11institutetext: Cosmic Dawn Center (DAWN), Denmark
11email<EMAIL_ADDRESS>22institutetext: DTU-Space, Elektrovej, Building
328 , 2800, Kgs. Lyngby, Denmark 33institutetext: Centre for Extragalactic
Astronomy, Department of Physics, Durham University, South Road, Durham DH1
3LE, UK 44institutetext: Astronomy Centre, University of Sussex, Falmer,
Brighton BN1 9QH, UK 55institutetext: Niels Bohr Institute, University of
Copenhagen, Jagtvej 128, DK-2200 Copenhagen N, Denmark 66institutetext: Max-
Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
77institutetext: Dept. of Physics and Astronomy, University College London,
Gower Street, London WC1E 6BT, United Kingdom 88institutetext: School of
Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
99institutetext: Dept of physics, Dalhousie University, Halifax NS, Canada
1010institutetext: Academia Sinica Institute of Astronomy and Astrophysics
(ASIAA), No. 1, Section 4, Roosevelt Road, Taipei 10617 1111institutetext:
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo,
181-8588, Japan 1212institutetext: Junior College, Fukuoka Institute of
Technology, 3-30-1 Wajiro-higashi, Higashi-ku, Fukuoka, 811-0295 Japan
1313institutetext: Department of Physics, General Studies, College of
Engineering, Nihon University, 1 Nakagawara, Tokusada, Tamuramachi, Koriyama,
Fukushima, 963-8642, Japan 1414institutetext: Graduate University for Advanced
Studies (SOKENDAI), Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan
1515institutetext: Cahill Center for Astronomy and Astrophysics, California
Institute of Technology, MS 249-17, Pasadena, CA 91125, USA 1616institutetext:
National Radio Astronomy Observatory, Pete V. Domenici Array Science Center,
P.O. Box O, Socorro, NM 87801, USA 1717institutetext: Leiden Observatory,
Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands

# The Structure of Massive Star-Forming Galaxies from JWST and ALMA: Dusty,
High Redshift Disk Galaxies

Steven Gillman  Ian Smail ORCIDs listed on final page1122 Bitten Gullberg 33
A. M. Swinbank 1122 Aswin P. Vijayan 33 Minju Lee 112244 Gabe Brammer 1122 U.
Dudzevičiūtė 1155 Thomas R. Greve 66 Omar Almaini 112277 Malte Brinch 88 Scott
C. Chapman 1122 Chian-Chou Chen 99 Soh Ikarashi 1010 Yuichi Matsuda
111112121313 Wei-Hao Wang 111114141515 Fabian Walter 1010 551616 Paul P. van
der Werf 1717

(June 7th 2024)

We present an analysis of the JWST NIRCam and MIRI morphological and
structural properties of 80 massive ($\log_{10}(M_{\ast}[M_{\odot}])$ = 11.2
$\pm$ 0.1) dusty star-forming galaxies at $z$ $=$ 2.7${}^{+1.2}_{-0.7}$,
identified as sub-millimetre galaxies (SMGs) by ALMA, that have been observed
as part of the JWST PRIMER project. To compare the structure of these massive,
active galaxies to more typical star-forming galaxies, we define a sample of
850 field galaxies with matched redshifts and specific star formation rates.
From visual classification of the dusty star-forming galaxies, we identify 20
$\pm$ 5% as candidate late-stage major mergers, a further 40 $\pm$ 10% as
potential minor mergers and 40 $\pm$ 10% which have comparatively undisturbed
disk-like morphologies, with no obvious massive neighbours on $\lesssim$ 20 –
30 kpc (projected) scales. These rates are comparable to those for the field
sample and indicate that the majority of the sub-millimetre-detected galaxies
are not late-stage major mergers, but have interaction rates similar to the
less-active and less massive field population at $z$ $\sim$ 2–3. Through a
multi-wavelength morphological analysis, using parametric and non-parametric
techniques, we establish that SMGs have comparable near-infrared, mass
normalised, sizes to the less active population, $\rm R_{50}^{F444W}$ = 2.7
$\pm$ 0.2 kpc versus $\rm R_{50}^{F444W}$ = 3.1 $\pm$ 0.1 kpc, but exhibit
lower Sérsic indices, consistent with bulge-less disks: $n_{\rm F444W}$ = 1.1
$\pm$ 0.1, compared to $n_{\rm F444W}$ = 1.9 $\pm$ 0.1 for the less active
field. The SMGs exhibit greater single-Sérsic fit residuals and their
morphologies are more structured at 2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$
relative to 4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ when compared to the
field galaxies. This appears to be caused by significant structured dust
content in the SMGs and we find evidence for dust reddening as the origin of
the morphological differences by identifying a strong correlation between the
F200W$-$F444W pixel colour and the 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$
surface brightness using high-resolution ALMA observations. We conclude that
SMGs and less massive and less actively star-forming galaxies at the same
epochs share a common disk-like structure, but the weaker bulge components
(and potentially lower black hole masses) of the SMGs results in a lower
dynamical stability. Consequently, instabilities triggered either secularly or
generally by minor external perturbations result in higher levels of activity
(and dust content) in SMGs compared to typical star-forming galaxies.

###### Key Words.:

Galaxies: high-redshift – Galaxies: structure – Galaxies: evolution – Sub-
millimetre: galaxies

##  1 Introduction

The relative proportions of highly-dust-obscured and less-obscured star
formation appears to vary over the history of the Universe, with the dust-
obscured component dominating in galaxy populations at $z$ $\sim$ 4–5 down to
the present day (e.g., Dunlop et al., 2017; Bouwens et al., 2020; Long et al.,
2023). The cause of this transition in star-formation mode may reflect the
growing metallicity of the interstellar medium (ISM) in galaxies, less
efficient removal of dust from deeper potential wells or structural or
geometrical changes in the star-forming regions within galaxies.

The most extreme examples at high redshifts of systems dominated by dust-
obscured star formation are the sub-millimetre galaxies (SMGs) with dust
masses of $M_{\rm d}$ $\sim$ 108-9 M⊙ and far-infrared luminosities of $L_{\rm
IR}$ $\sim$ 1012-13 L⊙ (e.g., Magnelli et al., 2012; Rowlands et al., 2014;
Miettinen et al., 2017b; Dudzevičiūtė et al., 2020), placing them into the
Ultra or Hyperluminous Infrared Galaxies (U/HyLIRGs), see Hodge & da Cunha
(2020) for a full review. Most of these galaxies show high star-formation
rates, SFR $\sim$ 102-3 M⊙ yr-1;(Swinbank et al., 2014), and correspondingly
short gas consumption timescales (e.g., Greve et al., 2005; Miettinen et al.,
2017a; Tacconi et al., 2018; Birkin et al., 2021), suggesting that they
represent relatively short-lived starbursts, $\lesssim$ 100 Myrs, which will
result in massive systems with stellar masses of $M_{\ast}$ $\sim$ 1011 M⊙
(e.g., Wardlow et al., 2011; Simpson et al., 2014; Miettinen et al., 2017a;
Dudzevičiūtė et al., 2020).

The high star formation rates and large stellar masses of SMGs have proved
challenging to reproduce in theoretical galaxy formation models (e.g., Baugh
et al., 2005; Swinbank et al., 2008; Hayward et al., 2013; McAlpine et al.,
2019), although more recent attempts have been more successful (e.g., Lower et
al., 2023; Cochrane et al., 2023). The models suggest that the high star
formation rates in this population are driven by a mix of secular
unstabilities in gas-rich disks and dynamical triggers due to minor and major
mergers (e.g., McAlpine et al., 2019). However, attempts to observationally
test these claims using the available rest-frame ultra-violet (UV) Hubble
Space Telescope (HST) imaging of $z$ $\sim$ 1–3 SMGs were challenging (e.g.,
Chapman et al., 2003). While the galaxies frequently exhibited irregular
morphologies with apparently multiple components (e.g., Swinbank et al., 2010;
Chen et al., 2015; Gómez-Guijarro et al., 2018; Zavala et al., 2018; Cowie et
al., 2018; Lang et al., 2019; Ling & Yan, 2022), their significant dust
attenuation ($A_{V}\gtrsim$ 2–6, e.g., Dudzevičiūtė et al. 2020) means that
assessing the intrinsic stellar mass morphology of the galaxies from these
data was incredibly challenging – especially for the subset of the population
that is undetectable in the near-infrared (“NIR-faint” SMGs, Simpson et al.
2014; Dudzevičiūtė et al. 2020; Smail et al. 2021; Ikarashi et al. 2022;
Kokorev et al. 2023). Detecting and resolving rest-frame near-infrared
emission of SMGs, which is much less affected by dust attenuation and reflects
the bulk of the stellar population, is essential to robustly constrain the
morphology of their stellar mass. However, this has been beyond the reach of
previous instrumentation such as the Infrared Array Camera (IRAC; Fazio et al.
2004) on the Spitzer Space Telescope, which, whilst providing the required
near-infrared wavelength coverage from 3.6 –
8$\text{\,}\mathrm{\SIUnitSymbolMicro m}$, lacked the spatial (sub-arcsecond)
resolution required to constrain the underlying morphologies of the stellar
emission in SMGs.

However, some progress has been made on understanding the structure of SMGs
using high-resolution observations of the dust continuum and gas kinematics in
SMGs (e.g., Simpson et al., 2015; Ikarashi et al., 2015; Fujimoto et al.,
2017). Thus FWHM $\sim$
0$\aas@@fstack{\prime\prime}$1–0$\aas@@fstack{\prime\prime}$2 sub-millimetre
mapping with ALMA has revealed compact disk-like dust continuum emission
arises from compact disk-like structures (i.e., $R_{\rm e}$ $\sim$ 1 – 2 kpc,
Sersíc $n$ $\approx$ 1), which are roughly half the size of the galaxy extent
in HST $H$-band imaging (Hodge et al., 2016; Gullberg et al., 2019; Chen et
al., 2020; Cochrane et al., 2021). At the highest resolutions, FWHM $\sim$
$0\aas@@fstack{\prime\prime}{05}$, Hodge et al. (2019) identified potential
arms and bar-like structures in the dust continuum emission from a small
sample of high-redshift SMGs. Resolved kinematic studies using molecular and
atomic fine structure emission lines in the rest-frame far-infrared and
sub-/millimetre have uncovered disk-like kinematics for at least a significant
fraction of the population (e.g., Hodge et al., 2012; Chen et al., 2017; Lelli
et al., 2021; Rizzo et al., 2021; Amvrosiadis et al., 2023). With the advent
of the James Webb Space Telescope (JWST, Gardner et al. 2023), high-resolution
observations from from the near (1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) to
the mid-infrared (25$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) are now
feasible, enabling the infrared emission from counterparts of sub-millimetre
bright galaxies to be detected and the issue of their stellar morphology and
structures to be finally quantified. Initial morphological studies with JWST
have found size evolution with wavelength in sub-millimetre galaxies and less
active colour-selected populations at $z$ $\sim$ 2 (Chen et al., 2022; Cheng
et al., 2023; Suess et al., 2022), with a reduction in half-light radius when
observed in the rest-frame near-infrared compared to the rest-frame optical/UV
as previously studied with HST. A number of studies have subsequently expanded
the samples with JWST and ALMA coverage, confirming that SMGs become more
compact (higher concentration, smaller size) at longer wavelengths (e.g. Price
et al., 2023; Cheng et al., 2023; Gillman et al., 2023) with the potential
impact of dust on the observed morphology becomingly less evident at longer
wavelengths (Kokorev et al., 2022; Wu et al., 2023; Kamieneski et al., 2023;
Sun et al., 2024). There are also claims of frequent stellar bars in many
high-redshift star-forming galaxies (Guo et al., 2023), including examples in
SMGs (Smail et al., 2023). However, all of these studies suffer from modest
sample statistics, limiting the interpretations of their findings.

In this paper, we present an analysis of the structural properties of a
statistically robust sample of ALMA-detected, sub-millimetre detected galaxies
that have been observed with JWST NIRCam and MIRI. In Section 2 we define the
sample of SMGs that we use in our analysis whilst in Section 3 we present the
observations, data reduction and analysis undertaken on the multi-wavelength
imaging of these systems (and a matched control sample of less active galaxies
selected from the field). In Section 4 we discuss the results from our
analysis before summarising our main conclusions in Section 5. Throughout the
paper, we assume a $\Lambda$CDM cosmology with $\Omega_{\rm m}=0.3$,
$\Omega_{\Lambda}=0.7$, and $H_{0}=70\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$. All
quoted magnitudes are on the AB system and stellar masses are calculated
assuming a Chabrier initial mass function (IMF) (Chabrier, 2003).

Figure 1: The combined AS2UDS and AS2COSMOS SMG sample in the PRIMER survey
ranked in descending ALMA 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ flux.
For each SMG we show the
3$\aas@@fstack{\prime\prime}$0$\,\times\,$3$\aas@@fstack{\prime\prime}$0 false
colour image (F444W/F356W/F277W as R/G/B), labelling the SMG ID, redshift
(magphys derived, $z_{\rm p}$, or spectroscopic, $z_{\rm s}$) and ALMA
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ flux density. We further label the
SMGs visually classified as major mergers (M) or affected by gravitational
lensing (Lens). The red cross indicates the ALMA
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ position.

##  2 Sample Selection

To build a sample of ALMA-detected SMGs with near-infrared JWST coverage, we
utilise the AS2UDS (Stach et al., 2019) and AS2COSMOS (Simpson et al., 2020)
surveys as our parent sample. The AS2UDS and AS2COSMOS surveys are ALMA
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ follow-up programs of 716 and 180
850$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ SCUBA-2 sources that are detected
at $>$ 4$\sigma$ in the S2CLS (Geach et al., 2017) map of the UKIDSS Ultra-
Deep Survey (UDS; Lawrence et al. 2007) and the S2COSMOS (Simpson et al.,
2019) map of the Cosmic Evolution Survey (COSMOS; Scoville et al. 2007)
respectively. These two surveys provide an initial candidate sample of 896
SMGs with precise ALMA identifications, selected at SNR $\gtrsim$ 4, for which
we can use to characterise their near-infrared JWST counterparts.

We cross-match the ALMA positions for the SMGs as presented in Stach et al.
(2019) for AS2UDS and Simpson et al. (2020) for AS2COSMOS, with the footprint
of the JWST/NIRCam and JWST/MIRI observations from The Public Release IMaging
for Extragalactic Research (PRIMER; Dunlop et al. 2021) survey. PRIMER is a
multi-band, multi-instrument survey of UDS and COSMOS covering 234 and 144 sq.
arcmin respectively. The observations consist of the seven wide-band and one
medium-band NIRCam filter (F090W, F115W, F150W, F200W, F277W, F356W, F410M,
F444W) as well as two wide-band MIRI filters (F770W, F1800W). Parts of the UDS
and COSMOS fields also benefit from HST ACS and WFC3 coverage from CANDELS
(Grogin et al., 2011) sampling the observed frame optical
(0.4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) to near-infrared
(1.6$\text{\,}\mathrm{\SIUnitSymbolMicro m}$).

For our analysis, we require the SMGs to be covered by the JWST/NIRCam long-
wavelength filter F444W ensuring that the observed-frame near-infrared is
sampled. This results in a sample of 66 AS2UDS and 22 AS2COSMOS SMGs. A
summary of the ALMA properties and HST and JWST coverage is presented in
Appendix A. Of the 88 SMGs, 12 have no HST coverage. Two SMGs have JWST
imaging in only three bands (F444W, F277W, F200W) while the other 86 SMGs are
covered by three or more JWST bands, with 37 SMGs having the maximum ten
available JWST filters covering from 0.9 to 18
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$.

The 88 SMGs have a median ALMA 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$
flux of $S_{\rm 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}$ = 3.8 $\pm$ 0.4
mJy, with a 16th to 84th percentile range of $S_{\rm
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}$ =1.8 – 6.1 mJy. The SMGs sample
the faint end of the full AS2COSMOS and AS2UDS $S_{\rm
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}$ distribution with ranges from
$S_{\rm 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}$ = 0.7 – 19.2 mJy and
$S_{\rm 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}$ = 0.6 – 13.6 mJy
respectively. Majority of the AS2UDS SMGs (51/66) were observed with ALMA at
resolutions of $\approxeq$ 0$\aas@@fstack{\prime\prime}$3 FWHM as presented in
Stach et al. (2019). The remaining 15 SMGs in UDS were observed at high-
resolution $\approxeq$ 0$\aas@@fstack{\prime\prime}$2 FWHM (Gullberg et al.,
2019). The ALMA maps of the 22 SMGs in the COSMOS field were tapered to a
resolution of 0$\aas@@fstack{\prime\prime}$8 FWHM (Simpson et al., 2020).

##  3 Reduction & Analysis

In this section, we present our reduction, analysis and compilation of the
photometric data that we use to characterise the multi-wavelength properties
of the SMGs.

###  3.1 JWST & HST

We homogeneously process the JWST NIRCam and MIRI observations, retrieving the
level-2 data products (version = jwst_1069.pmap) from the STScI website111
https://mast.stsci.edu/ and processing them with the grizli pipeline (Brammer
& Matharu, 2021; Brammer et al., 2022)222For full details of the reduction
process see: https://dawn-cph.github.io/dja/imaging/v7/. For the NIRCam data,
additional steps were employed to deal with diagonal striping seen in some
exposures, cosmic rays and stray light. Whilst for the MIRI exposures time-
dependent sky flats are applied in an approach similar to recent JWST studies
(e.g., Yang et al., 2023). We further incorporate the available optical and
near-infrared data available in the Complete Hubble Archive for Galaxy
Evolution (CHArGE, Kokorev et al., 2022), providing multi-band observed-frame
imaging from 0.4 to 1.6$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for a subset
of the sources. We align all the imaging to Gaia DR3 (Gaia Collaboration et
al., 2021), co-add, and drizzle the final mosaics to a
$0\aas@@fstack{\prime\prime}04$ pixel scale (Fruchter & Hook, 2002) for all
JWST and HST filters.

Figure 2: The multi-wavelength SEDs for four example SMGs (AS2UDS0301.0,
AS2UDS0346.0, AS2COS0002.1 and AS2UDS0237.0) that demonstrate the range of
observed-frame infrared colours displayed by the SMG sample. For each source,
we indicate the observed flux and error in each band with a red circle and
errorbar. Arrows show upper limits at 3$\sigma$ for wavelengths below
10$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and 1$\sigma$ for wavelengths
beyond 10$\text{\,}\mathrm{\SIUnitSymbolMicro m}$. We over plot the best-fit
magphys derived SED (orange line) and model fluxes (black circles). Below each
SED we display probability distributions of the magphys derived properties
(redshift (unless spectroscopic), stellar mass and AV) and report the best-fit
redshift and reduced chi-square at the top right. Above the SED we display the
multi-wavelength JWST and ALMA 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$
imaging used as part of the analysis, with the SMG centroid indicated by the
red tick markers. Appendix B shows the SEDS for the full sample.

###  3.2 Photometry

For JWST and HST bands we extract sources using sep (Barbary et al., 2016), a
python version of source extractor (Bertin & Arnouts, 1996a), with a noise-
weighted combined F277W+F356W+F444W NIRCam image as the detection image. For
each source we make a cutout in each of the HST and JWST bands, centred on
this NIRCam long-wavelength detected source. Three arcsecond colour images
made from the F444W/F356W/F277W NIRCam bands for the SMGs are shown in Figure
1. Aperture photometry is performed in elliptical apertures with a minimum
diameter of $1\aas@@fstack{\prime\prime}0$ and corrected to the “total” values
following Kron (1980). The aperture corrections are computed on the NIRCam LW
stacked image and applied to all bands. The MIRI observations were processed
prior to the release of the updated photometric calibrations. We thus scale
the measured flux in the F770W and F1800W bands by 0.85 and 1.03 respectively
following the JWST documentation. We determine a median F444W AB magnitude for
the SMG sample of $m_{\rm F444W}$ = 21.7 $\pm$ 0.3 with a 16th – 84th
percentile range of $m_{\rm F444W}$ = 20.3 – 23.1.

We compile the mid-infrared to radio (5.8$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ to 1.4GHz) photometry for our sources from Dudzevičiūtė et al. (2020) and
Simpson et al. (2020). For the SMGs with no MIRI F770W and F1800W imaging, we
adopt the IRAC channel 3 (5.8$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) and
channel 4 (8$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) photometry, if IRAC
channel 1 (3.6$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) flux is within 10
percent of the NIRCam F356W and IRAC channel 2
(4.5$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) flux is within 10 percent of the
NIRCam F444W. We employ the IRAC photometry for two out of seven AS2COSMOS
SMGs without MIRI coverage and 11 out of 38 AS2UDS SMGs.

###  3.3 Final Sample

Having collated a sample of 88 AS2UDS and AS2COSMOS SMGs lying within the JWST
PRIMER fields, we visually inspect each of the galaxies’ JWST imaging to
verify the association of the near-infrared counterpart to the ALMA source. Of
the 88 SMGs, we identify one SMG, AS2UDS0490.0, with no clear NIRCam
counterpart, with a F444W magnitude of $m_{\rm F444W}$ =26.7 $\pm$ 0.6
detected at 1.4$\sigma$. There is no MIRI coverage or any detection of this
S870 = 2.7 mJy (SNR = 4.5) source between UV and radio, thus we conclude it is
likely spurious, with the ALMA catalogue of 707 sources from Stach et al.
(2019) expected to have a two percent spurious fraction, and so exclude the
source from our sample. We also remove two SMGs, AS2COS0005.1 and
AS2COS0005.2, which appear gravitational lensed and thus the derivation of
their intrinsic properties including morphology would require detailed and
uncertain lens modelling (e.g. Amvrosiadis et al., 2018; Bendo et al., 2023;
Pearson et al., 2024). We remove three UDS sources (AS2UDS0106.0, AS2UDS0175.0
and, AS2UDS0069.0) and three COSMOS sources (AS2COS0017.1, AS2COS0032.1 and,
AS2COS0035.1) due to partial coverage in the JWST NIRCam imaging. Finally, one
ALMA source, AS2UDS00071.0, is deblended in the NIRCam F444W imaging, and
high-resolution ALMA observations (Gullberg et al., 2019), into two sources
which we label AS2UDS00071.0a and AS2UDS00071.0b. We model the morphology of
AS2UDS0071.0a and AS2UDS0071.0b independently and scale the blended photometry
by the flux ratio of the two sources. Thus in the final sample, we have 80
SMGs, for which the HST and JWST coverage for each SMG is detailed in Appendix
A.

###  3.4 SED Fitting

Having defined a final sample of 80 SMGs with robust near-infrared
counterparts, we use the SED fitting code Multi-wavelength Analysis of Galaxy
Physical Properties and Photometric Redshift (magphys+photo-$z$, hereafter
referred to as magphys; da Cunha et al., 2015; Battisti et al., 2019), to
derive the physical properties of each SMG333We note that we do not include an
AGN component in the magphys modelling as the fraction with AGN contributions
is expected to be small (e.g., Stach et al., 2019). For 22 of the SMGs
spectroscopic redshifts are available from the literature and ongoing
millimetre and near-infrared spectroscopic surveys (e.g., McLure et al., 2018;
Mitsuhashi et al., 2021). For these sources we use the high-redshift version
of magphys, (magphys+high$z$ (v2); da Cunha et al., 2015; Battisti et al.,
2019) with the redshift fixed to the spectroscopic redshift of each source, as
detailed in Appendix A.

magphys is a physically motivated SED fitting code that utilises the energy
balance technique to fit the multi-wavelength photometry from UV to radio.
This approach, as tested on SMGs by da Cunha et al. (2015) and Dudzevičiūtė et
al. (2020), and simulated galaxies (e.g., Dudzevičiūtė et al., 2020; Haskell
et al., 2023), models the sub-millimetre and optical emission as originating
from the same region of the galaxy. For a discussion of using the magphys SED
code to model high redshift SMGs, we refer the reader to Dudzevičiūtė et al.
(2020). For consistencies with Dudzevičiūtė et al. (2020), for non-detections
at wavelengths shorter than 8$\text{\,}\mathrm{\SIUnitSymbolMicro m}$, we
adopt a flux and uncertainty of 0$\pm$3$\sigma$ while for those beyond
10$\text{\,}\mathrm{\SIUnitSymbolMicro m}$, we use 1.5 $\pm$ 1.0$\sigma$.

In Figure 2, we show examples of the multi-wavelength photometry and magphys
SED fits, with the fits for the whole sample presented in Appendix B. We
summarise some of the key derived physical properties of the SMG sample in
Figure 3. We estimate a median redshift of $z$ = 2.7 $\pm$ 0.15 with a (16th
to 84th percentile range of $z$ = 1.9 – 3.9, which is comparable to that
derived by Dudzevičiūtė et al. (2020) for AS2UDS $z$ = 2.6 $\pm$ 0.8 and the
median redshift of the AS2COSMOS survey ($z$ = 2.7 $\pm$ 0.9) as derived by
Simpson et al. (2020), as well as other studies of SMGs (e.g., da Cunha et
al., 2015; Ling & Yan, 2022). From the magphys SED fitting, we derive a median
stellar mass for the SMGs of $\rm\log_{10}(M_{\ast}[M_{\odot}])$ = 11.20 $\pm$
0.10 with a 16th – 84th percentile range of
$\rm\log_{10}(M_{\ast}[M_{\odot}])$ = 10.6 – 11.6, and a median specific star-
formation rate of $\rm\log_{10}(sSFR[yr^{-1}])$ = $-$8.7 $\pm$ 0.1 with a 16th
– 84th percentile range of $\rm\log_{10}(sSFR[yr^{-1}])$ = $-$9.2 to $-$8.0.
We derive a median dust mass of $\rm\log_{10}(M_{d}[M_{\odot}])$ = 8.8 $\pm$
0.1 with a 16th – 84th percentile range of $\rm\log_{10}(M_{d}[M_{\odot}])$ =
8.4 – 9.1 and a median infrared luminosity of
$\rm\log_{10}(L_{IR}[L_{\odot}])$ = 12.6 $\pm$ 0.1 with a 16th – 84th
percentile range of $\rm\log_{10}(L_{IR}[L_{\odot}])$ = 12.3 – 12.8. These are
consistent with the parent sample of 707 SMGs in AS2UDS, for which
Dudzevičiūtė et al. (2020) derived a median stellar and dust mass of
$\rm\log_{10}(M_{\ast}[M_{\odot}])$ = $11.1^{+0.2}_{-0.3}$ and
$\rm\log_{10}(M_{d}[M_{\odot}])$ = $8.8^{+0.4}_{-0.4}$ and a median specific
star-formation rate and infrared luminosity of $\rm\log_{10}(sSFR[yr^{-1}])$ =
$-$8.73 $\pm$ 0.04 and $\rm\log_{10}(L_{IR}[L_{\odot}])$ = 12.45 $\pm$ 0.02

As expected given the JWST photometry agrees with earlier IRAC and HST or
ground-based observations, while typically being more sensitive, the basic
derived properties of the SMGs don’t alter when JWST photometry is included.
The main benefit of deeper observations at 1 –
3$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ is improved constraints on the
presence Balmer breaks at $z$ $\sim$ 1 – 6.

Figure 3: Distributions of the magphys derived SED properties for the SMG
sample (red) and field sample (open grey histograms). We show the F444W AB
magnitude (a), photometric redshift (b), stellar mass (c), star formation rate
(d), specific star formation rate (e), infrared luminosity (f), dust mass (g)
and $V$-band attenuation (AV) (h). For each distribution, we indicate the
bootstrapped median and uncertainty for SMGs (red marker and errorbar) and the
matched field sample (grey marker and errorbar). By construction, the field
sample mirrors the SMG sample in redshift and specific star-formation rate
distributions while having significantly lower dust masses, infrared
luminosity and star-formation rates. The resulting field sample exhibits much
lower AV than the SMGs.

###  3.5 Field Sample

To investigate the physical mechanism that drives and differentiates our SMG
sample from the typical star-forming population at the same epochs $z$ = 2 –
5, we compare their multi-wavelength properties to a sample of less active
field galaxies which we construct from the $K$-band selected sample analysed
by Dudzevičiūtė et al. (2020) in the UKIDSS UDS field for which deep 22-band
photometry is available covering the UV/optical through to the far-
infrared/submillimeter and radio. Dudzevičiūtė et al. (2020) used the magphys
code to derive photometric redshifts, stellar masses and other physical
properties for the $\sim$ 300,000 $K_{\rm AB}$ $\leq$ 25.7 galaxies in this
$\sim$ 0.8 degree2 field from the UKIDSS survey (Almaini in prep.). Starting
from this field catalogue we select galaxies with no photometric flags that
lie within the footprint of the JWST PRIMER survey and have estimated dust
masses and far-infrared luminosities that ensure they are less actively star-
forming than our SMG sample: $M_{\rm dust}$ $=$ 107—108 M⊙ and $L_{\rm IR}$
$=$ 1011—1012 L⊙. We then bin the redshift distribution of the SMGs and field
galaxies in $\Delta z$ $=$ 0.5 bins and in each bin we rank the field galaxies
based on their stellar masses. We then determine the number of SMGs for each
bin and select ten times as many field galaxies from the corresponding
redshift bin, starting with the most massive and going down the stellar-mass
ranked list. In this way, we construct a control sample that accurately
matches the redshift distribution of our SMG sample and comprises the most
massive galaxies at each epoch that have dust masses and far-infrared
luminosities below those determined for the SMG population. We adopt the
photometry and magphys SED fitting results from Dudzevičiūtė et al. (2020). In
Figure 3, we show the distribution of physical properties for the UDS field
sample in comparison to the SMGs. By construction, the field sample has
similar redshift and specific star-formation rates to the SMG sample, whilst
having significantly lower dust masses and AV. The field sample has a median
redshift and median absolute deviation of $z$ = 2.5 $\pm$ 0.1, whilst their
specific star-formation rates are sSFR = $-$8.88 $\pm$ 0.04 $\rm yr^{-1}$ and
AV = 0.90 $\pm$ 0.03. The field sample is fainter in F444W magnitude with a
median value of $m_{\rm F444W}$ = 22.74 $\pm$ 0.10 compared to $m_{\rm F444W}$
= 21.70 $\pm$ 0.30, which is reflected in the distributions of stellar mass.

###  3.6 Morphological Analysis

In Figure 1 we show NIRCam F277W/F356W/F444W colour images of the SMGs,
highlighting the diverse range of rest-frame optical – near-infrared
morphologies from faint and red galaxies, interacting and merging systems to
disks and grand-design spirals. These near-infrared observations sample the
galaxy population at $\leq$1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in the
rest frame at $\approx$ 1 kpc resolution and thus provide insights into the
structure and morphology of the stellar continuum emission which are much less
affected by dust than previously possible.

We first visually assess the morphologies of the SMGs and the field sample. In
addition, to quantify the rest-frame near-infrared morphology of the SMGs and
field galaxies, we employ both a non-parametric and parametric analysis of the
JWST observations. We exclude the HST observations from our morphological
analysis because at the median redshift of our sample ($z$ $\sim$2.7), HST
observations are sensitive to the rest-frame UV/optical emission of the
galaxies where SMGs are inherently faint. The longer wavelength HST
observations sampling the observed frame
1.6$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ emission is also well covered by
higher signal to noise JWST observations.

The parametric and non-parametric analysis of the JWST imaging employs
4$\aas@@fstack{\prime\prime}$0 $\times$ 4$\aas@@fstack{\prime\prime}$0 cutouts
of each source with pixel scales of 0$\aas@@fstack{\prime\prime}$04 per pixel.
The cutout in each filter is centred on the source detection in NIRCam long-
wavelength (F277W+F356W+F444W) stacked image, as detailed in Section 3.2. We
first smooth the source segmentation map generated from sep (see Section 3.2)
using the binary dilation routine in photutils (Bradley et al., 2022). Then,
excluding this segmented region, we mask the remaining sources in the cutout,
down to a 1$\sigma$ isophote. This ensures full masking of any contaminants
(spurious or otherwise). We further use photutils to model (and remove) the
background level in each cutout as well as to quantify the root-mean-square
(rms) noise. In the following sections “cutout” refers to these
4$\aas@@fstack{\prime\prime}$0 $\times$ 4$\aas@@fstack{\prime\prime}$0,
background subtracted and masked image that is used in the morphological
analysis that follows.

Prior to measuring the morphology of the galaxies we first derive the point
spread function (PSF) for each of the JWST bands. We use webbpsf (version
1.2.1; Perrin et al. 2014) to generate PSF models for the MIRI and NIRCam
detectors (for both short- and long-wavelength channels) which are calibrated
with wavefront models at the epoch of the observations. The PSFs for each
NIRCam and MIRI filter are then inserted into individual exposures of the
final mosaic and drizzled to the final world coordinate system solution,
producing a field of view averaged PSF model.

####  3.6.1 Visual Morphology

We undertake a crude initial assessment of the visual morphology of the SMGs
compared to a similar subset of the field sample. This involved interactive
inspection of both the colour images and galfit residual maps in the F444W
band (Figure 1 & 5) of the ALMA counterpart to identify distorted
morphologies, asymmetric structures or potential tidal features. In addition,
we assessed the presence of companions (either within $\sim$1 mag in
brightness of the target galaxy, or fainter) within a wider
10$\aas@@fstack{\prime\prime}$0 $\times$ 10$\aas@@fstack{\prime\prime}$0
region (out to a radius of $\sim$30kpc). Strongly disturbed galaxies, those
with tidal features or disturbed galaxies with bright companions were classed
as “major” mergers (these are marked in Figure 1), while less disturbed
galaxies or those with asymmetries and fainter companions were classed as
potential “minor” mergers.

####  3.6.2 Non-Parametric Morphology

To measure the half-light radii of the SMGs, we employ a curve of growth
approach that invokes no assumptions about the underlying structure to the
galaxy’s light distribution. We adopt this approach because SMGs have long
been assumed to originate from merger-driven events with clumpy unstable gas-
rich disks, (e.g., Smail et al., 1998; Greve et al., 2005; Tacconi et al.,
2008; Engel et al., 2010) and therefore the galaxy’s morphology may deviate
from simple parametric profiles.

We first perform a curve of growth analysis in each of the JWST bands from
0.9$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ to
18$\text{\,}\mathrm{\SIUnitSymbolMicro m}$. This is achieved by fitting a
Gaussian profile to the cutout of each galaxy, allowing the centroid ($x,y$),
axis ratio ($b/a$) and position angle (PA) to vary. We note the original
centroid of the cutout is derived from the sep source detection on the stacked
F277W+F356W+F444W NIRCam bands (Section 3.2), and thus may not be the apparent
centre of the galaxy at shorter wavelengths. A curve of growth is then derived
in each band using ellipses which align to the galaxy’s axis ratio and
position angle. From the curve of growth, we measure the convolved radii
containing 20, 50 and 80 per cent of the flux of each galaxy. The intrinsic
radii of the galaxies are derived by de-convolving the sizes with the PSF in
each band, measured through a similar curve of growth analysis.

To provide more quantitative, non-parametric, morphological indicators, we use
the statmorph444https://statmorph.readthedocs.io/en/latest/ code (Rodriguez-
Gomez et al., 2019) which measures the Concentration, Asymmetry and Clumpiness
(C, A, S; Abraham et al. 2003; Lotz et al. 2008) parameters that quantify how
concentrated, asymmetrical and clumpy the galaxies’ surface brightness
profiles are, with higher values indicating more concentrated, asymmetric, or
clumpier light profiles. We run statmorph on both SMG and field samples in all
JWST bands using the same segmentation maps and PSFs as for the growth curve
analysis described above.

In addition, the Gini and M20 parameters are also derived (for full
definitions see Lotz et al. 2004; Snyder et al. 2015). Briefly, the Gini
parameter defines the pixel distribution of the galaxy’s light, where $G$ = 1
corresponds to all of the light concentrated in one pixel whilst $G$ = 0
indicates each pixel contributes equally. The M20 parameter measures the
second moment of the brightest 20 percent of pixels in the galaxy. This is
normalised by the total moment for all pixels. Highly negative values indicate
a high concentration of light, not necessarily at the centre of the galaxy. To
validate the robustness of the statmorph measurements we compare the half-
light radius to that derived from our growth curve analysis. We derive a
median growth curve to statmorph median half-light radius ratio of $R_{\rm
h,GC}$ / $R_{\rm h,statmorph}$ = 1.06 $\pm$ 0.01 with a 16th – 84th percentile
range of $R_{\rm h,GC}$ / $R_{\rm h,statmorph}$ =0.93 – 1.45 for the field
sample in the F444W band. This indicates good agreement between the two
independent morphological measurements555We note however we expect some
variation between the two methods due to the definitions of centroid and total
fluxes used (see Lotz et al. 2004).

Figure 4: The distribution of NIRCam colours (F200W$-$F444W versus
F090W$-$F200W) (a), MIRI colours (F770W$-$F1800W versus F444W$-$F770WW) (b)
and F444W AB magnitude as a function of redshift (c), with lines of constant
stellar mass overlaid. A representative error bar is indicated in the lower-
right corner of each panel. Panel a) demonstrates the SMGs are much redder
than the field population, as expected. Panel b) highlights that a fraction of
SMGs and field galaxies may in fact host AGN with a very red F770W$-$F1800W
colour and bluer F444W$-$F770W indicating a strong upturn in the SED beyond
rest-frame 3$\text{\,}\mathrm{\SIUnitSymbolMicro m}$. We label the “AGN” and
star-forming galaxy (“SFG”) regions in the colour space adapted from
Kirkpatrick et al. (2013, 2017). We note the F770W$-$F1800W $>$ 1 colour can
also be driven by the 6.2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ PAH feature
detected in the F18000W filter at $z$ $\sim$ 1.9. Panel c) demonstrates that
the SMGs are the most massive (brightest) galaxies at their epoch with field
selected to be the most massive low far-infrared luminosity galaxies.

####  3.6.3 Parametric Morphology

To quantify both the parametric morphological profiles of the galaxies and the
deviations from these, we use the galfitm code (Häußler et al., 2013). galfitm
is a Python-wrapper for galfit (Peng et al., 2010), that allows multi-
component parametric models to be fit to a galaxy’s multi-wavelength light
distribution. For our analysis we use a single Sérsic model, convolved with
the PSF of the relevant JWST band. We fit each band independently thus
allowing us to constrain the intrinsic wavelength dependence of the galaxy’s
morphology.

To constrain the accuracy of the parametric analysis, we compare the galfitm
Sérsic index ($n$) to that derived by statmorph for the field galaxies in the
NIRCam F444W band. We establish a median ratio of $n_{\rm F444W,GalfitM}$ /
$n_{\rm F444W,statmorph}$ = 1.00 $\pm$ 0.01 and a 16th – 84th percentile range
of $n_{\rm F444W,GalfitM}$ / $n_{\rm F444W,statmorph}$ = 0.81 – 1.26,
indicating good agreement between the two independent codes.

Although a parametric Sérsic fit can model the overall distribution of a
galaxy’s light profile, it is the deviations from this simple profile
(residuals) that encode important information about the detailed structure of
the galaxies. To quantify the residuals we use the residual flux fraction
(RFF), as defined in Hoyos et al. (2011, 2012),

$\rm RFF\,=\,\frac{\sum_{i,j\in
A}|I_{i,j}\,-\,I_{i,j}^{model}|\,-\,0.8\,\times\,\sum_{i,j\in
A}\,\sigma_{Bkg\,i,j}}{\sum_{i,j\in A}I_{i,j}}$ (1)

where the sum is performed over all pixels within 2.5 times the Kron radius,
as derived in Section 3.2. $\rm|I_{i,j}\,-\,I_{i,j}^{model}|$ is the absolute
value of pixel $i,j$’s residuals to model Sérsic model fit, whilst
$\sum_{i,j\in A}I_{i,j}$ indicates the total flux measured in the source as
defined in Section 3.2. The 0.8 factor multiplied by the sum over the
background rms of the region ($\sigma_{Bkg\,i,j}$), ensures that a blank image
with constant variance has a RFF = 0.0 (see Hoyos et al. (2012) for details).

It is well known that morphological codes such as galfitm and statmorph
systemically underestimate the uncertainties on the derived morphological
parameters (e.g., van der Wel et al., 2012, 2024). To overcome this we employ
an empirical approach which utilises the unique wavelength coverage of the
NIRCam observations in the PRIMER Survey. Specifically, the majority of field
galaxies (816/850) and SMGs (75/80) in our sample have both F410M and F444W
observations. The F410M is a medium band filter covering the observed-frame
3.8 – 4.3$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ emission, whilst the wide-
band F444W filter is sensitive to the 3.8 –
4.9$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ emission. Thus, for each galaxy
with observations in both filters, we can make two independent measures of the
galaxy’s morphology at very similar rest-frame wavelengths. Analysing the
variance in morphological parameters between the two filters as a function of
signal-to-noise allows us to infer a representative uncertainty on the
morphological parameters at a given wavelength for each source given its
signal-to-noise in that band. We use this conservative approach to quantify
the uncertainties in the following analysis.

Figure 5: For both SMGs (left) and field galaxies (right) we show the examples
of the F356W/F277W/F115W RGB-colour image. For the SMGs we overlay the ALMA
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ 11$\sigma$ contour (purple) from
Stach et al. (2019) or Simpson et al. (2020). In the lower panel of each
source, we show the residuals of the galfitm single Sérsic model fit. The blue
ellipse marks the region within which we calculate the residual flux fraction
(RFF) of the Sérsic fit, as quantified in the lower-left corner of each panel.
The galaxies are selected to have an F444W AB magnitude of $m_{\rm F444W}$ =
20 – 22 and are ranked from low-to-high RFF. No clear distinction is
identified in the F444W RFF values between the SMGs and field galaxies.

##  4 Results and Discussion

From an initial sample of 88 SMGs, we have constructed a sample of 80 non-
lensed SMGs with reliable (S/N $>$ 4.5) ALMA
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ detections and multi-wavelength
HST and JWST coverage from 0.4 – 18 $\text{\,}\mathrm{\SIUnitSymbolMicro m}$.
Full details of the wavelength coverage for the individual SMGs in our sample
are given in Appendix A. From the initial sample, we omitted two strongly
lensed SMGs due to uncertainties on the photometry and structural properties
introduced by the lensing configuration of each source. Identifying 2 $\pm$
2$\%$ of SMGs in our sample are affected by foreground galaxy lensing matches
the prediction of Chapman et al. (2002), that between 3 and 5 per cent of
submm sources identified in blank-field SCUBA observations would be affected
by lensing.

For the 60 SMGs with HST coverage, we detect no F160W counterpart at S/N $<$ 3
in 10 sources. All of them have clear near-infrared counterparts in the NIRCam
F444W band at S/N $>$ 5, whilst three also have a S/N $>$ 3 in the NIRCam
F150W band. This leaves seven “NIR-faint” (sometimes imprecisely described as
“HST-dark”) SMGs with no detection in the $H$-band (S/N $<$ 3). These seven
SMGs have significant levels of dust attenuation as derived from magphys with
AV $>$ 3.9. This indicates that whilst the significant dust content of these
galaxies can lead to their dark nature in HST observations, it is also driven
by the lack of sensitivity and depth of previous observations.

Of the 78 SMGs with NIRCam-SW coverage, we identify one galaxy, AS2UDS0346.0
at $z$ = 4.1, that is undetected (S/N $<$ 3) blueward of
2.7$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and is first detected by JWST in
the F277W band at S/N $\geq$ 5\. From our magphys analysis we derive
significant dust attenuation with AV = 5.1 for AS2UDS0346.0 with a stellar
mass of $\log_{10}(M_{\ast}[M_{\odot}])$ = 11.2 that is representative of our
sample. For SMGs with suitable NIRCam coverage we identify detections (S/N $>$
3) in F090W for 59% (43/73), in F150W for 87% (68/78) and in F200W for 96%
(70/73) of the sources respectively. All have S/N $>$ 3 detections in the
NIRCam-LW and MIRI bands.

In Figure 4 we investigate the photometric properties of the SMGs in the JWST
bands by comparing the NIRCam and MIRI colours. Specifically, in Figure 4a we
compare the NIRCam F200W$-$F444W colour with the F090W$-$F200W colour. At the
median redshift of the SMG and field galaxies, these filters sample the rest-
frame $UVJ$ regime of the galaxies’ spectral energy distributions,
highlighting the distinct red nature of the SMGs compared to the general
field. Given this nature, it may be possible by colour selection to identify
the JWST counterpart to the sub-millimetre bright SCUBA-2 source without
requiring higher resolution ALMA observations (e.g., Alberts et al., 2013;
Chen et al., 2016; An et al., 2018; Hwang et al., 2021). To investigate this,
for each SMG we compare the NIRCam F200W – F444W colour of all sources
detected in the 14.8 arcsecond SCUBA-2 beam to that of the ALMA-selected SMG.
In 51% (41/80) of the SCUBA-2 observations, the ALMA source represents the
reddest source in the beam. This indicates that whilst colour is a good
identifier of SMGs, further information such as proximity to beam centre,
predicted 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ fluxes and multi-
wavelength observations from infrared to radio are required to isolate the
exact near-infrared counterpart (e.g., Downes et al., 1986; Ivison et al.,
2002; Hodge et al., 2013; Casey et al., 2013; Gillman et al., 2023).

Figure 4b compares the MIRI and NIRCam colours with the F770W$-$F1800W colour
shown as a function of F444W$-$F770W colour. At the median redshift of the SMG
and field galaxies, these filters sample the rest-frame near and mid-infrared.
The SMGs on average have redder F444W$-$F770W colours with comparable
F770W$-$F1800W colours to the field population, reflecting the dust
attenuation of the shorter wavelength light. The SMGs and field galaxies which
exhibit very red F770W$-$F1800W colours with bluer F444W$-$F770W colour may
indicate the presence of Active Galactic Nuclei (AGN) as noted by Ivison et
al. (2004) who used MIPS/24$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and IRAC
colours to identify AGN and starburst galaxies. We highlight the regions of
the colour diagram that an ”AGN” or star-forming galaxy (“SFG”) would likely
inhabit, adapted from Kirkpatrick et al. (2013, 2017). Of those with MIRI
coverage, we identify 24 $\pm$ 5% (69/282) of the field galaxies have near-
infrared colours that may indicate the presence of AGN activity whilst for the
SMGs we establish a lower fraction of 3 $\pm$ 1% (2/37). The two SMGs with
“AGN” like colours, AS2UDS0259.0 and AS2UDS0659.0, both exhibit extended
morphologies in the MIRI F770W and F1800W observations with no visible point
source, indicating any contribution from an AGN is minimal. This is in
agreement with previous studies which identify the AGN contribution in SMGs to
be small (e.g., Stach et al., 2019). The one SMG with a compact, point-source
like morphology, AS2UDS0173.0, is not covered by the MIRI observations. The
SFG and AGN classification in Figure 4b does not fully encapsulate the bi-
modality present in the colour space, especially in the field galaxies.
Galaxies with F1800W$-$F770W$>$1 and F444W$-$F770W$<$0, represent a bright
($m_{\rm F444W}$ = 21.5 $\pm$ 0.1) lower redshift subset ($z$ = 1.9 $\pm$
0.04) with significantly brighter F1800W emission ($m_{\rm F1800W}$ = 20.3
$\pm$ 0.1) compared to the “bluer” population ($z$ = 2.9 $\pm$ 0.1, $m_{\rm
F444W}$ = 22.9 $\pm$ 0.1, $m_{\rm F1800W}$ = 23.3 $\pm$ 0.1). At $z$ = 1.9,
the F1800W filter is sensitive to the 6.2$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ PAH feature, which can strongly enhance the mid-infrared emission in
massive galaxies, resulting in red F770W$-$F1800W colours (e.g., Draine et
al., 2007; Aniano et al., 2020; Shivaei et al., 2024).

In Figure 4c we show the correlation between NIRCam F444W magnitude and the
redshift of the galaxies. We overlay lines of constant stellar mass,
highlighting that the SMGs are the most massive galaxies at their epoch
(Dudzevičiūtė et al., 2020) with the field selected to massive with lower far-
infrared luminosity.

###  4.1 Near-Infrared Morphology

While SMGs have long been known to exhibit complex, potentially merger-like,
morphologies based on rest frame $UV$ imaging (e.g., Smail et al., 1998;
Chapman et al., 2004; Swinbank et al., 2010; Aguirre et al., 2013) the
influence of dust has meant the true stellar morphologies are still unknown.
The combination of near-infrared colour images (Figure 1) and F444W Sérsic fit
residual maps (Figure 5) provides an unprecedented insight into the embedded
stellar structures and asymmetries in the SMGs.

For 21/80 SMGs, from a visual inspection, we identify clear spiral or tidal
arm features in the Sérsic model residuals, as well as clear clumpy structures
in 30 $\pm$ 4% (24/80) of the SMGs. In particular, one galaxy AS2UDS0259.0,
shows a clear bar-like structure in the F444W image indicating complex multi-
phase structures may be present, similar to those identified in recent JWST
and ALMA studies (e.g., Hodge et al., 2019; Smail et al., 2023; Rujopakarn et
al., 2023; Liu et al., 2023).

We estimate that 40 $\pm$ 10% (32/80) of the SMGs are isolated systems, with
no strong perturbations or obvious neighbours on $\simeq$20 – 30 kpc
(projected) scales, while 16 SMGs (20 $\pm$ 5%) in our sample have potential
companions or are interacting with another massive galaxy suggesting major
mergers, the remaining 32 SMGs (40 $\pm$ 10%) have faint companions and show
signs of disturbance (e.g., asymmetries in the galfit F444W residuals) that
suggest potential minor interactions and mergers. The median far-infrared
luminosity of the candidate major mergers is $L_{\rm IR}$ $=$ 1012.53±0.05
$L_{\odot}$, compared to $L_{\rm IR}$ $=$ 1012.49±0.05 $L_{\odot}$ for the
remainder of the sample, indicating no strong dependence of far-infrared
luminosity on merger state (e.g., Hopkins et al., 2010). Indeed, an equivalent
visual classification of the less active field sample returns very similar
merger statistics with 25 $\pm$ 5% of the sample showing evidence for
potential major mergers and the remaining $\sim$ 75% showing much weaker or no
evidence for merger-related disturbance or companions on $\simeq$ 20–30 kpc
scales. This similarity in the rate of mergers between SMGs and less active
galaxies is consistent with the theoretical results from the eagle simulation
from McAlpine et al. (2019) who found that simulated SMGs had similar rates of
recent mergers to less active galaxies, in part because most galaxies at high
redshifts are undergoing continuous infall and merging.

Figure 6: The correlation between a) stellar mass and half-light radius, and
d) the Clumpiness ($S$) and Asymmetry ($A$) for the SMG and field sample in
the NIRCam F444W filter. In each panel we show histograms of each parameter
for the field (open grey) and SMG sample (red histograms). In panel a) we also
overlay the mass size relation for 2$<$ $z$ $<$3 star-forming galaxies from
Ward et al. (2024) and in panel d) the relation between Asymmetry and
Clumpiness identified by Conselice et al. (2003). In panels b) and c) we show
the distributions of Sérsic index ($n$) and axis ratio ($b/a$) in the F444W
band. For each distribution, we display the KS probability ($p_{\rm KS}$) that
the two distributions are drawn from the same parent population, where $p_{\rm
KS}$ $<$ 0.001 suggests a significant difference in the distributions. We plot
the bootstrap median and uncertainty for the two distributions at the top of
each panel. The SMGs, on average, have comparable sizes ($p_{\rm KS}$ = 0.06)
and lower Sérsic indexes ($p_{\rm KS}$ $<$ 0.001) than less active field
galaxies, whilst exhibiting similar axis ratios ($p_{\rm KS}$ = 0.16) and
clumpiness ($p_{\rm KS}$ = 0.02) with higher asymmetry ($p_{\rm KS}$ $<$
0.001).

To summarise, while signs of potential dynamical disturbance are frequently
seen in our SMG sample, we conclude that the majority of SMGs do not appear to
be the result of late-stage, major mergers. This is in contrast with the
situation for similar far-infrared luminous populations at $z$ $\sim$ 0, where
systems with far-infrared luminosities of $L_{\rm IR}$ $\geq$ 1012 L⊙ are
frequently associated with late-stage major mergers (e.g., Sanders et al.,
1988; Farrah et al., 2001), although there are claims that this fraction
declines at $z$ $\sim$ 1 (e.g., Kartaltepe et al., 2010), with an increasing
fraction of starburst galaxies appearing to be isolated systems (e.g., Faisst
et al., 2024). It is also in contrast to early studies of SMGs with resolved
CO kinematics (e.g., Engel et al., 2010) as well near-infrared spectroscopic
observations (e.g., Alaghband-Zadeh et al., 2012; Drew et al., 2020) which
suggested that the majority of SMGs are mergers, with distinct separated dust-
detected components. There are at least two such examples in our sample of
SCUBA-2 sources, AS2UDS0322 and AS2COS0034, and one ALMA source (AS2UDS0071.0)
that comprise multiple ALMA-detected, or NIRCam-F444W detected, galaxies that
show clear signs of galaxy interactions with AS2COS0034 comprising two SMGs
that are both detected in [Cii] emission at $z_{\rm[CII]}$ = 4.62 (Mitsuhashi
et al., 2021).

Figure 7: Top: The growth curve half-light radius ($R_{\rm h}$) of the SMGs,
normalised by the rest-frame 1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ half-
light radius of the respective galaxy as a function of rest-frame wavelength
and colour-coded by the galaxy integrated AV. We show individual measurements
for SMGs, and a representative error bar, as well as the running median for
the field sample. Bottom: Sérsic index derived from the galfitm parametric
fitting as a function of rest-frame wavelength. We indicate the NIRCam
measurements by circles and MIRI measurements by squares. We show a running
median, and standard error ($\sigma/\sqrt{n}$) in fixed logarithmic bins of
wavelength for the SMGs and field galaxies. In both panels, we plot the
parametric fit for the field (solid grey line) and SMGs (solid red line). We
find that the SMGs, on average, have a stronger size variation with
wavelength, becoming more compact at longer wavelengths quicker than field
galaxies, whilst exhibiting lower Sérsic index at all wavelengths.

####  4.1.1 Sizes, Sérsic Indices and Axis Ratios

We measure the half-light radius of the SMGs and field galaxies in the F444W
band, determining median values of $R_{\rm h}$ = 2.70 $\pm$ 0.23 kpc and
$R_{\rm h}$ = 2.50 $\pm$ 0.10 with 16th – 84th percentile ranges of $R_{\rm
h}$ = 1.82 – 4.36 kpc and $R_{\rm h}$ = 1.64 – 3.76 kpc respectively. To
establish whether the SMGs and field galaxies are drawn from the same
underlying distribution, we perform a Kolmogorov-Smirnov (KS) test on the mass
normalised distributions of half-light radius. To mass normalise the half-
light radius distributions, we adopt the rest-frame optical mass size relation
from Ward et al. (2024) at 2$<$ $z$ $<$3\. From the median stellar mass of the
field galaxies to the median stellar mass of the SMG sample, we derive an
increase in half-light radius of 27 $\pm$ 6%, which we apply to the field
galaxies’ half-light radii to account for the offset in stellar mass between
the two samples. For the non-Gaussian distributions of SMG and field galaxy
morphological properties, we require $p_{\rm KS}$ $\leq$ 0.003 ($>$3 $\sigma$)
to confirm the populations are inherently different. We conclude the SMGs and
field galaxies have indistinguishable distributions of mass normalised half-
light radius with $p_{\rm KS}$ = 0.06.

In Figure 6 we show the correlation between stellar mass and F444W half-light
radius for both field and SMGs. We overlay the rest-frame optical mass size
relation for star-forming galaxies at 2$<$ $z$ $<$3 from Ward et al. (2024).
On average, the field galaxies follow the trend identified by Ward et al.
(2024), whilst the SMGs, as indicated by the running median in Figure 6,
exhibit marginally smaller F444W sizes for stellar masses above
$\rm\log_{10}(M_{\ast}[M_{\odot}])$ $>$ 10.5. We note however, the majority of
galaxies used to define the mass size relation in Ward et al. (2024) have a
stellar mass of $\log_{10}(M_{\ast}[M_{\odot}])$ $<$ 10.5. In panel b) of
Figure 6, we compare the distribution Sérsic index for the field sample to
those of the SMGs, identifying more disc-like Sérsic indices for the SMGs with
a median of $n_{\rm F444W}$ = 1.10 $\pm$ 0.10 and a 16th – 84th percentile
range of $n_{\rm F444W}$ = 0.63 – 1.98 whilst the field galaxies have a higher
median value of $n_{\rm F444W}$ = 1.85 $\pm$ 0.07 with a 16th – 84th
percentile range of $n_{\rm F444W}$ = 0.88 – 4.35. Applying a KS test, we
identify the two distributions are distinctly different with a $p_{\rm KS}$
$<$ 0.001.

From our non-parametric analysis, we derive a median axis ratio of $b/a$ =
0.55 $\pm$ 0.03 for the SMGs and a 16th – 84th percentile range of $b/a$ =
0.37 – 0.82 in the NIRCam F444W band. This is comparable to the axis ratio
distribution for 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ dust continuum in
SMGs with $b/a$ = 0.63 $\pm$ 0.02 (Gullberg et al., 2019). For the field
galaxies, we derive a median F444W axis ratio of $b/a$ = 0.53 $\pm$ 0.01 and
16th – 84th percentile range $b/a$ = 0.31 – 0.77. The distribution of axis
ratios, as shown in Figure 6, is comparable to that of the SMGs with $p_{\rm
KS}$ = 0.16. The SMGs distribution reflects more that of the disk+spheroid
classification found in recent optical studies of high-redshift galaxies
(e.g., Kartaltepe et al., 2023; Pandya et al., 2024) with a median value of
$b/a$ = 0.51 and 16th – 84thpercentile range of $b/a$ = 0.35 – 0.68.

####  4.1.2 Residuals, Clumpiness and Asymmetry

Whilst the Sérsic profiles indicate more disc-like surface brightness
distributions for the SMGs, it is the deviations from the parametric light
profiles, as quantified by the RFF parameter, that encodes the unique
morphological properties of each galaxy. In Figure 5, we show examples of the
NIRCam F444W Sérsic model residuals, and the derived RFF values, for both SMGs
and field galaxies. Whilst some galaxies exhibit smooth residuals, and low RFF
values, several galaxies (both SMGs and field) display complex morphologies
with multiple clumps, spiral arms or bright compact point sources. For the
SMGs we identify a median RFF value in the F444W band of RFFF444W = 10.2 $\pm$
0.5 with a 16th – 84th percentile range of RFFF444W = 5.9 – 16.3 whilst the
field galaxies have a median value of RFFF444W = 8.5 $\pm$ 0.2 with a 16th –
84th percentile range of RFFF444W = 4.5 – 17.2. We compare the distributions
of RFF for SMGs and field galaxies finding a KS-statistic of $p_{\rm KS}$ =
0.002, indicating the are distinguishable at $>$3$\sigma$ level.

Although the 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ ALMA observations of
the majority of the SMGs in our sample are not high enough resolution (FWHM
$\leq$ 0$\aas@@fstack{\prime\prime}$2) to identify these structural features,
high-resolution sub-millimetre studies have identified spiral arms, bars and
star-forming rings embedded in exponential dust disks (e.g. Hodge et al.,
2019; Amvrosiadis et al., 2024). For a subset of the SMGs (15/80), however,
0$\aas@@fstack{\prime\prime}$2 resolution ALMA
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ observations are available as
presented in Gullberg et al. (2019). These resolved observations are
insufficient to identify complex dust structures, but the resolved
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ emission’s morphology provides
insight into any underlying structural features. For these 15 SMGs we first
compare the ALMA 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ size measured in
the $uv$-plane to the F444W growth curve size. We estimate a median ratio of
$R_{\rm h}^{\rm F444W}\,/\,R_{\rm h}^{\rm
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}\,$ = 2.7 $\pm$ 0.4 with a 16th –
84thrange of $R_{\rm h}^{\rm F444W}\,/\,R_{\rm h}^{\rm
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}\,$ = 1.5 – 3.5. As identified by
previous studies the far-infrared emission is much more compact than the
emission at bluer wavelengths (e.g. Simpson et al., 2015; Lang et al., 2019;
Gullberg et al., 2019). We perform a Spearman rank test on the correlation
between F444W/870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ size ratio and the
AV of the galaxy, identifying no significant correlation ($p_{\rm SR}$ =
0.33). However, a larger sample is required to robustly conclude the lack of
correlation.

To investigate the presence of complex dust structures we compare the
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ axis ratio and position angle to
that derived for the F444W emission. For the
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ emission we adopt the free Sérsic
fitting parameters from Gullberg et al. (2019). We identify median ratios of
$b/a_{\rm F444W}\,/\,b/a_{\rm 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}\,$
= 0.95 $\pm$ 0.11 and $PA_{\rm F444W}\,/\,PA_{\rm
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}\,$ = 0.94 $\pm$ 0.12, indicating
good agreement in the alignment of the near-infrared (rest-frame $\approxeq$
1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) and far-infrared (rest-frame
$\approxeq$ 250$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) emission, suggesting
they are tracing the same underlying structure, in contrast to the UV/optical
and far-infrared offsets identified in previous multi-wavelength high-
resolution studies (e.g., Chen et al., 2015; Calistro Rivera et al., 2018;
Hodge et al., 2019).

In panel d) of Figure 6, we show the correlation between asymmetry ($A$) and
clumpiness ($S$) in the NIRCam F444W band as derived from statmorph and over
plot the relation between $A$ and $S$ derived by Conselice et al. (2003)666The
relation is corrected for the different definitions of clumpiness given by
Lotz et al. (2004) and Conselice et al. (2003). We identify the SMGs and field
galaxies have similar clumpiness with a median value of $S_{\rm F444W,SMGs}$ =
0.02${}^{+0.03}_{-0.02}$ and $S_{\rm F444W,field}$ = 0.03${}^{+0.04}_{-0.04}$
respectively with a $p_{\rm KS}$ = 0.02, indicating they are broadly
consistent with being drawn from similar distributions. The asymmetry in the
F444W band for the SMGs is higher with a median value of $A_{\rm F444W,SMGs}$
= 0.13${}^{+0.09}_{-0.06}$ compared to the field galaxies ($A_{\rm
F444W,field}$ = 0.08${}^{+0.12}_{-0.06}$) and a $p_{\rm KS}<$ 0.001,
indicating the two distributions are distinct.

The correlation between asymmetry and clumpiness highlights two clear regions.
At constant asymmetry, there are two populations, one at low clumpiness ($S$
$<$ 0.04) and one at high clumpiness ($S$ $>$ 0.04), where the majority of the
SMGs and field galaxies have low clumpiness with smooth, symmetric light
distributions whilst those galaxies at high clumpiness show signs of
concentrated star-forming regions. The SMGs at $S$ $>$ 0.04 are more compact
in the F444W filter with a median size of $R_{\rm h}$ = 1.72 $\pm$ 0.14 kpc
compared to the SMGs with lower clumpiness ($S$ $<$ 0.04) with a median size
of $R_{\rm h}$ = 2.96 $\pm$ 0.25 kpc, whilst exhibiting comparable other
morphological and magphys derived properties. We note that several studies
have highlighted the uncertainty introduced in non-parametric morphological
measurements when the Petrosian radius of the galaxy ($R_{\rm p}$) is
comparable to the FWHM of the observations (e.g., Yu et al., 2023; Ren et al.,
2024), especially when the clumpiness parameter is measured between
0.25$R_{\rm p}$ and 1.5$R_{\rm p}$, see Lotz et al. (2004) for details.

###  4.2 Wavelength Dependent Morphology

Figure 8: We show the Gini – M20 relation for the field galaxies (grey dots
and contours) and SMG sample (red circles), in the a) F200W and b) F444W bands
as well as histograms showing the distribution of each parameter on each axis.
The solid-black line indicates the boundary line between mergers and non-
mergers as defined in Lotz et al. (2008). Both SMGs and field galaxies scatter
about the line in the F200W band whilst the majority lie in the non-merger
region of the equivalent F444W plot. In panels c) and d) we show the
distributions of M${}_{\rm 20}^{\rm F444W}$ $-$ M${}_{\rm 20}^{\rm F200W}$ and
RFFF444W $-$ RFFF200W. For each distribution, we indicate the KS-statistic
showing that the SMGs have a stronger variation in morphology with wavelength
with higher RFF and M20 values at 2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$
than 4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ indicating more structure in
the residuals and disturbed morphologies.

The preceding analysis of the SMGs and field galaxies stellar (near-infrared)
morphologies has revealed broad similarities between the two populations. Many
previous studies suggest the extreme properties of SMGs originate from merger-
driven events (e.g., Smail et al., 1998; Swinbank et al., 2010; Aguirre et
al., 2013). We do not expect the morphological signatures of these mergers to
show wavelength dependence in contrast to the effects of dust. Thus, by
quantifying the morphological variation with wavelength in the field and SMG
sample, we can test the legitimacy of the merger-driven scenario.

For the SMGs and field galaxies we measure a median F200W half-light radii of
$R_{\rm h,F200W}$ = 4.0 $\pm$ 0.3 kpc and $R_{\rm h,F200W}$ = 2.8 $\pm$ 0.1
kpc respectively. Compared to the F444W, for the SMGs this represents a 48%
reduction in size between 2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ whilst for the field galaxies the
reduction in size is only 11%, although we note this comparison is not done at
fixed stellar mass it highlights the variation of morphology with wavelength
for the two samples. To further investigate the variation in the SMGs and
field galaxy morphology as a function of wavelength, in Figure 7 we correlate
the half-light radius, normalised by the rest-frame
1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ half-light radius, and Sérsic index
with the rest-frame wavelength probed by the NIRCam and MIRI observations.

Below 1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$, for SMGs in Figure 7 there is
increased spread in half-light radius with an apparent correlation with dust
content quantified by AV. At rest-frame wavelengths greater than
3$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ where we use the MIRI F770W and
F1800W bands to quantify the morphology, we identify a decrease in the median
Sérsic index of both field and SMGs to $n$ $\sim$ 0.4 and an increase in the
half-light radius. We suspect this trend is driven by the larger beam size of
the MIRI observations with FWHM = 0$\aas@@fstack{\prime\prime}$27 and
0$\aas@@fstack{\prime\prime}$59 respectively for the F770W and F1800W filters,
in addition to the shallower depth compared to the NIRCam observations,
resulting in a more smoothed, less-structured, light distribution. In
addition, in the rest-frame near-infrared ($>$
3$\text{\,}\mathrm{\SIUnitSymbolMicro m}$) any AGN component that is present
in the galaxy starts to be more prominent over the stellar emission, with
point-source ($n$ $\sim$ 0.5) morphology.

To quantify the field galaxy and SMGs size evolution with wavelength, we
perform fits to the median values shown in Figure 7 up to rest-frame
3$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ using an orthogonal distance
relation (ODR) algorithm that takes into account the uncertainties on the
median values in both wavelength and size. We define the function as,

$\frac{R(\lambda)}{R_{1$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$}}\,=\,R_{0}+\frac{d(R_{\rm h}/R_{1$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$})}{d\lambda}\log_{10}(\lambda),$ (2)

where $\lambda$ is the rest-frame wavelength probed by the observations. For
the SMGs we derive a slope of $\frac{d(R_{\rm
h}/R_{1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$})}{d\lambda}$ = $-$0.60 $\pm$
0.09 and R0 = 1.02 $\pm$ 0.02, whilst for the field galaxies we estimate
$\frac{d(R_{\rm h}/R_{1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$})}{d\lambda}$
= $-$0.15 $\pm$ 0.07 and R0 = 1.02 $\pm$ 0.01. This indicates the SMGs have
stronger variation in size with wavelength, becoming more compact faster than
typical field galaxies, as highlighted by the best-fit solution plotted in
Figure 7. However, this trend may be driven by centrally concentrated dust
inflating the rest-frame optical sizes of the SMGs resulting in a stronger
observed variation with wavelength. To ensure size ($R_{\rm h}$) variation
with wavelength identified in the SMGs and field galaxies in Figure 7 is not
driven by the redshift evolution of the galaxies, in Appendix C, we correlate
the rest-frame 1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ size of the galaxies
with their redshift. On average we identify a consistent redshift evolution in
the near-infrared sizes of the SMGs and field galaxies, indicating redshift is
not driving the morphological wavelength variation.

Figure 9: A comparison of the 2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ morphological properties of the SMGs
and field galaxies. We compare the difference in M20 parameter between the
F444W and F200W bands (M${}^{\rm F444W}_{\rm 20}$ $-$ M${}^{\rm F200W}_{\rm
20}$) with dust attenuation (AV) in panel a). In panel b), we further compare
the difference in RFF between the F444W and F200W bands ($\rm
RFF^{F444W}-RFF^{F200W}$) with the difference in Asymmetry ($A^{\rm
F444W}-A^{\rm F200W}$). Finally we plot the difference in M20 between F444W
and F200W (M${}_{\rm 20}^{\rm F444W}$ $-$ M${}_{\rm 20}^{\rm F200W}$) with the
difference in Concentration (CF444W $-$ CF200W) (panel c) and the difference
in RFF (panel d). All four panels indicate the SMGs are much more structured
than the field population, with less uniform light distributions in the F200W
compared to the F444W band, in contrast, the field galaxies show minimal
wavelength variation.

Furthermore Figure 7 shows the SMGs, on average, have a lower Sérsic index
than the field galaxies at all wavelengths. To quantify the evolution of
Sérsic index with wavelength we fit a similar relation to that used to
quantify the size evolution of the form,

$n(\lambda)\,=\,n_{0}+\frac{dn}{d\lambda}\log_{10}(\lambda),$ (3)

up to a rest-frame wavelength of 3$\text{\,}\mathrm{\SIUnitSymbolMicro m}$.
The median Sérsic index of the SMGs have an $\frac{dn}{d\lambda}$ = $-$0.12
$\pm$ 0.11 and $n_{0}$ = 1.0 $\pm$ 0.04, whilst the field galaxies exhibit
strong variation with wavelength, but at higher average Sérsic index
($\frac{dn}{d\lambda}$ = $-$1.10 $\pm$ 0.23 and $n_{0}$ = 1.51 $\pm$ 0.10).
Thus indicating on average, the SMGs have less centrally peaked light
distributions, which may further be an indication of the central dust
obscuration.

To further investigate the variation of morphology with wavelength in the SMG
and field samples, in Figures 8a & b, we show the Gini – M20 relation which
has been used as a crude late-stage merger indicator (Lotz et al., 2008; Liang
et al., 2024; Polletta et al., 2024) in the F200W and F444W bands. We select
the F444W band as this most closely traces the stellar morphology of the
galaxies, whilst F200W band corresponds to the rest-frame $V$-band for the
median redshift of the samples, at a similar wavelength to the $R$-band where
the Gini – M20 “merger” and “non-merger” boundary was calibrated by Lotz et
al. (2008). At 2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (rest-frame $V$-band)
both field and SMG samples scatter about the boundary between “merger” and
“non-merger”, with 40 $\pm$ 5% of the SMGs lying in the merger region. The
SMGs are offset relative to the field though with higher M20 and lower Gini
values. At 4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (rest-frame $z$-band)
almost all SMGs (92 $\pm$ 2%) and field galaxies lie in the “non-merger”
region of the relation, with consistent Gini and M20 values. Between
2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ the relative shift in the Gini – M20
parameter space is larger for the SMGs than the field galaxies.

To understand the origin of this shift in the Gini-M20 plane, in Figure 8c we
show the difference between the M20 parameter in the F444W and F200W bands.
This plot highlights that the SMGs have higher M20 in the F200W than F444W
band which indicates SMGs have less concentrated F200W morphologies whilst the
field galaxies have more similar M20 values between the two bands. The
significance of the difference between the field and SMGs is further indicated
by the KS-statistic value of $p_{\rm ks}$ $<$ 0.001. To further highlight the
reduction in structured emission between the F200W and F444W bands, in Figure
8d we show the difference between RFF in the two bands for the SMGs and field
galaxies. On average the SMGs exhibit a greater difference in RFF across
bands, with more significant F200W residuals, with a median value of RFFF444W
$-$ RFFF200W = $-$10.0 $\pm$ 1.0 with a 16th – 84th percentile range of
RFFF444W $-$ RFFF200W = 2.0 – 17.4 whilst for the field galaxies the median is
RFFF444W $-$ RFFF200W = $-$4.6 $\pm$ 0.3 with a 16th – 84th percentile range
of RFFF444W $-$ RFFF200W = 0.2 – 11.6. This is further evidence of the dust
obscuration at shorter wavelengths in the SMGs, resulting in deviations from a
simple light profile. This comparison suggests the SMGs have more complex
morphologies at bluer wavelengths, which is likely to be linked to their
intense star formation rates and the presence of highly structured dust in the
SMGs, attenuating the shorter wavelength light.

To identify the physical mechanism driving the increase in structured emission
identified in the SMGs (as quantified by the RFF and M20) as a function of
wavelength, in Figure 9 we compare the difference in morphological parameters
measured between the F444W and F200W NIRCam bands for the SMGs and field
galaxies. In Figure 9a we compare the dust content, as quantified by the AV
from SED fitting (Section 3.2), with M${}_{20}^{\rm F444W}$ $-$ M${}_{20}^{\rm
F200W}$. As shown in Figure 3, the field galaxies have significantly lower AV
and less morphological variation with wavelength, with a median M${}_{20}^{\rm
F444W}$ $-$ M${}_{20}^{\rm F200W}$ = 0.06 $\pm$ 0.01. The SMGs on the other
hand, with higher AV indicate a greater disparity between the F200W and F444W
light distribution with a median value of M${}_{20}^{\rm F444W}$ $-$
M${}_{20}^{\rm F200W}$ = 0.34 $\pm$ 0.04. To quantify the trend between AV and
M${}_{20}^{\rm F444W}$ $-$ M${}_{20}^{\rm F200W}$ we perform an ODR fit to the
running median shown in Figure 9 of the form,

${\rm A}_{V}\,=\,{\rm A}_{V,0}+\alpha({\rm M}_{20}^{\rm F444W}-{\rm
M}_{20}^{\rm F200W}),$ (4)

We determine for the SMGs best-fit parameters of $\alpha$= $-$1.0 $\pm$0.3 and
AV,0 = 3.1 $\pm$ 0.1, indicating a strong negative correlation for the SMGs,
whereby more dust obscured (higher AV) SMGs, have a more negative
M${}_{20}^{\rm F444W}$ $-$ M${}_{20}^{\rm F200W}$, indicating less
concentrated light profiles in the F200W band compared to the F444W.

To analyse the connection to other morphological parameters, in Figures 9b & d
we plot RFFF444W $-$ RFFF200W against the difference in Asymmetry (AF444W $-$
AF200W) and M${}_{20}^{\rm F444W}$ $-$ M${}_{20}^{\rm F200W}$, whilst in
Figure 9c we compare the difference in Concentration (CF444W $-$ CF200W) with
M${}_{20}^{\rm F444W}$ $-$ M${}_{20}^{\rm F200W}$. All three relations
indicate that on average the SMGs in the F200W band are more asymmetric and
less concentrated, with more in-homogeneous light distributions leading to
larger residuals to a single Sérsic fit at
2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ as compared to their
4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ morphologies.

###  4.3 Does structured dust drive the distinction between field and SMGs?

The morphological properties of the SMGs in the NIRCam F444W band are
comparable to the field galaxies, with similar sizes at a fixed mass, slightly
lower Sérsic indices and higher asymmetry (Figure 6). The F444W filter traces
the rest-frame near-infrared ($\approx$1$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$) out to $z$ $\sim$ 3.5, and thus is less affected by dust obscuration and
recent star formation than shorter bands in most of our sample. A greater
difference between SMGs and field galaxies is identified at bluer wavelengths.

Figure 10: a) We plot the average F200W $-$ F444W colour of the faintest
pixels (below 80th percentile of flux) inside 0$\aas@@fstack{\prime\prime}$5
elliptical apertures in the F444W image for the SMGs and field galaxies, as a
function of the average colour for the top 20 per cent brightest F444W pixels.
The field galaxies exhibit almost uniform colours between faint and bright
regions, with a small offset to the equality line of 0.12 $\pm$ 0.03 mag (in
the sense that the brightest pixels are redder), whilst the SMGs are both
generally redder in fainter regions and significantly redder (1.11 $\pm$ 0.09
mag) in their brightest regions. In panel b) we show the average F200W $-$
F444W colour of the “Brightest 20%” and “Faintest 80%” pixels as a function of
ALMA pixel brightness. The brightest regions in the near-infrared (NIRCam
F444W), which have the reddest F200W $-$ F444W colour, correspond to the
brightest regions in the far-infrared (ALMA
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$).

By investigating the variation M20 parameter and RFF between the NIRCam F444W
band ($\lambda_{\rm rest}\approx$ 1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$)
and F200W band ($\lambda_{\rm rest}\approx$
0.5$\text{\,}\mathrm{\SIUnitSymbolMicro m}$), Figures 8 and 9 highlight that
the SMGs have more structured light profiles at shorter wavelengths, that
results in larger residuals to single Sérsic fits of the light distribution.
This morphological variation with wavelength was also highlighted by Chen et
al. (2016) for SMGs and Nedkova et al. (2024) for SFGs, identifying that the
most massive (M∗ $\gtrsim$1010M⊙) disc galaxies in their sample at 0.5 $<$ $z$
$<$ 3 have larger half-light radii in the rest-frame ultra-violet than
optical, which they attribute to the significant dust attenuation in the
central regions of the galaxies compared to the outskirts. A similar
connection between with inferred galaxy morphology and dust content was
identified in the Illustris – The Next Generation (TNG50; Pillepich et al.,
2019) simulation by Popping et al. (2022). They suggested that the observed
$H$-band to 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ size ratio increases
towards higher redshift (hence bluer rest-frame sampling) due to dust
attenuating the central regions of galaxies, resulting in larger half-light
radii in the $H$-band. The impact of dust on size measurements has also been
quantified in the First Light And Reionisation Epoch Simulations (FLARES;
Lovell et al., 2021; Vijayan et al., 2021), where intrinsically massive
compact galaxies appear significantly more extended when the effects of dust
are taken into account (Roper et al., 2022, 2023).

To isolate the contribution of dust to the SMGs morphological evolution as a
function of wavelength, we examine the F200W $-$ F444W pixel colours. In
particular, given the M${}_{20}^{\rm F444W}$ $-$ M${}_{20}^{\rm F200W}$
parameter indicates the greatest morphological difference between field
galaxies and SMGs, we calculate the average colour of the brightest 20 percent
of pixels in the F444W image inside the 0$\aas@@fstack{\prime\prime}$5
elliptical apertures of each galaxy (Section 3.2). In Figure 10a, for both
SMGs and field galaxies, we compare this “Brightest 20%” colour with the
average colour of the fainter regions inside the same aperture (‘Faintest 80%’
F200W $-$ F444W). Galaxies exhibiting no strong colour gradients between
bright and faint regions will have consistent “Brightest 20%” and “Faintest
80%” colours, lying close to the one-to-one line. The majority of the field
galaxies, as shown in Figure 10a, fall into this regime, with on average the
brightest regions of the field galaxies being 0.12 $\pm$ 0.03 mag, redder than
the faintest.

For the SMGs, the F200W $-$ F444W pixel colour of the fainter regions that
comprise the bulk of the galaxies (“Faintest 80%”) indicate on average redder
colours, with a median colour of 0.4 $\pm$ 0.06 mag compared to $-$0.74 $\pm$
0.02 mag for the field galaxies. For the “Brightest 20%” pixel colour, the
SMGs indicate significantly redder colours with a median value of 0.77 $\pm$
0.06 mag compared to $-$0.66 $\pm$ 0.02 mag for the field galaxies. To
understand whether the reddest (and brightest) regions of the SMGs are
physically associated with the dust content, and thus
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ emission, of the galaxies we
analyse high-resolution ALMA 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$
observations for a sub-sample of 15 SMGs with ALMA maps from Gullberg et al.
(2019), having a synthesised beam of FWHM
$\leq$0$\aas@@fstack{\prime\prime}$2.

We resample the ALMA maps to match the 0$\aas@@fstack{\prime\prime}$04 pixel
scale of the JWST NIRCam F444W imaging. We then extract the same average
“Brightest 20%” and “Faintest 80%” F200W $-$ F444W pixel colour as before for
each SMG. In Figure 10b, we correlate this pixel colour with the ALMA
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel brightness for the
“Brightest 20%” and “Faintest 80%” pixels. We identify a strong correlation
between F200W $-$ F444W pixel colour and
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ surface brightness, demonstrating
that the reddest colour that originates from the brightest regions of the
SMGs, is physically associated with the brightest regions of the
870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ emission and thus high dust column
density regions.

####  4.3.1 Dust Content and the Interstellar Medium of SMGs

A high dust column density in the SMGs, as Figure 10 implies, would suggest
that the optical to near-infrared emission of the SMGs is strongly attenuated.
Consequently, physical properties estimated from the SED fitting (e.g. AV) may
be uncertain due to heavily obscured regions of the galaxies being undetected.
We can derive the expected $V$-band extinction (AV) given the median dust mass
($\rm\log_{10}(M_{d}[M_{\odot}])$ = 8.9 $\pm$ 0.2) derived from SED fitting
(Sec 3.2) and compare this to the AV derived by magphys from fitting the
optical to near-infrared SED. As shown by Güver & Özel (2009), the column
density of hydrogen (in cm-2) can be approximated from the AV (in mag) as
follows,

$N_{H}\,=\,2.21\,\times 10^{21}\,{\rm A}_{V}\,$ (5)

Adopting a dust-to-gas ratio of $\delta$ = 63 $\pm$ 7 as derived by (Birkin et
al., 2021), for SMGs with typical metallicity, star-formation rates and
stellar masses (e.g., Rémy-Ruyer et al., 2014) and assuming the F444W half-
light radius provides an upper-limit on the physical extent of the dust
region, we obtain a lower-limit on the median $V$-band dust attenuation of AV
= 110 $\pm$ 20\. This is two orders of magnitude higher than that derived from
the SED fitting of SMGs with the median magphys estimated value of AV = 3.4
$\pm$ 0.16. For the AV derived from magphys, which constrains the dust
obscuration of the visible stars, an energy balance calculation is assumed
such that far-infrared emission is broadly consistent with the absorbed
stellar light of the system (Battisti et al., 2019). This assumption assumes
the UV/optical and far-infrared emission are co-spatial and well mixed
however, inaccuracies can arise as detectable optical emission does not encode
information about the ongoing obscured star formation of the galaxy (e.g.,
Simpson et al., 2017; Buat et al., 2019; Haskell et al., 2023; Killi et al.,
2024). In the derivation of AV from the dust mass, which defines the dust
obscuration of the deepest regions of the clouds, we have estimated a Compton
thick HI column where the dust is uniformly distributed in a smooth “disk-
like” component as identified in the high-resolution ALMA studies of SMGs
(e.g., Hodge et al., 2016; Gullberg et al., 2019). However, numerical studies
suggest that the star dust geometry plays a crucial role in determining the
attenuation curve of the galaxies (e.g., Inoue, 2005; Sachdeva & Nath, 2022;
Vijayan et al., 2024) as well as the metallicity of the interstellar medium
(e.g., Shivaei et al., 2020).

With such high levels of inferred dust obscuration, and intense star formation
rates, the question remains what are underlying interstellar medium conditions
that give rise to these extreme physical properties in the SMGs. To infer the
properties of the interstellar medium we compare the surface density of star
formation, ($\Sigma_{\rm SFR}$), to the gas surface density ($\Sigma_{\rm
gas}$) i.e., the density of fuel for star formation. For the SMGs, we use the
gas mass derived above, the star-formation rate from magphys and the F444W
half-light radius as a conservative estimate of the physical extent of the gas
content. For the field sample, we use the magphys derived dust masses with a
median value of $\rm\log_{10}(M_{d}[M_{\odot}])$ = 7.7 $\pm$ 0.1, which are
consistent with the dust mass inferred from converting the
$S_{870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$}$ limit, derived from stacks
in S2CLS UDS 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ map (Geach et al.,
2017), to a dust mass using the $S_{870$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$}$ to dust mass relation defined in Dudzevičiūtė et al. (2020). Adopting
the metallicity-dependent dust-to-gas ratio from Tacconi et al. (2018) for
massive star-forming galaxies and following the mass metallicity relation
defined in Genzel et al. (2015), we derive a median dust-to-gas ratio of
$\delta$ = 163 $\pm$ 32 which equates to a median gas mass of
$\rm\log_{10}(M_{g}[M_{\odot}])$ = 9.8 $\pm$ 0.1 for the field galaxies.

Combining this gas mass estimate for the field with the magphys derived star-
formation rates and F444W half-light radius, in Figure 11 we show the relation
between $\Sigma_{\rm SFR}$ and $\Sigma_{\rm gas}$ for both the field sample
and SMGs. Given the higher star-formation rates and dust masses of the SMGs
(Figure 3) and their comparable sizes in the F444W band to the field galaxies
(Figure 6), the SMGs have considerably higher star-formation rate surface
density and gas surface density. However, both field galaxies and SMGs have
comparable time scales for star formation, lying close to the 0.1 Gyr star
formation time scale.

Figure 11: The relation between star-formation rate surface density and gas
surface density for the field sample (grey points and contour) and SMGs (red
circles). We indicate a constant star-formation time scale of 0.1 Gyr with the
black line. Adopting the typical rotation velocity and velocity dispersion
from Birkin et al. (2023) derived for a sample of AS2UDS SMGs, we define the
boundary between stable ($Q$ $>$ 1) and unstable ($Q$ $<$ 1) gas disks. The
majority of the SMGs indicate unstable gas disks with a median Toomre $Q$
parameter of $Q$ = 0.47 $\pm$ 0.06.

By estimating the Toomre Q parameter (Toomre, 1964) we can place constraints
on the interstellar medium properties of the galaxies, in particular on the
stability of the gas disk. The Toomre Q is defined as,

$Q\,=\,\frac{\sigma\kappa}{\pi G\Sigma_{\rm gas}}$ (6)

where $\sigma$ is the radial velocity dispersion, $\kappa$ is the epicylic
frequency, for which we adopt $\kappa$ = $\rm\sqrt{2}V/R$ appropriate for a
galaxy with a flat rotation curve and $\rm\Sigma_{gas}$ is the gas surface
density. For the rotation velocity and velocity dispersion, we adopt the
median values from Birkin et al. (2023), for a sample 31 SMGs in the AS2UDS
survey, with comparable median redshift and stellar mass to our sample ($z$
$\sim$ 1.3 – 2.6, $\rm\log_{10}(M_{*}[M_{\odot}])$ = 11.11 $\pm$ 0.06). Birkin
et al. (2023) derive a median rotation velocity and velocity dispersion of
$V_{\rm circ}$ = 230 $\pm$ 20 km s-1 and $\sigma$ = 87$\pm$ 6 km s-1.

Adopting the F444W half-light radius as an estimate of the extent of the gas
disk, we can derive the gas-surface density required for a quasi-stable gas
disk, identifying a threshold value of $\log_{10}(\Sigma_{\rm gas}$) = 2.64
$\pm$ 0.05 $\rm M_{\odot}pc^{-2}$. This implies the gas disk is unstable to
collapse ($Q$ $<$ 1) for gas-surface densities higher than this value. We
estimate that the majority of the SMGs lie in this region of “instability”
with a median Toomre $Q$ parameter of $Q$ = 0.47 $\pm$ 0.06. Given the F444W
half-light radius provides a lower limit on the extent of gas disk, to
generate a quasi-stable interstellar medium in the SMGs, we require larger
rotation velocity or velocity dispersion. Requiring that the gas disk is
quasi-stable i.e Q $\geq$ 1, we derive a lower limit on the radial velocity
dispersion required for stability. Adopting the rotation velocity from Birkin
et al. (2023), we derive a median velocity dispersion for stability of
$\sigma_{\rm stable}$ $\geq$ 200 $\pm$ 30 km s-1 which is significantly larger
than that derived for ionised gas in previous studies of high redshift SMGs or
U/LIRGS (e.g. Hogan et al., 2021; Birkin et al., 2023; Amvrosiadis et al.,
2024), suggesting that the gaseous disks of the SMGs in our sample are
significantly unstable to gravitational collapse.

###  4.4 Implications for the nature of SMGs

The SMG and field samples share several characteristics. By construction, they
have similar number densities as a function of redshift and specific star
formation rates. Furthermore, we have demonstrated they have similar rates of
mergers and signatures of disturbance, with comparable rest-frame near-
infrared axis ratios and mass normalised stellar continuum (F444W) sizes. This
suggests that the major structural components in both populations comprise
(randomly orientated) disks that broadly follow the size-mass relation for
disk galaxies at $z$ $\sim$ 2 – 3. The similarity in the merger fractions for
the SMGs and field is consistent with the theoretical investigation of SMGs in
the EAGLE simulation by McAlpine et al. (2019), who concluded that there was
no difference in merger statistics of the SMGs and the general population,
instead most galaxies at these redshifts were undergoing minor or major
mergers.

However, there are several distinctions between the SMGs and less-active field
galaxies. The dust-mass-selected SMGs have much higher AV and asymmetry, and
they show stronger variations in their morphologies at bluer wavelengths,
indicating the presence of structured and centrally concentrated dust.
Moreover, the field has an average Sérsic index of $n$ $\sim$ 1.9, indicating
the potential presence of a bulge component in these systems. The SMGs have
consistently lower Sérsic index, with a median of $n$ $\sim$ 1.1, indicating
they are nearly pure exponential disks or that any bulge component if present
is invisible at rest-frame $\sim$1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$.
Either of these interpretations suggests that any bulge component in the SMGs
is of low mass compared to the disk or is likely to be young and so only
recently formed.

We also infer more than an order of magnitude higher molecular gas surface
densities for the SMGs than the field. These differences suggest that one
possible cause for a distinction between SMGs and less active galaxies arises
from the less developed bulge components present in the SMGs. Consequently,
their gas disks are more sensitive to developing low-order disk instabilities,
including $m$ = 1 bars (e.g., Marinova & Jogee, 2007; Pettitt & Wadsley,
2018). These instabilities can either be triggered by external perturbations
from major or minor mergers or tidal interactions, or from secular
instabilities in the dense gas disks. These structures, as predicted by
theoretical models (e.g., Fragkoudi et al., 2021; Bland-Hawthorn et al., 2023)
and identified in recent studies of individual high-redshift SMGs (e.g., Smail
et al., 2023; Amvrosiadis et al., 2024) serve to funnel gas from the dense gas
disk into the central regions of the galaxies, driving a central starburst
that creates both the compact sub-millimetre emission we see and the
corresponding highly obscured central regions of these systems.

##  5 Conclusions

We present a multi-wavelength morphological analysis of a complete sample of
SMGs from the AS2UDS and AS2COSMOS surveys (Stach et al., 2019; Simpson et
al., 2020) with $>$4.5$\sigma$ ALMA 870$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ detections and positions. Utilising the public JWST/NIRCam and MIRI
imaging from the PRIMER survey, we build a sample of 80 SMGs, determining
their multi-wavelength properties through a SED and morphological analysis. We
further define a redshift and specific star-formation rate matched sample of
less active and more typical $K$-band selected star-forming field galaxies in
the UDS field and analyse the differences between the two populations. Our
main conclusions are:

  * •

We identify F444W counterparts to 99% (87/88) of the ALMA-detected SMGs at
$m_{\rm F444W}$ = 20.3 – 23.1, showing that the vast majority of galaxies
hosting intense, dusty starbursts are detectable by JWST. Of those 87, we
identify two SMGs with morphologies indicative of strong galaxy-galaxy
lensing, a rate consistent with early estimates. Removing these lensed SMGs,
in addition to a further six sources with partial NIRCam coverage, one
spurious ALMA source and deblending one ALMA source into two NIRCam sources
results in a final sample of 80 SMGs which have clear NIRCam counterparts.

  * •

The SMGs have significantly redder F200W$-$F444W and F444W$-$F770W colours
than the field sample, with comparable F090W$-$F200W and F770W$-$F1800W. We
identify 24 $\pm$ 5% of the field galaxies and 3 $\pm$ 1% of the SMGs show red
F770W$-$F1800W combined with blue F444W$-$F770W colours, potentially
indicating the presence of AGN or a strong
6.2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ PAH feature present in the F1800W
filter at $z$ $\sim$ 1.9.

  * •

From visually inspecting the F277W/F356W/F444W colour images of the SMGs we
identify 20 $\pm$ 5% as candidate major mergers, a further 40 $\pm$ 10% as
potential minor mergers and the remaining 40% are isolated systems with no
obvious neighbours on $\simeq$20 – 30 kpc (projected) scales. We find no
dependence of the visual classification on far-infrared luminosity. These
statistics are very similar to the rates determined for the field sample and
demonstrate that the majority of SMGs are not ongoing major mergers, although
mergers (major or minor) and disturbed appearances are common in both the SMGs
and the less active field population at these redshifts.

  * •

Through a parametric and non-parametric morphological analysis, we determine
the SMGs and field galaxies exhibit similar rest-frame near-infrared axis
ratios and mass-normalised half-light radii with $R_{\rm h}$ = 2.7 $\pm$ 0.2
kpc and $R_{\rm h}$ = 3.1 $\pm$ 0.1 kpc for the SMGs and field respectively,
lying slightly below the rest-frame optical mass size relation at their epoch.

  * •

The SMG and field populations are more distinct in their detailed morphologies
in terms of Sérsic index ($n$) and Asymmetry ($A$) in the F444W band, with the
SMGs having lower Sérsic indices and higher Asymmetry ($n_{\rm F444W}$ = 1.1
$\pm$ 0.1, $A_{\rm F444W}$ = 0.13 $\pm$ 0.02) compared to the field galaxies
($n_{\rm F444W}$ = 1.9 $\pm$ 0.1, $A_{\rm F444W,}$ = 0.08 $\pm$ 0.01).

  * •

A similar disparity between the SMGs and typical star-forming galaxies is seen
in the variation of their morphologies as a function of wavelength. The size
of the SMGs declines more rapidly at longer wavelengths than field galaxies
($\delta(R_{\rm h}/R_{1$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$})/\delta\lambda$ = $-$0.60 $\pm$ 0.09 versus $\delta(R_{\rm
h}/R_{1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$})/\delta\lambda$ = $-$0.15
$\pm$ 0.07). Furthermore the SMGs exhibit lower Sérsic indices at all
wavelengths with $n_{0}$ = 1.0 $\pm$ 0.04 compared to the field galaxies
($n_{0}$ = 1.51 $\pm$ 0.10). The SMGs also exhibit a greater scatter in
morphology at bluer wavelengths that is likely to originate from both their
structured dust content and higher star formation rates compared to the field
galaxies.

  * •

A comparison of the Gini – $M_{20}$ relation for the SMGs and field sample at
2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (rest-frame $V$-band) and
4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (rest-frame $z$-band) underlines the
variation in morphology as a function of wavelength, with 40% of the SMGs
lying in the merger region (as defined at $z$ $=$ 0 in the rest-frame
$R$-band) at 2$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ whilst only 8% do so at
4$\text{\,}\mathrm{\SIUnitSymbolMicro m}$.

  * •

We establish that the variation of the $M_{20}$ and residual flux fraction
(RFF) parameter between the F200W and F444W NIRCam bands provides a clear
distinction between SMGs and field galaxies with a median value of RFFF444W
$-$ RFFF200W = $-$10.0 $\pm$ 1.2 for the SMGs whilst for the field galaxies
the median is RFFF444W $-$ RFFF200W = $-$4.6 $\pm$ 0.3. This demonstrates that
the F200W light-distributions of the SMGs are more structured, relative to
their appearance in F444W, resulting in greater residuals and M20 values
compared to the field galaxies.

  * •

To identify the cause of this behaviour, we explore the internal F200W $-$
F444W colour gradients of the galaxies. The SMGs are generally redder than the
field galaxies as expected, but crucially the brightest regions in F444W are
1.1 $\pm$ 0.1 magnitudes redder than than the fainter regions (this offset is
three times larger than that seen in the field population) indicating the
presence of centrally concentrated starbursts. We further determine the
brightest and reddest regions of the SMGs in the NIRCam imaging correspond to
the highest surface brightness emission at 870
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ seen by ALMA, indicating a strong
connection between the colour and the dust content of the galaxy.

  * •

To understand the physical origin of the difference in morphologies between
the SMGs and the field galaxies, we assume a representative gas-to-dust ratio
to define the relation between star-formation rate surface density and gas
surface density, suggesting that the SMGs have significantly higher gas
surface densities than field galaxies. The SMGs on average fall in the
unstable ($Q$ $<$ 1) regime with a median Toomre $Q$ parameter of $Q$ = 0.47
$\pm$ 0.06.

Our analysis indicates that SMGs and typical star-forming galaxies appear
morphologically distinct in the rest-frame optical due to the higher dust
content of the SMGs, which preferentially influences the central regions of
the galaxies. Whilst at longer wavelengths, sampling the rest-frame near-
infrared, the SMGs and less active field galaxies show more similar mass-
normalised sizes, although the SMGs exhibit lower Sérsic parameters,
suggesting they have weaker bulge components. Both the SMGs and field control
samples have comparable rates of candidate mergers and undisturbed galaxies,
suggesting that mergers are not a unique driver of the activity in SMGs.
Instead, we suggest that the higher gas surface densities and weaker bulge
components, coupled with the perturbations caused by either major or minor
mergers, as well as secular processes, lead to correspondingly more intense
star-formation activity in the SMGs, compared to the field. Thus the defining
characteristic of SMGs maybe their massive and gas-rich nature, coupled with
relatively underdeveloped bulge components and correspondingly low black hole
masses.

###### Acknowledgements.

We would like to thank the PRIMER team for designing and executing the
observations upon which this work is based. The observations analysed in this
work are made with the NASA/ESA/CSA James Webb Space Telescope (DOI:
10.17909/z7p0-8481) SG acknowledges financial support from the Villum Young
Investigator grants 37440 and 13160 and the Cosmic Dawn Center (DAWN), funded
by the Danish National Research Foundation (DNRF) under grant No. 140. IRS and
AMS acknowledge STFC grant ST/X00107511. BG acknowledges support from the
Carlsberg Foundation Research Grant CF20-0644 ‘Physical pRoperties of the
InterStellar Medium in Luminous Infrared Galaxies at High redshifT: PRISM-
LIGHT’. TRG is grateful for support from the Carlsberg Foundation via grant
No. CF20-0534. YM acknowledges support of JSPS KAKENHI Grant Numbers
JP17KK0098, JP22H01273 and JP23K22544. C.-C.C. acknowledges support from the
National Science and Technology Council of Taiwan (NSTC 111-2112M-001-045MY3),
as well as Academia Sinica through the Career Development Award (AS-
CDA-112-M02). Cloud-based data processing and file storage for this work is
provided by the AWS Cloud Credits for Research program. The data products
presented herein were retrieved from the Dawn JWST Archive (DJA). DJA is an
initiative of the Cosmic Dawn Center, which is funded by the Danish National
Research Foundation under grant No. 140

## Software

Astropy (Astropy Collaboration et al., 2013, 2018), Photutils (Bradley et al.,
2022), Source Extractor (Bertin & Arnouts, 1996b) SEP (Barbary et al., 2016)
Eazy-py (Brammer & Matharu, 2021) GriZli (Brammer et al., 2022) GalfitM
(Häußler et al., 2013) Statmorph (Rodriguez-Gomez et al., 2019) Topcat
(Taylor, 2005)

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## ORCIDs

Steven Gillman  0000-0001-9885-4589
Ian Smail  0000-0003-3037-257X
Bitten Gullberg  0000-0002-4671-3036,
A. M. Swinbank  0000-0003-1192-5837
Aswin P. Vijayan  0000-0002-1905-4194,
Gabe Brammer  0000-0003-2680-005X
Thomas R. Greve  0000-0002-2554-1837
Omar Almaini  0000-0001-9328-3991
Malte Brinch  0000-0002-0245-6365
Chian-Chou Chen  0000-0002-3805-0789
Wei-Hao Wang  0000-0003-2588-1265
Yuichi Matsuda  0000-0003-1747-2891
Fabian Walter  h0000-0003-4793-7880
Paul P. van der Werf  0000-0001-5434-5942

## Appendix A: SMG Properties

The table summarising the SMG properties is available online only.

## Appendix B: SEDs

Figure 12: For each SMG we plot the multi-wavelength photometry (red points)
and magphys derived SED fit (gold line), where arrows indicates the limits.
Beneath each SED we show histograms of the magphys probability density
functions of redshift, stellar mass and attenuation in $V$-band. We also
display the JWST and ALMA 870$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ imaging
for each source, with the derived photometric redshift and reduced chi-squared
of the fit in the top right corner.

Figure 13: Continued….

Figure 14: Continued….

Figure 15: Continued….

Figure 16: Continued….

Figure 17: Continued….

Figure 18: Continued….

## Appendix C: Rest-Frame Near-Infrared Sizes

Figure 19: The rest-frame 1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ half-light
radius for SMGs (red circles) and field galaxies (grey dots) as a function of
redshift ($a$) and stellar mass ($b$). In each panel, we show a running median
for SMGs (dashed blue line) and field galaxies (black dashed line) as well as
a representative uncertainty. We identify a consistent reduction in rest-frame
1$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ size with increasing redshift in
both field and SMG sample, as well as a consistent mass size relation to
Figure 6. This indicates the morphology variation with wavelength identified
in both samples in Figure 7 is not driven by redshift.