The Evolving Interstellar Medium of Star Forming Galaxies Since z=2 as Probed by Their Infrared Spectral Energy Distributions
Georgios E. Magdis, E. Daddi, M. Bethermin, M. Sargent, D. Elbaz, M. Pannella, M. Dickinson, H. Dannerbauer, E. Da Cunha, F. Walter, D. Rigopoulou, V.Charmandaris, H.-S. Hwang, J. Kartaltepe
aa r X i v : . [ a s t r o - ph . C O ] O c t to appear in ApJ Preprint typeset using L A TEX style emulateapj v. 10/09/06
THE EVOLVING INTERSTELLAR MEDIUM OF STAR FORMING GALAXIES SINCE Z=2 AS PROBED BYTHEIR INFRARED SPECTRAL ENERGY DISTRIBUTIONS
Georgios E. Magdis , E. Daddi , M. B´ethermin , M. Sargent , D. Elbaz , M. Pannella , M. Dickinson , H.Dannerbauer , E. da Cunha , F. Walter , D. Rigopoulou , V. Charmandaris , H.S Hwang J. Kartaltepe to appear in ApJ ABSTRACTUsing data from the mid-infrared to millimeter wavelengths for individual galaxies and for stackedensembles at 0 . < z <
2, we derive robust estimates of dust masses ( M dust ) for main sequence (MS)galaxies, which obey a tight correlation between star formation rate (SFR) and stellar mass ( M ∗ ),and for star-bursting galaxies that fall outside that relation. Exploiting the correlation of gas todust mass with metallicity ( M gas / M dust − Z ), we use our measurements to constrain the gas content,CO-to-H conversion factors ( α CO ) and star formation efficiencies (SFE) of these distant galaxies.Using large statistical samples, we confirm that α CO and SFE are an order of magnitude higher andlower, respectively, in MS galaxies at high redshifts compared to the values of local galaxies withequivalently high infrared luminosities ( L IR > L ⊙ ). For galaxies within the MS, we show thatthe variations of specific star formation rates (sSFR=SFR/ M ∗ ) are driven by varying gas fractions.For relatively massive galaxies like those in our samples, we show that the hardness of the radiationfield, h U i , which is proportional to the dust mass weighted luminosity ( L IR / M dust ), and the primaryparameter defining the shape of the IR-spectral energy distribution (SED), is equivalent to SFE/Z.For MS galaxies with stellar mass log( M ∗ /M ⊙ ) ≥ . h U i , showing that itdoes not depend significantly on either the stellar mass or the sSFR. This is explained as a simpleconsequence of the existing correlations between SFR − M ∗ , M ∗ − Z and M gas − SFR. Instead, we showthat h U i (or equally L IR / M dust ) does evolve, with MS galaxies having harder radiation fields and thuswarmer temperatures as redshift increases from z = 0 to 2, a trend which can also be understoodbased on the redshift evolution of the M ∗ − Z and SFR − M ∗ relations. These results motivate theconstruction of a universal set of SED templates for MS galaxies, that are independent of their sSFRor M ∗ , but which vary as a function of redshift with only one parameter, h U i . Subject headings: INTRODUCTION
Deep and wide multi-wavelength extragalactic surveyshave greatly enhanced our understanding of galaxy evo-lution. It has now been well established that the star for-mation rates (SFRs) in galaxies were on average higherin the past, with galaxies emitting the bulk of their bolo-metric energy in the infrared (IR) progressively domi-nating the star formation density of the Universe thatpeaked at z ≥ Department of Physics, University of Oxford, Keble Road,Oxford OX1 3RH CEA, Laboratoire AIM, Irfu/SAp, F-91191 Gif-sur-Yvette,France NOAO, 950 N. Cherry Avenue, Tucson, AZ 85719, USA Universit¨at Wien, Institut ¨ur Astronophysik,T¨urkenschanzstrasse 17, 1180 Wien, Austria Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, D-69117Heidelberg, Germany Space Science & Technology Department, Rutherford Apple-ton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX Department of Physics & ICTP, University of Crete, GR-71003, Heraklion, Greece IESL/Foundation for Research & Technology-Hellas, GR-71110, Heraklion, Greece Chercheur Associ´e, Observatoire de Paris, F-75014, Paris,France Smithsonian Astrophysical Observatory, 60 Garden Street,Cambridge, MA 02138, USA discovery that the majority of star-forming galaxies atevery redshift define a narrow locus in the stellar mass( M ∗ ) − star formation rate (SFR) plane. This correla-tion has been observed in the local Universe (Brinchmannet al. 2004; Peng et al. 2010), as well as at intermediateredshifts 0 . < z < M ∗ appears to be present at all epochs has been used to de-fine a characteristic specific star formation rate (sSFR ≡ SFR /M ∗ ) at each redshift and stellar mass, and fromits evolution with cosmic time, a main sequence (MS)mode of star formation that is followed by the majorityof star-forming galaxies. This main sequence also servesas a tool to distinguish starburst (SB) from normal galaxies at any redshift, simply by measuring the excesssSFR of the galaxy with respect to the SFR– M ∗ corre-lation at that redshift. Such outliers are known to existat any redshift. In the local Universe, a class of galaxiesthat are usually identified as starbursts are the (Ultra) Throughout the paper we will use the terms “normal” and“main sequence” galaxy interchangeably
Luminous Infrared Galaxies (ULIRGs, L IR > L ⊙ ,Sanders & Mirabel 1996, Elbaz et al. 2007). However, inthe distant Universe it has proven to be harder than ini-tially thought to associate pure starbursts with a specificclass of high − z galaxies, although at least a fraction ofSubmillimeter Galaxies (SMGs) seem to exhibit elevatedspecific star formation rates (Tacconi et al. 2006; 2008;Daddi et al. 2007; 2009, Takagi et al. 2008).The remarkable uniformity of MS galaxies, as indicatedby the SFR- M ∗ correlation, and their contrasting natureto that of starburst galaxies, has recently been furthermanifested with respect to two more sets of observableparameters. Using direct measurements of the total in-frared luminosity ( L IR = L − µm ) of distant galaxiesthat have now become possible with the Herschel
SpaceObservatory (Pilbratt et al. 2010), Elbaz et al. (2011)showed that galaxies that follow the SFR- M ∗ correlationare also part of a secondary, infrared main sequence, de-fined by a universal total-to-mid-IR luminosity ratio, IR8 ≡ L IR / L , where L is the rest-frame 8 µ m luminosity.The majority of MS sequence galaxies, at all luminosi-ties and redshifts, are found to obey this linear correla-tion between L IR and L , suggesting that they share acommon IR spectral energy distribution (SED), with amid-to-far-IR shape that has evolved little with cosmictime. Interestingly, starburst galaxies, which systemat-ically fall above the SFR- M ∗ main sequence, are alsooutliers to the L IR - L relation, exhibiting elevated IR8values with respect to normal galaxies.The third quantity that highlights the distinct natureof MS and starbursts encompasses the main driver of starformation activity: the molecular gas mass ( M H ), i.e.,the raw material out of which galaxies form stars. Recentstudies, by Daddi et al. (2010) and Genzel et al. (2010),found that normal galaxies at any redshift have lower starformation efficiencies (SFE ≡ SFR/ M H ), compared tostar-bursting systems that exhibit an accelerated modeof star formation activity, probably triggered by a ma-jor merger. These studies all suggest that there are tworegimes of star formation: i) a long–lasting mode, fol-lowed by the majority of galaxies at every redshift thatalso form a tight MS in the SFR − M ∗ and in the L IR − L planes, and ii) a short–lived starburst mode for galax-ies that can become strong outliers from both relations.However, this picture heavily relies on M H estimateswhich are still a matter of significant debate due to thepoorly determined conversion factor to derive molecu-lar gas mass from CO luminosities ( α CO = M H / L ′ CO ),which is known to vary as a function of metallicity and,perhaps, of the intensity of the radiation field (e.g., Leroyet al. 2011, Magdis et al. 2011b).Although the separation between starbursts and MSgalaxies is already apparent in the observed L IR - L ′ CO plane, the distinct nature of the star formation ac-tivity of the two populations becomes truly evident whendifferent α CO factors are used for the two classes of galax-ies. This differentiation of the α CO value has clearlybeen seen in the nearby universe, with local ULIRGs(starbursts) having, a value of α CO that is a factor of ∼ (e.g.,Downes & Solomon 1998), and seems to be true at high We note that Papadopoulos et al. (2012) presented evidencethat higher α CO values are possible in local ULIRGs redshift too. Using a dynamical and a dust-to-gas massratio analysis of star-forming disks at z ∼ .
5, Daddiet al. (2010a) and Magdis et al. (2011b) argued for aCO conversion factor α CO ∼ α CO ∼ α CO values for disksand mergers at all redshifts, although with a consider-able scatter (e.g., Narayanan et al. 2011, Feldmann et al.2012). These findings challenge the common approachof “blindly” applying a (local) ULIRG-like α CO = 0 . M H of high − z ULIRGs. Instead,they highlight the necessity of determining α CO in largersamples of high − z galaxies and of investigating how itvaries between normal galaxies and mergers/starburst,but also among galaxies on the main sequence.To this end, in Magdis et al. (2011b), we applied, forthe first time at high redshift, a method for measur-ing α CO that is commonly used in the local universe.The method relies on measuring the total dust mass ofa galaxy ( M dust ) and assuming that it is proportional to M gas (e.g., Leroy et al. 2011). Taking advantage of thedetailed characterization of the peak of the SED enabledby Herschel data, as well as of the Rayleigh-Jeans tailfrom ground based mm observations, we acquired robust M dust estimates for a normal disk at z ∼ . z = 4 .
05. The dust mass estimates weresubsequently used to infer an α CO value of ∼ ∼ L IR / M dust ) and α CO andSFE, with MS galaxies exhibiting lower L IR / M dust val-ues compared to SB galaxies.Having demonstrated the applicability of the methodat high redshift, here we extend this exercise to a largersample of main sequence disks at z ∼ . z ∼ . Herschel datafrom the
Herschel
Great Observatories Origins Deep Sur-vey (GOODS-
Herschel , PI D. Elbaz) as well as low-transition CO observations and mm continuum interfero-metric measurements. We use this to investigate the av-erage α CO value for high − z MS galaxies, finding consis-tent values with what is predicted by the local α CO ver-sus Z trend and what is inferred by dynamical analyses(Daddi et al. 2010b).Pushing the method further, we here analyse large sta-tistical samples of galaxies at z ∼ z ∼ The units of α CO , M ⊙ pc − (K km s − ) − , are omitted fromthe text for brevity. Also, α CO estimates in this work account forthe presence of Helium coexisting with the molecular hydrogen ust and Gas in Star Forming Galaxies to z = 2 3“thickness” of the SFR- M ∗ relation that has been shownto reflect the variation of the physical properties of MSgalaxies (e.g., Salmi et al. 2012, Elbaz et al. 2011). Fur-thermore, the available data allow us to investigate theSED shape of MS galaxies as function of redshift andalso as a function of their their offset from the main se-quence. Put together, in this study we attempt to charac-terize the gas, dust and SED properties of main sequencegalaxies throughout cosmic time and therefore provide abetter understanding of the nature of the sources thatdominate the star formation density at all redshifts (e.g.,Rodighiero et al. 2011, Sargent et al. 2012).This paper is organized as follows. In Section 2, wedescribe our sample and the multi-wavelength observa-tions. In Section 3 we present a detailed analysis of thefar-IR properties. In Section 4 we discuss the methodto derive α CO and present α CO and SFE estimates forMS and starburst galaxies. In Section 5, we explore thevariations of SFE within the MS, and discuss two pos-sible scenarios to explain the observed dispersion of theSFR- M ∗ correlation. In Section 6 we investigate thesetwo scenarios through stacking, while in Section 7 we ex-plore the shape of the SED of MS galaxies as a functionof cosmic time and build template SEDs of MS galaxiesin various redshift bins. Finally, in Section 8, we pro-vide a discussion motivated by the results of this study,while a summary of the latter is presented in Section 9.Throughout the paper we adopt Ω m = 0 . , H = 71 kms − Mpc − , Ω Λ = 0.7 and a Chabrier IMF (Chabrier etal. 2003). OBSERVATIONS AND SAMPLE SELECTION
The aim of this study is to investigate the far-IR andgas properties of high − z , normal, main sequence galax-ies. Instead of using a large, heterogeneous sample, wedecided to focus on a small but well defined set of sourcesselected to meet the following criteria: 1) available spec-troscopic redshifts; 2) rich rest-frame UV to mid-IR pho-tometry; 3) no excess in the specific star formation rate,i.e., sSFR/sSFR MS < MS is the MS trend,as detailed below) 4) available [1-0] or [2-1] low-transitionCO observations, to enable CO luminosity estimates,without the caveat of the uncertainties introduced bythe excitation corrections affecting higher CO transitionlines; 5) Herschel detections that offer a detailed sam-pling of the far-IR part of the SED; and, if possible, 6)mm continuum data that provide a proper characteriza-tion of the Rayleigh-Jeans tail, which is crucial for robustdust mass estimates.To derive a characteristic sSFR MS at a given redshiftand a given stellar mass, we define a main sequence,SFR MS ( z, M ∗ ), that varies with stellar mass with a slopeof 0.81 (e.g., Rodrighero et al. 2011), and evolves withtime as (1 + z ) . (e.g., Elbaz et al. 2011, Pannella et al.2009). In what follows we describe the Herschel observa-tions used in this study, as well as the sample of galaxiesconsidered here.
Herschel Data
We use deep 100 and 160 µ m PACS and 250, 350, and500 µ m SPIRE observations from the GOODS- Herschel program. Details about the observations are given in El-baz et al. (2011).
Herschel fluxes are derived from point-spread function (PSF) fitting using galfit (Peng et al. 2002). A very extensive set of priors, including all galax-ies detected in the ultra-deep Spitzer Multiband ImagingPhotometer (MIPS) 24 µ m imaging, is used for source ex-traction and photometry at 100, 160 and 250 µ m, whicheffectively allow us to obtain robust flux estimates forrelatively isolated sources, even beyond formal confusionlimits at 250 µ m. For 350 and 500 µ m, this approach doesnot allow accurate measurements due to the increasinglylarge PSFs. Hence, we use a reduced set of priors basedprimarily on Very Large Array (VLA) radio detections,resulting in flux uncertainties consistent with the confu-sion noise at the IR wavelengths. Our measurements arein good agreement with the alternative catalogs used inElbaz et al. (2011). The advantage of using galfit forPSF fitting is in its detailed treatment of the covariancematrix to estimate error bars in the flux measurements,which is crucial to eventually derive reliable estimate offlux errors for the case of blended/neighbouring sources.The effective flux errors in each band can vary substan-tially with position, depending on the local density ofprior sources over areas comparable to the PSF. A de-tailed description of the flux measurements and MonteCarlo (MC) derivations of the uncertainties will be pre-sented elsewhere (E. Daddi et al., in preparation). Wecorrect the PACS photometry for a small flux bias intro-duced (due to source filtering for background subtrac-tion) during data reduction (see H-GOODS public datarelease ; Popesso et al. in preparation). A Sample of Main Sequence Galaxies at z ∼ . and z ∼ . z ∼ . µ mdata, the sources are seen in the 16 µ m InfraRed Spec-trograph peak-up image (Teplitz et al. 2011). Althoughwe will revisit (and confirm) the star formation rates ofthese sources based on the Herschel data, the existingUV, mid-IR and radio SFR estimates, along with stel-lar mass measurements derived by fitting the Bruzual &Charlot (2003) model SEDs to their rest-frame UV tonear-IR photometry (Daddi et 2010a), consistently placethem in the SFR − M ∗ main sequence at z ∼ . z ∼ . n < . http://hedam.oamp.fr/GOODS-Herschel/index.php TABLE 1PACS, SPIRE and 1.3mm photometry for MS galaxies in this study
Source RA DEC S S S S S S . mm J2000 J2000 mJy mJy mJy mJy mJy mJy
ID-8049 188.9751587 62.1787071 10.7 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± we have CO[2-1] emission line detections (Daddi et al.2010b). Similar to the z ∼ . − M ∗ main sequence based on their 24 µ m–derived IR luminosities and SFRs, which are known tobe robust in this redshift range (Elbaz et al. 2010, 2011).The Herschel and millimetre photometry of the main se-quence galaxies considered here are summarised in Table1.
A Sample of High − z SMGs
As a comparison sample to our MS galaxies, we alsoinclude in our analysis a small sample of SMGs: GN20,SMMJ2135-0102 and HERMES J105751.1+573027. Theselection of the targets was driven by the need foravailable multi-wavelength photometry, including
Her-schel and mm continuum observations, as well as CO[1-0]emission line detections.GN20 was already studied in Magdis et al. (2011). Itis one of the best-studied SMGs to date, the most lumi-nous and also one of the most distant ( z = 4 .
05, Pope etal. 2006, Daddi et al. 2009) in the GOODS-N field.
Her-schel photometry and the far-IR/mm properties of thesource have already been presented in detail in Magdiset al. (2011b). In brief, the source is detected in all
Her-schel bands (apart from 100 µ m) and in the AzTEC 1.1mm map (Perera et al. 2008) while continuum emissionis also measured at 2.2, 3.3, and 6.6 mm (Carilli et al.2011) as well as at 1.4 GHz with the VLA (Morrison etal. 2010). Furthermore, Carilli et al. (2010) reported thedetection of the CO[1-0] and CO[2-1] lines with the VLA,and CO[6-5] and CO[5-4] lines with the Plateau de BureInterferometer (PdBI) and the Combined Array for Re-search in Millimeter Astronomy (CARMA), respectively.A compilation of the photometric data is given in Table1 of Magdis et al. (2011b).SMMJ2135-0102 (SMM-J2135 hereafter) is a highlymagnified SMG at z = 2 . µ = 32.4 ± µ m cooling line.Finally, HERMES J105751.1+573027 (HSLW-01 here-after), is a Herschel /SPIRE-selected galaxy at z=2.957,multiply-lensed (magnification factor µ = 10 . ± .
7) bya foreground group of galaxies. The source was discov-ered in Science Demonstration Phase
Herschel /SPIREobservations of the Lockman-SWIRE field as part of theHerschel Multi-tiered Extragalactic Survey (HerMES; S.Oliver et al. 2012). The optical to mm photometry of thesource is presented in Table 1 of Conley at al. (2011),while Riechers et al. (2011) reports the detection of CO[5-4], CO[3-2], and CO[1-0] emission using the PdBI andCARMA and the Green Bank Telescope.We note that due to the high magnification factor forSMM-J2135 and HSLW-01, these sources might not berepresentative of the bulk population of SMGs, tradi-tionally selected as S > A Statistical Sample of z ∼ and z ∼ MSGalaxies
In addition to our samples of individually-detected MSgalaxies at z ∼ . z ∼ .
5, we also perform a stack-ing analysis to derive the average SED of MS galaxiesat z ∼ z ∼
2. Specifically, we use the z ∼ n > . µ m detected galaxies fromthe GOODS ultra-deep Spitzer imaging. To remove star-bursts we proceed as follows: i) from M ∗ and redshift, wecompute sSFR MS , i.e., the fiducial mean sSFR expectedfor MS galaxies with a given mass and redshift, derivedas described at the start of § Herschel data wederive L IR and subsequently SFR estimates, and excludegalaxies with measured sSFR/sSFR MS >
3. Since notall starburst systems are expected to be detected by
Her-schel we also omit sources with sSFRs/sSFR MS > Spitzer estimates of Salmi etal. (2012). The z ∼ z ∼ z ∼ z ∼ • µ m: We use the Teplitz et al. (2011) maps.The stacking is performed using the IAS stackinglibrary (B´ethermin et al. 2010a) and PSF-fittingphotometry. •
24 and 70 µ m: We use the 24 µ m and 70 µ m (Frayeret al. 2006b) maps of GOODS, the IAS stackinglibrary and aperture photometry with parameterssimilar to that in B´ethermin et al. (2010a). •
100 and 160 µ m: We use the GOODS- Herschel
PACS data (Elbaz et al. 2011), the IAS stackinglibrary and PSF-fitting. We apply the appropriateflux correction for faint, non masked, sources to thePACS stacks (Popesso et al. in preparation). • µ m: We use the GOODS- Herschel
SPIRE (Elbaz et al. 2011) data and themean of pixels centred on sources as in B´etherminet al. (2012a). The bias due to clustering is esti-mated to be about 20% at 500 µ m and thus neg-ligible compared with the statistical uncertainties.This bias is smaller at shorter wavelengths wherethe beam is narrower (B´ethermin et al. 2012a). • µ m and 1100 µ m: We used the Weiß et al.(2009) LABOCA map of eCDFS and the Perera etal. (2008) AzTEC map of GOODS-N. Contrary toSPIRE, (sub-)mm data are noise-limited, it is thusoptimal to beam-smooth the map before stacking(Vieira et al. in prep.). We thus apply the Mars-den et al. (2009) method to perform our stacking,which takes the mean of pixels centered on sourcesin the beam-smoothed map.At all wavelengths, we used a bootstrap technique toestimate the uncertainties (Jauzac et al. 2011), and themean fluxes measured in the two fields are combinedquadratically to produce a mean SED at z ∼ z ∼ z ∼ . < log( M ∗ /M ⊙ ) < . M ∗ /M ⊙ ) =0 .
5, as well as in four bins of sSFR/sSFR MS over therange − . < log(sSFR / sSFR MS ) < .
4, with a bin sizeof ∆ log(sSFR / sSFR MS ) = 0 . DERIVATION OF FAR-IR PROPERTIES
Several key physical properties of distant galaxies, suchas infrared luminosities ( L IR ), dust temperatures ( T d )and dust masses ( M dust ), can be estimated by fittingtheir mid-to-far-IR SEDs with various models and tem-plates calibrated in the local Universe. However, the lackof sufficient data for a proper characterization of the SEDof distant galaxies has often limited this kind of analy-sis to models suffering from (necessarily) over-simplified assumptions and large generalizations. The Spitzer , Her-schel , and millimeter data available for the galaxies in ourhigh − z sample provide thorough photometric samplingof their SEDs, allowing the use of more realistic modelsthat previously have been applied mainly in the analysisof nearby galaxies. Here we consider both the physically-motivated Draine & Li (2007) (DL07 hereafter) models,as well as the more simplistic, but widely used, modifiedblack body model (MBB). The Draine & Li 2007 Model
We employ the dust models of DL07, which consti-tute an update of those developed by Weingartner &Draine (2001) and Li & Draine (2001), and which weresuccessfully applied to the integrated photometry of theSpitzer Nearby Galaxy Survey (SINGS) galaxies (Draineet al. 2007). These models describe the interstellar dustas a mixture of carbonaceous and amorphous silicategrains, whose size distributions are chosen to mimicthe observed extinction law in the Milky Way (MW),the Large Magellanic Cloud (LMC), and the SmallMagellanic Cloud (SMC) bar region. The properties ofthese grains are parametrized by the PAH index, q PAH ,defined as the fraction of the dust mass in the form ofPAH grains. The majority of the dust is supposed to belocated in the diffuse ISM, heated by a radiation fieldwith a constant intensity U min . A smaller fraction γ ofthe dust is exposed to starlight with intensities rangingfrom U min to U max , representing the dust enclosed inphoto-dissociation regions (PDRs). Although this PDRcomponent contains only a small fraction of the totaldust mass, in some galaxies it contributes a substantialfraction of the total power radiated by the dust. Then,according to DL07, the amount of dust dM dust exposedto radiation intensities between U and U + dU can be ex-pressed as a combination of a δ -function and a power law:dM dust dU = (1 − γ )M dust δ (U − U min ) + γ M dust α − − α min − U − α max U − α (1)with ( U min ≤ U max , α = 1), M dust the total dust mass, γ the fraction of the dust mass that is associated with thepower-law part of the starlight intensity distribution, and U min , U max , α characterizing the distribution of starlightintensities in the high-intensity regions.Following DL07, the spectrum of a galaxy can be de-scribed by a linear combination of one stellar componentapproximated by a blackbody with color temperature T ∗ = 5000K, and two dust components, one arising fromdust in the diffuse ISM, heated by a minimum radiationfield U min (“diffuse ISM” component), and one from dustheated by a power-law distribution of starlight, associ-ated with the intense photodissociation regions (“PDR”component). Then, the model emission spectrum of agalaxy at distance D is:f model ν = Ω ∗ B ν (T ∗ ) + M dust π D h (1 − γ )p (0) ν + γ p ν i , (2)where Ω ∗ is the solid angle subtended by stellar pho-tospheres, p (0) ν = p (0) ν ( q PAH , U min ) and p ν = p ν ( q PAH , U min , U max , α ) are the emitted power per unit frequencyper unit dust mass for dust heated by a single starlightintensity U min , and dust heated by a power-law distri- Fig. 1.—
Observed SEDs of z ∼ . U = U min (diffuse ISM component) and dust heated by U min < U < U max (“PDR” component) respectively. The fitted parametersfrom the best fit Draine & Li (2007) model fits are listed within each panel. Fig. 2.—
Same as Figure 1, but for the z ∼ . bution of starlight intensities dM/dU ∝ U − α extendingfrom U min to U max .In principle, the dust models in their most gen-eral form are dictated by seven free parameters,(Ω ∗ , q PAH , U min , U max , α, γ and M d ). However, Draine etal. (2007) showed that the overall fit is insensitive to theadopted dust model (MW, LMC and SMC) and the pre-cise values of α and U max . In fact they showed that fixedvalues of α = 2 and U max = 10 successfully describedthe SEDs of galaxies with a wide range of properties.They also favor the choice of MW dust models for whicha set of models with q P AH ranging from 0.4% to 4.6% is available. Furthermore, since small U min values corre-spond to dust temperatures below ∼
15 K that cannotbe constrained by far-IR photometry alone, in the ab-sence of rest-frame submm data, they suggest using 0.7 ≤ U min ≤
25. While this lower cutoff for U min preventsthe fit from converging to erroneously large amounts ofcold dust heated by weak starlight ( U min < Fig. 3.—
Same as Figure 1, but for the SMGs in our sample. the derived total dust masses.Under these assumptions, we fit the mid-IR to mmdata points of each galaxy in our sample, searching forthe best fit model by χ minimization and parametrizingthe goodness of fit by the value of the reduced χ , χ ν ≡ χ /df (where df is the number of degrees of freedom).The best fit model yields a total dust mass ( M dust ), U min , γ and q PAH while to derive L IR1 estimates we integratethe emerging SEDs from 8- to 1000 µ m: L IR = Z µm µm L ν ( λ ) × cλ d λ. (3)A by-product of the best fit model is also the dustweighted mean starlight intensity scale factor, h U i , de-fined as: h U i = L dust P M dust or (cid:20) (1 − γ ) U min + γ ln( U max /U min ) U − min − U − max (cid:21) , f or α = 2(4)where P is the power absorbed per unit dust mass in aradiation field with U = 1. Note that essentially h U i isproportional to L IR / M dust , and as we will discuss laterfor the definition of L IR adopted here, i.e. L − µ m ,our data suggest that P ≈ L IR and M dust are quantified using Monte Carlo simulations. Tosummarise, for each galaxy a Gaussian random num-ber generator was used to create 1000 artificial flux setsfrom the original fluxes and measurement errors. Thesenew data sets were then fitted in the same way, and thestandard deviation in the new parameters was taken torepresent the uncertainty in the parameters found fromthe real data set. Best fit values along with their corre-sponding uncertainties are listed in Table 2 for all sourcesin our sample. To check for possible contamination ofthe submm continuum broad band photometry from C+(158 µ m) emission (e.g., Smail et al. 2011), we repeatedthe fit excluding the affected bands (i.e., 350 µ m and500 µ m for z ∼ z ∼ . − . L dust quoted below is similar to L IR , but integrated from 0 to ∞ fit models along with the observed SEDs of the z ∼ . z ∼ . The Importance of Millimeter Data
While
Herschel data accurately probe the peak of theSED in the far-IR emission of distant galaxies, rest-framesubmm observations ( λ rest ≥ µ m) are necessary tosample the Rayleigh-Jeans tail. Since the available far-IR photometry for five of our sources is restricted to Her-schel observations, it is important to explore possible bi-ases or systematics introduced by the lack of mm contin-uum data. Given the ever increasing number of distantgalaxies with
Herschel photometry, this investigation willalso provide guidance for similar studies in the future. Toassess the significance of adding mm photometry in thederivation of the far-IR properties of the galaxies, andparticularly their dust mass, we repeat the fitting proce-dure, this time excluding any data at wavelengths longerthan rest-frame 200 µ m, for the four z ∼ . h M mm dust /M nomm dust i = 0 . ± .
2. Interestingly, the sourceswith the largest discrepancies are the SMGs, althoughthe sample is too small to clearly demonstrate the exis-tence of a systematic effect. However, the addition of mmdata has a noticeable impact on the uncertainties of thederived M dust estimates, which are reduced, on average,by a factor of ∼
2. Studies in the local universe reachsimilar conclusions, with the addition that in the absenceof rest-frame sub-mm data, dust masses tend to be un-derestimated for metal-poor galaxies. This could serveas an indirect indication that our sample mainly consistsof metal-rich sources, something that we will also arguein Section 4.The derived γ and U min are also in broad agreement be-tween the two cases. However, we notice a weak system-atic bias towards higher h U i values, i.e., stronger meanradiation fields, when mm data are considered in the fit,reflecting the fact that h U i ∝ L IR / M dust . We concludethat such trends in h U i and M dust suggest that mm data TABLE 2Physical properties of individually detected sources, based on Draine & Li 2007 Models
Source z spec χ ν log L IR log M d (DL07) U min γ q PAH h U i T d a β a L ⊙ M ⊙ % % KID-8049 0.507 2.1 11.22 ± ± ± b ID-5819 0.530 1.78 11.26 ± ± ± b ID-7691 0.637 0.65 11.54 ± ± ± b BzK-4171 1.465 1.56 11.98 ± ± ± b BzK-12591 1.600 1.04 12.44 ± ± ± b BzK-25536 1.459 1.94 11.46 ± ± ± b BzK-21000 1.523 1.12 12.32 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± c ± ± ± ± c ± ± ± ± d ± ± ± b Stack-z2 d ± ± ± b Notes:a: Derived based on single temperature MBBb: β fixed to this value in the MBB fitc: Values corrected for magnificationd: Best fit values accounting for the redshift distribution of the sample can place better constraints on the diffuse ISM emis-sion, as well as on the relative contribution of a PDRcomponent to the total radiation field, and consequentlyon the M dust of individual high − z galaxies. Finally, wenote that the detailed sampling of the peak of the far-IRemission provided by Herschel data can result in robust L IR estimates without the need of mm data. Comparison With Modified Black Body Fits
Another method for deriving estimates for the dustmasses and other far-IR properties such as dust temper-atures and dust emissivity indices ( β ), is to fit the far-IRto submm SED of the galaxies with a single-temperaturemodified blackbody, expressed as: f ν ∝ ν β e hνkTd − T d is the effective dust temperature and β is theeffective dust emissivity index. Then, from the best fitmodel, one can estimate M dust from the relation: M d = S ν D L (1 + z ) κ rest B ν ( λ rest , T d ) , with κ rest = κ ( λ o λ rest ) β (6)where S ν is the observed flux density, D L is the lumi-nosity distance, and κ rest is the rest-frame dust massabsorption coefficient at the observed wavelength. Whilethis is a rather simplistic approach, mainly adopted dueto the lack of sufficient sampling of the SED of distantgalaxies, it has been one of the most widely-used meth-ods in the literature. Therefore, an analysis based onMBB-models not only provides estimates of the effectivedust temperature and dust emissivity of the galaxies inour sample, but also a valuable comparison between dustmasses inferred with the MBB and DL07 methods.We fit the standard form of a modified black body,considering observed data points with λ rest > µm ,to avoid emission from very small grains that dominateat shorter wavelengths. For the cases where mm dataare available we let β vary as a free parameter, whilefor the rest we have assumed a fixed value of β = 1 . M dust through equation 6. Forconsistency with the DL07 models we adopt a value of κ µm = 5.1 cm g − (Li & Draine 2001). To obtain thebest fit models and the corresponding uncertainties of theparameters, we followed the same procedure as for theDL07 models. The derived parameters are summarizedin Table 2 and the best fit models are shown in Figures1, 2 and 3.A comparison between dust masses derived by DL07and MBB models in shown in Figure 4 (right). We seethat a modified black body appears to infer dust massesthat are lower than those derived based on DL07 mod-els on average by a factor of ∼ h M DL /M MBB dust i =1 . ± . S /S colors. Interestingly, when we con-volve the best fit DL07 rest-frame SEDs of our galaxieswith the 70- and 160 µ m PACS filters, we find that thesources with the warmest S /S are indeed those withthe best agreement in the dust masses derived from thetwo methods. The reason behind this discrepancy hasbeen addressed by Dunne et al. (2000). The grains ofa given size and material are exposed to different inten-sities of the interstellar radiation field and thus attaindifferent equilibrium temperatures which will contributedifferently to the SED. The single-temperature modelscannot account for this range of T d in the ISM and at-tempt to simultaneously fit both the Wien side of thegrey body, which is dominated by warm dust, as well asthe Rayleigh-Jean tail, sensitive to colder dust emission.The net effect is that the temperatures are driven to-wards higher values, consequently resulting in lower dustmasses. While restricting the fit to λ ≤ µ m does notprovide an adequate solution to the problem (Dale et al.2012), a two-temperature black body fit is more realis-tic and returns dust masses that are larger by a factor of ∼ T d MBB(Dunne & Eales 2001), in line with those inferred by theDL07 technique.Despite the large uncertainties associated with theust and Gas in Star Forming Galaxies to z = 2 9
Fig. 4.—
Left:
The significance of the addition of mm continuum data for the derivation of dust masses. A comparison between theDL07 M dust estimates inferred with and without the addition of mm data to the fit. Although, the two estimates seem to be overall ingood agreement, we note that in absence of mm continuum data we tend to overestimate the M dust in SMGs. Right:
Comparison betweendust masses derived based on a single temperature modified black body (MBB) and those derive by the Draine & Li (2007) models. Filledsquares and open circles indicate sources with and without mm data. For the former β was treated as a free parameter in the MBB fitwhile for the latter it was fixed to β = 1 .
5. Orange stars represent the SMGs considered in this study. In both panels the black solid linecorresponds to unity and the two grey dashed lines its offset by a factor of 2 and 0.5.
MBB analysis, it is worth noting that for all SMGs inour sample we measure an effective dust emissivity in-dex β ∼ .
0, in agreement with the findings of Magnelliet al. (2012). On the other hand, the far-IR to mm SEDsof all BzK galaxies are best described by β ∼ .
5, simi-lar to that found by Elbaz et al. (2011) for MS galaxies.However, we stress that the effective β does not neces-sarily reflect the intrinsic β of the dust grains due tothe degeneracy between β and the temperature distribu-tion of dust grains in the ISM. The β - T d degeneracy alsoprevents a meaningful comparison between the derived T d for the galaxies in our sample. THE GAS CONTENT OF MAIN SEQUENCE ANDSTAR-BURSTING GALAXIES
Several studies in the local Universe have revealed thatthe total gas-to-dust mass ratio ( δ GDR ) is correlated withthe gas-phase oxygen abundance, in the sense that moremetal-rich galaxies tend to exhibit lower δ GDR values(e.g., Mu˜noz-Mateos et al. 2009, Leroy et al. 2011 andreferences within). In addition to crucial informationregarding the amount of metals trapped in the dust,this correlation can serve as a valuable tool for deriv-ing indirect estimates of the CO to molecular gas mass( M H ) conversion factor. In particular, if we know themetallicity, the dust mass and the mass of the atomicgas mass ( M HI ) of a galaxy, then we can estimate the δ GDR through the δ GDR − Z relation, and M H throughthe following relation: δ GDR M dust ≡ M gas = M H + M HI (7)Subsequently, if L ′ CO is measured then we can estimate α CO , since M H = α CO × L ′ CO . This method has success-fully been applied in the local Universe (e.g., Leroy et al.2011) and has recently been extended to high − z galax-ies by the pilot study of Magdis et al. (2011b). Eventhough restricted to only two galaxies, which are alsopart of this study (GN20 and BzK21000), Magdis et al.(2011b) showed that this approach provides α CO esti-mates that are consistent with other independent mea- surements and dynamical arguments. Although it hasbeen a common practice to adopt a value of α CO = 0.8,typical of local ULIRGs, for high − z ULIRGs, our earlierstudy suggested that such low values apply only to thesubset of genuinely star-bursting systems at high red-shift, while high − z main sequence galaxies, even thosewith L IR > L ⊙ (i.e., those classified as ULIRGs)have larger α CO values, similar to those of local spirals.Here, we wish to extend this experiment, this time usinga substantially larger sample, and to investigate possi-ble correlations between α CO and starburst versus mainsequence indicators. Estimating Metallicities
A key ingredient of this method is the metallicity of thegalaxies, for which we have to rely on indirect measure-ments. We first derive stellar mass estimates by fittingthe Bruzual & Charlot (2003) model SEDs to their rest-frame UV to near-IR spectrum. Then for the z ∼ . M ∗ − Z relation at z ∼ z ∼ . z ∼ . z ∼ .
5, and the Erb et al. (2006) relationsaturates above M ∗ ∼ M ⊙ . For these two sourceswe adopt the line of reasoning of Magdis et al. (2011b).Namely, in addition to the metallicity estimates basedon the FMR relation, we also consider the extreme casewhere the huge SFR of the two sources ( ∼ ⊙ yr − )is due to a final burst of star formation triggered by amajor merger that will eventually transform the galaxyinto a massive elliptical. Once star formation ceases,the mass and metallicity of the resulting galaxy will0 Fig. 5.—
Left: M gas / M dust vs. metallicity for a sample of galaxies in the Local Group by Leroy et al. (2011) (grey circles) and localULIRGs by Downes & Solomon (1998) (grey stars). The solid black line is the best linear regression fit to Leroy’s sample and the greyshadowed area depicts the dispersion of the correlation. Filled black squares and orange stars indicate the position of z ∼ . − . − z SMGs respectively, based on the α CO vs. metallicity relation derived in the right panel (see eq. 8). The vertical,dashed line indicates the limiting metallicity for which the presented relation is used in this study. Right:
Inferred α CO values, basedon the δ GDR method, against metallicity for high − z MS galaxies (black squares), SMGs (orange stars). Similar to the left panel, weinclude the sample of galaxies in the Local Group by Leroy et al. (2011) (grey circles), as well as the local ULIRGs by Downes & Solomon(1998) (grey stars). All metallicities have been calculated on PP04 scale. The blue solid line represents the best regression fit to the data(excluding local ULIRGs), with a slope of -1.39. not change further, and one might therefore apply themass–metallicity relation of present-day elliptical galax-ies (e.g., Calura et al. 2009). Combining the metallic-ity estimates based on this scenario with those derivedbased on the FMR relation, we estimate that the metal-licities could fall in the ranges 12 + log[
O/H ] = 8.8 to 9.2for GN20, and 8.6 to 9.0 for HLSW-1. For the analysiswe will adopt 12 + log[
O/H ] = 9 . ± . O/H ] = 8 . ± . Derivation of the CO to M H Conversion Factor
To derive α CO estimates for our sample, we first derivea δ GDR − Z relation using the local sample presented byLeroy et al. (2011), after converting all metallicities tothe PP04 scale (Figure 5 left). The data yield a tightcorrelation between the two quantities described as:log δ GDR = (10 . ± . − (0 . ± . × (12+log( O/H )),with a scatter of 0.15 dex. Having obtained the M dust and metallicity estimates, we then use the δ GDR − Z relation to derive M gas and subsequentlyestimate α CO from the equation M gas = α CO × L ′ CO .For the last step we have assumed that at high − z , M H ≫ M HI or equivalently that M gas ≈ M H , assupported by both observational evidence (e.g., Daddiet al. 2010; Tacconi et al. 2010, Geach et al. 2011) andtheoretical arguments (Blitz & Rosolowsky 2006; Bigielet al. 2008, Obreschkow et al. 2009). All values and theircorresponding uncertainties, which take into accountboth the dispersion of the δ GDR − Z relation and theuncertainties in Z and M dust , are summarized in Table3. In Figure 5 (right), we plot the derived α CO valuesas a function of metallicity, along with the estimates of Adopting the relation quoted by Leroy et al. (2011), i.e.,log δ GDR = (9 . ± . − (0 . ± . × (12 + log[ O/H ]), has virtu-ally no impact on the results presented here, with a mean differencebetween the derived α CO estimates of a factor of ∼ . Leroy et al. (2011) for a sample of local normal galaxiesas well as for a sample of local ULIRGs from Downes& Solomon (1998), for which we were able to computetheir metallicities on the PP04 scale. Fitting high − z MS galaxies along with the local sample of Leroy et al.(2011), yields:log( α CO ) = − (1 . ± . × (12+log[ O/H ]) PP04 +12 . ± . α CO decreasing for higher metallicities, in agree-ment with previous studies (e.g., Wilson 1995, Israel etal. 1997, Schruba et al. 2012, and references within). Itis evident that main sequence galaxies at any redshifthave higher α CO values than those of local star-burstingULIRGs and more similar to those of local normal galax-ies. In particular, for high − z MS galaxies, we find amean α CO of 5.5 ± α CO ∼
3, while for the remainingSMGs we find α CO ∼
1, close to the average value of localULIRGs ( α CO ∼ .
8, e.g., Solomon et al. 1997, Tacconiet al. 2008). Finally, simply as a consistency check, wederive and plot in Figure 5 (left) the M gas / M dust val-ues of our targets, using α CO estimates as obtained fromequation 8. Limitations
Before trying to interpret our findings regarding the α CO values, it is important to discuss possible caveatsand limitations of the method. A key ingredient for thederivation of α CO is the M dust estimate. These estimatesrely heavily on the adopted model of the grain-size distri-bution. Dust masses based on different grain size compo-sitions and opacities in the literature can vary even by afactor of ∼
3, indicating that the absolute values shouldbe treated with caution (e.g., Galliano et al. 2011). How-ever, the relative values of dust masses derived based onthe same assumed dust model should be correct and pro-vide a meaningful comparison, as long as the dust hasust and Gas in Star Forming Galaxies to z = 2 11
Fig. 6.— L ′ CO / M dust against metallicity for the same sample ofgalaxies as in Figure 5. This plot serves as a sanity check for theassumption that the M gas / M dust vs. metallicity relation does notevolve considerably with cosmic time. similar properties in all galaxies. Therefore, any trendsarising from the derived M dust estimates are essentiallyinsensitive to the assumed dust model.One important assumption of our technique is thatthe δ GDR − Z relation defined by local galaxies does notevolve substantially with cosmic time. These quantitiesare very intimately related, as dust is ultimately madeof metals. For example, solar metallicity of Z ⊙ = 0.02means that 2% of the gas is in metals. The local δ GDR − Z relation suggests an average trend where 1% of the gasinto dust. This means that about 50% of the metalsare locked into dust. This is already quite an efficientprocess of metal condensations into dust, and it is hardto think how this could be even more efficient at high- z (where, e.g., less time is available for the evolution oflow-mass stars into the AGB phase), with a much higherproportion of metals locked into the dust phase, a situa-tion that would lead to an overestimate of M gas with ourtechnique. Similarly, chemical evolution studies suggesta small evolution of dust-to-metal ratio, i.e., by a maxi-mum factor of ∼ L ′ CO / M dust , as a function of metallicity,both local and high − z galaxies follow the same trend,suggesting that the local δ GDR − Z relation is valid athigh − z (Figure 6). Finally, while the Leroy et al. (2011)sample yields a slope of − . δ GDR − Z relation,Mu˜noz-Mateos et al (2009), find a rather steeper slopeof -2.45. However, adopting the Mu˜noz-Mateos relation(after rescaling it to PP04 metallicity), returns very sim-ilar α CO values, as the two relations intercept at metal-licities very close to the average metallicity of our sample(12 + log[ O/H ] ≈ . α CO values bya factor of ∼ α CO as a Function of Specific Star Formation Rate With robust L IR measurements in hand, we are in a po-sition to derive accurate estimates of the SFR and sSFRfor galaxies in our sample. We first convert the derived L IR to star formation rates by using the Kennicutt (1998)relation, scaled for a Chabrier IMF for consistency withour stellar mass estimates. We then infer the specific starformation rate of each source and compare it to the char-acteristic sSFR MS of the main sequence galaxies at thecorresponding redshift of the source, using the method-ology described in § z = 2 .
5. For the two SMGsat z ∼ z ∼
4, we use the SFR- M ∗ relations ofMagdis et al. (2010a) and Daddi et al. (2009) respec-tively. In order to conservatively identify MS galaxies,we classify starbursts as galaxies with an excess sSFRrelative to that of the MS galaxies by at least a factor of3, i.e., with sSFR/sSFR MS >
3. We note however thatthe sSFR/sSFR MS indicator is only a statistical measureof the star formation mode of the galaxies, and there is norigid limit that separates main sequence from starburstgalaxies.Our analysis suggests that high − z MS galaxies, asso-ciated with a secular star formation mode, exhibit higher α CO values at any redshift compared to those of merger-driven local ULIRGs. Since the latter are known to bestrong outliers from the local SFR-M ∗ relation, we ex-pect a dependence of the α CO value with sSFR. However,the functional dependence between the two quantities isnot straightforward. In the local universe, there is ev-idence for a bimodality in the α CO value, linked withthe two known star formation modes: normal disks (for Z ∼ Z ⊙ ) are associated with α CO ∼ α CO ∼ α CO of normal galaxies depends only on metallic-ity, then we expect only a weak increase of α CO as afunction of sSFR/sSFR MS within the MS. Consequently,in order to incorporate the observed steep decrease of α CO in starburst systems, α CO and the relative offsetfrom the main sequence (i.e., sSFR/sSFR MS ) will be re-lated with a step-function. On the other hand, if α CO also depends on other parameters than metallicity, suchas the compactness and/or the clumpiness of the ISM ofnormal galaxies, and if the ISM conditions of MS galaxiesdo vary significantly, then α CO could smoothly decreaseas we depart from the MS, and move towards the star-burst regime (e.g., Narayanan et al. 2012).The scenario of a continuous variation of α CO withsSFR/sSFR MS is depicted in Figure 7a. In addition toour galaxies we also include a sample of local normalgalaxies for which we have robust M ∗ and SFR estimatesfrom Leroy et al. (2008) and α CO measurements fromSchruba et al. (2012). A linear regression fit yields thefollowing relation: α CO = (5 . ± . × [sSFR / sSFR MS ] ( − . ± . (9)with a scatter of 0.3 dex. We stress that, given the lack ofa sufficient number of starbursts in our sample, this rela-tion is poorly constrained in the starburst regime. Never-theless, the locus of local ULIRGs, seems to be consistentwith the emerging trend. Note that since we lack a sam-ple of local ULIRGs for which both α CO and sSFR areaccurately determined, the position of local ULIRGs inFigure 7 indicates the average α CO and sSFR of the pop-ulation, as derived by Downes & Solomon (1998) and DaCunha et al. (2010b), respectively. To further check therobustness of the fit we also perturbed the original thedata within the errors and repeated the fit for 1000 reali-sations. The mean slope derived with this method is very2 Fig. 7.— a) Inferred α CO values against the offset from the main sequence. a) Inferred α CO values for the MS galaxies (black squares)and SMGs (orange stars) considered in this study against their offset from the main sequence, parametrized as sSFR/sSFR MS . Empty greycircles represent local disks from Leroy et al. (2008) and Schruba et al. (2012), while the empty grey star the locus of local ULIRGs. Thedata (only high − z galaxies) are best fit with a slope of -0.67 (red solid line) with a scatter of 0.3 dex and a Spearman’s rank correlationcoefficient of ρ = − . b) Same as the left panel but for the case of a metallicity-dependent α CO . Tracks show the variation predictedby Sargent et al. (2012b, in prep) based on (i) the relative importance of the starburst and main-sequence mode of star formation as afunction of sSFR/sSFR MS and (ii) a “metallicity- dependent” α CO , where the metallicity of main-sequence galaxies is inferred based on thestellar mass − star formation − metallicity relation of Mannucci et al. (2010). Blue (purple), solid, dashed and long-dashed lines correspondto z = 1 . z = 0 .
5) for M ∗ = 1.0 × M ⊙ , 5.0 × M ⊙ , and 1.0 × M ⊙ . The grey long-dashed line corresponds to z = 0 . M ∗ = 1.0 × M ⊙ . close to the one describing the original data. A Spear-man’s rank correlation test yields a correlation coefficientof ρ = − .
51, with a p − value of 0.03, suggesting a moder-ately significant correlation between sSFR/sSFR MS and α CO . However, repeating the Spearman’s test, this timeexcluding star-bursting systems, does not yield a sta-tistically significant correlation, with ρ = − .
15 and a p − value of 0.3, indicating a very small dependence, ifany, between α CO and sSFR within the MS.It is therefore unclear whether α CO varies inside theMS sequence, or if instead there is a bifurcation betweenthe mean values appropriate for MS versus SB galaxies.If the α CO conversion factor primarily depends on metal-licity, one would expect little or no variations with sSFRat constant mass within the MS. Detailed computationsfor this scenario are presented in Sargent et al. (2012b,in prep.), in which burst-like activity is assumed to becharacterised by a constant, low conversion factor, cho-sen here to be α SBCO = 0.8. To predict the variations of α CO as a function of sSFR/sSFR MS according to thisscenario, Sargent et al. (2012) compute the relative im-portance of main-sequence and starburst activity at agiven position within the stellar mass vs. SFR plane us-ing the decomposition of the sSFR-distribution at fixedstellar mass derived in Sargent et al. (2012a; based onthe data of Rodighiero et al. 2011). Metallicities, whichform the basis for computing α CO for an ISM experi-encing “normal” star-formation activity, vary smoothlyas a function of stellar mass and star formation rate ac-cording to the calibration of the fundamental metallicityplane given in Mannucci et al. (2010; see also Lara-Lopezet al. 2010). To compute the corresponding value of theconversion factor, Sargent et al. (2012b in prep.) assumea variation of α CO ∝ Z − as they find that this relationbetween metallicity and α CO reproduces the faint-endslope of the z = 0 CO-LF of Keres et al. (2003) best, under the set of assumptions just described.The colored tracks in Figure 7b delineate the varia-tions of α CO with sSFR/ h sSFR i MS expected for galax-ies in three bins of total stellar mass. Three regionscan be clearly distinguished: (i) the main-sequence lo-cus , characterised by a gradual increase of α CO withsSFR that is caused by the slight rise in metallicity pre-dicted by the FMR; (ii) the starburst region at highsSFR/ h sSFR i MS ≫
4, where the conversion factor, byconstruction, assumes a mass- and redshift-independent,constant value; and (iii) a narrow transition region (span-ning roughly sSFR/ h sSFR i MS ∈ [2 , α CO dropsfrom an approximately Milky Way-like conversion factorto the starburst value. Note that, in contrast to the pre-vious case, α CO varies only slightly among MS galaxies.This weak dependence of α CO on sSFR/sSFR MS intro-duces a step as we move from MS to starburst systems.In the emerging picture, the majority of the star-formingpopulation is dominated by either the main-sequence orstarburst mode, and only a small fraction consists of“composite” star-forming galaxies hosting both normaland starburst activity. For composite sources, the α CO should be interpreted as a mass-weighted, average con-version factor that reflects the relative amount of themolecular gas reservoir that fuels star-forming sites ex-periencing burst-like and secular star-formation events,respectively. Note also that variations with redshift (in-dicated by different colored lines in Figure 7b) are smallfor the limited range of stellar mass covered by our sam-ple, and would likely be indistinguishable within the nat-ural scatter about the median trends plotted in the Fig-ure.Both scenarios appear to be consistent with the data,leaving open the question of whether the transition fromnormal to starburst galaxies is followed by a smooth ora step-like variation of α CO . However, both scenariosust and Gas in Star Forming Galaxies to z = 2 13agree in that α CO should not vary much within the mainsequence. Indeed, even for the case of continuous vari-ation, the decrease of α CO becomes statistically signifi-cant only for strongly star-bursting systems, as equation9 indicates that α CO would vary at most by a factorof ∼ α CO ∼
5, as derived in this study, can be re-garded as representative for the whole population of MSgalaxies at any redshift, with stellar masses ≥ M ⊙ .We remind the reader that because sSFR MS increaseswith redshift as (1+z) . , at least out to z ≈ .
5, galax-ies with (U)LIRG-like luminosities can enter the MS athigher redshifts or at large stellar masses (e.g., Sargentet al. 2012). We stress that our analysis suggests thatthe α CO of these systems, i.e., high − z main sequenceULIRGs, is on average a factor of ∼ Comparison with Theoretical Predictions
The determination of the α CO value has also beenthe focus of several theoretical studies. In particularNarayanan et al. (2011), investigated the dependence of α CO on the galactic environment in numerical simula-tions of disk galaxies and galaxy mergers, and reporteda relationship between α CO and the CO surface bright-ness of a galaxy. Here, we compare our observationallyconstrained α CO values with those predicted by their the-oretical approach. According to Narayanan et al. (2011): α CO = 6 . × h W CO i − . . × × (Z / Z ⊙ ) . (10)where h W CO i , is the CO surface brightness of the galaxyin K Km s − . According to Solomon & Vanden Bout(2005) L ′ CO = 23 . × Ω B ∗ S D I ′ CO (1 + z) − (11)where L ′ CO is measured in K km s − pc , Ω B ∗ S is the solidangle of the source convolved with the telescope beammeasured in arcsec , and I ′ CO is the observed integratedline intensity in K km s − . In the case of an infinitelygood resolution, as assumed in Narayanan’s simulations,this becomes the solid angle subtended by the source.The CO line luminosity can also be expressed for a sourceof any size in terms of the total line flux:L ′ CO = 3 . × S CO ∆v ν − D (1 + z) − (12)where S CO ∆v is the velocity integrated flux in Jy kms − . From equations 11 and 12, and for the case of aninfinitely good resolution, we derive :W CO = 1 . × × ν − π (1 + z) θ − × S CO ∆v (13)where ν obs is the observed frequency and θ is the sizeof the source in arcsec . For our sources we use, wherepossible, the CO sizes, and UV sizes when CO observa-tions are too noisy to reliably measure the source extent. We introduce a (1 + z ) term here, not present in the originalNarayanan et al. formula, which is required in order to make α CO independent on redshift for fixed physical properties of the galaxies.Without that term the systematic difference between predicted andmeasured α CO values would grow to a factor of 2 Fig. 8.—
Comparison between the δ GDR inferred α CO values forthe galaxies in this study and those predicted by the theoreticalapproach of Narayanan et al. (2011). MS galaxies at z ∼ . z ∼ . Using equations 10 and 13, we then get an estimate of α CO for each source in our sample according to the pre-scription of Narayanan et al. (2011), and in Figure 8 wecompare them to the values derived based on our method.Although there seems to be a small systematic offset (onaverage by a factor of ∼ α CO values is very good when one considers the largeuncertainties and assumptions of the two independentmethods. We stress that the derived h W CO i and there-fore the estimated α CO values are very sensitive to thechoice of the size indicator. Implications for the Star Formation Activity ofHigh − z MS Galaxies
While the sSFR probes the star formation mode ofa galaxy only indirectly and from a statistical point ofview, accurate measurements of its star formation effi-ciency, SFE = SFR/ M gas , can provide more direct andreliable answers. With the robust α CO estimates de-rived in this study, we can convert the CO measurementsinto M gas and subsequently, infer the star formation effi-ciency of galaxies in our sample. In what follows we useSFE = SFR/ M gas and SFE = L IR / M gas interchange-ably, since SFR is linearly related to L IR through SFR = L IR × − (i.e., through the Kennicutt 1998 relation,calibrated for a Chabrier IMF).We have so far established that even though there ap-pears to be only small variation of α CO among MS galax-ies, the α CO of high − z MS galaxies is similar to that oflocal disks with lower L IR , and is approximately ∼ α CO value observed for lo-cal ULIRGs. The direct implication of this finding isthat for a given L ′ CO , one could expect a large variationin the amount of molecular gas for galaxies between MSand starburst galaxies. This also suggests that for a given L IR (or equally, SFR), galaxies in the main sequence havelower star formation efficiencies, as compared to star-bursting systems. Indeed, using the inferred α CO valueswe derive SFE estimates for each source in our sample4 Fig. 9.— a) Star formation efficiency, SFE= L IR / M gas , against the offset from the main sequence. Black squares and orange stars arethe MS galaxies and the SMGs considered in this study. Empty grey circles are local normal galaxies (Leroy et al. 2008 and Schruba et al.2012) and grey stars depict local ULIRGs (Zaurin et al. 2009 and Solomon et al. 1997). For local ULIRGs we have assumed ( α CO =0.8).The red solid line depicts the best fit to the data with a slope of 1.34, while a Spearman’s rank test indicates a tight correlation betweenthe plotted quantities with ρ = 0 . b) Same as the left panel but for the case of a weak increase of SFE with sSFR/sSFR MS within themain sequence. Tracks show the dependence of SFE on sSFR/sSFR MS as expected for a slightly sub-linear relation between M gas and SFRand the relative importance of the starburst and main-sequence mode of star formation as a function of sSFR/sSFR MS . Blue (purple),solid, dashed and long-dashed lines correspond to z = 1 . z = 0 .
5) for M ∗ = 1.0 × M ⊙ , 5.0 × M ⊙ , and 1.0 × M ⊙ . Greylong-dashed line corresponds to z = 0 and M ∗ = 1.0 × M ⊙ . and plot them against sSFR/sSFR MS in Figure 9a. Wesupplement our sample with a compilation of local disks(Leroy et al. 2008), as well as with a sample of localULIRGs (Solomon et al. 1997, Rodr´ıguez Zaur´ın et al.,2010).Although the actual dependence of SFE onsSFR/sSFR MS within the MS and the transitionfrom MS to the starburst regime will be discussed indetail in the next section, here we can derive somecrucial results about the SFE of the two populations(MS and starbursts galaxies) by employing a simple,empirical relation between SFE and sSFR/sSFR MS .Indeed, a linear regression fit and a Spearman’s testto our high − z data (including starbursts), yields astrong and statistically significant correlation ( ρ = 0.71, p -value = 0.0012) between star formation efficiency andsSFR/sSFR MS , with:SFE = (8 . ± . × [sSFR / sSFR MS ] . ± . (14)suggesting substantially higher star formation efficienciesfor galaxies with enhanced sSFR (Figure 9a). For MSgalaxies we find an average h SF E i = (14 ±
2) L ⊙ /M ⊙ ,corresponding to an average gas consumption timescale( τ gas = M gas /SF R ) of ∼ h SF E i = 200L ⊙ /M ⊙ , ∼
12 times higher than that of MS galaxies.Since the majority of galaxies at any redshift are MSgalaxies (e.g., Elbaz et al. 2011) and starbursts galaxiesseem to play a minor role in the star formation densitythroughout the cosmic time (e.g., Rodrighero et al. 2011,Sargent et al. 2012), our results come to support the re-cently emerging picture of a secular, long lasting starformation as the dominant mode of star formation in thehistory of the Universe.To ensure that our result is not an artifact of the as-
Fig. 10.—
Ratio of direct observables, L IR / L ′ CO against theoffset from the main sequence for the same set of objects as inFigure 9. The red solid line is the best fit to the data, with a slopeof 0.80. Coloured tracks corresponds to the scenario by Sargent etal. 2012b, following the convention of Figure 9. sumed α CO values, in Figure 10 we also plot the ratio ofthe direct observables, L IR / L ′ CO versus the offset fromthe main sequence for the same set of objects, omittingany assumptions for α CO . We find the two values tostrongly correlate with ρ = 0 .
79 and a p − value of 3.4 × − and a functional relationship of:L IR / L ′ CO = 34 . ± . × [sSFR / sSFR MS ] . ± . (15)with MS galaxies exhibiting lower L IR / L ′ CO values bya factor of ∼
4. We note, however, that the absenceof a well defined sample of high − z starbursts is strik-ing. SMGs, which are frequently regarded as prototypicalhigh − z starbursts, have recently turned out to be morelikely a mixed ensemble of objects, with a significant frac-tion of them exhibiting star formation rates and star for-ust and Gas in Star Forming Galaxies to z = 2 15 TABLE 3Stellar mass, metallicity and gas properties
Source log M ∗ Z PP04 a log L CO α CO M ⊙ L ⊙ K − km − s pc − M ⊙ K − km − s pc − ID-8049 10.97 8.80 9.47 13.4 ± ± ± ± ± ± ± ± ± ± ± ± M ∗ − Z relation of Erb et al. (2006), Mannucci et al. 2010 or theoretical arguments (GN20 and HLSW-01). We assumea typical uncertainty of ± mation efficiencies typical of MS galaxies (Ivison et al.2011, Rodighiero et al. 2011). Indeed, while we have onlythree SMGs in this study, we seem to face the same situa-tion. Of the three SMGs considered here, only HSLW-01appears to be a strong starburst, with sSFR/sSFR MS ∼
10 and SFE ∼
300 L ⊙ /M ⊙ . GN20 is only marginally out-side the MS regime, with sSFR/sSFR MS ∼
4, althoughwith high SFE ∼
120 L ⊙ /M ⊙ , while SMM-J2135 behaveslike a MS galaxy with sSFR/sSFR MS ∼ ∼
30 L ⊙ /M ⊙ , much lower than the star formation efficiencyobserved for local ULIRGs ( >
100 L ⊙ /M ⊙ ). Clearly alarger, objectively selected sample of high − z starburstsis essential to improve this investigation. VARIATIONS OF SFE WITHIN THE MAIN SEQUENCE
In the previous section, we demonstrated that the bulkof MS galaxies exhibit higher α CO values and have lowerstar formation efficiencies than starburst galaxies. Herewe will attempt to investigate possible variations of SFEwithin the MS, taking into account that the thickness,i.e., the spread of the SFR- M ∗ correlation as traced bynormally star-forming galaxies at any redshift, is not justan artifact produced by random noise, but a manifesta-tion of the variation of the physical properties of themain sequence galaxies, such as color and clumpiness(e.g., Salmi et al. 2012; see also Elbaz et al. 2011). Sincethe actual quantity that drives a galaxy above or be-low the main sequence is yet unknown, we will considertwo limiting scenarios, where the relative position of agalaxy with respect to the MS is driven by i) variationsin the gas fraction ( f gas = M gas / [ M gas + M ∗ ], or equallyin the gas to stellar mass ratio, M gas / M ∗ ) while the starformation efficiency remains roughly constant within themain sequence, or ii) variations in the star formation ef-ficiency of MS galaxies, while f gas remains constant, inorder to explain the observed dispersion in the SFR − M ∗ plane. Indeed, in practice there are two ways that a MSgalaxy could have higher SFR: either it has more raw ma-terial ( M gas ) to produce stars, or for the same amountof M gas it is more efficient at converting that gas intostars. The two scenarios have direct implications on thestar formation law (SF-law) in the galaxies. The firstcase implies the existence of a global L IR – M gas relationthat would apply to all MS galaxies, irrespective of theirsSFR, like the one presented by Daddi et al. (2010b) and Genzel et al. (2010). On the other hand, the second sce-nario would imply variations of the star formation law,with parallel M gas – L IR relations with constant slope,but with a normalisation factor that strongly increaseswith offset from the MS. While a combination of the twopossibilities might also be plausible, we will consider thetwo limiting cases for simplicity. Limiting Cases
Scenario I: a Global SF-Law for MS Galaxies; f gas asa Key Parameter In this scenario, the physical parameter that drives thesSFR of a main sequence galaxy is the gas fraction, whilethe star formation efficiency remains roughly constant.In this case we have an SF law in the form:log M gas = ξ gas × log SFR + C , (16)where ξ gas = 1 would imply M gas /SFR = constant. How-ever, there is observational evidence that ξ gas ≈ MS , for fixed stellar mass,) with a slope of ≈ .
2. On the other hand, dividing equation 16 by stel-lar mass indicates that M gas / M ∗ would vary as a functionof sSFR (or equally as a function of SFR at fixed stellarmass) with: M gas M ∗ ∝ [ sSFRsSFR MS ] . (17)In Figure 9b we explore the variations of SFE with nor-malised sSFR for three representative bins of mass andredshift, as predicted by Sargent et al. (2012 in prep.),based on the framework described above. The two fac-tors that contribute to the evolutionary tracks are (i) theobservation that at fixed SFR (or L IR ) starbursts displaymore than an order of magnitude higher SFE than thatof “normal” galaxies (e.g., Daddi et al. 2010b, Genzel etal. 2010, this study), and (ii) the fact that the depen-dence of SFR on M gas is slightly supra-linear, such thatSFE increases with L IR even when the main-sequencegalaxies and starbursts are considered individually (i.e.,eq. 16). Point (ii) is reflected in the weak increase ofSFE throughout the main-sequence and starburst regime6(sSFR/ h sSFR i MS < h sSFR i MS >
4, respec-tively), while the rapid rise in SFE in the transition re-gion is the manifestation of point (i) above. Note that the“jump” in SFE, from the normal to the starburst galaxiesis not forced by the assumption of a bimodal star forma-tion activity but naturally results from the weak increaseof SFE with sSFR/sSFR MS within the MS. Similar tracksare presented in Figure 10, considering L IR / L ′ CO insteadof L IR / M gas . Scenario II: a Varying SF-Law for MS Galaxies; SFEas a Key Parameter
This scenario assumes that f gas for MS galaxies re-mains constant, and that the physical parameter thatdictates the position of the galaxy on the SFR − M ∗ plane is the star formation efficiency. Since, f gas = const,then expressing SFE as a function of sSFR/sSFR MS , i.e.,at fixed stellar mass, we have:log SFE = log(SFR) + C (18)suggesting a linear dependence of SFE on sSFR/sSFR MS ,in reasonable agreement with the slope derived by a lin-ear fit ( ξ SFE = 1 . ± .
13, eq. 14). Although a simi-lar slope is found when the fit is redone for MS galax-ies alone, excluding the starbursts, a Spearman’s testsuggests that the correlation is statistically insignificant( ρ = 0.58, p − value = 0.13), leaving open the questionof whether the trend is valid within the MS, or if it isdriven solely by the starbursts. A similar picture emergeswhen, instead of M gas , we consider the directly observ-able quantity L ′ CO (Figure 10). Again, in this case, ex-cluding the starburst data results in a statistically in-significant correlation. If indeed the star formation ef-ficiency of MS galaxies follows such a steep increase asa function of sSFR/sSFR MS , aside the existence of par-allel M gas - L IR SF-laws, it would also imply a smooth,continuous transition from MS to starbursts galaxies.Both scenarios considered here appear to be consistentwith our data, and we cannot formally distinguish be-tween them based on these individual objects. However,as we will see in the next section, the shape of the SED,both for individually elected sources as well as for popu-lations averaged via stacking, can provide more definiteanswers. DISSECTING THE “THICKNESS” OF THE MAINSEQUENCE
So far, we have seen that the high-quality SEDs of-fered by
Herschel and mm continuum data can be usedto reveal a strong dependence of the α CO and SFE ofa galaxy on its deviation from the main sequence (eq.9and eq.14), highlighting significant differences betweenhigh − z MS galaxies and local ULIRGs, even though theformer may have (U)LIRG-like luminosities and SFRs.The well-sampled SEDs considered in this study can pro-vide the tools to further explore the implications of thetwo scenarios presented in the previous section.We have argued that the relation M gas / M dust ∝ Z − ,observed in the local universe, holds at high − z . A directconsequence of this assumption is that the ratio betweenthe infrared luminosity and the dust mass of a galaxy atany redshift would be:L IR M dust ∝ L IR M gas × Z = SFEZ (19) with L IR ∝ SFR for dusty galaxies where the extinctionis large. Based on this relation, we can make some pre-dictions for the different trends between L IR / M dust and M ∗ and sSFR/sSFR MS , for the two scenarios describedabove. Afterwards, we will attempt to constrain theobservational trend by stacking large samples of mass-selected high-z galaxies. Trends in L IR / M dust for SFE ≈ constant For the case where f gas varies within the MS (scenarioI, § z ∼ ξ z × log M ∗ + C (20)with ξ z ∼ ≤ log( M ∗ /M ⊙ ) ≤
11. Finally, from the SFR − M ∗ relation,we have: log SFR = ξ ms × log M ∗ + C (21)with ξ ms ≈ .
80. Combining the above relations yields:log SFEZ = ( ξ ms − ξ gas ∗ ξ ms − ξ z ) × log M ∗ + C . (22)Substituting the values quoted above for the various ξ coefficients very nearly cancels out any dependence onlog M ∗ , giving:log L IR M dust ∝ log SFEZ ≈ C (23)i.e., a negligible dependence of the dust-mass-weightedluminosity L IR / M dust with M ∗ . Expressing SFE as afunction of sSFR, i.e., as a function of SFR for fixedstellar mass (and therefore metallicity) yields:log L IR M dust = log SFE = (1 − ξ gas ) × log SFR + C , (24)suggesting a mild dependence of L IR / M dust with sSFR,with a slope of ∼ Trends in L IR / M dust for f gas ≈ constant In the case where f gas is constant among MS galaxies(scenario II, § IR M dust = log SFE + C = log SFR + C (25)since M gas is constant at a fixed stellar mass and f gas .This suggests a strong dependence of L IR / M dust onsSFR/sSFR MS . Note that L IR / M dust is not expectedto vary with M ∗ , as was also the case for the previousscenario (Eq. 23).Summarizing the analytical predictions, the two sce-narios result in two distinct behaviors of L IR / M dust and f gas as a function of sSFR/sSFR MS . In the case of a weakincrease of SFE within the MS (SFE ≈ const, or equally,of a global SF-law for MS galaxies), we expect a vari-ation of f gas (eq. 17) while L IR / M dust remains roughly In detail, L IR ∝ (SFR tot − SFR UV ), with SFR UV becomingsignificant in the case of low extinction, hence typically at very lowgalaxy masses and metallicities or at high redshifts. ust and Gas in Star Forming Galaxies to z = 2 17 Fig. 11.—
Top:
Observed average SEDs of z ∼ . L IR / M dust asa function of the offset from the main sequence for the z ∼ z ∼ MS is derived based on Herschel measurements. Thered solid line is the best fit to the local data, with a slope of 0.1. The black solid line shows the linear relation with a 0.5 dex offset. Theblack dashed line shows the expected trend for the case of a steep and continuous increase of SFE with sSFR/sSFR MS . Bottom:
Observedaverage SEDs of z ∼ . L IR / M dust as a function ofthe stellar mass for the z ∼ z ∼ L IR = 1 L ⊙ constant within the MS (eq. 25). The opposite trends areexpected for the case where f gas remains constant (orequally, of a varying SF-law), i.e., a steep increase of SFEwithin the MS and a linear increase of L IR / M dust withsSFR/sSFR MS (eq. 26). We note that both scenariospredict only weak dependence of L IR / M dust with M ∗ .Furthermore, the physical meaning of L IR / M dust is theluminosity emitted per unit of dust mass, or the strengthof the mean radiation field heating the dust, and couldserve as a rough proxy of the effective dust tempera-ture. Indeed, since, L IR ∝ σT d4 , two sources with thesame L IR / M dust should have similar T d . Similarly, fora given M dust , higher L IR indicates higher T d . There-fore, the above analysis also suggests a strong variationof the SED shape of the galaxies within the MS for thescenario where f gas ≈ constant, while only very little, ifany, change in the shape of the SED for the case whereSFE ≈ constant. L IR / M dust and Gas Fractions in MS Galaxies Using the stacked samples of z ∼ L IR / M dust − M ∗ and L IR / M dust − sSFR/sSFR MS .To derive the far-IR properties of the stacked sampleswe followed the same SED fitting procedure used forthe individually detected sources. However, this time wetake into account the redshift distribution of the stackedsources, to account for artificial SED broadening in thefar-IR and smearing of the spectral features in the mid-IR regime. Namely, we construct the whole set of DL07models at various redshifts and create an average SEDat the median redshift of the sources considered in thestack by co-adding the model SEDs at each redshift,weighted by the redshift distribution of stacked sources.The two methods return far-IR luminosities that are ingood agreement, although not accounting for the red-shift distribution of the stacked sources results in higher L IR / M dust values. This is expected as in this case the artificial broadening drives the fit, erroneously, to higher γ values, i.e. higher contribution of the PDR compo-nent, that result in lower M dust for a given L IR . Wealso validate the reliability of the inferred dust masses ofthe stacked samples against a possible artificial broaden-ing of the SEDs from the dispersion of the shape of theSED of the sources included in the stacking. Namely,based on the value of h U i derived from the best fit to thestacked data, we generated 1000 artificial SEDs adoptinga scatter of 0.2 dex in h U i and assigned to each of them aredshift based on the redshift distribution of the originalsample. Then we produced an average SED that we fit inthe same manner as the original data. We find that thederived h U i value for the simulated data is in very goodagreement with the one obtained for the real data. Thebest fit models for the various sSFR and stellar mass binsare shown in Figure 11, along with the stacked photomet-ric points while the inferred parameters are presented inTable 4. We note that for every sSFR bin, the derived L IR implies an average SFR, and subsequently an aver-age sSFR, that is very close to the initial corrected forextinction, UV-based sSFR estimate. This is also thefirst time that Herschel data provide evidence, that thethickness of the main sequence at z = 2 is real and not adue to scatter arising from uncertainties in the derivationof SFR.As a reference point, we also consider the large compi-lation of normal galaxies in the nearby universe ( h z i ≈ .
05) and local ULIRGs by da Cunha et al. (2010a,b).The dust mass estimates in these studies are derivedbased on a two-component fit for warm and cold dust,known to give results consistent with those from theDL07 models (Magrini et al. 2010). Therefore, a directcomparison with our sample is meaningful after applyinga correction factor of ∼ κ value adopted in their study.Figure 11 reveals a remarkable similarity in the aver-age SEDs of z ∼ Fig. 12.— a) Gas to stellar mass ratios (and gas fractions) as a function of deviation from the main sequence for the stacked sampleof z ∼ . z ∼ M gas / M ∗ ∝ [sSFR/sSFR MS ] . suggesting a strong increase of M gas / M ∗ (and f gas ) with increasing sSFR at a given redshift. The solid black line is the best fit to the z ∼ b) Gas to stellar mass ratios (and gas fractions) as a function of stellar mass for the same sample as in the left panel. The datasuggest a decrease of M gas / M ∗ with increasing M ∗ with M gas / M ∗ ∝ M − . ∗ . indicating a very small variation of the SED shape of thegalaxies within the MS. This is further manifested by theweak dependence of L IR / M dust with sSFR/sSFR MS (in-set panel), both for the z ∼ ± . L IR / M dust for both z ∼ z ∼ L IR / M dust vs. sSFR/sSFR MS and L IR / M dust vs. M ∗ are in striking agreement withthose derived by our analytical approach, favouring asmall variation of SFE within the MS, and therefore i)the existence of a global SF-law for MS galaxies, and ii)a step-like dependence of SFE with sSFR/sSFR MS . In-deed, the scenario of continuously increasing SFE wouldimply a considerable increase of L IR / M dust (shown in theinset panel of Figure 11 (top) with a dashed line), anda noticeable change of SED shape of galaxies within theMS, something that is not supported by our data.Our data can also be used to infer the dependenceof f gas on sSFR and M ∗ . Namely, from the derived M dust and Z values, we can use the δ GDR − Z relationto estimate M gas , and subsequently f gas or M gas / M ∗ . InFigure 12, we plot the derived M gas / M ∗ as a function ofsSFR/sSFR MS and M ∗ for the normal galaxies at z ∼ . z ∼
0. We find a clear trend of increasing M gas / M ∗ with increasing sSFR for both samples, with:M gas M ∗ = (2 . ± . × [ sSFRsSFR MS ] . ± . (26)very close to the slope derived in equation 17. This re-sult further supports that it is variations of f gas , ratherthan variations of star formation efficiency, that are re-sponsible for the thickness of the SFR- M ∗ relation atany redshift. We also reveal a clear trend of decreasing f gas with increasing stellar mass, with:log( M gas M ∗ ) = (5 . ± . − (0 . ± . × log(M ∗ )(27)( M ∗ in M ⊙ ) in agreement with various studies that pre-dict a similar behavior (e.g., Daddi et al. 2010a, Sain-tonge et al. 2011, Dav´e et al. 2012, Popping et al. 2012,Fu et al. 2012). Note that these trends are due to thesublinear slopes of the SFR vs. M ∗ and M gas vs. SFRrelations (see Daddi et al 2010a).We recall that the M gas derived with the δ GDR methodtraces the total gas of a galaxy, i.e., M H + M HI . Aswe have discussed above, in our analysis we have as-sumed that H dominates the gas mass of relativelymassive ( M ∗ > M ⊙ ) high-z galaxies. An indi-rect way to investigate this assumption is to comparethe inferred M gas and L IR of the z ∼ L IR - M H star formation law for MS galaxies as de-rived by Daddi et al. (2010), based on the dynamicalproperties of the individually detected BzK galaxies con-sidered in our study. If M HI contributed significantlyto the total gas mass, then the galaxies would appearto show an excess in M H with respect to L IR . Thiscomparison, for various subsets of our z ∼ M gas and the SF-law seems to val-idate our assumption (i.e., negligible contribution fromHI), at least for the stellar mass range considered in thisstudy. Indeed, our M dust measurements are (obviously)luminosity-weighted, and thus effectively SFR-weighted.Similarly, the metallicity estimates that we adopt fromthe literature are luminosity/SFR-weighted as well, soit is reasonable that our final estimates are most sensi-tive to the gas connected to the ongoing SFRs, i.e. themolecular gas. THE EVOLUTION OF L IR / M dust IN MS GALAXIES
Aside from the similar trend of a weak increase of L IR / M dust with sSFR for z ∼ z ∼ Fig. 13.— L IR vs. M gas for various stacked subsets in sSFRand M ∗ bins (black circles) as well as of the total sample (blackcircle with red dot) of z ∼ L IR - M H star formation law of local and high − z disk galaxiespresented by Daddi et al. (2010b). ies, Figure 11 implies that the shape of the SED of MSgalaxies at a given redshift, as traced by L IR / M dust , isnot expected to vary significantly with increasing L IR ,(i.e., SFR). Moreover, normal galaxies at z ∼ L IR / M dust thantheir local counterparts, suggesting a possible trend of L IR / M dust with cosmic time. To explore this further, weenhance our data set by performing SED fitting to themean SED of MS galaxies at z ∼ z ∼ z ∼ z ∼ z ∼ . z ∼ .
5, mean SEDsof MS galaxies at z ∼ z ∼
2, as well as SMGs atvarious redshifts. We also recall that L IR / M dust is pro-portional to the mean radiation field h U i in the DL07models (equation 4). Using the derived h U i , L IR and M dust values for our individuals sources as well as forthe stacked samples we find an average scaling factorbetween the two quantities of P ≈ M dust as a function of L IR forthe whole set of sources described above. Focusing atfirst on the local samples, we see that z ∼
0, normalgalaxies follow at tight relation with a slope close tobut not equal to unity, ( ξ ml = 0.95), possibly mirror-ing the L IR − T d relation observed both in the local aswell as in the high − z universe (e.g., Hwang et al. 2010).However, we notice that this is a very mild increase of L IR / M dust . Indeed, the L IR / M dust of the whole sampleof the local normal galaxies exhibits a Gaussian distribu-tion with a mean value of h log( L IR / M dust ) i = 2 .
89 anda dispersion of 0.15 dex. To further examine whethersources with higher L IR tend to have significantly higher L IR / M dust , we split the sample into two luminosity bins, There is a small scatter ( < L IR as L − µ m instead of L IR = L −∞ . Fig. 14.—
Observed average SEDs of main sequence galaxies at z ∼ . z ∼ . U = U min (diffuse ISM compo-nent) and dust heated by U min < U < U max (“PDR” component)respectively. The fitted parameters from the best fit Draine & Li(2007) model fits are listed within each panel. For comparison thebest fit SED of the z ∼ .
0, is also shown in the bottom panel witha blue-dotted line. L IR > L ⊙ and L IR < L ⊙ , and find that the twosub-samples follow almost identical distributions (Fig-ure 15 left, inset panel). In contrast, local ULIRGs arestrong outliers from the M dust - L IR relation formed bynormal galaxies, with significantly higher L IR / M dust val-ues, indicative of their warmer ISM. The IRAS selectionfor the normal galaxies considered here could, in princi-ple, introduce a bias towards warmer sources, and misscooler sources whose SEDs peak at longer wavelengths.Recent Herschel observations of local galaxies seem toconfirm this, revealing a population of normal galaxiesin the local universe that are systematically colder thanthe IRAS selected sample (e.g., Smith et al. 2012). How-ever, while the
Herschel -selected galaxies would increasethe scatter and shift the mean of L IR / M dust distributiontowards a lower value, they are also found to follow a L IR − M dust relation with a slope close to unity, leav-ing the overall picture described above unaffected. At z = 0 the ULIRGs have an order of magnitude larger L IR /M dust than normal (spiral) galaxies, consistent withthe fact that have a much higher SFE.Moving to the high − z samples of MS galaxies, we no-tice a small deviation from the local relation, exhibit-ing on average higher L IR / M dust values. Having al-ready seen that we do not expect large variations of L IR / M dust within MS galaxies at the same redshift, thisindicates a small change in the shape of the SEDs ofMS galaxies towards stronger radiation fields as we moveback in cosmic time. This is clearly depicted in Fig-ure 15 (right) where we plot L IR / M dust , or equally h U i ,as a function of redshift, for our samples, along withthat of local galaxies. Our data suggest an increase of h U i ∝ (1 + z ) . for MS galaxies, pointing also towardsan increase in their T d with look-back time. This is notto be confused with the general conception that ULIRGstend to get colder at higher redshifts. Indeed, when com-paring high − z MS ULIRGs to local galaxies of compa-0
Fig. 15.—
Left:
Dust mass as a function of infrared luminosity for: local normal galaxies from the sample of da Cunha et al. (2010)and the SINGS sample of Draine et al. 2007 (grey points and circles respectively), local ULIRGs from da Cunha et al. 2010b (grey stars),individually detected MS galaxies at z ∼ . z ∼ . z ∼ . z ∼ . − z SMGs (orange stars). The solid line corresponds to a linear relationbetween M dust and L IR , consistent with the data for local normal galaxies, although the best fit yields a slope of 0.95 (grey dotted line).The dashed lines show the linear relation with a ± Right:
Evolution of the mean radiation field h U i ∝ L IR / M dust asa function of redshift. Black squares with blue circles depict individually detected normal star-forming galaxies at various redshifts. At z ∼ − z the median values from the individually detected sources at z ∼ . z ∼ .
5. Black squares represent the stackingresults at z ∼ z ∼
2. Orange stars represent high − z SMGs considered in the study, while the grey star denotes the position of thelocal ULIRGs based on data from da Cunha et al. (2010b). The black solid line is the best fit to the MS galaxies, yielding a relation of h U i ∝ (1 + z ) . . The blue and red solid lines show the expected evolution of SFE/Z with redshift for the case of M ∗ = 1 × M ⊙ and M ∗ = 5 . × M ⊙ respectively, highlighting a co-evolution between SFE/Z and h U i . rable L IR (i.e., (U)LIRGs), the latter have much larger L IR / M dust values, indicative of a much stronger starlightintensity field and a much warmer ISM, in line with re-cent studies that find distant ULIRGs to be colder thantheir local counterparts (e.g., Symeonidis et al. 2009,Hwang et al. 2010, Magdis et al. 2010, Muzzin et al.2010). We also note that the evolution of T d with red-shift is directly demonstrated by the comparison of SEDsof the z ∼ z ∼ h U i , arisesfrom a systematic bias in the redshift distribution of thestacked samples. However, we find that for the two sam-ples to peak at the same wavelength, this bias should be∆ z ≈ z << . C Z ( z )) derived by themass-metallicity relation at various redshifts (Tremontiet al. 2004 for z=0, Savaglio et al. 2005 for z = 0 .
5, Erbet al. (2006) for z = 2, Sommariva et al. 2012 for z = 3).The other is the evolution of the normalization of thesSFR MS at fixed stellar mass ( C MS ( z )), which scales as(1+z) . . At fixed stellar mass, we have:log SFEZ (z) = C + (1 − ξ gas ) × C MS (z) + C Z (z) (28) and the emerging trend of SFE with redshift for the caseof M ∗ = 1 × M ⊙ and M ∗ = 5 . × M ⊙ are shownin Figure 15 (right), highlighting the striking agreementbetween the observed and the predicted trends. Westress that the metallicity evolution is mapped up to z ∼
3, so the values beyond this redshift are based on ex-trapolation. However, at very low metallicities, the SFRand L IR could deviate from their linear relation, with L IR tracing only a small fraction of the total star forma-tion activity as dust attenuation becomes small and thedirectly-visible UV emission becomes significant. In thatscenario, we would expect some flattening of the SFEevolution beyond z ∼
2. In any case, we conclude thatthe observed increase of h U i with redshift up to z ∼ . h U i with redshift is in line with both alternativescenarios, i.e, a weak and strong dependence of SFE onsSFR/sSFR MS for galaxies within the main sequence. Template SEDs of MS Galaxies
We have seen that MS galaxies at a given redshifttend to have uniform radiation fields, parametrized by L IR / M dust , and an overall small variation in shape oftheir SED. We also presented evidence that the meanradiation field of MS galaxies increases with redshift as ∼ (1+ z ) . . This indicates that we could build templateSEDs of MS galaxies at different redshifts. In the DL07models, the mean radiation field h U i is an interplay be-tween γ , which is the fraction of dust emission arisingfrom PDRs, and U min , which is the radiation field heat-ing the diffuse ISM. We stress that the same h U i couldarise from a different combination of γ and U min and itdoes not monotonically define the shape of the SED. Al-ust and Gas in Star Forming Galaxies to z = 2 21 Fig. 16.—
Template SEDs of MS galaxies at various redshift built based on DL07 models and the evolution of h U i with cosmic time as(1+z) . . The templates assume no evolution of the γ parameter in the DL07, i.e, the fractional contribution of the PDRs to the total IRemission of a galaxy and a small evolution of the q PAH beyond z ∼ .
0, as indicated from our data. The templates are color-coded basedon their redshift and normalised to 1L ⊙ . For starburst galaxies we show the best fit template of GN20 (grey line). The black-dashed lineshows the MS template SED of Elbaz et al. (2011). The templates can be found at http://georgiosmagdis.pbworks.com though our sample is not sufficiently large to break thisdegeneracy, we can use the mean h U i values at each red-shift to construct template SEDs of MS galaxies, underthe assumption that γ does not change significantly withtime. We adopt a constant γ = 0.02, similar to that re-ported for local galaxies by Dale et al. (2012) and Draineet al. (2007). Indeed, if we were to reproduce the same h U i , with higher γ values then the shape of the SEDwould become unphysically flat close to the peak. Also,the galaxies in our sample have a mean γ very close tothat value, so it seems like a valid simplification. Then,using the relation between h U i and redshift derived in theprevious section, we built template SEDs of MS galax-ies for a grid of redshifts up to z = 2 . z > .
5, we assume a flattening of theevolution of h U i , similar to that observed for the sSFR(e.g., Gonzalez et al. 2010). For the remaining free pa-rameter, q P AH , we adopt the mean value of 3.19% up toredshift z ∼ . q P AH = 2 .
50% at z > . z > h U i with redshift. Ourtemplates result in IR8 values that also mildly increase from IR8 ∼ z = 0 to IR8 ∼ z >
2, in agree-ment with Elbaz et al. (2011; and in preparation) andwith Reddy et al. (2012). Similar to Elbaz et al. (2011),for starbursts galaxies, we show here a unique template,using the best fit SED of GN20. Despite the simple andstraightforward nature of these templates, we note thatB´ethermin et al. (2012b) find that they manage to re-produce recent
Herschel source counts (e.g., Berta et al.2011; B´ethermin et al. 2012), including counts measuredin redshift slices. We note that to investigate the contri-bution of an AGN in our templates, we also repeated theSED fitting for the stacked samples, excluding this timephotometric points that are likely to be “polluted” by anAGN activity (i.e., λ rest < µ m). The inferred h U i val-ues are very close to the values derived when consideringthe whole set of photometric points, in agreement withvarious studies that find a negligible effect of an AGN inthe far-IR colours of a galaxy (e.g., Hatziminaoglou etal. 2010, Mullaney et al. 2012). We conclude that ourtemplates should be representative for the bulk of MSgalaxies, even for those that contain an average AGNcontribution in the mid-IR. The templates can be foundat http://georgiosmagdis.pbworks.com . DISCUSSION
It seems that the main physical parameter that drivesthe star formation rate of a normal galaxy is the gas frac-tion (or M gas / M ∗ ). Indeed, according to our analysis, atfixed stellar mass and redshift, there is a strong depen-dence of sSFR on M gas / M ∗ , suggesting that the varia-2tions within the main sequence are due to variations inthe f gas of a galaxy. Interestingly, we find that within theMS, M gas / M ∗ varies almost linearly with sSFR/sSFR MS (slope of ∼ L IR , and subsequentlySFR, is known to strongly correlate with the HCN lu-minosity, which is a measure of dense gas ( H volumedensities > cm − ), for spirals, local (U)LIRGs andQSOs, with an almost linear relation (Gao & Solomon2004; Juneau et al. 2009). The inferred dependence ofSFR to the total gas fraction, along with the fact the wedo not observe substantial changes in the star formationefficiency, is indicative of a rather constant fraction ofdense gas among MS galaxies. Alternatively, it suggeststhat the fluctuations of galaxies above and below MSare relatively long lasting, allowing the dense gas frac-tion to adjust. Indeed, given that the typical timescalefor dense gas consumption is 10 yr (and given that it isonly a fraction of the total gas), fluctuations have to lasta similar or longer time. This is also the timescale re-quired to allow integrated U − V colors to change (Salmiet al 2012). Furthermore, the fact that f gas decreaseswith M ∗ , implies that accretion does not keep up withSF and outflows at least at z < f gas (or M gas / M ∗ ) with cosmic time should be focused on nar-row stellar mass ranges or take into account the f gas de-pendence on both M ∗ and sSFR. Rescaling the f gas es-timates of the total stacked samples of z ∼ z ∼ M gas / M ∗ − M ∗ and M gas / M ∗ − sSF R/sSF R MS ,in Figure 17 we show the evolution of f gas with redshiftfor galaxies of sSF R/sSF R MS = 1 and M ∗ = 5 × M ⊙ . The evolution of f gas is in excellent agreement withthe the observationally motivated tracks of Sargent et al.(2012b in prep), that are built assuming M gas ∝ SFR . at all redshifts and an increase of sSFR as (1+ z ) . up to z ∼ . f gas at z > f gas , stellarmass, or sSFR that could be regarded as representa-tive for all MS galaxies at a given redshift. we findthat MS galaxies appear to share very similar IR-SEDshapes, with a characteristic h U i ∝ L IR / M dust at eachcosmic epoch. We find that MS galaxies tend to exhibithigher L IR / M dust values as we move back in time, sug-gesting that there is a evolution within the MS as a func-tion of time towards warmer T d . Nevertheless, we stressthat high-z MS galaxies with ULIRGs-like L IR , whilewarmer than local, normal galaxies, are colder than localULIRGs, in agreement with various studies that find anevolution in the T d of ULIRGs (e.g., Hwang et al. 2010,Muzzin et al. 2010). On the other hand, the uniformSED shape of MS galaxies at a given redshift suggeststhat T d does not change substantially with L IR withinthe MS. Consequently, it is possible that the strong evo-lution of T d with L IR reported by several studies (e.g.,Magdis et al. 2010, Hwang et al. 2010) is a result of mix-ing MS galaxies at various redshifts, or MS and starburst Fig. 17.—
Evolution of M gas / M ∗ with redshift of galaxies with sSF R/sSF R MS = 1 and M ∗ = 5 × M ⊙ . The black squarescorrespond to M gas / M ∗ of the total stacked samples of z ∼ z ∼ z ∼
0, corresponds to the mean f gas of the Leroy et al. (2008) sample. All measurements havebeen corrected to refer to M ∗ = 5 × M ⊙ . The black dashedline depicts the evolution of M gas / M ∗ with redshift for the case of M ∗ = 5.0 × M ⊙ , as implied by the cosmic evolution of sSFR(Sargent et al. 2012 in preparation). systems, the latter known to dominate the star-forminggalaxy population at high luminosities (e.g., Rodighieroet al. 2011, Sargent et al. 2012). Although the limitednumber of star-bursting galaxies in this study does notallow us to reach solid conclusions, based on Figure 15(right) we can speculate that a similar, but less strong,evolution of h U i , and therefore T d , with look-back timeis present for this population too (see B´ethermin et al.2012b for a possible implementation). A larger samplegalaxies with elevated sSFR with respect to the MS isnecessary to extend this investigation.We stress that the methodology presented in this studyopens an alternative window for a systematic investiga-tion of the gas properties for large samples of high − z galaxies, for which Herschel has provided a robust char-acterisation of their SEDs. While this approach does notrequire CO emission line measurements and is free fromthe uncertain nature of α CO , we stress that both tech-niques yield consistent results. However, it is importantto recall the limitations of this methodology. The keyassumption of this study is that the δ GDR − Z relationobserved in the local Universe does not evolve substan-tially with time, implying that roughly half of the metalsof high − z galaxies as well are locked into dust. Evi-dently, if the fraction is lower at higher redshifts, thenthe inferred M gas would be underestimated. However, aswe argued before, this is unlikely to be a strong effect,the opposite might actually be more plausibly expected.We also stress that the δ GDR − Z relation is poorly con-strained at the low metallicity end ( Z < ∼ . TABLE 4Derived properties for stacked sub-samples of z ∼ MS galaxies.
Stack a log L IR log M dust log < M ∗ > IR b Z PP04 log M gas c L ⊙ M ⊙ M ⊙ M ⊙ sSFR1 11.44 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < sSFR > / sSF R MS and < M ∗ > . The last linecorresponds to the total stacked sample of z ∼ L IR / L .c: Estimated through the δ GDR − Z relation based on the derived M dust and the assumed Z PP04 . fected from these uncertainties. Another possible caveatis also the assumed metallicities, for which we rely onempirical relations and measurements from the litera-ture. For example, since the adopted relation to derivemetallicities for the z ∼ M gas of the galaxies. However, we do not ex-pect this effect to impact our main conclusions, given theflat shape of the observed stellar mass − Z relation (e.g.,Erb et al. 2006). We also note that while stacking datafor thousands of sources erases interesting details on in-dividual sources, it also serves as a tool to average outthe dispersion in the M ∗ − Z and δ GDR − Z relations.However, this method is sensitive to M dust measurementsthat could, in principle, be affected by systematic biases,up to a factor of ∼ L IR of individual galaxies from a single detection inRayleigh-Jeans tail, requires extreme caution due to thescatter in h U i which is not fully constrained at high − z .Future, direct observations of individual sources in theRayleigh-Jeans tail will guide this investigation and alsoaddress the physical origin of the scatter, which couldbe linked to the thickness both of the M ∗ − Z relationinside the main sequence as well as of the star formationlaw. Finally, as indicated in Table 4, while the IR8 ofthe z ∼ < U > and possibly of other physical parameters suggest that asingle invariant SED for the whole MS should be treatedas a good first order approximation. CONCLUSIONS
We have used a sample of 9 normal galaxies at z ∼ . z ∼ . − z SMGs, all selected tobenefit from low-J CO observations and high quality far-IR photometry, to estimate their gas content and α CO conversion factors. In addition, large stacked samples of > . 4, similar to that of localspirals, and ∼ L IR (i.e., (U)LIRGs). Wealso find that high − z MS galaxies are ∼ 12 timesless efficient at converting molecular gas to starswhen compared to local starbursts, with SFE ∼ ⊙ /M ⊙ , corresponding to an average gas consump-tion time scale of 0.6 Gyr. • For MS galaxies at any redshift, we find a weakdependence of the dust mass-weighted luminosity( L IR / M dust ), or equally of the mean radiation field h U i , on sSFR/sSFR MS and M ∗ , complemented by amild evolution with cosmic time as (1+ z ) . . Also,for L IR = L − µ m , we find average an scalingfactor between h U i and L IR / M dust of P ≈ • We find clear trends of increasing M gas / M ast (orequally of f gas ) with increasing sSFR/sSFR MS ,with a slope of ξ frac ≈ . M gas / M ast with increasing M ∗ with a slope of ξ frac ≈ − . 5. Since at a given redshift f gas varieswith stellar mass and sSFR, any attempt to explorethe evolution of f gas with redshift should take intoaccount these emerging trends. • All the above, taken together, lead to the con-clusion that variation in the gas fraction ( f gas ) isthe driving physical parameter responsible for thespread in the SFR − M ∗ correlation traced by nor-mal galaxies at any redshift, and points towards asingle, tight L IR − M gas relation for MS galaxies. • We find that at a given redshift, MS galaxies seemto have uniform IR SED shapes, as parametrizedby the mean radiation field h U i ∝ L IR / M dust ofthe DL07 models. Based on this result and on thederived evolution of h U i with redshift, we build andprovide a set of redshift-dependent template SEDsof MS galaxies at various redshifts, and show thatthe evolution of the SED of MS galaxies is primarilydriven by the cosmic evolution of metallicity, and isonly marginally linked to the rise of average sSFRwith redshift.4Together with the pilot study of Magdis et al. (2011),we have demonstrated for the first time the importanceof studying the continuum SEDs of galaxies in order toplace constraints on their gas content, through dust massand metallicity estimates. We believe that this is a pow-erful technique: until we are in position to formally esti-mate α CO for high − z galaxies using the resolving powerof ALMA, it provides an alternative approach for thestudy of M gas in galaxies throughout out cosmic time.However, from our detailed investigation we can pointout two important results regarding the derivation ofdust masses, that similar studies should keep in mind: • Dust mass estimates based a single temperaturemodified black body model are, on average, a factorof ∼ • While rest-frame submm data ( λ rest > µ m) re-duce the uncertainties in the inferred M dust by afactor of two, excluding mm continuum data fromthe fit does not have an impact on the derived M dust estimates of MS galaxies. On the other hand,it appears that in the absence of mm continuumdata, M dust estimates of star-bursting systems canbe grossly overestimated. ACKNOWLEDGEMENTS GEM acknowledges support from the John Fell Ox-ford University Press (OUP) Research Fund and the University of Oxford and useful discussions with F.Galliano, DKX, LM and SB. E. Daddi, M. B´etherminand M. T Sargent were supported by grants ERC-StG UPGAL 240039 and ANR-08-JCJC-0008. Sup-port for this work was also provided by NASA throughan award issued by JPL/Caltech. PACS has beendeveloped by a consortium of institutes led by MPE(Germany) and including UVIE (Austria); KU Leuven,CSL, IMEC (Belgium); CEA, LAM (France); MPIA(Germany); INAFIFSI/OAA/OAP/OAT, LENS, SISSA(Italy); IAC (Spain). This development has been sup-ported by the funding agen- cies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Ger-many), ASI/INAF (Italy), and CICYT/MCYT (Spain).SPIRE has been de- veloped by a consortium of in-stitutes led by Cardiff University (UK) and includingUniv. Lethbridge (Canada); NAOC (China); CEA,LAM (France); IFSI, Univ. 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