SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES). II. Structural Properties and Near-infrared Morphologies of Faint Submillimeter Galaxies

We present structural parameters and morphological properties of faint 450 μm selected submillimeter galaxies (SMGs) from the JCMT Large Program, STUDIES, in the COSMOS-CANDELS region. Their properties are compared to an 850 μm selected and a matched star-forming samples. We investigate stellar structures of 169 faint 450 μm sources (S450 = 2.8–29.6 mJy; S/N > 4) at z < 3 using HST near-infrared observations. Based on our spectral energy distribution fitting, half of such faint SMGs (LIR = 1011.65±0.98 L⊙) lie above the star formation rate (SFR)/stellar mass plane. The size–mass relation shows that these SMGs are generally similar to less-luminous star-forming galaxies selected by NUV − r versus r − J colors. Because of the intrinsic luminosity of the sample, their rest-frame optical emission is less extended than the 850 μm sources (S850 > 2 mJy) and more extended than the star-forming galaxies in the same redshift range. For the stellar mass and SFR-matched sample at z ≃ 1 and z ≃ 2, the size differences are marginal between faint SMGs and the matched galaxies. Moreover, faint SMGs have similar Sérsic indices and projected axis ratios as star-forming galaxies with the same stellar mass and SFR. Both SMGs and the matched galaxies show high fractions (∼70%) of disturbed features at z ≃ 2, and the fractions depend on the SFRs. These suggest that their star formation activity is related to galaxy merging and the stellar structures of SMGs are similar to those of star-forming galaxies. We show that the depths of submillimeter surveys are approaching the lower luminosity end of star-forming galaxies, allowing us to detect galaxies on the main sequence.


INTRODUCTION
The population known as "Submillimeter galaxies" (SMGs) was first discovered using the Submillimeter Common User Bolometer Array (Holland et al. 1999, SCUBA) on the James Clerk Maxwell Telescope (JCMT) in the late 1990s in deep 850-µm images (Smail et al. 1997;Barger et al. 1998;Hughes et al. 1998).SMGs are understood to be a population of dusty starburst galaxies undergoing rapid stellar mass growth and thus they play an important role in our understanding of galaxy evolution and formation (see reviews by Blain et al. (2002) and Casey et al. (2014)).
SMGs represents sources of the most luminous galaxies (L IR 10 12 L ; e.g., Magnelli et al. 2012;Swinbank et al. 2014) at high redshifts (z 2; e.g., Chapman et al. 2005;Simpson et al. 2014).Their high luminosities are akin to local ultra-luminous infrared galaxies (ULIRGs, see the review by Sanders & Mirabel 1996), which are almost invariably mergers.All studies of local ULIRGS morphologies converge on a very high merger fraction (Clements et al. 1996;Surace et al. 2000;Farrah et al. 2001;Veilleux et al. 2002), according to their morphology in the optical and near-infrared (NIR).However, theoretical models provide different formation routes for SMGs.They can be major mergers with significant starbursts, similar to local ULIRGs (e.g., Narayanan et al. 2010); a heterogeneous population of mergerdriven starbursts and secularly evolving disk galaxies (e.g., Hayward et al. 2011); or simply represent the most massive star-forming galaxy population at high redshift (e.g., Kereš et al. 2005;Davé et al. 2010;Narayanan et al. 2015).Moreover, Lacey et al. (2016) suggested that SMGs are predominately disc-instability triggered starbursts.Additionally, using large-scale simulations, Cowley et al. (2015) found that SMGs detected in singledish surveys can be chance superpositions of starburstyuyenchang.astro@gmail.coming galaxies of very different redshifts along the same line of sight (see also Hayward et al. 2013;Muñoz Arancibia et al. 2015).Therefore, it is important to investigate structures and morphologies of SMGs in large submillimeter surveys to verify these different possibilities.
At high redshift, morphologies of IR-luminous galaxies (e.g., Melbourne et al. 2009;Ricciardelli et al. 2010;Bussmann et al. 2011;Zamojski et al. 2011;Kartaltepe et al. 2012;Alaghband-Zadeh et al. 2012;Ivison et al. 2012;Aguirre et al. 2013;Olivares et al. 2016;Farrah et al. 2017) and massive galaxies (e.g., Buitrago et al. 2008) have been investigated.Thanks to the highresolution imaging available with the Hubble Space Telescope (HST ), the stellar structure of SMGs has been investigated.Pope et al. (2005) used HST /Advanced Camera for Surveys (ACS) images to find larger sizes and a higher degree of asymmetry for 40 850 µm selected SMG.Swinbank et al. (2010) analyzed the HST F 160W -band images of 25 radio-identified SMGs (S 850 = 3-15 mJy) at 0.7 < z < 3.4 from the Chapman et al. (2005) survey, and found that the half-light radii of the SMGs and their asymmetries are not statistically distinct from a comparison sample of star-forming galaxies at similar redshifts.However, the intermediate Sérsic indices (n 2) suggest that the stellar structure of SMGs is best described by a spheroid/elliptical galaxy light distribution.Conselice et al. (2011) used F 160Wband images to study massive galaxies (M * > 10 11 M ) at 1.7 < z < 2.9, including galaxies detected in the submillimeter, finding that there is a gradual increase in size toward lower redshifts.Targett et al. (2013) used the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS, Grogin et al. 2011;Koekemoer et al. 2011) F 160W -band imaging to study 24 1.1mm and 870µm sources (S 870 µm = 1.7-9.1 mJy) at 1 < z < 3.They found that almost all the (sub-) millimeter galaxies are well described by either a single exponential disk (n 1), or a multiple-component system in which the dominant constituent is disk like.
The extended structures are consistent with the sizes of other massive star-forming disks at z 2. Toft et al. (2014) showed that 3 < z < 6 SMGs are consistent with being the progenitors of z = 2 quiescent galaxies, based on their size distributions and other properties.
More recently, observations with the Atacama Large Millimeter/submillimeter Array (ALMA) help to refine the counterpart identification of single-dish samples.Chen et al. (2015) analyzed HST F 160W -band imaging of 48 ALMA detected SMGs at 1 < z < 3.They found that 82% of them appear to have disturbed morphologies, meaning that they are visually classified as either irregulars or interacting systems.They also found significant differences in the sizes and the Sérsic indices between 2 < z < 3 SMGs and z 2 quiescent galaxies, and postulated that the majority of the 2 < z < 3 SMGs with S 870 2 mJy are early/mid-stage major mergers (also see Wiklind et al. 2014).Despite all the above studies, there does not seem to be a converging picture of whether SMGs are triggered by disc instability or mergers.This might be caused by the differences in sample selections, redshift ranges, or methods of analysis.Furthermore, the previous studies focused on single-dish 850 µm or 1.1 mm selected SMGs, with typical fluxes of S 850 2 mJy, roughly corresponding to L IR 10 12.3 L (dust temperature T d 30K).It is thus still difficult to study the variations as a function of star-formation rates (SFRs) from ULIRGs, luminous infrared galaxies (LIRGs), to normal star-forming galaxies that have L IR < 10 12 L .
The JCMT SCUBA-2 instrument (Holland et al. 2013) enables 450-µm surveys that probe deeper (rms 0.7 mJy; L IR 5 × 10 11 L ) than the 850-µm samples because of the roughly two times higher angular resolution (FWHM 7 ) and therefore lower confusion limit.Observations with SCUBA-2 at 450 µm can thus provide direct detections of fainter sources, and less ambiguous multi-wavelength counterpart identification.Chen et al. (2013a,b) and Hsu et al. (2016) carried out SCUBA-2 450 µm surveys in various blank fields and lensing cluster fields to detect 450 µm SMGs sources at S 450 =1-10 mJy.The SCUBA-2 Cosmology Legacy Survey (S2CLS, Geach et al. 2013Geach et al. , 2017) ) and Casey et al. (2013) conducted deep 450-µm imaging in the center of the Cosmic Evolution Survey (Scoville et al. 2007, COSMOS) field and various other fields.Roseboom et al. (2013) crossidentified 58 450-µm selected sources from the S2CLS sample (σ 450 = 1.5 mJy, Geach et al. 2013) with Spitzer and HST /WFC3 data.They showed a correlation between emissivity index β and both stellar mass and effective radius.However, the depth was not sufficient to investigate faint SMGs, in the regime of more normal star-forming galaxies.Zavala et al. (2018) presented 64 sources (σ 450 1.9 mJy; L IR 1.5 × 10 12 L at z < 4) of the S2CLS sample in the Extended Groth Strip field.They found that the dominant component for most of the galaxies at all redshifts is a disk-like structure (a median Sérsic index n 1.4 and half-light radius r e 4.8kpc) by using the HST F 160W -band imaging.They also showed a transition from irregular disks to disks with a spheroidal component at z 1.4 and suggested that SMGs are progenitors of massive elliptical galaxies.
To further expand the 450 µm sample and to push to fainter depth (σ 450 0.7 mJy) and lower luminosity (L IR 5 × 10 11 L ), our team recently started a new program, the SCUBA-2 Ultra Deep Imaging EAO (East-Asian Observatory) Survey (STUDIES, Wang et al. 2017).STUDIES targets the center of the COSMOS field where there are CANDELS NIR data ideal for a morphological study.We combine all the SCUBA-2 data in the COSMOS-CANDELS region to reach a detection limit of S 450 3 mJy (σ 450 0.7 mJy).Moreover, the 450 µm selection does not just enable finding fainter samples.Both the 450 µm and the parallel deep 850 µm observations (σ 850 0.12 mJy) help to constrain the shape of the spectral energy distribution (SED).Our faint SMG sample therefore probes luminosities of approximately L IR > 2-5×10 11 L at z = 1-2, corresponding to SFRs of > 40-80 M yr −1 , assuming the standard Kennicutt (1998) relation, overlapping with that of optically selected normal star-forming galaxies.Therefore, we will be able to compare cool dusty galaxies to unobscured starbursts with similar redshifts, SFRs, and stellar masses.The HST NIR imaging across the STUDIES region enables us to investigate the stellar structures and morphological properties of these faint 450-µm sources.
In this paper, we present morphological results based on structural analysis and visual classification for faint SMGs (450-µm sources) detected by STUDIES, as well as for a control sample matched to the STUDIES-SMGs.The structure of this paper is as follows.We describe the data, catalog matching, and SED fitting in Section 2. We analyze the physical and structural properties in Section 3. We discuss the implications in Section 4 and summarize in Section 5. We use AB magnitudes thrughout, adopt the cosmological parameters (Ω M ,Ω Λ ,h)=(0.30,0.70,0.70),and assume the stellar initial mass function of Chabrier (2003).

JCMT SCUBA-2 Data
In this paper, we use our extremely deep 450 and 850µm data obtained through the STUDIES program, as well as data from the JCMT archive.A full description of STUDIES is given by Wang et al. (2017), but we give a brief description here.STUDIES is a multi-year JCMT STUDIES 450-µm flux map which provides coverage over 700 arcmin 2 centered at R.A.=10:00:22.26,decl.=+02:24:05.06.We show our sample selection of 450-µm sources (red circles with 10 in radii, S/N > 4, S450 > 2mJy) and 850-µm sources (green circles with 15 in radii, S/N > 6, S850 > 2mJy) from the machine-learning method, 850-µm sources (green box, S/N > 6, S850 > 2mJy) from the cross-matched method, along with the comparison sample (blue circles with 5 in radii, M * > 10 10 M , NUV − r vs. r − J selection).We consider star-forming galaxies inside the STUDIES coverage as the comparison sample.The yellow region shows the CANDELS footprint.Large Program, aiming to reach the confusion limit and an rms noise below 0.6 mJy at 450-µm in the COSMOS-CANDELS region.In this paper, we include the first two years of data from STUDIES (170 hours).We also include the extremely deep archival data from the JCMT Legacy Program, S2CLS (Geach et al. 2013, 150 hours, program code: MJLSC01), and the shallower but wider archival data of (Casey et al. 2013, 20 hours, program code: M11BH11A, M12AH11A and M12BH21A).The Casey et al. (2013) data do not substantially increase the depth in the area covered by STUDIES and S2CLS, but provide a wider area for us to expand the sample size at the bright end.The data reduction and source extraction are identical to those described in Wang et al. (2017).The final combined 450-µm map as shown in Figure 1 achieves an rms sensitivity of 0.7 mJy in its center.The areas that have rms sensitivities better than 1 mJy and 5 mJy are ∼ 10 arcmin 2 and ∼ 30 arcmin 2 , respectively.For the 850-µm map, the areas that have rms sensitivities better than 0.12 mJy and 0.15 mJy are ∼ 10 arcmin 2 and ∼ 30 arcmin 2 , respectively.

Sample Selection and Catalog Matching
In our combined map, there are 248 450-µm sources detected above 4σ1 (σ 450 < 5 mJy) with a wide range of flux densities (2.8 mJy < S 450 < 29.6 mJy with a median value of 6.4 mJy).In the same area, there are 128 850-µm sources (σ 850 <1 mJy) above 2 mJy.The different cuts at 450σm and 850σm is due to their different confusion limits.Cowie et al. (2017) determined that the confusion limit at 850 µm is 1.65 mJy from their deep 850 µm map (see also Geach et al. 2017).Although our 850-µm map is slightly deeper than that in Cowie et al. (2017), here we conservatively select sources above 2 mJy to be free from the confusion effect.Above this 2 mJy limit, all our 850-µm sources have S/N > 6 and 2.0 mJy < S 850 < 16.7 mJy.
We used photometry from the optical to far-infrared (FIR) in the COSMOS2015 catalog (Laigle et al. 2016).First, we matched the 450-µm sources with sources in the VLA 3 GHz catalog (Smolčić et al. 2017;Delvecchio et al. 2017) using a 4 search radii (expected false match rate, the expected number of objects which are mismatched over the total number of the sample, based on the number density of the population and the search area, is 0.02).Among the 248 450-µm detected sources, 132 sources are matched to a VLA 3GHZ counterpart (see Figure 2).Then we used the VLA positions to find counterparts in the COSMOS2015 catalog.
For the remaining 450-µm sources, we matched them with mid-infrared (MIR) 24-µm sources (Le Floc'h et al. 2009) using 4 search radii (expected false match rate 0.09), and 80 sources are found (Figure 2).We then used 3 search radii to cross-match the 24-µm sources with Spitzer IRAC sources.After that, we used the IRAC positions to find the counterparts in the COS-MOS2015 catalog.As a result, there are 198 450-µm sources (expected false match rate 0.04) with COS-MOS2015 counterparts.
For the 850-µm sources, we first matched them with the 450-µm sources with 8 search radii (expected false match rate 0.09).We also matched 450-µmundetected 850-µm sources with the VLA catalog using 7 search radii (expected false match rate 0.07), and used the VLA positions to find their COSMOS2015 counterparts.77 counterparts can be found with this cross-matching method.
We also employ the machine-learning technique to identify optical counterparts of 850-um singledish sources (An et al., in preparation).
The machine-learning method identifies the likely multiwavelength counterparts to single-dish-detected submillimeter sources by utilizing a training set of precisely located SMGs from ALMA follow-up of the SCUBA-2 Cosmology Legacy Survey's UKIDSS-UDS field (AS2UDS).The precision of the machine-learning classification is 82 percent as shown in (An et al. 2018).In our work, the precision reaches to 88% (An et al. 2018, private communication) because we adopt a smaller search radius (5 ) to match the machine-learning classified counterparts to 850-µm sources.
There are 44 near-infrared detected galaxies classified as the counterparts of 850-µm sources by the machine-learning method.Among them, 39 850-µm single-dish sources have a counterpart identified by the machine-learning and the cross-matched method mentioned above.Among the 39 sources, 36 of them (>92%) lead to the same optical counterparts.The main results in this work are not changed no matter we use solely the cross-matched sample, solely the machine-learning sample, or both sample.As a result, we adopt the 44 machine-learning classifications as 850-µm counterparts, and then include an additional 39 cross-matched 850µm sources that do not have any counterparts in the machine-learning method (Figure 1).Overall, there are 83 850-µm sources (expected false match rate 0.07) with COSMOS2015 counterparts.
Among the 248 450-µm sources and 128 850-µm sources, 50 (20%) and 44 (34%), respectively, do not have any radio, MIR, and machine-learning counterparts.A plausible explanation for the unidentified sources is that the radio and MIR observations are not deep enough at high redshift.The SMG population may start to drop outside the 3 GHz and 24-µm detection limits above z ∼ 3 as shown in Figure 3.The unidentified sources are likely to be at z > 3, but we cannot confirm this until we have deeper radio and/or MIR observations or direct ALMA imaging.
In our sample, we remove infrared and X-ray selected (L X (2-10 keV)> 10 42 ergs/s) AGNs which are identified by previous work (Civano et al. 2016;Marchesi et al. 2016;Chang et al. 2017).Among the sources with COS-MOS2015 counterparts identified with the above procedure, there are 169 450-µm detected sources and 80 850µm detected sources with reliable COSMOS2015 photometric redshifts (a precision of σ ∆z/(1+zs) =0.034 and a catastrophic failure fraction of η=10% for z ∼ 2 sources according to Laigle et al. 2016).We finally reach a sample of 188 sources that are detected at either 450 or 850 µm, or both, and have photometric redshifts.These are listed in Table 1.We note that 64 of the sources in our sample are detected at both the 450 and 850 µm.There are 31 out of 188 SMGs with high confidence level spectroscopic redshifts (Lilly et al. 2007) in the COSMOS spectroscopic master catalog (Salvato et al., in preparation).These spectroscopic redshifts, the photometric redshifts of our SMGs are highly reliable (a precision of σ ∆z/(1+zs) =0.024 and a catastrophic failure fraction of η=3%).Therefore, we adopt the COSMOS2015 photometric redshifts in this paper.
We identified star-forming galaxies across the STUD-IES image using the COSMOS catalog and a NUV − r vs. r − J selection (see Ilbert et al. 2013 for more details).To perform a fair comparison, we only considered the 69,820 star-forming galaxies that are located in the same area (700 arcmin 2 ) as our JCMT sample (Figure 1) and are not classified as STUDIES SMGs.In this way, for all the star-forming galaxies undetected by SCUBA-2, we can set upper limits for their 450-µm and 850-µm flux densities for the SED fitting in § 2.4.
To define our comparison sample of star-forming galaxies, we removed sources identified as SMGs.However, at the high SFR end, some of these STUDIESundetected star-forming galaxies might be still somewhat bright at 450 µm.They were not detected simply because of the incompleteness of our source extraction and the shallower depth in the outer part of our 450 µm image.To test if our normal star-forming galaxies are significantly contaminated by dusty SMGs that lie just below our 450 µm detection threshold, we conducted stacking analyses.On star-forming galaxies with SFR > 100 M yr −1 at z = 1-3, we obtained a stacked flux of 0.96 ± 0.23 mJy, or approximately three times lower than the faintest 450 µm sources in our SMG sample.We therefore conclude that there is not significant SMG contamination in our comparison sample.As a side note, what is interesting here is the obscured SFR in these galaxies.The above stacked 450 µm flux corresponds to an infrared luminosity of L IR = 1.6 × 10 11 L , and thus an obscured SFR of 26 M yr −1 .This is much smaller than their mean total SFR of 166M yr −1 estimated by MAGPHYS, and implies that the majority of their star formation is unobscured and is seen in the rest-frame UV.

CANDELS Imaging
CANDELS (Grogin et al. 2011;Koekemoer et al. 2011) is an HST Multi-Cycle Treasury Program using the Wide Field Camera 3 (WFC3) in the NIR F 125W and F 160W bands to target five legacy fields (COS-MOS, GOODS-N, GOODS-S, UDS, and EGS).In the COSMOS field (Nayyeri et al. 2017), covers 9 × 24 to a limit of H 27 mag (F 160W , 5 σ).The CAN-DELS imaging has been reduced and drizzled to a 0. 06 pixel scale and high-resolution (FWHM 0. 2) mosaics.In the CANDELS region (yellow polygon in Figure 1), 139 out of our 169 450-µm sources with redshifts and 58 out of our 80 850-µm sources with redshifts can be matched to CANDELS sources, among the 38,671 CAN-DELS sources in the COSMOS field (van der Wel et al. 2012;Nayyeri et al. 2017) detected with SExtractor (Bertin & Arnouts 1996).For the comparison sample, 19,197 star-forming galaxies are matched to the CAN-DELS catalog.We are considering optical light of dusty sources.At z > 3, F 160W imaging traces rest-frame emission at <0.4 µm from galaxies.Therefore we focus on z < 3 sources in this paper.This leaves 128 450µm sources, 46 850-µm sources, and 17,108 compared star-forming galaxies for our stellar structural analysis.

SED Fitting
We model the observed photometry of our SMGs and the NUV − r vs. r − J star-forming sample with the Multi-wavelength Analysis of Galaxy Physical Properties (MAGPHYS) code (da Cunha et al. 2008).MAG-PHYS computes the emission from the stellar populations in galaxies from UV to NIR consistently with the emission from dust at MIR and FIR wavelengths using an energy balance technique.We use the version of the MAGPHYS code that has been modified for sources at high redshifts (see da Cunha et al. 2015).In the fitting, we included photometry from COSMOS2015 (optical: u, B, V , i + , z ++ ; MIR: Y , J, H, K s , 3.6 µm, 4.5 µm, 5.8 µm, 8.0 µm, 24 µm; FIR: 70 µm, 100 µm, 160 µm, 250 µm, 350 µm, 500 µm; the choice of aperture (3 ) and corrections is identical to those used in Chang et al. 2017) as well as 450 and 850-µm flux densities from the SCUBA-2 images.
For sources that are undetected by SCUBA-2, we adopt 4σ upper limits, and the higher value between 2mJy (confusion limit) and 6σ as the upper limit at 850 µm.Figure 4 shows two examples of the SMG photometry and SED fitting.We derive the stellar mass (M ), SFR, specific SFR (sSFR = SFR/M ) and infrared luminosity (dust luminosity at 3-2000 µm defined by MAGPHYS) from the SED fitting.The typical infrared luminosity of our faint SMGs (450-µm selected sources) is 10 11.7 L (mean L IR = 10 11.65±0.98L ; median L IR = 10 11.77 L ), which places these sources between the LIRG (L IR > 10 11 L ) and ULIRG (L IR > 10 12 L ) limits as shown in Figure 3.
The SED fitting significantly underestimates the infrared luminosities of some of the sources (see Figure 3), so we visually inspected their SEDs.We found that this is a result at both low significant photometry and catastrophic failure by MAGPHYS, which fits the optical and IR photometry simultaneously.The latter is probably because the dominant optical and IR emission of these galaxies do not come from the same physical regions (see Simpson et al. 2017, for a recent example) and therefore the energy balance for the UV and FIR in MAGPHYS breaks down.For significantly underestimated (> 4σ at 450-µm or 850-µm) sources ( 10%), we fitted the optical and infrared parts of the SEDs separately.Their SFRs are replaced by the sum of the infrared SFR and uncorrected UV SFR according to Kennicutt (1998); Kennicutt & Evans (2012).In rare cases (4%) where both the MAGPHYS fitting and our infrared fitting fail to reproduce the observed photometries (at 450-µm and 850-µm) within 4σ, the problem seem to lie in the photometries themselves.We thus remove those sources from our sample.
In this paper, we randomly select five star-forming galaxies with stellar mass and SFR (or sSFR) within 0.1 dex of every 450-µm SMG, in the same redshift bin as their comparison sample.However, we note that for z 2, 26±2% of the matched star-forming galaxies are included two to four times because of the limited sample size at the high stellar mass end.Therefore, we include these uncertainties by bootstrapping in our analyses.

Star-Forming Sequence
In order to investigate the star formation process in dusty galaxies compared to the general galaxy population, we compare our sample with the star-forming sequence (stellar mass vs. SFR, also called "main sequence;" e.g., Brinchmann et al. 2004;Elbaz et al. 2007;Noeske et al. 2007;Daddi et al. 2007;Ilbert et al. 2015;Schreiber et al. 2015;Chang et al. 2015).Based on our SED fitting results, we define our own star-forming sequence at different redshifts in Figure 5 (black solid lines).Here we only include galaxies with reasonable SED fitting results by visually inspecting them and de-ciding an empirical choice of reduced chi-square value (χ 2 < 50) in the MAGPHYS output files.There are 159 (out of 188) such SMGs and the stellar masses and SFRs are listed in Table 1.
With the same sample selection for star-forming galaxies, the median difference between COSMOS2015 and our SED fitting results are small (-0.01 dex for stellar masses and 0.07 for SFRs).We also show the main sequence relations from Whitaker et al. (2014) and Speagle et al. (2014).However, our SFR estimations are generally lower than those in the literature by ∼ 0.7 dex.The main reason might be selection of the starforming sample since our median values are close to the COSMOS2015 catalogs with the same sample selection.Moreover, our SFRs would be higher if we consider 24µm or Herschel selected sample.To avoid bias from different selection criteria, we use the NUV − r vs. r − J selection, but show the literature in Figure 5 for comparison.The SFR differences between the various works are more significant at the high stellar mass end, so it is important to compare SMGs with star-forming galaxies using SFRs derived with the same method.
In Figure 5 and Table 2, we show that the SMGs are above or on our star-forming sequence, that is, a higher or similar SFR than most of the population at that stellar mass, for both 450-µm and 850-µm sources at all redshifts.If we define the star-forming sequence spanning ±0.3 dex around our median values, about half (48±5%) of the faint SMGs (450-µm sources) lie above the main sequence, and half (43±4%) of them are on the main sequence.

GALFIT Measurements
We investigate the stellar structure of the STUD-IES SMGs that lie in the CANDELS/COSMOS region.We adopt the structural parameters of HST /F 160Wselected sources in the CANDELS field for available NIR filters (F 160W and F 125W ) in van der Wel et al. (2012).The best-fitting single-component Sérsic models are produced by GALFIT (Peng et al. 2010).According to van der Wel et al. ( 2012), a precision and accuracy of 20% or better can be reached for measurements of the effective radius (R e ) and projected axis ratio (q) for H < 24.5 (75% of our sample) and Sérsic index (n; the degree of curvature of the Sérsic profile) for H < 23.5 (60% of our sample) at typical CANDELS depth.In our structural and morphological analyses, we only consider STUDIES sources detected at H < 24.5 (for R e and q) or H < 23.5 (for n), ensuring that the desired properties both highly precise and accurate.
In order to show the rest-frame optical size dependence on magnitude and infrared luminosity, we chose two typical redshift ranges in Figure 6.Both the z 2.2 sample at F 160W and the z 1.5 sample at F 125W    (2014).Most of the SMGs are similar to star-forming galaxies, rather than passive galaxies.
Figure 8. Sérsic index and axis ratio measured in the F 160W band (H < 23.5) for the 450-µm-selected sources, 850-µm-selected sources, and a comparison sample of stellar mass and SFR matched star-forming galaxies at 0.5 < z < 2.5 and 1.5 < z < 2.5.In the histograms, the dash lines show the median values.There is no significant differences (PK−S > 0.05) between the SMGs and the matched sample.Figure 10.Disturbed feature fraction versus SFR and sSFR for 450-µm sources, 850-µm sources, and a comparison sample of M * > 10 10 M star-forming galaxies at 1.5 < z < 2.5.This shows that disturbed features depend on the SFRs for all types of galaxy.The error bars here represents the 68.3% binomial confidence limits, as described in Cameron (2011).We also show the classifications of previous SMGs by Chen et al. (2015) and Zavala et al. (2018).
correspond to a rest-frame wavelength of 5000 Å.For the 450-µm sources, the z 2.2 sample tends to have smaller sizes than the z 1.5 sample.This trend of smaller sizes lower redshift is consisent with the known size evolution of the overall galaxy population from z 3 to our local universe (e.g., Barro et al. 2013Barro et al. , 2014;;van der Wel et al. 2014).The median sizes of 450µm sources are slightly larger than normal star-forming galaxies at the same magnitude and infrared luminosity.In general, Figure 6 shows that the general population of 450-µm sources follow the most luminous end of normal star-forming galaxies.Therefore, we derive the effective radius (R e ) at a rest-frame wavelength of 5000 Å according to Eq. 1 2 in van der Wel et al. ( 2014), which considers the wavelength dependence of R e as a function of redshift and galaxy stellar mass.In Figure 7, we compare our stellar mass to size relation with that inferred by van der Wel et al. ( 2014) (see their Figure 5).Most of the SMGs are similar in size (for their stellar mass) to star-forming galaxies at all redshifts.
We then consider high accuracy objects (H < 24.5 for the effective radius) over the range 1.5 < z < 2.5.
2 Re=R e,F ( 1+z 1+zp ) ∆ log Re ∆ log λ , where F denotes either F125W (z < 1.5) or F160W (z > 1.5), and zp is the pivot redshift for these respective filters (1.5 for F125W and 2.2 for F160W).And The median effective radius is 4.26±0.05kpc, and the mean is 4.68±0.09kpc for 450-µm sources, while the median is 4.38±0.07kpc, and the mean is 5.28±0.10kpc for 850-µm sources, compared with a median of 3.13±0.12kpc, and a mean of 3.86±0.12kpc for a stellar-mass-and SFR-matched sample to the 450-µm galaxies.The uncertainties here and below are estimated from a bootstrapping analysis.A Kolmogorov-Smirnov (K-S) test shows that the matched star-forming sample is marginally different from both the 450-µm and the 850-µm samples (P K−S 0.05).The 850-µm sample seems to be more extended than the 450-µm sample, probably because they are more luminous, and massive sources.The sample sizes are not large enough to show significant differences with the K-S test (P K−S 0.95).
In the lower redshift range 0.5 < z < 1.5, the median effective radius is 4.90±0.26kpc, and the mean is 5.55±0.10kpc for the 450-µm sources, while the median is 4.85±0.61kpc, and the mean is 4.07±0.07kpc for the 850-µm sources, compared with a median of 4.28±0.09kpc, and a mean of 4.75±0.09kpc for the 450-µm matched sample.The sizes of both the 450-µm and the matched sample at z 1 are larger than those at z 2, which is consistent with the usual size evolution of galaxies (e.g., Zirm et al. 2007;Toft et al. 2007;van Dokkum et al. 2008;Newman et al. 2012;van der Wel et al. 2014).However, the sample size of the 850-µm sources is too small to constrain the z 1 population.On the other hand, the effective radius of the 450-µm sample seems to be larger than the matched sample, although the difference is not significant, (P K−S 0.49).
In Figure 8, we show the Sérsic index versus the projected axis ratio measured in the F 160W band for sources brighter than H = 23.5 (the Sérsic index measurement limit).For the comparison sample, we matched the stellar masses and SFRs of star-forming galaxies with the available 450-µm sources (H < 23.5) in the same diagram.At z 2, the median Sérsic index is 1.08±0.07,and the mean is 1.79±0.06for the 450-µm sources, while the median is 0.86±0.06,and the mean is 1.67±0.06for the 850-µm sources, compared with a median of 1.30±0.05,and a mean of 1.96±0.06for the comparison sample.At z 1, the median Sérsic index is 1.45±0.03,and the mean is 1.80±0.04for the 450-µm sources, while the median is 1.93±0.88,and the mean is 1.96±0.03for the 850-µm sources, compared with a median of 1.22±0.03,and a mean of 1.60±0.04for the comparison sample.However, according to the K-S test, there are little differences (P K−S > 0.05) between the SMGs (both the 450-µm and 850-µm selected sources) and the matched star-forming galaxies for their Sérsic index and projected axis ratio.

Visual Classification
We create a stellar-mass-matched sample of starforming galaxies to the STUDIES sources (H < 24.5) to investigate their morphology visually.We use the HST WFC3 F 160W band, WFC3 F 125W band, and ACS F 814W band images to study as presented in the Appendix.Due to the limited sample size at z 3, we focus on z 1 and z 2 sources in this subsection.
First, we compared visual classification of the SMGs with that of stellar mass and SFR matched star-forming galaxies.We classify them as disks, spheroids, and irregular/mergers.The fractions of these classes are presented in the left panel of Figure 9.These classes are mutually exclusive, so the classification represents the dominant morphology.All the sources are examined by five classifiers (Y.Y.C., F.F., W.H.W., C.F.L., and Y.T.).The error bar in each classification class represents the 68.3% (1-σ) confidence limits, derived with the method described in Cameron ( 2011), which estimates the confidence intervals for a population with a Bayesian approach.In the left panel of Figure 9, most of the SMGs have merger or disturbed features (irregular galaxies).However, the stellar mass and SFR matched star-forming sample also show a comparably high disturbed feature fraction.The classifiers used a strict definition for the class of irregular/mergers, which includes weak perturbed features.We also checked that the disturbed feature fractions of the SMGs and the comparison sample are still comparable and high if we conducted a less strict classification.Such high fractions could be explained by early-to-mid-stage major mergers.There is a hint of an elevated disturbed feature fraction in the 850-µm sample, compared to the 450-µm sample and the normal star-forming galaxies.However, the difference between the 850-µm sample and the star-forming galaxies is 2σ, and thus statistically insignificant.In Figure 9, we also show previous F 160W -band visual classification results.Chen et al. (2015) classified ALESS SMGs to five non-mutually exclusive classes: disk, spheroid, irregular, unresolved, and unclassified by four classifiers.Zavala et al. (2018) used a visual-like classification from Huertas-Company et al. (2015), which is based on neutral networks trained to reproduce the visual mophologies by Kartaltepe et al. (2015).Though the definition of classes are not the same, the high disturbed feature fractions are consistent with our results.
In order to investigate whether the disturbed feature fraction depends on SFR, we consider a comparison sample of M * > 10 10 M star-forming galaxies that lie at the same redshift as the SMGs.In the left panel of Figure 10, we show that the fraction of disturbed sources correlates with SFR for the 450-µm, 850-µm, and comparison sample.At z 2, fraction goes up mildly with SFR, although there are no clear distinctions among the disturbed feature fractions of the three samples at any given SFR.Using the star-forming sample, we find the disturbed feature fraction as a function of SFR to be: f irr/merg (%) = (32±8)+(11±15)×log SFR/(M yr −1 ) where f irr/merg is the irregular/merger fraction.Moreover, the correlations are very strong (Pearson correlation coefficient > 0.96) for all the samples.The disturbed fraction does not seem to depend on how dusty the starbursts are; the dependence only seems to be on SFR.At z 1, disturbed feature fractions are lower than those at z 2, as shown in Figure 9.A possible reason is that our selection at 450 µm and 850 µm identifies more massive and luminous sources at z 2 (Figure 3).Though the disturbed feature fractions of z 1 sources are slightly lower at fixed SFR, it is still difficult to conclude any redshift dependence due to the limited sample sizes.Nevertheless, both z 1 and z 2 samples show correlations between disturbed feature fractions and their star formation in Figure 10.
In parallel, we checked an sSFR (=SFR/M * ) matched sample that is randomly selected using five star-forming galaxies within 0.1 dex in sSFR of every 450-µm SMG at the same redshift bin.In the right panel of Figure 9, we find that the disturbed feature fractions of SMGs are higher than that of the sSFR matched sample.In the right panel of Figure 10, the correlation of the 450µm sources is still strong (Pearson correlation coefficient > 0.80), but not as strong as that of the sSFR-matched galaxies (Pearson correlation coefficient > 0.98).
4. DISCUSSION 4.1.How do SMGs compare with normal galaxies in the star-forming sequence?
According to our stellar mass and SFR estimation, most of the SMGs are on or slightly above the starforming sequence as shown in Figure 5.Despite a decade of observational study, the location of the most luminous, 850-µm selected SMGs relative to the starforming main sequence remains hotly debated.Indeed, various studies into the properties of luminous SMGs have concluded that these systems either represent starburst galaxies, which lie significantly above the main sequence (e.g., da Cunha et al. 2015;Danielson et al. 2017), or, conversely, that they are simply represent the massive 'tip of the known main sequence (Koprowski et al. 2016;Micha lowski et al. 2017).The reason for these discrepant results can typically be traced to systematic uncertainties on the measurement of stellar mass, which is strongly affected by different assumptions on the star formation history (Hainline et al. 2011;Micha lowski et al. 2012Micha lowski et al. , 2014)).STUDIES allows us to extend such studies to a sample of faint 450-µm sources.In Table 1, the stellar masses and SFRs of the STUDIES 450-µm sources are lower than those of 850-µm sources at z < 2.5.The main reason is that the SED peak of typical z∼2 SMGs is around 200-400 µm, and 450-µm observations can detect less luminous SMGs compared to 850-µm observations.However, 450-µm detected galaxies still have higher stellar mass and SFRs than normal star-forming galaxies.
Can our result that SMGs lie slightly above the starforming sequence a consequence of overestimated SFRs?Herschel observations may overestimate FIR fluxes (and hence SFRs) of dusty galaxies due to source clustering (Hwang et al. 2010;Wang et al. 2017) within coarse resolution (15-35 FWHM) of SPIRE imaging at 250-500 µm.Attempt to correct for this flux bias requires either a complete set of prior positions for deblending (e.g., Swinbank et al. 2014), or assumptions for the properties of the underlying population (e.g., Béthermin et al. 2012;Harris et al. 2016).
To test this, we conducted SED fitting by using only SPIRE (optical+Spitzer +PACS+SPIRE) and only SCUBA-2 (optical+Spitzer +PACS+SCUBA-2) data in the FIR bands.The resulting mean SFR offset is 4% with a scatter of 9% for SPIRE-detected sources (S/N > 3 at 250 µm, 350 µm, or 500 µm).The difference is relatively small because MAGPHYS estimates SFRs by considering photometry from UV to FIR wavelengths.The overestimation can be larger if SFRs are derived monochromatically from SPIRE and SCUBA-2 fluxes.In order to avoid such a bias in the SED fitting of our comparison sample, we also considered the upper limits at 450 µm for them.On the other hand, because Herschel fluxes are included in their SED fitting and the SCBUA-2 450 µm photometry is not deep enough for most of them, it is still possible that their SFRs are overestimated in Figure 5.However, this scenario would further strengthen our finding that the SMGs from our deep 450 µm survey can be on or slightly above the starforming galaxies on the SFR-M * plane.
We find that 450-µm selected SMGs (S 450 = 2.8-29.6 mJy; S/N> 4 at z < 3) are on or slightly above the star-forming sequence.This result seems robust against potential biases in the estimations of the SFR of our SMG and comparison samples.It is commonly assumed that galaxies above the sequence are undergoing merger-induced starbursts.However, Cowley et al. (2017) show that dynamically-triggered star formation (e.g.merger/disc-instability) does not necessarily segregate galaxies on the SFR-M * plane, which may also help to explain the half-on half-off results on the star-forming sequence.Hence even for the SMGs on the star-forming sequence, there may be additional dynamical processes occurring, such as merging.Therefore in the next subsection, we will turn our focus to the stellar structure of SMGs and look for evidence of merging and interaction.
We examined the source density and SFR density per comoving volume for z = 1-3.Above 200 M yr −1 , the SMG sample dominates over the normal galaxy sample in terms of both source density and SFR density, but the sample sizes are small for both samples.When we go down to > 100M yr −1 , the normal galaxy sample becomes roughly twice larger than the SMG sample, but their integrated SFR densities are comparable.Below 100M yr −1 , the normal galaxy sample strongly dominates in both the source density and SFR density.
It is now clear that once we probe down to SFR of ∼ 100 M yr −1 , we see both obscured galaxies (appearing as SMGs) and unobscured galaxies (appearing in the optical sample).Above this limit, SMGs are dominant, and below this, normal galaxies are dominant.Therefore, from the points of view of morphology (the topic of this paper), SED (obscured vs. unobscured star formation as tested with stacking analyses), and comoving SFR density, we see that as we go deeper in the submillimeter, we start to enter the regime where normal galaxies play more important roles, or dusty galaxies become less important.This is also in concordance with our 450 µm counts (Wang et al. 2017), which suggest that we can fully account for the 450 µm background once we can detect faint sources of roughly 0.5-0.8mJy.As we further deepen and widen our 450 µm map, we will publish better constrained faint-end counts at 450 µm.We also defer a complete SED analyses of 450 µm sources versus normal galaxies to a future paper.All these should help to better understand how ultra luminous dusty galaxies are connected to normal starforming galaxies and their relative contribution to the cosmic star formation history.

Structures of Dusty Galaxies
The stellar mass to size relation in Figure 7 shows that the sizes of SMGs are similar to those of star-forming galaxies, rather than passive galaxies.In general, 850µm sources are more extended (larger and flatter) than the 450-µm sources, and 450-µm sources are more extended than normal star-forming galaxies.The larger spatial extent of the 850-µm sources can be understood through their higher luminosities and stellar masses.Extended stellar structures were also found in previous SMG studies (e.g., Smail et al. 2000;Swinbank et al. 2010;Targett et al. 2013;Chen et al. 2015).
The slight difference in size might be explained if the NUV − r vs. r − J selections of the star-forming sample are contaminated by passive galaxies.However, such contamination can be removed using the SFR estimated from our SED fitting.After matching the stellar mass and SFR, we still find a small difference in size between our SMGs and the comparison sample at z ∼ 2 as discussed in § 3.2.A plausible explanation for the mild size difference is dust extinction.Recent high-resolution ALMA imaging shows that dust continuum emission from SMGs and massive star forming galaxies is quite compact, compared to their NIR stellar continuum emission (e.g., Ikarashi et al. 2015;Simpson et al. 2015;Iono et al. 2016;Hodge et al. 2016;Tadaki et al. 2017).Even if SMGs and normal star-forming galaxies are comparable in the sizes of their stellar components, the highly extincted cores caused by the compact dust components could bias the measured effective radii outward.More sophisticated analyses are clearly required to further investigate this possibility, including spatially resolved SED fitting for dust extinction and stellar mass, and high-resolution ALMA imaging for low SFR galaxies, as well as multi-wavelength image simulations.Such studies may explain the lack of obvious difference in Sérsic index and projected axis ratio between SMGs and the matched sample (as shown in Figure 8).
Figure 9 shows that most SMGs (around 70%) contain irregular/merger features.We find that the irregular/merger fraction is positively correlated with the SFR (Figure 10).Moreover, the comparison sample, which is plausibly less obscured, behaves identically to the submillimeter selected sample.Given the high SFRs of 850µm sources (as shown in § 3.1), it is thus natural to see them having the highest disturbed feature fraction in Figure 9.This is consistent with previous morphological studies of submillimeter samples (e.g., Conselice et al. 2003;Chapman et al. 2003;Swinbank et al. 2010;Wiklind et al. 2014;Chen et al. 2015).
The dependence on sSFR is consistent with that of Hung et al. (2013), who showed that the fraction of interacting merger systems increases with the deviation from star-forming sequence.Moreover, Hwang et al. (2011) also demonstrated that galaxy-galaxy interactions and mergers have been strongly affecting SFRs by using Herschel data.Unlike the result for the SFR, we see slightly different behaviors of the irregular/merger fractions with sSFR between the SMGs and the matched sample.The disturbed feature fraction of SMGs seems to be higher than a sSFR-matched sample, as shown in the right panels of Figures 9 and 10.What this implies is that for galaxies of the same sSFR, those in merging/disturbed systems tend to be more luminous at 450-µm or 850-µm, while the undisturbed ones tend to have lower dust obscuration.A naive explanation is that merging systems tend to have more compact starforming regions in their cores (as revealed in many recent ALMA observations), while undisturbed systems tend to have disk-wide star formation.The small spatial extent of dusty star-forming regions in the merging/disturbed systems then lead to stronger extinction in the UV and thus stronger dust re-radiation in the FIR and submillimeter.This scenario again remains to be tested with more observations and simulations.We also caution that the differences in irregular/merger fractions are far from huge (72 +7 −10 %, 67 +6 −7 %, 57 +15 −18 % for 850-µm sources, 450µm sources, and sSFR matched star-forming galaxies, respectively), and are statistically insignificant, indicating that even if merging events play a role in triggering SMGs among galaxies with the same sSFR, they are probably not the only factor (Hayward et al. 2011).
As well as having the high SFRs and sSFRs, SMGs also have globally low dust temperature and high attenuation (according to our SED fitting, see also Magnelli et al. 2012).Therefore, we checked dependence of the frequency of merger related features on dust temperature and attenuation.We found that the Pearson correlation coefficients are not high (0.05 for dust temperature and 0.11 for attenuation), as opposed to the value for SFR versus disturbed feature fraction (> 0.96).Most SMGs do have disturbed features, but the disturbed feature fraction mainly depends on the SFR .This suggests that galaxy merging takes place in bright galaxies with high SFRs and can be related to star formation activity.According to our structural and morphological analyses, dusty galaxies are very similar to star-forming galaxies in the rest-frame optical bands.
Recently, several SMGs were imaged at high resolution by ALMA and the results appear to be mixed.Some of them show clumpy and extended structures (i.e., disklike, e.g., Iono et al. 2016), while others show starbursts in compact regions (e.g., Oteo et al. 2017;Fujimoto et al. 2017) or irregular morphologies (e.g., Miettinen et al. 2017).These results show a great variation in the structure of dusty emitting regions in SMGs, and future observations are required to quantify the prevalence of different morphologies in a thorough manner.Moreover, recent findings show that the stellar morphologies of luminous SMGs appear significantly more extended and disturbed than their ALMA dust images at z ∼ 2.5 (Hodge et al. 2016;Chen et al. 2017).Given these diverse results, it is clear that further investigations of the dust and stellar morphologies of SMGs are necessary.
To summarize, we have found that faint SMGs selected with deep 450-µm observations have stellar structures similar to those of less luminous star-forming galaxies in the optical sample in terms of Sérsic index, projected axis ratio, and fraction of galaxies with perturbed features.The 450-µm sources are slightly more extended than normal star-forming galaxies and also lie on or slightly above the star-forming sequence, but these small differences might be a consequence of various selection effects or dust extinction.There is less similarity between the normal star-forming galaxies and the more luminous 850-µm selected SMGs, in terms of sizes of the stellar distribution.These results show that as our submillimeter surveys approach the lower luminosity end (< 10 12 L ), we start to detect normal galaxies on the main sequence statistically.

SUMMARY
In this paper, we have investigated physical and structural properties of SMGs in the NIR, especially for a faint 450-µm sample selected from our extremely deep STUDIES image.Our main findings are as follows.
1. 450-µm selected SMGs are located above or on the star-forming sequence at z < 3.If we define the star-forming sequence as being within ±0.3 dex around the median values, about half (48±5%) of the faint SMGs (450-µm-selected sources) lie above the main sequence, and half (43±4%) are on the main sequence.
2. SMGs are similar to star-forming galaxies in the size-mass relation at z < 3.
3. As a result of the intrinsic luminosity of each sample, the 850-µm sources are typically extended than 450-µm sources, and 450-µm sources are more extended than normal star-forming galaxies, in terms of the apparent sizes of their stellar components.For the stellar-mass-and SFR-matched sample, the size differences are only marginal between faint SMGs and the comparison galaxies.Such a minor difference may be explained by the sizes of their dusty regions.
4. SMGs have similar Sérsic index and projected axis ratio to star-forming galaxies with the same stellar mass and SFR at z 2.
5. Both SMGs and the matched star-forming sample show high fraction (∼80%) of disturbed features, and the irregular/merger fractions of both SMGs and normal star-forming galaxies show similar SFR dependence.
6. Our results suggest that galaxy merging can be related to star formation activity, and stellar structures of SMGs are similar to normal star-forming galaxies of comparable stellar mass.
7. Among SMGs and normal star-forming galaxies of similar sSFR, merging/disturbed systems tend to appear in the submillimeter sample as dusty sources, while undisturbed systems tend to show up in the optical sample.However, the tendency is not strong, indicating that galaxy merging is not the only factor in the triggering of SMGs.
8. Our results based on the STUDIES data show that as submillimeter surveys approach lower luminosities (< 10 12 L ).We start to detect large samples of normal galaxies that lie on the main sequence at z < 3. We thank the JCMT/EAO staff for the observational support and the data/survey management, and the contributions of the entire COSMOS collaboration.The James Clerk Maxwell Telescope is operated by the East Asian Observatory on behalf of The National Astronomical Observatory of Japan, Academia Sinica Institute of Astronomy and Astrophysics, the Korea Astronomy and Space Science Institute, the National Astronomical Observatories of China, and the Chinese Academy of Sciences (Grant No. XDB09000000), with additional funding support from the Science and Technology Facilities Council of the United Kingdom and participating universities in the United Kingdom and Canada.

Figure 3 .
Figure3.Photometric redshift to infrared luminosity plot for 450-µm sources identified by VLA and 24 µm position (red circles and blue triangles), as well as VLA and 24 µm detections (red and blue points, which are not 450-µm detections).The infrared luminosity is derived by MAGPHYS (see § 2.4 for more details).

Figure 4 .
Figure 4. Two typical SED fitting examples for 450-µm detected sources.The red points are the photometry and the red arrows are the upper limit of the photometry.The black lines show the best-fitting template.The orange circles label the JCMT detections.The upper example has both 450-µm and 850-µm detection, and the lower example has only 450-µm detection.The residuals and histograms of the physical parameters (stellar mass, SFR, sSFR, and infrared luminosity) are shown in the lower panels.In the histograms, the dashed lines are the median values.

Figure 5 .
Figure 5. Stellar mass versus SFR relation at z < 3 for 450-µm-detected sources (red), 850-µm sources (green), and a sample of star-forming galaxies (black).The values are derived from our SED fitting.Most of the SMGs lie on or above the star-forming sequence.The black solid lines are median SFRs of star-forming galaxies in bins of 0.5 dex of stellar mass.We also show the sequences derived by Whitaker et al. (2014) (magenta dash lines) and Speagle et al. (2014) (purple dash-dot lines) .

Figure 6 .
Figure6.Size to magnitude and infrared luminosity plot.Here we show the effective radius and magnitude at F 160W for z 2.2 sample (orange star: 450-µm-sources) and at F 125W for z 1.5 sample (green circle: 450-µm-sources.The nearinfrared observations correspond to a rest-frame wavelength of 5000 Å.The 16th, 50th, and 84th percentiles of size for the star-forming galaxies are shown at different magnitude and infrared luminosity bins.The median values of 450-µm-detected sources are labeled as red stars (z 2.2) and blue circles (z 1.5).

Figure 7 .
Figure7.Stellar mass versus size relation at z < 3 for 450-µm-detected sources, 850-µm-detected sources, and a comparison sample of star-forming galaxies.The black lines are fitted to normal star-forming and passive galaxies in van derWel et al.  (2014).Most of the SMGs are similar to star-forming galaxies, rather than passive galaxies.

Figure 9 .
Figure9.Visual classification of the 450-µm detected sources and 850-µm sources.The comparison star-forming galaxies are matched to stellar mass and SFR (left panel), as well as sSFR (right panel).Most of the SMGs contain merger features, similarly or slightly more frequently than the comparison sample.The error bars represent the 68.3% binomial confidence limits, as described inCameron (2011).For comparison, we show the visual classifications of SMGs providedbyChen et al. (2015) andZavala et al. (2018).The higher fractions of disks and spheroids in the literature are because of their non-mutually exclusive classifications.
Y.Y.C., W.H.W., and C.F.L. acknowledge financial support from the Ministry of Science and Technology of Taiwan (105-2112-M-001-029-MY3).WIC acknowledges financial support from the ERC consolidator grant 681627 BUILDUP.LCH was supported by the National Key R&D Program of China (2016YFA0400702) and the National Science Foundation of China (11473002, 11721303).M.J.M. acknowledges the support of the National Science Centre, Poland through the POLONEZ grant 2015/19/P/ST9/04010; this project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 665778.IRS acknowledges support from STFC (ST/P000541/1), the ERC Advanced Investigator programme DUSTYGAL 321334 and a Royal Society/Wolfson Merit Award.X.S. acknowledges the support from Chinese NSF through grant 11573001, and National Basic Research Program 2015CB857005.YT acknowledges support from JSPS KAKENHI (Grant No.18J01050).This work is based on observations taken by the CANDELS Multi-Cycle Treasury Program with the NASA/ESA HST, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.The submillimeter data used in this work include archival data from the S2CLS program (program code MJLSC01) and the PI program of Casey et al. (2013, program code M11BH11A, M12AH11A and M12BH21A).