The Star Formation History of Redshift z~2 Galaxies: The Role of The Infrared Prior
Lulu Fan, Andrea Lapi, Alessandro Bressan, Mario Nonino, Gianfranco De Zotti, Luigi Danese
aa r X i v : . [ a s t r o - ph . C O ] S e p The Star Formation History of Redshift z ∼ Galaxies: The Roleof The Infrared Prior.
Lulu Fan , , , Andrea Lapi , , Alessandro Bressan , Mario Nonino , Gianfranco De Zotti ,and Luigi Danese Received ; accepted Center for Astrophysics, University of Science and Technology of China, 230026 Hefei,China; [email protected] Key Laboratory for Research in Galaxies and Cosmology, University of Science andTechnology of China, Chinese Academy of Sciences, Hefei, Anhui, 230026, China Astrophysics Sector, SISSA, Via Bonomea 265, 34136 Trieste, Italy Dip. Fisica, Univ. ‘Tor Vergata’, Via Ricerca Scientifica 1, 00133 Roma, Italy INAF-Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, 40131 Trieste, Italy 2 –
ABSTRACT
We build a sample of 298 spectroscopically-confirmed galaxies at redshift z ∼
2, selected in the z -band from the GOODS-MUSIC catalog. By exploiting therest frame 8 µm luminosity as a proxy of the star formation rate (SFR) we checkthe accuracy of the standard SED-fitting technique, finding it is not accurateenough to provide reliable estimates of the galaxy physical parameters. We thendevelop a new SED-fitting method that includes the IR luminosity as a prior and ageneralized Calzetti law with a variable R V . Then we exploit such a new methodto re-analyze our galaxy sample, and to robustly determine SFRs, stellar massesand ages. We find that there is a general trend of increasing attenuation with theSFR. Moreover, we find that the SFRs range between a few to 10 M ⊙ yr − , themasses from 10 to 4 × M ⊙ , while the ages from a few tens of Myr to morethan 1 Gyr. We discuss how individual age measurements of highly attenuatedobjects indicate that dust must form within a few tens of Myr and be copiousalready at ≤
100 Myr. In addition, we find that low luminous galaxies harbor,on average, significantly older stellar populations and are also less massive thanbrighter ones; we discuss how these findings and the well known ‘downsizing’scenario are consistent in a framework where less massive galaxies form first, buttheir star formation lasts longer. Finally, we find that the near-IR attenuationis not scarce for luminous objects, contrary to what is customarily assumed; wediscuss how this affects the interpretation of the observed M ⋆ /L ratios. Subject headings: cosmology: observations — galaxies: evolution — galaxies: highredshift — galaxies: stellar content — dust, extinction
1. Introduction
Dust plays a crucial role in the formation and evolution of galaxies. It absorbsstellar light and re-emits in far infrared (FIR). Even a small amount of dust can leadto a significant underestimation of SFR. Poggianti & Wu (2000), Poggianti, Bressan, &Franceschini (2001) and Rigopoulou et al. (2000) reported independent evidence on bothlocal and high-redshift luminous starbursts in which ∼ H molecules (e.g. Cazaux & Tielens 2002, 2004), which act as aneffective coolant in metal-poor interstellar media (ISM). In fact, such a correlation has beenfound in both low and high redshift galaxies (Adelberger & Steidel 2000; Vijh et al. 2003;Ouchi et al. 2004; Shapley et al. 2001,2005).To represent dust attenuation, most of the authors use UV slope β UV , and adopt theMeurer relation as derived from a sample of local starburst galaxies (Meurer et al. 1999);other authors use instead the color excess E(B-V) as inferred from the spectral energydistribution (SED) of galaxies, and adopt a Calzetti extinction law similar to the Meurerrelation (Calzetti et al. 2000). However, not only the validity of the local Meurer relationat high redshift is currently under debate, but even in local normal star-forming galaxies(i.e. Bell 2002; Seibert et al. 2005; Boissier et al. 2007; Buat et al. 2005; Burgarella et al.2005; Gil de Paz et al. 2007; Cortese et al. 2006) and individual HII regions (Calzetti et 4 –al. 2005), there are clear deviations from it. The most useful indicator of dust obscurationshould be infrared to ultraviolet luminosity ratio ( IRX ), which is relatively independent onstar formation history (Buat et al. 2005) and on the dust configuration and distribution(Witt & Gordon 2000).Unfortunately, it’s difficult to trace the infrared luminosity of typical star forminggalaxies at high redshift directly by their far-infrared or submillimeter emission, due tocurrent sensitivity limits of bolometers and submillimeter interferometers. We must look forother portions of SED to examine dust emissions. A possible way is to use the mid-infrared(mid-IR) dust emission of galaxies as a tracer of total infrared luminosity. The correlationbetween mid-IR and infrared luminosity has been revealed in both the local and z ∼ Infrared Space Observatory(ISO) (Boselli et al. 1998;Adelberger & Steidel 2000; Dale et al. 2000; Helou et al. 2000; F¨orster Schreiber et al.2003) and the Spitzer MIPS (Rieke et al. 2009). This relation has been also examined at z ∼ µm observations (Reddy et al. 2010). Taking the IRX derived from rest-frame 8 µm luminosity L as a reference, one can test what extent the UV slope β UV is an effective probe of thedust attenuation.Another fundamental physical measurement for high redshift galaxies is constitutedby the stellar mass. Stellar population synthesis modeling is popularly used to estimatestellar mass at high redshift (e.g. Sawicki & Yee 1998; Papovich et al. 2001, 2004, 2006;Shapley et al. 2005; F¨orster Schreiber et al. 2004). In particular, a number of authors inrecent years have interpreted observed-frame UV to near-IR (even mid-IR) photometrywith stellar population synthesis models in order to infer stellar masses and the total massas a function of redshift (e.g. Papovich et al. 2001; Shapley et al.2001, 2005; Daddi etal.2004; Dickinson et al. 2003; Fontana et al. 2003; Labb´e et al. 2005;P´erez-Gonz´alez et al. 5 –2008). At z ∼ H α + [ N II ] line emissions will be moved into K S band, one has to takenebular spectrum into account in order to obtain precise evaluations of stellar masses. Westress that, although Papovich et al.(2001) has tested the impact of different metallicities,initial mass functions (IMFs) and star formation histories on stellar mass determinations,the effects of assumptions concerning the dust extinction law have to be checked in detail.In this paper, we investigate dust attenuations, star formation histories and stellarmasses in z ∼ µm photometry and spectroscopicredshift determinations. We aim at showing that, in order to robustly evaluate the starformation history and stellar mass at high redshift, the rest-frame SEDs from UV to near-IRmust be complemented by the IR luminosity, or at least by a robust prior for it.The plan of the paper is as follows: in § § § § § m = 0 .
27, Ω Λ = 0 .
73, and h =0.71.
2. The Sample Selection
The data are taken directly from the Version 2 release of the GOODS-MUSIC(GOODSMUlticolour Southern Infrared Catalog) sample (Santini et al. 2009). The main differencesbetween the Version 1 (Grazian et al. 2006) and the Version 2 of GOODS-MUSIC samplehave basically three points: (1) The IRAC photometry are improved using new IRACPSFs and background subtraction for the 3.6 µm , 4.5 µm , 5.8 µm and 8.0 µm bands; (2)New spectroscopic redshifts available after the Version 1 release are added; (3) The 24 µm z -selected catalog which has a typical z -bandmagnitude limit, z =26.0, for most of the catalog and extends down to z =26.18 inlimited areas. The galaxies are selected from the z -selected catalog with the flag selgal = 1. Thanks to the releases of new spectra in the GOODS-South Field (FORS2: Vanzellaet al. 2006, 2008; VIMOS: Popesso et al. 2009, Balestra et al. 2010), we can use a muchlarger spectroscopic sample than that presented in Grazain et al. (2006). The quality of allspectroscopic redshifts is marked with a quality f lag flag which is divided into four classes:very good, good, uncertain and very uncertain, represented by 0, 1, 2 and 3, respectively.We discard those galaxies with uncertain spectroscopic redshifts ( quality f lag = 2 or 3).The photometric measurements used to model the stellar populations are comprised by12 bands, namely U-band from the 2.2ESO ( U and U ) and VLT-VIMOS ( U V IMOS ), the
F435W (B-band),
F606W (V-band),
F775W (i-band), and
F850LP ( z -band) HST/ACSdata, the JH K S VLT data, and the 3.6 µm , 4.5 µm , 5.8 µm and 8.0 µm bands from SpitzerIRAC instrument. We use U V IMOS instead of U and U because the former is muchdeeper than the other two. We select only the galaxies with at least one of JH K S bands, atleast one of four IRAC bands and at least seven bands detected in total.In this way we get a spectroscopic sample of 298 z -selected galaxies within theredshift range 1 . ≤ z ≤ .
0. We notice that most of our low redshift galaxies at z ≤ . i − z colors ( i − z = 0 . ± .
21 inour sample). Most of our high redshift galaxies at z ≥ . i − z colors ( i − z = 0 . ± .
17 in our sample). Finally, public 24 µm Spitzer MIPS observations have also been exploited. A PSF-matching technique, which isperformed by the software
ConvPhot (De Santis et al. 2007), has been employed to properlydetect and deblend objects in the MIPS images (Santini et al.2009). As a result, 135 out of 7 –298 galaxies are also detected in 24 µm band. We emphasize that galaxies in z -selectedsample at z ∼ µm luminosity µL µ (hereafter L ) and the 8 − µm IR luminosity (hereafter L IR ), initially established forlocal star forming galaxies, has been confirmed for large galaxy samples in a wide rangeof luminosity and redshift, thanks to the advent of the Herschel satellite (see Chary &Elbaz 2001; Caputi et al. 2007; Dale et al. 2007; Bavouzet et al. 2008; Rieke et al. 2009;Elbaz et al. 2011; Nordon et al. 2010, 2012; Reddy et al. 2010, 2012a). Although thedependence on redshift and luminosity is very weak, it has been suggested that the mostrelevant parameter shaping the above relationship is the projected star formation density,as inferred from the IR surface brightness (Elbaz et al. 2011; Nordon et al. 2012; Reddyet al. 2012a). While extended galaxies exhibit a median ratio IR L IR /L ≈
5, themedian IR IR ≈ .
5, in agreement with the finding of Rigby et al. (2008) for a sample oflensed galaxies at z ∼
2. In the following, we will assume the median value IR . µm observations.Following Elbaz et al. (2011) this value will possibly overestimate the inferred L IR ofnormal star-forming galaxies while it will underestimate that of compact starbursts.Since the median redshift of our sample is z ∼
2, galaxies are typically selected in therest-frame U band with broad-band spectra from 1200˚ A to the near-IR. Moreover, for theobjects detected at 8 µm we can use the IR ≥ M ⊙ yr − . On the other hand, with our current selection we 8 –can reach SFR ≥ M ⊙ yr − . Thus our selection allows to perform a detailed study of thegalaxy properties over a wide range of parameters, such as stellar mass, age, SFR and dustcontent.
3. The
IRX − β UV relation at high redshift We have selected a sample of high redshift galaxies for which the whole rest-frame SEDfrom UV to near-IR is available, together with a robust proxy of the IR luminosity, i.e., theamount of light absorbed by dust. The latter quantity could be directly used together withthe observed UV luminosity to derive the bolometric luminosity and hence the ongoing SFRof the galaxy. However, in order to obtain other relevant physical parameters such as theage and the mass of the galaxy, we need to go through the population synthesis technique.This requires a few additional approximations concerning the dust attenuation, the starformation law, the initial mass function and the metallicity of the stellar populations.A detailed description of dust attenuation would require to exploit the chemicalcomposition and size of dust grains, the spatial distribution of dust and stars in the galaxy,and the solutions of the radiative transfer equation (see Mathis 1990; Dwek 1998; Silvaet al. 1998; Draine 2003, and many others). However, many observational results can berendered and understood by treating the galaxy as a point-like source behind a screen ofdust (see Calzetti et al. 1994; Meurer et al. 1999).To get insight on the form of the attenuation law, the observed UV data and the IRluminosity can be combined to construct the so called
IRX − β UV diagram; we recall that IRX is the IR to UV luminosity ratio and β UV is the rest-frame UV slope. In spite of thefact that both such quantities are expected to be strongly affected by the strength and bythe wavelength dependence of the attenuation law, Meurer et al. (1999) have pointed out 9 –the existence of a tight IRX − β UV correlation in local starburst galaxies, indicating a quiteuniversal form of the attenuation law. Such correlation has been found to hold even in highredshift z ∼ A − A .The observed L UV is approximated by the quantity L = λ (1600) L λ (1600), while the observed IR luminosity L IR is derived by the 8 µm rest-frame luminosity by assuming theratio IR . §
2. The results are shown in Fig. 1 where galaxies aredepicted with different colors, following their IR luminosities; in particular, galaxies with L IR > L ⊙ (ULIRGs) are in red, with 10 L ⊙ ≤ L IR ≤ L ⊙ (LIRGs) are in blue, with L IR < L ⊙ (LLIRGs) are in green. The solid line represents a model of solar metallicityand a constant SFR = 100 M ⊙ yr − with age of 0.1 Gyr. E(B-V) increases along the curve,starting from 0 at the bottom left. We have adopted the Calzetti law (cf. Eqs. [3] and [4]in Calzetti et al. 2000): A ( λ ) = E ( B − V )( f λ + R V ) (1)with f λ = 2 . × ( − .
857 + 1 . /λ ) for 0 . µm ≤ λ ≤ . µm or f λ = 2 . × ( − .
156 +1 . /λ − . /λ + 0 . /λ ) for 0 . µm ≤ λ ≤ . µm , and R V = 4 . L obs ( λ ) = L int ( λ )10 − . A ( λ ) (2)where L int ( λ ) is the intrinsic stellar luminosity. The IR luminosity of the model can bederived from L IR ≈ L abs = Z ∞ L int ( λ )[1 − − . A ( λ ) ] dλ ; (3)where L abs is the absorbed luminosity. We recall that the Calzetti law reproduces fairly wellthe Meurer relation for local starbursts. 10 –Fig. 1.— The rest-frame IRX − β UV relation for our sample. Data points are color-codedaccording to their IR luminosity which is obtained from the rest-frame 8 µm luminosity byadopting a ratio IR .
5, see § L IR > L ⊙ ,blue to 10 L ⊙ ≥ L IR ≥ L ⊙ , and green to L IR < L ⊙ . The solid line shows the localMeurer relation, while the dotted line shows the corresponding relation obtained on adoptingthe SMC extinction law. The dashed lines are our models with solar metallicity, 100 M ⊙ yr − constant SFR, and age of 0.1 Gyr for an increasing value of the R V parameter in the Calzettilaw (see Eq. [1]), from R V = 1.5 (bottom dashed curve) to R V = 10 (top dashed curve).Along the curves, E(B-V) increases from 0 to a suitable upper limit. The dot-dashed linesrepresent the same but with an average older age of 1 Gyr. 11 –From the Fig. 1 it is seen that on average our galaxies follow it consistently withother recent studies at z ∼ L IR > L ⊙ and the upperenvelope for the less luminous ones with L IR < L ⊙ . The scatter is larger than thatallowed by the uncertainty in the estimate of IR luminosity through the IR IRX ratios are also found in the local ULIRGs (Goldader et al. 2002),in z ∼ IRX ratioslower than predicted by the Meurer relation are generally ascribed to different extinctionlaws. An example is that of the Small Magellanic Cloud (SMC), which is represented bythe dotted line (e.g. Pettini et al. 1998).A few important points can be inferred from examining Fig. 1. First of all, the scatterof the data points shows that the SFR cannot be robustly predicted on the basis of UVSED alone. This highlights once more the importance of having a robust estimator of thetotal IR luminosity. Second, we infer that it is impossible to fit simultaneously the IR dataon one side and the UV SED on the other, if one assumes a single form (not strength) ofthe attenuation law (even by letting the age to change within the values allowed by theirobserved redshift, see below). To clarify better this point we have plotted in the samefigure the results of other attenuation curves (dashed lines). They have been obtainedfrom the solid curve by varying the parameter R V from the Calzetti value 4.05. It is seenthat the data can be fairly well reproduced if we let R V to change in the interval from 1.5 12 –(bottom dashed curve) to 10 (top dashed curve). Increasing the parameter R V flattens theattenuation law, as can be immediately seen by casting Eq. (1) in the following form A ( λ ) /A ( V ) = f λ /R V + 1 (4)Such variation of the parameter R V is meant not only to render the effects of differentproperties of the dust on the extinction , but also to describe at first-order other complexeffects such as variations of the dust/star geometry.Effects of age are also important, but only at low values of β UV ≤ − IRX − β UV diagram becomes insensitive to R V because the attenuation is also small. Onthe other hand, at high β UV ≥ −
4. Stellar Population Synthesis Modeling
In the light of the above discussion, now we turn to the issue of performing a robustestimation of the galaxy parameters via the SED fitting technique. Our procedure consistsof modeling simultaneously both the detailed rest frame SED, from the far UV to thenear-IR, and the total luminosity absorbed by dust as predicted from the observed 24 µm flux. To this purpose we use a set of simple stellar populations (SSPs) with solar metallicityand a Chabrier (2003) IMF extending from 0.15 to 120 M ⊙ . The adopted SSPs are describedin more detail in the Appendix A.As shown by Shapley et al. (2004, 2005), solar metallicity is a good approximationin z ≥ / ≤ . . ≤ z ≤ . Hubble and
Spitzer observations.We include in the calculation the total IR luminosity, and treat the predicted valueas a constraint in the SED-fitting minimization procedure. The predicted IR luminosity iscomputed after Eq. (3), while the observed IR luminosity is derived from the 24 µm fluxas described in §
2. The attenuation law is assumed to be independent of the age andparameterized by means of Eq. (1). However, according to the previous discussion on the
IRX − β UV relation in §
3, the R V value in Eq. (1) is considered as a free parameter in thefitting procedure (see also the discussion in Calzetti et al. 2000). It was let to vary in therange 1 . −
10, which as discussed before provides a fair representation of the dispersion inFig. 1.The model contains four parameters: the strength of the constant SFR, the age ofthe galaxy t g (limited only by the consistency with the observed redshift), the strengthof the attenuation parameterized by E(B-V), and the parameter R V . Then we compute 14 –the intrinsic spectrum of the galaxy, to which we apply the internal reddening. Theabsorbed spectrum is integrated to provide the model IR luminosity which is constrainedby the corresponding observed quantity. Finally, after applying the attenuation due to theintervening intergalactic neutral hydrogen (Madau 1995), we convolve the spectrum withthe transmission filters, and obtain the model fluxes to be compared with the observedones. The best fit model is obtained by minimization of the merit functionMF = n X i =1 (cid:18) M i − O i E i (cid:19) (5)where M i , O i and E i are the model values, the observed values and the observational errors,including the IR luminosity. The minimization is performed with an Adaptive SimulatedAnnealing algorithm (Ingber 1989).We stress that the IR luminosity is a prior that provides the unbiased level of theSFR. For a given IMF, the error on the SFR is mainly observational, though there issome dependence on the adopted attenuation law and on the metallicity of the stellarpopulations, as already discussed by Shapley et al. (2005). Determining the correct shapeof the SFR will require additional information, such as spectral emission, absorption lines,and (non-)thermal radio continuum. These effects probe the diverse contributions fromstellar populations of different ages and can be used, in principle, to disentangle the correctshape of the SFR (e.g. Bressan et al. 2002; Vega et al. 2008).With the SFR essentially determined by the IR luminosity, the observed UV continuummainly sets the level of the attenuation. This is also a quite robust result because the IRluminosity is mainly produced by the absorbtion of the UV light. The observed SED fromthe UV to the near-IR results from the combination of the attenuation shape and of thegalaxy age. There can be some level of degeneracy between age, metallicity and attenuationshape, but the number of constraints is also quite large. Finally, the stellar mass M ⋆ isobtained by multiplying the SFR by the galaxy age t g which amounts to the age of the 15 –Fig. 2.— Best fit models obtained with (right panels) or without (left panels) the IR priorderived from the IR R V parameter of the attenuationlaw is not fixed while in the latter case the value R V = 4 .
05 is adopted. The observedfluxes are plotted with crosses while corresponding model fluxes, after convolution with thetransmission filters, are plotted with triangles. The solid curve is the best fit model. Boththe SFR and the attenuation are kept constant with the age of the stellar populations. Errorbars on fluxes are also plotted but are in general smaller than the symbol size. 16 –oldest stellar population required by the fitting procedure.
5. Results
In this Section we present and discuss our main findings.
To begin with, we compare the results obtained with and without the use of the IRprior. We remind that in the latter case, which we name the standard procedure, we havealso assumed a definite attenuation shape, i.e., a Calzetti law with R V = 4 .
05. Fig. 2 (rightpanels) shows a few examples of best fit models obtained with the IR prior. The red crossesrefer to the observed fluxes, while the triangles to the corresponding model fluxes (afterconvolution with the transmission filters). All the galaxies have also been fitted with thestandard procedure and the best fit models are shown in Fig. 2 (left panels). We see thateven without the IR prior the best fit is in general fairly good , however the inferred starformation is different.In Fig. 3 we compare the SFR derived with and without the IR prior for the wholesample; symbols and color-codes are the same as in Fig. 1 for ULIRGs, LIRGs and LLIRGs.Data with uncertainties ≤
15% on the 24 µm flux are surrounded by boxes. For almostall the ULIRGs the SFR obtained without the IR prior is underestimated, even by a largefactor. On the other hand, LIRGs distribute across the one-tone relation with a quite largedispersion. The latter decreases for the less luminous LLIRGs. Part of the dispersion iscertainly due to our assumed value IR ≈ .
5, since less compact star-forming galaxies showa lower average value ( IR ≈
5) while more compact star-forming objects show a higheraverage value ( IR ≈ ≤
15% on the 24 µm flux have beensurrounded by boxes. 18 –compact galaxies and underestimated that of more compact objects, by about 50%, whichtranslates into a similar scatter in the plot of Fig. 2. However, the dispersion is actuallysignificantly larger than this estimate, reaching in some cases a factor of 5. Therefore itmust be intrinsic to some extent.The presence of galaxies for which the predicted SFR is underestimated is actuallyexpected, because a significant fraction of the SFR could be entirely hidden due to strongattenuation. It has already been shown that in several local LIRGs and ULIRGs the SFRdetermined by the H α or P a α luminosity, even corrected for attenuation with the Balmerdecrement method, turns out to be lower by even a factor of three than that obtained fromthe IR luminosity (see Poggianti et al. 2001; Vald´es et al. 2005). On the other hand, thepresence of objects for which the standard SED fitting technique overestimates the IR fluxis a bit more intriguing. As a matter of fact, in these objects the reddening deduced fromthe UV/near-IR SED, if interpreted by means of the usual Calzetti law, would require ahigher overall attenuation and this would produce a IR luminosity which is larger than theobserved one. For the LLIRGs the use of a prior in the IR luminosity is not as importantas for the higher luminosity galaxies. We will come back to this point at the end of theSection.To proceed with the comparison between the two synthesis methods, we show inFig. 4 the galaxy ages and in Fig. 5 the stellar masses. The latter mass is computedas the integral of the SFR over the galaxy age, and it does not take into account stellarrecycling into the interstellar medium. We see that the age determination is, in general,quite independent from the IR prior. However, there is a minority of galaxies for whichthere is a large discrepancy between the two age determinations, with the age determinedwith the IR prior turning out to be significantly larger than those based on the standardprocedure. Furthermore, when the IR prior implies larger ages then it implies also lower 19 –Fig. 4.— Same as Fig. 3 for the age. 20 –SFRs, so that the differences on the masses obtained with the two methods are smoothedout. Nevertheless, it is also clear that the standard procedure underestimates the totalmass by an average factor of about 50%, with some individual values that may be offset byeven a factor of 4.For LLIRGs the masses derived using the two different methods are in fair agreement.In this class the attenuation is not strong enough to totally enshroud the star-formingregions and the SFR can be obtained directly from the fit of the UV/near-IR SED.Actually, the SFRs obtained with the standard procedure are even slightly overestimatedfor the majority of these sources. The reason behind this effect is that the standardprocedure assumes the Calzetti law, whose R V is larger than the characteristic value oflow star-forming objects, as can be seen from Fig. 1. In fact, the median value of R V forobjects in the LLIRG class is R V ≈ .
0. Notice that, as shown in the following, the averageage of these LLIRGs is about 0.9 Gyr, and thus their location in Fig. 1 must be comparedwith the dashed line referring to a model with R V = 3 and an age of 1 Gyr. Once repeatedwith such a lower value of R V , the results obtained with the standard procedure comparefairly well to those obtained with the IR prior.This point is interesting because it allows us to increase the sample for which a robustestimate of the parameters can be obtained with SED fitting technique. In particular thenumber of LLIRGs is small and to draw more robust conclusions it would be desirable toextend the above analysis to the full z -selected sample. We remind that, in order toadopt the IR prior, we use only the sources detected at 24 µm , with a detection thresholdcorresponding to a SFR of about 10 M ⊙ yr − . With this selection criteria we cut about halfof our original z -selected sample, with the majority of the excluded objects belonging tothe lower luminosity class. The experiment described above shows that we may release theconstraint of the IR prior in the subsample of galaxies undetected at 24 µm provided that, 21 –Fig. 5.— Same as Fig. 3 for the stellar masses. 22 –in the standard procedure, we adopt a Calzetti law with a lower value of R V ≈ . R V for the 24 µm undetected sources. The SED fitting for these galaxies are not as good as those for thesample detected at 24 µm . These galaxies are intrinsically less luminous and the photometricuncertainties are on average larger, being typically between 0.2-0.5 mag in about half of thebands. In several objects the derived SFR is higher than the average threshold imposedby the 24 µm criterion, but the object was not detected at 24 µm either because of a lowerexposure depth or because the SED-inferred SFR was significantly affected by photometricerrors. We thus excluded from this sample those objects with a derived SFR ≥ M ⊙ yr − for which, according to Fig. 3, the knowledge of the IR prior is mandatory. After thisfurther cut we remain with 41 objects with L IR ≤ L ⊙ . This subsample is constitutedby the 24 µm undetected galaxies for which the standard procedure allows a fairly robustestimate of the physical parameters. In the following we will consider also the galaxies ofthis subsample that we will refer to as 24 µm undetected LLIRGs. Fig. 6 shows the distribution of the SFRs for our sample. The primary selectionin the z -band allows us to detect galaxies with a wide range of SFRs, from a few to ≥ M ⊙ yr − . We recall from the above that in the SED fitting technique we have assumed R V as a free parameter. The upper left panel in Fig. 7 shows the resulting values of R V as a function of the SFR. We notice a broad tendency of R V and the associated scatterto increase with the strength of the SFR. Part of the scatter could be due to the erroraccumulated in the process of obtaining the IR luminosity, whose largest contributionis given by the assumption of a single average relation with the 8 µm luminosity IR µm undetectedLLIRGs (purple) and to the overall sample (black). 24 –uncertainty is smaller, suggesting that there is an intrinsic dispersion connected with theshape of the attenuation law.As already discussed in §
3, at decreasing β UV the loci with different R V converge to asingle curve. Therefore one would expect that the scatter in the inferred R V , due to errorsin either β UV or L IR , increases at decreasing β UV . On the other hand, all LLIRGs withsmall β UV , exhibit a quite narrow scatter around R V ≈
3. Note that the peculiar objectrepresented by the green dot appearing in the upper left corner features a very high value R V = 10 and very old age 3 Gyr. It has been retained in the sample because formally the χ value of the SED fitting is low, but a visual inspection shows the corresponding data tosuffer large uncertainties.To better stress the meaning of the R V parameter, we remind that for the Calzetti law R V ≈ R V , the attenuation law becomes progressively flatter, i.e.,more neutral. In particular, while for a typical Calzetti law the ratio of the attenuation inthe K and V band is A K /A V ≈ .
1, for R V = 10 it increases to A K /A V ≈ .
6. Thus weexpect that there will be a number of galaxies for which the attenuation in the near-IR bandis not negligible with respect to that in the visual band, as usually assumed in star-forminggalaxies. Indeed, several ULIRGs of our sample are well fitted by an attenuation law whichis more neutral than the typical Calzetti law. In order to reproduce their observed IRluminosity together with the observed UV slope, a flat attenuation law is required, otherwisethe predicted spectral slope would be too steep. This is consistent with the evidence that,in several local ULIRGs, the molecular clouds associated with the star-forming regions areoptically thick even in the near-IR (Vega et al. 2008). In such galaxies the bulk of IR andUV luminosity could originate from different regions, as found in nearby starburst galaxies(Goldader et al. 2002). Thus the emerging UV radiation could not even directly mirrorthe global attenuation of the star-formation process, because the former may originate in 25 –regions that are occasionally located in a less dusty ambient, or in a few regions whereyoung stars emerge from the dusty ambient in a relatively shorter timescale (Silva etal. 1998; Panuzzo et al 2003). Our parametrization is meant to be a fair description ofthe attenuation resulting from the combination of all the intervening processes such asage-dependent extinction, geometrical effects, and real differences in the dust mixture.In the other panels of Fig. 7 we show the relation between the SFR and the attenuationin the UV ( A UV ), in the optical ( A V ) and in the near-IR ( A H ). In all cases the attenuationgrows with the SFR, as found by other authors, though the scatter is large. The scatterof the attenuation in the UV is not unexpected and is even consistent with the knottynature of UV images. The distribution of the UV attenuation is shown in Fig. 8. Themedian values for the different subclasses decrease at decreasing luminosity, while for thewhole sample the median value is A UV ≈ . A UV ≈ A UV ≈ A UV .Indeed, two thirds of the galaxies above the sharp drop are ULIRGs. As to the near-IR wenotice that the attenuation there may reach values that are significantly higher than thoseexpected in the UV (or in the visual) by assuming a standard extinction law. The stellar mass distribution of our sample is shown in Fig. 9. The masses rangefrom M ⋆ ≈ M ⊙ to M ⋆ ≈ × M ⊙ . ULIRGs have a quite flat mass distributionup to the higher values, and a median value of M ⋆ ≈ . × M ⊙ . In contrast, LIRGsand LLIRGs show more peaked distributions with median values of M ⋆ ≈ × M ⊙ and M ⋆ ≈ × M ⊙ . Notice that the median value for the LLIRGs detected in the mid-IR issignificantly larger than the corresponding value for the mid-IR undetected LLIRGs and is 26 –Fig. 7.— Dependence of the selective to global attenuation ( R V ), and of the attenuation inthe UV ( A ), in the visual ( A V ) and in the H-band ( A H ) on the SFR. Color-code is thesame as in Fig. 6. 27 –Fig. 8.— Distribution of the UV attenuation ( A ) in our galaxy sample. Color-code andline styles are the same as in Fig. 6. 28 –Fig. 9.— Distribution of the stellar masses in our galaxy sample. Color-code and linestylesare the same as in Fig. 6. 29 –Fig. 10.— Age distribution of our galaxy sample. Color-code and linestyles are the same asin Fig. 6. 30 –Fig. 11.— Specific star formation rate as a function of the stellar mass. Color-code is thesame as in Fig. 6. Dashed lines refer to a constant SFR of 10, 10 and 10 M ⊙ yr − from leftto right, respectively. 31 –more similar to that of LIRGs, M ⋆ ≈ . × M ⊙ . This shows that the 24 µm cut at lowluminosity introduces a bias toward the more massive objects.The age distribution of our galaxies is plotted in Fig. 10. Notice that the definitionwe give here to age is different from that usually adopted when galaxy SEDs are analyzedby means of a unique SSP. In this latter case one derives the luminosity-weighted meanage of all the stellar populations present in the galaxy. In our case we refer to the age ofthe oldest population present in the galaxy. This is a free parameter in the fit constrainedonly by a maximum value, which is the Hubble time at the galaxy redshift. The lowerlimit to the ages of ULIRGs and LLIRGs are not significantly different and, perhaps moreimportantly, both classes contain very young objects, with ages of only a few tens of Myr.This is particularly relevant for the ULIRGs because it is a strong and direct indicationthat a significant amount of dust must already be in place after such a short timescale.The median age of the sub-samples increases at decreasing IR luminosity. For ULIRGsit is ≈
150 Myr, for LIRGs it is ≈
200 Myr, and for LLIRGs it reaches ≈
900 Myr. Thelatter value decreases to ≈
600 Myr if we consider the LLIRGs undetected at 24 µm . Thedistribution of ULIRGs is significantly flatter than that of LIRGs and in all cases objectsas old as about 2 Gyr have been found. In contrast, the distribution of the LIRGs andLLIRGs is skewed toward significantly older ages. Given the meaning of our age, thisactually means that, on average, less luminous galaxies look older than more luminous ones.At first glance this evidence could appear to be against the popular downsizing scenario,according to which less massive galaxies should be younger (e.g., Noeske et al. 2007;Clemens et al. 2010). We notice, however, that the downsizing scenario is generally basedon luminosity-weighted ages that, as already said, are averaged over all the galaxy stellarpopulations. Thus a likely possibility to reconcile both observational results is that the starformation in low luminosity galaxies started first but, having a lower efficiency or being less 32 –suffering impulsive energy feedback (likely from quasars), can be maintained for a longertime. Thus low mass objects would on average form first but they would appear nowadaysyounger because their star formation lasted for a longer time. This interpretation would bealso fully consistent with the evidence that the partition of heavy elements in local lowerluminosity galaxies is progressively less α -enhanced (e.g., Clemens et al. 2010), another factthat can be explained by an increasing duration of the star formation process.Yet another possibility to explain the above observation is that the duty cycle of themore massive objects is shorter both because of a shorter duration of star formation and of arapid increase in the dust content that renders these objects undetectable in the UV/opticalafter a short timescale. In this case we will also preferentially observe younger objects.Despite this, relatively older massive galaxies could also be included in the current sampleif their average attenuation decreases near the completion of their star formation history. Inany case, our findings are consistent with the predictions of a downsizing scenario inducedby an anti-hierarchical mass assembly process in which lower mass galaxies on average doform first, but their star formation last for a longer period due to their inability to get ridof the gaseous component (see Granato et al. 2004; Lapi et al. 2011). In the more massiveobjects, instead the quasar feedback is able to remove the gas fueling in a shorter timescale(see Lapi et al. 2006).Fig. 11 shows the specific star formation rate (sSFR=SFR/ M ⋆ ) as a function of thestellar mass M ⋆ . We also plot the three loci with constant SFR = 10, 10 and 10 M ⊙ yr − ,from left to right. In a similar figure Reddy et al. (2006) showed that their galaxies lie ina narrow band, suggesting an eventual relation of the sSFR with the mass of the galaxy.However, their MIPS 24 µm undetected objects occupy a lower region, indicating that theabove hint may result from a bias induced by the adopted selection criteria. Our selectionallows us to extend the range both at higher and at lower SFR, and we do not find any 33 –noticeable trend of the sSFR with the mass of the galaxy. Actually, the sSFR may changeby about two order of magnitude for masses up to M ⋆ ≈ M ⊙ . In Fig. 12 we plot the intrinsic (i.e., the luminosity is corrected for attenuation) massto light ratio in the rest-frame H band, in solar masses per solar H-band luminosity, vs.the absolute H-band magnitude. In the left panel we plot the results obtained with ourprocedure while in the right panel we show for comparison the results obtained by adoptingthe standard procedure. The mass to light ratios span a factor of ≥
30 from 0.02 to 0.6,in both cases. The agreement is due to the fact that, for a constant SFR, the intrinsic M ⋆ /L ratio is only a function of age and the age distribution is similar (though the age ofindividual objects is not exactly same).However, we notice that in our case one cannot simply rely on the notion that theattenuation in the near-IR is low. Especially in the brightest galaxies the attenuation in thenear-IR may be large, and neglecting this effect would produce significantly higher M ⋆ /L ratio. To better clarify this point we plot in Fig. 13 the mass to light ratio versus the galaxyage. The data points correspond to the observed luminosity while the solid line representsthe locus of the unattenuated models. We see that the intrinsic M ⋆ /L ratios range from0.02 to about 0.6 while, obviously, the uncorrected M ⋆ /L ratio reach much higher values.The observed spread at a given age is only due to attenuation.Other authors claimed to have detected high M ⋆ /L ratios in high redshift galaxies,even consistent, in the near-IR passbands, with those of local old metal-rich systems (seeShapley et al. 2005, 2011). Since they have used the standard procedure, where at thesewavelengths the attenuation is negligible, we conclude that the difference with respect 34 –to our finding is simply due to the differences in the underlying stellar populations. Aswe already said, the M ⋆ /L ratios in models with constant SFRs depend only on the ageand thus these claims imply that, in the adopted models, the M ⋆ /L ratios of intermediateage populations are similar to those of old systems. Thus for a constant SFR model it isimpossible to reach, after a few of Gyr, the values of M ⋆ /L ≥ .
6. Summary
We have constructed a sample of 298 spectroscopically-confirmed galaxies at redshift z ∼
2, selected in the z -band from the GOODS-MUSIC catalog, with a SED well-sampledfrom the UV to the IR. This allows the analysis of the galaxy physical parameters by meansof the popular SED-fitting technique. In doing this, we have adopted simple and standardassumptions like constant SFR, solar metallicity, and age-independent attenuation.The z -selection includes objects with a wide range of SFR, between a few to10 M ⊙ yr − , and with different strengths of the attenuation. Since about half of the sample(135 objects) has been detected at 24 µm with Spitzer and since it has been claimed thatthe rest frame 8 µm luminosity is a quite good proxy of the SFR, we have checked, forthe first time in an intermediate redshift sample, the accuracy of the standard SED fittingtechnique.We find that the standard SED fitting technique is not accurate enough to providereliable estimate of the SFR and, correspondingly, of the attenuation, of the galaxy age andstellar masses.There is a large scatter in the predicted vs. expected IR luminosity (that can reacheven a factor of ≈ µm luminosity. The total mass is onaverage underestimated by an average factor of about 50%, but individual values may beoffset even by a factor of 4.Combining the observed IR luminosity with the observed UV spectral slope we havealso constructed the rest frame IRX − β UV diagram for this redshift z ∼ R V ) in the Calzetti law. We interpret this factas an actual difference between an extinction and an attenuation laws, the latter being theresult of the combination of many effects, such as an age-dependent extinction, complexgeometries of dust and stars, and possible differences between grain compositions and sizes.We have thus reanalyzed the 24 µm -detected subsample exploiting the constraintimposed by the total IR luminosity and the possibility of varying the attenuation law.Moreover, instead of adopting usual conversions from the IR to the SFR (see Kennicutt1998; Panuzzo et al. 2003), that hold only in particular conditions (e.g., fixed duration ofthe star formation episode, given geometry, etc.) we have used the observed IR luminosityas a constraint in the SED-fitting technique.As a result we have outlined a new method that should be used when the knowledge ofthe IR luminosity can be added to the global SED. The most noticeable difference betweenthe methodology used in the present with respect to previous works rests on • the use of the IR constraint, here derived from the observed 24 µm luminosity;
36 – • the use of a generalized Calzetti law with a variable R V . With this new method we have determined in an unprecedent robust way the physicalparameters that characterize our galaxies, namely SFR, attenuation and age. • Attenuation .There is a general trend of increasing attenuation with SFR, or,equivalently, with the unobscured absolute UV magnitude, but the correlation is nottight. The ratio R V shows a large scatter at all values of the SFR indicating a varietyof concomitant effects that may bear on the combined attenuation law. This wasalready suggested by our IRX − β UV diagram but the run of the scatter with theSFR is more indicative that these processes appear at any scale.The relation between the attenuation and the SFR become tighter toward largerwavelengths. This is consistent with the fact that in general at shorter wavelengthsimages show more knotty structures that overall combine to give a differentattenuation curve. High values of R V were generally required to fit the SEDs ofULIRGs. In this case the attenuation curve is very flat and the attenuation remainsrelatively significant even in the near-IR. Indeed, from the analysis of local ULIRGs,it was expected that a fraction of the star formation could be significantly attenuatedeven at these long wavelengths. For the low luminosity galaxies the knowledge ofthe IR prior is not as important as for those with high luminosity. This thresholdcorresponds to a SFR of about 20 M ⊙ yr − . However, if we use a pure Calzetti lowfor these galaxies, the standard procedure slightly overestimates the SFR. A moresuitable attenuation law is that with R V ≈ .
0. There is a fair relation of the UVattenuation and the z − . µm color. This could eventually be used to obtain theabsolute UV magnitude in absence of a IR luminosity prior, but its effective usefulnesshas not been studied in detail, and is deferred to a future work. 37 – • Star formation rates, ages and masses.
Our z -selected sample includes objectswith a wide range of SFR, between a few to 10 M ⊙ yr − . The average SFR is about80 M ⊙ yr − . In this respect the sample complements other ones selected by means ofthe drop-out technique.The mass distribution ranges from 10 to 4 × M ⊙ . If we take into account thesample of low luminosity 24 µm undetected sources there is a strong evidence thatthe average mass increases at increasing star formation. ULIRGs show a flat massdistribution with a minimum mass of 1 . × M ⊙ .The age distribution of our sample ranges from a few tens of Myr to more than1 Gyr. For the first time we have obtained accurate ages of severely obscured,intermediate redshift objects with very high SFRs. Individual age measurements ofhighly attenuated objects indicate that dust must form within a few tens of Myrand be copious already by the time the most massive AGB stars are evolved, i.e., attimes ≤
100 Myr. Low luminosity, star-forming galaxies detected at 24 µm show onaverage a significantly more prolonged star formation with respect to more luminousstar-forming objects, though their mass is not significantly different. However, the 24 µm detection threshold is too heavy for this subsample and must be released in orderto produce a statistically significant number of objects. By releasing this constraintand using the attenuation law with R V ≈ . µm constitute actually the brightest tail of thelow-luminosity subsample. Thus we confirm that the observed downsizing effect (lowermass galaxies appearing younger), is consistent with a picture where less massive 38 –galaxies actually form first, but their star formation lasts longer, consistent with ananti-hierarchical galaxy formation scenario. • Specific star formation rate.
We do not find any trend of the sSFR with the mass massof the galaxy as claimed by other authors. We discuss how the previously observedtrend can be spurious and results from a bias induced by the selection criteria of theanalyzed samples. • Mass to light ratios.
We find that care must be taken when dealing with M ⋆ /L ratios because, while it is customarily assumed that attenuation is scarce at near-IRwavelengths, one remarkable result of our investigation is that this is not the case forluminous objects. After imposing the IR constraint we find that, in order to fit thewhole SED, we need a flatter attenuation curve. This implies that the attenuationis not negligible at near-IR wavelengths. Correspondingly, the near-IR M ⋆ /L ratiosobtained after a proper attenuation correction never reach those of nearby galaxies, asclaimed by other authors, and remain lower by about a factor of three. In this respectthe objects with the higher M ⋆ /L ratio are the low luminosity sources, because theyare also the oldest galaxies.This work has been supported by the Chinese National Science Foundation (NSFC-11203023) and Chinese Universities Scientific Fund (WK2030220011,WK2030220004,WJ2030220007).L.F. thanks the partly financial support from the China Postdoctoral Science Foundation(Grant No.:2012M511411, 2013T60615). A.L. thanks partly support by ASI and MIUR. 39 –Fig. 12.— Left Panel: intrinsic mass to light ratio of our galaxies in the rest-frame H-band,in solar masses per solar H-band luminosity, vs. the absolute H-band magnitude. Rightpanel: the corresponding diagram obtained with the standard procedure. Color-code is thesame as in Fig. 6. 40 –Fig. 13.— Observed mass to light ratio in the rest-frame H-band vs. the galaxy age. Color-code is the same as in Fig. 6. The luminosities are the observed ones, i.e., without dustcorrection. The filled circles represent the results according to our SED-fitting technique (IRprior and variable R V ), while the crosses refer to the standard technique (no IR prior and R V = 4 . REFERENCES
Adelberger, K. L., & Steidel, C. C. 2000, ApJ, 544, 218Balestra, I., et al. 2010, A&A, 512, A12Bell, E. F. 2002, ApJ, 577, 150Boissier, S., et al. 2007, ApJS, 173, 524Boselli, A., et al. 1998, A&A, 335, 53Bouwens, R. J., et al. 2009, ApJ, 705, 936Bressan, A., Granato, G. L., & Silva, L. 1998, A&A, 332, 135Bressan, A., Silva, L., & Granato, G. L. 2002, A&A, 392, 377Buat, V., et al. 2005, ApJ, 619, L51Burgarella, D., Buat, V., & Iglesias-P´aramo, J. 2005, MNRAS, 360, 1413Calzetti, D., Kinney, A. L., & Storchi-Bergmann, T. 1994, ApJ, 429, 582Calzetti, D., Armus, L., Bohlin, R. C., Kinney, A. L., Koornneef, J., & Storchi-Bergmann,T. 2000, ApJ, 533, 682Calzetti, D., et al. 2005, ApJ, 633, 871Cazaux, S., & Tielens, A. G. G. M. 2002, ApJ, 575, L29Cazaux, S., & Tielens, A. G. G. M. 2004, ApJ, 604, 222Chabrier, G. 2003, PASP, 115, 763Chapman, S. C., Blain, A. W., Smail, I., & Ivison, R. J. 2005, ApJ, 622, 772 42 –Charlot, S., & Fall, S. M. 2000, ApJ, 539, 718Chary, R., & Elbaz, D. 2001, ApJ, 556, 562Clemens, M. S., Jones, A. P., Bressan, A., et al. 2010, A&A, 518, L50Cortese, L., et al. 2006, ApJ, 637, 242Daddi, E., et al. 2004, ApJ, 600, L127Dale, D. A., et al. 2000, AJ, 120, 583de Santis, C., Grazian, A., Fontana, A., & Santini, P. 2007, New A, 12, 271Dickinson, M., Papovich, C., Ferguson, H. C., & Budav´ari, T. 2003, ApJ, 587, 25Dwek, E. 1998, ApJ, 501, 643Elbaz, D., Dickinson, M., Hwang, H. S., et al. 2011, A&A, 533, A119Ferguson, H. C., et al. 2004, ApJ, 600, L107Fan, L., Lapi, A., De Zotti, G., & Danese, L. 2008, ApJ,689, L101Fan, L., Lapi, A., Bressan, A., et al. 2010, ApJ, 718, 1460Ferland, G. J. 1996, University of Kentucky Internal Report, 565 pages,Fontana, A., et al. 2003, ApJ, 594, L9F¨orster Schreiber, N. M., Sauvage, M., Charmandaris, V., Laurent, O., Gallais, P., Mirabel,I. F., & Vigroux, L. 2003, A&A, 399, 833F¨orster Schreiber, N. M., et al. 2004, ApJ, 616, 40Gil de Paz, A., et al. 2007, ApJS, 173, 185 43 –Goldader, J. D., Meurer, G., Heckman, T. M., Seibert, M., Sanders, D. B., Calzetti, D., &Steidel, C. C. 2002, ApJ, 568, 651Grazian, A., et al. 2006, A&A, 449, 951Granato, G. L., De Zotti, G., Silva, L., Bressan, A., & Danese, L. 2004, ApJ, 600, 580Helou, G., Lu, N. Y., Werner, M. W., Malhotra, S., & Silbermann, N. 2000, ApJ, 532, L21Hirashita, H., & Ferrara, A. 2002, MNRAS, 337, 921Ingber,L. 1989,Mathl. Comput. Modelling,12,967Isobe, T., Feigelson, E. D., & Nelson, P. I. 1986, ApJ, 306, 490Kong, X., Charlot, S., Brinchmann, J., & Fall, S. M. 2004, MNRAS, 349, 769Kroupa, P. 2001, MNRAS, 322, 231Kyeong, J.-M., Tseng, M.-J., & Byun, Y.-I. 2003, A&A, 409, 479Labb´e, I., et al. 2005, ApJ, 624, L81Lapi, A., Shankar, F., Mao, J., et al. 2006, ApJ, 650, 42Lapi, A., Gonz´alez-Nuevo, J., Fan, L., et al. 2011, ApJ, 742, 24Madau, P. 1995, ApJ, 441, 18Marigo, P., Girardi, L., Bressan, A., Groenewegen, M. A. T., Silva, L., & Granato, G. L.2008, A&A, 482, 883Meurer, G. R., Heckman, T. M., & Calzetti, D. 1999, ApJ, 521, 64Morgan, H. L., & Edmunds, M. G. 2003, MNRAS, 343, 427 44 –Munari, U., Sordo, R., Castelli, F., & Zwitter, T. 2005, A&A, 442, 1127Noeske, K. G., Weiner, B. J., Faber, S. M., et al. 2007, ApJ, 660, L43Noll, S., & Pierini, D. 2005, A&A, 444, 137Noll, S., Pierini, D., Pannella, M., & Savaglio, S. 2007, A&A, 472, 455Nordon, R., Lutz, D., Shao, L., et al. 2010, A&A, 518, L24Nordon, R., Lutz, D., Genzel, R., et al. 2012, ApJ, 745, 182Nowotny, W., Aringer, B., H¨ofner, S., Gautschy-Loidl, R., & Windsteig, W. 2005, A&A,437, 273Ouchi, M., et al. 2004, ApJ, 611, 660Panuzzo, P., Bressan, A., Granato, G. L., Silva, L., & Danese, L. 2003, A&A, 409, 99Papovich, C., Dickinson, M., & Ferguson, H. C. 2001, ApJ, 559, 620Papovich, C., et al. 2004, ApJS, 154, 70Papovich, C., et al. 2006, ApJ, 640, 92P´erez-Gonz´alez, P. G., et al. 2008, ApJ, 675, 234Pessev, P. M., Goudfrooij, P., Puzia, T. H., & Chandar, R. 2006, AJ, 132, 781Pettini, M., Kellogg, M., Steidel, C. C., Dickinson, M., Adelberger, K. L., & Giavalisco, M.1998, ApJ, 508, 539Poggianti, B. M., Bressan, A., & Franceschini, A. 2001, ApJ, 550, 195Poggianti, B. M., & Wu, H. 2000, ApJ, 529, 157 45 –Popesso, P., et al. 2009, A&A, 494, 443Prevot, M. L., Lequeux, J., Prevot, L., Maurice, E., & Rocca-Volmerange, B. 1984, A&A,132, 389Reddy, N. A., Steidel, C. C., Fadda, D., Yan, L., Pettini, M., Shapley, A. E., Erb, D. K., &Adelberger, K. L. 2006, ApJ, 644, 792Reddy, N. A., Steidel, C. C., Pettini, M., Adelberger, K. L., Shapley, A. E., Erb, D. K., &Dickinson, M. 2008, ApJS, 175, 48Reddy, N. A., Erb, D. K., Pettini, M., Steidel, C. C., & Shapley, A. E. 2010, ApJ, 712, 1070Reddy, N. A., Pettini, M., Steidel, C. C., et al. 2012, ApJ, 754, 25Reddy, N., Dickinson, M., Elbaz, D., et al. 2012, ApJ, 744, 154Rieke, G. H., Alonso-Herrero, A., Weiner, B. J., P´erez-Gonz´alez, P. G., Blaylock, M.,Donley, J. L., & Marcillac, D. 2009, ApJ, 692, 556Rigopoulou, D., et al. 2000, ApJ, 537, L85Salpeter, E. E. 1955, ApJ, 121, 161S´anchez-Bl´azquez, P., et al. 2006, MNRAS, 371, 703Santini, P., et al. 2009, VizieR Online Data Catalog, 350, 40751Sawicki, M., & Yee, H. K. C. 1998, AJ, 115, 1329Schaerer, D., & de Koter, A. 1997, A&A, 322, 598Schmutz, W., Leitherer, C., & Gruenwald, R. 1992, PASP, 104, 1164Seibert, M., et al. 2005, ApJ, 619, L55 46 –Shapley, A. E., Steidel, C. C., Adelberger, K. L., Dickinson, M., Giavalisco, M., & Pettini,M. 2001, ApJ, 562, 95Shapley, A. E., Erb, D. K., Pettini, M., Steidel, C. C., & Adelberger, K. L. 2004, ApJ, 612,108Shapley, A. E., Steidel, C. C., Erb, D. K., Reddy, N. A., Adelberger, K. L., Pettini, M.,Barmby, P., & Huang, J. 2005, ApJ, 626, 698Shapley, A. E. 2011, ARA&A, 49, 525Silva, L., Granato, G. L., Bressan, A., & Danese, L. 1998, ApJ, 509, 103Smith, L. J., Norris, R. P. F., & Crowther, P. A. 2002, MNRAS, 337, 1309Vanzella, E., et al. 2006, A&A, 454, 423Vanzella, E., et al. 2008, A&A, 478, 83Vega, O., Clemens, M. S., Bressan, A., et al. 2008, A&A, 484, 631Vijh, U. P., Witt, A. N., & Gordon, K. D. 2003, ApJ, 587, 533Witt, A. N., & Gordon, K. D. 2000, ApJ, 528, 799
A. Simple Stellar Population Models
Simple stellar population (SSP) models adopted here are computed following Bressanet al. (1998) but with the new empirical stellar spectral library MILES (S´anchez-Bl´azquezet al. 2006), which covers well the parameter space of metallicity, effective temperature andThis manuscript was prepared with the AAS L A TEX macros v5.2. 47 –gravity and thus ensures good optical broad-band starting colours. To cope with its spectralrange limitations we have extended the stellar spectra of MILES by means of matchedNEXTGEN (Allard et al. 2000) models both in the far-UV and in the near-IR/mid-IRspectral region. For temperatures above 10000 K we do not have NEXTGEN models andwe have used the library by Munari et al. (2005) with the extension of the Lejeune modelsbelow 2500˚ A and above 10000˚ A . In this way we have obtained three core libraries withaverage [ M/H ] = − .
5, 0.0 and +0 .
3. The stellar spectra extend from 10˚ A to 160 µm andthe spectral resolution is of about 2˚ A FWHM, from 2500˚ A to 10000˚ A . To take into accountthe effects of mass loss in hot supergiant stars we have considered two further extensions.For O stars we have considered the spectral models by Schaerer & de Koter (1997) while forWolf Rayet stars we have included the spectral models by Schmutz, Leitherer & Gruenwald(1992). The latter library provides only the continuum distribution of Wolf Rayet starswhile there are more recent stellar libraries that provide also spectral features (e.g., Smithet al. 2002). However, the Schmutz et al. library is suitable for our purposes becausewe are considering only broadband magnitudes here and, more importantly, because itsparametrization as a function of core temperature T ⋆ and transformed radius R t allows afair interpolation between stellar evolution quantities ( L and T eff ) and spectral models ofthick winds.For the young populations we have also considered the nebular spectrum, which iscalculated by means of CLOUDY (Ferland 1996) assuming case B recombination. To computethe nebular emission at different ages we have considered the corresponding spectra of theSSPs using the following parameters: mass of the ionizing cluster 10 M ⊙ , electron numberdensity n = 100 cm −3