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Accepted for publicationin the Astrophysical Journal(January16 2011) PreprinttypesetusingLATEXstyleemulateapjv.5/25/10 THE STAR FORMATION HISTORY OF MASS-SELECTED GALAXIES IN THE COSMOS FIELD A. Karim1,12, E. Schinnerer1, A. Mart´ınez-Sansigre2,3,4, M. T. Sargent1, A. van der Wel1, H.-W. Rix1, O. Ilbert5, V. Smolcˇic´6,7, C. Carilli8, M. Pannella8, A. M. Koekemoer9, E. F. Bell10 and M. Salvato11 Accepted for publication inthe Astrophysical Journal (January 16 2011) ABSTRACT We explorethe redshift evolutionofthe specific star formationrate (SSFR) for galaxiesof different 1 stellar mass by drawing on a deep 3.6 µm-selected sample of > 105 galaxies in the 2 deg2 COSMOS 1 field. The average star formation rate (SFR) for sub-sets of these galaxies is estimated with stacked 0 1.4 GHz radio continuum emission. We separately consider the total sample and a subset of galaxies 2 that shows evidence for substantive recent star formation in the rest-frame optical spectral energy n distributions. Atredshifts0.2<z <3bothpopulationsshowastrongandmass-independentdecrease a intheir SSFRtowardsthe presentepoch. Itisbest describedby apower-law(1+z)n,wheren 4.3 J ∼ for all galaxies and n 3.5 for star forming (SF) sources. The decrease appears to have started at 8 z > 2, at least for hig∼h-mass (M & 4 1010 M ) systems where our conclusions are most robust. 1 ∗ × ⊙ Our data show that there is a tight correlation with power-law dependence, SSFR M β, between ∗ SSFR and stellar mass at all epochs. The relation tends to flatten below M 1010∝M if quiescent ] ∗ ⊙ O galaxies are included; if they are excluded from the analysis a shallow index≈β 0.4 fits the SFG ≈ − correlation. On average, higher mass objects always have lower SSFRs, also among SF galaxies. At C z > 1.5 there is tentative evidence for an upper threshold in SSFR that an average galaxy cannot . h exceed,possibly due to gravitationallylimited moleculargasaccretion. It is suggestedby a flattening p of the SSFR-M relation (also for SF sources), but affects massive (> 1010 M ) galaxies only at the ∗ ⊙ - highestredshifts. Sincez =1.5therethusisnodirectevidencethatgalaxiesofhighermassexperience o a more rapid waning of their SSFR than lower mass SF systems. In this sense, the data rule out any r t strong ’downsizing’ in the SSFR. We combine our results with recent measurements of the galaxy s (stellar)massfunctioninordertodeterminethecharacteristicmassofaSFgalaxy: wefindthatsince a [ z 3 the majority of all new stars were always formed in galaxies of M∗ = 1010.6±0.4 M⊙. In this sen∼se, too, there is no ’downsizing’. Finally, our analysis constitutes the most extensive SFR density 2 determination with a single technique out to z = 3. Recent Herschel results are consistent with our v results, but rely on far smaller samples. 0 Subject headings: galaxies: evolution – surveys – radio continuum 7 3 6 1. INTRODUCTION forunderstandinggalaxyevolution. Onthe onehandan . 1 evolution of the observed number density of galaxies as Over the last years multi-wavebandsurveys of various 1 a function of stellar mass, i.e. the mass function, reveals wide fields haveleadto estimates ofstar formationrates 0 how the stars are distributed among galaxies at differ- (hereafter SFRs) andstellar masses for largenumbers of 1 ent cosmic epochs. If, on the other hand, an increase galaxiesouttohighredshifts. Bothquantitiesarecrucial : in stellar mass of any population of galaxies can solely v i 1Max-Planck-Institut fu¨r Astronomie, Königstuhl 17, D- be explained by the rate at which new stars are formed X 69117Heidelberg,Germany[email: [email protected]] within these systems or if other mechanisms are dom- r 2Institute of Cosmology and Gravitation, University inant can only be discussed if the corresponding SFRs a of Portsmouth, Dennis Sciama Building, Burnaby Road, themselves are known. Portsmouth, PO13FX,UnitedKingdom 3Astrophysics, Department of Physics, Universityof Oxford, A number of studies (e.g. Lilly et al. 1996; KebleRoad,OxfordOX13RH,UnitedKingdom Madau et al. 1996; Chary & Elbaz 2001; LeFloc’h et al. 4SEPnet,South-EastPhysicsnetwork 2005; Smolˇcić et al. 2009a; Dunne et al. 2009; 5Laboratoired’AstrophysiquedeMarseille,BP8,Traversedu Rodighiero et al. 2010b; Gruppioni et al. 2010; Siphon,13376MarseilleCedex12,France 6ESOALMACOFUNDFellow,EuropeanSouthernObserva- Bouwens et al. 2010; Rujopakarn et al. 2010 and tory,Karl-Schwarzschild-Strasse2,85748Garchingb. Mu¨nchen, for a compilation Hopkins 2004 and Hopkins & Beacom Germany 2006) revealed that the star formation rate density 7ArgelanderInstitutforAstronomy,AufdemHu¨gel71,Bonn, (hereafter SFRD), i.e. the SFR per unit comoving 53121, Germany 8National Radio Astronomy Observatory, P.O. Box 0, So- volume,rapidlydeclinesoverthelast 10Gyrfollowing ∼ corro,NM87801-0387, USA the purported maximum of star formation activity in 9Space Telescope Science Institute, 3700 San Martin Drive, the universe. The question of whether the stellar mass Baltimore,MD21218, USA 10Department of Astronomy, University of Michigan, 500 content of galaxies could be a major driver for this ChurchStreet, AnnArbor,MI48109,USA decline has gainedsignificantinterestafterthe discovery 11Max-Planck-Institutfu¨rextraterrestrischePhysik,Giessen- of a tight correlation of SFR and stellar mass for star bachstrasse1,D-85748Garching,Germany forming (hereafter SF) galaxies with an intrinsic scatter 12International Max Planck Research School for Astronomy of only about 0.3 dex (e.g. Brinchmann et al. 2004; andCosmicPhysicsattheUniversityofHeidelberg 2 A. Karim et al. Noeske et al. 2007b; Elbaz et al. 2007). This relation z in order to account for the purported constancy of the was studied in the local universe (Brinchmann et al. SSFR. This is in contrast to pure steady cold-mode gas 2004; Salim et al. 2007) suggesting an apparent bi- accretion above a limiting dark matter halo mass (the modality in the SFR-M∗ plane if all galaxies are taken so-called’massfloor’ofMDM 1011 M⊙)(Bouché et al. into account. It was also found to exist for SF galaxies 2010) reproducing well the ob∼served slope of the SSFR- at z . 1.2 (e.g. Noeske et al. 2007b; Elbaz et al. 2007; sequence at all z <2. Bell et al. 2007; Walcher et al. 2008) and further out to It was generally found that at z <2 all galaxies show z 2.5(Daddi et al.2007;Pannella et al.2009).13 Con- a significant (negative) slope of the SSFR-M relation ∗ ≈ sequently the stellar mass normalized SFR (hereafter leading to lower SSFRs in more massive galaxies. Star specific SFR or SSFR), i.e. the SFR at a given epoch forming galaxiesalsoseemtoshowthisbehaviorbutthe divided by the stellar mass the galaxy possesses at the trendtendstobe significantlyweakerespeciallyatz >1 same cosmic epoch, shows a tight (anti-)correlation. where, based on the sBzK selection technique, the slope By studying the SSFR galaxies of different stellar wasfoundtobepracticallyvanishing(Daddi et al.2007; masses can be directly compared. The SSFR itself de- Pannella et al. 2009). It therefore is an ongoing debate finesatypicaltimescalethatcanbeinterpretedasacur- if this phenomenon of a decreasing slope of the SFR- rent efficiency of star formation within a galaxy com- M relation for SF galaxies with redshift is real or just ∗ pared to its past average star formation activity. The an artifact (for an introduction and a summary of the compilationofthestudiesmentioned(e.g.Pannella et al. conflicting observational results see e.g. Fontanot et al. 2009; González et al. 2010; Dutton et al. 2010), not us- 2009). This effect is commonly interpreted as star for- ing a common tracer for star formation nor selection mation efficiency being shifted from higher mass ob- techniqueforseparatingtheSFgalaxyfractionanddata jects in the cosmic past to lower mass objects in the originatingfromvariouswidefields,suggestsasteepevo- present and sometimes referred to as ’cosmic downsiz- lutionofthenormalizationoftheSSFR-M relation14for ing’ (Cowie et al. 1996). Most recently, based on first ∗ SF galaxies. Studies, covering a broad dynamical range Herschel/PACS far-infrared data, even the opposite ef- in stellar mass, have been carried out for all galaxies fect, the so-called SSFR-upsizing at z & 1.5, has been and confirmed the SSFR, as a function of redshift, to be proposed (Rodighiero et al. 2010a).16 even more rapidly increasing from z = 0 to z 1 (e.g. More measurements are needed to understand the re- ≈ Feulner et al. 2005b; Zheng et al. 2007a; Damen et al. lation of SFR and stellar mass and its evolution with 2009b,2010)aswellasthroughoutanevenwiderrangein redshift. This holds especially true for the population of redshift (e.g. Feulner et al. 2005a; Pérez-Gonza´lez et al. SF galaxies. An accurate measurement of the (S)SFR- 2008; Dunne et al. 2009; Damen et al. 2009a). It has sequence at all epochs is key for a better understanding been claimed that the steepness of the SSFR-increase ofgalaxyevolution. Asitwasclaimed(e.g.Noeske et al. withredshiftmightbeachallengeforacolddarkmatter 2007b) a tight correlationof SFR andstellar mass disfa- concordance model (ΛCDM) suggested by comparisons vorsstarformationhistories(SFHs)ofindividualnormal to predictions from semi-analytical models (SAMs) (see galaxies that are mainly driven by stochastic processes, Santini et al. 2009; Damen et al. 2009a; Firmani et al. suchasmergers. Quite contrarilyit favorssmooth SFHs 2010and,e.g.,Guo & White2008,fortheoreticalresults in such a way that the SFH at any cosmic epoch of a based on a SAM). galaxy is solely determined by its stellar mass content It was recently discussed by Stark et al. (2009) and measuredatthecorrespondingredshiftunlessthegalaxy González et al. (2010), at least for moderately massive becomes subject to quenching of star formation. In this SF galaxies (M∗ 5 109 M⊙), that the rapidly evolv- sensetheSFR-M∗ relationatagivenredshiftisregarded ing SSFR might∼tur×n constant in the early universe. anisochroneforgalaxyevolutioninthesamemannerthe Their data show constant SSFRs up to the highest red- Hertzsprung-Russel-Diagramisanisochronefortheevo- shift ranges (z 7 8) probed so far. This signifi- lution of a stellar population at a given age.17 It should cant deviation of≈the−SSFR-evolution from a power-law bementioned,however,thatCowie & Barger(2008)dis- (SSFR (1+z)n), fitting well the data below z 2, agree with this conclusion which underlines the impor- couldbe∝ahintfordifferentphysicalmechanismsregu≈lat- tance of future studies that use a sufficiently deep direct ing star formation in the early universe (González et al. SFRtracertostudytheintrinsicdispersionoftheSSFRs 2010). However, this deviation could also be a result of .18 observational data significantly underestimating the SS- Several tracers across the electromagnetic spectrum FRs at these high redshifts (Dutton et al. 2010) caused 16 This trend is weakly supported by the earlier findings of byselectionbiases15. Recenttheoreticalmodelspropose Oliveretal.(2010). anenhancedmergerrate(Khochfar & Silk2010)athigh 17The(S)SFR-massrelationisthereforealsosometimesreferred toas’thegalaxymainsequence’ (Noeskeetal.2007b)thatis,for fou1n3dItanweeeadkstcoorbreelamteionntiobneetwdetehnatSFatRza∼nd2sEterlblaretmaal.ss(.20H0o6w)eovnelry, aanryintrdaicvkidsu(ael.gg.atlahxeysoo-fcasltleeldlartamu-amssodMel∗,dicsocnunsseecdteidnbNyoeevskoeluettioanl-. their galaxy sample selection at ultraviolet wavelengths preferen- 2007a)atdistinctcosmicepochs(seealsoNoeske2009,forasum- tiallytracesSFRratherthanstellarmass,thuspotentiallybiasing mary). theirresultstowardsaflatterSFR-M∗ relation. 18 Cowie&Barger (2008) cannot confirm the low level of in- 14 In the followingwe willrefer to this relation for SF galaxies trinsic dispersion in the SSFR-M∗ plane found by Noeskeetal. astheSSFR-sequence. (2007b)andtheydiscussotherhintstheyfindsupportingSFHsto 15 Note the very small number of galaxies currently stud- be rather dominated by episodic bursts. We emphasize that the ied in the extreme high redshift regime. Also note the highly largerdispersionofSSFRsmightbecausedbytherelativelybroad discrepant SSFR-estimates presented by Yabeetal. (2009) and binsinredshiftusedbyCowie&Barger(2008)giventhesteepin- Schaerer&deBarros(2010)atthemostextremeredshiftsassum- creasewithredshiftofSSFRsatz<1.5whilestudyingall massive marizedbyBouchéetal.(2010)intheirFig. 13. galaxies. The star formation history of mass-selected galaxies in the COSMOS field 3 are used to estimate the star formation rate of a nor- stacking approach. Therefore, current radio surveys al- mal galaxy19. While rest-frame ultraviolet (UV) light lowonetostudy averageSFRpropertieswhilethey can- originates mainly from massive stars and thus directly not shed light on the intrinsic dispersion of individual tracesyoungstellarpopulationsitwillbestronglyatten- sources. This situation will improve with future EVLA uated by dust. The absorbed UV emission is thermally surveys. reprocessed by heating the dust which in turn reemits Studying the stellar-mass dependence of the SFH re- at infrared (IR) wavelengths. Star formation also leads quires a mass-complete sample in order to prevent in- to emissionin the radio continuum since chargedcosmic ferredevolutionarytrends frombeing mimicked by sam- particles are accelerated in shocks within the remnants ple incompleteness. Early type galaxies containing pre- ofsupernovae(SNR)leadingtonon-thermalsynchrotron dominantly older stellar populations and showing there- radiation (e.g. Bell 1978a and e.g. Muxlow et al. 1994, fore a prominent 4000 ˚A break (see e.g. Gorgas et al. for observations of individual SNRs). Thermal free-free 1999) are likely to be excluded in optical surveys above emission (Bremsstrahlung) in general contributes only z 1 even at deep limiting magnitudes as the break weakly to the 1.4 GHz signal (see e.g. Condon 1992) is ∼redshifted into the selection band. Optical selec- but might become dominant in low-mass systems where tion, thus, potentially limits any study ofa stellar mass- the synchrotron emission was empirically found to be complete sample to the bright (i.e. high-mass) end or strongly suppressed (Bell 2003). Also empirically the is effectively rather a selection by unobscured SFR than phenomenon of radio emission triggered by star forma- by stellar mass if the full sample is considered for the tion results in its wellknownstrong correlationwith the analysis. far-IRoutputofagivenSFgalaxy(e.g.Helou et al.1985; Channel1oftheIRACinstrumentonboardtheSpitzer Condon 1992; Yun et al. 2001; Bell 2003) that appears Space Telescope provides us with the 3.6 µm waveband to persist out to high (z >2) redshifts in a non-evolving that samples the rest-frame K-band at z 0.5 to the fashion (e.g. Sargent et al. 2010a,b). rest-frame z-band at z 3. It is therefore i∼deal in prob- A major advantage of radio emission as a tracer for ingmainlythelightfrom∼oldlow-massstarswhilenotbe- starformationis its obviousindependence ofanycorrec- ing severely affected by dust. For the analysis presented tionfor dust attenuation. Due to wellknownunderlying here,hence,adeepandrich( 100,000sourcesatz 3) physical processes the spectral energy distribution of a 3.6µmgalaxysampleincom∼binationwithaccuratep≤ho- normal galaxy in the low (. 5) GHz regime shows a tometric redshifts and stellar-mass estimates has been Fν ναrc shape (e.g. Bell 1978a). While αrc = 0.8 is used (Ilbert et al. 2010). With a sky coverage of 2 deg2 ∝ − found to be a typical value for the radio spectral index the Cosmic EvolutionSurvey21 (COSMOS)providesthe (e.g. Condon 1992; Bell 2003, for a summary but also largestcosmologicaldeepfieldto-date(seeScoville et al. e.g. Scheuer & Williams 1968; Bell 1978b, for early re- 2007c, for an overview). The uniquely large COSMOS sults) no further spectral features are expected in this 3.6 µm galaxy sample offers uniform high-quality pan- frequency range thus leading to a robust K-correction chromatic data for all sources enabling us to study the up to high (z . 3) redshifts.20 Both advantages di- SSFRinsmallbinsinbothstellarmassandredshift. Ad- rectlyconfrontthe ratheruncertaindustattenuationco- ditionally the evolution of the stellar mass-functions has efficient for UV light and the presence of polycyclic aro- been studied already based on the same sample and its matic hydrocarbon (PAH) emission features redshifted SF sub-population (Ilbert et al. 2010). As it was argued (at z & 0.8) into the 24 µm band commonly used as (e.g. in Daddi et al. 2010a) the combination of the indi- an estimator for the total infrared (TIR) emission. Also vidual evolutions of the mass function and the (S)SFR- the combinationofUVandmid-IRemissiontracingstar sequencemightbethemostimportantobservationalcon- formation is limited since it is typically tested in mod- straints for understanding the stellar mass built-up on erately SF systems at low redshift (for a summary see cosmic scales jointly resulting in a potentially peaking Calzetti & Kennicutt 2009) which might not resemble and declining SFRD. high redshift galaxies with higher SFRs and larger dust Thispaperisorganizedasfollows. InSec. 2wepresent content. Finally, even at a resolution of 5′′ achieved our principle and ancillary COSMOS data sets and the ∼ by currentUV and IRtelescopes blending of sourcesbe- selection of our sample. Sec 3 contains a detailed de- comesa severeissue forthe faintend ofthe sources(see, scriptionof our stacking algorithmand the derivation of e.g., Zheng et al. 2007b). Current radio interferometers averageSFRsfromthe1.4GHzimagestacks. Additional suchas the (E)VLA and(e)Merlinachieveresolutionsof methodologicalconsiderationspertainingtobothsample . 2′′ that are needed to unambiguously identify optical selection and flux density estimation by image stacking counterparts. This unambiguity is particularly impor- areto be found in the Appendices. Readerswho wishto tant in a stacking experiment as otherwise flux density directly proceed to our results and their interpretations from nearby sources might contribute to the emission of canfindthoseregardingthe relationofSSFRandstellar anindividualobject. Adrawbackofusingradioemission mass in Sec. 4. Our measurements of the CSFH and to trace starformationis the generallylow sensitivity to a simple model that reproduces these observations are the normal galaxy population even in the deepest radio discussed in Sec. 5. Both Sections (4 and 5) contain a surveys to-date which usually limits the analysis to a detaileddiscussionofhowourresultsrelatetotherecent literature. We summarize our findings in Sec. 6. Throughout this paper all observed magnitudes are 19 ’Normal’galaxies aredefined assystems thatdonothostan activegalacticnucleus. given in the AB system. We assume a standard cosmol- 20 Unless radiative losses, e.g. inverse Compton scattering against the cosmic microwave background, steepen the spectral indextovalues -1.3. 21 http://cosmos.astro.caltech.edu ∼ 4 A. Karim et al. ogy with H =70 (km/s)/Mpc, Ω =0.3 and Ω =0.7 details). At a resolutionof 1.5′′ 1.4′′ the final map has 0 M Λ consistentwiththelatestWMAPresults(Komatsu et al. ameanrmsof 8µJy/beamin×thecentral30′ 30′ and ∼ × 2009) as well as a radio spectral index of α = 0.8 in 12 µJy/beam over the full area, respectively. Using rc − ∼ the notation given above if not explicitly stated other- the SADalgorithmwithinAIPS,a totalof2,865sources wise. A Chabrier (2003) initial mass function (IMF) is were identified at more than 5σ significance in the final used for all stellar mass and SFR calculations in this ar- VLA-COSMOS mosaic (Schinnerer et al. 2010). As the ticle. Resultsfrompreviousstudiesintheliteraturehave outermost parts of the map are not covered by multiple been converted accordingly.22 pointings the noise increases rapidly towards the edges. In this study we therefore exclude these peripheral re- 2. THEPAN-CHROMATICCOSMOSDATAUSED gions resulting in a final useable area of 1.72 deg2. In order to study the redshift evolution of galaxies in general, and the evolution of their SFRs in particular, a 2.2. A 3.6 µm selected galaxy sample within the completeandlargesampleofnormalgalaxiesisneededas COSMOS photometric (redshift) catalogs it not only provides representative but also statistically Deep Spitzer IRAC data mapping the entire COS- significant insights. MOS field in all four channels have been obtained dur- The large area of 2 deg2 covered by the COS- ing the S-COSMOS observations (Sanders et al. 2007). MOS survey, fully imaged at optical wavelengths The data reduction yielding images and associated un- by the Hubble space telescope (HST) (Scoville et al. certainty maps for all the four channels is described in 2007a; Koekemoer et al. 2007), is necessary to mini- Ilbert et al.(2010)(I10 hereafter). Forthe 3.6µmchan- mize the effect of cosmic variance. Deep UV GALEX nel a source catalog has been obtained by O. Ilbert and (Zamojski et al.2007)toground-basedopticalandnear- M. Salvato (private communication) using the SExtrac- infrared(NIR)(Taniguchi et al.2007;Capak et al.2007) tor package (Bertin & Arnouts 1996). Given the point imaging of the equatorial field23 yielded accurate pho- spread function (PSF) of 1.7” a Mexican hat filtering of tometric data products for 1 106 galaxies down the 3.6 µm image within SExtractor was used in order ∼ × to 26.5th magnitude in the i-band (Ilbert et al. 2009; to assure careful deblending of the sources. Capak et al. 2007). Thanks to extensive spectroscopic The resulting sampleof 3.6µmsourcesdownto a lim- efforts at optical wavelentghs using VLT/VIMOS and iting magnitude of m (3.6 µm) = 23.9 in the 2.3 deg2 AB Magellan/IMACS (Lilly et al. 2007; Trump et al. 2007) field, not considering the masked areas around bright the estimation of photometric redshifts for all these sources (K < 12), areas of poor image quality and the s sources could be accurately calibrated. Ongoing deep field boundaries, consists of 306,000sources.24 Keck/DEIMOScampaigns(PIsScoville,Capak,Salvato, As detailed in I10 photometric redshifts (hereafter SandersandKarteltepe)extentthespectroscopicallyob- photo-z’s) were assigned to all 3.6 µm detected sources. servedwavelengthregime to the NIR which is criticalto The vast majority of sources is also detected at opti- improve the photometric calibration for faint sources at calwavelengthsandthereforecontainedintheCOSMOS highredshifts. Inadditiontoobservationsofthewholeor photo-z catalog25 (Ilbert et al. 2009) so that in general parts of the COSMOS field in the X-ray (Hasinger et al. photometric information from 31 narrow-, intermediate 2007; Elvis et al. 2009) and millimeter (Bertoldi et al. and broad-band FUV-to-mid-IR filterbands was avail- 2007; Scott et al. 2008), imaging by Spitzer in the mid- able.26 Withintheremaining4%(i.e. atotalof8507)of to far-IR (Sanders et al. 2007) as well as interferometric the 3.6 µm sources 2714 are also contained in the COS- radio data (Schinnerer et al. 2004, 2007, 2010) covering MOSK bandselectedgalaxysample(McCracken et al. the full 2 deg2 have been obtained. 2010)an−darealsoregardedas realsources. I10assigned photo-z’stotheseextremelyfaintobjectsusingtheavail- 2.1. VLA-COSMOS radio data able NIR-to-IRAC photometry. Radio observations of the full (2 deg2) COSMOS field The qualityofthe photo-z’swasestimated(for details were carried out with the Very Large Array (VLA) at see I10) by using spectroscopic redshifts for a total of 1.4 GHz (20 cm) in several campaigns between 2004 4,148 sources at mAB(i+) < 22.5 from the zCOSMOS and 2006. The entire field was observed in A- and C- survey (Lilly et al. 2009). At a rate of <1 % of outliers configuration(Schinnerer et al. 2007) where the 23 indi- the accuracy was found to be σ(zphot−zspec)/(1+zspec) = vidual pointings were arranged in a hexagonal pattern. 0.0075downto the magnitude limit of the spectroscopic Additional observations of the central seven pointings sample. For all objects within the 3.6 µm selected cat- in the more compact A-configuration (Schinnerer et al. alog – regardless of i-band magnitude the accuracy was 2010)wereobtainedinordertoachieveahigher1.4GHz derivedbyusingthe1σuncertaintyonthephoto-z’sfrom sensitivity in the area overlapping with the COSMOS MAMBO millimeter observations (Bertoldi et al. 2007). 24 As a stacking analysis depends on the input sample prior In both cases the data reduction was done using stan- masked areas consequently reduce further the effective area for dard procedures from the Astronomical Imaging Pro- this study. All space densities reported inthis work aretherefore computedforaneffectivefieldsizeof1.49deg2. cessing System (AIPS) (see Schinnerer et al. 2007, for 25 This optically deep sample has a limitingmagnitude of 26.2 inthei+ selectionband(seeTab. 1inSalvatoetal.(2009)). 22 Logarithmic masses and SFRs based on a Salpeter (1955) 26 As described in detail by I10 all photo-z’s used inour study IMF, a Kroupa (2001) IMF and a Baldry&Glazebrook (2003) wereobtained usingaχ2 template-fitting procedure implemented IMFareconvertedtotheChabrierscalebyadding-0.24dex,0dex inthe code Le Phare (Arnoutsetal. 2002; Ilbertetal. 2006) and and0.02dex,respectively. a library of 21 templates. Additional stellar templates were used 23 The COSMOS field is centered at RA = 10 : 00 : 28.6 and to reject stars (i.e. sources with a lower χ2 values for the stellar Dec=+02:12:21.0(J2000) comparedtothegalaxytemplates) fromthefinalgalaxysample. The star formation history of mass-selected galaxies in the COSMOS field 5 the probability distribution function which yields a con- rest-frame color redder than (NUV r+) = 3.5 temp − servativeestimate of the photo-z uncertainty as detailed as quiescent. Several authors (e.g. Wyder et al. 2007; in Ilbert et al. (2009). At 1.25 < z < 2 the relative Martin et al. 2007b; Arnouts et al. 2007) suggest this photo-z uncertainty is 0.08 and thus higher by a fac- colortobeanexcellentindicatorforthe recentoverpast tor of four compared to the median value for the full averageSFRasitdirectlytracestheratioofyoung(light- (mAB(3.6 µm) 23.9) sample.27 We account for this weightedaverageageof 108yr)andold( 109yr)stel- whenbinning th≥e datainredshiftby choosingincreasing lar populations. Seeking∼for a color bimod≥ality that dis- bin widths with increasing redshift.28 It is worth not- criminates galaxies with currently high from those with ingthatthe photo-zaccuracyis degradedatmagnitudes low star formation activity the NUV r color appears fainterthan mAB(i+)=25.5(See Fig. 12in Ilbert et al. therefore to be superior to purely optic−al rest-frame col- (2009)). Our choice of lower stellar mass limits (see Sec. ors such as U V (e.g. Bell et al. 2004). 2.6) and our stellar mass binning-scheme (see Sec. 2.6) Using a dus−t uncorrected NUV r+ versus r+ J automatically ensures a low fraction (< 15 %) of these rest-frame color-color diagram30 I10−showed that in−the optically very faint objects within the lowest mass-bin range 0 z 2 for (NUV r+) > 3.5 quiescent temp aboveourmasslimitatanyredshift. Thefractionofsuch galaxiesa≤rew≤ellseparatedfro−mthe parentsample with- faint objects effectively vanishes towards higher masses out severe contamination by dust-obscured SF galaxies. as also pointed out by I10.29 Thisquiescentpopulationisthereforecomparableto the oneclassifiedbyWilliams et al.(2009)basedonaU V 2.3. Estimation of stellar masses versus V J rest-frame color-colordiagram. − − Furthermore our quiescent population shows a clear Stellarmassesforallobjectswithinthe3.6µmselected separationfromtheparentsamplewithrespecttogalaxy parent sample have been computed by I10. Here, we morphology. I10 visually classified a subset of 1,500 iso- briefly summarize the method and the important find- latedandbrightgalaxiesfromthe 3.6µm parentsample ings. For the estimation of stellar masses based on a using HST/ACS images and found the quiescent popu- Chabrier IMF stellar population synthesis models gen- lation among those to be clearly dominated by elliptical erated with the package provided by Bruzual & Charlot (E/S0) systems. A further cut ((NUV r+) < 1.2) (2003) (BC03) have been used. Furthermore an expo- temp − was shown to efficiently separate late type spiral and ir- nentially declining SFHanda Calzetti et al.(2000) dust regular galaxies from early type spirals as well as the extinction law have been assumed. Spitzer MIPS 24µm remaining tail of elliptical systems. As any such color flux densities (from LeFloc’h et al. 2009) have been in- cut effectively is a cut in star formation activity we dis- cluded in the SED template fitting as an additionalcon- cussthespectralpre-classificationofSFsystemsinmore straint on the stellar mass. Systematic uncertainties on detail in Appendix C. the stellar masses, caused by the use of photo-z’s, the choice of the dust extinction law and library of stellar 2.5. AGN contamination populationsynthesismodels,havebeeninvestigated. No systematic effect due to the use of photo-z’s is appar- A major concern arising in the context of using radio ent. Stellarmassesderivedfromthe BC03templatesare emission to trace star formation is contaminating flux systematically higher by 0.13-0.15 dex compared to the fromactivegalacticnuclei(AGN).Forsomegalaxiesthe newerCharlot&Bruzual(2007)versions(Bruzual2007) total radio signal might even be dominated by an AGN. that have an improved treatment of thermally pulsing For our study, ideally, we should therefore remove all asymptotical giant branch (TP-AGB) stars. As BC03 galaxies hosting an AGN from our sample. models are commonly used in the literature, both stud- Cross-matching the most recent XMM-COSMOS ies,I10andthiswork,arebasedonBC03massestimates. photo-z catalog (Salvato et al. 2009; Brusa et al. 2010) with the 3.6 µm selected parent sample delivered a to- 2.4. Spectral classification tal of 1,711 (i.e. 1 %) X-ray detected objects. Most ∼ of these sources exhibit best-fit composite AGN/galaxy A number of studies suggest the existence of a bi- SEDs31 while a minor fraction is well fitted by an SED modality in the SSFR-M plane (e.g. Salim et al. 2007; ∗ showing no AGN contribution. However, here all X-ray Elbaz et al. 2007; Santini et al. 2009; Rodighiero et al. detections are treated as potential AGN contaminants 2010a) leading to a tight SSFR-sequence to be in place and thus removed from our sample.32 onlyforSFgalaxies. Thereforeadeselectionofquiescent, Studies of the radio luminosity function (e.g. i.e. non SF, objects is needed. Sadler et al. 2002; Condon et al. 2002) agree that radio- FollowingI10 we classify galaxieswith a best-fit BC03 template that has an intrinsic (i.e. dust unextincted) 30Heretheabsolutemagnitudeswereinferredfromtheobserved magnitudesnotaccounting fordustreddening. 27Foracolor-selectedsub-setofgalaxiesforwhichspectroscopic 31 Based onthe Salvatoetal. (2009)classification that uses an redshifts from the zCOSMOS-faint survey (Lilly et al., in prep.) enhanced set of AGN/galaxy templates in order to fit the FUV- were available the photo-z accuracy was directly tested at 1.5 < to-mid-IR SED and that includes further priors (e.g. variability z < 3. This yields an accuracy of σ∆z/(1+z) = 0.04 with 10% of information)inthefittingprocedurewhiledeliveringaccuratepho- catastrophicfailures. tometricredshiftsforallthesesources. 28Itshouldbementioned,however,thattheprojected-pairanal- 32 Note that Hickoxetal. (2009) and Griffith&Stern (2010) ysisbyQuadri&Williams(2009)independentlyshowsthatphoto- yieldstrongevidence that X-rayand radioselected AGN aremu- z’sfromdatasetswithbroad-andintermediatebandphotometry tuallydistinctpopulations suchthatitisactuallyquestionable to likethe COSMOScatalog arenot expected to have very different remove X-ray selected objects from our samples. We confirmed photo-z errorsatz>1.5thanatlowerredshifts. that our results do not change significantly when including those 29 I10 use comparable mass limits and their Fig. 8 the strong objects and urge caution to remove more objects if deeper X-ray declineofthefractionofopticallyfaintobjectswithmassatallz. datacomparedtotheXMMimagingusedhereisathand. 6 A. Karim et al. AGN contribute half of the radio light in the local uni- We therefore excludedalsothese objectsrelying onindi- verse at radio luminosities slightly below L vidual photo-z’s in order to estimate the radio luminos- 1.4 GHz 1023 W/Hz and outnumber SF galaxies above ∼ ity. The total fraction of galaxies among all objects in a ∼ 2 1023 W/Hz. Detailed multi-wavelength studies given bin that we exclude by these two criteria amounts (H×ickox et al. 2009; Griffith & Stern 2010) yield that – on average – to less than 0.3 % such that only a frac- radio-AGN are hosted by red galaxies. The evolution tion of radio detections is rejected. We stress the small- out to z 1.3 of the radio-AGN fraction for luminous ness of this percentage as the advantage of our radio- (i.e. L ≈ > 4 1023 W/Hz) radio-AGN as a func- approach is its insensitivity to dust obscuration which 1.4 GHz tion of stellar mass×has been presented by Smolˇcić et al. mightbechallengedbyrelyingonindividualopticalbest- (2009b)whoselectedaparentsampleofredgalaxieswith fit SEDs as we partially do when removing some of the rest-frame U B colors in a range close to our quiescent radio-detectedobjects. Itshouldbenotedthatthehigh- galaxy fractio−n. The derived AGN-fractions at a given power radio-AGN candidates are exclusively hosted by stellar mass within the red galaxy population are there- red galaxies within our sample. Hence, X-ray detected fore applicable to our sample. sourcesaretheonlyobjectsthathavebeenremovedfrom Accordingto Smolˇcić et al.(2009b)(see their Fig. 11) our SF samples. theluminousradio-AGNfractionat0.7<z <1.3iswell Astheradio-basedSFR-resultspresentedinthispaper below 25 % at all log(M [M ]) < 11.5 where it drops (seeSec. 4)arebasedonamedianstackingapproach(see ∗ ⊙ quicklyto 1%atlog(M [M ])=11andcontinuously Sec. 3) a minor fraction of contaminating outliers such ∗ ⊙ tolowerlev∼elsasstellarmassdecreases. Atmasseslower as AGN is even tolerable. We conclude that contamina- than log(M [M ]) = 11 the radio-AGN fractions are tion of the stacked radio flux densities caused by AGN ∗ ⊙ subject to non-negligible evolution between 0 < z < 1 emissionatradiofrequenciesisnotasiginifcantsourceof whilethefractionsathighermassesincreaseonlymildly. uncertaintyinthecontextofthisstudyandthatourcon- However,giventhattheradio-AGNfractionsarewellbe- clusions would not change if we included the radio-AGN low1%intheformer(i.e. low)massrangeouttoz 1.3 candidates in our analysis. ∼ it is unlikely that they rise above 10 % at z 1. The ≫ 2.6. Completeness considerations evolutionoftheradio-AGNfractionatthehigh-massend is much slower but the fractions are high already in the In the following we will discuss the completeness of localuniverse. We therefore setanarbitrarybut reason- our (sub-)samples. It is important to distinguish be- able threshold and exclude all quiescent objects above tweentwokindsofeffects. Whilethefull3.6µm-selected log(M [M ]) = 11.6, where the expected radio-AGN source catalog (1) is subject to a flux density-dependent ∗ ⊙ fraction exceeds 50 %, from our stacking analysis. As levelofdetectionincompleteness we areinterestedin (2) the radio-AGN fraction sharply drops below this limit howrepresentativefortheunderlyingpopulationagiven the remainder of our full galaxy sample should be gen- subset of galaxies is at a given mass. Our lower mass erally free from radio-AGN contamination. Within the limits hence need to be chosen such that the objects at highest mass bin probed here (M > 1011 M ; see Fig. hand remain sufficiently representative. ∗ ⊙ 2), however, the average fraction of radio AGN among I10 evaluated the efficiency of the source extraction the quiescent galaxies could still be 25 % at z > 1. procedure (and hence the detection completeness) with This fraction appears high but among∼the entire galaxy Monte Carlo simulations of mock point-sources inserted population (quiescent and SF sources) the percentage into the 3.6 µm mosaic. At the flux density cut of drops to at most 10 % within our highest mass-bin at 1 µJy (mAB(3.6 µm) = 23.9) the catalog was found z 1. As shown by I10 globally, but in particular at to be 55 % complete; 90 % completeness is reached at M∼∗ >1011 M⊙ the fraction of quiescent galaxies among F3.6 µm ≈ 5 µJy (mAB(3.6 µm) = 22.15). This rather the entire sample decreases strongly towards higher red- shallow decline in detection completeness towards the shifts (see also Taylor et al. 2009).33 An upper bound magnitude limit is due to source confusion. of 10 % to the potential fraction of radio-AGN within Fig. 1 shows the distribution of 3.6 µm flux density our highest mass-bin hence is a well justified number at with stellar mass in narrow redshift slices for our source z >1. catalog, color coded by the spectral type of the galaxies DuetoprominentspectralfeaturesweregardtheSED- (see Sec. 2.4). The Monte Carlo detection completeness fits for quiescent objects as most trustworthy such that levels of the catalog are indicated by horizontal dashed also the SED-derived SFRs are expected to be accu- blacklinesstartingfromthefluxdensitylimitatthebot- rate for individual objects. These SFRs therefore serve tom to the 95 % completeness limit at the top in each as a prior for revealing potential radio-AGN among the panel. Eachsub-populationshowsaclearcorrelationbe- radio-detections in our sample. Hence we correlated our tween3.6 µm flux density and stellar mass,and the qui- sample with the latest version of the VLA-COSMOS escent population residing at the high-mass end at all catalog (Schinnerer et al. 2010) and excluded those ob- flux densities. While SF sources (the union of all blue jects showing radio-derived SFRs more than twice as and green data points) span the entire range of 3.6 µm large as the SED-derived values. We find that the over- flux densities at all redshifts, hardly any quiescent ob- all number of objects excluded in each sample to be jectswithlowfluxdensitiesareobservedatintermediate stacked is negligible. The same holds for very luminous andhighredshifts. Weconsequentlyfindfewerandfewer (L >1025 W/Hz) radio sources among the radio- low-mass quiescent objects as redshift increases. This is 1.4 GHz detections that are most likely high-power radio-AGN. certainlythecombinedeffectofageneralabsenceofsuch sources at higher redshifts plus the loss of these objects 33Theglobalstellarmassdensityofquiescentgalaxiesatz=1.5 at low flux densities due to the global detection incom- isaboutanorderofmagnitudelowerthantheSFone. pleteness of our catalog. The star formation history of mass-selected galaxies in the COSMOS field 7 Figure 1. Observed 3.6 µm flux versus stellar mass from SED fits. The 12 panels show photometric redshift bins, as 0.2 ≤ zphot ≤ 3 (in2d3.i9catisedthinetmheagunpiptuerdelefltimpiatrtoofftehaechcaptaanloegl.).FluBxludeenpsoiitnietssrdeelantoetetohAigBh-lmyaagcntiitvuedSesFvsiaysmteAmBs(,3.w6itµhmi)n=tri−ns2i.c5lroegst1-0f(rFam3.6eµtmem[pµlJayt]e)+co2l3o.r9s (NUV r+)temp < 1.2; red points denote quiescent (low star formation activity) galaxies with (NUV r+)temp > 3.5. Green points are obj−ects of intermediate intrinsic rest-frame color (and hence star formation activity). Horizontal das−hed lines mark the levels of the detection completeness, estimated through Monte Carlosimulations ofartificial sources (see Sec. 2.6). The vertical dashed-dotted linein each panel denotes the lower masslimit,towhichthe sampleofSFsystems (i.e. the unionof allblueandgreen points)is representative oftheunderlyingSFpopulation andtheSFRisnot affected bytheintrinsiccatalog incompleteness. Thesolidvertical lineineach panel denotes themasslimittowhichtheentire sampleisregardedasrepresentative. Detection incompleteness affects all sources in at a completeness level, which we shall refer to as sta- given 3.6 µm flux density, regardless of their spectral tistical completeness. By applying the analytical type. However,thedifferentdistributionofquiescentand scheme described in detail in Appendix A we en- SF sources with respect to 3.6 µm flux density necessi- surethatthestatisticalcompletenessofoursample tates that a different lower mass limit (‘representative- always reaches at least 95 %. This value sets the ness limit’,hereafter)beadopted,dependingonwhether actual level of representativeness of a given sub- we consider the redshift evolution of SF galaxies or that sample. In the following we will also present re- oftheentiregalaxypopulation. Wenowdiscusshowthe sults for sub-samples below the evaluated mass- limiting mass is set for these two samples: limits which will be indicated separately. Those results represent strict upper limits in (S)SFR. Inthe caseofthe entire galaxy population, itisim- • portant to be working with a sample in which the For studying the SF population we need not be as • fractionalcontributionofquiescentandSFsources conservative because we are dealing with a single reflects the true population fractions as closely as sub-populationthatissubjecttolessinternalvaria- possible. The probability that this is the case be- tionofSFactivityasa(bimodal)sampleincluding comes larger, the better the underlying popula- both quiescent and SF systems. We thus consider tion is sampled; i.e. it rises with increasing de- sources down to the limiting flux density of the tection completeness. We therefore require an in- 3.6 µm catalog when we compute the mass limits trinsic catalog completeness of 90 % (correspond- at a given redshift. Since this implies that at low ingm (3.6µm)=22.15)atallmassesconsidered. stellar masses the flux distribution is sharply cut AB Thisisanarbitrarybutreasonablethresholdasthe due to the magnitude limit of our catalog, we still intrinsiccatalogcompletenessrisesrapidlytowards need to use the scheme presented in Appendix A higher flux densities. to identify stellarmass limits that providea repre- In order to evaluate the actual mass representa- sentative flux density distribution for SF galaxies. tivenesslimitweneedtodefine yetanothertypeof As visible in all panels of Fig. 1, the lowest mass 8 A. Karim et al. galaxies) enter our analysis. This is by far the largest Table 1 galaxysampleusedforstudyingthedependencebetween Stellarmasslimitsforall/SFgalaxies SFR and stellar mass throughout cosmic time. Fig. 2 shows the adopted binning scheme and the number of Allgalaxies SFsystems galaxies contained in each stellar mass and photo-z bin. z log(M∗ [M⊙])lim log(M∗ [M⊙])lim 0.3 9.7 8.8 3. METHODANDIMPLEMENTATIONOFRADIOIMAGE 0.5 9.8 8.9 STACKING 0.7 10.0 9.1 The bulk of objects in our 3.6 µm selected sam- 0.9 10.1 9.1 1.1 10.2 9.3 ple is not individually detected in the 1.4 GHz contin- 1.3 10.4 9.4 uum. An estimation of the SFR based on the radio 1.5 10.4 9.5 flux density for every object in the sample is therefore 1.7 10.5 9.6 impossible. On the other hand, studying only radio- 1.9 10.8 9.7 2.1 10.8 9.8 detected galaxies in this sample yields effectively a se- 2.3 10.8 9.9 lection by SFR and not by stellar mass since only radio- 2.5 10.9 9.9 bright, i.e. highly active star forming, normal galax- 2.7 11.0 10.1 ies remain.35 By co-adding postage stamp cutout im- 2.9 11.1 10.2 ages of the 1.4 GHz map at the positions of sources in the sample it is possible to estimate the typical radio Note. — The lower stellar mass limits above which our samples are regarded rep- properties for a specific galaxy population. Usually re- resentative. Those limits are as shown in ferred to as stacking, this technique has proven to be Fig. 1and12and have been derivedbased a powerful tool to estimate the typical flux density of onthe schemethat isdetailed inAppendix galaxies with a given property, not only in the radio A. (e.g. White et al. 2007; Carilli et al. 2008; Dunne et al. bin always contains objects over the full range of 2009; Pannella et al. 2009; Garn & Alexander 2009; detection completeness, from 55 % to 100%. One Bourne et al. 2010; Messias et al. 2010) but also in the might expect – and the SED fits confirm this – mid-IR (e.g. Zheng et al. 2006, 2007a,b; Martin et al. thatamonggalaxiesofagivenmass,thosewiththe 2007a; Bourne et al. 2010), far-IR (e.g. Lee et al. 2010; fainter fluxes have lowerSSFRs. Failure to include Rodighiero et al. 2010a; Bourne et al. 2010) as well as them(duetodetectionincompleteness)wouldthus sub-mm (e.g. Greve et al. 2009; Mart´ınez-Sansigreet al. yield average radio-derived SSFRs that are biased 2009). The list can be extended to other wavebands al- towardshighervalues. Wewishtoemphasize,how- ways requiring a galaxy sample representative for the ever,thatourchoiceofthestatisticalcompleteness underlying population. levelensuresthatthis biasis smallaboveourmass limit and that our samples hence are ‘representa- 3.1. Median stacking and error estimates tive’inthe sensethatthey canbe expectedtoren- derameaningfulmeasurementof,e.g.,the average Our stacking algorithm uses cutouts with sizes of SSFR of the underlying population. 40′′ 40′′, centered on the position of the optical coun- × terpart. Since the COSMOS astrometric reference sys- Thestellarmassrepresentativenesslimitsforthewhole tem was provided by the VLA-COSMOS observations sampleandtheSFsystemsaremarkedinFig. 1asverti- thepositionalaccuracybetweenradioandopticalsources callinesforeachredshiftbinintherange0.2<zphot <3 shouldbe wellwithinthe errorsofbothdatasets. As de- and listed in Tab. 1. Note that they increase with tailed in Schinnerer et al. (2007) the relative and abso- redshift. As a consequence, our results will be based lute astrometry of the VLA data are 130 and < 55 mas on fewer mass bins at high redshift and the aforemen- respectively. In other words the average distribution of tioned bias in the lowest mass bin may therefore have radio flux follows the one at optical wavelengths and a larger impact on fitting trends. Very conservatively the central pixel in any stacked image was always the speaking, our results for SF objects presented in the fol- brightestone. Averagingoverpixels locatedat the same lowing should generally be regarded as most robust at position in each stamp hence is an astrometrically well- z . 1.5 while evolutionary trends inferred at the high defined problem. mass end are robust out to our redshift limit of z = 3. It can be approached by computing either the mean We will also show results for SF galaxies obtained at or the median of the mentioned set of pixels. The re- masses lower than the individual mass limits and treat sulting stamp then shows the spatial distribution of the them as not entirely representative. Such measurements average radio emission for the sample studied. For an will be indicated with different symbols in our plots and input sample of N galaxies its background noise level we will discuss any further implications in Sec. 4.4. should correspond to 1/√N of the noise measured The final sample ofgalaxieswith mAB(3.6 µm)=23.9 in a single radio stamp∼.36 Any sample of galaxies in a andz <3consistsof165,213sourcesoveraneffective phot area of 1.5 deg2. Fig. 3 in I10 shows the redshift quiescent galaxies as discussed in Sec. 2.5 and excludes further distribut∼ionwithamedianofz 1.1. Afteradopting 328sources(i.e. 0.3%)classifiedasradio-AGN. phot ∼ 35 The currently deepest radio surveys (e.g. Owen&Morrison a lower redshift limit of z = 0.2 in order to account for the small local volumepshaotmpled by our effective area 2S0F0R8s,&wi5th0Mrm⊙s1/.y4rGaHtza∼re3dsµhJifyt)oifnzdi=vid1.ually detect galaxies with and our binning scheme 113,610 sources34 (90,957 SF 36 Our image stacking implementation automatically monitors thedecreaseofthebackgroundnoiselevel. Forallresultspresented 34 This number already considers the upper limiting mass for hereitwasverifiedthatthisdecreasefollowsa 1/√N law. ∼ The star formation history of mass-selected galaxies in the COSMOS field 9 Figure 2. Binningschemeinstellarmassandphotometricredshiftfortheentire(left)andtheSF(right)sample. Hatchedbinsliebelow the corresponding limits denoted in Fig. 1 and are hence regarded representative of the underlying galaxy population. The top number in each box is the total number of galaxies used in the radio stack; the bottom number shows the signal to noise ratio achieved in the radiostack. Intheleftpanel,themiddlenumberistheamountofpotentialradio-AGN(notdetectedintheX-ray)thathasbeenexcluded fromthe stack. Inthe rightpanel this number gives the amount of optically veryfaint sources only detected redwards fromthe K-band. No radio-AGN candidate has been found among the radio-detected sources in the SF sample and only X-raydetected objects have been removed. Thetotalnumberofgalaxiesperredshiftbinisgivenbelowthepanels. givenbin of redshiftand stellarmass likely containsalso mean, White et al. (2007) showed that the median is a a fraction of sources with radio detections. Even if this well-definedestimatorofthemeanoftheunderlyingpop- fractionissmall,themeanissensitivetothelargeexcess ulation in the presence of a dominant noise background. in 1.4 GHz flux density compared to the average radio Although, strictly speaking, these arguments only ap- emission of the individual non-detections. On the other ply to the case of pure point sources, the condition of a hand, setting a thresholdand excluding radio detections dominant noise background is given in our study. One from the stack artificially changes the sample and the has to be aware of the fact that there is in principle results, hence, depend on the threshold applied. no possibility to access the intrinsic distribution of ra- Inaddition,foregroundobjectsandotherextendedra- dio peak fluxes of the underlying population as a whole. dio bright features (e.g. lobes from radio galaxies) need The observed distribution merely is the intrinsic one as tobehandledwithcareandmightbeasourceofcontam- smeared out by the gaussian noise background. How- inationaffectingthenoiseinthefinalstampbutalsopo- ever, it still contains information that needs to be used tentially the signal itself. It is therefore beneficial to ex- in order to find proper confidence limits for any statistic clude stamps showing these features from a mean stack. applied. Based on the above arguments, we expect the Typically,significantlylessthan1%ofobjectsinasam- broadened distribution to be not only shifted but also ple are rejected and the effect of this artificial cut on skewed towards positive flux density values. As a re- the sample thus is negligible. However, by resorting to sult, the uncertainty for the obtained peak flux density the median, the stacking technique becomes more ro- is poorly estimated by the background noise in the final bust against outliers allowing the use of the entire input stamp. Using a bootstrapping technique (see Appendix sample.37. Non-uniform noise properties within the ra- B.2)allowsus toobtainmorerealistic,asymmetricerror dio map can also be addressed by applying a weighted bars for our measured peak flux densities. schemetocomputethemedian(seeAppendixB). While itisoftenarguedthatthereisnostraight-forwardwayof 3.2. Integrated flux densities, luminosities and SFRs interpreting the sample median compared to the sample from stacked radio images Sofarweconsideredonlytheaveragepeakfluxdensity 37 Weappliedthedifferentstackingtechniques discussedabove which, to first order, would not require to stack individ- to some of our sub-samples. We found the median flux densities ual cutouts but only their central pixel. However, the obtainedtobewithin.7%ofthoseobtainedwhenusingamean typical galaxy of a given sample might exhibit extended stacking technique that excludes radio-stamps includingextended foreground features. For the mean stack we co-added objects in radio emission. In that case the peak flux density is no agivensub-samplethatarenotindividuallydetected intheradio longer equivalent to the total source flux but underesti- imagingandthefluxdensityofthedetectedsourceshasbeenadded mates the typical radio flux density and hence all other to the flux density obtained from the stack in a noise-weighted quantities derived from it. fashion. This ensures that those objects that arenot individually radio-detected – i.e. the bulk of our sources – are most strongly The effect of bandwidth smearing (BWS), chromatic weighted aberration caused by the finite bandwidth used during 10 A. Karim et al. Figure 3. Examples for40′′ 40′′ (i.e. (115 115)pixels)1.4GHzpostage stampimagesobtainedviamedianstackingofstarforming galaxies(seeSec. 2.4)inther×edshiftbinbetwe×en 1.6<z<2. Thenumberofgalaxies forwhichindividualradiocutout imagesfromthe VLA-COSMOSmap(resolutionof1.5′′ 1.4′′)havebeenco-addedisgivenattheupperleftofeachstampinthetoprowwhilethenumber atthelowerrightdenotesthebinextent×inlog(M∗ [M⊙]). Duetothehighsignal-to-noiseratios(SNRs)achieved,generally,aclear(dirty) beampatternisvisible. Thebottom rowshowsthecorrespondingCLEANedstamps(seeSec. 3.2,fordetails). Contourlevelsareat2,4, 5σbg andfollowedbystepsof5σbg (TheindividualSNRsaregiveninFig. 2andfluxdensitiesmeasuredaswellasthebackgroundnoise levelsreachedarelistedinTab. 3). theVLA-COSMOSobservationsleadstoaspatialbroad- sities have been estimated according to Hopkins et al. ening of a source even if it is intrinsically point-like. (2003)andrelyonthecombinedinformationonthebest- WithinasinglepointingtheBWSincreaseswithincreas- fit source model and the bootstrapping results from the ingradialdistancefromthepointingcenterandtheeffect image stacking: is analytically well determined (e.g. Bondi et al. 2008). For a mosaic like the VLA-COSMOS map that consists σ σ 2 σ 2 Total data fit of many overlapping pointings the effect becomes ana- = + , (1) lytically unpredictable due to the varying uncertainties hFTotali s(cid:18)hFTotali(cid:19) (cid:18)hFTotali(cid:19) introduced by the calibration and observing conditions. where(Windhorst et al.1984;Condon1997andalsothe For all our samples we constructed median co-added explanations in Schinnerer et al. 2004, 2010) cutout images (Fig. 3) and determined accurate RMS- noise estimates (hereafter σStack) for the image stacksas σ S −2 1 2 described in Sec. 3.1. These (115 115) pixel2 dirty data = + (2) maps were processed within AIPS.38× hFTotali s(cid:18)N(cid:19) (cid:18)100(cid:19) We used the task PADIM to make the stacked images equal in size to a (512 512) pixel2 image of the VLA- σfit 2 θBθb 2 2 COSMOS synthesized ×(dirty) beam by filling the outer F =vρ + θ θ ρ2 + ρ2 . (3) imageframewithadditionalpixelsofconstantvalueThe h Totali uu S (cid:18) M m(cid:19) ψ φ! t task APCLN with a circular CLEAN box of radius of θ = 1.5′′ is the major axis and θ = 1.4′′ the minor seven pixels (i.e. 2.45′′) around the central component aMxisofthe beamwhile θ andθ armethe majorandmi- M m wasthen usedto CLEANeachdirty mapdownto a flux nor axis of the measured (hence convolved) flux density density threshold of 2.5 σStack39. distribution. In orderto include the bootstrapping error × Integrated flux densities, as well as source dimensions estimates we set S/N = F /σ , i.e. the ratio of peak bs andpositionanglesafterdeconvolutionwiththeCLEAN the peak flux density in thhe staciked dirty map and the beamwereobtainedbyfitting asingle-componentGaus- 68 % confidence interval resulting from the bootstrap- sian elliptical model to the CLEAN image within a ping. The same applies to the parameter-dependent es- quadraticboxof(15 15)pixel2 aroundthecentralpixel timators of the fit entering equation (3) that are given × usingthetaskJMFIT.Errorsontheintegratedfluxden- by: 38 Note that only bright (> 45 µJy) radio sources have been a b 2 θ θ θ θ S CLEANedintheindividualpointingspriortotheassemblyofthe ρ2 = M m 1+ B 1+ b (4) final mosaic. Hence, a stack of fainter sources will displaya clear X 4θ θ θ θ N beampatternasseeninFig. 3whichmustbedeconvolved. B b (cid:18) M(cid:19) (cid:18) m(cid:19) (cid:18) (cid:19) 39 This is a conservative threshold. We confirmed that this and a = b = 1.5 for ρ , a = 2.5 and b = 0.5 for ρ as F M choicedoesnotleadtosystematicbiasesbyCLEANingindividual well as a=0.5 and b=2.5 for ρ . tsatainckededfriommagbeosthdoawpnprtooac1h×esσdSotancko.t dIniffteegrrbaytedmoflruexthdaenns3iti%esaonbd- Foragivensub-samplecenteremdatagivenmedianred- donotleadtomass-dependenteffects. Thementionedfluctuations shift zphot the average (median stacking based) inte- arewellwithintheerrormargins. gratedh fluxidensity F observed at 1.4 GHz can be Total h i