EDP Sciences
Free Access
Issue
A&A
Volume 514, May 2010
Article Number A67
Number of page(s) 51
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/200913634
Published online 28 May 2010

A&A 514, A67 (2010)

Cosmic evolution of submillimeter galaxies and their contribution to stellar mass assembly[*]

M. Micha\lowski1,2 - J. Hjorth1 - D. Watson1

1 - Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen Ø, Denmark
2 - Scottish Universities Physics Alliance, Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh, EH9 3HJ, UK

Received 10 November 2009 / Accepted 10 February 2010

Abstract
The nature of galaxies selected at submillimeter wavelengths (SMGs, $S_{850}\gtrsim 3$ mJy), some of the bolometrically most luminous objects at high redshifts, is still elusive. In particular their star formation histories and source of emission are not accurately constrained. In this paper we introduce a new approach to analyse the SMG data. Namely, we present the first self-consistent UV-to-radio spectral energy distribution fits of 76 SMGs with spectroscopic redshifts using all photometric datapoints from ultraviolet to radio simultaneously. We find that they are highly star-forming (median star formation rate $713~M_\odot~\mbox{yr}^{-1}$for SMGs at z>0.5), moderately dust-obscured (median $ A_V \sim 2$ mag), hosting significant stellar populations (median stellar mass $3.7 \times 10^{11}~M_\odot$) of which only a minor part has been formed in the ongoing starburst episode. This implies that in the past, SMGs experienced either another starburst episode or merger with several galaxies. The properties of SMGs suggest that they are progenitors of present-day elliptical galaxies. We find that these bright SMGs contribute significantly to the cosmic star formation rate density ($\sim $20%) and stellar mass density ($\sim $30-50%) at redshifts 2-4. Using number counts at low fluxes we find that as much as 80% of the cosmic star formation at these redshifts took place in SMGs brighter than 0.1 mJy. We find evidence that a linear infrared-radio correlation holds for SMGs in an unchanged form up to redshift of 3.6, though its normalization is offset from the local relation by a factor of $\sim $2.1 towards higher radio luminosities. We present a compilation of photometry data of SMGs and determinations of cosmic SFR and stellar mass densities.

Key words: galaxies: active - galaxies: evolution - galaxies: high-redshift - galaxies: ISM - galaxies: starburst - submillimeter: galaxies

1 Introduction

Submillimeter galaxies (SMGs; see Blain et al. 2002) were discovered at $850~\mu$m ( $S_{850}\gtrsim 3$ mJy) by the Submillimetre Common-User Bolometer Array (SCUBA; Holland et al. 1999) mounted on the James Clerk Maxwell Telescope (JCMT). Due to the coarse resolution of SCUBA, localizations derived from high-resolution radio maps had to be used to measure their spectroscopic redshifts (Chapman et al. 2005). Lots of studies have addressed the issue of characterizing the nature of SMGs (Eales et al. 2009; Younger et al. 2009a; Smail et al. 2004; Devlin et al. 2009; Swinbank et al. 2006; Kovács et al. 2006; Greve et al. 2004; Austermann et al. 2009; Scott et al. 2008; Perera et al. 2008; Murphy et al. 2009; Tacconi et al. 2006; Greve et al. 2005; Younger et al. 2007; Coppin et al. 2008; Hainline 2008; Borys et al. 2005; Aravena et al. 2010; Swinbank et al. 2008; Takagi et al. 2004; Dye et al. 2009; Younger et al. 2008; Alexander et al. 2005; Murphy 2009; Clements et al. 2008; Egami et al. 2004; Dye et al. 2008; Hainline et al. 2009; Swinbank et al. 2004; Weiß et al. 2009b; Laurent et al. 2006; Tamura et al. 2009; Takata et al. 2006; Pope et al. 2006; Tacconi et al. 2008, some of these works were based on surveys with sensitivity worse than 3 mJy quoted above). However they were usually based on limited samples ($\lesssim$20 sources), limited wavelength coverage or photometric redshifts. These limitations have made it difficult to solve several issues, including the characterization of the star formation histories of SMGs and their dominant source of emission.

An important open question concerns the contribution of SMGs to cosmic stellar mass assembly. This is important, because in order to understand galaxy evolution, the build-up of stellar mass must be mapped out to high redshifts. It is usually parametrized by the total star formation rate (SFR) density per unit comoving volume, ( $\rho_{\rm SFR}$; see e.g. Hopkins 2004; Hopkins & Beacom 2006). At high redshifts it is difficult to disentangle the contribution to $\rho_{\rm SFR}$from galaxy populations of different masses due to incompleteness at low luminosities.

Another approach to study stellar mass assembly is to consider directly the stellar mass density per unit comoving volume, $\rho_*$, which is equivalent to the integrated  $\rho_{\rm SFR}$over the age of the Universe. It is established that $\rho_*$ grows with cosmic time (stellar mass is accumulating; Marchesini et al. 2009; Pérez-González et al. 2008; Fontana et al. 2006; Elsner et al. 2008; Drory et al. 2005), but the contribution from different galaxy populations is not well-determined. Spitzer observations of SMGs (Egami et al. 2004; Ashby et al. 2006; Dye et al. 2008; Hainline et al. 2009; Hainline 2008; Laurent et al. 2006; Borys et al. 2005; Frayer et al. 2004; Pope et al. 2006; Ivison et al. 2004) have enabled studies of the rest-frame near-infrared (near-IR) part of the spectrum, where old stellar populations are dominant - an important step forward in getting full spectral energy distributions and accurate estimates of stellar masses of SMGs. The results indicate that SMGs are among the most massive galaxies in the Universe.

The dominant source of emission from SMGs is dust reprocessed emission either from young stars or active galactic nuclei (AGNs). One way to test it is to compare the infrared (IR) and radio luminosities of SMGs, because, at least locally, star-forming galaxies follow a remarkably tight correlation between IR and radio luminosities (Helou et al. 1985; Condon 1992). The correlation is believed to result from the fact that both IR and radio emissions are related to short-lived massive stars: the former originates from dust heated by ultraviolet (UV) light from blue, massive stars and the latter from synchrotron emission of electrons produced in supernova remnants. Therefore, a relation consistent with the local one is an indication of star formation dominating both the IR and radio emissions. There is growing evidence that the correlation holds at redshifts $z\lesssim1$ (Vlahakis et al. 2007; Gruppioni et al. 2003; Yang et al. 2007; Marleau et al. 2007; Appleton et al. 2004; Garrett 2002; Boyle et al. 2007). At higher redshifts sample sizes are small making it difficult to draw robust conclusions (Seymour et al. 2009; Sargent et al. 2010; Appleton et al. 2004; Ibar et al. 2008; Murphy et al. 2009; Rieke et al. 2009; Younger et al. 2009b; Kovács et al. 2006; Garn et al. 2009; Beswick et al. 2008; Murphy 2009; Sajina et al. 2008). The only sign of evolution was reported by Ivison et al. (2010) based on stacking analysis of the 24 $\mu $m-selected galaxies, though possibly interpreted as a selection effect.

The objective of this paper is to model for the first time the entire UV-to-radio spectral energy distributions of a statistically significant sample of SMGs in a self-consistent way. Using these models we i) consistently derive the properties of SMGs using all available data to characterize their nature and determine the dominant emission mechanism; ii) estimate the contribution of SMGs to the cosmic SFR and stellar mass densities; iii) investigate whether the local IR-radio correlation holds at high redshifts in an unchanged form. In Sect. 2 our SMG sample is presented. Our methodology is outlined in Sect. 3. We derive the properties of SMGs in Sect. 4 and discuss the implications in Sect. 5. Section 6 closes with our conclusions. We use a cosmological model with H0=70 km s-1 Mpc-1, $\Omega_\Lambda=0.7$ and $\Omega_m=0.3$.

2 Sample

We base our analysis on 76 SMGs ( $S_{850}\gtrsim 3$ mJy) from the sample of Chapman et al. (2005), all with spectroscopically measured redshifts spanning a range of 0.080-3.623.

The way the sample is selected involves complex biases, which are difficult to fully quantify and account for. The parent sample of Chapman et al. (2005) consists of 150 SMGs out of which 104 have radio identifications. The sample discussed here (76 galaxies) consists of the SMGs for which redshifts have been measured (spectroscopic completeness $\sim $75%). All this implies that the sample is biased against: i) faint submillimeter emitters (low dust content and/or hot dust, influence mostly the low-z portion of the sample); ii) faint radio emitters (high-z and cold dust, see Fig. 3 of Chapman et al. 2005); iii) faint optical emitters (difficult to obtain spectra); iv$z\sim1.2$-1.8 (``redshift desert'' where no emission lines enter the observable wavelengths). At low redshifts (z<1) the sample may also be incomplete due to a limited sky area (and therefore - volume) coverage making it difficult to detect rare strong submillimeter emitters (for details on the SMG selection effects see also Fig. 2 of Blain et al. 2004 and discussion in Sect. 4.4 of Michaowski et al. 2008).

\begin{figure}
\par\includegraphics[width=8.8cm,clip]{avsed.eps}
\end{figure} Figure 1:

Median spectral energy distribution (SED) of SMGs ( thick lines) and SEDs of individual SMGs ( thin lines). Dotted lines indicate z<0.5 objects. Shaded areas enclose 90% of the SEDs. Top: all SEDs were divided by the corresponding 850 $\mu $m datapoint and scaled, so that the median SED has a flux of 5 mJy at the rest-frame 283 $\mu $m (observed $850~\mu$m at z=2). Bottom: SEDs were normalized to an infrared star formation rate of $100~M_\odot$ yr-1.

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\begin{figure}
\par\includegraphics[width=8.6cm,clip]{zevol.eps}
\end{figure} Figure 2:

Redshift evolution of the properties ( full circles, see Table A.3 in Appendix) of the sample of 76 SMGs with spectroscopic redshifts (Chapman et al. 2005). Small symbols indicate z<0.5 objects. Typical errors (Sect. 4) are shown as crosses. From top-left to bottom-right: star formation rate (SFR) derived from spectral energy distribution modeling, ultraviolet, infrared and radio emission, SFR per unit stellar mass ( $\equiv\mbox{SFR}_{\rm IR}/M_*$), stellar mass, fraction of stellar population formed during the ongoing starburst, stellar mass-to-light ratio, dust mass and temperature. In the SFR$_{\rm IR}$ panel, we also show the minimum average SFRs (see Sect. 5.2.1) required to build up the total stellar mass within the age of the Universe at a given redshift ( empty circles) and to build up the fraction of stellar population that was not formed during the ongoing starburst ( plus signs). The location of plus signs indicates that SMGs must have been highly star-forming even before the onset of the ongoing starburst. When empty circles and plus signs overlap, the contribution of the ongoing starburst to the total stellar mass of a galaxy is negligible (i.e. $M_{\rm burst}/M_*\sim 0$).

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\begin{figure}
\par\includegraphics[width=8.5cm]{beta.eps}
\end{figure} Figure 3:

Derived dust mass of a mock galaxy with dust temperature $T_{\rm d}=40$ K and a flux density of 5 mJy at several infrared rest-wavelengths as a function of the assumed emissivity index $\beta $. For each wavelength the dust masses were normalized to 1 at $\beta =1.5$. The spread of the derived dust masses shows that the uncertainty of the dust mass resulting from unknown $\beta $ is a factor of a few.

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It is important to estimate what the influence of these selection effects on our results is. In total we analyse $\sim $50% (76/150) of the parent sample. Additionally, 25 radio-detected SMGs without spectroscopic redshifts have similar long-wavelength properties compared to the redshift sample (see Fig. 1 of Chapman et al. 2005), so their absence from the sample probably does not significantly bias our results. The same is true for the SMGs in the ``redshift desert'', since they are missed not due to their inherent properties. The remaining 46 radio-nondetected SMGs ($\sim $30%) could in principle have very different properties than our sample resulting in a potential limitation in our analysis.

Even if most of the SMGs without spectroscopic redshifts are similar to those in our sample, the incompleteness at z<1.8 implies that the estimates of SMG densities (Sects. 5.3.1, 5.3.2 and 5.2.3) in the three low-redshift bins (see Sect. 3.2) are strict lower limits.

Due to the negative K-correction at submillimeter wavelengths, SMGs at $z\gtrsim0.5$form a sample with homogenous IR luminosity (Blain 1997; Blain & Longair 1996). However, SCUBA sources at $z\lesssim0.5$belong to a different population of objects and are intrinsically fainter. The limited volume coverage at these low redshifts makes the sample of these objects small and incomplete. This prevents a separate study of their properties. We did not take into account these sources when we computed median values of the properties of SMGs.

The photometric datapoints (Tables A.1 and A.2 in Appendix[*]) were collected from the literature: Ivison et al. (2002, IK, radio), Ivison et al. (2005, R, 1.2 mm), Chapman et al. (2003b, VI), Chapman et al. (2005, BR, µm, radio), Capak et al. (2004, UBVRIzHK), Clements et al. (2004, UBVIK), Egami et al. (2004, 24 µm), Greve et al. (2004, 1.2 mm), Smail et al. (2004, IJK), Fomalont et al. (2006, Rz), Kovács et al. (2006, 350 µm, 1.2 mm), Laurent et al. (2006, 350 µm, 1.1 mm), Tacconi et al. (2006, 1.3 mm), Pope et al. (2006, R, 24 µm), Huynh et al. (2007, 160 µm), Hainline (2008, $3.6, 4.8, 5.6, 8.0, 24, 70~\mu$m). We have not used the existing mid-IR spectra (Pope et al. 2008; Menéndez-Delmestre et al. 2007,2009; Valiante et al. 2007), but for completeness we have indicated in Table A.1 those SMGs for which Spitzer/IRS spectra exist.

Table 1:   Mean values for SMGs in redshift bins.

3 Methodology

3.1 SED modeling

In order to model the spectral energy distributions (SEDs) of SMGs, we use all the photometric datapoints simultaneously. This has the advantage that all the galaxy properties are derived consistently regardless of the wavelength regime in which those properties shape the SEDs (for example, recent star formation governs the UV and far-IR parts of a spectrum of a galaxy, whereas accumulated stellar mass is responsible for near-IR emission). Moreover in the full SED modeling no single datapoint drives the fit alone.

We utilized the set of 35 000 models from Iglesias-Páramo et al. (2007) developed in GRASIL (Silva et al. 1998)[*] based on numerical calculations of radiative transfer within a galaxy. They cover a broad range of galaxy properties from quiescent to starburst. Their star formation histories are assumed to be a smooth Schmidt-type law (SFR proportional to the gas mass to some power, see Silva et al. 1998, for details) with a starburst (if any) on top of that starting 50 Myr before the time of the evolution of a galaxy at which the SED is computed. Additionally we fitted templates based on nearby galaxies (Silva et al. 1998) and gamma-ray burst host galaxies (Michaowski et al. 2008). We simultaneously used all the photometric datapoints from UV to radio (Tables A.1 and A.2). In cases where the data given by different authors were contradictory, we disregarded the obvious outliers. We scaled the SEDs to match the data and chose the one with the lowest $\chi^2$.

Based on the best fits we derived the properties of the galaxies as explained in Michaowski et al. (2009,2008). In particular, SFRs, stellar (M*) and starburst ( $M_{\rm burst}$) masses were given as output from GRASIL, rest-frame UV and K (LK) monochromatic luminosities were interpolated from the best-fitting SEDs, whereas IR luminosities ( $L_{\rm IR}$) were integrated in a range 8-$1000~\mu$m, UV and IR SFRs (SFR$_{\rm IR}$ was adopted for all subsequent calculations, because SFR$_{\rm UV}$ is on average two orders of magnitude lower) were calculated using Kennicutt (1998), dust masses ($M_{\rm d}$) were calculated from the $850~\mu$m detections using Eq. (5) of Michaowski et al. (2009) and radio SFRs were calculated from the 20 cm detections using the empirical formula of Bell (2003) (see Sect. 4.2 of Michaowski et al. 2009). Dust temperatures ($T_{\rm d}$) were estimated by identifying the peak of the dust emission and assuming an emissivity index $\beta=1.3$. The average extinction in the rest-frame V-band was calculated from the unextinguished starlight given in GRASIL: $ A_V=2.5\log$(unextinguished V-band starlight / observed V-band starlight). IR-radio correlation parameters were calculated according to the formula $q=\log(L_{\rm IR}[L_\odot] / 3.75\times10^{12}/L_{\nu~ 1.4~{\rm GHz}} [L_\odot~\mbox{Hz}^{-1}])$, where $L_{\nu~ 1.4~{\rm GHz}}$ is a rest-frame 1.4 GHz luminosity density computed from the observed 1.4 GHz flux assuming a spectral slope of -0.75.

3.2 Volume densities

In order to calculate the SFR density, the stellar density and the dust mass densities per unit comoving volume, $\rho_{\rm SFR}$, $\rho_*$and $\rho_{\rm dust}$, we used the following angular areas for the submillimeter surveys (Table 1 of Chapman et al. 2005): CFRS-03: 60 arcmin2 and CFRS-14: 48 arcmin2 (Webb et al. 2003b), Lockman Hole: 122 arcmin2 and ELAIS-N2: 102 arcmin2 (Scott et al. 2002), HDF-N: 100 arcmin2 (Chapman et al. 2001), SSA-13 and SSA-22: 100 arcmin2 each (Chapman et al. 2003a), totaling 632 arcmin2.

We divided our sample into four high-redshift bins (Table 1) with approximately the same number of SMGs plus an additional bin for z<0.5 sources (see Sect. 2). The densities in each bin were calculated as a sum of SFR$_{\rm IR}$ (or M*, or $M_{\rm d}$) of all SMGs in this bin divided by its comoving volume (a similar approach to calculate the SFR and number volume densities of SMGs was taken by Daddi et al. 2009b; Coppin et al. 2009; Younger et al. 2009a; Wang et al. 2009). The volumes (Col. 2) were found using the total area from the previous paragraph.

We removed the contribution of ten SMGs[*], which were observed by SCUBA in the photometry mode (as opposed to the blank-field mapping mode) targeting optically-faint radio galaxies (Chapman et al. 2005). These objects fall outside the fields discussed here.

The method is therefore to analyse the fraction of the sky observed by SCUBA and estimate the number of SMGs and their volume densities. However, the true number of SMGs in our fields could be higher. On the other hand, regardless of the selection effects, the true number of SMGs in our fields cannot be lower than the number of SMGs in our sample. In turn, the true values of SFR and M* densities cannot be lower than the values we derive. Therefore our results on volume densities should be regarded as robust lower limits.

Having this in mind we note that the parent sample of Chapman et al. (2005) includes only 29% of all the SMGs detected in the used survey fields (compare with Webb et al. 2003a; Scott et al. 2002; Webb et al. 2003b). Therefore even if we analysed the full parent sample the estimated densities would be conservative lower limits. We attempt to correct for this incompleteness by assuming that the parent sample of Chapman et al. (2005) is a fair representation of the total population. In this case our numbers should be multiplied by 3.5 ($\sim $1/29%). This correction should in principle be derived separately for each redshift bin, but the missing redshift information for the majority of the SMGs in the used survey fields makes such calculation impossible. We note that this correction does not remove the bias against SMGs that are faint at radio and optical wavelengths, as discussed in Sect. 2.

We have not applied a volume density correction for the AGN contribution, because it is at most minor. Even though a fraction of SMGs host AGNs and a few individual SMGs have been shown to exhibit a significant AGN contribution to their emission, it is established that on average AGN activity is responsible for at most $\sim $10-20% of the bolometric infrared emission of SMGs (Watabe et al. 2009; Hainline et al. 2009; Menéndez-Delmestre et al. 2007; Alexander et al. 2008; Valiante et al. 2007; Murphy et al. 2009; Pope et al. 2008; Alexander et al. 2005; Menéndez-Delmestre et al. 2009). Therefore a potential error associated with the AGN contribution in our analysis of a statistically significant sample is smaller than the systematic uncertainty (e.g. 30% error of luminosity-SFR conversion; Kennicutt 1998).

The percentage contribution of SMGs to the SFR and M* densities (Cols. 5 and 7 of Table 1) was calculated as $\rho_{\rm SMG}/(\rho_{\rm SMG}+\rho_{\rm other})$, where $\rho_{\rm SMG}$ is the density of SMGs at each redshift bin (Cols. 4 and 6) and $\rho_{\rm other}$ is the density of other galaxies assumed to be an average of determinations (excluding lower limits) reported by other authors (Fig. 4; Tables A.4 and A.5 in appendix), for which the redshift ranges overlap with our bins. This way of calculating the contribution is justified if SMGs do not enter the ``other'' samples of galaxies. This is usually the case because SMGs are faint in the optical. However, if this was not fulfilled, the real percentage contribution of SMGs would be even higher.

\begin{figure}
\par\includegraphics[width=8.8cm,clip]{sfrdz.eps}\end{figure} Figure 4:

Top: cosmic star formation density. The SMGs' contribution rises with redshift from $\sim $9% to $\sim $20% (Sect. 5.3.1 and Table 1). Filled Squares: data for SMGs at z>0.5 in four bins (Table 1 and Sect. 3.2). Small Squares: data for SMGs at z<0.5. Thick black arrows: the SMG data without incompleteness correction (factor of 3.5, Sect. 3.2). Black crosses and diamonds: star formation density of SMGs determined by Chapman et al. (2005) and Wall et al. (2008), respectively. Colored points with error bars: determination of the cosmic value based on different estimates - ultraviolet ( violet), emission lines: [O II], [O III], H$\alpha $, H$\beta $ ( green), mid-IR ( light blue), submillimeter ( black), radio ( red), X-ray ( yellow). Extinction correction and, in many cases, incompleteness correction have been applied by the authors. Arrows: lower limits. Bottom: cosmic stellar mass density. The SMGs' contribution rises with redshift from $\sim $5% to $\sim $50% (Sect. 5.3.2 and Table 1). Red points with error bars: determination of the cosmic value from literature. The data and the references are listed in Tables A.4 and A.5 in Appendix.

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4 Results

The best fits[*] are shown in Fig. A.1 and the median SEDs (in flux and luminosity domains) are shown in Fig. 1.

The resulting properties of the galaxies are listed in Table A.3 and shown in Fig. 2 as a function of redshift. We notice similar trends to Hainline (2008) that lower-z SMGs are less luminous and colder (see her Figs. 4.7 and 4.9).

In two cases we obtained much better fits using the templates of Silva et al. (1998) instead of those of Iglesias-Páramo et al. (2007), namely, an HR 10 template for SMMJ105151.69+572636.0 and a spiral Sc template for SMMJ221733.12+001120.2. In 9 cases[*] where our fits strongly underpredict the $850~\mu$m datapoint we adopted the $L_{\rm IR}$and $T_{\rm d}$ estimates of Chapman et al. (2005).

The determination of the IR luminosity suffers from systematic uncertainties depending on the choice of the SED template. Our approach of using all the optical, submillimeter and radio data to constrain the shape of the SED results in a moderate systematic error in the IR luminosity (less than a factor of $\sim $2; Bell et al. 2007). The choice of a Salpeter (1955) IMF with cutoffs of 0.15 and $120~{M}_\odot$introduces a maximum systematic error of a factor of $\sim $2 in the determination of the stellar masses and SFRs (Erb et al. 2006). Bell et al. (2007) have also found that random errors in stellar mass are less than a factor of $\sim $2. Estimates of dust temperatures have uncertainties of $\sim $5-10 K dominated by the unknown value of the emissivity index, $\beta $. The SFR determination based on radio observations is accurate up to 30% since it agrees with the detailed spectrophotometric SED fitting (Michaowski & Hjorth 2007). The uncertainties in q (defined in Sect. 3.1) are $\sim $0.3 (see also Kovács et al. 2006), dominated by the error in $L_{\rm IR}$.

In order to assess the influence of the choice of emissivity index $\beta=1.3$ on the dust mass estimates, we recalculated the dust temperatures and masses in a range of $\beta $ of 1-2. The resulting error was less than a factor of 3.5.

This is illustrated in Fig. 3 where we present a more systematic analysis of this problem. We calculated the dust mass of a mock galaxy with $T_{\rm d}=40$ K (this choice does not influence the results) using $\beta $ in the range 1-2 assuming a flux density of 5 mJy at a variety of infrared rest-wavelengths probed by observations. Then we normalized dust masses to 1 at $\beta =1.5$. We conclude that as long as the observations probe wavelengths longer than $\sim $150 $\mu $m ( $z\lesssim4.7$for observed wavelength of $850~\mu$m), then the error on the dust mass resulting from unknown $\beta $ is less than a factor of $\sim $5.

None of these errors significantly affects our conclusions, because the inferred nature of SMGs would not be different even in the worst case scenario when all systematic errors work in one direction (increasing or decreasing the obtained values). Moreover, we analyse a statistically significant sample of 76 galaxies, so random errors of a factor of 2 are reduced to <20% when an error of a mean is considered.

Table 1 contains the volume densities and mean IR-radio correlation parameter divided into five redshift bins (see Sect. 3.2). The uncertainties quoted on $\rho_{\rm SFR}$ and $\rho_*$ include the systematic 30% uncertainty of the $L_{\rm IR}$to SFR conversion (Kennicutt 1998) and a factor of $\sim $2 systematic uncertainty in the stellar mass (Michaowski et al. 2008). The systematic error resulting from our incompleteness correction (Sect. 3.2) is likely a factor of a few.

5 Discussion

5.1 Spectral energy distributions of SMGs

We have presented the first successful attempt to fit the entire UV-to-radio SEDs of SMGs in a self-consistent way taking into account all the available data simultaneously. Our study provides evidence that GRASIL models can reproduce the SMG data. Namely, we found good fits for all SMGs in our sample with the best IR/submillimeter wavelength coverage[*] except of SMMJ105238.30+572435.8.

As is evident from Fig. 1, regardless of whether SEDs were normalized to the same observed $850~\mu$m datapoint or SFR$_{\rm IR}$, the scatter at optical and near-IR wavelengths is significant, showing that SMGs exhibit a wide range of stellar population properties (as also noted by Ivison et al. 2002). This implies the need for an SED template library in SMG studies, as opposed to single-template fitting.

Having constrained the SEDs of SMGs we now turn to a discussion of what we can learn about these galaxies using the best-fitting models.

5.2 Properties of SMGs

5.2.1 Star formation rates

The very high (current) SFRs of SMGs (median $713~M_\odot$yr-1, Col. 5 of Table A.3 and Fig. 2) place them among the most powerful starburst galaxies in the Universe. Such extreme SFRs likely result from major mergers (e.g. Berciano Alba et al. 2010; Younger et al. 2007; Swinbank et al. 2004; Narayanan et al. 2010; Chapman et al. 2004; Narayanan et al. 2009; Younger et al. 2008; Tacconi et al. 2008,2006; Greve et al. 2005) and cannot be sustained for a long period (after a few hundred Myr at most the gas reservoir should be depleted; see Hainline et al. 2006; Greve et al. 2005).

On the other hand, their extinction-uncorrected UV SFRs are two orders of magnitude lower (median $\sim $$M_\odot$ yr-1, Col. 4). This implies that the majority of star formation in SMGs is hidden by dust. Therefore, optical observations alone are not sufficient to investigate their nature and contribution to cosmic star formation.

Using stellar masses of SMGs we placed lower limits on the time-averaged SFRs required to build their stellar masses within the age of the Universe ( $\equiv M_*/\mbox{age of the Universe at given redshift}$), shown as empty circles in Fig. 2. Their median value of $\sim $130  $M_\odot~\mbox{yr}^{-1}$indicates that SMGs had to be relatively highly star-forming throughout the age of the Universe to build up their stellar populations at a constant rate. Even if our estimates of stellar masses were underestimated by a factor of a few due to systematic uncertainties (Sect. 4), the SMGs would have had to be luminous infrared galaxies (LIRGs with SFR $\gtrsim$  $20~M_\odot$ yr-1) during their evolution.

Having constrained the mass of stars formed during the ongoing starburst episode, $M_{\rm burst}$, we can further constrain the minimum average SFR of SMGs before the onset of this starburst, $\equiv(M_*-M_{\rm burst})/ \mbox{age of the Universe}$(plus signs in Fig. 2). The median is still high, $\sim $ $100~M_\odot~\mbox{yr}^{-1}$, so SMGs must have been highly star-forming in the past too. At redshifts 2-3 the age of the Universe is $\sim $3-2 Gyr and it is unlikely that a galaxy can sustain this high SFR over such a long period. Therefore we conclude that either the stellar masses of SMGs have been formed in at least two strong (>100  $M_\odot~\mbox{yr}^{-1}$) starburst episodes or continuously over the period of 2-3 Gyr but in several smaller galaxies that eventually merged. In order to build up the stellar mass of one SMG, five such galaxies would need to form stars continuously at a rate of $20~M_\odot~\mbox{yr}^{-1}$, a value more likely to be sustainable over several Gyr. The latter scenario is consistent with the results of Dye et al. (2008) based on observed optical to mid-IR data of 51 SMGs with photometric redshifts. They found that approximately half the stellar mass in SMGs has been formed over a long ($\sim $1-2 Gyr) period of approximately constant star formation activity. The possibility that a significant part of stellar mass in SMGs was formed before the ongoing starburst has also been suggested by Hainline (2008), who compared the build-up timescale of stellar mass and the duration of the SMG phase.

The median value of the SFR per unit stellar mass (SSFR $\equiv$ SFR $_{\rm IR}/M_*$, Col. 7 of Table A.3) of $\sim $1.8  $\mbox{Gyr}^{-1}$is within the range for other high-z star-forming samples (compare with Figs. 2 and 4 of Castro Cerón et al. 2006,2009, respectively). This indicates that SMGs are forming stars intensely.

SSFRs are compared with (the inverse of) the age of the Universe in Fig. 2. The SMGs close to the solid line could have formed their stellar populations at the present rate within the age of the Universe. However, the SMGs close to, or above the dashed line could have formed their stars at the present rate within less than 10% of the age of the Universe, i.e., within $\lesssim$300 Myr at z=2. These galaxies are experiencing a powerful starburst episode.

At the extreme there are three high-z SMGs[*] with very high SSFRs  $> 10~\mbox{Gyr}^{-1}$(Col. 7 of Table A.3). They are all hot ( $T_{\rm d}>60$ K, Col. 13) and formed the majority of their stellar populations during the ongoing starburst ( $M_{\rm burst}/M_*>60$%, Col. 9). Therefore they are likely the most powerful cases of SMGs formed in major mergers of galaxies with huge gas reservoirs that were subsequently converted into stars.

Our median SSFR at z>1.7 ( $1.83~\mbox{Gyr}^{-1}$) is a factor of $\sim $2 lower than that of Dunne et al. (2009, 3-$4.5~\mbox{Gyr}^{-1}$; see their Fig. 12b) for $10^{11}<M_*<10^{12}~M_\odot$galaxies at these redshifts. This difference can be explained if the radio luminosities (used by Dunne et al. 2009, to estimate SFRs) are boosted by AGN activity more than the IR luminosities used here. Indeed, if we use SFR $_{\rm radio}$instead of SFR$_{\rm IR}$ to calculate SSFRs the median for the SMGs at z>1.7 increases to $3.20~\mbox{Gyr}^{-1}$ (see Sect. 5.4.2 for discussion of AGN contamination in our sample).

In order to assess the accuracy of SFR estimates based on radio emission (independent of SED modeling) we compared the ratio of $\mbox{SFR}_{\rm radio} / \mbox{SFR}_{\rm IR}$. Its median value is equal to $\sim $1.3. Hence, assuming that IR emission is a good proxy for SFR, then radio estimates suffer from a $\sim $30% systematic error. This is illustrated in Fig. 5 where the dashed line denotes the relation between IR and radio luminosities required to make SFR $_{\rm IR}= \mbox{SFR}_{\rm radio}$. Indeed the radio luminosity gives systematically higher SFRs for SMGs (most of the points are above the line). This can be caused by a significant AGN contamination boosting radio flux (see Sect. 5.4.2), or a strong bias favouring radio-bright galaxies, because those non-detected at radio do not enter our sample (Sect. 2). Alternatively, it could be that for luminous galaxies either the IR conversion of Kennicutt (1998) should be scaled up by a factor of 1.3, or the radio conversion of Bell (2003) scaled down.

\begin{figure}
\par\includegraphics[width=8.8cm,clip]{lirrad.eps}
\vspace*{3mm}
\end{figure} Figure 5:

Radio luminosity density as a function of infrared (8-$1000~\mu$m) luminosity of SMGs showing a linear relation, though with a normalization offset from the local relation by a factor of $\sim $2.1 towards higher radio luminosities (Sect. 5.4.1). Circles: values for individual SMGs color-coded by redshift. Solid line: linear fit to the data (Eq. (1)). Dotted line: the mean local relation (Bell 2003). Shaded area: its scatter. Dashed line: the track where SFR$_{\rm IR}$ (Kennicutt 1998) is equal to SFR $_{\rm radio}$(Bell 2003). The strong outliers (above the line) at high-luminosity end are probably caused by AGN activity increasing radio luminosities.

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5.2.2 Stellar masses

SMGs having stellar masses of $\sim $1011- $10^{12}~M_\odot$(Col. 8 of Table A.3 and Fig. 2) are among the most massive galaxies in the Universe, regardless of redshift (compare with Figs. 2 and 4 of Castro Cerón et al. 2006,2009, respectively). This property makes them natural candidates for the progenitors of the present-day ellipticals.

The relatively tight range of stellar masses is likely not a result of sensitivity limits at optical and near-IR. This is because i) galaxies with stellar mass as low as $\sim $ $10^9~M_\odot$would have been detected in deep Spitzer imaging at redshifts $z\sim2$ (e.g. Reddy et al. 2006); ii) our sample accounts for 50% of the parent Chapman et al. (2005) sample (and only 30% of the parent sample may have different properties than our sample, see Sect. 2), so it is unlikely that we miss only the low-mass objects. Therefore, high M* seems to be an intrinsic property of submillimeter-selected galaxies. Mergers of less massive galaxies could not result in a powerful starburst giving rise to detectable submillimeter emission (see also Davé et al. 2010).

Only a minor part (median $\sim $8%, Col. 9 of Table A.3 and Fig. 2) of the stellar populations present in SMGs has been formed during the ongoing starburst episodes. Hence, even though SMGs probably evolve into ellipticals, the majority of the stellar mass in such ellipticals had been created before the submillimeter-bright phase.

This could mean that the current SFRs and stellar masses of SMGs are only loosely connected and indeed this manifests itself in a very high spread (around two orders of magnitude) in SSFRs in our sample even though the stellar mass range is relatively tight: ${\sim}10^{11}$- $10^{12}~M_\odot$ (Fig. 2). This behaviour is unusual compared to other galaxies (see Castro Cerón et al. 2006,2009).

However we note that the low stellar masses created in the ongoing starburst may partially be an effect of the assumed starburst ages of 50 Myr. If a starburst duration of 100-200 Myr were adopted (Tacconi et al. 2008; Hainline 2008; Borys et al. 2005; Smail et al. 2004) the resulting $M_{\rm burst}$ could be higher by a factor of $\sim $2-4.

The mass-to-light ratios, M*/LK, of SMGs (Col. 10 of Table A.3 and Fig. 2) are typical for massive galaxies. Specifically, the median ( $0.68~M_\odot~L_\odot^{-1}$) is similar to the values for $M_*>10^{11}~M_\odot$galaxies (Drory et al. 2004, their Table 1) and to simulated massive galaxies at $z\sim1$ (Courty et al. 2007, their Fig. 4).

5.2.3 Dust properties

Our fits suggest that SMGs are moderately dust-obscured with a median $ A_V \sim 2$ mag (Col. 14 of Table A.3). Our estimates are consistent within 1-$2\sigma$ with the mean/median values obtained by Smail et al. (2004, 1.70-2.44), Swinbank et al. (2004, $3.0 \pm 1.0$), Borys et al. (2005, $1.7 \pm 0.2$) and Hainline (2008, $1.7\pm 0.1$) based on near-IR data. For individual SMGs we obtained systematically larger extinction (median difference of $\sim $0.3 mag) than Hainline (2008). The difference may be accounted for if there is significant extinction even in Spitzer IRAC data.

The dust density of SMGs at z<0.5 (Col. 9 of Table 1) is approximately 3% of the total local ( 0.013<z<0.18) dust budget of $\log\rho_{\rm dust}=5.57_{-0.17}^{+0.12}~M_\odot~\mbox{Mpc}^{-3}$given by Driver et al. (2007) based on an assumed dust-to-light ratio. Therefore SMGs contribute very little to the dust budget at low redshifts.

In our sample of SMGs $\rho_{\rm dust}$does not change significantly from $z\sim 3.6$ to $z\sim0.5$. We do not detect any evolution of dust mass in SMGs across the entire redshift range (Fig. 2). A constant dust mass density across redshifts 0-3.5 was also found by Pascale et al. (2009) based on a stacking analysis at submillimeter wavelengths of galaxies selected at $24~\mu$m.

The question is what happened to the dust produced in SMGs. If they evolve into dust-poor ellipticals, then the dust is not simply stored in their end-products (as is probably the case for stellar masses). It is therefore plausible that dust is either blown away (by stellar and/or AGN winds) or absorbed in star formation, or destroyed during subsequent evolution after the SMG event.

5.2.4 Comparison with GRB hosts

In Michaowski et al. (2008) we presented a hypothesis that gamma-ray burst (GRB) host galaxies may constitute a subsample of hotter/less luminous counterparts of SMGs. Indeed, the UV-to-IR SEDs of three $z\sim2$-3 SMGs[*] are consistent with $z\sim1$ submillimeter/radio bright GRB hosts (dashed lines in Fig. A.1 from Michaowski et al. 2008), but 1.2-3.9 times more luminous. These three SMGs are similar to GRB hosts with respect to their hot dust temperatures ($\sim $40-60 K), high SSFRs ($\gtrsim$2 Gyr-1, high fraction of stellar mass formed in the ongoing starburst (>10%) and blue optical colors.

If larger samples of GRB hosts shows a similar tendency that their brightest members overlap with the hotter subsample of SMGs, then GRB events will provide an effective way of selecting hot SMGs, otherwise difficult to localize.

5.3 Contribution to stellar mass assembly

5.3.1 Star formation rate volume density

SFR densities of SMGs were calculated as described in Sect. 3.2. In order to assess the accuracy of our simplified method of dividing the sum of the SFRs of the detected SMGs by the total survey volume, we compare our estimates with those resulting from detailed calculation of the volume contribution of individual SMGs done by Chapman et al. (2005, based on the same sample as we analyse) and Wall et al. (2008, based on 35 SMGs in GOODS-N field of which 17 have spectroscopic redshifts). The comparison is shown in Fig. 4. Our results in two high-redshift bins (z>2) corrected for incompleteness (Sect. 3.2) are consistent with that of Chapman et al. (2005) and Wall et al. (2008). At lower redshifts we find values similar to Chapman et al. (2005), but an order of magnitude lower than Wall et al. (2008). Therefore we conclude that i) our method to calculate volumes is accurate, since it gives consistent results with other estimates; and ii) our sample is incomplete in the three low-redshift bins as anticipated in Sect. 2.

From Fig. 4 (and Cols. 4 and 5 of Table 1) it is apparent that a $\rho_{\rm SFR}$ of SMGs starts to decline (with cosmic time) earlier ( about $z\sim2$) than that of other galaxies ($z\sim1$). More quantitatively, SMGs harbour $\sim $20% of the cosmic $\rho_{\rm SFR}$ at $z\sim2$-3.6 (Col. 5), but their contribution drops to $\sim $9% at 0.5<z<1.4. It is likely that at lower redshifts, due to the decreased rate of mergers (e.g. de Ravel et al. 2009; Rawat et al. 2008), there are fewer galaxies left that can still sustain high SFRs to be detected at submillimeter wavelengths. However, part of the decrease of SMG $\rho_{\rm SFR}$can be explained by the ``redshift desert'', which makes it difficult to measure redshifts of $z\sim1.2$-1.8 SMGs (see Sect. 2).

A high value of $\rho_{\rm SFR}$ of SMGs at $z\sim2$-3 and the subsequent decline are consistent with the hypothesis that the SMG population is a manifestation of powerful starburst episodes evolving into the present-day ellipticals (as discussed in Sect. 5.2.2). In this scenario galaxies detected in the submillimeter at high-z do not enter the sample of SMGs at low-z because they have already evolved into passive galaxies. It has indeed been found that ellipticals contain old stars formed at $z\sim1.5$-4 (Daddi et al. 2000; van de Ven et al. 2003; van Dokkum & Franx 2001). The evolution of SMGs into ellipticals has also been claimed by several authors based on their luminosity function (Smail et al. 2004), huge luminosities (Eales et al. 1999) and gas reservoirs (Smail et al. 2002; Greve et al. 2005), strong clustering (Ivison et al. 2000; Almaini et al. 2003), space density and morphology (Swinbank et al. 2006; Lilly et al. 1999; Trentham et al. 1999; Barger et al. 1999) and evolutionary SED models (Takagi et al. 2004).

Knudsen et al. (2008b) analysed number counts of SMGs fainter than the SCUBA confusion limit, using those behind clusters of galaxies magnified by lensing. They concluded that the integrated light produced by the SMGs brighter than 0.1 mJy (i.e. LIRGs and ULIRGs with roughly $L_{\rm IR} > 8 \times 10^{10}~L_\odot$and SFR  $> 15~M_\odot$ yr-1) is comparable to the extragalactic background light (EBL) at $850~\mu$m (see also Blain et al. 1999; Cowie et al. 2002). This means that these galaxies host the majority of the cosmic obscured star formation. Knudsen et al. (2008b) also found that sources brighter than 2.5 mJy (roughly the limit of the survey considered here) contribute $\sim $25% to the to EBL at $850~\mu$m (see also Hughes et al. 1998; Wang et al. 2004; Coppin et al. 2006; Barger et al. 1999). Together with our results this implies that as much as $\sim $80% ($4\times20$%) of the cosmic star formation at $z\sim2$-3.6 reside in SMGs brighter than 0.1 mJy. This is only true if the faint (<2 mJy) SMGs have similar dust temperatures to the brighter ones. If they are colder (hotter) their submillimeter fluxes corresponds to lower (higher) SFRs (because it is calibrated to total IR emission) and therefore the total SMG population contribute less (more) than 80% to the cosmic $\rho_{\rm SFR}$. This picture is however complicated, because based on stacking analysis it has been claimed that the distribution of the faint SMGs peaks at lower redshifts (z<1.5; Serjeant et al. 2008; Wang et al. 2006).

Our overall conclusion is that the SMG population plays a significant role at redshifts $z\sim2$-4, namely sources brighter than $\sim $3 (0.1) mJy at $850~\mu$m host 20% (80%) of cosmic star formation. Their contribution can however be lower in reality if very small (but numerous) galaxies are missed in all high-z flux-limited galaxy surveys. In such a case the total SFR density (color points in Fig. 4) would be underestimated. To solve this issue much deeper surveys at high-z are necessary, either blank-field or for well-selected dwarf galaxy samples (e.g., GRB hosts or Ly$\alpha $ emitters).

Zheng et al. (2007) estimated $\rho_{\rm SFR}$at $z\sim0.9$for massive galaxies ( $M_*>10^{11}~M_\odot$) down to R<24 mag (only $\sim $40% of SMGs satisfy the latter criterion) equal to $0.0052_{-0.0021}^{+0.0020}~M_\odot~\mbox{yr}^{-1}~\mbox{ Mpc}^{-3}$. This value is only a factor of 2 lower than our estimate for the SMGs at 0.5<z<1.4 (Table 1). Therefore, although SMGs do not host a major fraction of the cosmic SFR at these redshifts, they contribute significantly ( $ 0.0102/(0.0052\times0.6+0.0102)\sim66$%) to the SFR budget of massive galaxies.

5.3.2 Stellar mass volume density

Stellar mass densities of SMGs were calculated as described in Sect. 3.2. Figure 4 and Table 1 (Cols. 6 and 7) show that at $z\sim2$-3.6 a significant part ($\sim $30-50%) of the cosmic stellar mass had been formed in the progenitors of SMGs. At lower redshifts $\rho_*$ of SMGs (and hence their contribution to the cosmic $\rho_*$) drops, likely because the majority of SMGs at higher redshifts had already evolved into passive galaxies at $z\sim1.5$, and so dropped out of our submillimeter-selected sample. Moreover the sample is incomplete at $z\sim1.2$-1.8 due to the ``redshift desert'' (see Sect. 2). This brings down the densities of SMGs in the low-z bins.

Since most of the stellar mass of SMGs has not been formed in the ongoing starburst (Sect. 5.2.2), their $\rho_*$ reflects the integrated contribution of SMGs to the cosmic $\rho_{\rm SFR}$. Therefore the relatively high contribution of SMGs to the cosmic $\rho_*$ in the last redshift bin ($\sim $31%, Col. 7 of Table 1) means that SMGs play a non-negligible role in the cosmic stellar assembly even at z>3.6. This can be tested by analysis of a sample of $z\gtrsim4$ SMGs in a defined survey sky area (e.g. Younger et al. 2009a; Michaowski et al. 2010, note that these results are likely affected by cosmic variance). It has been confirmed that such distant SMGs exist (Knudsen et al. 2008a; Capak et al. 2008; Daddi et al. 2009b; Schinnerer et al. 2008; Coppin et al. 2009; Knudsen et al. 2010; Daddi et al. 2009a).

5.4 Source of emission

5.4.1 IR-radio correlation

With our full SED modelling of 76 SMGs we confirm the results of Hainline (2008) on the correlation between IR and radio luminosities. Figure 5 shows that SMGs follow a linear IR-radio correlation. The two outliers (with $q\sim1.3$, see Sect. 5.4.2) are probably caused by AGN activity contributing significantly to radio luminosities. A linear fit gives:

\begin{displaymath}\begin{array}{rcl}
\log \left(L_{\nu~ 1.4~{\rm GHz}} / L_\odo...
...{\rm IR} / L_\odot) \\
&&\mbox{}- (14.3\pm0.8).\\
\end{array}\end{displaymath} (1)

The slope is consistent (within errors) with unity, suggestive of the linear relation between $L_{\nu~ 1.4~{\rm GHz}}$ and $L_{\rm IR}$ at the high-end ( $L_{\rm IR}\gtrsim10^{11}~L_\odot$) of the galaxy luminosity function (a similar value of $1.064 \pm 0.025$ was found by Hainline 2008).

The IR-radio correlation is usually quantified by the ratio of IR and radio luminosities, q (see Sect. 3.1). The mean q for SMGs ( $2.32\pm0.04$, scatter: 0.34) is significantly lower than that of local star-forming galaxies (2.64 with a scatter of 0.26; Bell 2003). Similar offsets were reported by Kovács et al. (2006), Murphy et al. (2009) and Murphy (2009) based on smaller samples of SMGs. We conclude that at z>1.4 SMGs have radio luminosities on average a factor of $\sim $2.1 larger ( $\Delta q\sim -0.32$) than what would result from the local relation. The difference is significant at the level of 4-$5\sigma$ and can be explained in three ways.

Radio-loud AGNs have on average low q values (see e.g. Miller & Owen 2001; Yang et al. 2007; Yun et al. 2001). If $\gtrsim$50% of the radio emission of SMGs is powered by AGNs, then the radio luminosities of SMGs higher by a factor of $\sim $2.1 can be accounted for. However, there are indications that SMGs are starburst-dominated (see Sect. 5.4.2), so we deem this explanation less likely.

Another explanation is that the radio excess is a result of the bias against radio-faint sources in our sample (see Sect. 2). This can be tested when a sample of SMGs with localizations (and hence redshifts) independent of radio detections is available (e.g. Daddi et al. 2009b; Weiß et al. 2009a; Knudsen et al. 2010; Daddi et al. 2009a).

The third possibility is that some properties influencing the IR or radio emission are intrinsically different for SMGs and local galaxies. The sample of Bell (2003) includes local normal, star-forming spiral and irregular galaxies, blue compact dwarfs, starburst galaxies and ULIRGs. Therefore the difference in the properties between this sample and such extreme galaxies as SMGs is expected. Such explanation was offered by Lacki et al. (2009) and Lacki & Thompson (2009). Their numerical modelling showed that cosmic-ray electrons in ``puffy starbursts'' (vertically and radially extended galaxies with vertical scale heights $\sim $1 kpc) experience weaker bremsstrahlung and ionization losses resulting in stronger radio emission. Indeed, there are indications that SMGs are extended on vertical scales of $\sim $1 kpc (Genzel et al. 2008; Lacki & Thompson 2009; Law et al. 2009; Tacconi et al. 2008; Younger et al. 2008; Tacconi et al. 2006), so we find this explanation probable.

The systematic uncertainties in the determination of $L_{\rm IR}$(factor of $\lesssim$2, Sect. 4) may in principle also explain the offset. However, we find this unlikely because similar offsets were found by other authors using different fitting methods (Murphy et al. 2009; Kovács et al. 2006; Murphy 2009).

\begin{figure}
\par\includegraphics[width=8.8cm,clip]{qz.eps}
\end{figure} Figure 6:

The ratio of the infrared (8-$1000~\mu$m) and radio luminosities q (defined in Sect. 3.1) as a function of redshift of SMGs. It provides evidence that a linear IR-radio correlation holds for SMGs up to $z\sim 3.6$, though with a normalization offset from the local relation by a factor of $\sim $2.1 ( $\Delta q\sim -0.32$) towards higher radio luminosities (Sect. 5.4.1). Circles: values for individual SMGs. Squares: the mean values (and errors on the mean) in five redshift bins containing equal number of galaxies (Table 1 and Sect. 3.2). Small symbols indicate z<0.5 objects. Red crosses: SMGs classified as AGNs based on X-ray emission (Alexander et al. 2005). Light blue plus signs: SMGs classified as starbursts based on X-ray emission (Alexander et al. 2005). Violet triangles: SMGs classified as AGNs based on optical spectra (Chapman et al. 2005). Green diamonds: SMGs classified as AGNs based on a mid-IR power-law (Sect. 5.4.2). The mean local q=2.64 (Bell 2003) is shown as a solid line with 0.26 scatter ( dotted lines). The q values for majority of AGN-classified SMGs do not differ from the rest of the SMG population (see Sect. 5.4.2).

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The q values for SMGs are shown in Fig. 6 as a function of redshift. We do not detect any significant evolution across the redshift range 1.4-3.6. The only sign of evolution is that the mean q in the low-redshift bin (0.5<z<1.4) is above the value found at higher redshifts ($\sim $4$\sigma$). This can be explained either by the contribution of reprocessed emission from low-mass stars (cirrus emission, e.g. Yun et al. 2001, and references therein) to the IR, or by the fact that at low redshifts SMGs are more similar to other local galaxies and do not exhibit large vertical scale heights characteristic for ``puffy starbursts'' (see above).

It is important to note that the derived linear IR-radio correlation for SMGs is not a consequence of the use of the SED templates (which were tuned to fulfill this correlation locally), because the radio luminosities used here were derived based on the observational data only, independent of the SED modeling.

5.4.2 AGN activity

As discussed in Sect. 5.4.1, AGN activity could explain low q values of SMGs. This is at least true for the two SMGs with lowest q[*], spectroscopically classified as AGN (Chapman et al. 2005).

In the SEDs of SMGs there are clear signs that some of them host AGNs (though, not necessarily a bolometrically dominant ones). Radio datapoints are higher than model predictions by more than 3$\sigma$ in 36% (27/76) of SMGs, whereas they are lower than models only for 8% (6/76). This may hint at an AGN contribution in these galaxies. However, 4 out of 5 X-ray identified starbursts (Col. 16 of Table A.3) also exhibit radio excess, so we find other explanations of radio excess presented in Sect. 5.4.1 more reliable.

Another indication of an AGN contribution is that 18% (14/76) of SMGs show a mid-IR power-law AGN feature incompatible with our starburst models (see Fig. A.1 and Col. 16 of Table A.3). However, rest-frame 2-$5~\mu$m excess was also interpreted as a tracer of recent star formation (Mentuch et al. 2009).

Finally, three SMGs[*] have exceptionally high SFR$_{\rm UV}$ (> $500~M_\odot~\mbox{ yr}^{-1}$, Col. 4 of Table A.3). Strikingly, all of them were fitted with non-starburst models ( $M_{\rm burst}=0$, Col. 9), so modeling is consistent with these high SFRs being continuous (the same is true for three other non-starburst SMGs with high SFR$_{\rm IR}$). Such a scenario is unlikely, so this hints at an AGN contribution to the UV/IR emission.

However, the fact that we obtained reasonable SED fits for most of the SMGs using purely star-forming models (Fig. A.1) hints at the conclusion that AGN activity is not dominant in our sample.

We investigated the issue of AGN activity further by analysing the average q values of the following subsamples (see also Fig. 6): X-ray identified (Alexander et al. 2005) AGNs: $2.32\pm0.06$and starbursts: $2.12\pm0.18$; optically identified AGNs (Chapman et al. 2005): $2.27\pm 0.09$; and mid-IR identified AGNs (see above): $2.36\pm0.12$. All subsamples are consistent with the value derived for the entire sample (2.32) Hence, we confirm the finding of Hainline (2008) that even the AGN-classified SMGs follow a linear IR-radio correlation. This means that even if an AGN is present it does not contribute to the emission of an SMG significantly (with the exception of the two $q\sim1.3$ sources).

This is in line with i) the X-ray studies of SMGs indicating that the contribution of AGN activity to their IR emission is only $\sim $8% on average (Alexander et al. 2005); ii) mid-IR colors of SMGs indicating that AGNs dominate the emission at these wavelengths only in 13-19% cases (Hainline et al. 2009); iii) mid-IR spectroscopy of SMGs revealing only weak AGN-like continua (Watabe et al. 2009; Pope et al. 2008; Murphy et al. 2009; Menéndez-Delmestre et al. 2007,2009; Valiante et al. 2007); iv) near-IR spectroscopy revealing that starbursts dominate the emission of SMGs (Swinbank et al. 2004). Moreover, de Vries et al. (2007) found that star formation processes (if present) account for at least 75% of the radio luminosities of optically-selected AGNs.

Therefore we conclude that AGNs are present in a significant fraction of SMGs, but their contribution to the IR emission is at most minor.

5.5 Comparison of our results with the literature

For the sample of SMGs discussed in this paper there are previous estimates of some of their properties. In this section we compare them with our results.

Chapman et al. (2005) derived $L_{\rm IR}$and $T_{\rm d}$ based only on the $850~\mu$m and 1.4 GHz data. There is no systematic difference between the determinations of $T_{\rm d}$ (our median of 38.7 K, theirs: 38.3 K). The mean difference between individual datapoints is 4 K ($\sim $10%). However, our values for $L_{\rm IR}$ are systematically lower than theirs (the median ratio of individual datapoints is 1.7). We find our values more reliable since they are based on data spanning a wider wavelength range. Overestimation of $L_{\rm IR}$when using only $850~\mu$m and 1.4 GHz was also noticed by Kovács et al. (2006) and Pope et al. (2006).

Kovács et al. (2006) investigated a subsample observed at $350~\mu$m. Their median dust mass ( $9.04 \log~M_\odot$) and q value (2.20) are consistent with our estimates (9.01 and 2.35, respectively). The median difference between individual datapoints is $\sim $30% for dust masses and $\sim $13% for q.

The median stellar mass for a subsample of 13 SMGs investigated by Borys et al. (2005, $11.51~\log M_\odot$) is close to our value (11.70). However, estimates of Hainline (2008, median $10.82~\log M_\odot$) for 64 SMGs are a factor of $\sim $5.6 smaller than our values (11.57). Hainline (2008) postulated that the discrepancy between her results and those of Borys et al. (2005) arose from a combination of systematic differences between the applied SED models and a higher AGN contribution in the K-band (used by Borys et al. 2005) with respect to the H-band. Our estimates are based on all the available photometric data, and so we find the former explanation more likely. In particular, the differences in the applied stellar population models and their ages may explain the discrepancy.

6 Conclusions

We have investigated the UV-to-radio SEDs of 76 SMGs ( $S_{850}\gtrsim 3$ mJy) with spectroscopic redshifts (0.080-3.623). For the first time the properties of such a significant sample has been derived consistently using all available data. The resulting SFRs (median $713~M_\odot~\mbox{yr}^{-1}$) and stellar masses ( $11.57~\log~M_\odot$) are among the highest in the Universe.

Such high stellar masses, already present at redshifts $\sim $2-3, require that SMGs experienced either at least two starburst episodes, or a merger of several smaller galaxies. Our modeling suggests that only a minor fraction (8%) of their stellar populations was formed during the ongoing starburst episodes. This is supported by the fact that the SFRs and M* of SMGs are basically disconnected, i.e. we observe two orders of magnitude spread in SSFRs whereas the range of M* is relatively narrow: 1011- $10^{12}~M_\odot$. We concluded that dust is blown away or destroyed during the evolution of SMGs, since it is not stored in the likely end-products of SMGs, elliptical galaxies.

Indeed, the high stellar masses and the evolution of the SFR and stellar mass densities of SMGs are consistent with a scenario in which SMGs are progenitors of present-day ellipticals.

We found that SMGs contribute significantly to the cosmic SFR, $\rho_{\rm SFR}$($\sim $20%) and stellar mass, $\rho_*$ (30-50%) densities at $z\sim2$-4. If we consider submillimeter sources down to 0.1 mJy the contribution to $\rho_{\rm SFR}$ rises to $\sim $80%.

Our analysis suggests that a linear IR-radio correlation holds for SMGs at least up to a redshift of 3.6, but they are $\sim $2.1 times brighter at radio wavelengths than what would result from the local correlation.

Acknowledgements
We thank Joanna Baradziej, José María Castro Cerón, Thomas Greve, Brian Lacki, Kim Nilsson, Jesper Sommer-Larsen, Sune Toft, Bärbel Tress and Gunther Tress for discussion and comments; our referee for help with improving this paper; Scott Chapman for information on the survey areas; Jorge Iglesias-Páramo for kindly providing his SED templates; and Fabio Fontanot for kindly providing his model and data on star formation density. We acknowledge use of the extensive Spitzer database in the PhD thesis of Laura Hainline.

M. J. M. would like to acknowledge support from The Faculty of Science, University of Copenhagen. The Dark Cosmology Centre is funded by the Danish National Research Foundation. This research has made use of NASA's Astrophysics Data System Bibliographic Services.

References

Online Material

Appendix A: Long tables and figures.

Table A.1:   Photometry detections of SMGs.

Table A.2:   Photometry upper limits of SMGs.

Table A.3:   Properties of SMGs derived from the SED modeling.

\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA1.eps}
\end{figure} Figure A.1:

Spectral energy distributions (SEDs) of SMGs. Solid lines: the best GRASIL fits. Dashed lines: SEDs of GRB hosts (Michaowski et al. 2008) shown for comparison. Squares: detections with errors, in most cases, smaller than the size of the symbols. Arrows: $3\sigma $ upper limit (values marked at the base). In the cases where our fits strongly underpredict the observed data at $850~\mu$m, we adopted $L_{\rm IR}$and $T_{\rm d}$of Chapman et al. (2005).

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\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA2.eps}
\end{figure} Figure A.1:

(continued).

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\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA3.eps}
\end{figure} Figure A.1:

(continued).

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\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA4.eps}
\end{figure} Figure A.1:

(continued).

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\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA5.eps}
\end{figure} Figure A.1:

(continued).

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\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA6.eps}
\end{figure} Figure A.1:

(continued).

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\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA7.eps}
\end{figure} Figure A.1:

(continued).

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\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA8.eps}
\end{figure} Figure A.1:

(continued).

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\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA9.eps}
\end{figure} Figure A.1:

(continued).

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\begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA10.eps}
\end{figure} Figure A.1:

(continued).

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Table A.4:   Compilation of star formation rate density determinations in $M_\odot~\mbox{yr}^{-1}~\mbox{Mpc}^{-3}$.

Table A.5:   Compilation of stellar mass density determinations in $\log M_\odot~\mbox{Mpc}^{-3}$.

Footnotes

... assembly[*]
Appendix is only available in electronic form at http://www.aanda.org
... Appendix[*]
For convenience we make the compilation available in electronic form. We suggest that the original data source be consulted and referred to appropriately.
...(Silva et al. 1998)[*]
http://adlibitum.oat.ts.astro.it/silva/default.html
... SMGs[*]
SMMJ123553.26+621337.7SMMJ123555.14+620901.7SMMJ123600.10+620253.5SMMJ123600.15+621047.2, SMMJ123606.85+621021.4, SMMJ123716.01+620323.3, SMMJ163706.51+405313.8SMMJ221804.42+002154.4, SMMJ221806.77+001245.7
... fits[*]
The SED fits can be downloaded from http://archive.dark-cosmology.dk
... cases[*]
SMMJ030226.17+000624.5, SMMJ030231.81+001031.3, SMMJ030236.15+000817.1, SMMJ030238.62+001106.3, SMMJ123636.75+621156.1, SMMJ123651.76+621221.3, SMMJ123721.87+621035.3, SMMJ163639.01+405635.9, SMMJ221724.69+001242.1
... coverage[*]
SMMJ105201.25+572445.7, SMMJ105230.73+572209.5, SMMJ163650.43+405734.5, SMMJ163658.19+410523.8, SMMJ163706.51+405313.8
... SMGs[*]
SMMJ131201.17+424208.1, SMMJ141802.87+523011.1, SMMJ221806.77+001245.7 plus a low-mass, low-z case, SMMJ030238.62+001106.3
... SMGs[*]
SMMJ141750.50+523101.0, SMMJ141802.87+523011.1, SMMJ163627.94+405811.2
...q[*]
SMMJ131215.27+423900.9, SMMJ141813.54+522923.4
... SMGs[*]
SMMJ123716.01+620323.3, SMMJ131215.27+423900.9, SMMJ131222.35+423814.1

All Tables

Table 1:   Mean values for SMGs in redshift bins.

Table A.1:   Photometry detections of SMGs.

Table A.2:   Photometry upper limits of SMGs.

Table A.3:   Properties of SMGs derived from the SED modeling.

Table A.4:   Compilation of star formation rate density determinations in $M_\odot~\mbox{yr}^{-1}~\mbox{Mpc}^{-3}$.

Table A.5:   Compilation of stellar mass density determinations in $\log M_\odot~\mbox{Mpc}^{-3}$.

All Figures

  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{avsed.eps}
\end{figure} Figure 1:

Median spectral energy distribution (SED) of SMGs ( thick lines) and SEDs of individual SMGs ( thin lines). Dotted lines indicate z<0.5 objects. Shaded areas enclose 90% of the SEDs. Top: all SEDs were divided by the corresponding 850 $\mu $m datapoint and scaled, so that the median SED has a flux of 5 mJy at the rest-frame 283 $\mu $m (observed $850~\mu$m at z=2). Bottom: SEDs were normalized to an infrared star formation rate of $100~M_\odot$ yr-1.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.6cm,clip]{zevol.eps}
\end{figure} Figure 2:

Redshift evolution of the properties ( full circles, see Table A.3 in Appendix) of the sample of 76 SMGs with spectroscopic redshifts (Chapman et al. 2005). Small symbols indicate z<0.5 objects. Typical errors (Sect. 4) are shown as crosses. From top-left to bottom-right: star formation rate (SFR) derived from spectral energy distribution modeling, ultraviolet, infrared and radio emission, SFR per unit stellar mass ( $\equiv\mbox{SFR}_{\rm IR}/M_*$), stellar mass, fraction of stellar population formed during the ongoing starburst, stellar mass-to-light ratio, dust mass and temperature. In the SFR$_{\rm IR}$ panel, we also show the minimum average SFRs (see Sect. 5.2.1) required to build up the total stellar mass within the age of the Universe at a given redshift ( empty circles) and to build up the fraction of stellar population that was not formed during the ongoing starburst ( plus signs). The location of plus signs indicates that SMGs must have been highly star-forming even before the onset of the ongoing starburst. When empty circles and plus signs overlap, the contribution of the ongoing starburst to the total stellar mass of a galaxy is negligible (i.e. $M_{\rm burst}/M_*\sim 0$).

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm]{beta.eps}
\end{figure} Figure 3:

Derived dust mass of a mock galaxy with dust temperature $T_{\rm d}=40$ K and a flux density of 5 mJy at several infrared rest-wavelengths as a function of the assumed emissivity index $\beta $. For each wavelength the dust masses were normalized to 1 at $\beta =1.5$. The spread of the derived dust masses shows that the uncertainty of the dust mass resulting from unknown $\beta $ is a factor of a few.

Open with DEXTER
In the text

   \begin{figure}
\par\includegraphics[width=8.8cm,clip]{sfrdz.eps}\end{figure} Figure 4:

Top: cosmic star formation density. The SMGs' contribution rises with redshift from $\sim $9% to $\sim $20% (Sect. 5.3.1 and Table 1). Filled Squares: data for SMGs at z>0.5 in four bins (Table 1 and Sect. 3.2). Small Squares: data for SMGs at z<0.5. Thick black arrows: the SMG data without incompleteness correction (factor of 3.5, Sect. 3.2). Black crosses and diamonds: star formation density of SMGs determined by Chapman et al. (2005) and Wall et al. (2008), respectively. Colored points with error bars: determination of the cosmic value based on different estimates - ultraviolet ( violet), emission lines: [O II], [O III], H$\alpha $, H$\beta $ ( green), mid-IR ( light blue), submillimeter ( black), radio ( red), X-ray ( yellow). Extinction correction and, in many cases, incompleteness correction have been applied by the authors. Arrows: lower limits. Bottom: cosmic stellar mass density. The SMGs' contribution rises with redshift from $\sim $5% to $\sim $50% (Sect. 5.3.2 and Table 1). Red points with error bars: determination of the cosmic value from literature. The data and the references are listed in Tables A.4 and A.5 in Appendix.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{lirrad.eps}
\vspace*{3mm}
\end{figure} Figure 5:

Radio luminosity density as a function of infrared (8-$1000~\mu$m) luminosity of SMGs showing a linear relation, though with a normalization offset from the local relation by a factor of $\sim $2.1 towards higher radio luminosities (Sect. 5.4.1). Circles: values for individual SMGs color-coded by redshift. Solid line: linear fit to the data (Eq. (1)). Dotted line: the mean local relation (Bell 2003). Shaded area: its scatter. Dashed line: the track where SFR$_{\rm IR}$ (Kennicutt 1998) is equal to SFR $_{\rm radio}$(Bell 2003). The strong outliers (above the line) at high-luminosity end are probably caused by AGN activity increasing radio luminosities.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{qz.eps}
\end{figure} Figure 6:

The ratio of the infrared (8-$1000~\mu$m) and radio luminosities q (defined in Sect. 3.1) as a function of redshift of SMGs. It provides evidence that a linear IR-radio correlation holds for SMGs up to $z\sim 3.6$, though with a normalization offset from the local relation by a factor of $\sim $2.1 ( $\Delta q\sim -0.32$) towards higher radio luminosities (Sect. 5.4.1). Circles: values for individual SMGs. Squares: the mean values (and errors on the mean) in five redshift bins containing equal number of galaxies (Table 1 and Sect. 3.2). Small symbols indicate z<0.5 objects. Red crosses: SMGs classified as AGNs based on X-ray emission (Alexander et al. 2005). Light blue plus signs: SMGs classified as starbursts based on X-ray emission (Alexander et al. 2005). Violet triangles: SMGs classified as AGNs based on optical spectra (Chapman et al. 2005). Green diamonds: SMGs classified as AGNs based on a mid-IR power-law (Sect. 5.4.2). The mean local q=2.64 (Bell 2003) is shown as a solid line with 0.26 scatter ( dotted lines). The q values for majority of AGN-classified SMGs do not differ from the rest of the SMG population (see Sect. 5.4.2).

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA1.eps}
\end{figure} Figure A.1:

Spectral energy distributions (SEDs) of SMGs. Solid lines: the best GRASIL fits. Dashed lines: SEDs of GRB hosts (Michaowski et al. 2008) shown for comparison. Squares: detections with errors, in most cases, smaller than the size of the symbols. Arrows: $3\sigma $ upper limit (values marked at the base). In the cases where our fits strongly underpredict the observed data at $850~\mu$m, we adopted $L_{\rm IR}$and $T_{\rm d}$of Chapman et al. (2005).

Open with DEXTER
In the text

 \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA2.eps}
\end{figure} Figure A.1:

(continued).

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In the text

 \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA3.eps}
\end{figure} Figure A.1:

(continued).

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In the text

 \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA4.eps}
\end{figure} Figure A.1:

(continued).

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In the text

 \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA5.eps}
\end{figure} Figure A.1:

(continued).

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In the text

 \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA6.eps}
\end{figure} Figure A.1:

(continued).

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In the text

 \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA7.eps}
\end{figure} Figure A.1:

(continued).

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In the text

 \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA8.eps}
\end{figure} Figure A.1:

(continued).

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In the text

 \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA9.eps}
\end{figure} Figure A.1:

(continued).

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In the text

 \begin{figure}
\par\includegraphics[width=15.5cm,clip]{fA10.eps}
\end{figure} Figure A.1:

(continued).

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In the text


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