[OII] emitters in MultiDark-Galaxies and DEEP2
G. Favole, V. Gonzalez-Perez, A. Orsi, D. Stoppacher, J. Comparat, S. A. Cora, C. A. Vega-Martinez, A. R. H. Stevens, C. Maraston, D. Croton, A. Knebe, A. J. Benson, A. D. Montero-Dorta, N. Padilla, F. Prada, D. Thomas
MMNRAS , 000–000 (0000) Preprint 30 March 2020 Compiled using MNRAS L A TEX style file v3.0 [O II ] emitters in MULTIDARK-GALAXIES and DEEP2 G. Favole, (cid:63) V. Gonzalez-Perez, , , † D. Stoppacher, , ´A. Orsi, J. Comparat, S. A.Cora, , C. A. Vega-Mart´ınez, , A. R. H. Stevens, C. Maraston, D. Croton, A. Knebe, , , A. J. Benson, A. D. Montero-Dorta, N. Padilla, , F. Prada, D. Thomas Institute of Cosmology and Gravitation, Portsmouth University, Burnaby Road, Portsmouth PO13FX, UK Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK. Energy Lancaster, Lancaster University, LA1 4YB, UK Instituto de F´ısica Te´orica (IFT) UAM/CSIC, Universidad Aut´onoma de Madrid, Cantoblanco, E-28049 Madrid, Spain Departamento de F´ısica Te´orica, M´odulo 15, Facultad de Ciencias, Universidad Aut´onoma de Madrid, E-28049 Madrid, Spain Centro de Estudios de F´ısica del Cosmos de Arag´on, Plaza de San Juan 1, Teruel E-44001, Spain Max-Planck-Institut f¨ur extraterrestrische Physik (MPE), Giessenbachstrasse 1, D-85748 Garching bei M¨unchen, Germany Instituto de Astrof´ısica de La Plata (CCT La Plata, CONICET, UNLP), Paseo del Bosque s/n, B1900FWA, La Plata, Argentina Facultad de Ciencias Astron´omicas y Geof´ısicas, UNLP, Paseo del Bosque s/n, B1900FWA, La Plata, Argentina Instituto de Investigaci´on Multidisciplinar en Ciencia y Tecnolog´ıa, Universidad de La Serena, Ra´ul Bitr´an 1305, La Serena, Chile Departamento de Astronom´ıa, Universidad de La Serena, Av. Juan Cisternas 1200 Norte, La Serena, Chile International Centre for Radio Astronomy Research, The University of Western Australia, Crawley, WA6009, Australia Centre for Astrophysics & Supercomputing, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia Centro de Investigaci´on Avanzada en F´ısica Fundamental (CIAFF), Facultad de Ciencias, UAM, 28049 Madrid, Spain Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101, USA Instituto de F´ısica, Universidade de S˜ao Paulo, S˜ao Paulo, SP, Brazil Instituto de Astrof´ısica, Pontificia Universidad Cat´olica, Av. Vicu˜na Mackenna 4860, Santiago, Chile Centro de Astro-Ingenier´ıa, Pontificia Universidad Cat´olica de Chile, Av. Vicu˜na Mackenna 4860, Santiago, Chile Instituto de Astrof´ısica de Andaluc´ıa (IAA)/ CSIC, Granada, E-18008, Spain
ABSTRACT
We use three semi-analytic models (SAMs) of galaxy formation and evolution, runon the same 1 h − Gpc MultiDark Planck2 cosmological simulation, to investigate theproperties of [O ii ] emission line galaxies in the redshift range 0 . < z < .
2. Wecompare model predictions with different observational data sets, including DEEP2–
Firefly galaxies with absolute magnitudes. We estimate the [O ii ] luminosity, L [O ii ],using simple relations derived both from the models and observations and also usinga public code. This code ideally uses as input instantaneous star formation rates(SFRs), which are only provided by one of the SAMs under consideration. We use thisSAM to study the feasibility of inferring galaxies’ L [O ii ] for models that only provideaverage SFRs. We find that the post-processing computation of L [O ii ] from averageSFRs is accurate for model galaxies with dust attenuated L [O ii ] (cid:46) . erg s − ( <
5% discrepancy). We also explore how to derive the [O ii ] luminosity from simplerelations using global properties usually output by SAMs. Besides the SFR, the model L [O ii ] is best correlated with the observed-frame u and g broad-band magnitudes.These correlations have coefficients (r-values) above 0.64 and a dispersion that varieswith L [O ii ]. We use these correlations and an observational one based on SFR andmetallicity to derive L [O ii ]. These relations result in [O ii ] luminosity functions andhalo occupation distributions with shapes that vary depending on both the model andthe method used. Nevertheless, for all the considered models, the amplitude of theclustering at scales above 1 h − Mpc remains unchanged independently of the methodused to derive L [O ii ]. Key words: galaxies: distances and redshifts — galaxies: haloes — galaxies: statistics— cosmology: observations — cosmology: theory — large-scale structure of Universe (cid:63)
E-mail: [email protected] † E-mail: [email protected]
In the era of precision cosmology, surveys are starting torely on star-forming galaxies to go further into early cosmictimes, when dark energy is just starting to dominate theenergy-matter budget of the Universe. Star-forming galax- c (cid:13) a r X i v : . [ a s t r o - ph . GA ] M a r Favole et al. 2020 ies with strong nebular emission lines (ELGs) are amongthe preferred targets of the new generation of spectroscopicsurveys as SDSS-IV/eBOSS (Dawson et al. 2016), DESI(Schlegel et al. 2015), 4MOST , WFIRST , Subaru-PFS and Euclid (Laureijs et al. 2011; Sartoris et al. 2015), andwill be used to trace the baryon acoustic oscillation (BAO;Eisenstein et al. 2005) scale and the growth of structure bymeasuring redshift-space distortions in the observed clus-tering (Alam et al. 2015; Mohammad et al. 2018; Orsi &Angulo 2018). Star-forming galaxies will also be fundamen-tal to inform halo occupation distribution (HOD; Cooray& Sheth 2002; Berlind & Weinberg 2002; Kravtsov et al.2004; Zheng et al. 2007) and (sub)halo abundance matching(SHAM; Conroy et al. 2006; Behroozi et al. 2010; Trujillo-Gomez et al. 2011; Nuza et al. 2013) models to generate fastmock galaxy catalogues useful for cosmological tests.At z ∼ ii ] emitters. Therefore,measuring and modelling the relations between redshift andthe physical properties of these galaxies – such as [O ii ] lumi-nosity with star formation rate (SFR) – is crucial for capital-ising on the science that can be addressed from [O ii ] data. Inthis work, we aim to do exactly this, ultimately allowing usto build robust galaxy clustering predictions for near-future[O ii ] data sets dominated by star-forming galaxies.Modelling emission lines requires, at least, a certainknowledge of both the gas and the star formation historyof a given galaxy. [O ii ] emission is particularly difficult topredict, as it critically depends on local properties, such asdust attenuation, the structure of the H ii regions and theirionisation fields. For this reason, [O ii ] traces star forma-tion and metallicity in a non-trivial way (e.g., Kewley et al.2004; Dickey et al. 2016). Previous works on [O ii ] emit-ters have shown that semi-analytic models of galaxy forma-tion (SAMs) are ideal laboratories for studying the physicalproperties of these galaxies, since they can reproduce theobserved [O ii ] luminosity function (LF) at z ∼ ii ] emitters aredistributed in the dark matter haloes. They found typicalhost halo masses in agreement with the results from Fav-ole et al. (2016a), which were based on a modified SHAMtechnique combining observational data with the MultiDarkPlanck dark matter N-body simulation (MDPL; Klypinet al. 2016).For this project, we use the MultiDark-Galaxies mock products, which are publicly available at . These catalogues were produced using 3different SAMs to populate the snapshots of the MultiDark2(MDPL2; Klypin et al. 2016) dark matter cosmological sim-ulation, over the redshift range 0 < z < h − Gpc and 3048 particles withmass resolution of 1 . × h − M (cid:12) . The models used inthe production of these catalogues were: sag (Gargiulo et al.2015; Mu˜noz Arancibia et al. 2015; Cora et al. 2018), sage (Croton et al. 2016) and galacticus (Benson 2012).In this work, we explore the limitations of estimatingthe [O ii ] luminosity in post-processing using different ap- https://wfirst.gsfc.nasa.gov/ https://pfs.ipmu.jp/ http://sci.esa.int/euclid/ proaches, assessing how this quantity correlates with othergalactic properties within the studied SAMs. The resultsfrom model galaxies are compared with observations fromDEEP2 (Newman et al. 2013). The DEEP2 spectra havebeen fitted using firefly (Wilkinson et al. 2017; Com-parat et al. 2017) to extract physical properties for thesegalaxies. In our analysis, we assume a Planck Collaborationet al. (2015) cosmology with Ω m = 0 . Λ = 0 . h = 0 . firefly codefor spectral fitting. We compare the model SFR and stellarmass functions with current observations. In Section 3, wedescribe how we calculate the [O ii ] emission line luminosityin the SAMs using the publicly available code get emlines by Orsi et al. (2014) with instantaneous SFR and cold gasmetallicity as inputs. We analyse the impact of using aver-age rather instantaneous SFR in this calculation to be usedin those SAMs that do not provide instantaneous quantities.We compare the derived [O ii ] luminosity functions with cur-rent observations. In Section 4, we explore the correlationsbetween L [O ii ] and several galactic properties to establishmodel proxies for the [O ii ] luminosity. We provide scalingrelations among these quantities that can be used in mod-els without an emission line estimate. We further test theseproxies by checking the consistency of the evolution of their[O ii ] luminosity functions and clustering signal with obser-vations and direct predictions from SAMs. Section 5 sum-marises our findings. Semi-analytic models of galaxy formation (White & Frenk1991; Kauffmann et al. 1993) encapsulate the key mecha-nisms that contribute to form galaxies in a set of coupled dif-ferential equations, allowing one to populate the dark mat-ter haloes in cosmological N -body simulations with relativehaste (see e.g., Baugh 2006; Benson 2010; Somerville & Dav´e2015). In the last two decades, a huge effort has been madeto improve these models and account for the physical pro-cesses that shape galaxy formation and evolution, such asgas cooling (e.g., De Lucia et al. 2010; Monaco et al. 2014;Hou et al. 2017), gas accretion (e.g., Guo et al. 2011; Hen-riques et al. 2013; Hirschmann et al. 2016), star formation(e.g., Lagos et al. 2011), stellar winds (e.g., Lagos et al.2013), stellar evolution (e.g., Tonini et al. 2009; Henriqueset al. 2011; Gonzalez-Perez et al. 2014), AGN feedback (e.g.,Bower et al. 2006; Croton et al. 2006) or environmental pro-cesses (e.g., Weinmann et al. 2006; Font et al. 2008; Stevens& Brown 2017; Cora et al. 2018). Typically, SAMs do not at-tempt to resolve the scales on which these key astrophysicalprocesses take place, but rather they describe their effectsglobally. Inevitably, this leads to free parameters in the mod-els that require calibration; in essence, these compensate forthe lack of understanding of certain processes and also fornot resolving the relevant small scales.In this study, we use the results from three semi-analyticmodels of galaxy formation: SAG (Cora 2006; Gargiulo et al.2015; Mu˜noz Arancibia et al. 2015; Cora et al. 2018), SAGE(Croton et al. 2006, 2016) and Galacticus (Benson 2012).The three SAMs considered have been run on the same MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 MultiDark2 1 h − Gpc cosmological simulation with Planckcosmology (Klypin et al. 2016) to produce mock galaxy cat-alogues .The complete description of the first data release of the MultiDark-Galaxies products including sag , sage and galacticus mock catalogues can be find in Knebe et al.(2018). All these catalogues lack [O ii ] luminosity estimates.A version of Galacticus does have an emission line calcula-tion (Merson et al. 2018), but it has not been applied to theMultiDark models. sag We consider a modified version of the Semi-AnalyticalGalaxies (SAG; Cora 2006; Lagos et al. 2008; Gargiulo et al.2015; Mu˜noz Arancibia et al. 2015; Collacchioni et al. 2018;Cora et al. 2018) code, which involves a detailed chemicalmodel and implements an improved treatment of environ-mental effects (ram-pressure of both hot and cold gas phasesand tidal stripping of gaseous and stellar components). Italso includes the modelling of the strong galaxy emissionlines in the optical and far-infrared range as described inOrsi et al. (2014). The free parameters of the model havebeen tuned by applying the Particle Swarm Optimisationtechnique (PSO; Ruiz et al. 2015) and using as constraintsthe stellar mass function at z = 0 and 2 (data compilationsfrom Henriques et al. 2015), the SFR function at z = 0 . sage The Semi-Analytic Galaxy Evolution code (SAGE; Cro-ton et al. 2006, 2016) is a modular and customisable SAM.The updated physics includes gas accretion, ejection due tofeedback, a new gas cooling–radio mode AGN heating cycle,AGN feedback in the quasar mode, galaxy mergers, disrup-tion, and the build-up of intra-cluster stars. sage was calibrated to reproduce several statistical fea-tures and scaling relations of galaxies at z = 0, including thestellar mass function, tightly matching the observational un-certainty range (Baldry et al. 2008), the black hole-bulgemass relation, the stellar mass-gas metallicity relation, andthe Baryonic Tully-Fisher relation (Tully & Fisher 1977). galacticusgalacticus (Benson 2012) has much in common with theprevious two models, in terms of modularity, the range ofphysical processes included and the type of quantities thatit can predict. Although this model has not been re-tunedto this simulation, the original calibration was performedusing analytically built merger trees assuming a WMAP7cosmology (Benson 2012). The original model reproducedreasonably well the observed stellar mass function at z ∼ publicly available at and http://skiesanduniverses.org/ https://bitbucket.org/galacticusdev/galacticus/wiki/Home z l o g ( c S F R d e n s i t y [ M y r M p c ]) GalacticusSAGSAGEBehroozi et al. (2013)Madau & Dickinsion (2014)Driver et al. (2018)Gruppioni et al. (2015)
Figure 1.
Cosmic star formation rate density of sag , sage and galacticus MultiDark-Galaxies as a function of redshift, com-pared to four independent compilations of data sets from Behrooziet al. (2013) (this was corrected to a Chabrier et al. (2014) IMFby the same authors), Madau & Dickinson (2014), Driver et al.(2018) and Gruppioni et al. (2015). The error bars are the 1 σ dis-persion around each point. We show this result only up to z ∼ .
07 (Li & White 2009) and the HI mass function at z ∼ For a full comparison between the sag , sage and galacti-cus semi-analytic models adopted in this work, we refer thereader to Knebe et al. (2018). The main differences betweenthem are: i) the calibrations; ii) the treatment of mergers; iii)galaxies without a host halo, “orphans”, are not allowed in sage , while they can happen, due to mass stripping, within galacticus and sag ; and iv) the metal enrichment models,with galacticus and sage assuming an instantaneous recy-cling approximation and sag implementing a more completechemical model (Cora 2006; Collacchioni et al. 2018).Here we also recall some results from Knebe et al. (2018)that are important for interpreting the outcomes of ouranalysis and a further study of global properties can befound in Appendix C. As we impose a minimum limit of M (cid:63) > . M (cid:12) and SFR > − M (cid:12) to the three SAMs ofinterest, some of our model results will be slightly differentfrom those presented in Knebe et al. (2018). The cuts abovehave been chosen taking into account the resolution limitof the MultiDark cosmological simulation (see Knebe et al.2018). At z ∼
1, the limit on SFR excludes about 4% ofthe entire sag population, 17% of galaxies in sage , and nogalaxies from galacticus .Fig. 1 shows the redshift evolution of the
MultiDark-Galaxies cosmic star formation rate (SFR) density com-pared to a compilation of observations including estimates ofthe cosmic SFR from narrow-band (H α ), broad-band (UV-IR), and radio (1.4 GHz) surveys by Behroozi et al. (2013),and more recent results by Madau & Dickinson (2014),Gruppioni et al. (2015) and Driver et al. (2018). The ob-servational data sets are consistent, despite being affectedby different systematic errors. Fig. 1 only extends to z ∼ . < z < .
2. Beyond z = 2, sag and galacti- MNRAS000
2. Beyond z = 2, sag and galacti- MNRAS000 , 000–000 (0000)
Favole et al. 2020 log (SFR [M yr ]) l og ( [ M p c d e x ] ) z = 0 . SAGSAGEGalacticusGruppioni + 15 log (SFR [M yr ]) l og ( [ M p c d e x ] ) z = 1 . . . . . . . . . log (SFR [M yr ]) l og ( [ M p c d e x ] ) z = 2 Figure 2.
MultiDark-Galaxies average SFR function evolutionat z (cid:46) cus model galaxies maintain a good agreement with the dataout to z ∼ .
5, while sage overpredicts the SFR density at z (cid:38) sag model subdivides the time between snapshots in25. This timescale typically corresponds to ∼ z ∼
1, which is the timescale physically relevant for the [O ii ]emission. sage and galacticus split time in 10 steps.Fig. 2 displays the average SFR functions of the MultiDark-Galaxies at different redshifts compared tothe Herschel data from the PEP and HerMES surveys(Gruppioni et al. 2015). We find good agreement for SAGmodel galaxies over the whole SFR and z ranges consid-ered. galacticus is consistent with the measurements atSFR (cid:46) . yr − M (cid:12) , while sage agrees with the data upto 10 yr − M (cid:12) . At higher SFRs, sage under-predicts thenumber of star-forming galaxies by ∼ MultiDark-Galaxies stellar mass function compared to, from top tobottom, the SDSS-GALEX observations at z = 0 . . 65 (Moustakas et al. 2013), the BOSS CMASS obser-vations at 0 . < z < . log (M ? [M ]) l og ( [ M p c d e x ] ) z = 0 . SAGSAGEGalacticus log (M ? [M ]) l og ( [ M p c d e x ] ) z = 0 . log (M ? [M ]) l og ( [ M p c d e x ] ) z = 1 . . . . . . . . . log (M ? [M ]) l og ( [ M p c d e x ] ) z = 2 SDSS GALEXDEEP2PRIMUSBOSS CMASSZFOURGE / CANDELS Figure 3. Stellar mass function evolution of our model galax-ies (lines colour-coded as in the legend) compared to the SDSS-GALEX z = 0 . . < z < . 65 (Moustakas et al.2013, magenta triangles), the BOSS CMASS measurements at0 . < z < . . < z < . . < z < . FF data at 0 . < z < . 1, and the ZFOURGE/CANDELSstar-forming galaxies at 1 . < z < . > z ∼ sag and ZFOURGE/CANDELS data is especially good because MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 this model was calibrated against these observations. sage and galacticus over-predict the number of galaxies withlog(M (cid:63) [M (cid:12) ]) (cid:46) 11, and this excess is enhanced at higherredshift (from ∼ . z = 0 . ∼ . z = 2). sage under-estimates the number of galaxies more massivethan 10 M (cid:12) at all redshifts. We deem the MultiDark-Galaxies to be in sufficient agreement with observations interms of their stellar-mass and SFR evolution such that wecan draw meaningful predictions from the models that relyon these properties. We are interested in exploring the relationship between L [O ii ] and different galactic properties. For comparison,we use an observational data set, the DEEP2– Firefly (DEEP2-FF, hereafter) galaxy sample, which allows us totest whether the model galaxies cover similar ranges of pa-rameters, once the adequate selection functions are imple-mented.The DEEP2 survey obtained spectra of about 50,000galaxies brighter than R ∼ . 1, in four separate fieldscovering ∼ . (Newman et al. 2013). The redshiftmeasurement for each object in the DEEP2 DR4 databasewas inspected by eye and assigned an integer quality code − < Q < For this work, we consider galaxies with Q > 2, corresponding to secure redshifts, within the range0 . < z best < . We also use the extended pho-tometric catalogues developed by Matthews et al. (2013), which supplement the DEEP2 photometric catalogues with( u, g, r, i, z ) photometry from the Sloan Digital Sky Survey(SDSS). By applying the cuts specified above and taking intoaccount the cross-match between the mentioned catalogues,the spectra of 33 838 galaxies from the original DEEP2 DR4catalogue are used in this study. These spectra are fitted us-ing stellar population models to extract quantities such asstellar masses, stellar metallicities, star formation rates, andages. In particular, the DEEP2 SFR values are computed byfitting stellar population models to the spectral continuum,where the emission lines are masked for the fit. Thus, thisconstitutes an independent estimate from an [O ii ]-basedSFR.The spectral fit is performed using the firefly code(Wilkinson et al. 2017; Comparat et al. 2017) in which nopriors, other than the assumed model described immedi-ately below, are applied. firefly treats dust attenuationin a novel way, by rectifying the continuum before the fit;for full details see Wilkinson et al. (2017) and Comparatet al. (2017). The firefly fit is performed for spectraltemplates with ages below 20 Gyr and metallicities in therange 0 . < Z < 3. The maximum age found for theDEEP2-FF sample is 10.18 Gyr. It is noteworthy to re-mark that firefly does not interpolate between the agesof the templates used in the spectral fitting. For this study,we adopt spectral templates from Maraston & Str¨omb¨ack http://deep.ps.uci.edu/DR4/zquality http://deep.ps.uci.edu/DR4/photo.extended https://github.com/FireflySpectra/Firefly_release , (2011), assuming a Chabrier (2003) IMF, same as in the MultiDark-Galaxies , and the ELODIE stellar library.This latter covers the wavelength range 3900 − R = 10 , − ∼ firefly fits to the DEEP2 spectra described aboveare available at (340 MB). Another fit to the DEEP2 spectra has been per-formed by Comparat et al. (2017) assuming slightly differentage and metallicity ranges, and using a previous version of firefly that did not take into account the presence of massloss in the stellar population models. Here we refer to “stel-lar mass” as the sum of the mass of living stars and the masslocked in stellar remnants (i.e., white dwarfs, neutron starand black holes). The DEEP2-FF galaxy catalogue also provides SDSS( u, g, r, i, z ) apparent magnitudes. In order to compare theseobservations with the MultiDark-Galaxies absolute mag-nitudes, we have ( k + e ) corrected them (where “ e ” standsfor evolution). To this end, we have produced an evolving setof simple stellar populations (SSP; Maraston & Str¨omb¨ack2011) with ages, metallicities, and redshifts matching thoseused for the Firefly runs described above. In particular, weproduce a table of possible evolutionary paths that providesthe observed-frame properties of the given SSPs in the SDSSfilters and allows us to determine the k -correction in thosefilters without any approximation. Hereafter, we will call it“MS table”. This table calculates intrinsic magnitudes. TheDEEP2 data have been corrected from interstellar dust at-tenuation by applying Calzetti et al. (2000) extinction law.These SDSS observed-frame properties are computed byred-shifting the model SEDs to a fixed grid of redshifts from z = 3 . z = 0 . , with ∆ z = 0 . 1, and applying cos-mological dimming using the Flexible-k-and-evolutionary-correction algorithm ( FLAKE , Maraston, in prep.). We in-terpolate between the redshifts when needed. Such a tech-nique has been widely used in the literature (e.g., Marastonet al. 2013; Etherington et al. 2017) and can be generalisedto any arbitrary set of filters.From each SSP model in the MS table above we extractthe ( k + e ) correction as:( k + e ) j = M j ( z ) − m j = M j ( z ) − M j ( z = 0) , (1)where M j ( z ) are the galaxy SDSS j = ( u, g, r, i, z ) absolutemagnitudes at redshift z and m are the observed magni-tudes, i.e. the absolute magnitudes at z = 0.The Firefly spectral fitting code finds the best fit toa galaxy by weighting different SSPs and adding them to-gether. It turns out that the best Firefly fits to the DEEP2galaxy sample have only two SSP components. Thus, theDEEP2-FF galaxy sample can be cross-matched with thecomponents of the MS table, by using a linear combinationof the two SSP components of each Firefly (FF) best fit:SSP MS = w SSP FF0 + w SSP FF1 , (2)with w + w = 1. Then, each DEEP2-FF galaxy is assigned MNRAS000 FF1 , (2)with w + w = 1. Then, each DEEP2-FF galaxy is assigned MNRAS000 , 000–000 (0000) Favole et al. 2020 a ( k + e ) correction that is the weighted, linear combinationof the corrections from each SSP component:( k + e ) j = ( k + e ) j w + ( k + e ) j w . (3) FIREFLY galaxy sample For our analysis, we focus on DEEP2-FF galaxies withinthe redshift range 0 . < z < . 1. We consider the sumof the [O ii ] 3727˚A and 3729˚A line fluxes as the [O ii ] dou-blet. Here we impose a flux limit of F[O ii ] > σ F [OII] (where σ F [ OII ] is the flux error) to guarantee robust fluxestimates, and a minimum stellar mass uncertainty of[log (M σ up (cid:63) ) − log (M σ low (cid:63) )] / < . 4. In the previous ex-pression, M σ up , low (cid:63) represents the Firefly stellar masswithin ± σ from the mean value of the distribution.After applying the cuts described above, our final sam-ple includes 4478 emitters with minimum [O ii ] flux of2 . × − erg s − cm − , mean L [O ii ] ∼ . erg s − , M (cid:63) ∼ . M (cid:12) , age ∼ . yr, and mean cold gas metallic-ity Z cold ∼ . 72. Fig. 5 shows the distribution of L [O ii ] asa function of SFR. The observed sample only populates anarrow range of SFR, and this affects the comparison withthe model galaxies, which have SFRs lower than the mini-mum value of the DEEP2-FF sample. Other properties fromthis data set can be seen in Fig. 8 and in Appendix C. Weassume the dust attenuation of the nebular emission linesto be the same as for the continuum. Thus, we also correctthe L [O ii ] from interstellar dust attenuation by applyingCalzetti et al. (2000) extinction law, as we have detailedabove for the broad-band magnitudes.For the analysis, we select both observed and mod-els galaxies using a more conservative flux cut, F[O ii ] > × − erg s − cm − . This corresponds to L [O ii ] ∼ . erg s − at z = 1 in Planck cosmology (Planck Col-laboration et al. 2015), and roughly mimics the observa-tional limitations (see also Gonzalez-Perez et al. 2018). Thiscut reduces the sparse, faint tail of the observed distribu-tion (there are only 4 DEEP2 galaxies with flux lower than5 × − erg s − cm − ) and allows us to obtain much nar-rower SAM constraints.As shown in Fig. 4, most galaxies with L [O ii ] < . erg s − have been removed from the DEEP2-FF sam-ple, compared to the original DEEP2 population. Despitethis, the DEEP2-FF galaxy sample is statistically represen-tative of the original DEEP2 population. In fact, the cumu-lative distribution functions of these two samples, approx-imated by splines, differ by less than 5%, according to aKolmogorovSmirnov test.Fig. 4 shows the distribution of the dust-attenuated L [O ii ] computed with get emlines (see § z = 0 . 94 and with M (cid:63) > . M (cid:12) and SFR > − M (cid:12) (seeSec. 2.1.4). These model L [O ii ] distributions are statisticallydifferent from the DEEP2-FF one. However, they have sim-ilar mean values: (cid:104) L [O ii ] (cid:105) ∼ erg s − , (cid:104) age (cid:105) ∼ . yr, (cid:104) M (cid:63) (cid:105) ∼ . M (cid:12) .In order to draw a sample of model galaxies consistentwith DEEP2-FF observations, we select sag galaxies with a L [O ii ] distribution following the spline fit to the DEEP2-FFdistribution, as shown in Fig. 4. We perform such a draw-ing for sag [O ii ] luminosities computed both from instanta-neous and average SFR. The L [O ii ] of these new selectionshave mean values consistent with those from the DEEP2-FF . . . . . . . . log (L[OII] / erg s − ) − − − − N o r m a li ze d N ga l DEEP2 AllDEEP2 − FFsplinefitSAG avg z = 0 . 94 selectionSAG inst z = 0 . 94 selectionSAG avg z = 0 . 94 drawnfromsplineSAG inst z = 0 . 94 drawnfromspline Figure 4. Attenuated L [O ii ] distribution of the original DEEP2sample (black, empty dots) compared to the DEEP2-FF selection(black, filled dots), which we fit with a spline function. The areaunder the curves is normalized to unity. We compare these resultswith the sag model galaxies selected with M (cid:63) > . M (cid:12) andSFR > − M (cid:12) (empty squares; see Sec. 2.1.4), and with theSAG galaxies randomly drawn from the DEEP2-FF spline distri-bution (filled squares). The [O ii ] luminosity values in the modelgalaxies are calculated using the get emlines code, inputing ei-ther the instantaneous (purple) or average (salmon) SFR. All thedetails about these quantities and the calculations are given inSec. 3.1. sample. Meanwhile, the ages, (cid:104) age (cid:105) ∼ yr, and the stellarmasses, (cid:104) M (cid:63) (cid:105) ∼ . M (cid:12) , are lower than the observed ones.In Appendix A, the DEEP2-FF sample is directly com-pared to the sag model galaxies selected following theDEEP2-FF L [O ii ] distribution. These sag model subsetshave brighter L [O ii ], M u and M g values, slightly lowerages, higher stellar masses and span higher SFR valuescompared to the SAG selection at M (cid:63) > . M (cid:12) andSFR > − M (cid:12) .The main focus of this paper is to test the validity ofdifferent approaches for modelling emission lines in largegalaxy samples with volumes comparable to the observableUniverse. In this context, the comparison to the DEEP2-FFsample is meant to be a rough guide to the expected locationof observed galaxies in different parameter spaces. ii] EMITTERS IN THE SAMS The physics of [O ii ] emission lines is difficult to model, asit depends on local processes, such as dust extinction, andthe inner structure and the ionising fields of the H ii neb-ula in which they are embedded. Different approaches havebeen used to model the [O ii ] emission line: (i) assume a re-lation between L [O ii ] and SFR and, possibly, metallicity asit happens in observations (Kennicutt 1998; Kewley et al.2004; Moustakas et al. 2006; Jouvel et al. 2009; Sobral et al.2012; Talia et al. 2015; Valentino et al. 2017); (ii) assumean average H ii region for a range of metallicities (Gonzalez-Perez et al. 2018); (iii) couple a photoionisation model witha galaxy evolution one (Hirschmann et al. 2012; Orsi et al.2014). We address method (i) in Section 4 and method (iii)here.None of the MultiDark-Galaxies catalogues studied MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 in this work provides direct L [O ii ] estimates. Therefore, wecouple the SAMs with the get emlines model (Orsi et al.2014), which encapsulates the results from the MAPPINGS-III photoionisation code (Groves et al. 2004; Allen et al.2008). Here, the ionisation parameter of gas in galaxies isdirectly related to their cold gas metallicity, obtaining areasonable agreement with the observed H α , [O ii ] λ iii ] λ get emlines methodol-ogy requires as input the cold gas metallicity and the instan-taneous SFR. This latter quantity, however, is not usuallyoutput by SAMs. The instantaneous SFR is preferred to atime-averaged equivalent, as the latter can include contribu-tions from stellar populations older than those responsiblefor generating the nebular emission in star-forming galaxies. sag is the only semi-analytic model providing bothinstantaneous and average SFR values, while sage and galacticus only provide average SFRs. In the next sec-tion, we describe in detail the get emlines algorithm to beused in the L [O ii ] calculation for a semi-analytic model. Be-cause SAMs do not usually output the instantaneous SFR,which is needed as default input for the get emlines code,we test the usage of the average SFR and how this affectsdifferent galactic properties. GET EMLINES code We now describe step by step how we have implemented the get emlines nebular emission code to obtain [O ii ] lumi-nosities for the MultiDark-Galaxies . This methodology isbased on the photoionisation code MAPPINGS-III (Groveset al. 2004; Allen et al. 2008), which relates the ionisationparameter of gas in galaxies, q , to their cold gas metallicity Z cold as: q ( Z ) = q (cid:18) Z cold Z (cid:19) − γ , (4)where q is the ionisation parameter of a galaxy that hascold gas metallicity Z and γ is the exponent of the powerlaw. Following Orsi et al. (2014), from the pre-computedH ii region model grid of Levesque et al. (2010), we assume q = 2 . × cm s − and γ = 1 . α , [O ii ] λ iii ] λ get emlines code has been calibrated toreproduce a range of luminosity functions at different red-shifts and local line ratios diagrams, and it has been testedagainst observations up to z = 5 (Orsi et al. 2014). A differ-ent combination of q and γ changes the L [O ii ] results in acomplicated way. For instance, higher parameter values pro-duce a lower number density of bright emitters, which trans-lates into a substantial difference in the lower peak of the L [O ii ]-SFR bimodality shown in Fig. 5. Changing the q and γ parameters would require to recalibrate the get emlines model, and this goes beyond the scope of this work.The cold gas metallicity is defined as the ratio betweenthe cold gas mass in metals and the cold gas mass (e.g.,Yates 2014), considering both bulge and disc components,when available: Z cold = M Z cold M cold . (5) Another fundamental quantity needed to derive the[O ii ] line luminosity is the hydrogen ionising photon ratedefined as: Q H = (cid:90) λ λL λ hc dλ, (6)where L λ is the galaxy composite SED in erg s − ˚A − , λ = 912˚A, c is the speed of light and h is the Planck con-stant. Q H is a unit-less quantity calculated at each modelsnapshot just by solving the integral above. Assuming aKroupa (2001) IMF, one can express the ionising photonrate as a function of the instantaneous star formation rateas (Falc´on-Barroso & Knapen 2013): Q H = log . 35 + log (SFR / M (cid:12) yr − ) + 53 . . (7)Combining Eq. 7 with the attenuation-correctedemission-line lists from Levesque et al. (2010), normalisedto the H α line flux, we compute the [O ii ] luminosity as: L ( λ j ) = 1 . × − Q H F ( λ j , q, Z cold ) F ( Hα, q, Z cold ) , (8)where F ( λ j , q, Z cold ) is the MAPPINGS-III prediction of thedesired emission line flux at wavelength λ j for a given set of( q , Z cold ) and F ( Hα, q, Z cold ) is the H α normalisation flux.The total luminosity of the [O ii ] doublet is the sum ofthe luminosities of the two lines at λ j = 3727 , ii ] luminosity in Eq. 8 does not include any dustcontribution. In order to account for dust attenuation, weimplement the correction detailed in next Section usingCardelli et al. (1989) extinction curve. In this study, the intrinsic [O ii ] luminosity given in Eq. 8, L ( λ j ), is attenuated by interstellar dust as follows: L ( λ j ) att = L ( λ j )10 − . A λ ( τ zλ ,θ ) , (9)where A λ ( τ zλ , θ ) represents the attenuation coefficient de-fined as a function of the galaxy optical depth τ zλ and thedust scattering angle θ . Explicitly we have (Spitzer 1978; Os-terbrock 1989; Draine 2003; Izquierdo-Villalba et al. 2019): A λ ( τ zλ , θ ) = − . − exp( − a λ sec θ ) a λ sec θ , (10)where a λ = √ − ω λ τ zλ and ω λ is the dust albedo, i.e. thefraction of the extinction that is scattering. We assumecos θ = 0 . 60 and ω λ = 0 . 80, meaning that the scatteringis not isotropic but backward-oriented, and that 80% of theextinction is scattering. These are the values that return thebest agreement with DEEP2+VVDS observations in Fig. 9.The galaxy optical depth τ zλ that enters Eq. 10 is definedas (Devriendt et al. 1999; Hatton et al. 2003; De Lucia &Blaizot 2007): τ zλ = (cid:18) A λ A V (cid:19) Z (cid:12) (cid:18) Z cold Z (cid:12) (cid:19) s (cid:18) (cid:104) N H (cid:105) . × atoms cm − (cid:19) , (11)where the first two factors on the right-hand side representthe extinction curve. This depends on the cold gas metallic-ity Z cold defined in Eq. 5 according to power-law interpola-tions based on the solar neighbourhood, the Small and theLarge Magellanic Clouds. The exponent s = 1 . λ > MNRAS000 80, meaning that the scatteringis not isotropic but backward-oriented, and that 80% of theextinction is scattering. These are the values that return thebest agreement with DEEP2+VVDS observations in Fig. 9.The galaxy optical depth τ zλ that enters Eq. 10 is definedas (Devriendt et al. 1999; Hatton et al. 2003; De Lucia &Blaizot 2007): τ zλ = (cid:18) A λ A V (cid:19) Z (cid:12) (cid:18) Z cold Z (cid:12) (cid:19) s (cid:18) (cid:104) N H (cid:105) . × atoms cm − (cid:19) , (11)where the first two factors on the right-hand side representthe extinction curve. This depends on the cold gas metallic-ity Z cold defined in Eq. 5 according to power-law interpola-tions based on the solar neighbourhood, the Small and theLarge Magellanic Clouds. The exponent s = 1 . λ > MNRAS000 , 000–000 (0000) Favole et al. 2020 where the [O ii ] line is located. The ( A λ /A V ) Z (cid:12) term is theextinction curve for solar metallicity, which we take to bethat of the Milky Way, and (cid:104) N H (cid:105) the mean hydrogen col-umn density. We adopt the values Z (cid:12) = 0 . . µ m (cid:54) λ < . µ m (i.e., optical/NIR regime), one has: (cid:18) A λ A V (cid:19) = a ( x ) + b ( x ) /R V , (12)where x ≡ λ − , R V ≡ A V /E ( B − V ) = 3 . a ( x ) =1 + 0 . y − . y − . y +0 . y + 0 . y − . y + 0 . y ,b ( x ) =1 . y + 2 . y + 1 . y − . y − . y + 5 . y − . y , (13)with y = ( x − . (cid:104) N H (cid:105) = M disccold . m p π ( a R disc1 / ) atoms cm − , (14)where M disccold is the cold gas mass of the disc, m p = 1 . × − kg is the proton mass, a = 1 . 68 is such that the columndensity represents the mass-weighted mean column densityof the disc, and R disc1 / is the disc half-mass radius.Qualitatively for this dust attenuation model, galaxieswith large amounts of cold gas, metal rich cold gas and/orsmall scale sizes, will be the most attenuated ones (see alsoMerson et al. 2016). The get emlines code described in Section 3.1 ideally re-quires as inputs the instantaneous SFR and cold gas metal-licity of galaxies. The instantaneous SFR, which is definedon a smaller time-step compared to the average SFR (seeSec. 2.1.4), traces very recent or ongoing episodes of star-formation, that are the relevant ones for nebular emission.Fig. 5 shows, as a function of SFR, the intrinsic (i.e. cor-rected from dust attenuation) L [O ii ] that the coupling with get emlines gives for both the instantaneous (solid con-tours) and average (dashed) SFR from sag at z ∼ 1. Theinnermost (outermost) contours enclose 68% (95%) of ourmodel galaxies. The diagonal lines show the correlations be-tween SFR and L [O ii ]. These are tight correlations, whosebest-fitting parameters are reported in Table 1. Under laidare the DEEP2-FF observational data at 0 . < z < . L [O ii ] derived from either the in-stantaneous or the average SFRs. These distributions showa bimodality that can also be seen in the observations.The instantaneous and average SFR derived distribu-tions differ the most at SFR (cid:46) yr − M (cid:12) , with [O ii ] lumi-nosities from average SFR being ∼ . ∼ . yr − M (cid:12) , there areslightly less bright [O ii ] emitters from instantaneous SFR.DEEP2-FF galaxies in the upper density peak of theobserved bimodal distribution shown in Fig. 5 are older,more massive, more luminous and slightly more star-forming − . . . . . . log (SFR [M (cid:12) yr − ]) . . . . . l og ( L [ O II ][ e r g s − ] ) DEEP2 − FF 0 . < z < . . . N ga l / A b i n / V o l u m e [ − d e x − M p c − ] Figure 5. Intrinsic [O ii ] luminosity as a function of the SFR forthe sag model galaxies at z ∼ . < z < . − Mpc − ]. We haveimposed a minimum [O ii ] flux of 5 × − erg s − cm − to bothobservations and models. The model L [O ii ] values are calculatedby assuming instantaneous (solid, purple contours) and average(dashed, salmon) SFR as input for the get emlines prescrip-tion. The innermost (outermost) model contours encompass 68%(95%) percent of the galaxy distributions. The diagonal lines rep-resent the L [O ii ]-SFR correlations, whose coefficients are givenin Table 1. (mean values: (cid:104) age (cid:105) ∼ . yr, (cid:104) M (cid:63) (cid:105) ∼ . M (cid:12) , (cid:104) L [O ii ] (cid:105) ∼ . erg s − , (cid:104) SFR (cid:105) ∼ . yr − M (cid:12) ) compared totheir counterparts in the lower density area ( ∼ . yr, ∼ . M (cid:12) , ∼ . erg s − , ∼ . yr − M (cid:12) ). Overall,we find an opposite trend for model galaxies. In fact, the up-per peak of the bimodality is composed of younger, less mas-sive, slightly more luminous, less star-forming galaxies withmean values: (cid:104) age (cid:105) ∼ . yr, (cid:104) M (cid:63) (cid:105) ∼ . M (cid:12) , (cid:104) L [O ii ] (cid:105) ∼ . erg s − , (cid:104) SFR (cid:105) ∼ . yr − M (cid:12) ); the lower peakhas mean values: (cid:104) age (cid:105) ∼ . yr, (cid:104) M (cid:63) (cid:105) ∼ . M (cid:12) , (cid:104) L [O ii ] (cid:105) ∼ . erg s − , (cid:104) SFR (cid:105) ∼ . yr − M (cid:12) .At the end of this Section, we will discuss further theorigin of the DEEP2-FF L [O ii ]-SFR bimodal trend in con-nection with other galactic properties shown in Fig. 8.In the top panel of Fig. 6 we compare the average(dashed, salmon) and instantaneous (solid, purple) sag SFRfunctions at z ∼ 1, whose ratio is displayed in the bot-tom panel. The instantaneous and average SFR functionsremain within 5% of each other at SFR > yr − M (cid:12) (the5% region is highlighted by the yellow shade). There is aslightly larger fraction, within 20%, of SAG galaxies havinglow average SFR, SFR < yr − M (cid:12) , than instantaneousvalues. The main difference between average and instanta-neous SFRs is found for galaxies with the highest specificSFR (i.e., SFR/ M (cid:63) ) and stellar masses below 10 M (cid:12) .The top panel in Fig. 7 presents the intrinsic (thicklines) and attenuated (thin) [O ii ] luminosity functions de-rived from the average SFR (dashed, salmon line) and in-stantaneous SFR (solid, purple) from SAG. We impose onthe sag model galaxies the same [O ii ] flux limit of DEEP2-FF observations, 5 × − erg s − cm − (see Sec. 2.2.2),which corresponds to L [O ii ] ∼ . erg s − at z = 1 inPlanck cosmology (Planck Collaboration et al. 2015). Theinstantaneous-to-average amplitude ratios are displayed in MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 − − − − − l og ( Φ [ M p c − d e x − ] ) SAG z = 0 . − . . . . . . . . log (SFR [M (cid:12) yr − ]) − . − . − . . . . l og ( Φ i n s t / Φ a v g ) Figure 6. Average (dashed, salmon) versus instantaneous (solid,purple) SFR functions for SAG model galaxies. The bottom panelshows the ratio between the two, and the yellow, shaded regionhighlights the 5% region of agreement. − − − − − l og ( Φ [ M p c − d e x − ] ) SAG z = 0 . . . . . . . . log (L[OII] [erg s − ]) − . − . . . l og ( Φ i n s t / Φ a v g ) intrinsicattenuated Figure 7. Intrinsic (thick lines) and attenuated (thin) [O ii ] lu-minosity functions based on sag average (dashed, salmon) andinstantaneous SFR (solid, purple). The bottom panel shows theratios between the two and the yellow stripe highlights the 5% re-gion of agreement. We apply the mocks the same [O ii ] flux limit ofDEEP2-FF observations, 5 × − erg s − cm − (see Sec. 2.2.2). the bottom panel of Fig. 7. The intrinsic (attenuated) L [O ii ]functions have differences below 5% for luminosities in therange 10 − erg s − (10 − . erg s − ), which arehighlighted by the yellow shade. At lower (higher) luminosi-ties, the discrepancies grow up to 20% (30%). For the bright-est galaxies, the discrepancy remains within 50%. The dif-ference produced in L [O ii ] by assuming average instead ofinstantaneous SFR does not change significantly with red-shift over the range 0 . < z < . sag broad-band u and g absolute magnitudes, ages and stellar massesas a function of the average SFR (dashed, salmon contour)and instantaneous SFR (solid, purple). We compare them log (SFR [M (cid:12) yr − ]) − − − M u DEEP2 − FF0 . < z < . . . log (SFR [M (cid:12) yr − ]) − − − M g log (SFR avg [M (cid:12) yr − ]) . . . l og ( ag e [ y r ] ) − . . . . . . log (SFR [M (cid:12) yr − ]) . . . . . l og ( M ? [ M (cid:12) ] ) N ga l / A b i n / V o l u m e [ − d e x − M p c − ] Figure 8. From top to bottom: intrinsic magnitudes, ages andstellar masses as a function of star formation rate for sag (con-tours) at z ∼ . < z < . − Mpc − ].The dashed, salmon (solid, purple) contours represent the aver-age (instantaneous) SFRs. The innermost (outermost) contoursencompass 68% (95%) of the distributions. The diagonal lines arethe linear fits showing the significant correlations (i.e. r (cid:62) . A x + B A B σ y r y=log ( L [O ii ])x=log (SFR avg ) 0.625 ± ± (SFR inst ) 0.609 ± ± M u x=log (SFR avg ) -1.859 ± ± (SFR inst ) -1.934 ± ± M g x=log (SFR avg ) -1.951 ± ± (SFR inst ) -2.029 ± ± (M (cid:63) )x=log (SFR avg ) 0.897 ± ± (SFR inst ) 0.939 ± ± Table 1. Best-fit parameters of the linear scaling relations foundfor sag model galaxies at z = 1 and shown in Fig. 8. The param-eter r is the correlation coefficient and σ y is the scatter in the y -axis. All the L [O ii ] values are intrinsic. with the DEEP2-FF observations at 0 . < z < 11 (grey,shaded squares). Except for the age, all these propertiesare tightly correlated with both SFRs. The lack of corre-lation between age and SFRs is clear for both the modeland DEEP2-FF galaxies. We fit straight lines to the instan-taneous and average contours and report the best-fit param-eters and correlation coefficients in Table 1. For the broad-band magnitudes, the slopes of the average SFR correlations MNRAS000 MNRAS000 , 000–000 (0000) Favole et al. 2020 are only ∼ . 07 shallower than the instantaneous ones; forthe stellar mass they are even closer. Overall, the widthof the distributions as a function of both SFRs does notvary significantly. The average SFR contours extend downto slightly smaller values compared to the instantaneous con-tours.The DEEP2-FF age and stellar mass distributions asa function of SFR in Fig. 8 show a bimodal trend, with anupper population of older, more massive, luminous, quies-cent galaxies ( (cid:104) age (cid:105) ∼ . yr, (cid:104) M (cid:63) (cid:105) ∼ . M (cid:12) , (cid:104) L [O ii ] (cid:105) ∼ . erg s − , (cid:104) SFR (cid:105) ∼ . yr − M (cid:12) ) and a lowertail of younger, less massive, luminous, more star-formingemitters ( (cid:104) age (cid:105) ∼ . yr, (cid:104) M (cid:63) (cid:105) ∼ . M (cid:12) , (cid:104) L [O ii ] (cid:105) ∼ . erg s − , (cid:104) SFR (cid:105) ∼ . yr − M (cid:12) ). We obtain thesame mean galaxy properties splitting the DEEP2-FF sam-ple with a cut in either the age-SFR or Mstar-SFR planes.The mean DEEP2-FF values derived from splitting inage or stellar mass as a function of SFR are similar to thoseobtained by splitting in L [O ii ] versus SFR (see Fig. 5). Theage/mass-SFR bimodal trend observed in DEEP2-FF galax-ies is not reproduced by the SAG model galaxies, whichinstead look bimodal in the L [O ii ]-SFR plane (Fig. 5) be-cause of the non-trivial dependence of L [O ii ] on metallicitythrough the parameters q and γ (see Sec. 3.1).In this section, we have shown that using the SAG av-erage SFRs as input for the get emlines code gives resultswithin 5% from using the instantaneous value for galaxieswith attenuated L [O ii ] in the range 10 . − . erg s − ,and with intrinsic L [O ii ] between 10 . − erg s − . Theseare the ELGs with SFR within 10 − . − . yr − M (cid:12) . Athigher and lower SFRs, there is a larger discrepancy betweenthe average and instantaneous values, which translates intoa larger difference ( < ii ]emitters. Thus, this effect is not significant for the averagegalaxy population. ii] luminosity functions In the top panel of Fig. 9, we present the MultiDark-Galaxies dust attenuated [O ii ] luminosity functions at z = 0 . 94 compared to a compilation of DEEP2 and VVDSdata from Comparat et al. (2016). Note that similar resultshave been found within the redshift range 0 . < z < . ii ] lumi-nosities have been derived using the get emlines codedescribed above coupled with instantaneous SFR for SAGmodel galaxies, and average SFR for SAGE and Galacticus,for which the instantaneous quantity is not available. Thedust attenuation has been accounted for by correcting theseluminosities applying Eq. 9 with Cardelli et al. (1989) extinc-tion curve. There are varying degrees of agreement betweenthe models and observational data across the ∼ ii ] luminosity and redshift range considered. Nevertheless,the trends from all the data sources are consistent. This plothighlights that the shape and normalisation of a predicted[O ii ] luminosity function from a SAM are robust to boththe precise prescriptions that govern galaxy evolution in themodel, and the calculation of [O ii ] from either instantaneousor average SFR.In the top panel of Fig. 9, we see a drop in the number ofGalacticus [O ii ] emitters at intermediate luminosities thatis independent of the stellar mass. This is mainly determinedby the half mass radii of the disc, R disc1 / , that enter the dustattenuation correction (see Eq. 14). These radii in Galacticus log (L[OII] [erg s ]) l og ( [ M p c d e x ] ) z = 0 . . . . . . . log (L[OII] [erg s ]) . . . . . . . . . l og ( i n t r / a tt ) z = 0 . Figure 9. Top: Dust attenuated [O ii ] luminosity functions of the MultiDark-Galaxies at z ∼ × − erg s − cm − . All the [O ii ] luminosities arecomputed using the get emlines code with SFR and cold gasmetallicity as inputs (see Section 3.1). The SAG L [O ii ], whichare estimated using the instantaneous SFR, are in good agree-ment with the SAGE and Galacticus results based on the averageSFR. Bottom: Ratios between the model intrinsic [O ii ] luminos-ity functions (given by Eq. 8) and the dust attenuated ones (seeSec. 3.2) shown in the upper panel. are about 50% smaller than in SAG and SAGE. At L [O ii ] (cid:38) . erg s − and z < . 2, Galacticus predicts about 0.5 dexmore [O ii ] emitters than the other two models.In the bottom panel of Fig. 9, we display the ratios of theattenuated-to-intrinsic L [O ii ] functions. As expected, thelargest effect of attenuation occurs at L [O ii ] (cid:38) erg s − ,where more massive galaxies are located, while in the low-luminosity, low-mass regime, the observed and intrinsic sig-nals tend to overlap. The ratio between the intrinsic and at-tenuated luminosity functions is model dependent. In par-ticular, the largest variations are due to the dust model,which depends on the metallicity, gas content and size ofeach galaxy, as described in § sage model galaxies,this ratio increases for brighter L [O ii ] galaxies. For sag , theratio also increases up to L [O ii ] (cid:38) . erg s − , althoughwith a steeper slope, and beyond this value it reaches aplateau. The ratio for galacticus has a prominent bumpin the luminosity range 10 . − . erg s − , where theeffect of attenuation is more pronounced, and this featurecorresponds to the drop seen at intermediate L [O ii ] in theupper panel. At higher luminosities, there is almost no differ-ence between the intrinsic and dust attenuated galacticus L [O ii ] functions. ii] LUMINOSITY PROXIES Observational studies have shown tight correlations betweenthe [O ii ] luminosity, SFR (Kennicutt 1998; Sobral et al.2012; Kewley et al. 2004; Moustakas et al. 2006; Comparatet al. 2015) and the galaxy UV-emission (Comparat et al. MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 without the need to introduce any dependence onmetallicity (Moustakas et al. 2006). This has prompted au-thors of theoretical papers to treat star-forming galaxies asELGs when making predictions for upcoming surveys (e.g.Orsi & Angulo 2018; Jim´enez et al. 2019).Here we explore the possibility of using simple, linear re-lations to infer the [O ii ] luminosity from global galaxy prop-erties that are commonly output in SAMs. For this purpose,we investigate both observationally motivated prescrip-tions (Section 4.1), and we derive model relations from the get emlines code coupled with the SAMs considered (Sec-tions 4.2 and 4.3). For this last study, we quantify the cor-relation between the model L [O ii ] from get emlines withthe average SFR, broad-band magnitudes, stellar masses,ages and cold gas metallicities. Directly using the measured L [O ii ]-SFR linear relation is useful to understand when isadequate to consider ELGs equivalent to star-forming galax-ies and when it is not.We find that the stellar mass of the MultiDark-Galaxies are unaffected by the change in proxies for es-timating their [O ii ] luminosities. As a consequence, thestellar-to-halo mass relation (SHMR) is also unchanged us-ing different L [O ii ] proxies.We remind the reader that, unless otherwise specified,we exclusively select emission line galaxies with fluxes above5 × − erg s − cm − in both the DEEP2-FF observationsand MultiDark-Galaxies . This flux limit corresponds toa L [O ii ] > . erg s − at z = 1 in the Planck cosmology(Planck Collaboration et al. 2015). All the results in whatfollows have these minimum cuts applied. ii] relation In this Section, we derive intrinsic L [O ii ] from the aver-age SFR of the MultiDark-Galaxies using three differ-ent, published relations assuming a Kennicutt (1998) IMF.These are: the Moustakas et al. (2006) conversion (see alsoComparat et al. 2015) calibrated at z = 0 . Moust[OII] (erg s − ) = SFR(M (cid:12) yr − )2 . × − , (15)the Sobral et al. (2012) formulation optimised at z = 1 . Sob[OII] (erg s − ) = SFR(M (cid:12) yr − )1 . × − , (16)the Kewley et al. (2004) conversion calibrated at z = 1,L Kew[OII] (erg s − ) = SFR(M (cid:12) yr − )7 . × − × ( a [12 + log (O / H) cold ] + b ) . (17)The coefficients ( a, b ) in the equation above are the valuesfrom Kewley et al. (2004) derived for the R metallicitydiagnostic (Pagel et al. 1979). The [12+log (O / H) cold ] termis the [O ii ] ELG gas-phase oxygen abundance, which weproxy with the cold gas-phase metallicity Z cold given in Eq. 5through the solar abundance and metallicity. Explicitly wehave:12 + log (O / H) cold = [12 + log (O / H) (cid:12) ] Z cold Z (cid:12) , (18)where we assume Z (cid:12) = 0 . (O / H) (cid:12) ] = 8 . 69 (Allende Prieto et al. 2001). Asthe above relations are for intrinsic luminosities, dust atten-uated quantities are obtained following the description in § log ( M * [ M ]) + l o g ( / H ) z=0.1 GalacticusSAGSAGESDSS ELG Figure 10. Mean gas-phase oxygen abundance in bins of stellarmass of the SDSS emission line galaxies at z ∼ . MultiDark-Galaxies models. The abun-dance is computed for the SAMs using Eq. 18. The error bars onthe SDSS measurements are the 1 σ scatter around the mean. For sag and galacticus , galaxies’ cold gas is brokeninto bulge and disc components (see their respective papersfor their definitions of a ‘gas bulge’); we therefore take amass-weighted average of these components’ metallicities toobtain Z cold . sage instead always treats cold gas as beingin a disc. In addition, the sag catalogues also output the(O / H) cold values, which are mass density ratios, that we usein the calculation of Eq. 17 for sag model galaxies. In orderto derive the correct abundances in terms of number den-sities, we need to rescale them by the Oxygen-to-Hydrogenatomic weight ratio, A O /A H ∼ . ii ] ELGsat z ∼ . cata-logue of spectrum measurements and are built according tothe works of Tremonti et al. (2004) and Brinchmann et al.(2004). Overall, we find that the gas-phase oxygen abun-dance in MultiDark-Galaxies increases with stellar massup to M (cid:63) ∼ M (cid:12) . Beyond this value it drops and reachesa plateau.The sag and sage model galaxies under-predict thegas-phase oxygen abundance by an average factor of ∼ . 02 dex. This systematic offset for SAGE is not predictive,but purely due to the fact that this model was calibratedby assuming a different value of (O / H) (cid:12) /Z (cid:12) , specifically[12 + log (O / H)] = [9 + log ( Z cold / . M (cid:63) < . M (cid:12) , galacticus also under-predictsthe gas-phase abundance by the same factor. However, thismodel exhibits a bump at M (cid:63) ∼ . M (cid:12) . This feature isrelated to the excess of galaxies around this stellar mass,which is seen in the galaxy stellar mass function (see Fig. 3).This excess was found to be produced by the depletion ofgas due to the extreme AGN feedback mechanism imple-mented in galacticus , where the galaxies have almost noinflow of pristine gas, and rapidly consume their gas supply(for further details, see Knebe et al. 2018). MNRAS , 000–000 (0000) Favole et al. 2020 We have investigated further this feature finding that, ifwe exclude galaxies with progressively higher cold gas frac-tion (CGF), which is defined as CGF= M cold / M (cid:63) , the bumpshrinks continuously. Fig. 10 is produced by combining twocuts: CGF > . > − yr − . The first one elim-inates about half of the galacticus model galaxies, mostof them with unrealistically small CGFs, possibly meaningthat their metallicities are not reliable due to the precisionused in evolving the relevant ordinary differential equations(Benson 2012). The second cut selects only very star-forminggalaxies. The bump completely disappears for CGF > . ∼ 70% of the galaxies are excluded fromthe sample.Fig. 11 compares the intrinsic [O ii ] luminosity as a func-tion of SFR for the three SAMs (coloured, filled contours)with the DEEP2-FF data at z ∼ L [O ii ] iscomputed using the get emlines code coupled with in-stantaneous SFR for SAG, and average SFR for the othersemi-analytic models. The distributions of sag , sage and galacticus behave in a similar way, reproducing the bi-modality observed in the data. The coloured lines (dashed,salmon; solid, yellow; dot-dashed, blue) are the linear fitsto the model L [O ii ]-SFR correlations. The best-fit param-eters, correlation coefficients ( r -values) and dispersions inboth directions are reported in Table 2.Fig. 11 shows that all the model galaxies consideredoverlap with the DEEP2-FF observations and extend fur-ther towards lower SFR values. All three SAMs cover the L [O ii ] observational range with their 2 σ regions. sage and galacticus get to the very bright domain of the parameterspace, while sag is limited to fainter L [O ii ] values.All the SAMs are tightly correlated in the SFR–luminosity plane and such a trend is in reasonable agreementwith the observationally derived relations from Eqs. 15-17(diagonal, black and green lines).In Fig. 11, the Kewley et al. (2004) parametrisation(green line and contours in Fig. 11) appears above all the get emlines derivations. These contours are obtained fromEq. 17, by inputting instantaneous (average) SFR and coldgas metallicity for sag ( sage , galacticus ) model galaxies.The green, straight lines are calculated by feeding the me-dian metallicity values in bins of SFR into Eq. 17. Althoughboth the Kewley et al. (2004) relation and the get emlines code assume the same cold gas metallicity values as inputs,the obtained distributions are very different. The width ofthe distributions is model-dependent and the L [O ii ] ob-tained for galaxies in sag and Galacticus present bimodaldistributions. This bimodality comes from the MAPPINGS-III term F ( λ j , q, Z cold ) in Eq. 8, that is a non-linear functionof Z cold . ii] versus broad-band magnitudes At a given redshift range, the broad-band magnitudes trac-ing the rest-frame UV emission of a galaxy are expectedto be tightly correlated with the SFR and the produc-tion of emission line galaxies. The rest-frame UV slope(1000 − z ∼ u andthe g − bands ( ∼ ii ] luminosityfor the sample under study.The correlations between the broad-band u and g ab- solute magnitudes and the intrinsic [O ii ] luminosity in MultiDark-Galaxies at z ∼ L [O ii ] values. We over plot allthe strong correlations (i.e. those with correlation coefficient r (cid:62) . 6) as linear scaling laws with an associated scatter σ y .Their best-fit parameters ( A, B ) and correlation coefficients( r ) can be found in Table 2, where relations with r < . u and g magnitudesto be tightly correlated with L [O ii ], and thus they have thepotential to be used as proxies for the [O ii ] luminosity, usingthe relations presented in Table 2. ii] versus age, metallicity and stellar mass We also study the dependence of the [O ii ] luminosity ongalaxy properties that are relevant to the L [O ii ] and ( k + e )calculations: the age, metallicity, and stellar mass.The right column of panels in Fig. 12 shows the relation-ship between the intrinsic [O ii ] luminosity and the stellarmass in both DEEP2-FF and our model galaxies. In sage we identify a correlation, but none is found for sag and galacticus model galaxies. The DEEP2-FF data do notexhibit any particular trend, maybe due to the narrow lu-minosity range that the sample covers.In the third column of Fig. 12, we display the relation-ship between the intrinsic L [O ii ] and age, which is mostlyflat both in MultiDark-Galaxies and DEEP2-FF obser-vations, with the latter showing a bimodal distribution. Only galacticus model galaxies exhibit an anti-correlation inthe age- L [O ii ] plane.No correlation is found between the metallicity and L [O ii ] for any of the models (this is not shown in Fig. 12).We conclude that none of the galaxy properties explored inthis Section are good candidates as proxies for L [O ii ]. ii] The L [O ii ] derived from the get emlines code is tightlyrelated to the SFR by construction, but we found it to bealso tightly related with the broad-band u and g magnitudes( r (cid:62) . 64, see Table 2). Here, we quantify the usability ofthe linear relations found as proxies to derive L [O ii ] fromaverage SFR and broad-band magnitudes. For this purpose,we compare the luminosity functions and galaxy clusteringsignal for [O ii ] emitters selected using the aforementionedlinear relations and the relations from Section 4.1, with thoseobtained by coupling the SAMs with the get emlines code(see Section 3.1). ii ] luminosity functions In the left column of Fig. 13, from top to bottom, weshow the attenuated [O ii ] luminosity functions of the sag , sage and galacticus model galaxies at z ∼ 1. We com-pare the L [O ii ] predictions from coupling the models withthe get emlines code (thick, coloured lines without er-ror bars) with those from using the SFR (solid, black), M u (dashed, green) and M g (dot-dashed, orange) proxies es-tablished above and summarised in Table 2. The shaded re-gions represent the effect of the scatter σ y on the proxy- MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 − . . . . . (SFR [M (cid:12) yr − ])40 . . . . . l og ( L [ O II ][ e r g s − ] ) DEEP2 − FFSAG inst z = 0 . − . . . . . (SFR [M (cid:12) yr − ]) SAGE avg z = 0 . − . . . . . (SFR [M (cid:12) yr − ]) Galacticus avg z = 0 . N ga l / A b i n / V o l[ − d e x − M p c − ] Figure 11. Intrinsic [O ii ] luminosity as a function of the SFR from the MultiDark-Galaxies at z ∼ . < z < . sag model galaxies, the [O ii ]luminosities have been computed from instantaneous SFRs, while for the other SAMs they are based on average SFRs. Both data andmodel ELGs are selected imposing a minimum [O ii ] flux of 5 × − erg s − cm − . The thick, coloured, diagonal lines are the linearfits to each SAM distribution, and their best-fit parameters are reported in Table 2. The black dot-dashed and dashed, diagonal lines arethe L [O ii ] predictions obtained from the SFR range of interest using Eqs. 15 and 16, respectively. The green, empty contours are theKewley et al. (2004) predictions obtained using Eq. 17 with SFR and cold gas metallicity as inputs. The green, solid lines are the samepredictions assuming median metallicity values in bins of SFR. . . . . l og ( L [ O II ][ e r g s − ] ) SAG inst z = 0 . . . . . l og ( L [ O II ][ e r g s − ] ) SAGE avg z = 0 . − − − M u . . . . l og ( L [ O II ][ e r g s − ] ) DEEP2 − FF − − − M g Galacticus avg z = 0 . . . . . log (age [yr]) . . . . . log (M ? [M (cid:12) ]) N ga l / A b i n / V o l u m e [ − d e x − M p c − ] Figure 12. From top to bottom and from left to right: sag , sage and galacticus z ∼ ii ] luminosities versus broad-bandmagnitudes, ages and stellar masses (contours) compared with the DEEP2-FF observations at 0 . < z < . L [O ii ] values are computed using the get emlines code with instantaneous SFR for sag and average SFR for sage and galacticus .The innermost and outermost model contours represent 68% (1 σ ) and 95% (2 σ ) of the distribution. A minimum [O ii ] flux cut of5 × − erg s − cm − has been applied to both data and model galaxies. The diagonal lines are the linear fits for strong correlationswith r > . 6, as reported in Table 2.MNRAS000 6, as reported in Table 2.MNRAS000 , 000–000 (0000) Favole et al. 2020 z=1 sag sage galacticus log ( L [O ii ] / erg s − ) = A log (SFR/M (cid:12) yr − )+ B A ± ± ± B ± ± ± σ log(SFR) σ log(L[OII]) r ( L [O ii ] / erg s − ) = A M u + B A -0.231 ± ± ± B ± ± ± σ M u σ log(L[OII]) r ( L [O ii ] / erg s − ) = A M g + B A -0.218 ± ± ± B ± ± ± σ M g σ log(L[OII]) r ( L [O ii ] / erg s − ) = A log(age/yr)+ B A — — -0.646 ± B — — 47.17 ± σ log(age) — — 0.54 σ log(L[OII]) — — 0.46 r -0.44 -0.47 -0.76log ( L [O ii ] / erg s − ) = A log( M (cid:63) /M (cid:12) )+ B A — 0.563 ± B — 35.70 ± σ log(M (cid:63) ) — 0.52 — σ log(L[OII]) — 0.45 — r Table 2. Best-fit parameters of the linear scaling relations shown in Figs. 11 and 12. All the [O ii ] luminosities here are intrinsic andcomputed using the get emlines code with input the instantaneous SFR for sage and average SFR for sage and galacticus . L [O ii ] relation and are derived from LFs estimated from 100Gaussian realisations G( σ y , µ ) with mean µ =(SFR, M u , M g ) and fixed scatter σ y = ( σ SFR , σ M u , σ M g ) from Table 2.The [O ii ] luminosity functions derived from the proxiesare strongly model dependent, with varying levels of suc-cess for each model and proxy, as can be seen in Fig. 13. In sag , the M u proxy produces a luminosity function which,in the L [O ii ] range 10 . − . erg s − , is consistent withthat derived from coupling the model with the get emlines code, while the other two proxies are lower. In sage , the M g proxy returns a LF in very good agreement with the get emlines estimate on all luminosity scales. M u givesgood agreement at L [O ii ] (cid:46) erg s − , while beyond thisvalue it slightly overestimates the number of [O ii ] emitters.The SFR proxy is consistent with the get emlines resultat L [O ii ] (cid:46) . erg s − , while at higher L [O ii ] values itoverpredicts the luminosity function by ∼ . L [O ii ] function based on the SFR proxy from galacticus is in reasonable agreement with that from cou-pling the model with get emlines , while the magnitudeproxies produce a lack of emitters on all luminosity scales ( ∼ . ∼ . erg s − , ∼ . ∼ . erg s − and ∼ . ∼ erg s − ). Fig. 12 shows that galacticus magnitudes are below those from DEEP2-FF. This discrep-ancy is likely to be the cause of the lack of [O ii ] emitters.In the right column of Fig. 13, we display the intrin-sic L [O ii ] functions colour-coded as the left panels. In sag and sage model galaxies, the effect of dust attenuation isstronger at higher luminosities, while in galacticus it ismore significant at L [O ii ] (cid:46) erg s − . We overplot, asdashed, blue lines, the [O ii ] luminosity functions obtainedby applying the Kewley et al. (2004) conversion (Eq. 17) toeach one of the model catalogues. This lies below (above) the other results in the bright end for sag and sage ( galacti-cus ) model galaxies. The relation from Kewley et al. (2004)produces very different L [O ii ] functions compared to theones obtained from the SAM model galaxies coupled withthe get emlines prescription. This result highlights thatthe dispersion in the model gas metallicities is not the onlysource of the variation seen in the luminosity function inFig. 13.In this Section, we have investigated the impact in the[O ii ] luminosity function of using the L [O ii ] proxies es-tablished above. We find the L [O ii ] proxies to be model-dependent and to overall result in either a lack or an excessof bright [O ii ] emitters. These outcomes emphasise the in-appropriateness of using simple relations to derive the [O ii ]emission from global galaxy properties. In fact, besides intro-ducing systematic uncertainties, they can also result in [O ii ]luminosity functions with very different shapes dependingwhich properties are used. We further check how the clustering of our model ELGsis sensitive to an [O ii ] luminosity selection, where L [O ii ] iscomputed either from the get emlines code, or the proxiesestablished above. We consider sag , sage and galacticus model galaxies at z ∼ L [O ii ] > . erg s − .Fig. 14 shows the ratios between the projected two-pointcorrelation functions obtained from the proxy-to- L [O ii ] re-lations and those derived from L [O ii ] computed using the get emlines code with instantaneous SFR ( sag ) or aver-age SFR ( sage and galacticus ). In Fig. 14, we also showthe clustering of the data obtained using the conversion from MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 log (L[OII] att [erg s ]) l og ( a tt [ M p c d e x ] ) SAG inst z = 0 . . (L[OII] att [erg s ]) l og ( a tt [ M p c d e x ] ) SAGE avg z = 0 . . . . . . . . . log (L[OII] att [erg s ]) l og ( a tt [ M p c d e x ] ) GAL avg z = 0 . . . 94 SFR proxyM u proxyM g proxy log (L[OII] intr [erg s ]) l og ( i n t r [ M p c d e x ] ) log (L[OII] intr [erg s ]) l og ( i n t r [ M p c d e x ] ) . . . . . . . log (L[OII] intr [erg s ]) l og ( i n t r [ M p c d e x ] ) Kewley Figure 13. Left column: From top to bottom, attenuated [O ii ] luminosity functions of the sag , sage and galacticus model galaxiesat z ∼ 1. We show as thick lines the results with L [O ii ] computed using the get emlines code described in Section 3.1 with eitherinstantaneous or average SFR and metallicity as inputs. We compare these results with the L [O ii ] functions derived from the three L [O ii ] proxies established above: SFR (solid, black line), M u (dashed, green) and M g (dotted, orange). The shaded regions represent the ± σ y scatter in the proxy- L [O ii ] linear scaling laws, which is given in Table 2. Right column: Same as left column, but here the L [O ii ] areintrinsic. The lines are colour-coded as the left panels. We show as blue dashed lines the results from the Kewley et al. (2004) conversion. Kewley et al. (2004) given in Eq. 17. For all the models, thisclustering is in excellent agreement with the data derivedfrom the get emlines L [O ii ] estimation.For the clustering we adopt the Landy & Szalay (1993)estimator and the two-point function code from Favole et al.(2016b). The shaded regions present the effect of the σ y scat-ter given in Table 2 in the proxy- L [O ii ] linear relations. Thedispersion is computed from the covariance of 100 Gaussianrealisations with mean the desired proxy and scatter σ y (seeSection 4.4.1 for further details).The clustering amplitude remains similar (within 12%)for the different L [O ii ] calculations in all the SAM consid-ered. In particular, in sag and sage galaxies, all the proxiesagree within 5% with the get emlines and Kewley et al.(2004) results on all scales. On small scales, the SFR proxyin sag declines by 5% and in sage it shows some small fluc-tuations. In Galacticus, the clustering amplitude diminishesby up to 12% (4%) on small (intermediate) scales when as-suming any proxy.The two point correlation functions at r p > h − Mpcare consistent with each other, agreeing within the 1 σ y dis-persion.We have investigated further the redshift evolution at0 . < z < . L [O ii ]thresholds of the MultiDark-Galaxies clustering ampli- tude, both based on estimates from coupling the modelswith get emlines and on the proxies above. In general,we find that increasing both redshift and the L [O ii ] thresh-old, the galaxy number density decreases returning a ten-dentially higher, more noisy clustering amplitude. The mag-nitude proxies tend to overpredict the signal, with largerdiscrepancies below 1 h − Mpc. The error bars open up onsmall scales and become tighter on larger scales, where mostmassive galaxies are located, and contribute to smooth theclustering signal.Overall, we find that the MultiDark-Galaxies clus-tering signal is model-dependent. The linear bias is mostlyunchanged, however differences are seen at small scales, be-low 1 h − Mpc. The dispersion changes between the differentproxies, with the SFR presenting the largest scatter, overall.Our ELG clustering results show that simple L [O ii ] es-timates based on a linear relation with SFR are sufficient formodelling the large scale clustering of [O ii ] emitters, even ifthey are not accurate enough to predict the [O ii ] luminosityfunction. ii ] ELG Halo Occupation Distribution In Fig. 15, we show the MultiDark-Galaxies mean halooccupation distribution (HOD) for model galaxies selected MNRAS000 MNRAS000 , 000–000 (0000) Favole et al. 2020 . . . w p r o xy p / w L [ O II ] p SAG z = 0 . SFRM u M g Kewley . . . w p r o xy p / w L [ O II ] p SAGE z = 0 . r p [h − Mpc] . . . w p r o xy p / w L [ O II ] p Galacticus z = 0 . Figure 14. Proxy-to- L [O ii ] ratios of the projected two-point cor-relation functions of, from top to bottom, sag , sage and galacti-cus model galaxies at z ∼ 1. The SAG L [O ii ] is estimated usingthe get emlines code with instantaneous SFR, while sage and galacticus using the average quantity. Galaxies have been se-lected to have L [O ii ] > . erg s − . The shaded regions repre-sent the effect of the σ y scatter in the proxy- L [O ii ] linear relationsreported in Table 2. These regions are the 1 σ uncertainties derivedfrom the co-variance of 100 Gaussian realisations with the L [O ii ]proxy considered as mean and σ y as scatter. We over plot theKewley et al. (2004) result as a dashed, blue line. . . . . . . . . log (M halo [M (cid:12) ]) − − − h N i dashed : h N cen i dot − dashed : h N sat i solid : h N tot i SAG z = 0 . . . Figure 15. Mean halo occupation distribution of the sag (salmonsolid line), sage (yellow solid line) and galacticus (blue solidline) model galaxies with L [O ii ] > . erg s − at z ∼ 1. Themodel L [O ii ] has been computed using get emlines with in-stantaneous SFR for sag galaxies and average SFR for sage and galacticus . The contribution from central galaxies is shown bydashed lines and that for satellites by dot-dashed lines. . . . . h N p r o xy i / h N L [ O II ] i SAG z = 0 . 94 SFR proxyMu proxyMg proxy . . . . h N p r o xy i / h N L [ O II ] i SAGE z = 0 . . . . . . . . . log (M halo [M (cid:12) ]) . . . . h N p r o xy i / h N L [ O II ] i Galacticus z = 0 . dashed : h N cen i dot − dashed : h N sat i solid : h N tot i Figure 16. Ratio between the HOD obtained from the L [O ii ]calculated from the proxies indicated in the legend, and L [O ii ]obtained using get emlines . From top to bottom, results areshown for the sag , sage and galacticus models. with L [O ii ] > . erg s − . Here, the model [O ii ] lumi-nosities have been calculated using the get emlines code.We highlight contributions from central and satellite modelgalaxies. The shapes of the HODs are qualitatively con-sistent among the different models, with an asymmetricGaussian for central galaxies, plus maybe a plateau, anda very shallow power law for satellite galaxies. A similarshape has been found using different models for either youngor star-forming galaxies, selected in different ways (Zhenget al. 2005; Contreras et al. 2013; Cochrane & Best 2018;Gonzalez-Perez et al. 2018) and also in measurements de-rived from observations (Geach et al. 2012; Cochrane et al.2017; Guo et al. 2018).The shape of the HOD for central star-forming galaxiesis very different from those selected with a cut in either rest-frame optical broad-band magnitudes or stellar mass, whichis close to a smooth step function that reaches unity (e.g.Berlind & Weinberg 2002; Kravtsov et al. 2004). As it can beseen in Fig. 15, the HOD of MultiDark-Galaxies central[O ii ] emitters does not necessarily reach unity, i.e. it is notguaranteed to find an [O ii ] emitter in every dark matterhalo above a given mass.We find that the SAG HODs peak at higher halo massescompared to the other two SAMs. The mean halo massespredicted by the sag , sage and galacticus model galaxiesare in agreement with the results of Favole et al. (2016a) forBOSS [O ii ] ELGs at z ∼ . ii ] ELGs at z ∼ . MultiDark-Galaxies satellite [O ii ]emitters is a very shallow power law, closer to a smoothstep function. This is similar to what has been inferred MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 for eBOSS [O ii ] emitters (Guo et al. 2018), but very dif-ferent to the findings using the galform semi-analyticalmodel (Gonzalez-Perez et al. 2018). This difference is mostlikely related to a different treatment of gas in this model, asthe distribution of satellites in dark matter haloes of differ-ent masses is very sensitive to both the modelling of feedbackand environmental processes.In Fig. 16, we display the ratios between the MultiDark-Galaxies HODs selected in L [O ii ], where theluminosity is calculated from either using the get emlines code or the proxies indicated in the legend. We find thatthe differences in the HODs from proxies and get emlines are negligible for galacticus and less than 20% for sag at M halo (cid:38) M (cid:12) , while sage shows differences above afactor 1.5 in most cases. The L [O ii ] proxies behave verysimilarly, with negligible differences between them, exceptfor the galacticus SFR proxy, which is slightly lower thanthe magnitude ones.In summary, we find different levels of agreement withthe get emlines results depending on the model consid-ered. However, the HOD remains almost unchanged whendifferent L [O ii ] proxies are assumed. In this work, we have explored how the [O ii ] luminosity canbe estimated for semi-analytic models of galaxy formationand evolution using different methods: (i) by coupling theSAMs with the get emlines code (Section 3.1) and (ii) us-ing simple relations between L [O ii ] and global propertiessuch as SFR, broad-band magnitudes and metallicity (Sec-tion 4.1).We have studied the following models from the MultiDark-Galaxies products (Knebe et al. 2018): sag (Cora et al. 2018), sage (Croton et al. 2016) and galacti-cus (Benson 2012). All these models are run on the MDPL2cosmological simulation (Klypin et al. 2016). They were cal-ibrated to a number of observations within 0 < z < 2, andthey produce SFR and stellar mass functions that evolvesimilarly to what is observed in this redshift range.Throughout this study, we have compared our modelresults with different observational data sets, includingDEEP2-FF galaxies with absolute magnitudes (see Sec-tion 2.2).The get emlines code to calculate nebular emissionlines is publicly available and ideally uses instantaneous SFRas input. However, usually SAMs only output SFRs that areaveraged over long time intervals, corresponding to the out-puts of the underlying dark matter simulation. From theSAMs under study, only sag provides instantaneous SFRs.We have coupled the get emlines code with the sag modelusing both instantaneous and average SFRs to study theimpact that this choice has on the L [O ii ] calculation inpost-processing. Assuming as input for the get emlines code either the instantaneous or the average SFR, we seea variation below 5% for the dust attenuated [O ii ] lumi-nosity functions in the range 10 − . erg s − , and inthe range 10 − erg s − for the intrinsic [O ii ] lumi-nosity functions. These ranges correspond to model ELGswith 1 < SFR (yr − M (cid:12) ) < . . At higher and lower SFRs,there is a larger discrepancy, < get emlines is a good approach when studying averagegalaxy populations.The luminosity functions of the MultiDark-Galaxies with L [O ii ] computed using the get emlines algorithm arein good agreement with the DEEP2 and VVDS observationsover the redshift range 0 . < z < . 2. The [O ii ] luminosity,SFR and stellar mass functions of the SAMs all consistentlypredict a smaller number of massive, star-forming emittersas the redshift increases.We have also investigated the viability of obtaining L [O ii ] from simple relations with global galactic proper-ties that are usually outputted by galaxy formation mod-els. For this purpose, we use observationally derived rela-tions (Kewley et al. 2004) and linear relations derived foreach model. In particular, we explore the L [O ii ] derived us-ing the get emlines code as a function of SFR, broad-bandmagnitudes, age and stellar mass. The SFR, both instanta-neous and average, is the physical quantity that, by con-struction, is most correlated with the [O ii ] luminosity (withcorrelation coefficients r (cid:62) . 80 for all the SAMs). Such atight correlation is well described by a linear scaling law withan associated scatter σ log(SFR) that varies with L [O ii ] (seeTable 2). Other valuable proxies to derive L [O ii ] are theobserved-frame u and g broad-band magnitudes, M u and M g , which trace the rest-frame UV emission in our redshiftrange of interest.We test how feasible it is to use these correlationsas proxies for L [O ii ] by studying the evolution of the de-rived [O ii ] luminosity functions, mean halo occupation dis-tribution (HOD) and the galaxy clustering signal in L [O ii ]thresholds.The different methods explored to calculate L [O ii ] re-sult in a range of [O ii ] luminosity functions. Taking intoaccount the effect of the scatter in the SAG L [O ii ]–proxy re-lations, the luminosity functions from the proxies (includingthe Kewley et al. (2004) relation from Eq. 17) are in reason-able agreement with the direct get emlines estimates. Thedifferences are larger for the relations derived from M g andSFR in sag at all luminosities, for SFR in sage at L [O ii ] > erg s − , and for the magnitude proxies in galacti-cus . At high luminosities, L [O ii ] derived with most linearproxies result in a lack of bright emitters that increases withluminosity, but remains approximately constant with red-shift. The Kewley et al. (2004) relation (Eq. 17) results in alower number of bright [O ii ] emitters compared to all theother methods to obtain L [O ii ] in sag and sage , and in ahigher number in galacticus .We find a large variation between the derived [O ii ] lu-minosity functions among both the SAMs and the methodsused to obtain L [O ii ]. Thus, it is important to highlightthat, despite the model SFR density evolution being in rea-sonable agreement with observations, simple relations basedon global galaxy properties are not robust estimators for L [O ii ].We further test the use of simple relations to obtain L [O ii ] for SAMs by measuring the galaxy two-point auto-correlation function for [O ii ] emitters. We compare the clus-tering measured from the [O ii ] proxies with direct predic-tions from the SAMs coupled with the get emlines codeand with the Kewley et al. (2004) relationship. The resultsvary from model to model and the largest fluctuations areseen below 1 h − Mpc. However, if we account for the effectof the scatter in the proxy- L [O ii ] relation, the discrepancies MNRAS000 80 for all the SAMs). Such atight correlation is well described by a linear scaling law withan associated scatter σ log(SFR) that varies with L [O ii ] (seeTable 2). Other valuable proxies to derive L [O ii ] are theobserved-frame u and g broad-band magnitudes, M u and M g , which trace the rest-frame UV emission in our redshiftrange of interest.We test how feasible it is to use these correlationsas proxies for L [O ii ] by studying the evolution of the de-rived [O ii ] luminosity functions, mean halo occupation dis-tribution (HOD) and the galaxy clustering signal in L [O ii ]thresholds.The different methods explored to calculate L [O ii ] re-sult in a range of [O ii ] luminosity functions. Taking intoaccount the effect of the scatter in the SAG L [O ii ]–proxy re-lations, the luminosity functions from the proxies (includingthe Kewley et al. (2004) relation from Eq. 17) are in reason-able agreement with the direct get emlines estimates. Thedifferences are larger for the relations derived from M g andSFR in sag at all luminosities, for SFR in sage at L [O ii ] > erg s − , and for the magnitude proxies in galacti-cus . At high luminosities, L [O ii ] derived with most linearproxies result in a lack of bright emitters that increases withluminosity, but remains approximately constant with red-shift. The Kewley et al. (2004) relation (Eq. 17) results in alower number of bright [O ii ] emitters compared to all theother methods to obtain L [O ii ] in sag and sage , and in ahigher number in galacticus .We find a large variation between the derived [O ii ] lu-minosity functions among both the SAMs and the methodsused to obtain L [O ii ]. Thus, it is important to highlightthat, despite the model SFR density evolution being in rea-sonable agreement with observations, simple relations basedon global galaxy properties are not robust estimators for L [O ii ].We further test the use of simple relations to obtain L [O ii ] for SAMs by measuring the galaxy two-point auto-correlation function for [O ii ] emitters. We compare the clus-tering measured from the [O ii ] proxies with direct predic-tions from the SAMs coupled with the get emlines codeand with the Kewley et al. (2004) relationship. The resultsvary from model to model and the largest fluctuations areseen below 1 h − Mpc. However, if we account for the effectof the scatter in the proxy- L [O ii ] relation, the discrepancies MNRAS000 , 000–000 (0000) Favole et al. 2020 reconcile with direct luminosity predictions. The large scalebias remains similar for all the models.There is no direct correspondence between a proxy re-sulting in a good luminosity function and providing a similaroutcome for the clustering.We also test how the mean HOD of [O ii ] emitterschanges when assuming different proxies compared to the get emlines code in the L [O ii ] calculation of our SAMs.We find that the shape of the HOD is consistent with thatexpected for a star-forming population of galaxies. Quan-titatively, the HOD is strongly model-dependent, and wefind different levels of agreement between the proxies andthe get emlines results, in particular at M halo (cid:38) M (cid:12) .However, the distributions remain substantially unchangedfrom one proxy to another for all the models under study.Our results show that ELGs are different from SFR-selected samples and that the L [O ii ] estimation needs morecomplex modelling than assuming a linear relation withSFR. Simple L [O ii ] estimates are not accurate enough topredict direct statistics of L [O ii ], as the luminosity func-tion, but they are sufficient for modelling the large scaleclustering of [O ii ] emitters.New-generation optical and infra-red surveys will pro-vide enormous data sets with unprecedented spectroscopicprecision and imaging quality. These observations, togetherwith models of galaxy formation and evolution, will enableus to reach a complete and consistent understanding of boththe Universe large scale structure, and the galaxy formationand evolution processes within dark matter haloes. In thiscontext, simple derivations of L [O ii ] might be adequate forthe clustering above 1 h − Mpc, although at least two simpleapproximations might be needed to determine the uncer-tainties. ACKNOWLEDGMENTS GF and VGP acknowledge support from the University ofPortsmouth through the Dennis Sciama Fellowship award.VGP acknowledges support from the European ResearchCouncil grant No. 769130. DS is funded by the Spanish Min-istry of Economy and Competitiveness (MINECO) underthe 2014 Severo Ochoa Predoctoral Training Programme.DS also wants to thank the Mam´ua Caf´e Bar -team fortheir kind (g)astronomical support. DS and FP acknowl-edge funding support from the MINECO grant AYA2014-60641-C2-1-P. AO acknowledges support from the Span-ish Ministerio de Economia y Competitividad (MINECO)project No. AYA2015-66211-C2-P-2, and funding from theEuropean Union Horizon 2020 research and innovationprogramme under grant agreement No. 734374. SAC ac-knowledges funding from Consejo Nacional de Investiga-ciones Cient´ıficas y T´ecnicas (CONICET, PIP-0387), Agen-cia Nacional de Promoci´on Cient´ıfica y Tecnol´ogica (AN-PCyT, PICT-2013-0317), and Universidad Nacional de LaPlata (11-G124 and 11-G150), Argentina. CVM acknowl-edges CONICET, Argentina, for the supporting fellowship.AK is supported by the MINECO and the Fondo Europeode Desarrollo Regional (FEDER, UE) in Spain throughgrant AYA2015-63810-P as well as by the MICIU/FEDERthrough grant number PGC2018-094975-C21. He furtheracknowledges support from the Spanish Red ConsoliderMultiDark FPA2017-90566-REDC and thanks ChristopherCross for sailing. 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L., Zehavi I., 2007, ApJ, 667, 760 APPENDIX A: SAG MODEL GALAXIESSELECTED FROM DEEP2-FF SPLINE We study the properties of a subset of SAG model galaxiesselected to reproduce the L [O ii ] distribution of the DEEP2- FF data approximated by a spline fit in Fig. 4. We com-pare these model properties with the observational ones fromDEEP2- FF .Fig. A1 displays the SAG non-attenuated [O ii ] lumi-nosities computed from average and instantaneous SFRs asa function of SFR. The bimodality observed in Fig. 5, wherethe model galaxies are selected by cutting at SFR > ( M (cid:63) / M (cid:12) ) > . 87, has now disappeared, but the dis- y= A x+ B A B σ y r y=log ( L [O ii ])x=log (SFR avg ) 0.741 ± ± (SFR inst ) 0.574 ± ± M u x=log (SFR avg ) -2.021 ± ± (SFR inst ) -2.084 ± ± M g x=log (SFR avg ) -2.006 ± ± (SFR inst ) -2.032 ± ± (M (cid:63) )x=log (SFR avg ) 0.859 ± ± (SFR inst ) 0.846 ± ± Table A1. Best-fit parameters of the linear scaling relationsfound for sag model galaxies at z = 1 and shown in Fig. A2. Theparameter r is the correlation coefficient and σ y is the scatter inthe y -axis. SAG galaxies have been selected in L [O ii ] randomlydrawn from the DEEP2-FF spline fit shown in Fig.4. log (SFR [M (cid:12) yr − ]) − − − M u log (SFR [M (cid:12) yr − ]) − − − M g log (SFR avg [M (cid:12) yr − ]) . . . l og ( ag e [ y r ] ) − . . . . . . log (SFR [M (cid:12) yr − ]) . . . . . l og ( M ? [ M (cid:12) ] ) DEEP2 0 . < z < . . . . . . . N ga l / A b i n / V o l u m e [ − d e x − M p c − ] Figure A2. From top to bottom: intrinsic magnitudes, ages andstellar masses as a function of star formation rate for sag modelgalaxies at z ∼ . < z < . − Mpc − ]. The dashed, salmon (solid, purple) con-tours represent the average (instantaneous) SFRs. The innermost(outermost) contours encompass 68% (95%) of the distributions.The diagonal lines are the linear fits showing the significant cor-relations, whose coefficients are reported in Table 2, together withthe best-fit parameters. MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 crepancy between the two sets of contours is larger, withthe instantaneous correlation much shallower than the av-erage one. At SFR (cid:38) yr − M (cid:12) , the instantaneous SFRreturns higher L [O ii ] values compared to the average SFR.Instead, at SFR (cid:46) yr − M (cid:12) , the average contours reachfainter luminosities. Compared to the sag results based onsimple SFR and stellar mass cuts (see Fig. 5), here bothsets of contours span a higher range of L [O ii ] and SFR val-ues. The L [O ii ]-SFR correlation based on average (instan-taneous) SFR is stronger (less strong) and with a steeper(shallower) slope compared to that for galaxies selected withsimple cuts (compare Tabs. 1 and A1), while the scatter isthe same.The DEEP2-FF observations in Fig. A1 seem to span anarrower range in SFR and to go fainter in L [O ii ] com-pared to the model galaxy contours. However, we highlightthat the low-luminosity observational tail has a very low-density of emitters ( ∼ − in Fig. A1).In Fig. A2, from top to bottom, we display the intrin-sic u - and g -band absolute magnitudes, the age and stellarmass of the SAG model galaxies selected from the DEEP2-FF spline fit as a function of the average and instanta-neous SFRs. Compared to the results based on simple cutsat SFR > − M (cid:12) and M (cid:63) > . M (cid:12) (see Fig. 8), herethe correlations between SFR and magnitudes are steeperand M u shows a wider scatter in the y -axis. On the con-trary, the correlation between SFR and stellar mass is shal-lower for sag galaxies drawn from the DEEP2-FF splinefit and with less scatter in the y -axis. The specific valuesof the correlation parameters and coefficients are reportedin Table A1. Overall, sag galaxies selected from the splinefit reach brighter values of u - and g -band magnitudes com-pared to their counterparts based on simple SFR and stellarmass cuts (see Fig. 8), which also extend down to faintermagnitudes and smaller stellar masses. As already noticedin Fig. 8, model galaxies have lower ages and stellar massesand they extend into larger SFR values, compared to theDEEP2-FF sample. APPENDIX B: EVOLUTION OF L[O ii] FROMINSTANTANEOUS AND AVERAGE SFR We investigate further the redshift evolution of the smalldiscrepancy generated in L [O ii ] by assuming average insteadof instantaneous SFR as input for the get emlines code.In Section 3.3, we have studied what happens at z ∼ 1, nowwe look over the redshift range 0 . < z < . ii ] luminosity func-tions obtained from average and instantaneous SFR at dif-ferent redshifts. We have explored the entire range 0 . 2, we observe a larger discrepancy in both ratios inthe faint region due to the larger effect of incompleteness. − . − . . . l og ( Φ i n s t / Φ a v g ) z = 0 . intrinsicattenuated . . . . . . . (L[OII] [erg s − ]) − . − . . . l og ( Φ i n s t / Φ a v g ) z = 1 . intrinsicattenuated Figure B1. Ratios between the SAG [O ii ] luminosity functions(thick, blue lines: intrinsic LFs; thin, green: attenuated LFs) atdifferent redshifts computed from average and instantaneous SFRusing the method presented in 3.1. The yellow, shaded areas rep-resent the 5% confidence region. APPENDIX C: GLOBAL PROPERTIES OF MultiDark-Galaxies We compare pair properties in MultiDark-Galaxies andDEEP2-FF observations to better understand their mutualcorrelations. We then fit these dependences using linear scal-ing relations. Fig. C1 displays, from top to bottom, the cor-relations between broad-band magnitudes, age and stellarmass as a function of SFR and stellar mass of the DEEP2-FF galaxies (grey, shaded squares, colour-coded according totheir galaxy number density normalized by the 2D bin area)compared to the MultiDark-Galaxies (contours indicat-ing the 68% and 95% of each distribution). Data and modelsoverlap covering the brighter, more massive and more star-forming region of the parameter space. In particular, the MultiDark-Galaxies only cover the SFR range above theknee shown in Fig. 2.For such a small observational sample, it is difficult toestablish and fit clear correlations among these quantitiesand between these quantities and L [O ii ] (see also Fig. 12).In order to do this properly, one should account for all theDEEP2-FF incompleteness effects, which goes beyond thescope of our work. Here we show the comparison between theDEEP2-FF emitters and the MultiDark-Galaxies onlyto verify that our models cover the parameter space of theobservational data set.From the model point of view, we do find clear corre-lation among most of the physical quantities presented inFig. C1. Each set of panels shows the results for one model:from top to bottom we display sag , sage and galacti-cus model galaxies. The relevant correlations ( r (cid:62) . 6) arerepresented as linear fits and the optimal parameters arereported in Table C1, together with their correlation coeffi-cient ( r ) and the associated scatter in the y -axis ( σ y ).As expected, tight correlation is observed between thestar formation rate and the broad-band u and g magnitudesthat trace the rest-frame UV emission of a galaxy (see alsoSection 4.2). Tight correlation is observed also between themagnitudes and the stellar mass in all our model galaxies,except for galacticus . Overall, the DEEP2-FF observa-tions and the MultiDark-Galaxies show a good overlapin the brighter, more star-forming and massive portion of MNRAS000 MNRAS000 , 000–000 (0000) Favole et al. 2020 z=1 SAG SAGE Galacticus M u = A log (SFR/(M (cid:12) yr − ))+ B A -1.934 ± ± ± B -18.06 ± ± ± σ log(SFR) σ M u r M g = A log (SFR/(M (cid:12) yr − ))+ B A -2.029 ± ± ± B -18.98 ± ± ± σ log(SFR) σ M g r (age/yr) = A log (SFR/(M (cid:12) yr − ))+ B A — — -0.869 ± B — — 9.58 ± σ log(SFR) — — 0.48 σ age — — 0.54 r -0.21 -0.34 -0.77log (M (cid:63) /M (cid:12) ) = A log (SFR/(M (cid:12) yr − ))+ B A ± ± B ± ± σ log(SFR) σ log(M (cid:63) ) r M u = A log (M (cid:63) /M (cid:12) )+ B A -1.779 ± ± B -1.75 ± ± σ log(M (cid:63) ) σ M u r M g = A log (M (cid:63) /M (cid:12) )+ B A -1.941 ± ± B -1.17 ± ± σ log(M (cid:63) ) σ M g r Table C1. Best-fit parameters of the linear scaling relations found in MultiDark-Galaxies at z ∼ r is the correlation coefficient and σ y is the scatter in the y -axis. The SFR values are instantaneous for sag and averagefor sage and galacticus . We highlight that we do not quantify the correlation in the DEEP2-FF sample, since this calculation wouldrequire accounting for all the observational incompleteness effects, which goes beyond the aim of this work. any parameter space. All the model galaxies then extendfurther down in SFR, stellar mass and magnitudes.Age does not correlate with SFR neither in the obser-vations, nor in SAG and SAGE mocks. In galacticus , weobserve an anti-correlation between age and SFR, mean-ing that older galaxies are more star-forming, as expected.Age does seem to correlate with stellar mass in DEEP2-FF,however this feature is not reproduced by any of our modelgalaxies. DEEP2-FF galaxies show a bimodal distribution inage and stellar mass, with an older, less star-forming, verymassive population ( age (cid:38) . yr; M (cid:63) (cid:38) . M (cid:12) ) anda younger, more star-forming distribution with less massivegalaxies. None of the model galaxies seem to reproduce thisbimodality. sag and sage stellar masses are tightly correlated withtheir SFRs, but no dependence is observed in galacticus .While the DEEP2-FF quenched population is too sparse toidentify any dependence in the stellar mass–SFR plane, thestar-forming selection might show some correlation in thehigher-mass end of the distribution. However, as alreadymentioned above, in order to correctly quantify this correla-tion, we should take into account the incompleteness effectsin the data set, but this calculation goes beyond the aimof our analysis. We do not to show the dependence of theabove quantities on metallicity since they do not correlatesignificantly in any of the model galaxies considered. MNRAS , 000–000 (0000) O ii ] emitters in MultiDark-Galaxies and DEEP2 log (SFR [M (cid:12) yr − ]) − − − M u log (SFR [M (cid:12) yr − ]) − − − M g log (SFR [M (cid:12) yr − ]) . . . . l og ( ag e [ y r ] ) log (M ? [M (cid:12) ]) − . . . . . log (SFR [M (cid:12) yr − ]) . . . . l og ( M ? [ M (cid:12) ] ) . . . . log (M ? [M (cid:12) ]) DEEP2 − FFSAG inst z = 0 . N ga l / A b i n / V o l u m e [ − d e x − M p c − ] log (SFR[M (cid:12) yr − ]) − − − M u log (SFR[M (cid:12) yr − ]) − − − M g log (SFR[M (cid:12) yr − ]) . . . . l og ( ag e [ y r ] ) log (M ? [M (cid:12) ]) − . . . . . log (SFR[M (cid:12) yr − ]) . . . . l og ( M ? [ M (cid:12) ] ) . . . . log (M ? [M (cid:12) ]) DEEP2 − FFSAGE inst z = 0 . N ga l / A b i n / V o l u m e [ − d e x − M p c − ] log (SFR[M (cid:12) yr − ]) − − − M u log (SFR[M (cid:12) yr − ]) − − − M g log (SFR[M (cid:12) yr − ]) . . . . l og ( ag e [ y r ] ) log (M ? [M (cid:12) ]) − . . . . . log (SFR[M (cid:12) yr − ]) . . . . l og ( M ? [ M (cid:12) ] ) . . . . log (M ? [M (cid:12) ]) DEEP2 − FFGalacticus avg z = 0 . N ga l / A b i n / V o l u m e [ − d e x − M p c − ] Figure C1. Comparison of pairs of properties for MultiDark-Galaxies at z = 1 (contours) and DEEP2–FF observations at0 . < z < . sag , sage and galacticus results. A mini-mum [O ii ] flux cut of 5 × − erg s − cm − has been appliedto both data and model galaxies. In each set of panels, from topto bottom, we compare broad-band u and g absolute magnitudes,age and stellar mass as a function of, from left to right, averageSFR and stellar mass. The model contours, from inner to outer,represent 68% and 95% of the distributions. The diagonal linesare the linear fits showing the significant correlations, whose co-efficients are given in Table 2.MNRAS000