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Mon. Not. R. Astron. Soc.000, 1–18 (2005) Printed 25 November 2018 (MN LATEX style file v2.2)

Semi-empirical analysis of Sloan Digital Sky Survey galaxies:II. The bimodality of the galaxy population revisited

Abılio Mateus1⋆, Laerte Sodre Jr.1, Roberto Cid Fernandes2, Grazyna Stasinska3,William Schoenell2, Jean M. Gomes21Departamento de Astronomia, IAG-USP, Rua do Matao 1226, 05508-090, Sao Paulo, Brazil2Depto. de Fısica - CFM - Universidade Federal de Santa Catarina, Florianopolis, SC, Brazil3LUTH, Observatoire de Meudon, 92195 Meudon Cedex, France

25 November 2018

ABSTRACTWe revisit the bimodal distribution of the galaxy population commonly seen in the localuniverse. Here we address the bimodality observed in galaxyproperties in terms of spec-tral synthesis products, such as mean stellar ages and stellar masses, derived from the ap-plication of this powerful method to a volume-limited sample, with magnitude limit cutoffM(r) = −20.5, containing about 50 thousand luminous galaxies from the SDSS Data Re-lease 2. In addition, galaxies are classified according to their emission line properties in threedistinct spectral classes: star-forming galaxies, with young stellar populations; passive galax-ies, dominated by old stellar populations; and, hosts of active nuclei, which comprise a mixof young and old stellar populations. We show that the extremes of the distribution of somegalaxy properties, essentially galaxy colours, 4000A break index, and mean stellar ages, areassociated to star-forming galaxies at one side, and passive galaxies at another. We find thatthe mean light-weighted stellar age of galaxies is the direct responsible for the bimodality seenin the galaxy population. The stellar mass, in this view, hasan additional role since most ofthe star-forming galaxies present in the local universe arelow-mass galaxies. Our results alsogive support to the existence of a ‘downsizing’ in galaxy formation, where massive galaxiesseen nowadays have stellar populations formed at early times.

Key words: galaxies: evolution — galaxies: formation — galaxies: fundamental parameters— galaxies: stellar content — stars: formation

1 INTRODUCTION

It is usual to group galaxies in distinct types or classes, trying tofind their general properties and to understand their differential for-mation and evolution. In the last few years, this galaxy ‘taxonomy’has been interestingly simplified. As a by-product of recentredshiftsurveys, the study of galaxy populations has quantitatively revealedthe existence of a bimodal distribution in some fundamentalgalaxyproperties, found both in photometric and spectroscopic data. Thisbimodality of galaxy populations, despite its apparent simplicity,figures out as an important key in our whole comprehension of theprocesses which drive galaxy evolution.

Perhaps the most representative bimodal distribution seeningalaxy properties is that found in galaxy colours. Since photometricparameters are easily measured, their bimodal behaviour has beenstudied for galaxies in the local universe by using both the SloanDigital Sky Survey (SDSS) and the Two Degree Field Galaxy Red-shift Survey (2dFGRS) data (Strateva et al. 2001; Hogg et al.2002;Blanton et al. 2003a; Wild et al. 2005), and, for distant galaxies to

⋆ E-mail: abilio@astro.iag.usp.br

z ∼ 1, in the COMBO-17 photometric redshift survey (Bell et al.2004) and in the DEEP galaxy redshift survey (Weiner et al. 2005).This behaviour also persists for even higher redshifts (z ∼ 1.4Wiegert, de Mello & Horellou 2004). As galaxy colours reflectthestar formation history of galaxies, a bimodality in their distributionssuggests that they have evolved through two different majorpaths.

Amongst local galaxies, Kauffmann et al. (2003b) have anal-ysed the star formation history and its dependence on stellar massfor a large sample of SDSS galaxies. They have found a transitionin the physical properties of galaxies at a stellar massM⋆ ∼ 3 ×1010 M⊙, which results in a bimodality between low-mass galax-ies with low concentration indices typical of discs and young stel-lar populations, and massive ones, with high concentrationindicesand old stellar populations. The connection between this bimodaldistribution and that observed in galaxy colours has been done,at least partially, by Baldry et al. (2004) in a work on the colour-magnitude diagram for a sample of SDSS galaxies. These authorshave demonstrated that the transition in galaxy propertiesoccursaround(1.5 − 2.2) × 1010 M⊙ for the red sequence and around(2− 3)× 1010 M⊙ for the blue sequence, close to the value ofM⋆

found by Kauffmann et al. (2003b) using spectroscopic data.This

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2 Mateus et al.

transition stellar mass is also associated to a shift in galaxy gas massfractions, as pointed out by Kannappan (2004). Another impor-tant characteristic of bimodality in galaxy colours is its dependenceon environment. This issue was addressed by Balogh et al. (2004)who have complemented the analysis by Baldry et al. (2004) toac-count for, besides luminosity dependences, the environmental de-pendence of the red and blue galaxy fractions.

A bimodal behaviour is also seen in the star formation prop-erties of galaxies. From the 2dFGRS data, Madgwick et al. (2002)have derived a spectral parameterη via a principal component anal-ysis method that is strongly correlated with the star formation rate(SFR) of a galaxy. A bimodal distribution is clearly seen in thisparameter (Wild et al. 2005), with a characteristic value that splitsgalaxies in two classes according to their star formation activity.Brinchmann et al. (2004) also find a similar distribution, showingthat galaxies are from two kinds: one composed by concentratedgalaxies, with low specific SFRs, and the other composed by lessconcentrated ones with high specific SFRs.

In the first paper of this series on semi-empirical analysis ofgalaxies (Cid Fernandes et al. 2005a, hereafter SEAGal I) wehavepresented a spectral synthesis method able to derive the main phys-ical properties of galaxies from their spectral data only. The reli-ability of this approach was investigated by three different ways:simulations, comparison with other works, and an empiricalanal-ysis of the consistency of results for a SDSS galaxy sample. Wefind that spectral synthesis provides reliable physical parameters,mainly stellar ages and stellar metallicities. Stellar masses, velocitydispersions and extinction are also obtained through this method.The analysis of residual spectra (observed minus synthesised) alsoprovides useful information on the overall properties of emissionline regions, like the nebular extinction and metallicities.

The joint spectroscopic and photometric data provided bySDSS, in addition to the arsenal of physical parameters obtainedby spectral synthesis, turns out as a great opportunity to studygalaxy populations by analysing both spectral and structural clas-sifications. In this work, we will produce a spectral classification,initially based on the emission line properties of galaxiesand thepresence of nuclear activity, and subsequently we will comparethis classification with a structural (morphological) one,which usesSDSS photometric information to separate galaxies betweenearlyand late-types. The bimodality of the galaxy populations will beanalysed here with the starting point placed in these classifications.

This paper is organised as follows. Section 2 presents anoverview of our synthesis method, detailed in SEAGal I, focus-ing on the main outputs resulting from its application to a volumelimited sample of SDSS galaxies. Section 3 describes the classifi-cation scheme used along this work, based on a diagnostic diagramof emission line ratios. Section 4 discusses the bimodal characterof the galaxy population, with emphasis in the emission lineprop-erties of galaxies. In Section 5 we discuss the main findings of thiswork. Finally, Section 6 summarises our results.

2 THE SPECTRAL SYNTHESIS METHOD

In this section we present an overview of the spectral synthesismethod used in this work and its main output. We also present thevolume limited sample of SDSS galaxies analysed here, as wellas our procedure for measuring emission line intensities from theresidual spectra.

2.1 The method

In this work we use the STARLIGHT code to derive stellar popu-lation properties directly from the galaxy spectra (continuum andabsorption lines only). STARLIGHT is built upon computationaltechniques originally developed for empirical populationsynthesiswith additional ingredients from evolutionary synthesis models. Inbrief, we fit an observed spectrum with a combination ofN⋆ SimpleStellar Populations (SSP) from the evolutionary synthesismodelsof Bruzual & Charlot (2003) (hereafter BC03). We use the “Padova1994” tracks recommended by BC03 and a Chabrier (2003) IMFbetween 0.1 and 100 M⊙. (Experiments with a Salpeter IMF withthe same mass limits were also performed, yielding nearly identi-cal results except for stellar masses, which are 1.5 times larger thanfor a Chabrier IMF.) Extinction is modelled as due to foregrounddust, with the reddening law of Cardelli, Clayton & Mathis (1989)with RV = 3.1, and parameterised by the V-band extinctionAV .Line of sight stellar motions are accounted for using a Gaussiandistribution. The fits are carried out with a simulated annealingplus Metropolis scheme, with regions around emission linesandbad pixels excluded from the analysis (see SEAGal I for details).

Since SEAGal I, STARLIGHT has undergone a major revi-sion. The main technical change is that whereas in SEAGal I weworked with a single Markov chain all the way from an initialguess to the final model, we now run several parallel chains. Ateach level of the annealing scheme (i.e., for each “temperature”)we run the chains until they satisfy a convergence criterionsimilarto that proposed by Gelman & Rubin (1992). Adaptive step sizesare employed to improve efficiency. These and other details will bedescribed in a future communication accompanying a public ver-sion of STARLIGHT.

A second and more important difference with respect to SEA-Gal I is that we now use a larger base of SSPs, comprisingN⋆ =150 elements of 25 different ages between 1 Myr and 18 Gyr, and6 metallicities:Z = 0.005, 0.02, 0.2, 0.4, 1 and 2.5Z⊙. The agegrid was chosen by exploring an implicit assumption in spectralsynthesis with a discrete base, namely, that the spectrum ofa pop-ulation with aget betweentj and tj+1 is well represented by alinear combination of thej andj + 1 SSPs. We started from theset of 15 ages in the SEAGal I base, and then fitted each of 221BC03 SSP spectra for the sameZ with the two components whichbracket its age. This allows us to identify SSPs whose spectra arepoorly interpolated by combinations of the closest elements in thebase, and thus should be included in a finer base. Following thisprocedure (graphically illustrated in Leao 2006), we arrived at a setof 25 ages. The difference between original and interpolated SSPspectra with this base is better than 1 per cent on average, exceed-ing 5 per cent only for a fewt < 107 yr models atZ 6 0.2Z⊙,corresponding to short-lived phases when massive red-supergiantsshow up.

The refinement in the age grid is not as relevant as the in-clusion of lower metallicity components in the base. Whereas theN⋆ = 45 base in SEAGal I comprised onlyZ > 0.2Z⊙, we nowallow for Z = 0.005 and0.02Z⊙. These very metal poor SSPsare bluer than those ofZ > 0.2Z⊙ SSPs, particularly at old ages.Such lowZ populations, if present in a galaxy but ignored in thefits, may lead to an underestimation of ages, as the code triestocompensate for their lack with younger components of higherZdue to the age-Z degeneracy. To illustrate this point, Fig 1 showsthe predicted evolution of the 4000A break indexDn(4000) (Sec-tion 4.1) and its observed distribution for the sample described be-low. The peak atDn(4000) ∼ 1.3 matches well the value reached

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Bimodality of the galaxy population 3

Figure 1. (a) Observed distribution of the 4000A break index for our vol-ume limited sample. (b) Evolution of Dn(4000) for SSPs of 6 differentmetallicities. From right to left:Z = 2.5, 1, 0.4, 0.2, 0.02 and 0.005Z⊙. (c)Relation between their Dn(4000) andz-band mass-to-light ratio for SSPsof 6 different metallicities. From right to left:Z = 2.5, 1, 0.4, 0.2, 0.02and 0.005Z⊙. The dotted lines mark the location of the lower peak in theobserved Dn(4000) distribution.

by Z 6 0.02Z⊙ SSPs of ages from 1 Gyr to over 10 Gyr. To re-produce this value withZ > 0.2Z⊙ one must either accept thatthese galaxies formed less than∼ 1 Gyr ago or else invoke morecontinuous star-formation regimes (exponentially decaying, multi-ple bursts or other variants). Whereas the latter is in fact alikelyexplanation for galaxies with lowDn(4000), our point here is thatby excluding lowZ components from the base one would be inpractiseimposingthis interpretationa priori. Besides this “math-ematical” argument, the mere fact that very metal poor starsexistprovides physical motivation to include them in the base. Havingsaid that, one must also recall that the synthetic SEDs of such pop-ulations are affected by a number of caveats, as discussed byBC03.

One must also realise that the inclusion of 0.02 and 0.005Z⊙

SSPs is bound to have an effect on the stellar masses. This is illus-trated in the top panel of Fig 1, which shows that the mass-to-lightratio in thez-band of∼ 10 Gyr, 0.02 and 0.005Z⊙ SSPs is up toone order of magnitude larger than forZ > 0.2Z⊙ models of simi-larDn(4000). To monitor the magnitude of this difference we havealso fit the data with a base excluding the 0.02 and 0.005Z⊙ SSPs.Throughout the paper we will mention results obtained with thisalternative base whenever they differ substantially from the onesobtained with the full set of metallicities. We anticipate that suchchanges are mostly quantitative; they do not affect the overall qual-itative conclusions of our analysis.

Another difference with respect to the base in SEAGal I is thatwe now allow for SSPs as old as 18 Gyr, which is formally incon-sistent with the∼ 13.5 Gyr old Universe implied by our adoptedcosmology,H0 = 70 km s−1 Mpc−1, ΩM = 0.3 andΩΛ = 0.7.We relax the cosmological limit merely to avoid the crowdingof

Parameter S/N atλ = 4020 A5 10 15 20 30

logM⋆ 0.11 0.08 0.06 0.05 0.04〈log t⋆〉L 0.14 0.08 0.06 0.05 0.04〈log t⋆〉M 0.20 0.14 0.11 0.10 0.08log〈Z⋆〉L 0.15 0.09 0.08 0.06 0.05log〈Z⋆〉M 0.18 0.13 0.11 0.09 0.08A⋆

V0.09 0.05 0.03 0.03 0.02

Table 1. Summary of parameter uncertainties. Each row corresponds to aparameter constructed by combining the parameters given bythe synthe-sis. The different columns list the rms difference between output and inputvalues of the corresponding quantity, as obtained from simulations with dif-ferent signal-to-noise ratios (see SEAGal I for details). The units are dex forlogarithmic quantities and mag forA⋆

V .

mean stellar ages at the upper age limit (visible, for instance, inSEAGal I’s Fig. 13b). Given the uncertainties in stellar evolution,cosmology, and the spectrophotometry measurements, we do notregard this inconsistency as critical, and, in any case, we stress thatthis choice has no consequence for the main conclusion of this pa-per.

The result of this procedure is a list of parameters for eachgalaxy. As explained in SEAGal I, instead of working with thefull population vector, whose individual components are hopelesslyplagued by mathematical and astrophysical degeneracies, we de-scribe the results of the spectral synthesis in terms of a small num-ber of robust parameters. The most important for the discussionin this paper are: a) the dust-corrected present stellar mass insidethe fibre; the total stellar mass (M⋆) is computeda posterioriaftercorrecting for the fraction of luminosity outside the fibre assumingthat the galaxy mass-to-light ratio does not depend on the radius(but see Appendix A); b) the mean stellar age, weighted either bylight, 〈log t⋆〉L, or by mass〈log t⋆〉M ; c) the mean stellar metal-licity, light and mass-weighted,log〈Z⋆〉L and log〈Z⋆〉M , respec-tively; and d) the V-band stellar extinctionA⋆

V . A summary of theuncertainties in the main parameters that will be used in this workis shown in Table 1. These uncertainties were determined in SEA-Gal I through the difference between output and input valuesof thecorresponding quantity, as obtained from simulations withdifferentsignal-to-noise ratios. In addition to this list of parameters, by sub-tracting the synthesised spectrum from the observed one, weget a“pure-emission” residual spectrum, which is useful for analysis ofthe galaxy emission lines. These are discussed next.

2.2 Application: SDSS data

We apply our synthesis method to a large sample of SDSS galaxiesaiming to investigate the properties and the origin of the bimodalgalaxy distribution. The SDSS spectra cover a wavelength rangeof 3800–9200A, have a mean spectral resolutionλ/∆λ ∼ 1800,and were taken with 3 arcsec diameter fibres. The spectroscopicsample studied here is the same discussed in SEAGal I. Briefly, weselected a volume limited sample from the SDSS Data Release 2(DR2 Abazajian et al. 2004), with a redshift range of0.05 < z <0.1, corresponding to an absolute magnitude limit cutoffM(r) =−20.5, or M∗(r) + 1. The absolute magnitudes adopted here arek-corrected (Blanton et al. 2003b). We also restricted our sampleto objects for which the observed spectra show a signal-to-noiseratio greater than 5 in theg, r, andi bands. In addition, we havedetected a minor fraction of galaxies with multiple spectral data,

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4 Mateus et al.

from which we have excluded those with smaller signal-to-noiseratios. All these criteria leave us with a sample containing49917galaxies, corresponding to a completeness level of 98.5 percent.

The spectra are corrected for Galactic extinction with the mapsof by Schlegel, Finkbeiner & Davis (1998) and the extinctionlawof Cardelli et al. (1989), shifted to the rest-frame and resampledfrom 3400 to 8900A in steps of 1A. Notice that this is a slightlywider range than that employed in SEAGal I (3650–8000A), al-though not all galaxies have data close the edges of this new spec-tral range.

2.2.1 Masks

A further novelty is that now each galaxy has its own emissionlinemask, as opposed to the single general mask for all galaxies usedin SEAGal I. General masks may unduly throw away data whenemission lines do not exist, and, conversely, ignore lines which arenormally weak but may occasionally be strong enough to deservebeing masked. (e.g. HeII λ4686). The individual masks are con-structed from an initial STARLIGHT fit with a general mask. Thestrongest lines are fitted in the residual spectrum (observed minusmodel) using the code described in the next section, and the infor-mation on line widths and velocity off-sets are used to search forother emission lines out of a list of 52 lines in the 3400 to 8900A range. When present, these lines are masked in windows whosesizes are defined by theλ’s at which their assumed Gaussian pro-files become weaker than 1/2 the local rms noise flux density. Vi-sual inspection of hundreds of cases shows that this scheme is ableto identify and mask even weak emission lines satisfactorily.

Besides emission line masks, we also exclude four other win-dows from the fits: 5880–5906A, to skip the Na Dλλ5890,5896doublet, which is partly produced in the interstellar medium; the6850–6950 and 7550–7725A, for which BC03 had to resort to the-oretical spectra due to problems in these ranges in the STELIB li-brary. Curiously, when residual spectra are averaged over thousandsof galaxies, these two windows stand out as strong “emission” fea-tures which are clearly spurious (Gomes 2005). The last window,in the 7165–7210A range, shows a similar systematic broad resid-ual in emission, so we have masked it out too, even though it isnotlisted as problematic by BC03.

2.3 Emission line measurements

One of the products of our spectral synthesis procedure is a resid-ual spectrum suitable for measurements of emission lines, as thestellar continuum and absorption features are well modelled. Evenweak lines, as the [OIII ]λ4363 auroral line, can be easily mea-sured (when present, of course). Indeed, such an approach has beenadopted by other authors (e.g. Tremonti et al. 2004) to investigateSDSS emission line spectra.

We have developed a code to measure the intensity of mainemission lines from the residual spectrum by fitting Gaussianfunctions to the line profiles, characterised by three parameters:width, offset (with respect to the rest-frame central wavelength),and flux. Lines from the same ion are assumed to have the samewidth and offset. Additionally, [OIII ]λ5007/[O III ]λ4959 = 2.97and [N II ]λ6584/[N II ]λ6548 = 3 flux ratio constraints are im-posed. Furthermore, only lines detected with signal-to-noise ra-tio (S/N ) greater than 3 are considered in the analysis. This isthe same value adopted by Brinchmann et al. (2004) in their studyof physical properties of star-forming SDSS galaxies, and is 1σ

Figure 2. The BPT diagram for our subsample of galaxies with emissionlines measured withS/N greater than 3. The solid line is the curve definedby Kauffmann et al. (2003c) and the dashed one is the curve defined byKewley et al. (2001) (see text for details). In this and otherfigures, the lin-ear grey scale level represents the number of galaxies in each pixel, darkerpixels having more galaxies.

greater than the detection limit adopted by Miller et al. (2003)in an environmental analysis of active galactic nuclei, also inthe SDSS. The lines that are currently being measured by ourcode include [OII ]λλ3726,3729, Hδ, Hγ, [O III ]λ4363, Hβ,[O III ]λλ4959,5007, [OI]λ6300, [N II ]λ6548, Hα, [N II ]λ6584and [SII ]λλ6716,6731. For each emission line, our code returns therest-frame flux and its associated equivalent width (EW), the linewidth, the velocity displacement relative to the rest-frame wave-length, and theS/N of the fit. In the case of Balmer lines, the un-derlying stellar absorption is also measured directly fromthe syn-thetic spectra, yielding absorption fluxes and equivalent widths.

Additionally, we have also identified broad emissionlines in the residual spectra, characteristic of galaxies host-ing Seyfert 1 nuclei, following a procedure similar to that ofVeron-Cetty, Veron & Goncalves (2001). As a result of this anal-ysis we have identified 335 objects with significant broad compo-nents.

3 DEFINITION OF SPECTRAL CLASSES OF GALAXIES

In this section we present the galaxy types that will be used here-after. This galaxy classification is based on spectral properties, i.e.on the presence or absence of emission lines and on their ratios inthe case they are present in the spectra.

3.1 Galaxy classification

In general, the classification of narrow emission line galaxies ismade according to the mechanism by which lines are produced,grouping galaxies into two types. The first group is composedby normal star-forming galaxies, with HII region-like spectra, inwhich the gas is photoionised by young, hot OB stars. The secondone is formed by galaxies hosting active galactic nuclei (AGN),which produce a much harder radiation field ionising the surround-ing gas.

These emission line galaxies are generally classified withthe help of diagnostic diagrams formed by line ratios of thestrongest lines present in their spectra. Here we will use the

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Bimodality of the galaxy population 5

Figure 3.Examples of galaxy spectra of the spectral classes analysedin thiswork. The residual spectra are also shown as thin lines at thebottom of eachpanel. These spectra have been smoothed in order to improve appearance.

[O III ]λ5007/Hβ versus [N II ]λ6584/Hα diagram firstly pro-posed by Baldwin, Phillips & Terlevich (1981) and updated byVeilleux & Osterbrock (1987); hereafter we will refer to it as theBPT diagram. In it, galaxies form two distinct branches, which looklike the wings of a seagull. The left wing contains star-forminggalaxies and the observed sequence corresponds to a change inmetallicity of the H II regions emitting the lines. The right wingappeared clearly only with the most recent galaxy surveys (e.g.Kauffmann et al. 2003c) and corresponds to galaxies hostingac-tive nuclei; photoionization models show that galaxies in this wingcannot be ionised only by radiation from massive stars, an addi-tional heating/ionising source is necessary to explain theobservedline ratios (e.g. Kewley et al. 2001).

The BPT diagram for our sample is shown in Fig. 2. We haveconsidered only those galaxies having a signal-to-noise ratio in allfour emission lines greater than 3; this limit results in a subsamplecontaining23080 narrow emission line galaxies. Here we have notconsidered galaxies with spectra containing broad emission lines(following Section 2.3 above). After an analysis of SDSS data,Kauffmann et al. (2003c) have defined a curve (shown in Fig. 2 asa solid line) in the BPT diagram to distinguish pure star-forminggalaxies from those contaminated by nuclear non thermal emission.Although the exact position of this curve could be questionned (seeBrinchmann et al. 2004; Stasinska et al. 2006), we have adoptedit for easy reference to recently published work (e.g. Hao etal.2005; Brinchmann et al. 2004) to distinguish normal star-forminggalaxies (below the curve) from galaxies hosting an active nucleus(above it). In Fig. 2 we also show the curve given by Kewley et al.

(2001), which we use in Sect. 4.2.1 to define galaxies with ‘com-posite’ spectra, as done by Brinchmann et al. (2004).

The normal star-forming galaxies in our sample show sig-nificant amount of star formation (more than 99 per cent haveEW(Hα) > 5A). Note that as we are studying a volume limitedsample built with an absolute magnitude cutoffM(r) < −20.5, inthis diagram we do not see the faint star-forming galaxy populationthat inhabits the extremes of its left wing (corresponding to a lineratio of [N II ]/Hα . 0.1).

Galaxies hosting active nuclei (hereafter AGN hosts), on theother hand, populate the upper right wing of the BPT diagram.Inaddition, we do not distinguish these galaxies from the ‘composite’or ‘transition’ galaxies, which have a substantial contribution oftheir Hα emission due to active nuclei, and populate the regionnear the solid curve shown in Fig. 2.

The objects that do not appear in Fig. 2 because of insuffi-cient S/N in at least one of the four relevant lines also receive aclassification. For instance, galaxies that host active nuclei are alsoidentified if they have only the emission lines of Hα and [N II ]measured with 3σ confidence (e.g. Coziol et al. 1998; Miller et al.2003). We have selected these galaxies by considering the limitlog ([N II ]/Hα) > −0.2, and classified them as AGN hosts. Wenote that the fraction of galaxies with active nuclei identified bythis way is about 54 per cent of the total of AGNs hosts in oursample. Additionally, galaxies with broad emission lines whichhost Seyfert 1 nuclei, are naturally added to the spectral class ofAGN hosts. Galaxies without evidence of significant star forma-tion, whose spectra do not show the emission lines of Hα and Hβ,or show them with equivalent widths smaller than 1A, are classi-fied as passive galaxies. Note that with this definition we arenotincluding the fraction of elliptical galaxies which show evidence ofstar formation activity (e.g. Nakamura et al. 2004; Fukugita et al.2004) in our subsample of passive galaxies. The remaining galax-ies, for which we can not give a classification based on the BPTdiagram, tend to include mainly star-forming and passive galaxies.These unclassified galaxies represent a reduced fraction ofgalaxiesin our sample (about 3 per cent) and will not be analysed in thiswork.

A summary of the spectral classes described above, which willbe analysed in the following sections, is shown in Table 2. Thenumber and per percentage of each spectral class, as well as the me-dian values of their concentration indices, colours, 4000A break,mean light-weighted stellar ages and stellar masses, are shown inthis table. In Fig. 3 we show some examples of galaxy spectra forthe distinct classes of galaxies discussed above. In each panel isalso shown the residual spectrum after removing the model ob-tained by our synthesis method. These spectra correspond togalax-ies with both stellar age and stellar mass equal to their median val-ues for each class, therefore they are very illustrative of the differentspectral features which characterise the classes we discuss here.

3.2 Sources of bias

As mentioned in Section 2.3, in this work we are imposing a limitin the S/N of the measured lines in order to consider them inemission or not. The choice of this limit affects the distributionof objects in each spectral class, as we shown in Table 3, wherethe number and percentage of galaxies in our classes are listed forthree limiting values of theS/N . For a change inS/N going from2 to 5, the proportion of star-forming galaxies increases byonly 6per cent, but that of passive galaxies increases by 50 per cent. Incontrast, the proportion of active nuclei hosts decreases by about

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Class Number Per cent C (u− i) Dn(4000) 〈log t⋆〉L logM⋆/M⊙

All 49917 100.00 2.67 2.76 1.69 9.53 10.79Star-forming 16108 32.27 2.25 2.10 1.35 8.91 10.56

Passive 10485 21.00 2.97 3.06 1.93 9.86 10.87AGN Hosts 21733 43.54 2.77 2.88 1.78 9.66 10.90

Unclass. 1591 3.19 2.67 2.83 1.73 9.58 10.77

Table 2.Summary of the spectral classes defined in this work and the median values of their mean light-weighted stellar ages and stellar masses.

S/N Star-forming Passive AGN Hosts Unclass.

2 16024 32.1 8626 17.3 24321 48.7 946 1.93 16108 32.3 10485 21.0 21733 43.5 1591 3.25 17034 34.1 12998 26.0 17382 34.8 2503 5.0

Table 3.Number and percentage of objects in each spectral class as a func-tion of the limit inS/N when considering a line in emission. Here we areusing aS/N limit equals to 3.

S/N limits Star-forming Passive AGN Hosts Unclass.

2 and 3 99.99 99.99 50.97 31.383 and 5 99.92 99.99 0.30 25.12

Table 4.Kolmogorov-Smirnov (KS) probability parameter for redshift dis-tributions when comparing theS/N limits of 2, 3 and 5 for considering aline in emission. Results are shown for each spectral class.Low values ofthe KS probability imply statistically different distributions.

28 per cent. It is interesting to note that the fraction of unclassifiedgalaxies is always smaller than 5 per cent.

We have investigated how the choice of theS/N limit affectsour analysis by looking for differences in the redshift distributionsof our classes. This approach can also test possible aperture biasin our class definition. Since SDSS spectra are taken with only 3

Figure 4. Testing aperture effects. The fraction of galaxies in each spec-tral class is shown in different bins of redshift. Solid lines are for fractionsobtained with theS/N > 3 limit for detection of emission lines, whereasdashed lines are for the limitS/N > 5. The error bars follow a Poissonstatistics.

arcsec fibre diameter, for the nearest galaxies they might tend tosample mainly the bulge component, increasing the fractionof nonemission line galaxies (especially passive ones). Therefore, the red-shift distributions for each spectral class defined by usingdifferentS/N limits, will be similar if the aperture bias does not play a sig-nificant role in our sample, or it does in an uniform way indepen-dently of theS/N value. In Table 4 we show the Kolmogorov-Smirnov (KS) probability parameter for the redshift distributionsof our distinct spectral classes. We have compared the distributionsof classes defined by using aS/N limit equals to 2 and 5, withthose of our classes defined by the adopted value ofS/N = 3.The values of the KS probability are very large for passive andstar-forming galaxies, indicating statistically similardistributionsfor these spectral classes. In the case of AGN hosts, the value ofthe KS probability parameter is large when comparingS/N limitsof 2 and 3, but it is very small forS/N limits of 3 and 5, indicatingstatistically different redshift distributions when comparing theseS/N limits. For unclassified galaxies the KS probability valuesarelarger than 25 per cent in the two cases investigated here.

In Fig. 4 we show the redshift dependence of the fraction ofgalaxies in each spectral class obtained by considering twovaluesof theS/N limit to detect emission lines (3 and 5). The expectedeffects due to aperture bias would tend to, for instance, increase thefraction of star-forming galaxies relative to that of passive alongthe redshift range of our study. In fact, what we note in this figureis an increment in the fraction of star-forming galaxies with in-creasing redshift. In addition, for lower redshifts, we also observe ahigher fraction of AGN hosts probably as a result of the significantsampling of the central regions of nearby galaxies. In contrast, thefraction of passive galaxies does not significantly increase in theregime of low redshifts. Following these trends, we infer that ourclasses seem to be affected by aperture bias in the sense thatthefraction of star-forming galaxies increases with redshift, and thatof AGN hosts decreases withz. Some aspects of this effect in oursample are discussed in Appendix A.

4 BIMODALITY OF THE GALAXY POPULATION

In this section, we discuss the characterisation of the two galaxypopulations that inhabit the local universe. Our starting point is thedefinition of the spectral classes discussed in the last section.

4.1 Spectral versus structural galaxy types

Many works on the SDSS data have found that the concentra-tion index (C), defined as the ratio of PetrosianR90 to R50

radii in r-band can be used to separate early and late-type galax-ies (Shimasaku et al. 2001; Strateva et al. 2001; Goto et al. 2002),since early-type galaxies tend to have light profiles more centrallyconcentrated than the late-types (Morgan 1958). Shimasakuet al.

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Bimodality of the galaxy population 7

Figure 5. Concentration index versus(u − r) colour for all galaxies in our sample (panel a) and for our distinct spectral classes (panels b-d). In this andin other figures of this paper, the top numbers on the right arethe number of galaxies in each panel and the Spearman rank correlation coefficient (rS). Themedian relation between colour and concentration index in three bins of galaxyr-band luminosity containing the same number of galaxies is shown as distinctlines. The ranges of each bin are shown in the top-left legend.

(2001) studied this parameter for a sample of morphologically clas-sified bright galaxies from SDSS. They found a strong correla-tion betweenC and morphological types, suggesting that this pa-rameter can be used to classify galaxies morphologically (see alsoDoi, Fukugita, & Okamura 1993; Abraham et al. 1994). However,they also noted that it is difficult to construct a pure early-typegalaxy sample based only on the concentration index, since theresulting sample has∼ 20 per cent contamination by late-typegalaxies. Strateva et al. (2001) also studied the reliability of theconcentration index to separate early and late-type galaxies. Theyadopt a value ofC = 2.63 as a morphological separator (differ-ent from Shimasaku’s value ofC ∼ 3). On the other hand, sincegalaxy colours are a more conventional estimator of galaxy types(e.g., Sandage 1986), Strateva et al. concentrate their analysis onthe (u − r) colour, finding that(u − r) = 2.22 clearly separatesearly (E, S0, and Sa) and late (Sb, Sc, and Irr) morphologicaltypes,with the(u−r) colour also expected to correlate with Hubble type.

How are these parameters associated with the spectral classeswe defined before? In Fig. 5 we show the relation of these two mainmorphological identifiers,C and(u−r), for all objects in our sam-ple and discriminated according to our distinct spectral classes (ex-cept for unclassified galaxies). In this figure, we also plot as lineswith different shapes the median values of(u − r) colour alongbins of concentration index for three luminosity ranges contain-ing the same number of galaxies. As found by other works (e.g.Strateva et al. 2001), the concentration index and(u − r) colourpresent an evident correlation (quantified by the Spearman non-parametric correlation coefficient,rS = 0.65) when all objects areconsidered. Star-forming galaxies also show a correlationbetweenthese parameters, in a less significant level, in the sense that redstar-forming objects tend to be more concentrated than blueones.On the other hand, passive galaxies do not show a correlation; thecolours of these objects are almost independent of their concentra-tion, in all ranges of galaxy luminosity. Indeed, for passive galaxiesin our sample we have the following mean values and dispersions:〈C〉 = 2.96 ± 0.08 and〈u− r〉 = 2.71 ± 0.22. In Fig. 5 we alsonote that star-forming and passive galaxies are responsible for thedistinction of the two main groups of galaxies in the colour–C dia-gram. The class of AGN hosts is composed by mixtures of blue andred galaxies, with a large range in the concentration parameter.

We show in Fig. 6a-b the distributions of concentration indexand(u− r) colour for our spectral classes (also including unclas-sified galaxies). In these figures, we can easily see the dominanceof star-forming galaxies in the blue and less concentrated galacticpopulation; passive galaxies, contrarily comprise the reddest and

more concentrated galaxies. We also note that AGN hosts occupyan intermediate locus in both colour and concentration index distri-butions, showing again the mix of populations present in this spec-tral class.

From the distributions shown in Fig. 6, we can obtain an opti-mal value that separates those two extreme classes formed bystar-forming and passive galaxies. Following Strateva et al. (2001), wecan define two parameters, reliability and completeness, which areused to do this task. The reliability (RSF andRP, for star-formingand passive spectral classes, respectively) is the fraction of galax-ies from a given spectral class that are correctly classifiedby us-ing the optimal value, while the completeness (CSF andCP) is thefraction of all galaxies of a given spectral class that are actuallyselected. In this way, we can find the optimal value that maximisethe productCSFRSFCPRP (c.f. Baldry et al. 2004). We find thatC = 2.62 and(u − r) = 2.35 are the optimal separators amongstar-forming and passive galaxies (close to the values obtained byStrateva et al. to classify galaxies into early and late-types), with re-liability and completeness parameters (in per cent) ofRSF = 86.0,RP = 89.8, CSF = 93.0 andCP = 80.3 for concentration in-dex andRSF = 93.6, RP = 93.8, CSF = 96.0 andCP = 90.4for (u − r) colour. Here it is important to stress that we are notaccounting for the variation of the colour divider along themagni-tude range of our sample. Indeed, as shown by Baldry et al. (2004)the colour value which divides the blue and red populations shouldslightly decrease with decreasing galaxy luminosity.

Another parameter useful to distinguish between early andlate-type galaxies is the 4000A break, which is small for galax-ies with younger stellar populations, and large for older galaxies(as shown in Fig. 13 of SEAGal I). We measured this index fol-lowing the narrow definition introduced by Balogh et al. (1999),with the continuum bands at 3850–3950 and 4000–4100A; thisnarrow index will be referred asDn(4000). Fig. 6c shows the dis-tribution of this index for our spectral classes. We clearlynotethe bimodal distribution of this parameter, with a divisoryline atDn(4000) = 1.67 separating star-forming and passive galaxieswith the highest values of both reliability and completeness (> 98per cent).

In Fig. 7 we show theDn(4000) index as a function of bothconcentration index and(u− r) colour for all galaxies in our sam-ple, and for the spectral classes analysed here. The median val-ues ofDn(4000) in bins of C and (u − r) for three ranges ofgalaxy luminosity are also shown as lines with different shapes.When all galaxies are considered, theDn(4000) index shows acorrelation with both concentration index (rS = 0.65) and colour

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Figure 6. Distributions of (a) concentration indexC, (b) (u− r) colour, and (c)Dn(4000) index, for all galaxy sample, star-forming, passive and AGNhostsspectral classes; the distributions for unclassified objects are also shown. The vertical dashed lines are the best population separators when we consider onlydistributions of star-forming and passive galaxies.

(rS = 0.81). For star-forming galaxies there is a significant corre-lation only with colour (rS = 0.63), implying that these two quan-tities are linked for this type of galaxies. A natural explanation forthese relations is that young and blue stellar populations are respon-sible for maintaining the correlation among colour andDn(4000)for star-forming galaxies. On the other hand, as the concentrationindex is more associated with the shape of a galaxy than with itsstellar population properties, the absence of correlationamongCandDn(4000) index reflects that star-forming galaxies with samemean stellar age (orDn(4000) value) span a wide range of mor-phological types (or concentration values). We also note inFig. 7that passive galaxies do not show significant correlations amongthe quantities analysed here, and galaxies hosting AGN showcor-relations in both colour andC versusDn(4000) plots, as expecteddue to the mixture of populations comprised by this spectralclass.

We thus conclude that by using spectroscopic information(emission lines and spectral features) one can obtain a better split-ting between the star-forming and passive galaxy populations thanby using concentration and colours. Our results also indicate thatgalaxies hosting AGNs tend to present intermediate behaviour withrespect to these two populations. Additionally, hereafterwe willconsider the star-forming and passive galaxies as the extremesof both blue and red galaxy distributions. Moreover, the optimalvalues that distinguish these spectral classes, mainly that for theDn(4000) index, will be used to define the two main galaxy pop-ulations which inhabit the local universe, historically the early andlate galaxy types.

4.2 Physical properties of spectral classes

Here we analyse the properties of the main physical parametersderived from our spectral synthesis method for each spectral classdefined above.

4.2.1 Mean stellar age

The mean light-weighted stellar age of a galaxy reflects the epochof formation of massive and bright O and B stars, frequently asso-ciated to starbursts. Thus, it is strongly affected by the recent starformation history of a given galaxy. On the other hand, the meanmass-weighted stellar age is associated with the epoch of formation

of the stellar population which nowadays contributes most signif-icantly to the galaxy mass. Consequently, it is associated with themass assembly history of a given galaxy.

In Fig. 8 we show the distributions of these two age estimatesfor all galaxies in our sample, and for each spectral class separately.The distribution for the mean light-weighted stellar age shows aconspicuous bimodality with the star-forming and passive galaxiesat their extremes, and the spectral class of AGN hosts occupying anintermediate locus in it. For this distribution,〈log t⋆〉L ≃ 9.53 isthe age which best divides the extreme galaxy populations (shownin Fig. 8 as a vertical dashed line). On the other hand, the distribu-tion of 〈log t⋆〉M is single peaked at older ages, with median valueof about 12.4 Gyr for all sample. This implies that galaxies of allspectral classes in our sample have a large fraction of theirstellarmasses in old stellar populations. Thus, it is seen that the bimodal-ity noted in some galaxy properties, as discussed above, is pri-marily related to ‘light-weighted’ quantities. In other words, recentepisodes of star formation present in star-forming galaxies, in con-trast with the absence of significant amount of young stars inpas-sive galaxies, produce the bimodal distribution seen in the〈log t⋆〉Ldistribution, as well as in the(u− r) colour andDn(4000) indexdistributions.

We have also investigated the behaviour of these trends for theresults obtained with a base excluding the low-Z SSPs, which, asshown in Fig. 1, tend to result in older ages for young stellarpopu-lations. Actually, we found this is true: the values of the mean stel-lar ages obtained by using the base without the 0.005 and 0.02Z⊙

SSPs, compared to that obtained with the base adopted in thiswork,decrease about 0.18 dex when all galaxies are considered and0.31dex for star-forming galaxies. The age with best divide the galaxypopulations for this ‘metallic’ base is〈log t⋆〉L ≃ 9.32. We alsonote that the distribution of〈log t⋆〉M for this base shows a secondpeak at younger ages, besides that at older ages. As discussed inSection 2.1, this is a consequence of usingZ > 0.2Z⊙ in the spec-tral base, which imply that one has to assume that younger galaxieswere formed less than∼ 1 Gyr ago, contrarily to the assumption ofmore continuous star-formation regimes generally invokedto ex-plain the properties of these galaxies.

As shown in Fig. 8, AGN hosts constitute an intermediate pop-ulation of galaxies. We analyse this behaviour of AGN hosts by in-vestigating the distribution of the [OIII ]λ5007 luminosity,L[O III ](thought to be a tracer of the AGN power, e.g. Kauffmann et al.2003c), as a function of the mean light-weighted stellar age. This

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Bimodality of the galaxy population 9

Figure 7. Concentration index and(u − r) colour versusDn(4000) for all galaxies in our sample and for our distinct spectral classes. It is also shown thenumber of galaxies in each panel as well as the Spearman rank correlation coefficient (rS). The median values ofDn(4000) in bins ofC and(u − r) forthree ranges of galaxy luminosity are also shown as lines with different shapes.

Figure 8. Distribution of mean stellar age weighted by light (left) and by mass (right) for all galaxy sample, star-forming, passive and AGN hosts spectralclasses. The vertical dashed line in the left panel is the optimal separator between the star-forming and passive galaxydistributions.

relation is shown in Fig. 9, where we also plot the median values ofL[O III ] as a function of〈log t⋆〉L for three ranges in galaxy lumi-nosity (shown as lines with different shapes); the age valuewhichbest separates star-forming and passive galaxies is also shown asa vertical dashed line. The correlation among these quantities isin the sense that the[O III ] luminosity is low in older galaxies,with median values larger for brighter galaxies. In galaxies hostingAGNs with 〈log t⋆〉L > 9.53 theL[O III ] is almost constant, asindicated by its median values in all galaxy luminosity bins. AGNhosts with younger stellar populations have the [OIII ] luminositydecreasing with age (see also Kauffmann et al. 2003c, for similarresults). In other words, Fig. 9 shows that even AGN hosts have abimodal distribution with old galaxies having [OIII ] luminositieslower and constant along age bins (but increasing with galaxy lu-minosity), and galaxies with young stellar populations having high

values ofL[O III ], which increases as a galaxy becomes youngerand brighter.

In order to investigate this apparent bimodal character of AGNhosts, we have divided this class in three subclasses according totheir emission line properties. The approach used here is analo-gous to that of Brinchmann et al. (2004). The subclasses are:(i)‘composite’ galaxies, which appear in the BPT diagram betweenthe curves defined by Kauffmann et al. (2003c) and Kewley et al.(2001); (ii) hosts of ‘Seyfert 2’ nuclei types, located in the BPTdiagram above the curve defined by Kewley et al.; and (iii) hostsof low-luminosity AGN (LLAGN), which do not appear in this di-agram as they have only the [NII ] and Hα emission lines mea-sured withS/N > 3, and are classified by using only the crite-rion log([N II ]/Hα) > −0.2 (see Miller et al. 2003). In Fig. 10 weshow the distribution of light-weighted mean stellar ages for these

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Figure 9. Luminosity of [O III ]λ5007 emission line as a function of themean light-weighted stellar age. The median values ofL[O III ] as a functionof age for three ranges in galaxy luminosity are shown as lines with differentshapes. The vertical dashed line is the age value with best distinguish star-forming and passive galaxies.

Figure 10.Distribution of mean light-weighted stellar age for distinct typesof AGN hosts (see text for details).

three subclasses of AGN hosts, as well as for all galaxies in thisspectral class. It is interesting to note that composite galaxies atone side, and LLAGN hosts at another, are in the tails of the distri-bution for all AGN hosts. The majority of AGN hosts in our sam-ple is composed by galaxies with old stellar populations, mainlyrepresented by the LLAGN hosts which show low values for the[O III ]λ5007 luminosity. We conclude from theL[O III ] versus agerelation shown in Fig.9 and the distributions seen in Fig. 10thatthe AGN activity is closely linked to the star-formation activity ofa galaxy, in the sense that galaxies with younger stellar populationstend to have more powerful AGNs.

4.2.2 Stellar mass

The distribution of stellar mass for our sample is presentedinFig. 11. As in Fig. 8, we show the distributions for the full sampleand for each spectral class discussed here. The value of stellar masswhich best divides star-forming and passive galaxies is shown as avertical dashed line, and corresponds toM⋆ ∼ 4.7×1010 M⊙. Thereliability and completeness parameters obtained with these valuesare∼ 71 per cent.

This value is susbtantially larger than the3 × 1010 M⊙ atwhich Kauffmann et al. (2003b) find a sharp transition in the phys-ical properties of galaxies. As mentioned in SEAGal I, this differ-ence cannot be attributed to the differences in IMF. Kauffmann etal. used the Kroupa IMF, whereas we use the one by Chabrier, butas show in the BC03 paper, these two IMFs yield identicalM/Lratios.

A more relevant source of discrepancy is related to the ap-proach used to determine the transition mass. In Kauffmann et al.(2003b), there is no objective criteria to define the stellarmassvalue at which galaxy properties change, whereas we have useda clear procedure to find the stellar mass transition atM⋆ ∼4.7× 1010 M⊙.

We have also verified if the use of a volume-limited samplein such analysis, with an absolute magnitude limit cutoffM(r) =−20.5, affects the determination of the transition mass value, beingresponsible for the difference discussed above. In order toinvesti-gate this issue we have determined the transition mass for galaxiesin a flux-limited sample containing 20000 galaxies selectedat ran-dom from the main galaxy sample of SDSS. This results in an evenlarger transition mass,M⋆ ∼ 6.3× 1010 M⊙.

As anticipated in section 2.1, the inclusion of very lowZSSPs in the base inevitably leads to larger stellar masses. TheKauffmann et al. (2003b) mass estimates are based on a library ofmodel galaxies constructed withZ > 0.25Z⊙, whereas the SSPsin our base go down to0.005Z⊙ . This is a systematic source of dis-crepancy between the mass scales in these two studies. In SEAGalI, which used onlyZ > 0.2Z⊙ SSPs, we have shown that the stel-lar masses estimated via the spectral synthesis approach are about0.1 dex larger than that obtained by Kauffmann et al. (MPA/JHUgroup). Repeating this comparison for our new stellar masses yieldsa median offset of 0.2 dex. As discussed in SEAGal I, part of thisdifference (∼ 0.1 dex) could be attributed to technical details em-ployed to estimate the stellar masses. The remaining difference isdue to the inclusion of low-Z SSPs in our spectral base. We haveconfirmed this hypothesis through the analysis of the results ob-tained with a base excluding the 0.002 and 0.005Z⊙ SSPs. Asexpected, theM⋆ values obtained by this way are only about 0.1dex larger than the stellar masses obtained by the MPA/JHU group.The transition mass for this base isM⋆ ∼ 3.9× 1010 M⊙.

Therefore, discrepancy between the values of the stellar masstransition obtained here and in Kauffmann et al. (2003b) is due to acombination of differences in the methodology to define thismassand differences in the metallicities in reference set of model stellarpopulations.

4.2.3 Stellar extinction

Another important quantity related to physical processes occurringin galaxies is the amount of dust present in the interstellarmedium.Our spectral synthesis approach estimates this value by obtainingthe attenuation of starlight by dust parametrised inV -band, i.e. thestellar extinction,A⋆

V . We plot in Fig. 12 this parameter against theDn(4000) index. The results for all galaxies in our sample are de-picted in Fig. 12a. There is a clear anti-correlation betweenA⋆

V andDn(4000) with rS = −0.66. However, the relation between thesetwo quantities is better appreciated when we consider separatelystar-forming, passive and AGN host galaxies. Indeed, star-forminggalaxies (Fig. 12b) do not show significant correlation betweenA⋆

V

andDn(4000), with rS = 0.03, and passive galaxies (Fig. 12c)exhibit only a small anti-correlation (rS = −0.17). The median

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Bimodality of the galaxy population 11

Figure 12.V -band stellar extinction versusDn(4000) for (a) all galaxy sample, (b) star-forming, (c) passive, and (d) AGN host galaxies. The median valuesof A⋆

Vin bins ofDn(4000) index for three luminosity intervals are shown as differentlines.

Figure 11. Distribution of stellar mass for all galaxies in our sample,andfor classes of star-forming, passive and AGN hosts. The vertical line is theoptimal separator between star-forming and passive galaxies.

of A⋆V for star-forming and passive galaxies are 0.33 and -0.12,

respectively.The relation betweenA⋆

V and Dn(4000) is weak for star-forming and passive galaxies, but strong for galaxies harbouringan AGN, as can be appreciated in Fig. 12d. The Spearman correla-tion coefficient between these two quantities is−0.60. It is not easyto interpret this finding, considering that the measured spectrum ofthis kind of object is a composite of the AGN spectrum plus theun-derlying stellar population. A better understanding of what is goingon requires spatially-resolved spectroscopy of the central regions ofthis kind of galaxy.

It is interesting to verify how the trends above behave if weuse galaxy colours. This is shown in Fig. 13 for the colour(u− i).The trends of stellar extinction with colour are, qualitatively, quitesimilar to those betweenA⋆

V and Dn(4000), when all galaxiesare considered. However, in the case of star-forming galaxies, thecorrelation become stronger with colour (the Spearman coefficientbeing 0.33). This is in agreement with the results reported byStasinska et al. (2004) for the nebular extinction of spiral galaxies:it tends to increase with galaxy colour. On the other hand, the smallcorrelation shown in Fig. 12c for passive galaxies disappear in theplot of A⋆

V versus(u − i) colour. We discuss other properties ofextinction in another paper of this series (Sodre et al. 2006).

4.2.4 A note about negative extinction

As discussed in SEAGal I, for both statistical and physical reasons,we did not constrain the extinctionA⋆

V to be positive. Interest-ingly, A⋆

V < 0 galaxies are nearly all passive, in agreement withKauffmann et al. (2003a), who found negative extinction primarilyin galaxies with a largeDn(4000). As a whole, the distributionof A⋆

V for passive galaxies indicates that they have essentially nodust, as expected given that they are dominated by old stellar pop-ulations. Still, the fact that this distribution is centered on slightlynegative values ofA⋆

V deserves some explaining, as it cannot beattributed purely to random errors, which would produceA⋆

V = 0on average. Although this has no impact on the main conclusionsof this paper, we find it useful to open a parenthesis to look atthisissue more closely.

We find that one of the factors which is responsible forthis tendency isα-enhancement. As reported by Sodre et al.(2005), our STARLIGHT fits for passive galaxies underpre-dict the strength ofα-element features, which is not sur-prising given that the STELIB-based BC03 SSPs do not ac-count for theα-enhancement known to occur in massive ellipti-cals (Worthey, Faber, & Gonzalez 1992; Davies, Sadler, & Peletier1993; Thomas, Maraston, & Bender 2002). Furthermore, the resid-uals in these features are larger asσ⋆ increases, in analogy with the[Mg/Fe]–σ⋆ anti-correlation.

Gomes (2005) carried out simulations to test the effects of en-hancingα-features in test galaxy spectra constructed with the BC03SSPs. To emulate this effect realistically, he has added to the mod-els the mean residual spectrum of passive galaxies in the regions ofCN, Mg and NaD. These controlled experiments showed that in or-der to try to match these artificially enhanced bands, STARLIGHToverpredicts the strength of the older components, where these fea-tures are deeper. Furthermore, even though the test galaxies wereconstructed withA⋆

V = 0, the fits yield systematically negativeextinction, of orderA⋆

V ∼ −0.1, as found in passive galaxies(Fig. 12b). This happens because the older components invokedto match the deeperα-spectral features are also redder, implying acontinuum mismatch which is compensated by a slightly negativeA⋆

V .

The bottom line is that negative extinctions in passive galaxiesare at least partly due to the use of a base of SSPs which do nothave the proper chemical mixture. Recently publishedα-enhancedlibraries should help fixing this mismatch (e.g. Coelho et al. 2005;Munari et al. 2005).

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12 Mateus et al.

Figure 13.Same as Fig. 12, but now with(u− i) colour in the ordinate.

5 DISCUSSION

5.1 Origin of the bimodal distribution

An easy way to visualise the bimodality of the galaxy population isin the colour-magnitude diagram, which shows two separate coloursequences, a broad blue sequence, and a narrower red one (seee.g. Baldry et al. 2004). Here we investigate the nature of bimodal-ity through the mass-luminosity relation. Fig. 14 shows thestellarmass as a function of the dust-correctedz-band luminosity (in so-lar units) for the full galaxy sample and for the galaxy populationsdivided by using the valueDn(4000) = 1.67. Robust linear fits tothe mass-luminosity relation for these two galaxy sequences yield:

log(M⋆/M⊙) = −4.89 + 1.48 log(Lz/L⊙), for late-types

and

log(M⋆/M⊙) = −1.50 + 1.18 log(Lz/L⊙), for early-types.

Here, the two galaxy sequences commonly seen in the colour-magnitude diagram are well characterised with that correspondingto early-type galaxies being less steep than that of late-type galax-ies. The relation for early-types also shown the best correlation co-efficient (rS = 0.93) and less scatter. For late-type galaxies, thescattering observed in theM⋆ − Lz relation is associated to thelarge spread in the mass-to-light ratio and star formation historiesshown by these objects.

Recently, Baldry et al. (2004) have found that a change in thedistribution of galaxy colours occurs around(1 − 3) × 1010 M⊙,close to the value at which the galaxy properties also change(seeKauffmann et al. 2003b). However, from Fig. 14 we note that an-other parameter is needed in order to achieve a better separationbetween the two galaxy populations characterised by the extremeclasses of star-forming and passive galaxies. For instance, the valuelogM⋆/M⊙ > 10.5 can select almost all early-type galaxies, buta large number of massive late-type galaxies is also selected by us-ing this criterion. In fact, as shown in Table 5, the reliability andcompleteness parameters for star-forming and passive galaxies ob-tained with the optimal value oflogM⋆/M⊙ = 10.67 are lowerthan those obtained when considering the mean light-weighted stel-lar age to split the galaxy populations. Thus, it seems that the galaxymass is not playing a main role in defining the bimodal galaxy dis-tribution seen in local galaxies, reinforcing the idea thatthe ob-served bimodality is related to the presence of a young componentin low-mass, blue galaxies.

Another way to investigate this issue is presented in Fig. 15,where we show the(u− r) colour andDn(4000) index versus themean light-weighted stellar age and stellar mass for star-formingand passive galaxies in our sample. The values which better dividethese extreme galaxy populations are shown as vertical and hor-

izontal dashed lines. The median values of colour andDn(4000)for three bins of galaxy luminosity are also shown as different lines.

With the help of this figure, we have investigated the trendof the mean light-weighted stellar age to distinguish the extremegalaxy populations in a better way than if using stellar mass. Con-sidering the optimal values of(u− r) colour andDn(4000) index,and that of〈log t⋆〉L and logM⋆, to characterise early and late-type galaxies, there are two sets ofabnormalgalaxies (located inthe top-left and bottom-right quadrants of Fig. 15): late-type galax-ies (e.g. withDn(4000) < 1.67) with old stellar ages or high stel-lar masses, and early-type galaxies (withDn(4000) > 1.67) withyoung stellar ages or low stellar masses. We find that the fractionof late-type ‘old’ plus that of early-type ‘young’ galaxiesis about6 per cent, whereas the fraction of late-type ‘massive’ plusearly-type ’low-mass’ galaxies is 29 per cent. Thus, taking a single valueto characterise the two main galaxy populations (star-forming andpassive), for instance based on theDn(4000) index, the fractionof those uncommon galaxies is higher when we consider the opti-mal value of the stellar mass, in contrast with the fraction obtainedwhen considering the mean stellar age to split the galaxy popula-tion. A similar trend is also seen when all galaxies are takenintoaccount.

Thus, supported by these findings, we argue that the bimodal-ity of the galaxy population, commonly seen in colour-magnitudediagrams, single colour distributions, and in the mass-luminosityrelation discussed above, is related to the presence of a young andluminous stellar component in galaxies currently undergoing starformation, in contrast with the stellar content of passive galaxies,where old stars are the responsible for most of their luminosities.

5.2 The role of stellar mass

Colours of galaxies reflect their star formation histories,which arealso linked to the stellar populations that we are seeing today. Forinstance, a galaxy that has suffered recent bursts of star formationwill contain a considerable fraction of young and hot stars that willbe responsible for a large fraction of the light we receive from it.On the other hand, earlier events of huge star formation activity willkeep the fraction of old stellar populations even higher, leading togalaxies with redder colours and spectra dominated by absorptionlines.

We also observe that red, passive galaxies tend to be moremassive than blue, star-forming galaxies. Thus, the stellar mass ofa galaxy is related to the bimodality seen in the colour distributionof local galaxies, in the sense that only less massive galaxies appearto be forming stars in the last few gigayears.

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Bimodality of the galaxy population 13

Figure 14.Mass-luminosity relation for (a) all galaxies in our sample, and for (b) late-type galaxies withDn(4000) < 1.67 and (c) early-type galaxies withDn(4000) > 1.67. Solid lines are robust fits for the relations.

Optimal value RSF RP CSF CP CSFRSFCPRP

C 2.62 86.0 89.8 93.0 80.3 57.6(u− r) 2.35 93.6 93.8 96.0 90.4 76.2(u− i) 2.68 91.7 95.2 96.7 88.2 74.4

Dn(4000) 1.67 98.8 98.2 98.6 98.1 93.9〈log t⋆〉L 9.53 94.8 92.9 95.4 92.0 77.3

log M⋆/M⊙ 10.67 64.2 79.9 83.0 59.2 25.2

Table 5.Reliability and completeness parameters for concentration index,(u− r) and(u− i) colours,Dn(4000) index, mean light-weighted stellar age andstellar mass optimal values obtained to split the distributions of star-forming and passive galaxies.

We have investigated this tendency by examining the mass-weighted mean stellar age,〈t⋆〉M 1, of galaxies in our sample, asa function of their stellar masses. This age is related to theepochof formation of the stellar population which nowadays contributessignificantly to the galaxy mass. In Fig. 16 we show the relation be-tween stellar mass and〈t⋆〉M (in Gyr), for (a) all galaxy sample, (b)star-forming, and (c) passive galaxies. There is a clear correlationbetween stellar mass and〈t⋆〉M , with a Spearman rank coefficientof rS = 0.69 for all galaxy sample. The median values of stellarmass in bins of stellar age containing the same number of objectsare also shown in this figure. Note that the median stellar mass in-crease from1.4 × 1010 to 1.5 × 1011 M⊙, from the young to theoldest age bin. This trend is particularly related to the existence ofa dominant fraction of passive galaxies, with high stellar massesand without signs of recent star formation activity, at the oldest agebins shown in Fig. 16c. In addition, less massive galaxies are stillforming stars which will contribute to increase their masses further.

When examining these plots, it is fit to recall that we are us-ing a volume-limited sample. The limiting magnitude ofM(r) =−20.5 (corresponding toM∗(r)+1) is large enough to detect mas-sive galaxies of any age, but old low-mass systems will be excludedby construction. To examine this issue quantitatively, we use theSSPs in BC03 and determine, for each age and metallicity, thestel-lar mass which results inM(r) = −20.5. The results are shownas solid lines, one for eachZ, in Fig. 17, overplotted to theM⋆

versus〈t⋆〉L andM⋆ versus〈t⋆〉M relations for our sample. TheM⋆(t, Z)M(r)=−20.5 lines trace very well the lower envelope ofthe data points in the left panel of Fig. 17. The lower envelopbe-comes fuzzier using〈t⋆〉M , but the overall conclusion is still the

1 actually〈t⋆〉M = 10〈log t⋆〉M

same. Except for a handful of cases, all galaxies in this sample lieabove these lines. Old, low mass objects (“dwarf elliptical”-like)which would populate the lower-right region of this diagramaretoo faint to satisfy ourM(r) < −20.5 cut. On the other hand, andperhaps more interestingly, the nonexistence of massive galaxieswith young stellar populations (mainly noted in the relation with〈t⋆〉M ), which should appear at the top-left corner of Fig. 17, isclearly unrelated to our sample selection. Thus, our claim that mas-sive galaxies have essentially older stellar populations whereas, incontrast, less massive ones have younger populations, doesnot de-pend on the limiting magnitude adopted in this work.

5.3 Downsizing in galaxy formation

In a biased galaxy formation scenario (e.g. Cen & Ostriker 1993),massive galaxies form from the highest peaks in the initial den-sity fluctuation field. In this scenario, massive galaxies formed athigh redshifts tend to inhabit the high-density regions associated togalaxy clusters and rich groups seen today. Indeed, Kodama et al.(2004) in a photometric analysis of galaxies in colour-selectedhigh-density regions atz ∼ 1, have shown that galaxy forma-tion processes, including mass assembly and star formation, takeplace rapidly and are completed early in massive systems, while inthe less massive ones these processes (at least star formation) areslower.

This galaxy formation scenario, in which more massivegalaxies are formed at higher redshift, was first proposed byCowie et al. (1996), who found that the maximum luminosity (ormass) of galaxies undergoing rapid star formation has been declin-ing smoothly with decreasing redshift sincez ∼ 1. Recently, manyobservational results have supported this idea by suggesting that themost luminous galaxies formed the bulk of their stars in the first

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14 Mateus et al.

Figure 15.Mean stellar age and stellar mass as a function of(u− r) colour (top panels) andDn(4000) index (bottom panels), for star forming and passivegalaxies in our sample. It is also shown the number of objectsand the Spearman rank correlation coefficient for each panel.

∼ 3 Gyr of cosmic history (McCarthy et al. 2004; Kodama et al.2004; Juneau et al. 2005, and others).

Hence, even atz ∼ 1 there would be a red and luminouspopulation composed by massive and old galaxies, and a blueand faint one, formed by less massive galaxies with still ongoingstar formation. Recently, evidence for this bimodal distribution ofgalaxy properties (at least in colour) around this redshifthas beenfound by many works through different approaches and using dif-ferent observational data sets (Bell et al. 2004; Wiegert etal. 2004;Weiner et al. 2005).

In the local universe, the bimodality of galaxy propertieswas firstly noted in the colour distribution of SDSS galaxies(e.g. Strateva et al. 2001) and in the star formation properties ofgalaxies from the 2dFGRS (e.g. Madgwick et al. 2002). In thelast years many works have focused their analysis on the de-pendence of galaxy properties on the stellar mass. For instance,Kauffmann et al. (2003b) have shown that at a stellar mass above3× 1010 M⊙ there is a rapidly increasing fraction of galaxies withold stellar populations, high surface mass densities and high con-centrations typical of bulges. These results, and similar ones basedon the star formation properties of galaxies (e.g. Brinchmann et al.2004), together with our own findings derived from the analysisof the mass-weighted mean stellar age of galaxies, are in perfect

agreement with the ‘downsizing’ scenario proposed by Cowieet al.(1996).

Notwithstanding the numerous observational reasons to be-lieve in this scenario, it is still very puzzling when we assumethe hierarchical galaxy formation (bottom-up) scenario ofΛCDMmodels, which predicts that small systems collapse first andmas-sive galaxies form later via the assembly of these already col-lapsed structures. The theoretical ‘downsizing’ picture still re-quires significant improvements, mainly concerning galaxyforma-tion and related processes occurred sincez = 1, as pointed out byHammer et al. (2005). At this point it is also important to stress therecent advance of semi-analytic models based on hierarchical clus-tering to explain some observational properties of galaxies, suchas the bimodality in galaxy colours (e.g. Menci et al. 2005).In thisframework, distinct merging and star formation histories for pro-genitors with different masses lead to a high-z origin of the bi-modality seen in the properties of galaxies up toz ∼ 1, particularlyduring the formation and merging of their progenitors.

Despite the uncertainties in the scenarios for galaxy evolutionand the current status of ‘downsizing’ in galaxy formation and hi-erarchical models, here we have shown that our spectral synthesismethod discussed in SEAGal I enables us to investigate the star for-mation history of local galaxies, making a link among these objectsand their progenitors, which have been recently explored bycur-

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Bimodality of the galaxy population 15

Figure 16. Stellar mass versus the mass-weighted mean stellar age of formation of the stellar population which more contributes inmass, for (a) all galaxysample, (b) star-forming, and (c) passive galaxies. The solid lines are the median and quartile values of stellar mass inage bins containing the same number ofgalaxies.

Figure 17.Stellar mass as a function of the mean light-weighted stellar age (left panel) and mass-weighted stellar age (right panel). The solid lines representthe stellar mass for which a SSP of age〈t⋆〉L has an absoluter-band magnitude of−20.5. Each line corresponds to a stellar metallicity. From bottom to top:Z = 0.005, 0.02, 0.2, 0.4, 1 and 2.5Z⊙.

rent high-redshift galaxy surveys. In future works we will discussin detail this and other related issues.

6 SUMMARY

In this second paper of the SEAGal collaboration, we have investi-gated the bimodality observed in galaxy populations by inspectingthe spectral properties of SDSS galaxies. We have used the physi-cal parameters derived from the spectral synthesis method appliedto a sample of about 50 thousand galaxies extracted from the SDSSData Release 2. Galaxies are classified according to their emissionline properties in three distinct groups: star-forming, passive, andAGN hosts. The bimodality of galaxy properties is investigatedwith emphasis on these spectral classes. Our main findings are sum-marised below:

(i) The bimodality of the galaxy population can be representedby two extreme spectral classes, corresponding to star-forminggalaxies at one side, containing young stellar populationsand pref-erentially of low stellar masses, and passive galaxies at the otherside, without ongoing star formation and populated by olderstars.

(ii) In an intermediate locus, there are the AGN hosts, which

comprise a mix of young and old stellar populations. However, thisspectral class also shows a bimodal behaviour when considering the[O III ] emission line luminosity, with younger galaxies showing thelarger values ofL([O III ]), and older ones presenting the same lowluminosities (L([O III ]) < 106 L⊙) essentially at all stellar ages.

(iii) As a main result, we found that the mean light-weightedstellar age of galaxies is the direct responsible for the bimodalityobserved in the galaxy population.

(iv) The stellar mass, in this view, has an additional role sincemost of the star-forming galaxies present in the local universe arelow-mass galaxies. Our results also reinforce the idea of a ‘down-sizing’ in galaxy formation, where massive galaxies seen nowadayshave stopped to form stars more than 10 Gyr ago.

In this work we have explored a piece of the arsenal of physi-cal parameters provided by the spectral synthesis method, in orderto investigate the spectral properties of galaxies and revisited thebimodal character of the galaxy population. Other papers inthisseries will bring more insight to some fundamental problemscon-cerning to the physical properties of local galaxies.

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16 Mateus et al.

ACKNOWLEDGEMENTS

We thank the anonymous referee for comments and suggestionsthat helped improve the paper. We thank financial support fromCNPq, FAPESP and the CAPES/Cofecub program. All the authorsalso wish to thank the team of the Sloan Digital Sky Survey fortheirdedication to a project which has made the present work possible.

Funding for the Sloan Digital Sky Survey has been providedby the Alfred P. Sloan Foundation, the Participating Institutions,the National Aeronautics and Space Administration, the NationalScience Foundation, the U.S. Department of Energy, the JapaneseMonbukagakusho, and the Max Planck Society. The SDSS is man-aged by the Astrophysical Research Consortium (ARC) for thePar-ticipating Institutions. The Participating Institutionsare The Uni-versity of Chicago, Fermilab, the Institute for Advanced Study, theJapan Participation Group, The Johns Hopkins University, the Ko-rean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institutefor Astrophysics (MPA), New Mexico State University, Universityof Pittsburgh, University of Portsmouth, Princeton University, theUnited States Naval Observatory, and the University of Washing-ton.

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APPENDIX A: APERTURE EFFECTS

A particular effect acting in modern galaxy redshift surveys isrelated to the fixed-size apertures used to obtain spectroscopicdata. In the 2dFGRS the fibre diameter is only 2 arcsec, whereasin the SDSS the fibres cover 3 arcsec of the sky, leading to asmall sampling of the integrated light of nearby galaxies. Recently,

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Bimodality of the galaxy population 17

Figure A1. (Top) Cumulative distribution of the ratio of the fibre radiusto the galaxy radius for all sample and for each spectral class discussedin this work. (Bottom) Cumulative distribution of the correction factor tobe applied to correct for aperture effect, also for all sample and spectralclasses. The vertical dashed lines in these plots are the median values of thedistributions for all sample.

Kewley, Jansen & Geller (2005) have examined this problem inde-tail by investigating the effect of aperture size on the starformationrate, metallicity, and extinction determinations for galaxies selectedfrom the Nearby Field Galaxy Survey. The main result obtainedby these authors is the need to select galaxies withz > 0.04, inthe case of the SDSS, to minimise aperture effects in the spectralmeasurements. This redshift limit is required to assure that a fibrecaptures more than 20 per cent of the galaxy light.

In this work, the galaxy sample was built to contain onlygalaxies with redshifts larger thanz = 0.05. Hence, following therecommendation given by Kewley et al., the aperture effectsin oursample tend to be strongly minimised. On the other hand, in Fig. 4we have shown that the fraction of star-forming galaxies increasessignificantly with increasing redshift, probably due to thefact thatin nearby galaxies the fibre is capturing mainly their bulge regions,whereas the nebular emission lines (used here to classify galaxies)come essentially from their discs. Here, we inspect some aspects ofthis effect.

In Fig. A1 we show the cumulative distributions of two quanti-ties related to the covering fraction of the fixed-size aperture for allgalaxy sample, and for each spectral class discussed in thiswork.

In the top panel of this figure, it is shown the ratio between the fi-bre radius (1.5 arcsec) and the Petrosian radius containing90 percent of the galaxy flux (inr-band). Thus, this ratio represents thefraction of the galaxy size that is actually covered by the fibre. Themedian value for all galaxy sample, and also for each spectral classtaken individually, is about 23 per cent. Thus, the fibre covers, onaverage, the same fraction of galaxy size almost independently ofthe galaxy type.

The bottom panel of Fig. A1 shows the aperture correction,A,to be applied in flux related measurements, based on the differencesbetween the total galaxy magnitude in ther-band and the mag-nitude inside the fibre (rfibre), explicitly A = 10−0.4(r−rfibre)

(Hopkins et al. 2003). This correction factor is commonly appliedto emission line derived parameters (like Hα SFR), and assumesthat the regions where the lines are formed (mainly HII regions)have a distribution identical to that where the continuum ispro-duced by the old stellar populations. In Fig. A1 we note thatstar-forming galaxies have aperture corrections larger than that ofother classes. This may be somewhat problematic, because thiskind of correction is performed just in this type of galaxies(e.g.Hopkins et al. 2003).

From the plots shown in Fig. A1 we conclude that while the3 arcsec diameter fibres cover about the same fraction of galaxysize for all galaxies, the fraction of light gathered by their smallapertures are biased towards lower values (or consequentlyhigheraperture corrections) for star-forming galaxies, and higher valuesfor passive galaxies. Since the expected aperture effects would tendto increase the number of passive galaxies relative to that of star-forming at lower redshifts, the low aperture corrections obtainedfor these galaxies indicate that, on average, there are not substantialeffects acting on the fraction of this spectral class along the redshiftrange considered in this work.

A1 Mass-to-light ratio

In order to estimate the total stellar mass of a galaxy from the spec-tral synthesis, we have assumed that it has a constant radialM/L.In other words, total stellar masses are computed from the fibreand Petrosian (total) magnitudes by considering theM/L insidethe fibre as representative of the whole galaxy. The effects of thisassumption on our stellar mass determination is investigated here.

We have carried out the following tests to address this inter-esting question. From the SDSS photometry data we have both fi-bre and total fluxes and colours, from which one can also computeoutside-the-fibre fluxes and colours. We have examined the corre-lations between inside-the-fibreM⋆/Lz and fibre-colours and cho-sen theM⋆/Lz versus(r− z) colour as the best one (though othercolours yield about equally good correlations). Having establishedan empirical relation parametrised byM⋆/Lz = a(r − z) + b(which we did separately for passive and star-forming galaxies),we can then, from an observed outside-the-fibre colour estimatethe corresponding outside-the-fibreM⋆/Lz .

In the top panel of Fig. A2, we show the relation betweenthe M⋆/Lz obtained inside the fibre and outside it, for star-forming and passive galaxies. Compared to the inside-the-fibrevalue,M⋆/Lz is, in the median 0.13 dex smaller in the outside.This applies to star-forming galaxies. This is expected, asthe out-side light is dominated by disk-light, whereas the fibre dataalsoincludes the bulge. Differences for the passive galaxies were negli-gible (−0.03 dex).

Total masses computed with this approximate correction are,in the median, only 0.09 dex smaller than those obtained extrapo-

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Figure A2. Top: relation between the mass-to-light ratio obtained inside the3′′ fibre and outside it (see details in text) for star-forming galaxies (bluepoints) and passive galaxies (red points). Bottom: distribution of the differ-ences between the total stellar masses estimated by considering a constantM⋆/Lz along the radius of a galaxy and estimated via the outside-the-fibreM⋆/Lz , for star-forming galaxies (blue) and passive ones (red).

lating theM⋆/Lz derived from the fibre-spectroscopic data to thewhole galaxy, as can be seen in the bottom panel of Fig. A2. Be-cause this is a small difference, and also because theM⋆/Lz versuscolour calibration has a good deal of scatter, we prefer not to applythis correction in our analysis.

This paper has been typeset from a TEX/ LATEX file prepared by theauthor.

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