S2CLS: properties of the galaxies unveiled in the deep 850{\mathbf{\rm\mu m}} survey

# The SCUBA-2 Cosmology Legacy Survey: galaxies in the deep 850\mn@boldsymbolμm survey, and the star-forming ‘main sequence’

M.P. Koprowski, J.S. Dunlop, M.J. Michałowski, I. Roseboom, J.E. Geach, E-mail: mpk@roe.ac.uk    M. Cirasuolo, I. Aretxaga, R.A.A. Bowler, M. Banerji, N. Bourne,    K.E.K. Coppin, S. Chapman, D.H. Hughes, T. Jenness, R.J. McLure,    M. Symeonidis, P. van der Werf
SUPA, Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh, EH9 3HJ
Centre for Astrophysics Research, Science & Technology Research Institute, University of Hertfordshire, College Lane, Hatfield AL10 9AB
UK Astronomy Technology Centre, Royal Observatory, Edinburgh EH9 3HJ
Instituto Nacional de Astrofisica, Optica y Electronica (INAOE), Aptdo. Postal 51 y 216, 72000 Puebla, Pue., Mexico
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA
Department of Physics and Atmospheric Science, Dalhousie University, Coburg Road, Halifax, NS B3H 1A6, Canada
LSST Project Office, 933 N. Cherry Ave, Tucson, AZ 85719 USA
Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey RH5 6NT
Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, the Netherlands
Scottish Universities Physics Alliance
Accepted ???. Received ???; in original form ???
###### Abstract

We investigate the properties of the galaxies selected from the deepest 850-m survey undertaken to date with SCUBA-2 on the JCMT as part of the SCUBA-2 Cosmology Legacy Survey. A total of 106 sources (5) were uncovered at 850 m from an area of  arcmin in the centre of the COSMOS/UltraVISTA/CANDELS field, imaged to a typical depth of  mJy. We utilise the available multi-frequency data to identify galaxy counterparts for 80 of these sources (75%), and to establish the complete redshift distribution for this sample, yielding . We have also been able to determine the stellar masses of the majority of the galaxy identifications, enabling us to explore their location on the star-formation rate : stellar-mass (SFR:) plane. Crucially, our new deep 850-m selected sample reaches flux densities equivalent to , enabling us to confirm that sub-mm galaxies form the high-mass end of the ‘main sequence’ (MS) of star-forming galaxies at (with a mean specific SFR of at ). Our results are consistent with no significant flattening of the MS towards high masses at these redshifts. However, our results add to the growing evidence that average sSFR rises only slowly at high redshift, resulting in sSFR being an apparently simple linear function of the age of the Universe.

###### keywords:
galaxies: high-redshift, evolution, starburst - cosmology: observations - submillimetre: galaxies
pagerange: The SCUBA-2 Cosmology Legacy Survey: galaxies in the deep 850 survey, and the star-forming ‘main sequence’Bpubyear: ???

## 1 Introduction

It is now well known that approximately half of the starlight in the Universe is re-processed by cosmic dust and re-emitted at far-infrared wavelengths (Dole et al. 2006). However, due to a combination of the inescapable physics of diffraction, the molecular content of our atmosphere, and the technical difficulties of sensitive high-background imaging, it has proved difficult to connect the UV/optical and far-infrared/sub-mm views of the Universe into a consistent and complete picture of galaxy formation/evolution. Thus, while the advent of SCUBA on the 15-m James Clerk Maxwell Telescope (JCMT) in the late 1990s (Holland et al. 1999) enabled the first discovery of distant dusty galaxies with star-formation rates (e.g. Smail et al. 1997; Hughes et al. 1998; Barger et al. 1998; Eales et al. 1999), such objects initially seemed too extreme and unusual to be easily related to the more numerous, ‘normal’ star-forming galaxies being uncovered at UV/optical wavelengths at comparable redshifts () by Keck (e.g. Steidel et al. 1996) and the Hubble Space Telescope (HST) (e.g. Madau et al. 1996). In recent years the study of rest-frame UV-selected galaxies has been extended out beyond (see Dunlop 2013 for a review, and Coe et al. 2013; Ellis et al. 2013; McLure et al. 2013; Bouwens et al. 2015; Bowler et al. 2012, 2014; Oesch et al. 2014; Finkelstein et al. 2015; Ishigaki et al. 2015; McLeod et al. 2015), while a number of sub-mm selected galaxies have now been confirmed at (Capak et al. 2008; Coppin et al. 2009; Daddi et al. 2009a,b; Knudsen et al. 2010; Riechers et al. 2010; Cox et al. 2011; Combes et al. 2012; Weiss et al. 2013) with the current redshift record holder at (Riechers et al. 2013). However, while such progress is exciting, at present there is still relatively little meaningful intersection between these UV/optical and far-infrared/sub-mm studies of the high-redshift Universe (although see Walter et al. 2012).

At more moderate redshifts, however, recent years have seen increasingly successful efforts to bridge the gap between the unobscured and dust-enshrouded views of the evolving galaxy population. Of particular importance in this endeavour has been the power of deep m imaging with the MIPS instrument on board Spitzer, which has proved capable of providing a useful estimate of the dust-obscured star-formation activity in a significant fraction of optically-selected galaxies out to (e.g. Caputi et al. 2006; Elbaz et al. 2010). Indeed, MIPS imaging of the GOODS survey fields played a key role in establishing what has proved to be a fruitful framework for the study of galaxy evolution, namely the existence of a so-called “main sequence” (MS) for star-forming galaxies, in which star-formation rate is found to be roughly proportional to stellar mass (; Noeske et al. 2007; Daddi et al. 2007; Renzini & Peng 2015), with a normalisation that rises with increasing redshift (e.g. Santini et al. 2009; Oliver et al. 2010; Elbaz et al. 2011; Karim et al 2011; Rodighiero et al. 2011, 2014; Tasca et al. 2015; Salmon et al. 2015; Schreiber et al. 2015; Johnston et al. 2015).

Interest in the MS of star-forming galaxies has continued to grow (see Speagle et al. 2014 for a useful and comprehensive overview), not least because of the difficulty encountered by most current models of galaxy formation in reproducing its apparently rapid evolution between and (e.g. Mitchell et al. 2014). However, it has, until now, proved very difficult to extend the robust study of the MS beyond and to the highest masses (e.g. Steinhardt et al. 2014; Salmon et al. 2015; Leja et al. 2015). This is because an increasing fraction of star formation is enshrouded in dust in high-mass galaxies, and Spitzer MIPS and Herschel become increasingly ineffective in the study of dust-enshrouded SF with increasing redshift (due to a mix of wavelength and resolution limitations), as the far-infrared emission from dust is redshifted into the sub-mm/mm regime.

A complete picture of star-formation in more massive galaxies at high-redshift can therefore only be achieved with ground-based sub-mm/mm observations, which provide image quality at sub-mm wavelengths that is vastly superior to what can currently be achieved from space. The challenge, then, is to connect the population of dusty, rapidly star-forming high-redshift galaxies revealed by ground-based sub-mm/mm surveys to the population of more moderate star-forming galaxies now being revealed by optical/near-infrared observations out to the highest redshifts. On a source-by-source basis this can now be achieved by targeted follow-up of known optical/infrared-selected galaxies with ALMA (e.g. Ono et al. 2014). However, this will inevitably produce a biased perspective which can only be re-balanced by also continuing to undertake ever deeper and wider sub-mm/mm surveys capable of detecting highly-obscured objects (again, potentially, for ALMA follow-up; Karim et al. 2013; Hodge et al. 2013), and thus completing our census of star-forming galaxies in the young Universe.

This is one of the primary science drivers for the SCUBA-2 Cosmology Legacy Survey (S2CLS). The S2CLS is advancing the field in two directions. First, building on previous efforts with SCUBA (e.g. Scott et al. 2002; Scott, Dunlop & Serjeant 2006; Coppin et al. 2006), MAMBO (e.g. Bertoldi et al. 2000; Greve et al. 2004), LABOCA (e.g. Weiss et al. 2009) and AzTEC (e.g. Austermann et al. 2010; Scott et al. 2012), the S2CLS is using the improved mapping capabilities of SCUBA-2 (Holland et al. 2013) to extend surveys for bright ( mJy) sub-mm sources to areas of several square degrees, yielding large statistical samples of such sources (). Second, the S2CLS is exploiting the very dryest (Grade-1) conditions at the JCMT on Mauna Kea, Hawaii to obtain very deep 450 m imaging of small areas of sky centred on the HST CANDELS fields (Grogin et al. 2011), which provide the very best multi-wavelength supporting data to facilitate galaxy counterpart identification and study. The first such deep 450 m image has been completed in the centre of the COSMOS-CANDELS/UltraVISTA field, with the results reported by Geach et al. (2013) and Roseboom et al. (2013). Here we utilise the ultra-deep 850 m image of the same region, which was automatically obtained in parallel with the 450 m imaging. While the dryest weather is more essential for the shorter-wavelength imaging at the JCMT, such excellent conditions (and long integrations) inevitably also benefit the parallel 850 m imaging. Consequently, the 850 m data studied here constitute the deepest ever 850 m survey ever undertaken over an area  arcmin.

The depth of the new S2CLS 850 m imaging is typically . This is important because it means that galaxies detected near the limit of this survey have , which is much more comparable to the highest SFR values derived from UV/optical/near-infrared studies than the typical SFR sensitivity achieved with previous single-dish sub-mm/mm imaging (i.e. as a result of ). Ultimately, of course, ALMA will provide even deeper sub-mm surveys with the resolution required to overcome the confusion limit of the single-dish surveys. However, because of its modest field of view ( arcsec at 850 m) it is observationally expensive to survey large areas of blank sky with ALMA, and contiguous mosaic surveys are hard to justify at depths where the source surface density is significantly less than one per pointing. Thus, at the intermediate depths probed here, the S2CLS continues to occupy a unique and powerful niche in the search for dust-enshrouded star-forming galaxies.

The fact that previous sub-mm/mm surveys were only generally capable of detecting very extreme objects has undoubtedly contributed to some of the confusion/controversy over the nature of galaxies selected at sub-mm/mm wavelengths; while Michałowski et al. (2012b) and Roseboom et al. (2013) have presented evidence that sub-mm selected galaxies lie on the high mass end of the MS at , others have continued to argue that, like many local ULIRGs, they are extreme pathological objects driven by recent major mergers (e.g. Hainline et al. 2011). Some of this debate reflects disagreements over the stellar masses of the objects rather than their star-formation rates (e.g. Michałowski et al. 2014). Nevertheless, the fact that even high-mass galaxies on the MS lay right at the detection limits of previous sub-mm surveys inevitably resulted in many sub-mm selected objects apparently lying above the MS, fueling arguments about whether they were indeed significant outliers, or whether we have simply been uncovering the positive tail in SFR around the MS (see Roseboom et al. 2013).

The much deeper 850 m survey studied here is capable of settling this issue, provided of course we can overcome the now customary challenge of identifying the galaxy counterparts of most of the sub-mm sources, and determining their redshifts, SFRs and stellar masses () (e.g. Ivison et al. 2007; Dunlop et al. 2010; Biggs et al. 2011; Wardlow et al. 2011; Michałowski et al. 2012a; Koprowski et al. 2014). However, in this effort, we are also aided by the depth of the SCUBA-2 data, and by the additional positional information provided by the (unusual) availability of 450 m detections (with FWHM 8 arcsec) for 50% of the sample. We also benefit hugely from the unparalleled multi-frequency supporting data available in the CANDELS fields, provided by HST, Subaru, CFHT, Vista, Spitzer, Herschel and the VLA.

The paper is structured as follows. In Section 2 we present the SCUBA-2 and other multi-wavelength data utilized in this work. Then, in Section 3 we explain how optical/infrared galaxy counterparts were established for the SCUBA-2 sources, and summarize the resulting identification statistics. Next, in Section 4 we explain the calculation of the photometric redshifts, both from the optical-infrared data for the galaxy identifications, and from the long-wavelength data for the unidentified or spuriously identified sources. The resulting redshift distribution for the complete 106-source S2CLS sample is presented here, and compared with the redshift distributions derived from other recent sub-mm/mm surveys. In Section 5 we move on to derive and discuss the physical properties of the sources (such as dust temperature, bolometric luminosity, SFR, stellar mass), culminating in the calculation of specific SFR, and the exploration of the star-forming MS. Our conclusions are summarized in Section 6. All magnitudes are quoted in the AB system (Oke 1974; Oke & Gunn 1983) and all cosmological calculations assume and  kmsMpc.

## 2 Data

### 2.1 SCUBA-2 imaging & source extraction

We used the deep 850  and 450  S2CLS imaging of the central of the COSMOS/UltraVISTA field, coincident with the Spitzer SEDS (Ashby et al. 2013) and HST CANDELS (Grogin et al. 2011) imaging. The observations were taken with SCUBA-2 mounted on the JCMT between October 2011 and March 2013, reaching depths of  mJy and  mJy (Geach et al. 2013, Roseboom et al. 2013, Geach et al. 2016 in preparation). In order to enable effective 450  observations, only the very best/dryest conditions were used (i.e. ), and to maximise depth the imaging was undertaken with a “daisy” mapping pattern (Bintley et al. 2014).

The details of the reduction process are described in Roseboom et al. (2013), and so only a brief description is given here.

The data were reduced with the smurf package V1.4.0 (Chapin et al. 2013) with flux calibration factors (FCFs) of 606 Jy pW Beam for 450 m and 556 Jy pW Beam for 850 m (Dempsey et al. 2013).

The noise-only maps were constructed by inverting an odd half of the min scans and stacking them all together. In the science maps the large-scale background was removed by applying a high-pass filter above 1.3 Hz to the data (equivalent to 120 arcsec given the SCUBA-2 scan rate). Then a “whitening filter” was applied to suppress the noise in the map whereby the Fourier Transform of the map is divided by the noise-only map power spectrum, normalised by the white-noise level and transformed back into real space. The effective point-source response function (PRF) was constructed from a Gaussian with a full-width-half-maximum (FWHM) of 14.6 arcsec following the same procedure. Finally, the real sources with a signal-to-noise ratio (SNR) of better than five were extracted by convolving the whitened map with the above PRF (see §4.2 of Chapin et al. 2013).

The 850 m image and the sources extracted from it are shown in Fig. 1, while the positions and sub-mm photometry for the sources are listed in Appendix A, Table 3.

A total of 106 850 m sources were found within the map with a SNR . The photometry at 450 m was performed in the same manner,but assuming the PRF at 450 m to be a Gaussian of FWHM = 8 arcsec. The 450 m counterparts to the 850 m sources were adopted if a 450 m-selected source was found within 6 arcsec of the 850 m centroid. As seen in Fig. 2, 53 850 m sources have 450 m counterparts with the mean separation of  arcsec. Otherwise, for the purpose of SED fitting, the 450 m flux density was measured at the 850 m position (flags 1 and 0 in Table 3 respectively).

The completeness of the 850 m catalogue was assessed by injecting sources of known flux density into the noise-only maps. Overall objects were used, split into 10 logarithmically-spaced flux-density bins between 1 and 60 mJy. In total 2000 simulated maps were created and the source extraction was performed in the same way as with the real maps. The completeness was then assessed by dividing the number of extracted sources by the number of sources inserted into the noise-only maps, and the results are shown in Fig. 3.

### 2.2 Supporting multi-frequency data

This first deep S2CLS pointing within the COSMOS/UltraVISTA field was chosen to maximise the power of the available ancillary multi-wavelength data, in particular the HST Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) imaging (Grogin et al. 2011). In addition, the optical Canada-France-Hawaii Telescope Legacy Survey (CFHTLS; Gwyn 2012), the Subaru/Suprime-Cam z’-band (Taniguchi et al. 2007; Furusawa et al., in preparation) and UltraVISTA near-infrared data (McCracken et al. 2012) were used. The catalogues were made by smoothing all the ground-based and HST data to the seeing of the UltraVISTA Y-band image with the Gaussian of FWHM = 0.82 arcsec (for details, see Bowler et al. 2012, 2014, 2015). The catalogue was selected in the smoothed CANDELS H-band image and photometry was measured in 3 arcsec apertures using the dual-mode function in SExtractor (Bertin & Arnouts 1996) on all other PSF homogenised images.

The Spitzer IRAC flux densities at 3.6 m and 4.5 m were measured from the S-COSMOS survey (Sanders et al. 2007), after image deconfusion based on the UltraVISTA K-band image; using galfit (Peng et al. 2002) the -band images were modelled, and the corresponding structural parameters were then applied to both the 3.6 m and 4.5 m data and the flux-densities allowed to vary until the optimum fit to the IRAC image of each object was achieved (after convolution with the appropriate PSFs). The infinite-resolution scaled model IRAC images created in this way were than smoothed again to match the seeing of the UltraVISTA Y-band image, after which the IRAC flux densities were measured within 3 arcsec apertures. For the small number of objects selected from the SCUBA-2 map which lay outside the area with CANDELS HST imaging (see Fig. 1) the K-band UltraVISTA image was used as the primary image for near-infrared candidate counterpart selection.

The 24 m catalogue was constructed using the MIPS 24 m imaging from the S-COSMOS survey (LeFloch et al. 2009). The source extraction was performed on the publicly-available imaging using the starfinder idl package (Diolaiti et al. 2000). The resulting catalogue covers deg and reaches the depth of Jy (for details, see Roseboom et al. 2013).

For the extraction of far-infrared flux densities and limits we used the Herschel (Pilbratt et al. 2010) Multi-tiered Extragalactic Survey (HerMES; Oliver et al. 2012) and the Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al. 2010) Evolutionary Probe (PEP; Lutz et al. 2011) data obtained with the Spectral and Photometric Imaging Receiver (SPIRE; Griffin et al. 2010) and PACS instruments, covering the entire COSMOS field. We utilised Herschel maps at , , , and m with beam sizes of , , , , and arcsec, and sensitivities of , , , , and  mJy, respectively. We obtained the fluxes of each SCUBA-2 source in the following way. We extracted 120-arcsec wide stamps from each Herschel map around each SCUBA-2 source and used the PACS (, m) maps to simultaneously fit Gaussians with the FWHM of the respective map, centred at all radio and 24  sources located within these cut-outs, and at the positions of the SCUBA-2 optical identifications (IDs, or just sub-mm positions if no IDs were selected). Then, to deconfuse the SPIRE (, and m) maps in a similar way, we used the positions of the m sources detected with PACS (at ), the positions of all radio sources, and the SCUBA-2 ID positions.

Finally the Very Large Array (VLA) COSMOS Deep catalogue was used where the additional VLA A-array observations at 1.4 GHz were obtained and combined with the existing data from the VLA-COSMOS Large project (for details, see Schinnerer et al. 2010). This catalogue covers  arcmin and reaches a sensitivity of Jy beam.

## 3 SCUBA-2 source identifications

In order to find the optical counterparts for sub-mm sources, for which positions are measured with relatively large beams, a simple closest-match approach is not sufficiently accurate. We therefore use the method outlined in Dunlop et al. (1989) and Ivison et al. (2007) where we adopt the search radius around the SCUBA-2 position based on the signal-to-noise ratio (SNR): , where  arcsec. In order to account for systematic astrometry shifts (caused by pointing inaccuracies and/or source blending; e.g. Dunlop et al. 2010) we enforce a minimum search radius of 4.5 arcsec. Within this radius we calculate the corrected Poisson probability, , that a given counterpart could have been selected by chance.

For reasons explained below, the VLA 1.4 GHz and Spitzer MIPS 24 m and IRAC 8 m (with addition of 3.6 m) bands were chosen for searching for galaxy counterparts. In the case of the MIPS 24 m band, the minimum search radius was increased to 5 arcsec to account for the significant MIPS beam size ( arcsec). The optical/near-infrared catalogues were then matched with these coordinates using a search radius of  arcsec and the closest match taken to be the optical counterpart. In addition, we utilised the Herschel, SCUBA-2 and VLA photometry to help isolate likely incorrect identifications (Section 4.2).

The results of the identification process are summarized in Table 4, where the most reliable IDs () are marked in bold, the tentative IDs () are marked in italics, and incorrectly identified sources (as discussed in Section 4.2) are marked with asterisks.

Given the depth of the 850 m imaging utilised here, it is important to check that source positions have not been significantly distorted by source confusion. We have therefore checked that the distribution of positional offsets between the 850 m sources and their adopted multi-frequency frequency counterparts is as expected, assuming the standard formula for positional uncertainty (i.e. ). The results, shown in Fig. 4, provide reassurance that the vast majority of source positions have not been significantly distorted by confusion/blending, and that our association process is statistically valid.

### 3.1 Radio and 24 \mn@boldsymbolμm counterparts

The 850 m band is sensitive to the cool dust re-radiating energy absorbed from hot, young stars. The radio band also traces recent star formation via synchrotron radiation from relativistic electrons produced within supernovae (SNe; Condon 1992). The 24 m waveband is in turn sensitive to the emission from warm dust, and since sub-mm selected galaxies are dusty star-forming galaxies, they are also expected to be reasonably luminous in this band. There is thus a good physical motivation for searching for the counterparts of SCUBA-2 sources in the VLA and MIPS imaging. In addition, the surface density of sources in these wavebands is low enough for chance positional coincidences to be rare (given a sufficiently small search radius).

As seen in Table 1 (before the corrections of Section 4.2) at 1.4 GHz the ID success rate is only 14 (15 out of 106 sources, all with ) but at 24 m the success rate is 69 (73 out of 106, 62 of which have ). Combining both methods, the successful identification rate is 70 (74 out of 106, 63 of which have ). The striking difference in these statistics is due to the fact that the S-COSMOS 24  imaging utilised here is relatively deeper than the radio data currently available in the COSMOS field.

### 3.2 8 \mn@boldsymbolμm counterparts

In order to maximise the identification success rate we also searched for counterparts in the the S-COSMOS IRAC 8 m imaging. At the redshifts of interest, this waveband traces the rest-frame near-infrared light coming from the older, mass-dominant stellar populations in galaxies. Given the growing evidence that sub-mm galaxies are masssive, it is expected they will be more luminous than average in this waveband (e.g. Dye et al. 2008; Michalowski et al. 2010; Biggs et al. 2011; Wardlow et al. 2011). We found that 57 of the 106 SCUBA-2 sources (54%) had 8 m counterparts, 37 of which have . However, unsurprisingly, several of these identifications simply confirmed the identifications already secured via the radio and/or 24 m cross matching, and the search for 8 m counterparts only added 5 new identifications (2 of which have ) to the results described in the previous sub-section.

### 3.3 Optical counterparts

In total, therefore, we identified radio/mid-infrared counterparts for 80 of the 106 SCUBA-2 850 m sources (67 of which have ; see Table 4), and hence achieved an identification success rate of 75. The identification success rate achieved in each individual waveband is given in Table 1. In addition, we present postage-stamp images for all the sources in the online version (Fig. B1), with all the identifications marked with the appropriate symbols.

To complete the connection between the SCUBA-2 sources and their host galaxies, within the area covered by the CANDELS HST WFC3/IR imaging (Fig. 1) we matched the statistically-significant mid-infrared and radio counterparts to the galaxies in the CANDELS -band imaging using a maximum matching radius of 1.5 arcsec. This yielded accurate positions for the optical identifications of 60 of the SCUBA-2 sources (Table 5). For those few SCUBA-2 sources which lie outside the CANDELS HST imaging, we matched the statistically-significant mid-infrared and radio counterparts to the galaxies in the -band UltraVISTA imaging (using the same maximum matching radius). This yielded accurate positions for the optical identifications of the remaining 20 sources (Table 6). We note that galaxies SC850-37, 46 and 61, even though successfully identified in the optical/near-infrared, turned out to be too close to a foreground star for reliable photometry (Fig. B1 in the online version) and therefore no optical redshifts or stellar masses were derived and utilised in the subsequent analysis.

## 4 Redshifts

### 4.1 Photometric redshifts

For all the identified sources, the multi-band photometry given in Tables 5 and 6 was used to derive optical-infrared photometric redshifts using a -minimization method (Cirasuolo et al. 2007, 2010) with a template-fitting code based on the HYPERZ package (Bolzonella et al. 2000). To create template galaxy SEDs, the stellar population synthesis models of Bruzual & Charlot (2003) were applied, using the Chabrier (2003) stellar initial mass function (IMF) with a lower and upper mass cut-off of and respectively. A range of single-component star-formation histories were explored, as well as double-burst models. Metallicity was fixed at solar, but dust reddening was allowed to vary over the range , assuming the law of Calzetti (2000). The HI absorption along the line-of-sight was applied according to Madau (1995). The optical-infrared photometric redshifts for the 77 optically-identified sources for which photometry could be reliably extracted (i.e. the 80 identified sources excluding SC850-37, 46 and 61) are given in Table 7. Also given in this table are the optical spectroscopic redshifts where available. We note that, in general, and are in excellent agreement, except for the two SCUBA-2 sources which are associated with active galactic nuclei (AGN; sources 65 and 72), presumably because no AGN template was included in the photometric redshift fitting procedure.

In addition, for every SCUBA-2 source we used the 450 and 850 m photometry as well as the Herschel , , , , m and VLA 1.4 GHz flux densities (or limits) to obtain ‘long-wavelength’ photometric redshifts (). This was achieved by fitting the average SED template of sub-mm galaxies from Michalowski et al. (2010) to the measured flux densities and errors in all 8 of these long-wavelength bands (including flux-density measurements corresponding to non detections). The resulting ‘long-wavelength’ redshift estimates for all 106 sources are also given in Table 7.

### 4.2 Redshift/identification refinement

Given the statistical nature of the identification process described above, there is always a possibility that some identifications are incorrect (as revealed by interferometric follow-up – e.g. Hodge et al. 2013; Koprowski et al. 2014), and indeed, even when the probability of chance coincidence is extremely small, it can transpire that the optical counterpart is not, in fact, the correct galaxy identification, but is actually an intervening galaxy, gravitationally lensing a more distant sub-mm source (e.g. Dunlop et al. 2004). In either case, a mis-identification will lead to an under-estimate of the true redshift of the sub-mm source, and indeed dramatic discrepancies between and can potentially be used to isolate mis-identified sources.

In Fig. 5 we have therefore plotted versus in an attempt to test the consistency of these two independent redshift estimators. From this plot it can be seen that, for the majority of sources, the two redshift estimates are indeed consistent, with the normalized offset in () displaying a Gaussian distribution with . However, there is an extended positive tail to this distribution, indicative of the fact that a significant subset of the identifications have a value of which is much smaller than the (identification independent) ‘long-wavelength’ photometric redshift of the SCUBA-2 source, . Given the aforementioned potential for mis-identification (and concomitant redshift under-estimation) we have chosen to reject the optical identifications (and hence also ) for the sources that lie more than above the 1:1 redshift relation (see Fig. 5 and caption for details). This may lead to the rejection of a few correct identifications, but this is less important than the key aim of removing any significant redshift biases due to mis-identifications, and also the value of retaining only the most reliable set of identified sources for further study.

The effect of this cut is the rejection of 18 of the 80 optical identifications derived in Section 3. These rejected optical IDs are flagged with asterisks in Table 4 and zeros in Table 7. We emphasize that the rejection of these low-redshift identifications does not impact significantly on the investigation of the physical properties of the sub-mm sources at pursued further below, because if the low-redshift IDs were retained they would not feature in the relevant redshift bins, while adoption of the long-wavelength redshift for these sources means that we do not include these sources in the sample of objects with reliable stellar masses. We also stress that only a small subset of these objects are likely lenses (5 possible examples are highlighted in Fig. B2 available in the online version), but while a revised search for galaxy counterparts for the other sources might yield alternative counterparts with consistent with , we prefer not to confuse subsequent analysis by the inclusion of what would be inevitably less reliable galaxy identifications.

As tabulated in Table 1, with this redshift refinement, the effective optical ID success rate for the most reliable () IDs drops from 63 to 51, while the overall () ID success rate drops from 75 to 58. However, while this reduces the number of reliably identified SCUBA-2 sources to % of the sample, this has the advantage or removing the most dubious identifications. Moreover, we stress that we retain redshift information for every one of the 106 SCUBA-2 sources, in the form of if neither nor a reliable value for are available.

In Fig. B2 (available in the online version) we present 12 12 arcsec near-infrared postage-stamp images for every source, with the positions of all the IDs marked. In this figure we give the source name in red if the optical ID was in fact subsequently rejected in the light of . It can be seen from this figure that at least some of these incorrect identifications are indeed due to galaxy-galaxy lensing (see figure caption for details).

### 4.3 Redshift distribution

The differential redshift distribution for our SCUBA-2 galaxy sample is presented in Fig. 6. In the left-hand panel the black area depicts the redshift distribution for the sources with reliable optical IDs (and hence or ), while the histrogram indicated in blue includes the additional unidentified SCUBA-2 sources with meaningful measurements of . Finally, the green histogram containing the green arrows indicates the impact of also including those sources for which only lower limits on their estimated redshifts could be derived from the long-wavelength photometry. The mean and median redshifts for the whole sample are (strictly speaking, a lower limit) and respectively whereas, for the confirmed optical IDs with optical spectroscopic/photometric redshifts the corresponding numbers are and . This shows that, as expected, the radio/infrared identification process biases the mean redshift towards lower redshifts, but in this case only by about in redshift. In addition, to make sure that our unidentified sources are in fact not spurious, which would manifest itself as them having low SNR values, we also plot in Fig. 7 the 850 m flux as a function of redshift for the whole sample used here, colour-coded according to SNR. It can be clearly seen that the unidentified sources exhibit a wide range of SNRs and hence are most likely real.

In the right-hand panel of Fig. 6 we compare the redshift distribution of the deep 850 m selected sample studied here with example redshift distributions from previous studies. Although our sample is somewhat deeper/fainter than the sub-mm samples studied previously by Chapman et al. (2005) and Michałowski et al. (2012a), the redshift distributions displayed by the optically-identified subset of sources from each study are remarkably consistent; we find , while Chapman et al. (2005) reported , and Michałowski et al. (2012a) reported .

While inclusion of our adopted values of for our unidentified sources moves the mean redshift up to at least , it is clear that the redshift distribution found here cannot be consistent with that found by Koprowski et al. (2014) for the subset of very bright sub-mm/mm sources in the COSMOS field (see also Smolcic et al. 2012), for which . This is not due to any obvious inconsistency in redshift estimation techniques, as can be seen from Table 2 (discussed further below), and indeed the analysis methods used here are near identical to those employed by Koprowski et al. (2014). Rather, as discussed in Koprowski et al. (2014), there must either be a trend for the most luminous sub-mm/mm sources (i.e.  mJy) to lie at significantly higher redshifts than the more typical sources studied here, or the COSMOS bright source sample of Scott et al. (2008) imaged by Younger et al. (2007, 2009) and Smolcic et al. (2012) must be unusually dominated by a high-redshift over-density in the COSMOS field.

### 4.4 Previous literature associations

Five of the sub-mm sources in our SCUBA-2 sample have been previously studied in some detail, and so, in Table 2, we compare our ID positions and redshifts with the pre-existing information. Four of these bright sources were previously the subject of interferometric mm/sub-mm observations, yielding robust optical identifications and photometric redshifts in good agreement with our results. The source separation for SC850-29 (2.03 arcsec) is perfectly plausible since this is the separation between the original AzTEC single-dish coordinate and our chosen ID. The small separations between the positions of our adopted IDs for SC850-6 and 31 and their mm/sub-mm interferometric centroids confirm the reliability of our ID selection. For SC850-1 the rather large source separation of 2.62 arcsec supports our rejection of the optical ID for this source. Finally, the rather large separation for SC850-14 clearly casts doubt on our adopted ID, but in this case is very similar to (which, of course, is why we did not reject the ID) and so the final redshift distribution is unaffected by whether or not the ID is correct.

## 5 Physical Properties

### 5.1 Stellar masses and star-formation rates

For the 58 SCUBA-2 sources for which we have secure optical identifications+redshifts (after the sample refinement discussed in Section 4.2) we were able to use the results of the SED fitting (used to determine ) to obtain an estimate of the stellar mass, , for each galaxy. The derived stellar masses were based on the models of Bruzual & Charlot (2003) assuming double-burst star-formation histories (see Michałowski et al. 2012b), and we assumed a Chabrier (2003) IMF.

We were also able to estimate the star-formation rate, SFR, for each of these sources by using the average long-wavelength SED of the sub-mm galaxies from Michałowski et al. (2010), applied to the 850 m flux-density of each source at the relevant photometric redshift, to estimate the far-infrared luminosity of each source.

The resulting SFRs are plotted against in Fig. 8. In the main plot, for clarity we have confined attention to the sources with because, as shown in the inset plot, due to the impact of the negative K-correction at 850 m, at the flux-density limit of the current sample essentially equates to at all higher redshifts. In this plot we also show the position of the ‘Main-Sequence’ (MS) of star-forming galaxies, as deduced at by Elbaz et al. (2011), and at by Rodighiero et al. (2011). The sensitivity of our deep SCUBA-2 sample to values of SFR as low as means that, for objects with stellar masses , we are able for the first time to properly compare the positions of sub-mm selected galaxies on the SFR: plane with the MS in an unbiased manner.

### 5.2 Specific star-formation rates

In Fig. 9, we collapse the information shown in Fig. 8 into distributions of specific SFR. The black histogram shows the distribution of sSFR for the whole robustly-identified sample of SCUBA-2 sources at , but this can be subdivided by mass into the sub-sample with (blue histogram) and the complementary sub-sample of sources with (red histogram). Refering back to Fig. 8, it can be seen that, at lower stellar masses, the measurement of sSFR is inevitably biased high by the effective SFR limit , and so it is difficult to tell if these SCUBA-2 sources genuinely lie above the MS, or if we are simply sampling the high-sSFR tail of the distribution around the MS. However, at it is clear that the SFR limit would not produce a significantly biased sampling of the distribution of galaxies on the MS. In essence, because of the depth of the SCUBA-2 imaging, for sub-mm selected galaxies with we should now be able to perform the first unbiased estimate of their sSFR at .

In fact, for the high-mass sub-sample, in which SFR is not biased by the effective flux-density limit of the deep SCUBA-2 survey, the distribution of sSFR resembles closely a Gaussian peaked at with . This Gaussian fit is shown by the green curve in Fig. 9, and is completely consistent with the normalization and scatter ( dex) in the MS reported by Rodighiero et al. (2011).

Finally, to check whether we could be biased towards high-mass (and hence low sSFR) objects at high redshift, as a consequence of the flux-density limits of our optical/near-infrared catalogues, we plot the near-infrared (CANDELS -band and UltraVISTA -band) absolute magnitudes of our source IDs against redshift in Fig. 10. The measured values are generally not close to the detection limits of our catalogues and therefore we conclude that the sample is not biased against high sSFRs at high redshifts on account of an inability to detect low-mass galaxies.

We conclude, therefore, within the stellar mass range where we are able to sample the distribution of sSFR in an unbiased way, the sub-mm sources uncovered from this deep SCUBA-2 850 m image, display exactly the mean sSFR and scatter expected from galaxies lying on the high-mass end of the star-forming main-sequence at .

### 5.3 The ‘main sequence’ and its evolution

Given that the SCUBA-2 sources seem to, in effect, define the high-mass end of the star-forming main sequence (MS) of galaxies over the redshift range probed by our sample (i.e. ) it is of interest to explore how the inferred normalization and slope of the MS as derived here compares to that derived from other independent studies based on very different selection techniques over a wide range of redshifts.

Thus, in Fig. 11 we divide our (high-mass) sample into three redshift bins to place the inferred evolution of sSFR within the wider context of studies spanning virtually all of cosmic time (i.e. ).

The first obvious striking feature of Fig. 11 is that our new determination of average sSFR over the redshift range follows very closely the trend defined by the original studies of the MS undertaken by Noeske et al. (2007) and Daddi et al. (2007). Since such studies were based on very different samples, sampling lower stellar masses, this result also implies that we find no evidence for a high-mass turnover in the MS at these redshifts (i.e. a decline in sSFR, or change in the slope of the MS above some characteristic mass). Evidence for a decline in the slope of the MS above a stellar mass has been presented by several authors (e.g. Whitaker et al. 2014; Tasca et al. 2015) but these results are based on optical/near-infrared studies, and suffer from two problems. First, as recently discussed by Johnston et al. (2015), the results of optically-based studies depend crucially on how one selects star-forming galaxies, and colour selection can yield an apparent turn-over in the MS at high masses simply due to increased contamination from passive galaxies/bulges (see also Renzini & Peng 2015; Whitaker et al. 2015). Second, and more important, at the high SFRs of interest here, it is well known that SED fitting to optical-infrared data struggles to capture the total star-formation rate because the vast majority of the star-formation activity in high-mass galaxies is deeply obscured. It is therefore interesting that other recent studies of the MS based on far-infrared/sub-mm data also find no evidence for a high mass turnover in the MS at high-redshift; for example Schreiber et al. (2015), from their Herschel stacking study of the MS, report that any evidence for a flattening of the MS above becomes less prominent with increasing redshift and vanishes by .

As is clear from Fig. 8, the present study does not provide sufficient dynamic range to enable a new measurement of the precise value and redshift evolution of the slope of the MS (see Speagle et al. 2014 for results from a compilation of 25 studies). Nevertheless, the advantages of sub-mm selection for an unbiased study of the high-mass end of the MS are clear (i.e. no contamination from passive galaxies, and a complete census of dust-enshrouded star formation), and our results show that the slope of the MS must remain close to unity up to stellar masses at . We note that it is sometimes claimed that studies of the MS based on far-IR or sub-mm selected samples yield vastly different determinations of the SFR– relation from the MS (e.g. Rodighiero et al. 2014), but it needs to be understood that this is because previous studies based on such samples did not reach sufficient sensitivity in SFR (for individual objects) to properly sample the MS at high redshift. As emphasized in Section 5.2, and in Fig. 8, even the deepest ever 850 m survey analysed here only enables us to properly explore the MS at the very highest masses, due to the effective SFR sensitivity limit; clearly the sources detected in the present study at lower masses are outliers from the MS, and can only provide indirect information of the scatter in the MS at masses of a few , rather than its normalization.

Finally, looking to higher redshifts, Fig. 11 shows that the present study does not provide useful information on characteristic sSFR beyond , but also demonstrates that the trend indicated here over extends naturally out to our previous determination of sSFR in very high-redshift sub-mm/mm galaxies at (Koprowski et al. 2014). There is currently considerable debate over the normalization of the MS at , due in large part to uncertainty over the impact of nebular emission lines on the estimation of stellar masses (see e.g. Stark et al. 2013; Smit et al. 2014). However, the sub-mm studies of high-mass star-forming galaxies are clearly consistent with the results of several existing studies (e.g. Steinhardt et al. 2014), and (despite their supposedly extreme star-formation rates) sub-mm–selected galaxies provide additional support for the presence of a ‘knee’ in the evolution of sSFR around (as originally suggested by the results of Gonzalez et al. 2010, 2012). The ability of theoretical models of galaxy formation to reproduce this transition remains the subject of continued debate, with smooth cold accretion onto dark matter halos leading to expectations that sSFR should rise (Dekel et al. 2009, 2013; Facher-Giguére et al. 2011; Rodríguez-Puebla et al. 2016), and a range of hydrodynamical and semi-analytic models of galaxy formation yielding predictions of characteristic sSFR at that fall short of the results shown in Fig. 11 by a factor of (see discussion in Johnston et al. 2015, and references therein). However, in Fig. 12 we show that when the redshift axis is re-cast in terms of cosmic time, there is really no obvious feature in the evolution of characteristic sSFR. Rather, the challenge for theoretical models is to reproduce the apparently simple fact that sSFR is a linear function of the age of the Universe, at least out to the highest redshifts probed to date.

## 6 Summary

We have investigated the multi-wavelength properties of the galaxies selected from the deepest 850-m survey undertaken to date with SCUBA-2 on the JCMT. This deep 850-m imaging was taken in parallel with deep 450 m imaging in the very best observing conditions as part of the SCUBA-2 Cosmology Legacy Survey. A total of 106 sources (5) were uncovered at 850 m from an area of  arcmin in the centre of the COSMOS/UltraVISTA/CANDELS field, imaged to a typical depth of  mJy. Aided by radio, mid-IR, and 450-m positional information, we established statistically-robust galaxy counterparts for 80 of these sources (%).

By combining the optical-infrared photometric redshifts, , of these galaxies with independent ‘long-wavelength’ estimates of redshift, (based on Herschel/SCUBA-2/VLA photometry), we have been able to refine the list of robust galaxy identifications. This approach has also enabled us to complete the redshift content of the whole sample, yielding , a mean redshift comparable with that derived from all but the brightest previous sub-mm samples.

Because our new deep 850-m selected galaxy sample reaches flux densities equivalent to star-formation rates , we have been able to confirm that sub-mm galaxies form the high-mass end of the ‘main sequence’ (MS) of star-forming galaxies at (with a mean specific SFR of at ). Our results are consistent with no significant flattening of the MS towards high stellar masses at these redshifts (i.e. SFR continues ), suggesting that reports of such flattening are based on contamination by passive galaxies/bulges, and/or under-estimates of dust-enshrouded star-formation activity in massive star-forming galaxies. However, our findings contribute to the growing evidence that average sSFR rises only slowly at high redshift, from at to at . These results are consistent with a rather simple evolution of global characteristic sSFR, in which sSFR is a linear function of the age of the Universe, at least out to the highest redshifts probed to date.

## Acknowledgments

MPK acknowledges the support of the UK Science and Technology Facilities Council. JSD and RAAB acknowledge the support of the European Research Council via the award of an Advanced Grant (PI J. Dunlop). JSD also acknowledges the contribution of the EC FP7 SPACE project ASTRODEEP (Ref.No: 312725). MJM acknowledges the support of the UK Science and Technology Facilities Council, and the FWO Pegasus Marie Curie Fellowship. MC acknowledges the support of the UK Science and Technology Facilities Council via an Advanced Fellowship.

## References

• [1] Aravena M., Younger J.D., Fazio G.G., Gurwell M., Espada D., Bertoldi F., Capak P., Wilner D., 2010, ApJ, 719, L15
• [2] Ashby M.L., et al., 2013, ApJ, 768, 80
• [3] Austermann J.E., et al., 2010, MNRAS, 401, 160
• [4] Barger A.J., Cowie L.L., Sanders D.B., Fulton E., Taniguchi Y., Sato Y., Kawara K., Okuda H., 1998, Nat, 394, 238
• [5] Bertin E., Arnouts S., 1996, A&AS, 117, 393
• [6] Bertoldi F., et al., 2000, A&A, 360, 92
• [7] Biggs A.D., et al., 2011, MNRAS, 413, 2314
• [8] Bintley D., et al., 2014, SPIE, 9153, 3
• [9] Bolzonella M., Miralles J.-M., Pelló R., 2000, A&A, 363, 476
• [10] Bowler R.A.A., et al., 2012, MNRAS, 426, 2772
• [11] Bowler R.A.A., et al., 2014, MNRAS, 440, 2810
• [12] Bowler R.A.A., et al., 2015, MNRAS, 452, 1817
• [13] Bouwens R.J., et al., 2012, ApJ, 754, 83
• [14] Bouwens R.J., et al., 2015, ApJ, 803, 34
• [15] Brammer G.B., et al., 2012, ApJS, 200, 13
• [16] Bruzual G., Charlot S., 2003, MNRAS, 344, 1000
• [17] Calzetti D., et al., 2000, ApJ, 533, 682
• [18] Capak P., et al., 2008, ApJ, 681, L53
• [19] Caputi K.I., et al., 2006, ApJ, 637, 727
• [20] Chabrier G., 2003, PASP, 115, 763
• [21] Chapin E.L., Berry D.S., Gibb A.G., Jenness T., Scott D., Tilanus R.P.J., Economou F., Holland W.S., 2013, MNRAS, 430, 2545
• [22] Chapman, S.C., Blain, A.W., Smail, I., Ivison, R.J., 2005, ApJ, 622, 772
• [23] Cirasuolo M., et al., 2007, MNRAS, 380, 585
• [24] Cirasuolo M., McLure R.J., Dunlop J.S., Almaini O., Foucaud S., Simpson C., 2010, MNRAS, 401, 1166
• [25] Combes F., et al., 2012, A&A, 538, L4
• [26] Coppin K.E.K., et al., 2006, MNRAS, 372, 1621
• [27] Coppin K.E.K., et al., 2009, MNRAS, 395, 1905
• [28] Coe D., et al., 2013, ApJ, 762, 32
• [29] Condon J.J., 1992, ARA&A, 30, 575
• [30] Cox P., et al., 2011, ApJ, 740, 63
• [31] Daddi E., et al., 2007, ApJ, 670, 156
• [32] Daddi E., Dannerbauer H., Krips M., Walter F., Dickinson M., Elbaz D., Morrison G.E., 2009a, ApJ, 695, L176
• [33] Daddi E., et al., 2009b, ApJ, 694, 1517
• [34] Damen M., Forster Schreiber N.M., Franx M., Labbé I., Toft S., van Dokkum P.G., Wuyts S., 2009, ApJ, 705, 617
• [35] Dekel A., et al., 2009, Nature, 457, 451
• [36] Dekel A., Zolotov A., Tweed D., Cacciato M., Ceverino D., Primack J.R., 2013, MNRAS, 435, 999
• [37] Dempsey J.T., et al., 2013, MNRAS, 430, 2543
• [38] Diolaiti E., Bendinelli O., Bonaccini D., Close L., Currie D., Parmeggiani G., 2000, A&AS, 147, 335
• [39] Dole H., et al., 2006, A&A, 451, 417
• [40] Dunlop J.S., 2013, ASSL, 396, 223
• [41] Dunlop J.S., Peacock J.A., Savage A., Lilly S.J., Heasley J.N., Simon A.J.N., 1989, MNRAS, 238, 1171
• [42] Dunlop J.S., et al., 2004, MNRAS, 350, 769
• [43] Dunlop J.S., et al., 2010, MNRAS, 408, 2022
• [44] Dye S., et al., 2008, MNRAS, 386, 1107
• [45] Eales S., Lilly S., Gear W., Dunne L., Bond J.R., Hammer F., Le Févre O., Crampton D., 1999, ApJ, 515, 518
• [46] Elbaz D., et al., 2010, A&A, 518, L29
• [47] Elbaz D., et al., 2011, A&A, 533, 119
• [48] Ellis R.S., et al., 2013, ApJ, 763, L7
• [49] Faucher-Giguère C.-A., Keres D., Ma C.-P., 2011, MNRAS, 417, 2982
• [50] Finkelstein S.L., et al., 2015, ApJ, 810, 71
• [51] Geach J.E., et al., 2013, MNRAS, 432, 53
• [52] González V., et al., 2010, ApJ, 713, 115
• [53] González V., et al., 2012, ApJ, 755, 148
• [54] Greve T.R., Ivison R.J., Bertoldi F., Stevens J.A., Dunlop J.S., Lutz D., Carilli C.L., 2004, MNRAS, 354, 779
• [55] Griffin M.J., et al., 2010, A&A, 518, L3
• [56] Grogin N.A., et al., 2011, ApJS, 197, 35
• [57] Gwyn S.D.J., 2012, AJ, 143, 38
• [58] Hainline L.J., Blain A.W., Smail I., Alexander D.M., Armus L., Chapman S.S., Ivison R.J., ApJ, 740, 96
• [59] Hodge J.A., et al., 2013, ApJ, 768, 91
• [60] Holland W.S., et al., 1999, MNRAS, 303, 659
• [61] Holland W.S., et al., 2013, MNRAS, 430, 2513
• [62] Hughes D.H., et al., 1998, Nat, 394, 241
• [63] Ishigaki M., et al., 2015, ApJ, 799, 12
• [64] Ivison R.J., et al., 2007, MNRAS, 380, 199
• [65] Johnston R., Vaccari M., Jarvis M., Smith M., Giovannoli E., Haussler B., Prescott M., 2015, arXiv:1507.07503
• [66] Karim A., et al., 2011, ApJ, 730, 61
• [67] Karim A., et al., 2013, MNRAS, 432, 2
• [68] Koprowski M.P., Dunlop J.S., Michałowski M.J., Cirasuolo M., Bowler R.A.A., 2014, MNRAS, 444, 117
• [69] Knudsen K.K., Neri R., Kneib J.-P., van der Werf P.P., 2010, A&A, 496, 45
• [70] Le Floc’h E., et al., 2009, ApJ, 703, 222
• [71] Leja J., van Dokkum P., Franx M., Whitaker K.E., 2015, ApJ, 798, 115
• [72] Lilly S. J., et al., 2007, ApJS, 172, 70
• [73] Lutz D., et al., 2011, A&A, 532, 90
• [74] Madau P., 1995, ApJ, 441, 18
• [75] Madau P., et al., 1996, MNRAS, 283, 1388
• [76] McCracken H.J., et al., 2012, A&A, 544, 156
• [77] McLeod D.J., McLure R.J., Dunlop J.S., Robertson B.E., Ellis R.S., Targett T.T., 2015, MNRAS, 450, 3032
• [78] McLure R.J., et al., 2013, MNRAS, 432, 2696
• [79] Michałowski M.J., et al., 2010, A&A, 514, 67
• [80] Michałowski M.J., et al., 2012a, MNRAS, 426, 1845
• [81] Michałowski M.J., et al., 2012b, A&A, 541, 85
• [82] Michałowski M.J., et al., 2014, A&A, 571, 75
• [83] Mitchell P.D., Lacey C.G., Cole S., Baugh C.M., 2014, MNRAS, 444, 2637
• [84] Noeske K.G., et al., 2007, ApJ, 660, L43
• [85] Oesch P.A., et al., 2014, ApJ, 786, 108
• [86] Oke J.B., 1974, ApJS, 27, 21
• [87] Oke J.B., Gunn J.E., 1983, ApJ, 266, 713
• [88] Oliver S.J., et al., 2010, MNRAS, 405, 2279
• [89] Oliver S.J., et al., 2012, MNRAS, 424, 1614
• [90] Ono Y., Ouchi M., Kurono Y., Momose R., ApJ, 795, 5
• [91] Peng C.Y., Ho L.C., Impey C.D., Rix H.W., 2002, AJ, 124, 266
• [92] Pilbratt G.L., et al., 2010, A&A, 518, L1
• [93] Poglitsch A., et al., 2010, A&A, 518, L2
• [94] Reddy N.A., Pettini M., Steidel C.C., Shapley A.E., Erb D.K., Law D.R., 2012, ApJ, 754, 25
• [95] Renzini A., Peng Y.-J., 2015, ApJ, 801, L29
• [96] Riechers D.A., et al., 2010, ApJ, 720, L131
• [97] Riechers D.A., et al., 2013, Nat, 502, 459
• [98] Rodighiero G., et al., 2011, ApJ, 739, L40
• [99] Rodighiero G., et al., 2014, MNRAS, 443, 19
• [100] Rodríguez-Puebla A., Primack J.R., Behroozi P., Faber S.M., 2016, MNRAS, 455, 2592
• [101] Roseboom I.G., et al., 2013, MNRAS, 436, 430
• [102] Salmon B., et al., 2015, ApJ, 799, 183
• [103] Sanders D.B., et al., 2007, ApJS, 172, 86
• [104] Santini P., et al., 2009, A&A, 504, 751
• [105] Schinerrer E., et al., 2010, ApJS, 188, 384
• [106] Schreiber C., et al., 2015, A&A, 575, 74
• [107] Scott K.S., et al., 2008, MNRAS, 385, 2225
• [108] Scott K.S., et al., 2012, MNRAS, 423, 575
• [109] Scott S.E., et al., 2002, MNRAS, 331, 817
• [110] Scott S.E., Dunlop J.S., Serjeant S., 2006, MNRAS, 370, 1057
• [111] Skelton R.E., et al., 2014. ApJS, 214, 24
• [112] Smail I., Ivison R.J., Blain A.W., 1997, ApJ, 490, L5
• [113] Smit R., et al., 2014, ApJ, 784, 58
• [114] Smolcic V., et al., 2012, A&A, 548, 4
• [115] Speagle J.S., Steinhardt C.L., Capak P.L., Silverman J.D., 2014, ApJS, 214, 15
• [116] Stark D.P., et al., 2009, ApJ, 697, 1493
• [117] Stark D.P., et al., 2013, ApJ, 763, 129
• [118] Steidel C.C., et al., 1996 ApJ, 462, L17
• [119] Steinhardt C.L., et al., 2014, ApJ, 791, L25
• [120] Taniguchi Y., et al., 2007, ApJS, 172, 9
• [121] Tasca L.A.M., et al., 2015, A&A, 581, 54
• [122] Walter F., et al., 2012, Nat, 486, 233
• [123] Wardlow J.L., et al., 2011, MNRAS, 415, 1479
• [124] Weiss A., et al., 2009, ApJ, 707, 1201
• [125] Weiss A., et al., 2013, ApJ, 767, 88
• [126] Whitaker K.E., et al., 2014, ApJ, 795, 104
• [127] Whitaker K.E., et al., 2015, ApJ, 811, L12
• [128] Younger J.D., et al., 2007, ApJ, 671, 1531
• [129] Younger J.D., et al., 2009, ApJ, 704, 803

## Appendix A Data Tables

In this appendix we provide tables detailing: i) the sub-mm properties of the deep 106-source 850m-selected SCUBA-2 sample utilised in this study, ii) the results of the galaxy counterpart identification process, iii) the optical-infrared photometry for the galaxy identifications, and iv) the estimated redshifts and derived physical properties of the sub-mm galaxies.