SED fittingcode ProSpect (Robotham et al. 2020) to recover thecosmic star formation history (Bellstedt et al. 2020a), thereare significant benefits to be gained when carefullymodelling the evolving gas-phase metallicity in galaxies,rather than simply assuming this value to be constant overtime.In this paper, we extend the work presented by Bellstedtet al. (2020a) to show that not only can this techniqueaccurately reproduce the star formation history of theUniverse, but it can also successfully recover the metallicitydistributions of galaxy populations. This recovery isimportant, as it highlights that a more complex approach tometallicity modelling in SED fitting can produce physicalresults in a broad range of parameter spaces. We describethe GAMA data in Sec. 2, and the SED fitting technique inSec. 3. Our derived MZR is presented in Sec. 4, followed byan analysis of the evolving MZR in Sec. 4.2. We additionallypresent our derivation of the mass–metallicity–SFR planeevolving through cosmic time in Sec. 5. We finally discussthese results in Sec. 6.For all stellar mass measurements presented in this work,we have utilised a Chabrier (2003) initial mass function(IMF). The cosmology assumed throughout this paper is H = 67 . − Mpc − , Ω m = 0 .
308 and Ω Λ = 0 . The GAMA survey (Driver et al. 2011; Liske et al. 2015) isa large program that gathered redshifts for ∼ m r (cid:54) . (or m i (cid:54) . z < .
06 and m r (cid:54) . ProSpect (Robotham et al. 2020). The panchromatic photometrycatalogue for the GAMA survey was recently updated toinclude the KiDS imaging in the optical bands, and also toutilise the
ProFound source detection software (Robothamet al. 2018). This updated photometry was presented inBellstedt et al. (2020b). These data include photometry in19 bands from the far-UV (FUV) to the far-IR (FIR).As in Bellstedt et al. (2020a), we do not explicitly identifypotential AGN in the sample to be removed. We expect thatthis will have a minimal impact on our results, as the AGNcontamination in this sample is expected to be very small(fewer than 30 galaxies, Prescott et al. 2016).In this work we use v1 of the GAMAKidsVikingFIR
DMU. With the development of the updated photometric catalogue forthe survey (Bellstedt et al. 2020b), the completeness limit has beenupdated from m r (cid:54) . m r (cid:54) . , 1– ?? (2019) AMA: Forensic Mass–Metallicity We implement the same method as outlined in Bellstedtet al. (2020a), using the GAMA photometry presented inBellstedt et al. (2020b) and passed into the
ProSpect
SEDfitting code (Robotham et al. 2020). For a detaileddescription of the fitting we direct the reader to Bellstedtet al. (2020a), however we provide a brief summary in thissection. The stellar templates we use in this analysis arefrom Bruzual & Charlot (2003), and the star formationhistory is parametrised by the massfunc snorm trunc function within
ProSpect . This parametrisation takes onthe form of a skewed Normal distribution, with the peakposition ( mpeak ), peak SFR ( mSFR ), SFH width ( mperiod ),and SFH skewness ( mskew ) set as free parameters. Apositive value of the skewness produces a SFH tailing offtoward the present day, whereas a negative skewness causesthe SFH to tail off towards the start of the Universe. TheSFH is anchored to 0 at a lookback time of 13.4 Gyr,deemed in this work to be the age at which galaxies startforming. As outlined by Bellstedt et al. (2020a), this valuewas selected to correspond with the epoch at which thehighest- z galaxies are known to exist ( z = 11, Oesch et al.2016).In this ProSpect analysis, we implement an evolvingmetallicity where the shape of the stellar mass evolution islinearly mapped onto the shape of the metallicity evolutionfor each galaxy, given by the
Zfunc massmap lin function.This ensures that chemical enrichment in the galaxiesfollows the assumed star formation rate, where increasedstar formation is associated with an increased rate of metalproduction in the galaxy. The final metallicity of the galaxyis allowed to be a free parameter,
Zfinal . We highlight thatthis value represents the present-day gas-phase metallicityof the object, and correspondingly the metallicity of theyoungest stars in the galaxy (as opposed to a time-averagedstellar metallicity). This approach is a significantimprovement over the typical approach in SED fitting,which is to assume that the metallicity is constant over agalaxy’s history. The impact of the metallicity assumptionon the cosmic star formation history (CSFH) wasdemonstrated in fig. 4 of Bellstedt et al. (2020a). The rangein
Zfinal values is limited by the range of metallicity in theBruzual & Charlot (2003) stellar templates. The upper limitof these templates is 0.05, and hence our recovered
Zfinal values cannot extend beyond this value. The resultingCSFH and SMD that are derived using this metallicityimplementation are shown in appendix B of Bellstedt et al.(2020a).The fitting outputs used in this work were first presentedby Bellstedt et al. (2020a), where they were used to derivethe cosmic star formation history, and the cosmic metaldensity evolution. While the main results in that study werederived using a closed-box metallicity implementation in
ProSpect (as given by the
Zfunc massmap box function),appendix B presented the cosmic star formation history andcosmic stellar mass density when assuming linear metallicityevolution, as given by the
Zfunc massmap lin function.Because the yields are not assumed to be constant in thelinear metallicity implementation (unlike the closed-boximplementation), the late-time enrichment of galaxies isslightly reduced when this metallicity evolution is prescribed. While the selected metallicity implementationdoes not have a large impact on the results, we noted thatthe number of objects hitting the upper metallicity limit islower when assuming linear metallicity evolution. Weinterpret this to indicate that the metallicity outputsderived when using the
Zfunc massmap lin are morephysical. This assumption of allowing the metallicity togrow in proportion to the stellar mass growth is similar towhat is seen in the chemical enrichment of galaxies insemi-analytic models (as seen in, for example, Robothamet al. 2020), providing motivation to use thisimplementation. See the discussion in Appendix A for amore detailed analysis of the enrichment in
Shark ,highlighting the degree to which the proportionalityassumption is accurate in this semi-analtyic model. As such,we use the outputs as derived by the
Zfunc massmap lin function in this work.In addition to the five free parameters specifying the starformation and metallicity histories, we include four freeparameters to describe the dust contribution to the SED.The dust is assumed to exist in two forms; either in birthclouds formed around young stars, or distributed as a screenin the interstellar medium (ISM). For each of thesecomponents, we include two free parameters, describing thedust opacity ( tau birth , tau screen ), and the dustradiation field intensity ( alpha birth , alpha screen ).Hence, we model the SED in our work using a total of ninefree parameters. The fitting ranges and priors are presentedin table 2 of Bellstedt et al. (2020a).Out of the 6,688 galaxies analysed in the z < .
06 samplepresented in Bellstedt et al. (2020a), in this analysis wefocus only on a subset of these objects that have areasonable constraint on the metallicity parameter fromSED fitting. In order to determine this subset, we removefrom analysis any objects for which the 1 σ uncertainty fromthe MCMC sampling is greater than 0.5 dex for the Zfinal parameter. After removing these objects, we are left with asample of 4,531 galaxies for which we have constrainedmetallicity estimates.
A subset of the objects analysed in this work havespectroscopically-derived metallicities from SDSS (Tremonti et al. 2004; Brinchmann et al. 2004). We compareour derived metallicity values against these observationalmeasurements as an assessment of the accuracy of ourSED-fitting approach to modelling this quantity. The subsetconsists of 2,220 objects, and a comparison of themetallicities is presented in Fig. 1. Here we show that theSED-derived values follow the spectroscopically-derivedvalues generally well, with a mean offset of − .
06 dex and ascatter of ∼ MNRAS , 1– ????
06 dex and ascatter of ∼ MNRAS , 1– ???? (2019) Bellstedt et al. − − Z gas [SDSS - Tremonti+04]10 − − Z ga s [ P r o Sp ec t ] + l og ( O / H ) [ P r o Sp ec t ] / H) [SDSS - Tremonti+04]
Figure 1.
Comparison of the
ProSpect -derived metallicity valueswith the corresponding measured metallicites from Tremonti et al.(2004) for a matched sample. The dashed black line shows theone-to-one, and the thin grey vertical and horizontal lines show theupper metallicity limit of the Bruzual & Charlot (2003) templates.The solid blue line shows the running median, with the 1 σ scatterindicated by the dotted blue lines. The scatter in our metallicityrecovery is ∼ − .
06 dex. the Bruzual & Charlot (2003) templates, the highestmetallicities are similar to this limit.The SED-derived uncertainties are significantly largerthan the spectroscopically-derived uncertainties, which isindicative of the lower constraint that broadbandphotometry is able to provide. The broad agreementbetween the observationally-measured values from SDSSand the inferred values from our SED fitting highlight thatthe values we recover are not simply “nuisance” parameters,and are instead physically meaningful (albeit withsignificant uncertainty).
While there was no fitting prior set on the resulting gas-phase metallicity values in our implementation, we recover inour analysis a mass–metallicity distribution that is consistentwith trends recovered by other observations. This is shownin Fig. 2, where for each galaxy in our sample, we plot theresulting stellar mass against the fitted
Zfinal value. Theoverall trend of our MZR is shown via the solid black lineshowing the moving median, and the dashed black lines thatindicate the 1 σ range in metallicity at any given stellar mass.In calculating these values, we demand that each bin includesat least 300 galaxies. The scatter in the relation at stellarmasses below 10 M (cid:12) is significant, but this scatter reducesat larger stellar masses. We see a bending of this relationat M ∗ ∼ M (cid:12) . Below M ∗ ∼ M (cid:12) our sample becomesincreasingly incomplete, so the MZR at these masses is proneto bias.A clear artefact in this image is the upper limit in the range M ∗ / M (cid:12) )10 − − Z ga s solar 7.58.08.59.0 + l og ( O / H ) This workTremonti+04Jimmy+15 Lara-L´opez+13L´opez-S´anchez 10Berg+12 James+15Jimmy+15Lee+06
Figure 2.
The resulting mass-metallicity relationship whenassuming a metallicity that evolves with the star formation history.The blue line indicates the median MZR recovered by Tremontiet al. (2004), orange points indicate the binned metallicitymeasurements by Lara-L´opez et al. (2013b), and the magenta lineshows the fit to the MZR by Jimmy et al. (2015). We additionallyinclude observations that extend to lower stellar masses from Leeet al. (2006); L´opez-S´anchez (2010); Berg et al. (2012); James et al.(2015); Jimmy et al. (2015). of metallicity values at 0.05. This is particuarly stark at M ∗ > . M (cid:12) , where the upper region of our 1 σ range is at thislimit. This limit is the highest-metallicity template present inthe Bruzual & Charlot (2003) stellar population templates,and hence our application of ProSpect is not sensitive togas-phase metallicity values larger than Z gas = 0 . ProSpect , and also to theobservational measurements of Tremonti et al. (2004) andLara-L´opez et al. (2013b). We summarise the parametersand calibrators used by each of these studies to determinemetallicities in Table 1.While the aforementioned MZR measurements are madeusing massive galaxies, we also include in Fig. 2 acomparison to metallicity measurements made for galaxiesin the dwarf regime by Lee et al. (2006), L´opez-S´anchez
MNRAS , 1– ?? (2019) AMA: Forensic Mass–Metallicity Table 1.
Metallicity indicators and calibrations applied in each of the observational studies presented in Fig. 2. T e refers to the electrontemperature, which is derived using auroral lines, and is regarded as a “direct” method of measuring metallicity. PP04 refers to Pettini& Pagel (2004), and CL01 refers to Charlot & Longhetti (2001).Study Parameters/Emission lines Calibration CommentsTremonti et al. (2004) [O ii ], H β , [O iii ], H α , [N ii ], [S ii ] Simultaneous fit using CL01Lee et al. (2006) [O iii ] λ e derivationL´opez-S´anchez (2010) [O iii ]( λ λ λ ii ]( λ λ λ e derivation[O ii ]( λ λ λ λ iii ] λ e derivationJimmy et al. (2015) N2 Denicol´o et al. (2002) Strong line derivationJames et al. (2015) [O ii ] λ λ e derivation M ∗ / M (cid:12) ) − . − . − . − . l og ( Z ga s ) ES0-SaSab-ScdSd-Irr N u m b e r Figure 3.
The mass–metallicity relation, as divided by the visuallyclassified morphological types. (2010) , Berg et al. (2012), James et al. (2015), Jimmyet al. (2015), in each case correcting the stellar masses to aChabrier IMF where necessary using the conversion factorspresented in table 1 of Driver et al. (2013). We find that,while these observations overlap with the distribution ofpoints derived by ProSpect , these metallicitymeasurements (all derived using T e methods) all have onaverage slightly lower values than those we derive in thelow-mass range. Similarly, these values are alsosystematically lower than the observations by Tremontiet al. (2004), Lara-L´opez et al. (2013b) and Jimmy et al.(2015) for the overlapping mass range.At the highest stellar masses ( M ∗ > . M (cid:12) ) ourmedian MZR is greater than that measured by otherobservations. Observations by Tremonti et al. (2004) andLara-L´opez et al. (2013b) are necessarily restricted togalaxies with star-formation, as the metallicitymeasurement is made on the emission lines that areproduced by star formation. Early-type galaxies likeellipticals and lenticulars are very metal-rich and dominate We exclude from Fig. 2 the galaxies from L´opez-S´anchez (2010)that are undergoing mergers. the massive end of the MZR, and as such the high-massMZR may be biased high in our analysis. We determinethat a cut in specific SFR does not cause the medianmetallicity value at high-mass to reduce, however, andtherefore the presence of early-type galaxies in our analysisis unlikely to account for the larger metallicities that wederive at large stellar masses.We show how galaxies with different visual morphologiescontribute to the MZR in Fig. 3. Here, elliptical galaxies areshown in red,
S0-Sa galaxies in orange,
Sab-Scd galaxies ingreen, and
Sd-Irr galaxies in blue. The histogram abovethe main panel of the plot shows how the morphologies aredistributed with stellar mass, whereas the histogram to theright of the main panel shows how they are distributed withgas-phase metallicity. Fig. 3 highlights that early-typegalaxies dominate the MZR at high mass and highmetallicity, whereas the low metallicity portion of the plot isalmost entirely occupied by late-type galaxies. Additionally,Fig. 3 shows that the dispersion of the MZR in thelow-metallicity regime (dominated by
Sd-Irr galaxies) ismuch higher than the high-mass regime.
The MZR has historically been very difficult for simulationsand semi-analytic models (SAMs) to reproduce, due to theintricate nature of chemical evolution in galaxies.In recent years, there has been an increased reporting ofstudies that are producing MZR trends more likeobservations. In Fig. 4 we briefly compare our derived MZRwith those prodocued by leading simulations/SAMs. Weinclude the MZR derived by the cosmological,hydrodynamic simulations Illustris (Torrey et al. 2014),IllustrisTNG (Torrey et al. 2019), MUFASA (Dav´e et al.2017), SIMBA (Dav´e et al. 2019) and EAGLE (Zenocrattiet al. 2020), and the semi-analytic models GAEA (De Luciaet al. 2020) and
Shark (Lagos et al. 2018).Torrey et al. (2014) demonstrate with Illustris that theadopted feedback model has a dramatic influence on theresulting MZR, with no feedback resulting in much highermetallicities (shown in Fig. 4 by the dashed magenta linethat extends beyond the upper limit of our probedmetallicity range), whilst strong feedback reduces thenormalisation of the MZR. While the bending of the MZRwas recovered by Illustris when feedback was removed, thebending of the MZR at high stellar masses was not presentwhen feedback was included. For the default feedback modelhowever, the agreement between the Illustris MZR and the
MNRAS , 1– ?? (2019) Bellstedt et al. M ∗ / M (cid:12) )10 − − − Z ga s solar 7.58.08.59.09.5 + l og ( O / H ) This workTorrey+14 ( illustris )Torrey+14 (no feedback)Torrey+14 (strong winds)Torrey+19 ( tng ) Dav´e+17 ( mufasa )Dav´e+19 ( simba )Zenocratti+20 ( eagle )de Lucia+20 ( gaea )Lagos+18 ( shark ) Figure 4.
Comparison of our MZR with simulations. Herewe include the cosmological hydrodynamic simulations Illustris(Torrey et al. 2014, both the default model, and also variationsof the feedback model including no feedback, and string winds),IllustrisTNG (Torrey et al. 2019), MUFASA (Dav´e et al. 2017),SIMBA (Dav´e et al. 2019), EAGLE (Zenocratti et al. 2020), andthe semi-analytic models GAEA (De Lucia et al. 2020) and
Shark (Lagos et al. 2018).
MZR recovered in this work is consistent at stellar masses M ∗ < . M (cid:12) .Unlike Illustris, where little bending was observed, theMZR for IllustrisTNG (Torrey et al. 2019, shown in Fig. 4in cyan) does recover a saturation metallicity. Both thestellar mass at which this bending occurs, as well as themetallicity value, is significantly lower in IllustrisTNG thanwe recover using ProSpect .In addition to a systematically lower normalisation, theshape of the MZR recovered by SIMBA (Dav´e et al. 2019,shown in green) is different to that of other simulations. Itdisplays a dip at around 10 M (cid:12) , without an indication of asaturation in metallicity at the highest stellar masses.Interestingly a predecessor of SIMBA, MUFASA (Dav´eet al. 2017, dashed light green), displays an MZR shape thatis more consistent with the other trends presented in Fig. 4.This is despite the fact that Dav´e et al. (2019) describe theMUFASA MZR as being too steep.We also include in Fig. 4 the MZR from the EAGLEsimulations by Zenocratti et al. (2020, solid red line). Onaverage, EAGLE galaxies seem to have a higher metallicitythan other simulations and observations, with supersolarvalues at all stellar masses. Furthermore, EAGLE does notrecover the characteristic MZR shape with lower metallicities in low-mass galaxies, displaying instead arelatively constant metallicity with varying stellar mass.The GAEA MZR (De Lucia et al. 2020, dashed blue line)recovers the typical lower metallicities for low-mass galaxies,and a saturation of metallicities for high-mass galaxies,although the difference in metallicity between low-mass andhigh-mass systems is less extreme than what we derive. Thescatter from De Lucia et al. (2020) was reported to be muchlarger than observations at lower stellar masses, althoughwe note that their scatter is only slightly larger than the 1 σ range that we derive. The MZR from the semi-analyticmodel Shark (Lagos et al. 2018, dashed orange line) isconsistent in the stellar mass range 10 < M ∗ / M (cid:12) < . ,however at the high-mass end the predicted MZR issignificantly higher than what we infer.Simulations frequently compare against observations ofthe MZR as a way of assessing how closely the physicalimplementation of the simulation can reproduce reality. Oneset of observations that are frequently used for comparisonis the SDSS dataset by Tremonti et al. (2004), shown inFigures 1 and 2. Due to the biases introduced by differentmethods of metallicity calibration (as emphasised in thework by Kewley & Ellison 2008), the absolutenormalisation of the Tremonti et al. (2004) dataset isdebated in the literature. When compared againstsimulations in the works by Torrey et al. (2019), Dav´e et al.(2017) and Dav´e et al. (2019), the Tremonti et al. (2004)vaues were scaled downwards by 0.26 dex, to be consistentwith the calibration of Pettini & Pagel (2004). As a result,the agreement between the observations and simulations inthose works appears closer than the agreement presented inour Fig. 4. The complexity of comparing observationalmetallicity measurements with simulations is discussed indetail in Lagos et al. (2012).In all of the mass–metallicity relations recovered bysimulations, the lower mass limit in each comparison isdetermined by the resolution limit of the underlying darkmatter in each simulation. As a result, the simulatedbehaviour at low stellar masses cannot be determined. Assuch, there is no way of comparing whether the low-massturnover in the MZR we recover is also replicated by eitherhydrodynamic simulations or semi-analytic models.The important aspect to consider when comparingdifferent simulations, is that current state-of-the-art models(either cosmological or semi-analytic) of galaxy evolutionstill predictly widely varying mass-metallicity relations. Infact, the variation between these MZR predictions issignificantly greater than the discrepancies we see betweenour inferred MZR and that of observations. This highlightsthat our approach to metallicity evolution in galaxies iscompetitive, if not perfect. Due to the forensic nature of our analysis, we can not onlyextract the z = 0 mass-metallicity relation, but also theevolution of this relation over cosmic time, by analysing thestar formation and metallicity histories derived using ProSpect for individual galaxies. As such, at any arbitraryvalue of lookback time, we can determine theforensically-inferred gas-phase metallicity, SFR and stellarmass at that epoch. This enables us to contruct the MZR of
MNRAS , 1– ?? (2019) AMA: Forensic Mass–Metallicity Figure 5.
Tracks of four individual galaxies in the mass–metallicity plot a) over cosmic time. For each example galaxy, we show themodelled star formation histories and metallicity histories, as well as the model fit to the SED. These galaxies are: b) 7839; c) 3895257;d) 425755; and e) 7551. The SFR and metallicity values at 1 Gyr intervals are shown in coloured points, with the corresponding positionon the mass–metallicity plot shown in panel a). Symbols are used to differentiate between different example galaxies. The distribution ofmass–metallicity points for our full sample is shown as grey points in panel a). the sample not only at the epoch of observation, but also atother epochs in the Universe’s history. The followingsections will present an analysis of the evolving MZR thatwe derive.The manner in which we use our metallicity and starformation histories to trace back the MZR is shown in Fig.5. For four example galaxies (7551, 425755, 3895257 and7839), we present the star formation history (SFH) andmetallicity history (ZH) as modelled by
ProSpect , in atwo-panel subplot, with the corresponding model fit to theSED shown above. The MCMC sampled distribution isshown as 1000 grey lines, and the median SFH and ZH areshown as solid coloured lines. For each of these histories, we indicate the value at 1 Gyr intervals using coloured points.In the top middle panel, we show the mass–metallicity plotat z = 0, where a track has been added for each examplegalaxy. These example galaxies vary from low-mass galaxiesthat form their stars more recently, to massive galaxies thatformed their stars early in the Universe. This is evident inthe mass–metallicity plot, where each galaxy has a track ina different part of the parameter space. It is interesting tonote that these tracks bear much resemblance to the varioustracks for galaxies of different morphologies presented in fig.5 by Calura et al. (2009), who produced theoreticalchemical enrichment models of galaxies with different MNRAS , 1– ????
ProSpect , in atwo-panel subplot, with the corresponding model fit to theSED shown above. The MCMC sampled distribution isshown as 1000 grey lines, and the median SFH and ZH areshown as solid coloured lines. For each of these histories, we indicate the value at 1 Gyr intervals using coloured points.In the top middle panel, we show the mass–metallicity plotat z = 0, where a track has been added for each examplegalaxy. These example galaxies vary from low-mass galaxiesthat form their stars more recently, to massive galaxies thatformed their stars early in the Universe. This is evident inthe mass–metallicity plot, where each galaxy has a track ina different part of the parameter space. It is interesting tonote that these tracks bear much resemblance to the varioustracks for galaxies of different morphologies presented in fig.5 by Calura et al. (2009), who produced theoreticalchemical enrichment models of galaxies with different MNRAS , 1– ???? (2019) Bellstedt et al. morphologies by applying assumptions about chemicalenrichment via star formation, inflows and outflows.
The changing mass-metallicity relation at 1 Gyr intervals isshown in each subpanel of Fig. 6. For each time interval, themedian and 1 σ values are shown in solid and dashed blacklines respectively. In generating the median and 1 σ ranges,we demand that each bin includes at least 300 galaxies. Forcomparison, in each subpanel we show the z ∼ / H) values to absolute metallicity via: Z gas = Z (cid:12) × [12+log(O / H)] − [12+log(O / H)] (cid:12) , (1)where Z (cid:12) = 0 . and [12 + log(O / H)] (cid:12) = 8 .
69 (Asplundet al. 2009). We additionally correct all stellar massmeasurements to be consistent with a Chabrier (2003) IMF,employing correction factors as derived by Driver et al.(2013) .A number of different methods were used to make theobserved metallicity measurements presented in Fig. 6. TheR parameter (Pagel et al. 1979) and the N2 parameterwere used, as well as the O3N2 parameter and the O parameter. Even if the same parameters are applied tomeasure metallicity, they can be differently calibrated. Thedefinitions of these parameters are:R ≡ [O II ] λ III ] λ , λ β (2)O ≡ [O III ] λ III ] λ II ] λ ≡ log (cid:18) [N II ] λ α (cid:19) (4)O3N2 ≡ log (cid:18) [O III ] λ / H β [N II ] λ / H α (cid:19) (5)Frequently applied calibrations include the N2 and O3N2calibrations by Pettini & Pagel (2004), which were laterupdated by Tremonti et al. (2004), and the calibration ofthe R parameter by Kobulnicky & Kewley (2004). Wesummarise the parameters and calibrators used by each ofthese studies in Table 2. Note that in the high-mass regime,strong line derivations are generally employed, whereas inthe low-mas regime, electron temperature-based derivationsare employed. Some scatter between the observationsthemselves is to be expected due to these differentindicators alone, as highlighted by Kewley & Ellison (2008); Note that this value differs from the commonly-assumed valueof 0.02. To convert from a Salpeter (1955) IMF we multiply by a factorof 0.65, and for a Baldry & Glazebrook (2003) IMF we use a factorof 1.2.
L´opez-S´anchez & Esteban (2010); L´opez-S´anchez et al.(2012).The agreement between the trends recovered byobservations and our forensically-determined MZR at eachepoch is remarkable, at all stellar mass ranges. Note that inclassical SED fitting approaches, where metallicity isassumed to be constant with time, the inferred metallicitydistribution would be recovered to be constant across allsubpanels of Fig. 6, with only stellar masses evolving withtime. This would be in clear tension with observations,highlighting the improvement that has been gained throughthe implementation of an evolving metallicityparametrisation in our modelling. We note that themetallicities derived for the most massive galaxies in oursample ( M ∗ > . M (cid:12) ) tend to be slightly higher thanobserved metallicities at these stellar masses, and hence theflattening of our derived MZR is slightly weaker thanobserved relations. Observations between 9-11 Gyr (Yabeet al. 2014; Zahid et al. 2014b; Erb et al. 2006; Gillmanet al. 2020) recover metallicities lower than our forensicvalues in the highest stellar mass bins. This looks likely tobe the result of metallicity saturation from the N2indicator, which is known to occur for metallicities above12 + log(O / H) (cid:62) . Z gas (cid:62) . e -basedmetallicity measurements.The potential presence of saturation in observationalmetallicity measurements makes a comparison between ourvalues and observations for massive galaxies at 9-11 Gyrpotentially biased. To visually demonstrate how the form of the MZR evolveswith time, we present the median MZR at each epoch inFig. 7, coloured by lookback time. As expected, the MZRreduces in normalisation with increasing lookback time, withthe bending at higher masses becoming less pronounced atearlier times. This changing shape (albeit subtle) seems tosuggest a “saturation” of metallicities occurring in galaxiesat recent times.This evolution in the metallicity can be described as afunction of stellar mass and lookback time ( t lb ) by:log( Z gas )( M ∗ , t lb ) = (cid:88) i =0 f i ( t lb ) m i (6)where m = log( M ∗ / M (cid:12) ) −
10 (7) f i ( t lb ) = (cid:88) j =0 a i,j t j lb , (8)and the a i,j coefficients are provided in Table 3. These fits areshown in the lower panel of Fig. 7. The scatter (in dex) can MNRAS , 1– ?? (2019) AMA: Forensic Mass–Metallicity − − − Z ga s z = 0.07) 2 Gyr( z = 0.15) 3 Gyr( z = 0.25) 4 Gyr( z = 0.35)10 − − − Z ga s z = 0.47) 6 Gyr( z = 0.62) 7 Gyr( z = 0.8) 8 Gyr( z = 1.02)6 8 10log( M ∗ / M (cid:12) )10 − − − Z ga s z = 1.31) 6 8 10log( M ∗ / M (cid:12) )10 Gyr( z = 1.72) 6 8 10log( M ∗ / M (cid:12) )11 Gyr( z = 2.35) 6 8 10log( M ∗ / M (cid:12) )12 Gyr( z = 3.51) 7.07.58.08.59.0 + l og ( O / H ) + l og ( O / H ) + l og ( O / H ) Median (This work) z < .
06 (This work)Brown (PhD)Lara-L´opez+13 ( z ∼ . , . , . , . z < .
3) Ly+16 (0 . < z < . z ∼ . , . , . . < z < . ∼ . < z < . z ∼ . < z < . z ∼ . < z < .
8) Yabe+14 (z ∼ ∼ ∼ ∼ .
3) Horstman+20 (2 < z < . z ∼ . , . z ∼ . z ∼ . Figure 6.
The resulting mass–metallicity relation at 1Gyr intervals resulting from the
ProSpect fits. At each interval, the runningmedian is indicated with a solid black line and black points, and the 1 σ range in the scatter is shown in dotted black lines. Where possible,we have included observational measurements at the relevant epochs as a comparison. These studies include those of Savaglio et al. (2005),Erb et al. (2006), Maiolino et al. (2008), Mannucci et al. (2009), Henry et al. (2013a), Henry et al. (2013b), Lara-L´opez et al. (2013b),Yabe et al. (2014), Zahid et al. (2014b), Ly et al. (2016), Huang et al. (2019), Cameron et al. (2019), Horstman et al. (2020), Weldonet al. (2020), Sanders et al. (2020), Gillman et al. (2020). For measurements of the MZR that span a large redshift range (including thoseof Ly et al. 2016), we plot the same values over multiple subpanels, and show the data using open symbols. be described by the same functional form. The correspondingcoefficients are also shown in Table 3.The evolution of the MZR shown in Fig. 7 shows that thechemical enrichment of a 10 M (cid:12) galaxy is significantlymore different at high- z versus low- z , than that of a10 M (cid:12) galaxy, which displays less variation in metallicitywith cosmic time. This behaviour is attributed to the“galaxy downsizing” phenomenon that is recovered in thisanalysis (as highlighted by Bellstedt et al. 2020a). Massivegalaxies tend to assemble earlier, and hence their late-timechemical enrichment is minimal, whereas low-mass galaxiescontinue to form stellar mass at the present day.Consequently, this stellar mass range experiences moreprolonged chemical enrichment. For each cosmic epoch shown in Fig. 6, we now assess howthe galaxy SFRs change across the mass-metallicityrelation. In each subpanel in Fig. 8, each galaxy is nowcoloured by log(SFR), with galaxies lighter in colourrepresenting objects that are more rapidly forming stars.Fig. 8 shows clearly that the position of a galaxy within theMZR is highly dependent on the star formation rate. Inparticular, we highlight that this trend is strongest atearlier times, and becomes less distinct in the last 5 Gyr,where galaxies start to saturate in gas-phase metallicity.This plot shows that in the early Universe, metallicityenrichment and SFR are directly linked to stellar mass, suchthat at fixed stellar mass, the SFR is relatively constant fordifferent metallicity values. A vertical gradient in colour (adependence of SFR on metallicity), only starts becomingapparent at a lookback time of 10 Gyr — the same epoch inwhich the bending of the MZR starts to become apparent.
MNRAS , 1– ????
MNRAS , 1– ???? (2019) Bellstedt et al.
Table 2.
Metallicity indicators and calibrations applied in each of the observational studies presented in Fig. 6. PP04 refers to Pettini &Pagel (2004), KK04 refers to Kobulnicky & Kewley (2004), M08 refers to Maiolino et al. (2008). T e refers to the electron temperature,which is derived using auroral lines, and is regarded as a “direct” method of measuring metallicity.Study Parameters/Emission lines Calibration CommentsSavaglio et al. (2005) R , O KK04 Strong line derivationErb et al. (2006) N2 PP04 Strong line derivationMaiolino et al. (2008) [O iii ] λ β , [O iii ] λ ii ] λ e at low- Z , andphotoionisation at high- Z Mannucci et al. (2009) R , [O iii ] λ β M08Yabe et al. (2014) N2 PP04 Strong line derivationLara-L´opez et al. (2013b) O3N2 PP04 Strong line derivationHenry et al. (2013a) R KK04 Strong line derivationHenry et al. (2013b) R M08 Strong line derivationZahid et al. (2014b) N2 PP04 Strong line derivationLy et al. (2016) [O ii ] λ λ β , [O iii ] λ λ β T e derivationCameron et al. (2019) O3N2 PP04 Strong line derivationHuang et al. (2019) R , O KK04 Strong line derivationHorstman et al. (2020) N2, O3N2 PP04 Strong line derivationWeldon et al. (2020) [O ii ] λ λ β , [O iii ] λ λ β T e derivationSanders et al. (2020) [O iii ] λ β , O , [Ne iii ] λ ii ] λ Table 3.
Coefficients to describe the time evolution of the MZR median and scatter, as used in Equation 6.Median evolution coefficients a i, a i, a i, a i, a i, a i, a ,j − .
67 6 . × − − . × − . × − − . × − a ,j . × − − . × − . × − − . × − . × − a ,j . × − − . × − . × − − . × − . × − − . × − a ,j − . × − − . × − . × − − . × − . × − − . × − Scatter evolution coefficients a i, a i, a i, a i, a i, a i, a ,j − . × − − . × − . × − . × − . × − a ,j − . × − . × − − . × − . × − − . × − a ,j − . × − . × − − . × − . × − − . × − . × − a ,j − . × − . × − − . × − . × − − . × − . × − It is conceivable that the recovered behaviour is simply aconsequence of the parametrisation of SFHs that weimplement, and that therefore the trends in the earlyUniverse are highly simplified. Additionally, the actualconstraint on the SFH and ZH at such large lookback timesis also very small when applying SED fitting, so there maynot actually be any real signal here - only what our modelsare telling us. Note however, that if this behaviour really issimply the consequence of the adopted SFH, then the factthat the evolving MZR is so well recovered providesconfidence that the adopted SFH and ZH parametrisation isindeed appropriate.We highlight that Fig. 8 also conveys the clearmass-dependence of the CSFH. In particular, at allredshifts, the highest-mass systems have the greatest SFRs.The value of this maximum SFR changes with redshift, inaccordance with the overall decline in the CSFH over thepast ∼
10 Gyr (as shown by Madau & Dickinson 2014;Bellstedt et al. 2020a). This is evident when observing thechanging SFR within galaxies at a fixed stellar mass overtime: At a lookback time of 11 Gyr, galaxies with M ∗ = 10 M (cid:12) have SFRs ∼
10 M (cid:12) yr − , whereas by 1 Gyrlookback time the star-forming galaxies in this mass rangehave SFRs ∼ (cid:12) yr − .We do not apply a selection in Fig. 8 based on sSFR,which means the plot features both star-forming, and quenched galaxies. The presence of quenched/quenchingsystems is first apparent at a lookback time of 10 Gyr,where the first high-mass galaxies — log( M ∗ / M (cid:12) ) >
10 —are becoming dark purple in colour, corresponding tolog(SFR / M (cid:12) yr − ) < −
1. By 7-8 Gyr lookback time, theseobjects become much more prevalent. The presence of thesesystem causes a noticeable visual dilution of the SFRtrends, which is maximised by 1 Gyr, when a significantfraction of the high-mass galaxies is quenched. As such,there is only a minimal trend with SFR in the 1 Gyr panelof this plot.To assess how the trends in Fig. 8 change with sSFR, wepresent the same parameter space coloured by sSFR in Fig.9. In addition to the running median in each subpanel of thetotal population, we include the running medianfor the star-forming population (as defined by log(sSFR / yr − ) > − . MNRAS , 1– ?? (2019) AMA: Forensic Mass–Metallicity − − − Z ga s M ∗ / M (cid:12) )10 − − − Z ga s L oo k b a c k T i m e [ G y r ] Figure 7.
The top panel shows the median MZR measured at eachepoch (as shown in each subpanel of Fig. 6), coloured by lookbacktime. The bottom panel shows the functional form of the evovingMZR, as given by Equation 6. possible that the high-mass high-SFR objects in the panels athigh lookback times could be an artefact of this assumption,and that in reality such galaxies do not exist.
It is now understood that the mass–metallicity relation is aprojection of the 3D mass–metallicity–SFR plane (Magriniet al. 2012; Lara-L´opez et al. 2013c; Peeples & Somerville2013). Using the outputs of SED fitting, we can present ourdata in this plane, with a broad range of stellar masses,metallicities and SFRs.To fit the plane in three dimensions, we employ the R package Hyperfit (Robotham & Obreschkow 2015). Whenfitting a plane to our derived values of stellar mass, SFRand metallicity, we have converted our absolute metallicityvalues to oxygen abundances, for the sake of easycomparison against observations. We additionally restrictour fit to galaxies with specific SFR valueslog(sSFR / yr − ) > − .
5, so that we do not includequenched and quenching galaxies in our fit.Our fit to the z ∼ / H)] = α (cid:18) SFRM (cid:12) yr − (cid:19) + β log (cid:18) M ∗ M (cid:12) (cid:19) + γ (9) where α = − . β = 1 . γ = − . ∼ M (cid:12) , and assuch a discrepancy of the plane at low stellar masses isunsurprising. We additionally present the 3D fitted surfaceby Mannucci et al. (2010) in cyan, which only covers thehigh-mass, high-metallicity regime of the 3D space.Similarly, we show the 3D surface fitted by Curti et al.(2020) is shown in blue. We find that the surfaces fromMannucci et al. (2010) and Curti et al. (2020) have asignficantly stronger tilt than ours, and also saturate at amuch lower metallicity that the maximum metallicities wederive. The structure in the surfaces fitted by bothMannucci et al. (2010) and Curti et al. (2020) do notvisually provide a better fit to the mass–metallicity–SFRrelation we derive than a simple plane does. In fact, theplane derived by Lara-L´opez et al. (2013c) is in much betteragreement with the distribution of our derived data thaneither of the two other surfaces.We highlight here that, because the Zfinal parameter is afree parameter in our implementation, the planar structureof our mass–metallicity–SFR plane was not prescribed by ourevolving metallicity model.
Our forensic analysis also allows us to measure theevolution of the Mass–Metallicity–SFR plane. The evolutionof the planes with cosmic time is shown in Fig. 11. Eachsubpanel shows the mass–metallicity–SFR plane in aspecific lookback time interval. The projection of the pointsonto each of the three related two-dimensional spaces (i.emass–metallicity, mass–SFR and SFR–metallicity) isindicated on the edges of the plot with blue/green points. Aconsequence of the functional form of the star formationhistory, is that the early build-up of galaxies in this sampleis very similar, due to the truncation of each SFH at earlytimes. As a result, the main sequence (the 2D projection atthe bottom of each subpanel) can be seen to be extremelynarrow at high lookback times. At this epoch, the resultingstellar masses are limited by the SFR, and hence they arevery tightly correlated.The plane can be seen to evolve with cosmic time. Inparticular, with time the plane tilts toward high-mass,low-SFR systems with increasing time. The low-metallicityportion of the plane tilts toward higher SFRs, however thisis unconstrained at recent times due to the lower mass limitof our observations. This evolution is most notable inlookback times beyond 7 Gyr, in the 9 and 11 Gyr panels.We highlight that, as mentioned above, this epoch is highlyinfluenced by our choice of SFH parametrisation, and hencethe measurement of this evolution must be assessed withthis caveat.
MNRAS , 1– ????
MNRAS , 1– ???? (2019) Bellstedt et al. − − − Z ga s z = 0.07) 2 Gyr( z = 0.15) 3 Gyr( z = 0.25) 4 Gyr( z = 0.35)10 − − − Z ga s z = 0.47) 6 Gyr( z = 0.62) 7 Gyr( z = 0.8) 8 Gyr( z = 1.02)6 8 10log( M ∗ / M (cid:12) )10 − − − Z ga s z = 1.31) 6 8 10log( M ∗ / M (cid:12) )10 Gyr( z = 1.72) 6 8 10log( M ∗ / M (cid:12) )11 Gyr( z = 2.35) 6 8 10log( M ∗ / M (cid:12) )12 Gyr( z = 3.51) − − log(SFR/M (cid:12) yr − ) 7.07.58.08.59.0 + l og ( O / H ) + l og ( O / H ) + l og ( O / H ) Figure 8.
The mass–metallicity relation in 1 Gyr intervals for the same galaxy population, coloured by the SFR at that epoch. As inFig. 6, the median and 1 σ MZR are shown in solid and dashed black lines in each subpanel.
The evolution of the plane with lookback time can beexpressed as:[12 + log(O / H)] = α ( t lb ) log (cid:18) SFRM (cid:12) yr − (cid:19) + β ( t lb ) log (cid:18) M ∗ M (cid:12) (cid:19) + γ ( t lb ) (10)where α ( t lb ) = − . . t lb − . t β ( t lb ) = 1 . − . t lb + 0 . t γ ( t lb ) = − .
785 + 2 . t lb − . t Here, t lb is the lookback time in Gyr. The scatter in the planeis seen to evolve as: σ ( t lb ) = 0 . − . t lb + 0 . t This fit to the evolving plane parameters is shown in Fig. B1.In an analysis of stellar masses, SFRs and metallicitiesspanning a wide redshift range, Mannucci et al. (2010)concluded that there was no evolution in themass-metallicity–SFR plane from z = 0 to z = 2 .
5. This isin constrast with the subtle evolution that we derive in ouranalysis. Note that the study by Mannucci et al. (2010)focussed on galaxies with M ∗ > . M (cid:12) , and hence the stellar mass range may well have been too small to detectthe evolution that we infer. Lara-L´opez et al. (2010) alsoconcluded in their analysis that there was no evidence foran evolution in the plane. There are numerous caveats associated with the analysispresented in this work, both in the manner in which ourvalues are compared against the observed metallicity values,and also inherent to the modelling method we have applied.We discuss these issues in this section.A major challenge associated with any comparison ofmodelled metallicities to spectroscopically-derived values, isthat there are significant biases that accompanyspectroscopic measurements. This is the result of relying ondifferent emission lines between different datasets, differentstrong line parameters, and finally different calibrationmethods to transform the strong line measurements intoabundances. This challenge was highlighted by S´anchezet al. (2019b), who circumvented some of these systematicsby electing to use 11 different calibrators in their analysis,rather than only selecting one. The resultingmass–metallicity relations that they derive not only vary in
MNRAS , 1– ?? (2019) AMA: Forensic Mass–Metallicity − − − Z ga s z = 0.07) Medianlog(sSFR / yr − ) > -11.31 z = 0.15) 3 Gyr( z = 0.25) 4 Gyr( z = 0.35)10 − − − Z ga s z = 0.47) 6 Gyr( z = 0.62) 7 Gyr( z = 0.8) 8 Gyr( z = 1.02)6 8 10log( M ∗ / M (cid:12) )10 − − − Z ga s z = 1.31) 6 8 10log( M ∗ / M (cid:12) )10 Gyr( z = 1.72) 6 8 10log( M ∗ / M (cid:12) )11 Gyr( z = 2.35) 6 8 10log( M ∗ / M (cid:12) )12 Gyr( z = 3.51) − − − − − log(sSFR/yr − ) 7.07.58.08.59.0 + l og ( O / H ) + l og ( O / H ) + l og ( O / H ) Figure 9.
The mass–metallicity relation in 1 Gyr intervals for the same galaxy population, coloured by the sSFR at that epoch. As inFig. 6, the median and 1 σ MZR are shown in solid and dashed black lines in each subpanel. The running median for the star-formingpopulation (as defined by log(sSFR / yr − ) > − .
31) is shown in grey. normalisation by up to 0.5 dex, but the resulting slopes alsovary dramatically. A similar depiction of this challenge waspresented earlier by Kewley & Ellison (2008);L´opez-S´anchez & Esteban (2010); L´opez-S´anchez et al.(2012).Not only is measuring the absolute oxygen abundancechallenging, but there is extra uncertainty associated withthe conversion of oxygen abundance to total metallicity,which is the quantity we model in our analysis. This washighlighted by Gallazzi et al. (2005) who, using stellarpopulation models to infer the total metallicities of SDSSspectra, compared the total metallicities against oxygenabundances determined for the same sample as Tremontiet al. (2004). While there was a clear correlation betweenthese parameters, the scatter was also significant.Consequently, scatter between the observed and ourmodelled metallicities could also arise from the scalingbetween oxygen abundances and total metallicities.A key simplification in the SED fitting approach that wehave taken, is that mergers that may have occurred in agalaxy’s past are ignored. It would be reasonable to assumethat a massive galaxy that only has a single progenitor thathas epochs of extremely high star formation would likelyhave different metallicities to a massive galaxy that formed as the result of a series of major mergers, each progenitor ofwhich may have had smaller star formation rates. In ourapproach, we would not differentiate such systems, as wesimply model the history of all the stars currently present ina galaxy. In an analysis focussing on the metallicities ofmerging galaxies, Horstman et al. (2020) found thatgalaxies in mergers had suppressed metallicities versusisolated galaxies at the same stellar mass at 2 < z < . MNRAS , 1– ????
31) is shown in grey. normalisation by up to 0.5 dex, but the resulting slopes alsovary dramatically. A similar depiction of this challenge waspresented earlier by Kewley & Ellison (2008);L´opez-S´anchez & Esteban (2010); L´opez-S´anchez et al.(2012).Not only is measuring the absolute oxygen abundancechallenging, but there is extra uncertainty associated withthe conversion of oxygen abundance to total metallicity,which is the quantity we model in our analysis. This washighlighted by Gallazzi et al. (2005) who, using stellarpopulation models to infer the total metallicities of SDSSspectra, compared the total metallicities against oxygenabundances determined for the same sample as Tremontiet al. (2004). While there was a clear correlation betweenthese parameters, the scatter was also significant.Consequently, scatter between the observed and ourmodelled metallicities could also arise from the scalingbetween oxygen abundances and total metallicities.A key simplification in the SED fitting approach that wehave taken, is that mergers that may have occurred in agalaxy’s past are ignored. It would be reasonable to assumethat a massive galaxy that only has a single progenitor thathas epochs of extremely high star formation would likelyhave different metallicities to a massive galaxy that formed as the result of a series of major mergers, each progenitor ofwhich may have had smaller star formation rates. In ourapproach, we would not differentiate such systems, as wesimply model the history of all the stars currently present ina galaxy. In an analysis focussing on the metallicities ofmerging galaxies, Horstman et al. (2020) found thatgalaxies in mergers had suppressed metallicities versusisolated galaxies at the same stellar mass at 2 < z < . MNRAS , 1– ???? (2019) Bellstedt et al.
Figure 10.
The mass–metallicity–SFR plane as determined bythe fitted parameters. The values in 3D space, as well as theirprojections onto the three 2D spaces, are all plotted. Coloursindicate the orthogonal distance of the point to the place. 3Dvalues are shown in red/orange hues, while their correspondingprojections are shown in blue/green hues, to allow them to bedistinguished. The fit made to the plane by Lara-L´opez et al.(2013c) is shown in orange. The tilt of the plane in this fitis significantly larger than the tilt we measure. Note that thedisagreement is greatest at low metallicities, where observationsare sparse. The cyan surface is the measurement by Mannucci et al.(2010), and the blue surface is the fit to the 3D space by Curtiet al. (2020). Here, the surface has a significantly larger tilt, andthe saturation metallicity is lower than the maximum metallicitieswe recover. See online version for 3D video. example, L´opez-S´anchez et al. 2015). Some allowance forthe occurrence of gas inflows is provided by the linearmetallicity evolution implementation, unlike the closed-boxmodel (which was utilised in the main body of Bellstedtet al. 2020a, see Robotham et al. 2020 for further details),however this is not explicit. Work by Rupke et al. (2010)demonstrated that the metallicity gradients of galaxiesundergoing interactions are significantly flatter thannon-interacting galaxies caused by interaction-induced gasinflow. Note that in our approach we cannot model thespatially-resolved nature of metallicity within galaxies.Chisholm et al. (2018) looked at outflows as a mechanismfor producing the shape of the MZR. Based on an extensivemodelling of UV spectral observations for 7 local galaxies,Chisholm et al. (2018) determined that the metal outflowrate in galaxies linearly correlates with their stellar mass.Contrastingly, Calura et al. (2009) determined that windswere not required to explain the shape of the MZR, andthat it could instead be explained by the lower starformation efficiency of lower-mass systems. The analysispresented in this work suggests that an explicit treatment of outflows is not required to reproduce the general shape ofthe MZR.An additional phenomenon that is unconsidered in ourapproach is that of galaxy starvation, in which the gasinflow to a galaxy is disrupted, leading to a gradualtruncation of star formation within a galaxy. This processwas discussed in detail by Peng et al. (2015), who inparticular noted that in a starvation scenario, the final starformation epoch is likely to be more chemically enrichedthan any previous star formation, due to the lack of dilutioncaused by gas inflows. This effect is predicted to beresponsible for the discrepancy between stellar metallicitiesof passive and star-forming galaxies at fixed stellar mass (aspresented by, for example, Peng et al. 2015; Trussler et al.2020). Such a late-time acceleration of chemical enrichmentof galaxies would not be considered in our approach.While the present-day gas-phase metallicities of ourgalaxies are free parameters within our analysis, themetallicity at the beginning of each galaxy’s history is fixedto the lower limit of the Bruzual & Charlot (2003) stellarpopulation templates. It is conceivable that a galaxyforming later in the Universe is formed out of non-pristinegas, and therefore we might be underestimating its initialmetallicity. Contrastingly, this lower metallicity limit of10 − is likely too high for galaxies that form very early inthe Universe, where the formation gas is likely to bepristine. It is unknown to what extent these simplificationsimpact the metallicity evolution of galaxies that we infer,however we point the reader to the discussion in AppendixA, where we highlight a potential consequence of the initialmetallicity value on the assumption of linearity in themetallicity evolution prescription. SED fitting techniques are widespread in use, and arefrequently employed to measure the stellar masses ofgalaxies. Historically, SED fitting techniques have employeda simple parametrisation of the star formation history, andhave typically modelled the corresponding metallicityhistory with a single value held constant over the history ofthe galaxy. This simplification has a significant impact onnot only the star formation histories of galaxies (asdiscussed in Bellstedt et al. 2020a), but as a consequencethe derived stellar masses can also be affected. Using theSED fitting code
ProSpect (Robotham et al. 2020), wehave used a simple prescription to model an evolvingmetallicity for individual galaxies (used in Bellstedt et al.2020a, to extract a cosmic star formation history consistentwith observational measurements) to derive themass–metallicity relation for a sample of ∼ z < . MNRAS , 1– ?? (2019) AMA: Forensic Mass–Metallicity Figure 11.
The Mass–Metallicity–SFR plane at regular lookback time intervals between 1 and 11 Gyr. The values themselves are plottedin red/orange hues, while their corresponding projections onto the three 2D spaces is plotted in blue/green hues, for clarity. As in Fig.10, points are coloured according to their orthogonal distance from the fitted plane. The plane at each epoch is shown in solid grey, andfor comparison the z ∼ , 1– ????
The Mass–Metallicity–SFR plane at regular lookback time intervals between 1 and 11 Gyr. The values themselves are plottedin red/orange hues, while their corresponding projections onto the three 2D spaces is plotted in blue/green hues, for clarity. As in Fig.10, points are coloured according to their orthogonal distance from the fitted plane. The plane at each epoch is shown in solid grey, andfor comparison the z ∼ , 1– ???? (2019) Bellstedt et al. mass–metallicity–SFR space. We show that this space canbe well described by a plane over cosmic time, and showthat as galaxies increase in stellar mass and metallicity, andreduce the rate at which they are formig stars, themass–metallicity–SFR plane tilts. This evolution mostlyoccurs at lookback times greater than 7 Gyrs. We presentthe evolution of this plane in functional form in Equation10.Combined with the accurate cosmic star formationhistory derived using this implementation of
ProSpect (aspresented in Bellstedt et al. 2020a), the analysis presentedin this work reaffirms that galaxy stellar populations can bemodelled accurately using SED fitting of broadbandphotometry alone, if careful consideration is given to theevolution of the gas phase metallicity in addition to theevolution of the star formation history.
The
ProSpect catalogue will be collated into a DMU, andcan be accessed via a GAMA collaboration request . SB thanks Mat´ıas Bravo for providing
Shark data, and DrAdam Stevens for many useful discussions.GAMA is a joint European-Australasian project basedaround a spectroscopic campaign using theAnglo-Australian Telescope. The GAMA input catalogue isbased on data taken from the Sloan Digital Sky Survey andthe UKIRT Infrared Deep Sky Survey. Complementaryimaging of the GAMA regions is being obtained by anumber of independent survey programmes includingGALEX MIS, VST KiDS, VISTA VIKING, WISE,Herschel-ATLAS, GMRT and ASKAP providing UV toradio coverage. GAMA is funded by the STFC (UK), theARC (Australia), the AAO, and the participatinginstitutions. The GAMA website is .SB and SPD acknowledge support by the AustralianResearch Council’s funding scheme DP180103740. ASGRacknowledges support from the ARC Future Fellowshipscheme (FT200100375), and LPD acknowledges supportfrom the ARC Future Fellowship scheme (FT200100055).This work was supported by resources provided by the
Pawsey Supercomputing Centre with funding from theAustralian Government and the Government of WesternAustralia. We gratefully acknowledge
DUG Technology fortheir support and HPC services.We have used R (R Core Team 2017) and python forour data analysis, and acknowledge the use of Matplotlib (Hunter 2007) for the generation of plots in this paper. Thisresearch made use of
Astropy , a community-developed core python package for astronomy (Astropy Collaboration et al.2013, 2018), Pandas (McKinney 2010), and
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APPENDIX A: VALIDITY OFPROPORTIONALLY EVOLVINGMETALLICITIES
In order to assess the validity of our “linearly-evolving”metallicity evolution parametrisation, we turn to outputsfrom the semi-analytic model
Shark (Lagos et al. 2018).For a sample of ∼ z = 0 .
07 snapshot (Bravos et al. in prep), weextract the mass build-up, and gas-phase metallicityhistories for each galaxy. In order to test how well thesegalaxies are, on average, approximated by our model, weneed to identify the extent to which the mass build-up andmetallicity evolution are proportional to each other. To dothis we scale the mass profiles to the metallicity profilesuntil the differences between them are minimised, and thenwe quantify the difference between these profiles in logspace. If a galaxy has purely proportional evolution, thenthis value would be 0 at all epochs. Some examples of howthis behaves for galaxies in
Shark are shown in Fig. A1.Note that the metallicity build-up does in general follow thestellar mass build-up fairly closely, with the greatestdiscrepancies typically displayed in the first few billion yearsof the galaxy’s lifetime. Note that this discrepancy isapparent in the scaled Mass/Z ratio shown in the bottompanels of the figure.Although the lower limit of gas-phase metallicityprescribed within
Shark is 10 − , the value tends to be ∼ − as soon as star formation has started. This is closeto the initial value of 10 − that we are forced to implementdue to the limit of the Bruzual & Charlot (2003) stellarpopulation templates.The result of this analysis over the full sample of galaxiesis shown in Fig. A2. The relative mass and metallicitybuild-up are shown in the top panel, and their ratio isshown in in the bottom panel, with the 1- and 2 σ regionsshown in shading. This plot shows that the proportionalapproximation is consistent with the evolution in Shark inthe most recent 8 Gyr, with deviations from thisapproximation occuring in the early Universe. We highlightthat there are complexities in the nature of the modellingitself within
Shark that make this comparison difficult.Instantaneous recycling of metals will likely cause themetallicity to build up more quickly than in reality, as anexample. From the perspective of SED fitting, theage–metallicity degeneracy is greatest at this epoch wherethe discrepancy between the linear model and
Shark is atits maximum. Furthermore, because the stellar populationsformed early on in the history of a galaxy contribute to sucha small fraction of the galaxy’s observed flux, theconstraining power of the SED fitting process is very smallfor this epoch. These factors make distinguishing betweenmetallicity evolution models in the early Universe verydifficult. Further work would be required with a larger rangeof semi-analytic and cosmological simulations to properly
MNRAS , 1– ????
MNRAS , 1– ???? (2019) Bellstedt et al. − − − − l og ( M ∗ , s c a l e d ) l og ( Z ) ID 1008
MassMetallicity
ID 1041 ID 10092 ID 100430 − . − . − . − . . . l og ( M ∗ , s c a l e d ) - l og ( Z ) Figure A1.
The relative stellar mass and metallicity build-up of four example
Shark galaxies (top panel), and the resulting ratio betweenthese (bottom). The dashed black line indicates proportional metallicity evolution. conclude the extent to which “linearity” is physical, howeversuch an analysis is well beyond the scope of this work.We reiterate that the implementation of the linearmetallicity evolution is a significant improvement overmodels in which the metallicity is assumed to be constantover the duration of a galaxy’s history. As discussed in Sec.3, the linear metallicity evolution model is currentlyfavourable over the closed-box model (presented in detail inBellstedt et al. 2020a), as the resulting metallicitydistributions are more physical. This implies that the mostrecent epoch of evolution (to which SED fitting is mostsensitive), is better modelled by linear metallicity evolutionthan the closed-box.
ProSpect can be implemented withany model of metallicity evolution, and therefore this isstraightforward to adapt in the future if desired.
APPENDIX B: FITTING THE EVOLVINGPLANE
The fit to the evolving plane parameters, as presented byEquation 10 is presented in Fig. B1. Note that the evolutionin the parameters is only significant beyond a lookback timeof 7 Gyr.
MNRAS , 1– ?? (2019) AMA: Forensic Mass–Metallicity − − − − − − l og ( M ∗ , s c a l e d ) l og ( Z ) MassMetallicity2 . . . . . − . − . − . . . l og ( M ∗ , s c a l e d ) - l og ( Z ) “linear” Z evolution median1 σ range2 σ range Figure A2.
Top: Overall relative build-up of mass (black) andmetallicity (orange) for a sample of ∼ Shark . Bottom: Distribution of the correspondingstellar mass build-up to gas-phase metallicity evolution ratios(blue, with shaded regions indicating the 1- and 2- σ ranges). Thedashed black line indicates the assumption of our proportionalmetallicity evolution (given by the Zfunc massmap lin function).Note that
Shark is consistent with linear evolution to lookbacktimes of ∼ − − α FitMeasured parameter24 β − γ . . . . . . . s c a tt e r Figure B1.
Measured parameters describing the fit to the plane ineach epoch between 1 and 11 Gyr lookback times. The fit, showingthe time evolution of the plane and presented in Equation 10 isshown in blue. MNRAS , 1– ????