Table Of Content

Draft version June 20, 2014 PreprinttypesetusingLATEXstyleemulateapjv.5/2/11 SUB-MILLIMETER GALAXIES AS PROGENITORS OF COMPACT QUIESCENT GALAXIES S. Toft 1, V. Smolcˇic´2, B. Magnelli3, A. Karim3,4, A. Zirm1, M. Michalowski5,6,18, P. Capak7,8, K. Sheth9, K. Schawinski10 J.-K. Krogager1,11, S. Wuyts12, D. Sanders13, A. W. S. Man1, D. Lutz12, J. Staguhn12,14 S. Berta12, H. Mccracken15, J. Krpan2, D. Riechers16,17 Draft version June 20, 2014 ABSTRACT Three billion years after the big bang (at redshift z = 2), half of the most massive galaxies were already old, quiescent systems with little to no residual star formation and extremely compact with 4 stellar mass densities at least an order of magnitude larger than in low redshift ellipticals, their 1 descendants. Little is known about how they formed, but their evolved, dense stellar populations 0 suggest formation within intense, compact starbursts 1-2 Gyr earlier (at 3 < z < 6). Simulations 2 show that gas-rich major mergers can give rise to such starbursts which produce dense remnants. Sub-millimeter selected galaxies (SMGs) are prime examples of intense, gas-rich, starbursts. With a n new,representativespectroscopicsampleofcompactquiescentgalaxiesatz =2andastatisticallywell- a J understood sample of SMGs, we show that z =3−6 SMGs are consistent with being the progenitors of z =2 quiescent galaxies, matching their formation redshifts and their distributions of sizes, stellar 7 massesandinternalvelocities. Assuminganevolutionaryconnection, theirspacedensitiesalsomatch ] if the mean duty cycle of SMG starbursts is 42+40 Myr (consistent with independent estimates), −29 A which indicates that the bulkof stars in these massive galaxies were formed in a major, early surge of G star-formation. Theseresultssuggestsacoherentpictureoftheformationhistoryofthemostmassive galaxies in the universe, from their initial burst of violent star-formation through their appearance as . h high stellar-density galaxy cores and to their ultimate fate as giant ellipticals. p Subject headings: cosmology: observations – galaxies: evolution – galaxies: high redshift – galaxies: - starburst – galaxies: formation– submillimeter: galaxies o r t s 1. INTRODUCTION One of the most remarkable discoveries in galaxy evo- a lution studies in the past years is that up to half of the [ most massive galaxies (log(M /M )>11) at z≈2 are 1 DarkCosmologyCentre,NielsBohrInstitute,Universityof ∗ (cid:12) 1 Copenhagen,JulianeMariesvej30,DK-2100Copenhagen,Den- oldquiescentsystemswithextremelycompactstructure, v mark;[email protected] corresponding to stellar densities orders of magnitudes 0 2Physics Department, University of Zagreb, Bijeniˇcka cesta higher than seen in local elliptical galaxies (e.g. Toft 1 32,31A0r0g0e2laZnadgerrebIn,sCtritouatteiafor Astronomy, Auf dem Hu¨gel 71, etal.2007;vanDokkumetal.2008;Szomoruetal.2012). 5 Bonn,53121,Germany Muchefforthasgoneintoconfirmingtheirextremeprop- 1 4InstituteforComputationalCosmology,DurhamUniversity, ertiesandinvestigatingtheirevolutionarypathtothelo- 1. SouthRoad,Durham,DH13LE,UK cal universe. Virial arguments and simulations indicate 5Scottish Universities Physics Alliance, Institute for Astron- 0 omy, University of Edinburgh, Royal Observatory, Edinburgh, that the most important process is likely to be minor 4 EH93HJ dry merging (e.g. Bezanson et al. 2009; Oser et al. 2012; 1 6SterrenkundigObservatorium,UniversiteitGent,Krijgslaan Cimatti et al. 2012; Toft et al. 2012), but observations : 281S9,9000Gent,Belgium suggest that other processes are likely also important, v 7Spitzer Science Center, 314-6 Caltech, 1201 East California e.g. the continuous addition of increasingly larger newly i Boulevard,Pasadena,CA91125,USA X 8Department of Astronomy, 249-17 Caltech, 1201 East Cali- quenched galaxies to the quenched population with de- forniaBoulevard,Pasadena,CA91125,USA creasing redshift (e.g. Newman et al. 2012; Carollo et al. ar 9National Radio Astronomy Observatory, 520 Edgemont 2013; Cassata et al. 2013; Krogager et al. 2013). The Road,Charlottesville,VA22903 10ETH Zurich,Institute for Astronomy, Department of formation path of these extreme systems is largely un- Physics,Wolfgang-Pauli-Strasse27,8093Zurich,Switzerland known. Simulations indicate that highly dissipational 11European Southern Observatory, Alonso de Cordova 3107, interactions on short timescales provide plausible mech- Vitacura,Casilla19001,Santiago19,Chile anisms for creating compact stellar populations, either 12MPE,Postfach1312,85741Garching,Germany 13InstituteforAstronomy,2680WoodlawnDrive,University through major mergers (e.g. Naab et al. 2007, 2009), or ofHawaii,Honolulu,HI96822 dynamical instabilities fed by cold gas accretion (Dekel 14TheHenryA.RowlandDepartmentofPhysicsandAstron- et al. 2009). A possible scenario is major gas-rich merg- omy, Johns Hopkins University, 3400 N. Charles Street, Balti- ersathighredshift(Wuytsetal.2010), inwhichthegas more,MD21218,USA 15InstitutdAstrophysiquedeParis,UMR7095CNRS,Univer- is driven to the center, igniting a massive nuclear star- sitePierreetMarieCurie,98bisBoulevardArago,75014Paris, burst, followed by an AGN/QSO phase that quenches France the star formation, and leaves behind a compact rem- 16Department of Astronomy, Cornell University, 220 Space nant (Sanders et al. 1988; Hopkins et al. 2006; Wuyts SciencesBuilding,Ithaca,NY14853,USA 17Astronomy Department, California Institute of Technol- et al. 2010). This is consistent with local stellar archae- ogy,MC249-17,1200EastCaliforniaBoulevard,Pasadena,CA ology studies which imply that massive ellipticals must 91125,USA 2 Toft et al. have short formation timescales of less than 1 Gyr, (e.g. 350−800kms−1, with a mean equivalent rotational ve- Thomas et al. 2005). locity (cid:104)v (cid:105)=392±134km/s; Tacconi et al. 2006). The c Several authors have pointed out that sub-millimeter line emitting gas of SMGs, as traced by high-J CO lines, galaxies (SMGs) may be examples of the above scenario isfoundtobespatiallyverycompact,withameansizeof (e.g. Blain et al. 2004; Chapman et al. 2005; Tacconi (cid:104)R (cid:105)=2.0±0.3kpc(Tacconietal.2006),comparableto e et al. 2006; Toft et al. 2007; Cimatti et al. 2008; Capak themeanspatialextent(cid:104)R (cid:105)=1.96±0.8kpc,ofthestel- e et al. 2008; Tacconi et al. 2008; Schinnerer et al. 2008; larpopulationsinthequiescentz∼2galaxies(Krogager Coppin et al. 2008; Michal(cid:32)owski et al. 2010a; Smolˇcić etal.2013). Wenotehoweverthatstudiesoflower-JCO et al. 2011), but see Riechers (2013) for a counter ex- lines suggest that some SMGs may have more extended ample. The SMG population is dominated by galaxies CO-disks (Ivison et al. 2011; Riechers et al. 2011a). undergoing intense, dust enshrouded starbursts. A large The median dynamical masses measured from CO(1-0) fraction of SMGs with measured CO profiles, show dou- for z∼2 SMGs, (cid:104)M (cid:105)=(2.3±1.4)×1011M (Ivison dyn (cid:12) ble peaked profiles, evident of ongoing major mergers or et al. 2011), is similar to that measured for z∼2 quies- rotation(Frayeretal.1999;Nerietal.2003;Shethetal. cent galaxies (cid:104)M (cid:105)=(2.5±1.3)×1011M (Toft et al. dyn (cid:12) 2004; Kneib et al. 2005; Greve et al. 2005; Tacconi et al. 2012). 2006; Riechers et al. 2011b; Ivison et al. 2013; Fu et al. DespitethemanysimilaritiesbetweenSMGsandz∼2 2013). Theauto-correlationlengthofSMGsissimilarto quiescent galaxies, a major obstacle in establishing an that of optically selected QSOs, suggesting that SMGs evolutionary link between the two galaxy types is their and QSOs live in similar mass haloes and that the igni- similar redshift distribution. While the quiescent na- tion of a QSO could be the event that quenches the star ture and derived ages for z∼2 quiescent galaxies sug- formation in SMGs (Hickox et al. 2012). This is consis- gest they formed at z(cid:38)3 the peak of the known SMG tent with observations suggesting that the hosts of the population was until recently found to be at z∼2 with mostluminousQSOs,i.ethoselikelyassociatedwiththe very few examples known at z(cid:38)3 (e.g. Chapman et al. formation of massive quiescent galaxies, are found to be 2005), rendering an evolutionary link between the two primarily major mergers (Treister et al. 2012; Riechers populations unlikely. Recently, improved selection tech- et al. 2008), a result which is cooborated by Olsen et al. niqueshavehoweveruncoveredasubstantialtailstretch- (2013) who find that luminous AGN in massive z ∼ 2 ing out to redshifts of z∼6 (Capak et al. 2008; Schin- galaxies must be triggered by external processes. Inter- nerer et al. 2008; Daddi et al. 2009a,b; Knudsen et al. estingly, Olsen et al. (2013) also finds evidence for low 2010; Carilli et al. 2010, 2011; Riechers et al. 2010; Cox luminosityAGNinthevastmajorityofmassivequiescent et al. 2011; Combes et al. 2012; Yun et al. 2012; Smolˇcić galaxies at z ∼ 2, suggesting that AGN play an active etal.2012a;Michal(cid:32)owskietal.2012b;Hodgeetal.2012, role in the quenching their star-formation. The correla- 2013a; Riechers et al. 2013). tion length of SMGs is similar to that of z∼2 galax- Inthispaperwepresentevidenceforadirectevolution- ies with M∗ >5×1010M(cid:12) (r0 =7.66±0.78), while arylinkbetweenthetwoextremegalaxypopulations,by z∼2 galaxies with M∗ >1011M(cid:12) cluster more strongly comparing the properties of two unique samples in the (r0 =11.49±1.26 Wake et al. 2011). COSMOS field: (i) a spectroscopically confirmed, rep- Recent advances in near infrared (NIR) spectroscopy resentative sample of compact z∼2 quiescent galaxies havemadeitpossibleforthefirsttimetoaccuratelycon- withhighresolutionHST/WFC3imaging,and(ii)asta- strain the age, dust content and past star formation his- tisticalsampleofz(cid:38)3SMGs. InSection2weintroduce toryofthebrightestz∼2quiescentgalaxiesthroughab- the samples, and in Section 3 we present our results. In sorption line diagnostics and spectral fitting in the rest particular, in Section 3.1 we show that the distribution frame-optical(Krieketal.2009;Onoderaetal.2010;van of formation redshifts for the z∼2 quiescent galaxies deSandeetal.2011;Toftetal.2012;Onoderaetal.2012; is similar to the observed redshift distribution of z(cid:38)3 van de Sande et al. 2012). These galaxies have spectra SMGs, and in Section 3.2 we compare the co-moving typicalofpoststarburstgalaxies,withnodetectedemis- number densities of the two populations. In Section 3.3 sion lines, but with strong Balmer absorption lines, sug- we derive structural properties of the z(cid:38)3 SMGs and gestingthattheyunderwentmajorstarburstswhichwere in Section 3.4 show that their stellar mass-size relation quenched 1-2 Gyr prior to the time of observation (i.e. is similar to those of z∼2 quiescent galaxies. In Sec- at 3<z<6). Several of these galaxies show evidence of tion3.5and3.6weshowthatthedutycycleofthez >3 significant dust abundance (with AV’s up to ∼ 1 mag- SMGstarburst(derivedassumingtheyareprogenitorsof nitude), and they are baryon dominated, as is the case z∼2 quiescent galaxies), is consistent with independent for local post starburst galaxies (Toft et al. 2012). In estimates, and with the formation time scale derived for combination with their extremely compact stellar pop- z ∼ 2 quiescent galaxies, assuming they formed in Ed- ulations these observations suggest that the majority of dington limited starbursts. In Section 4 we summarize the stars in z∼2 quiescent galaxies formed in intense, and discuss the results. possibly dust enshrouded nuclear starbursts, a scenario Throughout this paper we assume a standard very similar to what is observed in z∼2 SMGs. flat universe with Ω =0.73, Ω =0.27 and λ m Velocity dispersions of z∼2 quiescent galaxies mea- H =71kms−1Mpc−3. All stellar masses are derived 0 suredfromthewidthofabsorptionlinesareintherange assuming a Chabrier (2003) IMF. 300 − 500kms−1 (e.g. Toft et al. 2012; van de Sande et al. 2012), significantly higher than in local ellipticals of similar stellar mass, but comparable to the FWHM 2. SAMPLES of molecular lines in 2<z<3 SMGs (in the range 2.1. Sample of z (cid:38)3 SMGs Sub-millimeter galaxies as progenitors of compact quiescent galaxies 3 outofthese18interferometricallydetectedgalaxieshave Table 1 spectroscopicredshifts(fourareconfirmedtobeatz(cid:38)3; Sampleofz>3submillimetergalaxiesinCOSMOS.Thetop11 Capak 2009; Capak et al. 2010; Schinnerer et al. 2009; galaxiesconstitutetheS/Nlimited,relativelycompletestatistical sampleweuseforestimatingthecomovingnumberdensity. The Riechers et al. 2010; Karim et al., in prep), while for the bottomtwoarespectroscopicallyconfirmedz>3galaxieswhich remainder precise photometric redshifts (σ = weaddtothesampleforstructuralanalysisonly. Wereferto ∆z/(1+zspec) 0.09) were computed by Smolˇcić et al. (2012a). The Smolˇcićetal.(2012a)fordetailsaboutthesample. Thelisted (cid:112) z(cid:38)3 SMGs from this sample are listed in Table 1. The effectiveradiireportedarecircularized,i.e. re,c=re,m b/a, top 11 objects constitute our statistical sample. We will wherere,m istheeffectiveradiusalongthemajoraxis,andb/ais theaxisratio. re,FIR[kpc]arerestframeFIRsizesfromthe use these in the following sections to estimate the red- litterature,measuredfromhighresolutionmmobservations(see shift distribution and comoving number density of z (cid:38)3 tablenotes). ForeasycomparisontotheNIReffectiveradii,we SMGs. The bottom two objects, are additional spectro- herequoteGaussianHWHMs. scopically confirmed z(cid:38)3 SMGs in the COSMOS field which we add to the sample for structural analysis only. z re,NIR note re,FIR The flux-limited sub-mm selection ensures a relatively (kpc) (kpc) homogenous sample of the most intensely starforming AzTEC1 4.64a <2.6 unresolved 1.3−2.7c dust obscured galaxies at z (cid:38)3: Due to the negative k- AzTEC3 5.299a <2.4 unresolved <3±2d correction, the sub-mm flux detection limit corresponds AzTEC4 4.93+0.43 <2.5 unresolved - −1.11 roughly to a cut in SFR over the considered redshift AzTEC5 3.971a 0.5±0.4 HST/WFC3 - AzTEC8 3.179a <3.0 unresolved - range. Note that while a fraction of single dish detected AzTEC10 2.79+1.86 0.7±0.1 - - SMGs break up into multiple components when studied −1.29 AzTEC11-S >2.58b - notdetected - with interferometry at ≤ 2(cid:48)(cid:48) resolution, this is only the AzTEC13 >3.59b - notdetected - case for two of the galaxies studied here (AzTEC 11 and AzTEC14-E >3.03b - notdetected - 14). In the present study we assume that the close indi- AzTEC15 3.17+0.29 5.0±0.8 veryfaint - vidual components are related and count them as one in −0.37 J1000+0234 4.542a 3.7±0.2 - - thenumberdensitycalculations(thusassumingtheywill Vd-17871 4.622a 1.3±1.4 - - eventually merge into one galaxy). As the galaxies are GISMO-AK03 4.757a 1.6±0.6 HST/WFC3 - not resolved in the MIR-mm photometry, derived prop- a SpectroscopicRedshift erties (infrared luminosities, star formation rates, dust b mm-to-radiofluxratiobasedredshift c Youngeretal.(2008) masses etc) are for the combined systems. Neither of d Riechersetal.(2010) the two galaxies are detected in the optical-NIR so the derived sizes and stellar masses for the sample are not Based on dedicated follow-up studies with sub-mm- affected. interferometers(PdBI,SMA,CARMA)andoptical/mm- spectroscopy (with Keck/DEIMOS, EVLA, PdBI) to- 2.2. Far-infrared emission of the z(cid:38)3 SMGs wards 1.1 mm and 870 µm selected sources in the COS- MOS field Smolˇcić et al. (2012a) presented the redshift In order to directly constrain the SFRs, dust and gas distribution of SMGs. This sample shows a tail of z(cid:38)3 massesofthez(cid:38)3SMGs,wemadeuseofthe(sub)-mm SMGs, corresponding to a significantly larger number (AzTEC, LABOCA, MAMBO, SMA, CARMA, PdBI) density at these high redshifts than found in previous andFIR(SpitzerMIPS,HerschelPACSandSPIRE)ob- surveys (e.g. Chapman et al. 2005; Wardlow et al. 2011; servations of the COSMOS field (Sanders et al. 2007; Yun et al. 2012; Michal(cid:32)owski et al. 2012b). A possible Lutz et al. 2011; Oliver et al. 2012; Scott et al. 2008; reason for the difference is that previous surveys did not Aretxaga et al. 2011; Bertoldi et al. 2007; Younger et al. have (sub)-mm followup interferometry, and therefore 2007, 2008; Smolˇcić et al. 2012a,b). The Herschel data maybesubjecttoidentificationbiases. E.g. Hodgeetal. consistofdeepPACS100and160µmobservations,taken (2013b) show that many of the galaxies in the Wardlow as part of the PACS Evolutionary Probe (PEP, Lutz etal.(2011)samplebreakupintomultiplesourceswhen etal.2011)guaranteedtimekeyprogramme,andSPIRE studied at high resolution, which enevitably lead to mis- 250, 350 and 500µm observations taken as part of the identifications for some of the sources. Herschel Multi-tiered Extragalactic Survey (HerMES, Here we use the Smolˇcić et al. (2012a) sample to esti- Oliver et al. 2012). mate the comoving number density and other properties PACS and SPIRE flux densities were measured using of z(cid:38)3 SMGs. Our starting point is a 1.1 mm-selected a PSF fitting analysis (Magnelli et al. 2009; Roseboom sample, drawn from the AzTEC/JCMT 0.15 square de- etal.2010),guidedbythepositionofsourcesdetectedin gree survey of the COSMOS field (Scott et al. 2008), the deep COSMOS 24 µm observations from the Multi- andobservedwiththeSMAat890µmand∼2(cid:48)(cid:48) angular band Imaging Photometer (MIPS; Rieke et al. 2004) on- resolution to unambiguously associate multi-wavelength board the Spitzer Space Observatory (3σ∼45µJy; Le counterparts (Younger et al. 2007, 2009). The 17 SMGs Floc’h et al. 2009). We cross-matched our z (cid:38) 3 SMGs identified by the SMA follow-up form a statistical sam- sample with this MIPS-PACS-SPIRE catalogue using a ple as they are drawn from a signal-to-noise limited matching radius of 2(cid:48)(cid:48). Results of these matches were (S/N >4.5), and flux-limited (F (cid:38)4.2 mJy), all visually checked. For z (cid:38) 3 SMGs not included in 1.1mm 1.1mm 1.1 mm-selected sample, drawn from a contiguous area the MIPS-PACS-SPIRE catalogue because of a lack of of 0.15 square degrees. We include one more SMG MIPS counterpart, we compute their PACS and SPIRE in this sample, J1000+0234 (F = 4.8 ± 1.5 mJy, fluxdensitiesusingaPSFfittinganalysisguidedbytheir 1.1mm S/N ∼ 3), which is confirmed to be at z=4.542 positions. FurtherdetailsoftheFIRphotometryarepre- 1.1mm (Capak et al. 2008; Schinnerer et al. 2008, 2009). Nine sented in Smolˇcić et al. (in prep.). 4 Toft et al. Table 2 Far-infraredSEDpropertiesofthez(cid:38)3SMGsample. log(M(cid:63))a qPAHb γb Uminb log(Mdust)b log(LIR)b SFRb,e log(Mgas)b FIRdetectiond log(Mgas)COf [M(cid:12)] [M(cid:12)] [L(cid:12)] [M(cid:12)yr−1] [M(cid:12)] [M(cid:12)] AzTEC1 10.9+0.1 0.47% 0.070 25.0 9.1±0.1 13.36±0.09 2291±528 11.7±0.1 secure −0.1 AzTEC3 11.2+0.1 0.47% 0.290 25.0 9.3±0.1 13.37±0.04 2344±226 11.3±0.1 secure 10.7 −0.1 AzTEC4 11.2+0.1 4.58% 0.080 25.0 9.6±0.2 13.25±0.15 1778±733 11.6±0.2 tentative −0.1 AzTEC5 10.9+0.5 0.47% 0.190 25.0 9.4±0.1 13.43±0.02 2692±127 11.4±0.1 secure −0.5 AzTEC8 11.5+0.1 0.47% 0.090 25.0 9.7±0.1 13.45±0.01 2818±66 11.7±0.1 secure −0.1 AzTEC10 10.5+0.1 2.50% 0.060 5.00 9.6±0.1 12.58±0.10 380±98 11.8±0.1 secure −0.1 AzTEC11-S - 0.47% 0.040 25.0 9.6±0.1 13.30±0.01 1995±46 - secure AzTEC13 - 4.58% 0.160 2.00 9.9±0.3 12.70±0.20 501±293 - upperlimits AzTEC14-E - 0.47% 0.290 0.70 9.8±0.2 12.48±0.18 302±155 - upperlimits AzTEC15 11.2+0.1 3.19% 0.010 20.0 9.3±0.1 12.73±0.08 537±108 11.4±0.1 secure −0.1 J1000+0234 10.7+0.1 1.77% 0.150 25.0 9.3±0.1 13.17±0.09 575±275 11.8±0.4 tentative 10.4 −0.1 Vd-17871 10.9+0.1 4.58% 0.250 25.0 9.1±0.1 13.09±0.06 1230±182 11.2±0.2 secure −0.1 G.ISMO-AK03 12.1+0.1 4.58% 0.290 3.00 9.5±0.2 12.66±0.19 457±250 11.5±0.2 secure −0.1 a DerivedusingMAGPHYSfromtheoptical-FIRSED.Theerrorsaretheformalerrorsassociatedwiththefit, anddonotincludesystematicerrorswhich canbeupto±0.5Dex,seeSection2.3 b The DL07 model describes the interstellar dust as a mixture of carbonaceous and amorphous silicate grains. Here we list the best fitting values of its 4 free parameters: (i) qPAH which controls the fraction of dust mass in the form of PAH grains. (ii) γ which controls the fraction of dust mass exposed to a power-law(α=2)radiationfieldrangingfromUmintoUmax;therestofthedustmass(i.e.,1−γ)beingexposedtoaradiationfieldwithaconstantintensity Umin. (iii)Umin whichcontrolstheminimumradiationfieldseenbythedust(Umax isfixedtoavalueof106). (iv)Mdust whichcontrolsthenormalization oftheSED. b QuantitiesderivedfromthebestfittingDL07models(seeSection2.2). d “Secure”: ThesourceisrelativelyisolatedanddetectedatS/N>3. “Tentative”: ThesourceisdetectedatS/N>3,butthefluxdensityestimatesmaybe affectedbybrightclosebyobjects. “Upperlimit”: ThesourceisnotdetectedatS/N>3. e SFRsarenotoriouslymodeldependent,e.g,fromadetailedanalysisofallavailabledataforAzTEC-3,andassumingatopheavyIMF,Dweketal.(2011) foundasignificantlylowerSFRthanderivedherefromtheDL07fits. f GasmassesderivedfromCOobservations(Schinnereretal.2008;Riechersetal.2010) Among the 13 z(cid:38)3 SMGs, 9 have secure mid/far- comparable to or larger than the derived stellar masses: infrareddetections,2havetentativemid/far-infraredde- (cid:104)f (cid:105)=(cid:104)M /(M +M )(cid:105)=0.71±0.03, in agreement g gas (cid:63) gas tections and 2 are undetected at infrared wavelengths. with the high gas fractions found in previous studies From the FIR–mm SED of the z(cid:38)3 SMGs, we infer of high redshift SMGs (e.g. Carilli et al. 2010; Riechers their infrared luminosities and dust masses using the et al. 2011a). We caution however, that gas masses dust model of Draine & Li (2007, hereafter DL07) as de- estimated from FIR SED fits are relatively uncertain scribed in detail in Magnelli et al. (2012). The infrared (potentially up to a factor of 5 -10). E.g. in Table 2 we luminosity(L )isderivedbyintegratingthebestfitting list gas masses for two objects in our sample which have IR normalized SED templates from the DL07 library from independent estimates derived from CO line emission. rest-frame 8 to 1000µm. From these we can accurately ThesearesignificantlydifferentfromourSEDestimates. estimate the star-formation activity of the z(cid:38)3 SMGs, The main factors contributing to the uncertainties in usingthestandardL -to-SFRconversionof(Kennicutt the SED estimates are that the sub-mm measurements IR 1998), assuming a Chabrier IMF : donttracecoldgasverywell, inwhichthe(sub)mm/CO flux ratio is much lower than in the starburst nucleus, SFR[M(cid:12)yr−1] = 10−10LIR[L(cid:12)]. (1) but where a lot of the gas mass may reside. The others are the metallicity correction (which has a large scatter) Finally we estimate the gas and the assumption about the gas-to-dust ratio. The masses of the sample through main factors contributing to the uncertainty of the log(M /M )=−0.85∗Z+9.4 (Leroy et al. 2011), gas dust CO measurements is the assumed α which can be where Z=2.18×log(M )−0.0896∗log(M )2−4.51 CO (cid:63) (cid:63) uncertainbyafactor>2,andtheexcitationcorrections, (Erb et al. 2006; Genzel et al. 2012) 18. This method which can be uncertain by a factor of ∼2−4. has been used successfully in the local Universe (e.g. Leroy et al. 2011; Bolatto et al. 2011) as well as at 2.3. Stellar Mass Estimates for the z (cid:38)3 SMGs high redshift (Magdis et al. 2011, 2012; Magnelli et al. 2012). Assumptions and limitations of this method We estimate stellar masses of the z (cid:38) 3 SMGs from in the case of high redshift galaxies are extensively their UV-MIR (8µm) broad band photometry as de- discussed in Magnelli et al. (2012). Results of the scribed in Smolˇcić et al. (in prep.). Briefly, stellar FIR SED fits and derived quantities are summarized masses were derived by fitting the observed broadband in Table 2, and used in the following analysis to es- UV-MIR spectral energy distributions with the MAG- tablish an evolutionary link between z (cid:38)3 SMGs and PHYS code (da Cunha et al. 2008). The stellar com- quiescent z ∼2 galaxies. The derived gas masses are ponent in the MAGPHYS models is based on Bruzual &Charlot(2003)stellarpopulationsynthesismodelsas- 18thusmakingtheassumptionthatthemass-metallicityrelation suming various star formation histories (exponentially- atz∼2applytogalaxiesatz>3 declining SFHs (with random timescales) + superim- Sub-millimeter galaxies as progenitors of compact quiescent galaxies 5 posed stochastic bursts) and a Chabrier (2003) IMF. ofz (cid:38)3SMGsdescribedinSection2.1. Duetothesmall ThestellarmassesfortheSMGs,andtheirformaluncer- number of galaxies in both samples, a one to one corre- taintiesdrawnfromtheprobabilitydistributionfunction spondence is not expected. However, we stress that the (generated from the χ2 fit values by MAGPHYS) are two distributions are similar, with a peak at z ∼3 and a given in Tab. 2. We note however, that stellar masses tailtowardshigherredshifts. Atwo-sampleKolmogorov- for SMGs are strongly dependent on the assumed star Smirnov(K-S)testyieldsastatisticof0.29withap-value formation histories, and may lead to systematic discrep- of54%,andisthusnotinconsistentwiththetworedshift anciesof±0.5dexgivendifferentassumptionsandstellar distributionsbeingdrawnfromthesameparentdistribu- populationsynthesismodels(seeTable.1inMichal(cid:32)owski tion. et al. 2012a), and whether or not emission lines are included in the templates (Schaerer et al. 2013). For ex- ample, using the double SFHs implemented in GRASIL (Silva et al. 1998; Iglesias-Páramo et al. 2007), we find systematically higher stellar masses, consistent with the results from Michal(cid:32)owski et al. (2010b). On the other hand, dynamical mass considerations based on CO line observations for two objects in our sample (Schinnerer et al. 2008; Riechers et al. 2010) suggest lower stellar masses than inferred by MAGPHYS. Hence, here we adoptthemiddlevalues,i.e.thestellarmassescomputed by MAGPHYS+BC03, noting that these may be subject to systematic uncertainties. 2.4. Sample of z ∼2 Compact Quiescent Galaxies It is well established from deep multi-waveband photometric surveys, that a substantial population of qui- Figure 1. Comparisonoftheredshiftdistributionofz(cid:38)3SMGs escent massive galaxies with extremely compact struc- and the formation redshifts of z ∼ 2 quiescent galaxies. The red histogram shows the distribution of formation redshifts esti- ture exists at z ∼2 (Daddi et al. 2005; Toft et al. 2005; mated for a spectroscopically confirmed sample of compact qui- Trujillo et al. 2006; Toft et al. 2007; Franx et al. 2008; escent galaxies at z∼2, from their observed redshift and derived Toft et al. 2009; Williams et al. 2010; van Dokkum et al. luminosity weighted ages of their stellar populations (K13). The 2010; Brammer et al. 2011; Szomoru et al. 2011; Dam- blue histogram shows the distribution of redshifts of the statistical sample of z(cid:38)3 SMGs. Note that the galaxies which only janov et al. 2011; Szomoru et al. 2012; Newman et al. havelowerlimitsontheredshiftshavebeenplacedinthebinscor- 2012; Cassata et al. 2013). Samples of spectroscopically responding to those limits, and that the histogram includes two confirmed, z ∼2 quiescent galaxies with accurate stel- galaxieswherethebestfittingredshiftisslightlybelow3, butfor lar population model fits and high angular resolution which a z > 3 photometric redshift solution falls within the 99% confidence interval. The smooth curves shows probability density space based NIR imaging are much more sparse (van distributions (kernel density estimates (KDEs)) of the two popu- Dokkum et al. 2008). As a high quality comparison set lations. Thetworedshiftdistributionsaresimilar,consistentwith to the z >3 SMGs we use the sample of Krogager et al. thehypothesisthatz(cid:38)3SMGsarethedirectprogenitorsofz∼2 (2013,K13hereafter). Thissampleconsistof16spectro- cQG. scopically confirmed massive quiescent galaxies, selected from the 3DHST survey in the COSMOS field by re- quiring strong 4000˚A breaks in the grism observations. 3.2. Co-moving Number Densities As shown in K13 this effectively selects a representative The next step in establishing an evolutionary connec- sample of massive (logM>10.9) evolved quiescent galax- tionbetweenz (cid:38)3SMGsandquiescentgalaxiesatz ∼2 iesaroundz ∼2. ThehighS/Ngrismspectraaroundthe is to compare their co-moving number densities. The break in combination with multi-waveband photometry comoving number density of massive quiescent galaxies from the COSMOS survey allows for strong constraints as a function of redshift is well constrained from photo- on the stellar populations including stellar masses, dust metric redshift and stellar population model fits to deep contents, mean stellar ages, i.e the time elapsed since multi-waveband photometry (e.g. Williams et al. 2010; the last major episode of star formation, as well as for- Brammeretal.2011). Brammeretal.(2011)studiedthe mation redshifts (derived from the stellar ages). The number density evolution of star forming and quiescent sample is also covered by high resolution NIR imaging galaxies(separatedusingtheirrest-frameUVJcolors)in with HST/WFC3 from the CANDELS survey (Grogin asamplecompleteatstellarmasseslog(M/M )>11out (cid:12) et al. 2011; Koekemoer et al. 2011) yielding accurate toz ∼2.2. Hereweestimateacomovingnumberdensity constraints on the rest-frame optical surface brightness of6.0±2.1×10−5Mpc−3 forquiescentgalaxiesatz ∼2 profiles, and effective radii (r ). with log(M/M )>11 as the mean of the densities mea- e (cid:12) sured at z =1.9 and z =2.1 by Brammer et al. (2011). 3. RESULTS The error includes a contribution of cosmic variance of 3.1. Redshift Distributions 12% (Moster et al. 2011). Fromthespectroscopicredshiftsandmeanstellarages Toderivethesurfacenumberdensityofz (cid:38)3SMGswe availableforthequiescentz ∼2galaxysampledescribed take all SMGs from the 1.1 mm-selected COSMOS sam- in Section 2.4 we can estimate the distribution of their plethatcouldlieatz >3giventheirlowerorupper99% formationredshifts. InFigure1thisdistributioniscom- confidencelevelsofthephotometricredshift(reportedin paredtotheobservedredshiftdistributionofthesample Tab. 4 in Smolˇcić et al. 2012a). We then derive an aver- 6 Toft et al. agevalueofthesurfacedensitybytakingthemostproba- imaginggiventhehigherresolution(FWHM∼0.2(cid:48)(cid:48)). For blephotometricredshift(orspectroscopicredshiftwhere the remaining galaxies we use deep NIR imaging pro- available)19, and the lower20 and upper21 surface den- vided by the UltraVista survey (5σ AB depths range sity values by taking the limiting redshifts correspond- from 23.7 in the K-band to 24.6 in the Y-band, Mc- ing to the 99% confidence intervals of the photometric Cracken et al 2012). The resolution of these observa- redshifts. This yields a surface density of z (cid:38) 3, bright tions is lower (FWHM∼0.8(cid:48)(cid:48)), but it has been demon- (F (cid:38) 4.2 mJy) SMGs of 60±10 deg−2. Note that stratedthatrelativelyunbiasedsizes(downtoafraction 1.1mm conservativelyexcludingfromtheanalysisall3SMGsin of the FWHMPSF) can be derived from such data when the sample that are not significantly detected at other the S/N is high and the PSF is well known (e.g. Tru- wavelengths (AzTEC11S, AzTEC13, AzTEC14E), and jillo et al. 2006; Toft et al. 2009; Williams et al. 2010). thusonlyhavelowerredshiftlimits,yieldsasurfaceden- To increase the S/N we stack the Y, J, H and K band sity of 40 deg−2. images. Thederivedsurfacedensityvaluesforz (cid:38)3SMGsmay Postage stamp images of the galaxies are shown in the be subject to systematic effects. The completeness of top panel of Figure 2. NIR counterparts of 10 of the the AzTEC/JCMT COSMOS survey, shown in Fig. 8 13 sources are detected, 8 of which have relatively high in Scott et al. (2008), is roughly 50%, 70%, and 90% signal to noise (the faintest ones have S/N∼10). We fit at F = 4.2,5, and 6 mJy. Taking this into ac- 2DSersicmodelstotheirsurfacebrightnessdistributions 1.1mm count in combination with the deboosted 1.1 mm fluxes with galfit (Peng et al. 2002), using similarly stacked of the SMGs (see Younger et al. 2007, 2009) yields that images of nearby stars as PSF models. We find the ser- the derived surface densities could be roughly a factor sic n to be relatively poorly constrained from the data. of 1.5 higher than that reported above. On the other Leavingitfreeinthefitsinallcasesresultsinlowvalues hand, the AzTEC/JCMT COSMOS field may be over- n < 2, with a median value of (cid:104)n(cid:105)=0.6±0.1, but with dense(Austermannetal.2009), whichwouldimplythat relatively large errors. To limit the degrees of freedom the true z (cid:38)3 SMG surface density averaged over larger in the fits we therefore fix it to n = 1. The reduced χ2 area would be lower. of these fits are in all cases similar to those with n free, Our best estimate of the co-moving number density of and better than fits with n fixed to 4. 3<z <6SMGsis2.1±0.4×10−6 Mpc−3,significantly The best fitting effective radius encompassing half the lower than the space density of z ∼2 quiescent galaxies. light of the model, are reported in Table 1. Half of the This is expected as z (cid:38)3 galaxies only enter the mm- detected galaxies (5) have close companions. In these selection criterion during their intense starburst phase. cases we model both components simultaneously and re- InSection3.5weusetheobserveddifferenceinco-moving port the parameters for the main component (closest to numberdensitiestoconstrainthedutycycleoftheSMG the center of the mm-emission). Also listed in Table 1 starbursts. arerestframeFIRsizesfortwogalaxiesinoursamplede- rivedfrominterferometricsub-mmimagingobservations. 3.3. Rest-frame UV-Optical Structure of z>3 SMGs: These agree with the sizes derived from the NIR data. Disks, Spheroids or Mergers? The restframe FIR sizes directly measures the extend The high redshifts and large amounts of dust in the of the starforming regions which we hypothesize evolves z (cid:38)3 SMGs renders them extremely faint in the rest- intothecompactstellarpopulationsatz=2,sotheagree- frame UV and optical, despite their high stellar masses ment is encouraging. and star formation rates. This makes it challenging to Our analysis shows, that apart from being very com- constrain their structure. To achieve the least biased pact, the z > 3 SMGs are not isolated, smooth single estimates of the distribution of stellar mass one would component galaxies. All the detected galaxies show evi- need to study the surface brightness distributions in the dence of close companions or clumpy sub-structure (see rest-frame optical/NIR, or as close to these wavebands Figure2). Fromtheseobservationsalone, itisnotpossi- as possible. Ideally, the observations would be done in ble to deduce whether this is due to chance projections, the observed mid infrared, but at the low spatial resolu- ongoing minor/major mergers, or perhaps multiple star tionofcurrentfacilities(e.g.Spitzer)thegalaxiesremain forming regions in individual galaxies, as resolved pho- unresolved. Until JWST becomes operational the best tometryandspectroscopyisnotavailable. Wenotehow- that can be achieved is to study the galaxies in the ob- everthatthetwogalaxieswithHST/WFC3dataappear served NIR. For most of the galaxies in the sample this to have well separated individual components of com- wavelength range probes rest-frame wavelengths around parable brightness, favoring the merger interpretation. the 4000 ˚A break, and thus should be a relatively good This is consistent with direct observational evidence for SMGs being major mergers, i.e. having multiple close tracer of the stellar mass distribution. For two galaxies componentsatthesameredshift(e.g.Fuetal.2013;Ivi- (AzTEC5 and GISMO-AK03) we use space based NIR son et al. 2013). Simulations suggest that the timescale imaging with HST/WFC3, which is available from the for major mergers are typically 0.39 ± 0.30 Gyr (Lotz CANDELS survey. This is preferable to groundbased et al. 2010). The cosmic time available between the ob- 19 Taking the most probably photometric redshift yields that served epoch of the SMGs at z=3-6 and their proposed 9 SMGs (AzTEC1, AzTEC3, AzTEC4, AzTEC5, AzTEC8, remnants at z=2 is 1-2 Gyr. If (some of) the SMGs are AzTEC13,AzTEC14E,AzTEC15&J1000+0234),areatz>3 major mergers, there is thus sufficient time available for 20 Inthiscase8SMGs(AzTEC1,AzTEC3,AzTEC4,AzTEC5, them to coalesce to a single quiescent remnant at z =2. AzTEC8,AzTEC13,AzTEC14E&J1000+0234),areatz>3 21 In this case 10 SMGs (AzTEC1, AzTEC3, AzTEC4, In the local universe most star forming galaxies are AzTEC5,AzTEC8,AzTEC10,AzTEC11S,AzTEC13,AzTEC14E wellfitbyexponentialdiskprofilescorrespondington=1 &J1000+0234),areatz>3 (Wuyts et al. 2011), while irregular galaxies and (pre- Sub-millimeter galaxies as progenitors of compact quiescent galaxies 7 Figure 2. Galleryofz>3SMGs. Top: NIRimages,8”onaside. ForAzTEC5andGISMO-AK03weshowHST/WFC3F160Wimages fromtheCANDELSsurvey. FortherestweshowstackedY,J,HandKbandimagesfromtheUltraVISTAsurvey. Middle: Sersicn=1 galfit models of the 2D surface brightness distributions of the SMGs and their nearby companions. Bottom: Residual images, i.e. the originalimagesinthetoppanel,subtractedthebestfittingmodelsinthemiddlepanel. coalescence) mergers are often best fit by models with lower n-values (n<1). At the S/N and resolution of the galaxies in the Ultravista data the confidence in derived Sersic parameters are limited. However, the per- sisting low values found for the whole z > 3 SMG sample,includingthetwogalaxieswiththehigherresolution HST/WFC3 data, suggests that the galaxies are more consistent with disks or mergers than spheroids. A similar conclusion was found for a sample of 22 SMGs at 1 < z < 3 with HST/WFC3 data (Targett et al. 2012) forwhichthemajoritywerebestfitbylownSersicmod- els, with a mean (cid:104)n(cid:105)=1.2±0.1. If z >3 SMGs are progenitors of z ∼2 quiescent galaxies, then their evolution must include a transformation of their surface brightness profiles which increase their Sersic indices, as surface brightness profiles of quiescent galaxies at z ∼2 are Figure 3. Comparison of the stellar mass-size plane of z (cid:38) 3 morecentrallyconcentrated(Wuytsetal.2011;Szomoru SMGs,z∼2quiescentgalaxiesandlocalgalaxies. Theredpoints et al. 2011; Bell et al. 2012), e.g. the sample of K13 has represent z∼2 quiescent galaxies. Black points represent z (cid:38) 3 (cid:104)n(cid:105)=4.0±0.1. Wediscussapossiblemechanismforthis SMGs. For the latter, the solid error bars represent the errors associated with the MAGPHYS SED fits. The dotted error bars transformation in Section 4. arepossiblesystematicerrorsthatextendtovalueswederiveusing the Micha(cid:32)lowski et al. (2010a) templates. The grey cloud shows the mass-size distribution of massive local galaxies in the SDSS survey. The mass-size distributions of SMGs is similar to that of 3.4. Mass-Size relation z∼2quiescentgalaxies,significantlyoffsetfromthelocalrelation, Combining the derived stellar masses and effective consistent with a direct evolutionary connection between the two populations. radii of the 3 < z < 6 SMGs, in Figure 3 we compare theirstellarmass-sizedistributiontothatofz =2quies- 3.5. Duty Cycle of SMG Starbursts centgalaxiesandofmassiveearlytypegalaxiesinthelo- The observed space density of z (cid:38)3 SMGs is a factor caluniverse. TwoofthetenNIR-detectedSMGsarerel- of ∼30 lower than the space density of z ∼2 quiescent ativelyextendedwitheffectiveradiicomparabletothose galaxies(seeSection3.2). However,theSMGsonlyenter in local galaxies of similar mass. Both of these (AzTEC the sub-mm selected (F (cid:38)4.2 mJy) sample during 10 and AzTEC 15) appear from their NIR images to be 1.1mm their intense starburst phase where they have very high ongoingmergers. Theremaining8galaxiesareextremely star formation rates. The duration of this phase, i.e. compact, with r (cid:46)2.5 kpc. Four are unresolved in the e the duty cycle t , which ends when the supply of gas Ultravistadata. Fortheseweadoptupperlimitsontheir burst is depleted or the star formation is quenched, e.g. by effective radii corresponding to 0.5×FWHM . PSF feedback from supernovae or active galactic nuclei, has The stellar mass-size distribution of the 3 < z < been estimated to be in the range 40-200 Myr, based 6 SMGs is similar to that of z ∼2 quiescent galax- on gas depletion timescales (Greve et al. 2005; Tacconi ies. Both populations are smaller by an average fac- etal.2006;Riechersetal.2011c)andclusteringanalysis tor of ∼ 3 than local galaxies of similar mass. From (Hickox et al. 2012). If we assume that all the z (cid:38)3 the derived quantities we can infer the mean inter- SMGsevolveintoz ∼2quiescentgalaxies,andthatthey nal stellar mass surface densities within the effective onlyundergooneSMGphasewecanestimatetheaverage radius (Σ=0.5M /πr2) of the z > 3 SMGs and (cid:63) e dutycycleoftheirstarburstsfromtheobservedcomoving z = 2 compact quiescent galaxies (cQGs) which we number densities of the two populations, as find to be similar (cid:104)log(Σ)(cid:105) ∼9.9±0.1M kpc−2, SMGs (cid:12) (cid:104)log(Σ)(cid:105) ∼9.8±0.1M kpc−2 morethananorderof tburst =tobs×(nSMG,z(cid:38)3/nq,z=2), (2) cQGs (cid:12) magnitudehigherthaninlocalearlytypegalaxiesofsim- where t is the cosmic epoch corresponding to the red- obs ilar mass. This is consistent with a picture where the shift interval 3<z <6 from which the z (cid:38)3 SMGs are SMGs passively evolve into compact quiescent galaxies selected. Using the comoving number densities we can after their starbursts are quenched. thus constrain the duty cycle of the SMGs to t = burst 8 Toft et al. 42+33Myr. This number however does not include pos- at high rates 500−3000M yr−1, close to the Eddington −15 (cid:12) sible systematics uncertainties on the number density of limit. E.g. (Younger et al. 2010) estimated the maxi- SMGs discussed in Section 3.2. If we conservatively as- mum starformation rate of AzTEC4 and AzTEC8 to be sume the two extreme cases where (i) the SMG sam- intherange1900−3800M yr−1,comparabletotheval- (cid:12) ple is 100% complete, and the field is three times over- ues derived here (see Tab.2). dense, and (ii) the sample is a factor of 1.5 incomplete In the following we investigate if the observed proper- butnotoverdense,thederivedtimescaleareintherange ties of z ∼2 quiescent galaxies are consistent with hav- 14<t <62Myr. The systematic uncertainties on ing formed under such conditions. Assuming that z ∼2 SMG the timescale is thus of the order of 24 Myr. There- quiescent galaxies formed in Eddington limited maxi- fore our constraints on the average dutycycle in z (cid:38)3 mumstarbursts,wecanestimatethemaximumSFRand SMGs is t =42+40Myr, where the errors have been the duration of this burst, from the observed size, ve- burst −29 added in quadrature. This value is consistent with the locity dispersion and stellar mass of the quiescent rem- independently estimated duty cycles based on gas deple- nants. In Figure 4 the red curve shows the distribution tiontimescales,thusaffirmingtheideathatz (cid:38)3SMGs of SFRMAX for the sample of z ∼2 quiescent galaxies are progenitors of z ∼2 quiescent galaxies. The derived described in Section 2.4, calculated from Equation 3, as- timescale does not depend strongly on the z =6 upper suming κ100 = 1, Dkpc =2re,c (where re,c are the ef- limit adopted for the SMG redshift distribution. Adopt- fective radii measured for the individual galaxies) and ing limits of z=5.5 or z=7 instead, leads to timescales of σ =(cid:104)σ(cid:105)/400kms−1, where (cid:104)σ(cid:105)=363±100kms−1 is 400 44 and 37 Myr, respectively. We note that the validity the mean velocity dispersion measured for z ∼2 quies- of the timescale calculation presented here, relies on the centgalaxiesinthelitterature(Toftetal.2012). Weuse assumption of a direct evolutionary connection between this mean value as measured velocity dispersions for the the two populations, implying that all z = 2 quiescent K13 sample are not available. galaxies were once z > 3 SMGs, and all z > 3 SMGs There is a good general correspondence between the evolve into z =2 quiescent galaxies. SFR distributionofquiescentz ∼2galaxies,andthe MAX SFR distribution of z (cid:38)3 SMGs. The SFR distri- 3.6. Star formation Rate and Timescale of z=2 MAX butionpeaksathigherSFRsthantheobserveddistribu- Quiescent Galaxies During their Formation tion in z (cid:38)3 SMGs, indicating that some of the z ∼ 2 We can infer a lower limit on the star formation rate quiescent galaxies may have formed in starbursts with of the z=2 quiescent galaxies during their formation by sub-Eddington SFRs. Also plotted in Figure 4 (b) is the assuming that they started forming stars at z = 10 and duration of this “maximum starburst” did so at a constant rate until their inferred formation redshifts. The minimum average SFR needed to acquire tburst =∆M(cid:63)/SFRMAX (4) their observed stellar masses at z=2 calculated in this assuming a constant star fomation rate SFR = SFR way is (cid:104)SFR (cid:105) = 115±5M yr−1. This is a factor of max min (cid:12) during the burst, and that all the stellar mass of the >3largerthantheobservedaverageSFRinstar-forming z∼2 quiescent galaxies was created during this burst, Lyman break galaxies (LBGs) at z > 3 (Carilli et al. i.e. ∆M =M . While consistent within the errors, 2008). Furthermore,thespacedensityofz ∼2quiescent (cid:63) (cid:63) the mean derived timescales for Eddington limited star- galaxies with logM /M >11, is 5, 10 and >100 times ∗ (cid:12) bursts is about a factor of two longer than the starburst larger than that of similar mass LBGs at z=4,5 and 6 timescalederivedfromcomparingcomovingnumberden- respectively (Stark et al. 2009). Their progenitors must sities. Thiscanbeaccountedforbychangingsomeofthe therefore have had much larger SFRs and are missing assumptions, e.g., if the SMG starbursts are triggered from LBG samples. This suggests that they must be by major mergers, a fraction of the stellar mass must dust obscured starburst galaxies. havebeenformedintheprogenitorgalaxies, priortothe Basedontheobservedlinewidthsandcompactspatial merger. In Figure 4 (c) we show that if we assume that extentofmolecularlineemittingregions,SMGsareoften only half of the observed stellar mass in z ∼2 quiescent arguedtobemaximumstarbursts,i.etobeformingstars galaxies was created in a z (cid:38)3 Eddington limited star- atarateclosetotheEddingtonlimit. Assumingaspher- burst, i.e. ∆M =0.5M , there is excellent agreement ical symmetric geometry, an isothermal sphere density (cid:63) (cid:63) between the derived timescales, consistent with the idea structure, a small volume filling factor for molecular gas that z (cid:38)3 SMGs are the progenitors of z ∼2 quiescent and a Chabrier IMF, based on Thompson et al. (2005), galaxies. Interestingly this is consistent with the results Younger et al. (2010) approximate this “maximum star of Michal(cid:32)owski et al. (2010b) who found that on average formation rate” as ∼ 45% of the stellar mass in a sample of z >4 SMGs SFR =480σ2 D κ−1 [M yr−1] (3) was formed in their ongoing starbursts. If half the stel- MAX 400 kpc 100 (cid:12) larmassformedpriortothemergerthatignitetheSMG where σ is the line-of-sight gas velocity dispersion in 400 starburst, an implication is that the merger progenitors unitsof400kms−1,κ istheopacityinunitsofcm2g−1 100 must have been gas rich star forming galaxies, in agree- (usually taken to be ≈1, Murray et al. 2005; Thompson ment with the high gas fractions found in high redshift et al. 2005), and D is the characteristic physical scale kpc star forming galaxies (Tacconi et al. 2013) of the starburst (usually approximated as the Gaussian FWHM of the line emitting region). In Figure 4, the 3.7. Additional Stellar Mass Growth and Quenching of blue curves show probability distributions for a 1000 re- alizationsofongoingSFRsinthez (cid:38)3SMGs,estimated the z (cid:38)3 SMGs from their total infrared luminosity and associated er- The similar mass-size distribution of the z (cid:38)3 SMGs rors, through Equation 1. The SMGs are forming stars and z ∼2 quiescent galaxies is in agreement with what Sub-millimeter galaxies as progenitors of compact quiescent galaxies 9 Figure 4. Comparison of the SFRs and starburst timescales derived for the z (cid:38)3 SMGs z ∼2 quiescent galaxies. Left: The red curve showtheprobabilitydensitydistribution(KDE)ofSFRsofthez∼2quiescentgalaxiesduringtheirformation,calculatedassumingthey formedinEddingtonlimitedstarbursts. Thebluecurvesshowprobabilitydistributionsfor1000realizationsofongoingSFRsinthez(cid:38)3 SMGs, estimated from their total infrared luminosity and associated errors. The two distributions span the same range, in support of a evolutionary connection between quiescent galaxies and SMGs. Middle: Probability density distribution of the duration of the cQG starbursts,calculatedassumingalltheirobservedstellarmassformedinEddingtonlimitedbursts. Thegreyareaindicatestheconstraints onthedutycycleoftheSMGstarburstsderivedfromtheirnumberdensity. Right: Sameasthemiddleplot,butassumingthatonlyhalf ofthez∼2quiescentgalaxies’stellarmassformedintheEddingtonlimitedburst. Thetwoindependentmeasuresoft areconsistent, burst inagreementwithz(cid:38)3SMGsbeingprogenitorsofz∼2quiescentgalaxies onewouldexpectifthez (cid:38)3SMGsevolvepassivelyinto the mechanism needed to transform the observed low- z ∼2 quiescent galaxies, after they have been quenched. n disk-like surface brightness profiles observed in SMGs Prior to the quenching however the ongoing starburst to the higher n bulge-like profiles observed in quiescent will increase the stellar masses of the galaxies. In Fig- galaxiesatz ∼2(Wuytsetal.2011;Szomoruetal.2011; ure 5 we show that the distribution of stellar masses in Bell et al. 2012). Most of the stellar mass will be added thez (cid:38)3SMGsisbroaderthanthatoflog(M/M )>11 inthenuclearregionsoftheSMGs,whichislikelyhighly (cid:12) quiescent galaxies at z ∼2. We can estimate the growth obscured by dust. Once the quenching sets in and most of stellar mass in the individual z (cid:38) 3 SMGs from their of the dust is destroyed or blown away, a more centrally gasmasses,inferredfromtheFIRSEDfits(seeTable2). concentrated surface brightness distribution could be re- Fromthesewecanestimatethefinalstellarmassesofthe vealed. Note that if, as assumed here, only 10% of the z (cid:38)3 SMGs if we assume a star formation effeciency, i.e large derived gas masses in the z (cid:38) 3 SMGs is turned the fraction of gas that is turned into stars during the intostarsduringtheremainderoftheburst,thefollowing starburst. In the simulations of Hayward et al. (2011) quenchingmechanismmustbehighlyeffecientatheating the gas fraction decrease from 45% to 40% in isolated or expelling the substantial amounts of leftover gas. A disks and from 17.5% to 15% in merging galaxies, from possible mechanism for expelling the gas is through out- the peak of the starburst to when it ends, corresponding flows, driven by strong winds associsted with the max- toadecreaseingasmassof5%and15%duringthistime. imum starbursts. Tentative evidence for such outflows If we assume that this gas is turned into stars, and that have recently been observed in the 163µm OH line pro- weareobservingtheSMGsatthepeakoftheirstarburst, fileinanSMGatz=6.3(Riechersetal.2013). Westress the models thus indicate that ∼10±5% of the observed that the large systematic uncertainties on the derived gas mass in the z (cid:38) 3 SMGs will be turned in to stars stellar masses for the SMGs could potentially influence during the remainder of the burst. In Figure 5 we com- our conclusions. parethefinalstellarmassdistributionofthez (cid:38)3SMGs with that of quiescent z ∼2 quiescent galaxies, assum- 4. SUMMARYANDDISCUSSION ing that 10% of the derived gas mass in the z (cid:38)3 SMGs 4.1. The Link between z (cid:38)3 SMGs and z ∼2 Compact, are turned into stars before the starbursts are quenched. Quiescent Galaxies The two distributions are similar, with a K-S test statis- In this paper we presented evidence for a direct evo- tic of 0.33 and a probability of 67%, in agreement with lutionary connection between two of the most extreme a direct evolutionary link between the two populations. galaxytypesintheuniverse, thehighestredshift(z (cid:38)3) ThemassincreasefromthetimetheSMGsareobserved SMGs which host some of the most intense starbursts uptotheendofthestarburstwilllikelynotsignificantly known, and quiescent galaxies at z ∼2 which host the increase the effective radii, since the process is highly densest conglomerations of stellar mass known. The dissipative, resulting in a slight horizontal shift in the comparison was motivated by the recent discovery of a M −r plane (blue points in Figure 3). The continued (cid:63) e significantpopulationofSMGat3<z <6andhighres- starbursts and subsequent quenching, may also provide olutionimagingandspectroscopicstudiesofz ∼2quies- 10 Toft et al. ies spend above the main sequence of star formation t <70Myr(Wuytsetal.2011). Importantly, asour burst estimate of the SMG starburst timescale is based only on number density arguments, it is relatively indepen- dentonassumptionsoftheunderlyingstellarinitalmass function(IMF),whichisalargepotentialsystematicun- certainty, e.g. in depletion timescale estimates. Based on stellar masses derived from UV-MIR photometry and sizes derived from deep NIR imaging, we have shown that the mass-size distribution of the z (cid:38)3 galaxies is remarkably similar to that observed for compact quiescent massive galaxies at z ∼2, with similar mean internal stellar mass surface densities (cid:104)log(Σ)(cid:105)∼9.8M kpc−2. The surface brightness distri- (cid:12) butions of the z (cid:38)3 SMGs are best fit by Sersic models withlowSersicnparameters,typicaloflocalstarforming diskgalaxiesormergers,andthemajorityshowmultiple components or irregularities indicative of ongoing merging and/or clumpy structure. Manysimilaritiesbetweenz ∼2quiescentgalaxiesand SMGs exist: they have similar stellar masses, characteristic internal velocities, dynamical masses, sizes, cor- relation lengths etc. Millimeter measurements of z (cid:38)3 SMGs in continuum and CO show signatures of merging or rotation (Younger et al. 2008, 2010; Riechers et al. 2011b,a), with molecular emission line widths in the range 300 − 700 km s−1 (with a few outliers), and a mean (cid:104)FWHM(cid:105) = 456±253 km s−1 (Schinnerer et al. 2008; Daddi et al. 2009a; Coppin et al. 2010; Riech- ers et al. 2010, 2011b,a; Swinbank et al. 2012; Wal- ter et al. 2012) similar to stellar velocity dispersions σ =300−500kms−1 measuredinz ∼2quiescentgalax- ies. Forexample,forAzTEC3,atz =5.3,Riechersetal. (2010) measured a CO linewith of 487km s−1, and a gas depletion timescale of 30 Myr, similar to the SMG starburst timescale derived here. At the depth and resolution of the present data, it is impossible to make strong claims about how many z (cid:38) 3 SMGs are in the process of merging. However all the detected galaxies show Figure 5. Redhistogramsshowthedistributionofstellarmasses evidence of close companions, multiple components or tinhelobgl(uMe/hMis(cid:12)to)g>ram11sqhuoiwesctehnetdgiastlarixbiuestioant zof∼st2e.llaInr mthaessteospinpatnheel clumpy structure, and have low derived Sersic indices, z(cid:38)3 SMGs. In the bottom panel the blue histogram show the consistent with expectations for merging galaxies. In finalstellarmassesofthez(cid:38)3SMGsassumingthat10%±5%of particular the two galaxies with HST/WFC3 data ap- theirderivedgasmassisturnedintostarsduringtheremainderof pears to be major mergers. theongoingstarburstHaywardetal.(2011). The evidence presented in this paper is in support of a direct evolutionary connection between z(cid:38)3 SMGs, cent galaxies which show that the majority of their stars throughcompactquiescentgalaxiesatz ∼2,togiantel- likelyformedinmassivenuclear,possiblydusteshrouded lipticalgalaxiesinthelocaluniverse. Inthisscenario(il- starbursts in this redshift range. From a unique flux- lustratedinFigure6)gasrich,majormergersintheearly limited statistical sample of z (cid:38)3 SMGs in the COS- universe, trigger nuclear dust enshrouded starbursts22, MOS field, we have put robust constraints on their co- which on average last 42+40 Myr, followed by star for- moving number density, which we then put in context −29 mationquenching,eitherduetogasexhaustion,feedback of the comoving number densities of quiescent galaxies of similar mass at z ∼2. If z (cid:38)3 SMGs are progeni- from the starburst or the ignition of an AGN, leaving behind compact stellar remnants to evolve passivly for tors of z ∼2 quiescent galaxies, then our data implies about a Gyr into the compact quiescent galaxies we ob- that the SMG duty cycle must be t =42+40Myr, burst −29 serve at z ∼2. Over the next 10 Gyr, these then grow where the errorbars include our best estimates of the gradually, primarily through minor merging, into local effects of cosmic variance, photometric redshift errors elliptical galaxies. andincompleteness. Thistimescaleisindependentfrom, but in good agreement with estimates based on SMG gasdepletiontimescalest ∼40−200Myr,estimates burst fromhydrodynamicalmergersimulationst ∼50Myr burst (e.g. Mihos & Hernquist 1996; Cox et al. 2008), and 22 The SMG image in the figure is adopted from Targett et al, estimates based on the time, compact starburst galax- 2013