(Sub)millimetre interferometric imaging of a sample of COSMOS/AzTEC submillimetre galaxies IV. Physical properties derived from spectral energy distributions
Key Words.:Galaxies: evolution – Galaxies: star formation – Radio continuum: galaxies – Submillimetre: galaxies
Context:Submillimetre galaxies (SMGs) in the early universe are the potential antecedents of the most massive galaxies we see in the present-day universe. An important step towards quantifying this galactic evolutionary connection is to investigate the fundamental physical properties of SMGs, like their stellar mass content () and star formation rate (SFR).
Aims:We attempt to characterise the physical nature of a 1.1 mm-selected, flux-limited, and interferometrically followed up sample of SMGs in the COSMOS field.
Methods:We used the latest release of the MAGPHYS code to fit the multiwavelength (UV to radio) spectral energy distributions (SEDs) of 16 of the target SMGs, which lie at redshifts . We also constructed the pure radio SEDs of our SMGs using three different radio bands (325 MHz, 1.4 GHz, and 3 GHz). Moreover, since two SMGs in our sample, AzTEC1 and AzTEC3, benefit from previous CO line observations, we studied their properties in more detail.
Results:The median and 16th–84th percentile ranges of , infrared (m) luminosity (), SFR, dust temperature (), and dust mass () were derived to be , , , K, and , respectively. We found that of our target SMGs lie above the galaxy main-sequence by more than a factor of 3, and hence are starbursts. The 3 GHz radio sizes we have previously measured for the target SMGs were compared with the present estimates, and we found that the SMGs are fairly consistent with the mass–size relationship of compact, quiescent galaxies (cQGs). The median radio spectral index is found to be . The median IR-radio correlation parameter is found to be , which is lower than measured locally (median ). The gas-to-dust mass ratio for AzTEC1 is derived to be , while that for AzTEC3 is . AzTEC1 is found to have a sub-Eddington SFR surface density (by a factor of ), while AzTEC3 appears to be an Eddington-limited starburster. The gas reservoir in these two high- SMGs would be exhausted in only and Myr at the current SFR, respectively.
Conclusions:A comparison of the MAGPHYS-based properties of our SMGs with those of equally bright 870 m-selected, ALMA followed-up SMGs in the ECDFS field (the ALESS SMGs), suggests that the two populations share fairly similar physical characteristics, including the parameter. The somewhat higher for our sources (factor of on average) can originate in the longer selection wavelength of 1.1 mm. Although the derived median is consistent with a canonical synchrotron spectral index, some of our SMGs exhibit spectral flattening or steepening, which can be attributed to different cosmic-ray energy gain and loss mechanisms. A hint of negative correlation is found between the 3 GHz size and the level of starburstiness, and hence cosmic-ray electrons in more compact starbursts might be more susceptible to free-free absorption. Some of the derived low and high values (compared to the local median) could be the result of a specific merger/post-starburst phase of galaxy evolution. Overall, our results, like the –3 GHz radio size analysis and comparison with the stellar masses of cQGs, in concert with the star formation properties of AzTEC1 and 3, support the scenario where SMGs evolve into today’s giant, gas-poor ellipticals.
Submillimetre galaxies or SMGs (e.g. smail1997 (); hughes1998 (); barger1998 (); eales1999 ()) are a population of some of the most extreme, dusty star-forming galaxies in the universe, and have become one of the prime targets for studying massive galaxy evolution across cosmic time (for a recent review, see casey2014 ()). Abundant evidence has emerged that high-redshift () SMGs are the potential antecedents of the compact, quiescent galaxies (cQGs), which ultimately evolve into the present-day massive ( M), gas-poor elliptical galaxies (e.g. swinbank2006 (); fu2013 (); toft2014 (); simpson2014 ()). A better, quantitative understanding of the interconnected physical processes that drive the aforementioned massive galaxy evolution requires us to determine the key physical properties of SMGs, like the stellar mass () and star formation rate (SFR). Fitting the observed multiwavelength spectral energy distributions (SEDs) of SMGs provides an important tool for this purpose. The physical characteristics derived through SED fitting for a well-defined sample of SMGs – as done in the present study – can provide new, valuable insights into the evolutionary path from the SMG phase to local massive ellipticals. However, these studies are exacerbated by the fact that high-redshift SMGs are also the most dust-obscured objects in the early universe (e.g. dye2008 (); simpson2014 ()).
Further insight into the nature of SMGs can be gained by studying the infrared (IR)-radio correlation (e.g. helou1985 (); yun2001 ()) of this galaxy population. On the basis of the relative strength of the continuum emission in the IR and radio wavebands, the IR-radio correlation can provide clues to the evolutionary (merger) stage of a starbursting SMG (bressan2002 ()), or it can help identify radio-excess active galactic nuclei (AGN) in SMGs (e.g. delmoro2013 ()). Moreover, because submillimetre-selected galaxies have been identified over a wide redshift range, from (e.g. chapman2005 ()) to (riechers2013 ()), it is possible to examine whether the IR-radio correlation of SMGs has evolved across cosmic time. A potentially important bias in the IR-radio correlation studies is the assumption of a single radio spectral index (usually the synchrotron spectral index ranging from to , where is defined at the end of this section) for all individual sources in the sample. Hence, the sources that have steep (), flat (), or inverted () radio spectra will be mistreated under the simplified assumption of a canonical synchrotron spectral index (see e.g. thomson2014 ()). As done in the present work, this can be circumvented by constructing the radio SEDs of the sources when there are enough radio data points available, and derive the radio spectral index values for each individual source.
Ultimately, a better understanding of the physics of star formation in SMGs (and galaxies in general) requires us to investigate the properties of their molecular gas content – the raw material for star formation. Two of our target SMGs benefit from previous CO spectral line observations (riechers2010 (); yun2015 ()), which, when combined with their SED-based properties derived here, enable us to investigate a multitude of their interstellar medium (ISM) and star formation properties.
In this paper, we study the key physical properties of a sample of SMGs in the Cosmic Evolution Survey (COSMOS; scoville2007 ()) deep field through fitting their panchromatic SEDs. The layout of this paper is as follows. In Sect. 2, we describe our SMG sample, previous studies of their properties, and the employed observational data. The SED analysis and its results are presented in Sect. 3. A comparison with previous literature and discussion of the results are presented in Appendix C and Sect. 4, respectively (Appendices A and B contain photometry tables and details of our target sources). The two high-redshift SMGs in our sample that benefit from CO observations are described in more detail in Appendix D. In Sect. 5, we summarise the results and present our conclusions. The cosmology adopted in the present work corresponds to a spatially flat CDM (Lambda cold dark matter) universe with the present-day dark energy density parameter , total (dark+luminous baryonic) matter density parameter , and a Hubble constant of km s Mpc. A Chabrier (2003) Galactic-disk initial mass function (IMF) is adopted in the analysis. Throughout this paper we define the radio spectral index, , as , where is the flux density at frequency .
2.1 Source sample: the JCMT/AzTEC 1.1 mm-selected SMGs
The target SMGs of the present study were first uncovered by the mm survey of a COSMOS subfield (0.15 deg or 7.5% of the full 2 deg COSMOS field) carried out with the AzTEC bolometer array on the James Clerk Maxwell Telescope (JCMT) by Scott et al. (2008). The angular resolution of these observations was (full-width at half maximum or FWHM). The 30 brightest SMGs that comprise our parent flux-limited sample were found to have de-boosted flux densities of mJy, which correspond to signal-to-noise ratios of S/N (see Table 1 in scott2008 ()). The 15 brightest SMGs, called AzTEC1–15 (S/N), were followed up with the Submillimetre Array (SMA) at 890 m ( resolution) by Younger et al. (2007, 2009; see also younger2008 (), 2010; smolcic2011 (); riechers2014 (); M. Aravena et al., in prep.); all the SMGs were interferometrically confirmed. Miettinen et al. (2015a; hereafter Paper I) presented the follow-up imaging results of AzTEC16–30 (S/N) obtained with the Plateau de Bure Interferometer (PdBI) at mm ( resolution). In Paper I, we combined our results with the Younger et al. (2007, 2009) SMA survey results, and concluded that of the 30 single-dish detected sources AzTEC1–30 are resolved into multiple (two to three) components at an angular resolution of about , making the total number of interferometrically identified SMGs to be 39 among the 30 target sources (but see Appendix B.3 herein for a revised fraction). Moreover, the median redshift of the full sample of these interferometrically identified SMGs was determined to be , where the quoted error refers to the standard error of the median computed as , where is the sample standard deviation, and is the size of the sample (e.g. lupton1993 ()). This high median redshift of our target SMGs can be understood to be caused by the long observed-wavelength of mm at which the sources were identified (bethermin2015 (); see also strandet2016 ()). The corresponding median rest-frame wavelength probed by 1.1 mm observations, m, is very close to that of the classic 850 m-selected SMGs lying at a median redshift of ( m; chapman2005 ()).
Miettinen et al. (2015b; hereafter Paper II) found that of the present target SMGs are associated with GHz radio emission on the basis of the observations taken by the Karl G. Jansky Very Large Array (VLA)-COSMOS 3 GHz Large Project, which is a sensitive ( noise of 2.3 Jy beam), high angular resolution () survey (PI: V. Smolčić; smolcic2016b ()). In Paper II, we focused on the spatial extent of the radio-emitting regions of these SMGs, and derived a median deconvolved angular FWHM major axis size of . For a subsample of 15 SMGs with available spectroscopic or photometric redshifts we derived a median linear major axis FWHM of kpc. In a companion paper by Smolčić et al. (2016a; hereafter Paper III), we present the results of the analysis of the galaxy overdensities hosting our 1.1 mm-selected AzTEC SMGs. In the present follow-up study, we derive the fundamental physical properties of our SMGs, including , total infrared (IR) luminosity ( m), SFR, and dust mass. In addition, we study the centimetre-wavelength radio SEDs of the sources, and address the relationship between the IR and radio luminosities, i.e. the IR-radio correlation among the target SMGs. These provide an important addition to the previously determined redshift and 3 GHz size distributions (Papers I and II), and allow us to characterise further the nature of these SMGs.
The target SMGs, their coordinates, and redshifts are tabulated in Table 1. The ultraviolet (UV)–radio SEDs in the present work are analysed for a subsample of 16 (out of 39) SMGs whose redshift could have been determined through spectroscopic or photometric methods (i.e. not only a lower limit), and that have a counterpart in the employed photometric catalogues described in Sect. 2.2 below. We note that additional nine sources (AzTEC2, 11-N, 14-W, 17b, 18, 19b, 23, 26a, and 29b) have a or value available, but they either do not have sufficiently wide multiwavelength coverage to derive a reliable UV–radio SED, or no meaningful SED fit could otherwise be obtained (see Appendix B.2 for details). The remaining 14 sources have only lower redshift limits available (due to the lack of counterparts at other wavelengths). As we have already pointed out in Papers I and II (see references therein), AzTEC1–30 have not been detected in X-rays, and hence do not appear to harbour any strong AGN. In Paper II, we found that the GHz radio emission from our SMGs is powered by processes related to star formation rather than by AGN activity (the brightness temperatures were found to be K). This is further supported by the fact that none of these SMGs were detected with the Very Long Baseline Array (VLBA) observations at a high, milliarcsec resolution at GHz (N. Herrera Ruiz et al., in prep.). Furthermore, in the present paper we find no evidence of radio-excess emission that would imply the presence of AGN activity (Sect. 4.4). We also note that Riechers et al. (2014) did not detect the highly-excited CO line (the upper-state energy K) towards AzTEC3 in their Atacama Large Millimetre/submillimetre Array (ALMA) observations, which is consistent with no AGN contributing to the heating of the gas.
2.2 Multiwavelength photometric data
Our SMGs lie within the COSMOS field, and hence benefit from rich panchromatic datasets across the electromagnetic spectrum (from X-rays to radio). To construct the SEDs of our sources, we employed the most up-to-date photometric catalogue COSMOS2015, which consists of extensive ground and space-based photometric data in the optical to mid-IR wavelength range (laigle2016 (); see also capak2007 (); ilbert2009 ()).
The wide-field imager, MegaCam (boulade2003 ()), mounted on the 3.6 m Canada-France-Hawaii Telescope (CFHT), was used to perform deep -band (effective wavelength Å) observations. Most of the wavelength bands were observed using the Subaru Prime Focus Camera (Suprime-Cam) mounted on the 8.2 m Subaru telescope (miyazaki2002 (); taniguchi2007 (), 2015). These include the six broad-band filters , , , , , and , the 12 intermediate-band filters IA427, IA464, IA484, IA505, IA527, IA574, IA624, IA679, IA709, IA738, IA767, and IA827, and the two narrow bands NB711 and NB816. The Subaru/Hyper Suprime-Cam (miyazaki2012 ()) was used to perform observations in its HSC- band (central wavelength m). Near-infrared imaging of the COSMOS field in the (1.02 m), (1.25 m), (1.65 m), and (2.15 m) bands is being collected by the UltraVISTA survey (mccracken2012 (); ilbert2013 ())222The data products are produced by TERAPIX; see http://terapix.iap.fr. The UltraVISTA data used in the present work correspond to the data release version 2 (DR2). The Wide-field InfraRed Camera (WIRCam; puget2004 ()) on the CFHT was also used for - and -band imaging. Mid-infrared observations were obtained with the Infrared Array Camera (IRAC; 3.6–8.0 m; fazio2004 ()) and the Multiband Imaging Photometer for Spitzer (MIPS; 24–160 m; rieke2004 ()) on board the Spitzer Space Telescope as part of the COSMOS Spitzer survey (S-COSMOS; sanders2007 ()). The IRAC 3.6 m and 4.5 m observations used here were taken by the Spitzer Large Area Survey with Hyper Suprime-Cam (SPLASH) during the warm phase of the mission (PI: P. Capak; see steinhardt2014 ()). Far-infrared (100, 160, and 250 m) to submm (350 and 500 m) Herschel333Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. continuum observations were performed as part of the Photodetector Array Camera and Spectrometer (PACS) Evolutionary Probe (PEP; lutz2011 ()) and the Herschel Multi-tiered Extragalactic Survey (HerMES444http://hermes.sussex.ac.uk; oliver2012 ()) programmes.
From the ground-based single-dish telescope data, we used the deboosted JCMT/AzTEC 1.1 mm flux densities reported by Scott et al. (2008; their Table 1). Moreover, for three of our SMGs (AzTEC5, 9, and 19a) we could use the deboosted JCMT/Submillimetre Common User Bolometer Array (SCUBA-2) 450 m and 850 m flux densities from Casey et al. (2013) (for AzTEC9 only a deboosted 850 m flux density was available). More importantly, our SMGs benefit from interferometrically observed (sub)mm flux densities. Among AzTEC1–15, we used the 890 m flux densities measured with the SMA by Younger et al. (2007, 2009), while for sources among AzTEC16–30 we used the PdBI 1.3 mm flux densities from Paper I. AzTEC1 was observed at 870 m with ALMA during the second early science campaign (Cycle 1 ALMA project 2012.1.00978.S; PI: A. Karim), and its 870 m flux density – as measured through a two-dimensional elliptical Gaussian fit – is mJy. We also used the PdBI 3 mm flux density for AzTEC1 from Smolčić et al. (2011; mJy). Riechers et al. (2014) used ALMA to measure the 1 mm flux density of AzTEC3 ( mJy). Finally, we employed the 1.3 mm flux densities from the ALMA follow-up survey (Cycle 2 ALMA project 2013.1.00118.S; PI: M. Aravena) by M. Aravena et al. (in prep.) of 129 SMGs uncovered in the Atacama Submillimetre Telescope Experiment (ASTE)/AzTEC 1.1 mm survey (aretxaga2011 ()). Among the ALMA 1.3 mm-detected SMGs there are nine sources in common with the current SED target sources (AzTEC1, 4, 5, 8, 9, 11-S, 12, 15, and 24b; moreover, AzTEC2, 6, and 11-N were detected with ALMA at mm).
To construct the radio SEDs for our SMGs, we employed the 325 MHz observations taken by the Giant Meterwave Radio Telescope (GMRT)-COSMOS survey (A. Karim et al., in prep.). We also used the radio-continuum imaging data at 1.4 GHz taken by the VLA (schinnerer2007 (), 2010), and at 3 GHz taken by the VLA-COSMOS 3 GHz Large Project (PI: V. Smolčić; smolcic2016b (); see also Paper II). Hence, we could build the radio SEDs of our SMGs using data points at three different frequencies.
A selected compilation of mid-IR to mm flux densities of our SMGs are listed in Table 6, while the GMRT and VLA radio flux densities are tabulated in Table 7. Because of the large beam size (FWHM) of Herschel/PACS ( and at 100 and 160 m, respectively) and SPIRE (, , and at 250, 350, and 500 m, respectively) observations, the Herschel flux densities were derived using a point-spread-function-fitting method, guided by the known position of Spitzer/MIPS 24 m sources, i.e. we used the 24 m-prior based photometry (magnelli2012 ()) given as part of the COSMOS2015 catalogue (laigle2016 ()) whenever possible. Because AzTEC1, 3, 4, 8, 9, 10, and 17a are reported as non-detections at 24 m in the COSMOS2015 catalogue, we adopted their Herschel flux densities from the PACS and SPIRE blind catalogues555http://irsa.ipac.caltech.edu/Missions/cosmos.html.
3 Analysis and results
3.1 Spectral energy distributions from UV to radio wavelengths
To characterise the physical properties of our SMGs, we constructed their UV to radio SEDs using the multiwavelength data described in Sect. 2.2. The observational data were modelled using the Multiwavelength Analysis of Galaxy Physical Properties code MAGPHYS (dacunha2008 ())666MAGPHYS is publicly available, and can be retrieved at http://www.iap.fr/magphys/magphys/MAGPHYS.html. The commonly used MAGPHYS code has been described in a number of papers (e.g. dacunha2008 (), 2010; smith2012 (); berta2013 (); rowlands2014a (); hayward2015 (); smolcic2015 (); dacunha2015 ()), to which we refer the reader for a detailed explanation. Very briefly, MAGPHYS is based on a simple energy balance argument: the UV-optical photons emitted by young stars are absorbed by dust grains in star-forming regions and the diffuse ISM, and the absorbed energy, which heats the grains, is then thermally re-emitted in the IR.
Here we have made use of a new calibration of MAGPHYS, which is optimised to fit simultaneously the UV–radio SEDs of star-forming galaxies, and hence better suited to derive the physical properties of SMGs than the previous versions of the code (see dacunha2015 ()). The modifications in the updated version include extended prior distributions of star formation history and dust optical thickness, and the addition of intergalactic medium absorption of UV photons. A simple radio emission component is also taken into account by assuming a far-IR( m)-radio correlation with a distribution centred at (the mean value derived by Yun et al. (2001) for galaxies detected with the Infrared Astronomical Satellite), and a scatter of to take possible variations into account (see Sect. 3.5 herein). The thermal free-free emission spectral index in MAGPHYS is fixed at , while that of the non-thermal synchrotron emission is fixed at . The thermal fraction at rest-frame 1.4 GHz is assumed to be . We note that these assumptions might be invalid for individual SMGs (see our Sects. 3.2, 4.3, and 4.4). The SED models used here assume that the interstellar dust is predominantly heated by the radiation powered by star formation activity, while the possible, though presumably weak, AGN contribution is not taken into account; as mentioned in Sect. 2.1, our SMGs do not exhibit any clear signatures of AGN in the X-ray or radio emission. An AGN contamination is expected to mainly affect the stellar mass determination by yielding an overestimated value (see hayward2015 (); dacunha2015 ()). We note that Hayward & Smith (2015) found that MAGPHYS recovers most physical parameters of their simulated galaxies well, hence favouring the usage of this SED modelling code. On the other hand, Michałowski et al. (2014) found that MAGPHYS, when employing the Bruzual & Charlot (2003) stellar population models and a Chabrier (2003) IMF, yields stellar masses that are, on average, 0.1 dex (factor of 1.26) higher than the true values of their simulated SMGs.777The stellar emission library we have used is built on the unpublished 2007 update of the Bruzual & Charlot (2003) models (referred to as CB07), where the treatment of thermally pulsating asymptotic giant branch stars has been improved (see bruzual2007 ()).
3.1.2 SED results
The resulting SEDs are shown in Fig. 1, and the corresponding SED parameters are given in Table 2. We note that the intermediate and narrow-band Subaru photometry were not used because their effective wavelengths are comparable to those of the broad-band filters, they pass only a small portion of the spectrum, and they can be sensitive to optical spectral line features not modelled by MAGPHYS. Following da Cunha et al. (2015), the flux density upper limits were taken into account by setting the value to zero, and using the upper limit value (here ) as the flux density error. As can be seen in Fig. 1, in a few cases the best-fit model disagrees with some of the observed photometric data points or upper limits. For example, the Herschel/PACS flux density upper limits (set to ) for AzTEC4, 5, and 21a lie slightly below the best SED-fit line. As discussed in detail in Paper I, some of our SMGs have uncertain redshifts. Indeed, our initial SED analysis showed that the redshifts we previously adopted for AzTEC9 and 17a might be underestimated, and the revised redshifts of these SMGs are described in Appendix B.1. Moreover, the SED for AzTEC3 was fit using only photometry at and longward of band ( Å) as the shorter wavelength photometry is likely contaminated/dominated by an unrelated foreground () galaxy as detailed in Appendix D.2. Finally, as described in Appendix B.2, we could not obtain a meaningful SED fit for the following five SMGs: AzTEC2, 6, 11-N, 19b, and 26a.
To calculate the total SFR (0.1–100 M) averaged over the past 100 Myr (column (4) in Table 2), we used the standard Kennicutt (1998) relationship scaled to a Chabrier (2003) IMF. The resulting relationship is given by . We note that the Kennicutt (1998) calibration assumes an optically thick starburst, and it does not account for contributions from old stellar populations (see bell2003 ()). The MAGPHYS code also gives the SFR as an output, and the model allows for the heating of the dust by old stellar populations. We found a fairly good agreement with the 100 Myr-averaged SFRs calculated from and those directly resulting from the SED fit: the ratio was found to range from 0.94 to 3.43 with a median of , where the errors represent the 16th–84th percentile range. We note that when this comparison was done using the values averaged over the past 10 Myr (rather than 100 Myr), the ratio was found to lie between 0.70 and 1.36, with a median of (consistent with dacunha2015 ()). In column (5) in Table 2, we give the specific SFR, defined by . The quantity sSFR is unaffected by the adopted stellar IMF (in the case where the newly-forming stars have a same IMF as the pre-existing stellar population). The SFR with respect to that of a main-sequence galaxy of the same stellar mass is given in column (6) in Table 2, and will be described in Sect. 3.3. Finally, we note that the dust temperature given in column (7) is a new MAGPHYS output parameter in the latest version, and refers to an average, dust luminosity-weighted temperature (see Eq. (8) in dacunha2015 () for the formal definition).
Most of the SMGs analysed here have only a photometric redshift estimate available (the following 12 sources: AzTEC4, 5, 7, 9, 10, 12, 15, 17a, 19a, 21a, 21b, and 24b). As shown in Table 1, some of the photometric redshift uncertainties (here reported as the 99% confidence interval; see e.g. Paper I) are large, and we took those uncertainties into account by fitting the source SED over the quoted range of redshifts using a fine redshift grid of . We computed the 16th–84th percentile range of the resulting distribution for each MAGPHYS output parameter listed in Table 2, and propagated those values as the uncertainty estimates on the physical parameters. The uncertainties derived using this approach should be interpreted as lower limits to the true uncertainties. We note that da Cunha et al. (2015) left the redshift as a free parameter in their MAGPHYS analysis, in which case the derived photometric redshift uncertainties could be directly and self-consistently included in the uncertainties of all other output parameters. However, this option is not yet possible in the publicly available version of the MAGPHYS high- extension (E. da Cunha, priv. comm.).
3.2 Pure radio spectral energy distributions, and spectral indices
To study the radio SEDs of our SMGs, we used the 325 MHz GMRT data, and 1.4 GHz and 3 GHz VLA data as described in Sect. 2.2. The radio SEDs for the SMGs detected in at least one of the three radio frequencies are shown in Fig. 2. A linear least squares regression was used to fit the data points on a log–log scale to derive the radio spectral indices. In most cases (the following 15 sources: AzTEC1, 4, 5, 6, 7, 8, 10, 11-N, 11-S, 12, 15, 17a, 19a, 24b, and 27) the observed data are consistent with a single power-law spectrum. However, for AzTEC2 and AzTEC9 the upper limit to the 325 MHz flux density lies below a value suggested by the 1.4–3 GHz part of the SED, while in the AzTEC3 and AzTEC21a SEDs the 1.4 GHz upper flux density limit lies below the fitted power-law function. We note that because we only have three data points in our galaxy-integrated radio SEDs, we did not try to fit them with anything more complex than a single power law, like a broken or curved power law. The derived spectral indices are tabulated in column (2) in Table 3.999In Paper II, we derived the values of for our SMGs (see Table 4 therein). Those are almost identical to the corresponding present values, but the quoted uncertainties differ in some cases because of the difference in the method they were derived. In the present study, the uncertainties represent the standard deviation errors weighted by the flux density uncertainty, while in Paper II the spectral index uncertainty was directly propagated from that associated with the flux densities. For AzTEC2, the reported spectral index refers to a frequency range between 1.4 and 3 GHz. We also note that for AzTEC21b we could not constrain the radio spectral index needed in the IR-radio correlation analysis (Sect. 3.5). Hence, for this source we assumed a value of to be consistent with the canonical non-thermal synchrotron spectral index range of (e.g. niklas1997 (); lisenfeld2000 (); marvil2015 ()), but it is not included in the subsequent radio analysis.
The derived values contain both lower and upper limits. To estimate the median of these doubly-censored data, we applied survival analysis. First, we used the dblcens package for R101010https://cran.r-project.org/web/packages/dblcens/, which computes the non-parametric maximum likelihood estimation of the cumulative distribution function from doubly-censored data via an expectation-maximization algorithm. This was used to estimate the contribution of the right-censored data. We then used the Kaplan-Meier (K-M) method to construct a model of the input data by assuming that the left-censored data follow the same distribution as the non-censored values (for this purpose, we used the Nondetects And Data Analysis for environmental data (NADA; helsel2005 ()) package for R). Using this method the median of was found to be , where the uncertainty represents the 16th–84th percentile range. Although the derived median spectral index is fully consistent with the value of assumed in the MAGPHYS analysis, some of the individual nominal values are significantly different, which is reflected as poor fits in the radio regime as shown in Fig. 1. The distribution of the derived values as a function of redshift is plotted in Fig. 3. We note that the large number of censored data points allowed us to calculate the median values of the binned data showed in Fig. 3, but not the corresponding mean values. The binned median data points suggest that there is a hint of decreasing (i.e. steepening) spectral index with increasing redshift. To quantify this dependence, we fit the binned data points using a linear regression line, and derived a relationship of the form , where the uncertainty in the slope is based on the one standard deviation errors of the spectral index data points. The Pearson correlation coefficient of the binned data was found to be . Hence, a negative relationship is present, but it is not statistically significant.
3.3 Stellar mass-SFR correlation: comparison with the main sequence of star-forming galaxies
In Fig. 4, we plot our SFR values as a function of stellar mass. A tight relationship found between these two quantities is known as the main sequence of star-forming galaxies (e.g. brinchmann2004 (); noeske2007 (); elbaz2007 (); daddi2007 (); karim2011 (); whitaker2012 (); speagle2014 (); salmon2015 ()). For comparison, in Fig. 4 we also plot the values for ALMA 870 m-detected SMGs from da Cunha et al. (2015; the so-called ALESS SMGs) who used the same high- extension of MAGPHYS in their analysis as we have used here. Here, we have limited the da Cunha et al. (2015) sample to those SMGs that are equally bright to our target sources (AzTEC1–30; see Sect. 4.2 for a detailed description).
To illustrate how our data compare with the star-forming galaxy main sequence, we overlay the best fit from Speagle et al. (2014), which is based on a compilation of 25 studies, and is given by , where is the age of the universe in Gyr, i.e. the normalisation rises with increasing redshift. We show the main sequence position at the median redshift of our analysed SMGs () and that of the aforementioned ALESS SMG sample (). We also plot the factor of 3 lines below and above the main sequence at ; this illustrates the accepted thickness, or scatter of the main sequence (see e.g. magdis2012 (); dessauges2015 ()). To further quantify the offset from the main sequence, we calculated the ratio of the derived SFR to that expected for a main sequence galaxy of the same stellar mass, i.e. . The values of this ratio are given in column (6) in Table 2, and they range from to with a median of . The values of are plotted as a function of redshift in Fig. 5. The binned data suggest a bimodal behaviour of our SMGs in the sense that the sources at are consistent with the main sequence, while those at lie above the main sequence. The -SFR plane of our SMGs will be discussed further in Sect. 4.1.
3.4 Stellar mass-size relationship
In Fig. 6, we plot the 3 GHz radio continuum sizes of our SMGs derived in Paper II against their stellar masses derived in the present paper. We also show the rest-frame UV/optical radii for AzTEC1, 3, 4, 5, 8, 10, and 15 derived by Toft et al. (2014), but which were scaled to our adopted cosmology, and we used the revised redshifts for AzTEC1, 4, 5, and 15. The radio size data points of the SMGs lying at are highlighted by green star symbols in Fig. 6, while the UV/optical sizes are for SMGs, out of which 6/7 (86%) lie at . As shown in the figure, with a few exceptions the largest spatial scales of both stellar and radio emission are seen among the highest stellar mass sources (). We also note that most of the data points ( () of all the plotted data (radio sizes)) are clustered within the dispersion of the mass-size relationship of cQGs derived by Krogager et al. (2014), namely , where and for their galaxies having spectroscopic redshifts. The -size plane analysed here will be discussed further in Sect. 4.1.
3.5 Infrared-radio correlation
The quantities derived in the present study allow us to examine the IR-radio correlation among our SMGs (e.g. vanderkruit1971 (); dejong1985 (); helou1985 (); condon1991 (); yun2001 ()). As usually done, we quantify this analysis by calculating the parameter, which can be defined as (see e.g. sargent2010 (); magnelli2015 ())
where the value is the normalising frequency (in Hz) corresponding to m, and is the rest-frame monochromatic 1.4 GHz radio luminosity density. Since our is calculated over the wavelength range of m, our value refers to the total-IR value, i.e. .111111A FIR luminosity () calculated by integrating over m is sometimes used to define . We note that . The 1.4 GHz luminosity density is given by
where is the luminosity distance. Following Smolčić et al. (2015), the 1.4 GHz flux density was calculated as , because the observed-frame frequence of MHz corresponds to the rest-frame frequence of GHz at , which is only a 16% higher redshift than the median redshift of the SMGs analysed here (). Hence, the smallest and least uncertain -correction to rest-frame 1.4 GHz is needed to derive the value of . The derived values of are listed in column (3) in Table 3.
As in the case of (Sect. 3.2), our values contain both lower and upper limits. Hence, to estimate the sample median, we employed the K-M survival analysis as described in Sect. 3.2. The median value and the 16th–84th percentile range is found to be . In Fig. 7, we show the derived values as a function of redshift, and discuss the results further in Sect. 4.4.
The SEDs of some of our COSMOS/AzTEC SMGs have already been analysed in previous studies. We discuss those studies and compare their results with ours in Appendix C. AzTEC1 and 3 both have a gas mass estimate available in the literature (yun2015 () and riechers2010 (), respectively), which allows us to examine their ISM physical properties in more detail; these two high-redshift SMGs are discussed in more detail in Appendix D. After discussing the stellar mass-SFR and mass-size relationships of our SMGs in Sect. 4.1, we compare the physical properties of our SMGs with those of the ALESS SMGs derived by da Cunha et al. (2015), and discuss the similarities and differences between the two SMG samples in Sect. 4.2. The radio SEDs and IR-radio correlation are discussed in Sects. 4.3 and 4.4, while the present results are discussed in the context of evolution of massive galaxies in Sect. 4.5.
4.1 How do the COSMOS/AzTEC SMGs populate the -SFR and -size planes ?
4.1.1 Comparison with the galaxy main sequence
We have found that 10 out of the 16 SMGs ( with a Poisson counting error of ) analysed here lie above the main sequence with . AzTEC8 is found to be the most significant outlier with a ratio of about 13. The remaining six SMGs have , and hence lie on or within the main sequence. Our result is consistent with previous studies where some of the SMGs are found to be located on or close to the main sequence (at the high-mass end), while a fair fraction of SMGs – especially the most luminous objects – are found to lie above the main sequence (e.g. magnelli2012 (); michalowski2012 (); roseboom2013 (); dacunha2015 (); koprowski2016 ()). This suggests that SMGs are a mix of populations of two star formation modes, namely “normal-type” star-forming galaxies and starbursts. Hydrodynamic simulations have also suggested that the SMG population can be divided into two subpopulations consisting of major-merger driven starbursts and disk galaxies where star formation, while possibly driven by mergers or smooth gas accretion, is occuring more quiescently (e.g. hayward2011 (), 2012, and references therein).
4.1.2 Stellar mass-size relationship
As we discussed in Paper II, the rest-frame UV/optical sizes (i.e. the stellar emission size scales), derived by Toft et al. (2014) for a subsample of seven of our SMGs, are smaller than the radio size for AzTEC4 and 5, in agreement for AzTEC15, and the upper stellar emission size limits for AzTEC1, 3, and 8 are larger than their radio sizes, and hence formally consistent with each other (AzTEC10 was also analysed by Toft et al. (2014), but it is not detected at 3 GHz). A difference in the radio and stellar emission sizes can be partly caused by the fact that rest-frame UV/optical emission can be subject to a strong, and possibly differential dust extinction, and stellar population effects.
In the present work, we have revised the stellar masses of the aforementioned seven SMGs, and for those sources where the redshifts used in the analysis were similar, our values are found to be 0.3 to 1.6 (median 0.6) times those from Toft et al. (2014) (see Appendix C). Despite these discrepancies, the way our SMGs populate the -size plane shown in Fig. 6 is consistent with the finding of Toft et al. (2014), i.e. the distribution of SMGs is comparable to that of cQGs at . Hence, our result supports the authors’ conclusion of high- SMGs being potential precursors of the cQGs, where the quenching of the starburst phase in the former type of galaxies leads to the formation of the latter population (Sect. 4.5).
It is worth noting that five of our SMGs plotted in Fig. 6 also exhibit stellar masses and radio sizes that place them in the cQGs’ mass-size relationship from Krogager et al. (2014). While these authors found that the slope and scatter of this mass-size relationship are consistent with the local () values, the galaxies grow in size towards lower redshifts (e.g. via mergers). However, as can be seen in Fig. 7 of Krogager et al. (2014; see also references therein), the median size of the quiescent galaxy population at a fixed stellar mass of M is kpc in the redshift range . In the context of massive galaxy evolution, the SMGs could potentially evolve into lower-redshift () cQGs, and then grow in size at later epochs (see Sect. 4.5). As mentioned in Sect. 3.4, there is a hint that the largest 3 GHz radio sizes are found among the most massive of our analysed SMGs (see the ouliers at M in Fig. 6). While this is not statistically significant, also the most extended stellar emission spatial scale is found for the most massive SMG with available rest-frame UV-optical size measurement, namely AzTEC15. Although these largest radio sizes have large error bars, it is possible that the spatially extended radio emission in these massive SMGs is caused by processes not related to star formation, like galaxy mergers leading to magnetic fields being pulled out from the interacting disks (see Paper II and references therein; O. Miettinen et al., in prep.). Interestingly, all the three SMGs that exhibit the largest radio sizes in our sample, namely AzTEC4, 15, and 21a, are found to lie on the main sequence or only slightly above it (factor of 3.2 for AzTEC4), but they have high SFRs of , which could be induced by gravitational interaction of merging galaxies. This is further supported by the fact that many of our target SMGs exhibit clumpy or disturbed morphologies, or show evidence of close companions at different observed wavelengths, e.g. in the UltraVISTA NIR images (younger2007 (), 2009; toft2014 (); Paper I).
4.2 Comparison with the physical properties of the ALESS 870 m-selected SMGs
Our main comparison sample of SMGs from the literature is the ALESS SMGs studied by da Cunha et al. (2015). The ALESS SMGs were uncovered in the LABOCA (Large APEX BOlometer CAmera) 870 m survey of the Extended Chandra Deep Field South (ECDFS) or LESS survey by Weiß et al. (2009), and followed up with resolution Cycle 0 ALMA observations (hodge2013 (); karim2013 ()). The reasons why we compare with the da Cunha et al. (2015) study are that i) we have also used the new, high- version of MAGPHYS as first presented and used by da Cunha et al. (2015) to derive the SMG physical properties, which allows for a direct comparison, and ii) the SMG sample from da Cunha et al. (2015) is relatively large: they analysed the 99 most reliable SMGs detected in the ALESS survey (hodge2013 ()).
4.2.1 Description of the basic physical properties of the ALESS SMGs
For their full sample of 99 ALESS SMGs, da Cunha et al. (2015) derived the following median properties (see their Table 1): , , M yr, Gyr, K, and . The quoted uncertainties represent the 16th–84th percentile of the likelihood distribution. The value of reported by da Cunha et al. (2015) refers to the total dust IR ( m) luminosity, which we have found to be almost equal to with the ratio ranging from 0.91 to 0.99 (both the mean and median being 0.95). We also note that da Cunha et al. (2015) defined the current SFR over the last 10 Myr, while the corresponding timescale in the present study is 100 Myr. When comparing the MAGPHYS output SFRs, we found that the 10 Myr-averaged values are 1.0 to 4.7 times higher than those averaged over the past 100 Myr (the mean and median being 2.1 and 1.6, respectively). The authors concluded that the physical properties of the ALESS SMGs are very similar to those of local ultraluminous IR galaxies or ULIRGs (see dacunha2010 ()).
For a more quantitative comparison, we limit the da Cunha et al. (2015) sample to those SMGs that have 870 m flux densities corresponding to our AzTEC 1.1 mm flux density range in the parent sample (AzTEC1–30), i.e. mJy. Assuming that the dust emissivity index is , this flux density range corresponds to mJy.131313We note that in the high- model libraries of MAGPHYS, the value of is fixed at 1.5 for the warm dust component (30–80 K), while that for the colder (20–40 K) dust is . A manifestation of this -dependent is that scaling the 1.1 mm flux densities to those at 870 m with a simple assumption of yields slightly different values than suggested by the MAGPHYS SEDs shown in Fig. 1. The LESS SMGs that fall in this flux density range are LESS1–18, 21–23, 30, 35, and 41, where LESS1, 2, 3, 7, 15, 17, 22, 23, 35, and 41 were resolved into multiple components with ALMA (hodge2013 (); karim2013 ()). The photometric redshifts of these SMGs, as derived by da Cunha et al. (2015), lie in the range of with a median and its standard error of . We note that this median redshift is only 9.5% higher than that of our analysed SMGs (). As mentioned in Sect. 3.1.2, the error bars for the ALESS SMGs’ parameters were propagated from the photo- uncertainties by da Cunha et al. (2015), and they are typically much larger than those of our parameters (see e.g. Fig. 4 herein).
For the aforementioned flux-limited sample, the median values of the physical parameters are , , M yr, Gyr, K, and , where we quote the 16th–84th percentile range. All the other quantities except are higher than for the aforementioned full sample, up to a factor of 1.7 for sSFR and , which is not surprising because the subsample in question is composed of the brightest ALESS SMGs.
4.2.2 Comparison of the AzTEC and ALESS SMGs
In what follows, we compare the physical properties of our SMGs with those of the aforementioned flux-limited ALESS sample composed of equally bright sources. The ratios between our median , , SFR, sSFR, , and values and those of the ALESS SMGs are given in Table 4. We note that for a proper comparison, the comparison of the SFR and sSFR values were done using the MAGPHYS output values averaged over the past 10 Myr. As can be seen in Table 4, the median values of and are similar, and our median value is a factor of 1.5 times higher than for the equally bright ALESS SMGs. On the other hand, our dust luminosities and (s)SFR values appear to be about two times higher on average.
We also performed a two-sided KolmogorovâSmirnov (K-S) test between the aforementioned physical parameter values to check if our SMGs and the flux-limited ALESS SMG sample could be drawn from a common underlying parent distribution. The null hypothesis was that these two samples are drawn from the same parent distribution. The K-S test statistics and -values for the comparisons of the , , , , and values are also given in Table 4. The K-S test results suggest that the underlying stellar mass distribution is the same (), while those of the remaining properties might differ. We note that for , for which the median value between our AzTEC SMGs and the ALESS SMGs was found to be very similar, the K-S test -value is 0.29, the second highest after the stellar mass comparison. It should also be noted that the comparison samples are small (16 AzTEC and 25 ALESS sources, respectively), and hence the K-S tests presented here are subject to small number statistics. Nevertheless, we cannot exclude the possibility that at least part of the differences found here is caused by the different selection wavelength ( mm versus m), and different depths of the optical to IR observations available in COSMOS and the ECDFS, although the stellar mass estimates based on the optical regime of the galaxy SED are found to be similar.
da Cunha et al. (2015) found that, at , about half of the ALESS SMGs (49%) lie above the star-forming main sequence (i.e. ), while the other half (51%) are consistent with being at the high-mass end of the main sequence, where the main sequence definition was also adopted from Speagle et al. (2014). For the ALESS SMG sample flux-limited to match our sample limit, which has a median redshift of , only of the sources are found to have , while the remaining lie within a factor of 3 of the main sequence (see our Fig. 4). It should be noted, however, that the ALESS sources have significant error bars in their SFR and values (propagated from the photo- uncertainties; dacunha2015 ()). The fractions we have found for the analysed AzTEC SMGs are nominally more extreme, i.e. are above the main sequence, and are consistent with the main sequence. If we base our analysis on the 10 Myr-averaged MAGPHYS output SFRs as da Cunha et al. (2015) did, we find that the fraction of the AzTEC SMGs having is the same as derived above from the Kennicutt (1998) calibration.
In Fig. 8, we plot the sSFR as a function of cosmic time (lower -axis) and redshift (upper -axis). For legibility purposes, we only show the binned version of the data; the plotted data points represent the mean values of the full data with four SMGs per bin in our AzTEC sample, and five SMGs per bin in the ALESS sample. The sSFR of the ALESS comparison sample appears to be relatively constant as a function of cosmic time, while our individual SMGs, lying in a similar redshift range, show more scatter with a factor of higher median sSFR (our median sSFR is higher by the same nominal factor of when the comparison is done between the 10 Myr-averaged MAGPHYS outputs; Table 4). The blue dash-dot line overplotted in the figure represents the sSFR-cosmic time relationship derived by Koprowski et al. (2016). As can be seen, our lowest redshift data point (corresponding to the latest time) lies slightly (by a factor of 1.57) above the normalisation of this relationship, and the second lowest redshift data point, though having a factor of 1.82 higher sSFR than suggested by the Koprowski et al. (2016) relationship, is still consistent with it within the standard error. However, our two highest redshift bins lie at much higher sSFRs than computed from the Koprowski et al. (2016) relationship (by factors of ), but as mentioned by the authors, their study could not set tight constraints on the sSFR beyond redshift of ( Gyr), where many of our SMGs are found. Indeed, as can be seen in Fig. 10 of Koprowski et al. (2016), the scatter of data increases at , and many data points lie above their derived relationship. It should also be pointed out that our SFRs and stellar masses were derived using a different method than those in Koprowski et al. (2016) and their reference studies, and this can be part of the reason why our values lie above the Koprowski et al. (2016) sSFR() function. On the other hand, while the three lowest redshift ALESS data points shown in Fig. 8 show a trend similar to ours, with a jump in sSFR near , the two highest redshift ALESS bins are only by factors of 1.43–1.56 above the Koprowski et al. (2016) relationship. Larger, multi-field samples of SMGs are required to limit cosmic variance, and examine the evolution of SMGs’ sSFR as a function of cosmic time further, particularly at .
Figure 9 plots the dust-to-stellar mass ratio as a function of redshift for our SMGs and the comparison ALESS SMG sample. The median values for these samples are and , respectively, where the quoted uncertainties represent the 16th–84th percentile range. The binned data points shown in Fig. 9 show a hint of decreasing dust-to-stellar mass ratio towards higher redshifts. The AzTEC (ALESS) data points suggest a linear regression of the form (), with a Pearson of (). These trends are not statistically significant, but the fact that both the samples show a comparable behaviour is indicative of a star formation and dust production history being fairly similar between the AzTEC and ALESS SMGs, and hence suggesting a similar level of metallicity, which is not surprising given that these SMGs lie at the same cosmic epoch.
Thomson et al. (2014) studied the radio properties of the ALESS SMGs. They used 610 MHz GMRT and 1.4 GHz VLA data, and derived a medianstandard error radio spectral index of for a sample of 52 SMGs. Again, if we limit this comparison sample to those sources that are equally bright to ours, we derive a median spectral index of from the values reported in their Table 3 (survival analysis was used to take the lower limits into account). This is the same as for their full sample, and also consistent with our median value of although our observed frequency range is broader.