figuret

# Resolving a dusty, star-forming SHiZELS galaxy at $\mathbf{z=2.2}$ with
_HST_ , ALMA and SINFONI on kiloparsec scales

R. K. Cochrane,1,2 P. N. Best,2 I. Smail, 3 E. Ibar, 4 C. Cheng, 5,6,4 A. M.
Swinbank,3J. Molina, 7 D. Sobral, 8 U. Dudzevičiūtė3
1Harvard-Smithsonian Center for Astrophysics, 60 Garden St. Cambridge, MA
02138, USA
2SUPA, Institute for Astronomy, Royal Observatory Edinburgh, EH9 3HJ, UK
3Centre for Extragalactic Astronomy, Department of Physics, Durham University,
South Road, Durham DH1 3LE, UK
4Instituto de Física y Astronomía, Universidad de Valparaíso, Avda. Gran
Bretaña 1111, Valparaíso, Chile
5Chinese Academy of Sciences South America Center for Astronomy, National
Astronomical Observatories, CAS, Beijing 100101, China
6CAS Key Laboratory of Optical Astronomy, National Astronomical Observatories,
Chinese Academy of Sciences, Beijing 100101, China
7Kavli Institute for Astronomy and Astrophysics, Peking University, 5 Yiheyuan
Road, Haidian District, Beijing 100871, P.R. China
8Department of Physics, Lancaster University, Lancaster, LA1 4YB E-mail:
<EMAIL_ADDRESS>
(Accepted 2021 February 10. Received 2021 February 10; in original form 2020
August 21)

###### Abstract

We present $\sim 0.15^{\prime\prime}$ spatial resolution imaging of
SHiZELS-14, a massive ($M_{*}\sim 10^{11}\,\rm{M_{\odot}}$), dusty, star-
forming galaxy at $z=2.24$. Our rest-frame $\sim 1\rm{kpc}$-scale, matched-
resolution data comprise four different widely used tracers of star formation:
the $\rm{H}\alpha$ emission line (from SINFONI/VLT), rest-frame UV continuum
(from HST F606W imaging), the rest-frame far-infrared (from ALMA), and the
radio continuum (from JVLA). Although originally identified by its modest
$\rm{H}\alpha$ emission line flux, SHiZELS-14 appears to be a vigorously star-
forming ($\rm{SFR}\sim 1000\,\rm{M_{\odot}yr^{-1}}$) example of a
submillimeter galaxy, probably undergoing a merger. SHiZELS-14 displays a
compact, dusty central starburst, as well as extended emission in
$\rm{H}\alpha$ and the rest-frame optical and FIR. The UV emission is
spatially offset from the peak of the dust continuum emission, and appears to
trace holes in the dust distribution. We find that the dust attenuation varies
across the spatial extent of the galaxy, reaching a peak of at least
$A_{\rm{H}\alpha}\sim 5$ in the most dusty regions, although the extinction in
the central starburst is likely to be much higher. Global star-formation rates
inferred using standard calibrations for the different tracers vary from $\sim
10-1000\,\rm{M_{\odot}yr^{-1}}$, and are particularly discrepant in the
galaxy’s dusty centre. This galaxy highlights the biased view of the evolution
of star-forming galaxies provided by shorter wavelength data.

###### keywords:

galaxies: high redshift – galaxies: evolution – galaxies: starburst –
galaxies: star formation – submillimetre: galaxies – infrared: galaxies

††pubyear: 2021††volume: in press††pagerange: Resolving a dusty, star-forming
SHiZELS galaxy at $\mathbf{z=2.2}$ with _HST_ , ALMA and SINFONI on kiloparsec
scales–3

##  1 Introduction

Galaxy surveys have long shown that star-formation rates within individual
galaxies increase towards high redshift. At a given stellar mass, typical
star-formation rates increase by over an order of magnitude between the
present day and the peak of cosmic star formation at $z\sim 2$ (Sobral et al.,
2013a; Madau & Dickinson, 2014; Speagle et al., 2014). This is thought to
reflect the large reservoirs of molecular gas that cool from the high rates of
gas accretion onto galaxies’ host halos in the early universe (Tacconi et al.,
2010; Tacconi et al., 2013, 2017; Papovich et al., 2016; Falgarone et al.,
2017; Jiménez-Andrade et al., 2018; Dudzeviciute et al., 2020).
Although highly luminous dusty galaxies are rare at $z=0$ and known as ‘ultra
luminous infrared galaxies’ (ULIRGs, with total infrared luminosities
$L_{\rm{TIR}}>10^{12-13}\,\rm{L_{\odot}}$), galaxies with typical ULIRG
luminosities are more common around the peak of cosmic star formation (Smail
et al., 1997; Barger et al., 1998). Submillimeter galaxies (SMGs; Blain et al.
2002) are ULIRGs at high redshift with bright submillimeter fluxes that
suggest star-formation rates (SFRs) of $\sim 100-1000\,\rm{M_{\odot}yr^{-1}}$.
Sustained star-formation rates of this magnitude have the potential to form
massive galaxies (with stellar masses of $\sim 10^{11}\,\rm{M_{\odot}}$) on
sub-Gyr timescales (Simpson et al., 2014; Dudzeviciute et al., 2020). Chapman
et al. (2005) found that the volume density of SMGs increases by a factor of
$\sim 1000$ between $z=0$ and $z=2.5$, with the redshift distribution peaking
at $z\sim 2.0-2.5$ (see also Koprowski et al. 2014; Simpson et al. 2014;
Danielson et al. 2017; Stach et al. 2019; recent studies using larger samples
derive a redshift distribution that peaks slightly higher). SMGs at $1<z<5$
appear to account for $\sim 20-30$ per cent of the total comoving star-
formation rate density at these redshifts (Swinbank et al., 2014; Smith et
al., 2017; Dudzeviciute et al., 2020). Even in less far-infrared
(FIR)-luminous high redshift galaxies, a significant amount of star formation
is obscured by dust. Dunlop et al. (2017) combined long- and short-wavelength
data from two premier observatories: the Atacama Large Millimeter Array (ALMA,
probing the dust continuum emission at 1.3mm) and the Hubble Space Telescope
(HST, Wide Field Camera 3, probing rest-frame UV), in the well-studied Hubble
Ultra Deep Field (e.g. Bouwens et al., 2010; Oesch et al., 2010; Illingworth
et al., 2013; Dunlop et al., 2013). These complementary data enabled them to
confirm that $\sim 85$ per cent of the total star formation at $z\sim 1-3$ is
enshrouded in dust. Emission from the most massive galaxies is most highly
attenuated: for galaxies with $M_{*}\sim 5\times 10^{10}\,\rm{M_{\odot}}$,
they suggest a ratio of obscured to unobscured star formation of $\sim 50$.
However, lower mass galaxies are still affected, with the ratio decreasing to
$\sim 5$ for galaxies with $M_{*}\sim 5\times 10^{9}\,\rm{M_{\odot}}$ (see
also Magnelli et al., 2020).
While studies of wide areas are important in tracking the evolving properties
of star-forming galaxies and the build-up of stellar mass in the Universe,
understanding the physical processes of star formation within individual
galaxies requires higher angular resolution. Until recently, resolved studies
of distant star-forming (SF) galaxies tended to be based on observations from
near-infrared integral field unit spectrographs, which probe rest-frame
optical emission lines such as $\rm{H}\alpha$ and [OIII] at $z\sim 2$ (e.g.
Genzel et al., 2008; Swinbank et al., 2012a; Reddy et al., 2015; Stott et al.,
2016; Simons et al., 2017), or from HST at rest-frame UV wavelengths (e.g.
Wuyts et al., 2012; Fisher et al., 2017). These claim a physical picture in
which star formation takes place within massive clumps embedded in turbulent
disk structures (Genzel et al., 2008; Elmegreen et al., 2013; Genzel et al.,
2013; Guo et al., 2015, 2017; Soto et al., 2017). Emission at these short
wavelengths is, however, strongly attenuated by dust, and the significant
global obscuration of star formation at $z<4$ suggests that our understanding
of galaxy evolution from short-wavelength studies is likely to be highly
biased by dust, even at high spatial resolution. As such, the importance and
even the reality of these clumps has been questioned (e.g. Hodge et al., 2016,
2019; Ivison et al., 2020). Indeed, star formation in the dustiest regions of
high redshift galaxies is expected to be totally hidden from view (Simpson et
al., 2017).
Recent work made possible by new submillimeter interferometers, in particular
ALMA, which offers both high sensitivity and spatial resolution, has focused
on characterising the spatially-resolved properties of high redshift galaxies
at long wavelengths (see the recent review by Hodge & da Cunha 2020). The
spatial extent of dust emission and molecular gas has been of particular
interest in recent years. The dust continuum emission and CO emission appear
very compact for distant ($z>1$), sub-millimeter-bright galaxies, with typical
effective radii $\sim 1-2\,\rm{kpc}$ (Simpson et al., 2015; Tadaki et al.,
2016, 2017, 2018; Hodge et al., 2016, 2019; Oteo et al., 2017; Strandet et
al., 2017; Calistro Rivera et al., 2018; Lang et al., 2019; Gullberg et al.,
2019; Dudzeviciute et al., 2020). A number of studies have shown that these
sizes are comparable to the optical sizes of $z\sim 1-2$ compact quiescent
ellipticals, galaxies that must have formed a huge amount of stellar mass and
then quenched early (Krogager et al., 2014; Onodera et al., 2015; Belli et
al., 2016; Lang et al., 2019). This, together with the large estimated stellar
masses of SMGs ($M_{*}\sim 10^{11}\rm{M_{\odot}}$; Hodge et al. 2019;
Dudzeviciute et al. 2020) has fuelled speculation that the SMGs detected at
$z\sim 3-6$ are the progenitors of $z=2$ massive ellipticals (e.g. Toft et
al., 2014; Simpson et al., 2014; Oteo et al., 2017; Gómez-Guijarro et al.,
2018; Tadaki et al., 2020), possibly tracing a rapid phase of bulge-building
(e.g. Tadaki et al., 2016; Simpson et al., 2017; Nelson et al., 2019).
However, observations of compact dust continuum sizes are in contrast to the
extended, clumpy structures traced by HST imaging (Chen et al., 2015; Barro et
al., 2016; Hodge et al., 2015, 2016, 2019; Rujopakarn et al., 2019). In some
cases, kpc-scale offsets have been found between the peaks of the FIR and UV
emission (Hodge et al., 2015; Tadaki et al., 2016; Chen et al., 2017; Calistro
Rivera et al., 2018). These offsets could potentially bias interpretations of
global measurements (particularly for fits to photometry that focus solely on
the rest-frame optical to near-infrared, but also for ‘energy-balance’
spectral energy distribution fitting). Indeed, Simpson et al. (2017) argue
that attenuation in the dusty regions of SMGs is so great that essentially all
the co-located stellar emission is obscured at optical-to-near-infrared
wavelengths; for $\sim 30$ per cent of their sample, the data available at
these wavelengths is insufficient to put constraints on photometric redshifts
and stellar masses (see also work on ‘NIR-dark’ sources; e.g. Simpson et al.
2014; Franco et al. 2018; Wang et al. 2019; Dudzeviciute et al. 2020; Smail et
al. 2020)
Overall, it has become clear that drawing conclusions from single-wavelength
surveys, especially in the rest-frame UV, is subject to substantial bias and
uncertainty, even where data is at high angular resolution. In this paper, we
present multi-wavelength, $0.15^{\prime\prime}$-resolution imaging of
SHiZELS-14, a highly star-forming, $\rm{H}\alpha$-selected galaxy at $z=2.24$.
Of the ALMA-studied SHiZELS parent sample (which is presented in a companion
paper, Cheng et al. 2020), SHiZELS-14 is the most FIR luminous, with the
largest of all $\rm{H}\alpha$-derived effective radii ($4.6\pm 0.4\,\rm{kpc}$)
(Swinbank et al., 2012a, b; Gillman et al., 2019). Although its $\rm{H}\alpha$
flux is modest, it displays SMG-like dust continuum emission. Our observations
comprise matched-resolution imaging of the $\rm{H}\alpha$ emission line (from
SINFONI/VLT), rest-frame UV and optical continuum (from HST), and the rest-
frame far-infrared (from ALMA), as well as the radio continuum (from the Karl
G. Jansky Very Large Array; JVLA). We find bright, extended structures in the
multi-wavelength imaging, with clear clumps in $\rm{H}\alpha$ and extended
dust continuum emission. Given this extended structure and the high signal-to-
noise that results from its high SFR, we have been able to resolve star
formation on kpc scales at multiple wavelengths.
The structure of this paper is as follows. In Section 2, we provide an
overview of the data available for our study of SHiZELS-14. We review the high
quality, but less well-resolved multi-wavelength data available from imaging
of the COSMOS field, and present the new $0.15^{\prime\prime}$ resolution
imaging from SINFONI/VLT, HST, ALMA and JVLA. We discuss the astrometric
alignment of these data in Section 2.8. In Section 3, we present the global
properties of SHiZELS-14 that may be inferred from spectral energy
distribution (SED) fitting. In Section 4, we present maps of the spatially-
resolved SFRs inferred from different SFR indicators, and derive a spatially-
resolved dust attenuation map. In Section 5, we compare the properties of
SHiZELS-14 to the submillimeter galaxy population. In Section 6, we summarise
our results.
We assume a $\Lambda$CDM cosmology with
$H_{0}=70\,\rm{km}\,\rm{s}^{-1}\,\rm{Mpc}^{-1}$, $\Omega_{M}=0.3$ and
$\Omega_{\Lambda}=0.7$. We use a Kroupa (2002) initial mass function (IMF).

##  2 Observations and data reduction

The High-Redshift(Z) Emission Line Survey, HiZELS, used a combination of
narrow-band and broad-band filters to select star-forming galaxies via their
emission line fluxes (Sobral et al., 2013a; Sobral et al., 2015) in fields
with high-quality multi-wavelength coverage (COSMOS, UDS & SA22). This survey
has yielded thousands of $\rm{H}\alpha$ emitters at $z=0.4$, $0.8$, $1.47$ &
$2.23$, providing sufficiently large samples to constrain $\rm{H}\alpha$
luminosity functions, stellar mass functions and halo environments of typical
star-forming galaxies around the peak of cosmic star formation (Geach et al.,
2008; Sobral et al., 2009; Sobral et al., 2010, 2014; Cochrane et al., 2017,
2018).
As well as providing the sample sizes for population studies such as these,
HiZELS has also provided parent samples for more detailed follow-up
observations (Sobral et al., 2013b; Magdis et al., 2016; Stott et al., 2016;
Molina et al., 2017; Molina et al., 2019; Gillman et al., 2019). In
particular, by exploiting the wide area HiZELS coverage, a sample of bright
$\rm{H}\alpha$ emitters ($f_{\rm{H}\alpha}>0.7\times
10^{-16}\,\rm{erg}\,\rm{s}^{-1}\rm{cm}^{-2}$) which by chance lie within
$30^{\prime\prime}$ of bright natural guide stars ($R$<15) could be identified
and targeted for IFU spectroscopy of the $\rm{H}\alpha$ line using adaptive
optics with the SINFONI Integral Field Unit on the Very Large Telescope (VLT).
This campaign, known as SINFONI-HiZELS (SHiZELS), yielded high-resolution
spectral maps for $20$ galaxies at $z=0.8$, $z=1.47$ and $z=2.23$ at $\sim
0.15^{\prime\prime}$ (rest-frame $\sim 1\,\rm{kpc}$) resolution (see Swinbank
et al., 2012a, b; Molina et al., 2017; Gillman et al., 2019).
We complemented these data with imaging at similar angular resolution but
different wavelengths. Nine HiZELS galaxies were targeted at $\sim
0.2^{\prime\prime}$ resolution with ALMA (Band 6 or 7, depending on redshift),
to map the dust continuum emission (see Cheng et al. 2020). UVIS Imaging in
the rest-frame UV (F606W) and rest-frame optical (F140W) filters obtained
during HST Cycle 24 completes this dataset. We now have FIR-UV-$\rm{H}\alpha$
matched-resolution observations of a small sample of HiZELS galaxies. Since
these galaxies are $\rm{H}\alpha$-selected, they are likely to be a less
biased sub-sample of the high-redshift star-forming galaxy population than UV-
selected samples, which target the bluest and least dusty galaxies, at an
epoch where dust is important (see Oteo et al., 2015).
Here, we present data for SHiZELS-14, which is the brightest, most extended
and more extreme source in our sample. SHiZELS-14 (10:00:51:6 +02:33:34.5) is
a $z=2.24$ galaxy, with high stellar mass ($M_{*}\sim
10^{11}\,\rm{M_{\odot}}$; Swinbank et al. 2012a; Laigle et al. 2016), and a
star-formation rate of $\sim 1000\,\rm{M_{\odot}yr^{-1}}$ These properties
enable a detailed investigation of the multi-wavelength extended structures of
this galaxy. In the following subsections, we provide details of the new high-
resolution imaging we have recently obtained as part of the SHiZELS campaign.
We present new radio continuum imaging from the JVLA (at comparable angular
resolution to the other new imaging), which were obtained only for SHiZELS-14.
We also describe the existing data available for our multi-wavelength
characterisation of this galaxy.

Figure 1: Astrometrically-calibrated, high-resolution observations of
SHiZELS-14 in the rest-frame UV (HST F606W filter; upper left panel), rest-
frame optical (HST F140W filter; upper right panel), $\rm{H}\alpha$
(SINFONI/VLT; lower left) and dust continuum (rest-frame $370\,\micron$
imaging from ALMA, reduced with Briggs weighting; lower right). The red
contours on all panels outline the ALMA dust continuum emission at 50, 200,
and 300$\,\mu\rm{Jy\,beam^{-1}}$. The green contours outline the $3\sigma$
emission $\rm{H}\alpha$ emission from SINFONI as described in Section 2.1.
Pale grey contours outline the peak of the F140W image. The emission imaged by
SINFONI, ALMA and the HST F140W filter span the same extended region, but
display very different morphologies. The peaks of the short-wavelength
emission are clearly offset from the peaks of the dust continuum emission.
This is particularly striking for the F606W UV emission, which is concentrated
in regions with little dust emission and does not extend down to the southern
regions that are clearly probed by the other bands. Figure 2: Left: the HST
F140W image, with contours of the $260\,\rm{GHz}$ ALMA data with two
weightings overlaid. The image produced using natural weighting is shown with
purple contours tracing $25\,\mu\rm{Jy\,beam^{-1}}$. The red contours outline
the Briggs-weighted image ($50$, $200$, and $300\,\mu\rm{Jy\,beam^{-1}}$, as
in Figure 1). The slightly lower angular resolution natural-weighted image
shows flux towards the North East and the South West, in the regions with
extended F140W flux. This gives us confidence in the astrometric alignment of
the images. Centre: $0.75^{\prime\prime}$ imaging from the VLA-COSMOS
$3\,\rm{GHz}$ Large Project (Smolčić et al., 2017). Right: new, $\sim
0.33^{\prime\prime}$, $4-8\,\rm{GHz}$ continuum imaging from the JVLA. The
peak of the radio continuum emission coincides with the peak of the ALMA map.
On both radio images, the beam is plotted in grey.

###  2.1 Resolved $\rm{H}\alpha$ emission from SINFONI

SINFONI observations of SHiZELS-14 took place in March 2010, in good seeing
and photometric conditions ($\sim 0.6^{\prime\prime}$), with total exposure
time $12\rm{ks}$ (each individual exposure was $600\rm{s}$). This yielded the
sub-kpc resolution $\rm{H}\alpha$ map shown in the lower left-hand panel of
Figure 1. SHiZELS-14 was the only $z\sim 2.2$ source resolved in this initial
Swinbank et al. (2012a, b) campaign (though note that five more $z\sim 2.2$
galaxies were targeted in the campaign presented by Molina et al. 2017).
Data reduction and analysis procedures are outlined in full in Swinbank et al.
(2012a, b) (see also Molina et al. 2017 and Gillman et al. 2019). In summary,
the SINFONI ESOREX data reduction pipeline was used to perform extraction,
flat fielding and wavelength calibration, and to create the data cube for each
exposure. These data cubes were then stacked and combined using an average
with a $3\sigma$ clip, to reject cosmic rays and sky line residuals. Flux
calibration was performed using observations of standard stars taken
immediately before/after science exposures, which were reduced in the same
way. $\rm{H}\alpha$ and [Nii]$\lambda\lambda 6548,6583$ emission lines were
fitted on a pixel-by-pixel basis, using a $\chi^{2}$ minimisation procedure.
This yielded intensity, velocity, and velocity dispersion maps. An angular
resolution of $\sim 0.15^{\prime\prime}$ was achieved. The spectral resolution
of the instrument is $\lambda/\Delta\lambda\sim 4500$.
The $\rm{H}\alpha$ flux derived from the SINFONI observations of SHiZELS-14
was $1.6\pm 0.1\times 10^{-16}\,\rm{erg\,s^{-1}\,cm^{-2}}$. The
$\rm{H}\alpha$-derived effective radius is $4.6\pm 0.4\,\rm{kpc}$ (Swinbank et
al., 2012b). Using the same SINFONI data, Gillman et al. (2019) derive
$V_{\rm{rot}}/\sigma=0.6\pm 0.3$ (indicating that SHiZELS-14 is dispersion
dominated), though, as noted by (Swinbank et al., 2012a), this galaxy shows a
substantial (in their paper, $480\pm 40\,\rm{km\,s^{-1}}$) peak-to-peak
velocity gradient. Swinbank et al. (2012a) comment that the one- and two-
dimensional velocity fields are consistent with an early-stage prograde
encounter. This suggests that the disordered morphology and extreme star
formation may be related to a merger event.

###  2.2 Resolved UV and optical light from _HST_

SHiZELS-14 was observed over two HST orbits during Cycle 24 (Program 14719,
PI: Best). One orbit ($2700\,\rm{s}$ exposure) used the WFC3/UVIS F606W
filter, and the other used the WFC3/IR F140W filter. Orbits were split into a
3-point dither pattern in the UVIS channel, as a compromise between maximising
sensitivity and sub-sampling the point spread function (PSF). Since angular
resolution was preferred over sensitivity in the IR channel, a 4-point dither
pattern was used for these orbits. At $z=2.24$ (the redshift of SHiZELS-14),
the filters correspond to the rest-frame near-UV at $\sim 1900\,\mbox{\AA}$,
and the rest-frame optical at $\sim 4400\,\mbox{\AA}$. Our observations were
designed to span the $4000\,\mbox{\AA}$ break, and therefore sample both young
and more evolved stellar populations, in line-free regions of the galaxy
spectrum. The HST images are made using standard HST procedures and shown in
the upper panels of Figure 1. We derive the effective radius of the F140W
image via a two-dimensional Sérsic profile fit, obtaining effective radius
along the semi-major axis $R_{e,\,\rm{opt}}^{\rm{maj}}=4.6\pm 0.2\,\rm{kpc}$
(in good agreement with the $\rm{H}\alpha$ measurement) and axial ratio
$q=0.64$ (with a Sérsic index fixed at $n=1$; fitting this parameter gives
$n=0.9$).

###  2.3 Resolved far-infrared emission from ALMA

SHiZELS-14 was observed with ALMA during August 2016 as part of ALMA Cycle 3
(project code 2015.1.00026.S, PI: Ibar). Our observations, taken in
configuration C36-5, used Band 6 ($260\,\rm{GHz}$, $7.5\,\rm{GHz}$ bandwidth).
The time on-source was $26\,\rm{minutes}$. We used flux calibrator J1058+0133
and phase calibrator J0948+0022. These observations resolved the rest-frame
$840\,\rm{GHz}$ ($367\micron$) emission of SHiZELS-14 at $\sim
0.2^{\prime\prime}$ resolution.
The image was manually cleaned down to $3\sigma$ ($\rm{rms}\sim
25\,\mu\rm{Jy\,beam^{-1}}$) at the source position. We used Briggs
(robust=0.5) visibility weighting, which assigns higher weights to longer
baselines, producing an image with higher angular resolution (see the image in
the lower right-hand panel of Figure 1). To investigate the impact of
visibility weighting on the reduced ALMA image, we re-imaged the ALMA data
using a natural weighting, which weights visibilities only by the rms noise
(see the left-hand panel of Figure 2). This method minimises the noise level
but provides poorer angular resolution, given that the density of visibilities
falls towards the outskirts of the $uv$-plane and there is thus higher noise
in the longer-baseline visibilities. Using the re-reduced, lower angular
resolution natural-weighted image, we probe to slightly lower flux density per
beam. This will be used to assess the quality of our astrometric calibration
in Section 2.8.
SHiZELS-14 has an observed-frame $260\,\rm{GHz}$ flux density of $2.7\pm
0.2\,\rm{mJy}$. It displays a compact, $\sim 3\,\rm{kpc}$ diameter core of
dust emission, with extended emission contributing substantially to the flux.
Its effective radius is notably larger, due to this extended faint emission.
We derive this radius using multiple methods. First, we fit a Gaussian model
with varying axis ratio in the $uv$-plane, using CASA’s uvmodelfit task (see
Figure 10). The effective radius along the semi-major axis,
$R_{e}^{\rm{maj}}$, is $4.5\pm 0.2\,\rm{kpc}$, with fitted axial ratio
$q=0.36\pm 0.01$. A two-dimensional Sérsic profile fit in the image plane
yields $R_{e,\rm{FIR}}^{\rm{maj}}=4.6\pm 0.2\,\rm{kpc}$ and $q=0.47$ (with the
Sérsic index fixed at $n=1$; allowing this to vary gives $n=1.1$). These
measurements of effective radius are broadly consistent with those derived
from the SINFONI $\rm{H}\alpha$ and the HST rest-frame optical data.

###  2.4 Existing radio observations from COSMOS-VLA

We make use of the deep existing radio observations in the COSMOS field from
the VLA-COSMOS surveys. The VLA-COSMOS Large Project (Schinnerer et al., 2007)
surveyed $2$ square degrees in VLA A- and C-array configurations at
$1.4\,\rm{GHz}$ ($20\,\rm{cm}$). The project yielded images with rms noise
$\sim 10-15\,\mu\rm{Jy\,beam^{-1}}$ at angular resolution
$1.5^{\prime\prime}\times 1.4^{\prime\prime}$. The VLA-COSMOS Deep project
(Schinnerer et al., 2010) added further A-array observations at
$1.4\,\rm{GHz}$ in the central region of the COSMOS field. The VLA-COSMOS
$3\,\rm{GHz}$ Large Project (Smolčić et al., 2017) subsequently surveyed
$2.6\,\rm{deg}^{2}$ at a wavelength of $10\,\rm{cm}$ with the upgraded JVLA in
A configuration, reaching a mean rms depth of $\sim
2.3\,\mu\rm{Jy\,beam^{-1}}$ at $0.75^{\prime\prime}$ angular resolution.
SHiZELS-14 is one of the sources detected by these VLA surveys. The measured
flux densities are $S_{1.4\rm{GHz}}=122\pm 13\,\mu\rm{Jy}$ and
$S_{3\rm{GHz}}=68\pm 4\,\mu\rm{Jy}$. From these two flux densities, we derive
a radio spectral index of $\alpha=-0.77\pm 0.16$ (where
$S_{\nu}\propto\nu^{\alpha}$), in good agreement with measurements of star-
forming galaxies (Condon, 1992). The lower angular resolution of the radio
images limits our ability to probe resolved structure (see Figure 2, centre
panel), but the source is still extended at $0.75^{\prime\prime}$ resolution.
We will use the total flux density to estimate a star-formation rate later in
the paper.

###  2.5 New resolved radio observations from the JVLA

We obtained C-band ($4-8\,\rm{GHz}$) observations of SHiZELS-14 using 27
antennas of the JVLA, arranged in A-array configuration ($\sim
0.33^{\prime\prime}$ spatial resolution). Observations took place during
October 2019, as part of Cycle 19A (project 19A-205). We used 3C147 for flux
calibration, and J1024-008 for phase calibration. The data presented were
obtained during a $4\,\rm{hr}$ observing block, with around $3\,\rm{hrs}$ of
on-source time.
We reduced the data using standard CASA calibration pipelines, and manually
cleaned the images down to $2\,\mu\rm{Jy\,beam^{-1}}$. We present our Briggs-
weighted image in Figure 2. We obtain a total continuum flux density of $20\pm
2\,\mu\rm{Jy}$ at $6\,\rm{GHz}$. This is only roughly half the expected flux,
based on the $1.4\,\rm{GHz}$ and $3\,\rm{GHz}$ data (assuming the spectral
index calculated from these observations, $\alpha=-0.77$). One explanation for
this is that the image is not sufficiently deep to resolve the lower surface
brightness emission in the faint outskirts of the galaxy seen by ALMA. This
would suggest that the radio emission takes the form of a bright compact core,
with fainter extended structure (i.e. the radio emission is not driven
primarily by a point source). This is consistent with the nature of the JVLA
$3\,\rm{GHz}$ image, which is clearly extended even at lower angular
resolution (Figure 2, centre panel). The peak of the radio continuum emission
coincides with the peak of the dust continuum emission, which gives confidence
in the astrometric accuracy of our ALMA data (see Section 2.8).

Figure 3: NUV-NIR imaging of SHiZELS-14 from CFHT (u* from the CLAUDS survey;
Sawicki et al. 2019), Subaru (HSC-DR2; Aihara et al. 2019), and VISTA
(UltraVISTA DR4; McCracken et al. 2015). These observations are seeing-
limited, with angular resolution $\sim 0.65-0.9^{\prime\prime}$. We show the
typical angular resolution on the CFHT $u^{*}$ image. We overlay contours from
our resolved imaging on relevant panels. Overplotted on the HSC $i$-band image
are contours from HST F606W imaging (blue). The contours on the UltraVISTA
$H$-band image are from HST F140W imaging (orange). Both SINFONI
$\rm{H}\alpha$ (green) and ALMA dust continuum emission (black) contours are
overplotted on the UltraVISTA $K_{s}$-band image.

###  2.6 Optical/IR data from the COSMOS field

A wealth of lower resolution data exists for this galaxy due to its location
within the well-imaged COSMOS field (Scoville et al., 2007). At NUV-optical
wavelengths, COSMOS was imaged in the $u*$-band from the Canada-France-Hawaii
Telescope (CFHT/MegaCam), and in six broad bands ($B$, $V$, $g$, $r$, $i$,
$z+$), 12 medium bands (IA427, IA464, IA484, IA505, IA527, IA574, IA624,
IA679, IA709, IA738, IA767, and IA827), and two narrow bands (NB711, NB816),
all from the COSMOS-20 survey (Subaru Suprime-Cam; Taniguchi et al. 2007,
2015). $Y$-band imaging was obtained with Hyper-Suprime-Cam on Subaru (HSC;
Miyazaki et al. 2012). In the NIR, $Y$, $J$, $H$, & $K_{s}$ data are provided
by the UltraVISTA-DR2 release (McCracken et al., 2015), which uses the VIRCAM
instrument on the VISTA telescope. These are supplemented by $H$ and $K$
WIRCAM data from CFHT (McCracken et al. 2010). Mid-IR data are drawn from IRAC
channels 1, 2, 3 and 4 ($3.6\,\mu\rm{m}$, $4.5\,\mu\rm{m}$, $5.8\,\mu\rm{m}$
and $8.0\,\mu\rm{m}$), collected by the Spitzer Large Area Survey with HSC
(SPLASH survey; Lin et al. 2017; Capak et al. in prep). Laigle et al. (2016)
collate these observations and provide an NIR-selected photometric redshift
catalogue. For consistency, we use their $3^{\prime\prime}$ diameter aperture
fluxes extracted for SHiZELS-14. We tabulate these measurements in Table 3 of
the Appendix, along with the new measurements from this paper.
In Figure 3 we show deeper imaging from more recent surveys: the $u^{*}$ band
(from the CLAUDS survey on CFHT; Sawicki et al. 2019), $i$-band (from HSC-DR2;
Aihara et al. 2019), and in the $H$ and $\rm{K}_{s}$ bands from UltraVISTA-
DR4. These show interesting differences, with emission in the $u^{*}$-band
peaking to the North East compared to the $K_{s}$-band emission (this is not
driven by astrometric offsets in the $u^{*}$-band data).

###  2.7 Data at mid-IR and far-IR wavelengths

We draw data at mid-IR and far-IR wavelengths from Spitzer and Herschel
imaging. We adopt the $24\,\micron$ flux density from the Spitzer Multiband
Imaging Photometer (MIPS; Rieke et al. 2004). The Herschel Multi-tiered
Extragalactic Survey (HerMES; Oliver et al. 2012) targeted COSMOS at
$100-500\,\micron$. The survey used Herschel-Spectral and Photometric Imaging
Receiver (SPIRE) at $250\,\micron$, $350\,\micron$ and $500\,\micron$ and the
Herschel-Photodetector Array Camera and Spectrometer (PACS) at $100\,\micron$
and $160\,\micron$. One of the main aims of the Herschel Extragalactic Legacy
Project (HELP)111http://herschel.sussex.ac.uk was to develop the advanced
statistical tools needed to de-blend the low-resolution data from Herschel, in
order to assign fluxes to components (Hurley et al., 2017; Pearson et al.,
2017). We use these publicly available, catalogued flux densities for
SHiZELS-14 (see Table 3).
We also use the ALMA Band 7 flux density measured by Scoville et al. (2014).
The observed-frame continuum $350\,\rm{GHz}$ total flux density is $4.7\pm
0.8\,\rm{mJy}$, and the peak flux density is $1.9\pm
0.3\,\rm{mJy\,beam^{-1}}$. SHiZELS-14 is also one of the sources in the
catalogue of bright sub-mm sources detected by SCUBA-2 in the COSMOS field
(Simpson et al., 2019). The observed-frame $850\,\micron$ flux density
measured there is $5.4\pm 1.3\,\rm{mJy}$.

###  2.8 Astrometric alignment

Accurate astrometric alignment is critical when comparing multi-wavelength
emission on small angular scales. However, due to the small fields of view of
both the SINFONI ($\sim 3^{\prime\prime}\times 3^{\prime\prime}$) and ALMA
($\sim 30^{\prime\prime}$ diameter) data, aligning the images is non-trivial.
Here, we describe the alignment of the images.
The ALMA image is expected to be tied to the International Celestial Reference
System (ICRS). Although calibration errors and self-calibration processes can
lead to astrometric offsets, this is unlikely to be larger than the pixel
level ($0.06^{\prime\prime}$). The JVLA data should also be on the ICRS, and
the spatially coincident emission seen by the JVLA and ALMA (Figure 2, right-
hand panel), give us confidence in the astrometry of both.
We then align all other images to the ICRS. The SINFONI $\rm{H}\alpha$ image
was aligned to the same reference frame as the main wide-field HiZELS survey
images. We used a broad-band-subtracted narrow-band image from HiZELS, which
had been aligned to the Two Micron All-Sky Survey (2MASS), which itself uses
the ICRS. We shifted the $\rm{H}\alpha$ image obtained from the SINFONI cube
by sub-pixel quantities, and convolved down to the resolution of the broad-
band image. Subtracting the images enabled a $\chi^{2}$ fit to define the
optimal alignment. Based on these comparisons, we are able to achieve an
accuracy on the SINFONI image alignment of $\sim 0.2^{\prime\prime}$.
We calibrated the astrometry of the HST images by aligning to HSC-DR2 (Aihara
et al., 2019), which inherits its astrometric accuracy from Gaia. Sources were
extracted from the HSC $Y$ and $R$-band images, as well as the two HST images,
using the SEXTRACTOR software (Bertin & Arnouts, 1996). We matched sources
detected in the HSC $Y$-band and the HST F140W (and then the $R$-band and the
HST F606W), and constructed histograms of the small offsets between their RA
and Dec positions. The peaks of these histograms were selected as the offset
to be applied to both the HST images (the same procedure was used in the
companion paper, Cheng et al. 2020). We also performed this process using
catalogued 2MASS sources, and derived essentially identical results. Based on
this, and the narrow widths of both histograms, we estimate that the alignment
is correct to within $\sim 0.1^{\prime\prime}$. Inspecting our images, gives
us confidence in the alignment. As shown in the middle panel of Figure 2,
there is faint ALMA flux in the regions that show extended F140W flux. The
F140W image also aligns with the SINFONI image in terms of both area covered
and areas where the flux peaks.

Figure 4: Data presented in Table 3, fitted with MAGPHYS (Da Cunha et al.,
2008). The red points are the observational data, and the open black circles
show the model results. The blue line shows the intrinsic stellar SED for the
best-fitting model, and the black line shows the SED after dust reprocessing.
Residuals are shown in the lower panel. The fitting yields $\rm{SFR}=690\pm
30\,M_{\odot}\rm{yr}^{-1}$, $\log_{10}M_{*}/\rm{M_{\odot}}=11.2\pm 0.1$,
$\log_{10}M_{\rm{dust}}/\rm{M_{\odot}}=8.9\pm 0.1$ $A_{v}=1.9\pm 0.1$ and
$\log_{10}(L_{\rm{TIR}}/\rm{L_{\odot}})=12.85\pm 0.01$.

###  2.9 Morphologies of astrometrically-calibrated images

Figure 1 shows our four spatially resolved maps after these small astrometric
corrections were applied. The emission in all bands is aligned along the same
axis. However, the peak of the dust emission probed by ALMA (and confirmed by
the $4-8\rm{GHz}$ JVLA imaging) is clearly offset from the peaks of the FUV
and $\rm{H}\alpha$ emission. These offsets are far larger than the residual
astrometric uncertainties ($0.1-0.2^{\prime\prime}$). The dust emission is
centrally concentrated, whereas there are a number of $\rm{H}\alpha$ peaks
along the extended region where dust emission is faint. There is a peak in the
emission from both HST bands towards the North-East of the image, yet no
detectable dust emission. This is in line with the excess in the CFHT
$u^{*}$-band emission (compared to the longer wavelength bands) shown in
Figure 3. Such offsets are seen in observed dusty galaxies (e.g. Chen et al.,
2015, 2017), and also in simulations (Cochrane et al., 2019).

##  3 Global properties of SHiZELS-14

Before examining the resolved structures of SHiZELS-14 further, we place these
into context by deriving the global properties of the galaxy.

###  3.1 SED fitting with MAGPHYS

Spectral Energy Distribution (SED) fitting provides a powerful basis for
estimating galaxy properties from photometry. The MAGPHYS energy balance SED
fitting code (Da Cunha et al., 2008, 2015; Battisti et al., 2019) was used to
derive physical parameters in Cheng et al. (2020). We provide details of the
fitting here. MAGPHYS employs an energy balance method to match the
attenuation of the stellar emission in the UV/optical by dust, and the re-
radiation of this energy in the far-infrared. The code uses the stellar
population models of Bruzual & Charlot (2003), with a Chabrier IMF (Chabrier,
2003) and metallicities between 0.2 and 2 times solar. The star-formation
history (SFH) is parametrised as a continuous delayed exponential function and
to reproduce starbursts, MAGPHYS also adds bursts to the star-formation
history. Dust attenuation is modelled using two components following Charlot &
Fall (2000). The code was extensively tested with both observational
constraints on SMGs and against model star-forming galaxies from the EAGLE
simulation by Dudzeviciute et al. (2020) and shown to perform well for these
highly dust-obscured galaxies.
We fit the photometry presented in Table 3. We estimate
$\log_{10}M_{*}/\rm{M_{\odot}}=11.2\pm 0.1$,
$\log_{10}M_{\rm{dust}}/\rm{M_{\odot}}=8.9\pm 0.1$, and $\rm{SFR}=690\pm
30\,\rm{M_{\odot}yr^{-1}}$ (see Table 1). The estimated total infrared
luminosity is $\log_{10}(L_{\rm{TIR}}/\rm{L_{\odot}})=12.85\pm 0.01$, and the
estimated dust attenuation in the $V$-band is $A_{v}=1.9\pm 0.1$. We obtain
consistent results using another SED fitting code, BAGPIPES (see appendix). We
have also used BAGPIPES to experiment with different SFH parametrisations,
which yield very similar fits to the photometry and consistent values for
stellar mass. All parametrisations, even those allowing multiple bursts,
favour a recent (at $z=2.24$), rapid burst of star formation in which the vast
majority of the stellar mass is formed.

Basic property | Measurement | Reference
---|---|---
RA (J2000) | 10:00:51.6 | Swinbank+12
Dec (J2000) | +02:33:34.5 | Swinbank+12
$z_{\rm{H}\alpha}$ | 2.2418 | Swinbank+12
Derived property | Measurement | Reference
$\log_{10}M_{*,\rm{SED}}/\rm{M_{\odot}}$ | $11.2\pm 0.1$ | This paper
$\log_{10}M_{\rm{gas}}/\rm{M_{\odot}}$ | $10.1\pm 0.4$ | Swinbank+12
$\log_{10}M_{\rm{dust}}/\rm{M_{\odot}}$ | $8.9\pm 0.1$ | This paper
$\log_{10}L_{\rm{TIR}}/\rm{L_{\odot}}$ | $12.85\pm 0.01$ | This paper
$\rm{SFR}_{SED}/\rm{M_{\odot}yr^{-1}}$ | $690\pm 30$ | This paper
$R_{e,\,\rm{H}\alpha}/\rm{kpc}$ | $4.6\pm 0.4$ | Swinbank+12
$R_{e,\,\rm{opt}}^{\rm{maj}}/\rm{kpc}$ | $4.6\pm 0.2$ | This paper
$R_{e,\,\rm{FIR}}^{\rm{maj}}/\rm{kpc}$ | $4.5\pm 0.2$ | This paper
$A_{v}$ | $1.9\pm 0.1$ | This paper
Table 1: Summary of properties of SHiZELS-14. Full details of SFRs derived
using different methods are presented separately in Table 2.

###  3.2 Fitting the dust SED

To assess the sensitivity of the derived MAGPHYS parameters in the far-
infrared, we also fit the MIR-to-FIR SED of SHiZELS-14 separately, using only
data from ALMA and Herschel. We parametrise the emission from cold and warm
dust using a simple two-body model:

$f_{\nu}(\rm{mJy})=A_{\rm{warm}}\lambda^{-\beta_{warm}}B_{\nu}(T_{\rm{warm}})+A_{\rm{cold}}\lambda^{-\beta_{cold}}B_{\nu}(T_{\rm{cold}}),$
(1)

where $A_{\rm{warm}}$ and $A_{\rm{cold}}$ are normalisations and $B_{\nu}(T)$
is the Planck function, from dust grains radiating at rest frequency $\nu$, at
temperature T. All wavelengths were input at their rest-frame. In line with
the literature, we have fixed $\beta=2$ for both the cold and warm dust
components, to minimise the number of fitting parameters. We use the EMCEE
MCMC python package (Foreman-Mackey, 2016), with 300 walkers and 5000 steps.
This yields posterior estimates: $\log_{10}A_{\rm{warm}}=5.4\pm 0.3$,
$T_{\rm{warm}}=64\pm 6\,\rm{K}$, $\log_{10}A_{\rm{cold}}=7.6\pm 0.1$, and
$T_{\rm{cold}}=28\pm 2\,\rm{K}$. The best-fitting model is shown in Figure 5.
Note that there is a known strong degeneracy between $\beta_{\rm{cold}}$ and
$T_{\rm{cold}}$, and a 5-parameter fit that allows $\beta_{\rm{cold}}$ to vary
favours a higher $\beta_{\rm{cold}}$ and a lower $T_{\rm{cold}}$.
To derive the dust temperature in a consistent way to other studies in the
literature, we additionally fit a single modified black body model to the
data, also shown in Figure 5. We derive a characteristic dust temperature of
$T_{\rm{dust}}^{\rm{BB}}=32\pm 2\,\rm{K}$, in good agreement with the values
derived by Dudzeviciute et al. (2020) for their sample of SMGs. However, this
single component model struggles to fit the $100\,\mu\rm{m}$ PACS data point,
and it is necessary to boost the errors on that point artificially to get a
good fit to the longer wavelength data. This suggests a contribution from
hotter dust, perhaps indicative of an obscured AGN. We will discuss this
further in Section 3.6.

Figure 5: The dust SED of SHiZELS-14, constructed using collated archival data
and the new ALMA $260\rm{GHz}$ data. Error bars are plotted on the data
points, but are small. A two grey body model parametrisation (blue fitted
curve) provides a good fit to both the cold and warm dust components.
Integrating the $8-1000\,\micron$ emission gives
$\log_{10}(L_{\rm{TIR}}/\rm{L_{\odot}})=12.81\pm 0.02$ and
SFR${}_{8-1000\,\mu\rm{m}}=950\pm 50\,\rm{M_{\odot}}\rm{yr}^{-1}$. A single
component model (grey fitted curve) is unable to fit the $100\,\mu\rm{m}$ PACS
data. The characteristic dust temperature derived from this fit
($T_{\rm{dust}}^{\rm{BB}}=32\pm 2\,\rm{K}$) enables us to constrain the dust
mass ($\log_{10}M_{\rm{dust}}/\rm{M_{\odot}}=9.0\pm 0.1$).

###  3.3 Calculation of cold dust mass and TIR luminosity

Assuming the dust is optically thin at the rest-frame frequency, the dust mass
is given by (e.g. James et al. 2002):

$M_{\rm{dust}}=\frac{1}{1+z}\frac{S_{\rm{obs}}D_{L}^{2}}{\kappa_{\rm{rest}}B_{\nu}(T_{\rm{dust}}^{\rm{BB}})},$
(2)

where $S_{\rm{obs}}=2.7\,\rm{mJy}$ is the observed flux density of the source
at $260\,\rm{GHz}$, $D_{L}$ is the luminosity distance, $\nu=836\,\rm{GHz}$ is
the rest-frame frequency, $\kappa_{\rm{rest}}$ is the mass absorption
coefficient at this frequency, and $T_{\rm{dust}}^{\rm{BB}}=32\pm 2\,\rm{K}$
is the characteristic temperature derived from the single component modified
black body fit. We used $\kappa_{850}=0.07\pm 0.02\,\rm{m}^{2}\rm{kg}^{-1}$
(James et al., 2002), which gives
$\log_{10}M_{\rm{dust}}/\rm{M_{\odot}}=9.0\pm 0.1$ (in good agreement with the
value derived from MAGPHYS fits, $\log_{10}M_{\rm{dust}}/\rm{M_{\odot}}=8.9\pm
0.1$). These estimates are consistent with a high dust-to-stellar mass ratio,
$\log_{10}(M_{\rm{dust}}/M_{*})=-2.2\pm 0.2$, which is comparable to the
ratios derived by Calura et al. (2017) for SMGs of stellar mass $\sim
10^{11}\,\rm{M_{\odot}}$ at $z\sim 1-3$ (see also Figure 3). We also integrate
the two-body fits at wavelengths $8-1000\,\micron$ within the MCMC fit
(enabling us to fold in the correlations between fitted parameters), obtaining
an estimate for the total IR luminosity,
$\log_{10}(L_{\rm{TIR}}/\rm{erg\,s^{-1}})=46.39\pm 0.02$, and
$\log_{10}(L_{\rm{TIR}}/\rm{L_{\odot}})=12.81\pm 0.02$. The TIR-based SFR is
$950\pm 50\,\rm{M_{\odot}}\rm{yr}^{-1}$ (using the Kennicutt & Evans 2012 SFR
calibration, with a Kroupa 2002 IMF).

Waveband (Instrument) | Formula for $\log_{10}(\rm{SFR}/M_{\odot}\rm{yr}^{-1})$ | $\rm{SFR}/M_{\odot}\rm{yr}^{-1}$
---|---|---
SFRs from individual tracers |  |
${\rm\bf{TIR_{8-1000\micron}}}$ (dust SED fit) | $\log_{10}(L_{\rm{TIR}}/\rm{erg\,s^{-1}})-43.41$ | $\mathbf{950\pm 50}$
Radio (1.4 GHz, VLA, Bell 2003 conversion) | $\log_{10}(L_{1.4\rm{GHz,\,rest}}/\rm{erg\,s^{-1}\,Hz^{-1}})-28.43$ | $1180\pm 100$
Radio (1.4 GHz, VLA, Kennicutt & Evans 2012) | $\log_{10}(L_{1.4\rm{GHz,\,rest}}/\rm{erg\,s^{-1}\,Hz^{-1}})-28.2$ | $2010\pm 170$
$\rm{H}\alpha$ (SINFONI/VLT) | $\log_{10}(L_{\rm{H}\alpha}/\rm{erg\,s^{-1}})-41.27$ | $33\pm 2$
” |  $L_{\rm{H}\alpha}$ corrected using $1\,$mag dust extinction | $83\pm 5$
” |  $L_{\rm{H}\alpha}$ corrected using $M_{*}$-dependent dust extinction | $180\pm 10$
| of Garn et al. (2010), $\log_{10}M_{*}/\rm{M_{\odot}}=11.2$ |
” |  $L_{\rm{H}\alpha}$ corrected using $A_{\rm{H}\alpha}=1.6\pm 0.1$, derived from scaled $A_{V}$ | $140\pm 20$
” |  $L_{\rm{H}\alpha}$ corrected using $A_{\rm{H}\alpha}=3.7\pm 0.1$, derived from scaled $A_{V}$ & | $1000\pm 100$
” | preferential extinction of birth clouds |
FUV (HST F606W) | $\log_{10}(\nu L_{\nu}/\rm{erg}\,\rm{s}^{-1})-43.17$ | $13\pm 1$
” | corrected using $A_{1600}$ derived from $\beta$, with $\beta=-0.5\pm 0.1$ | $300^{+70}_{-50}$
” | corrected using $A_{\rm{UV}}=4.3\pm 0.2$, derived from scaled $A_{V}$ | $680\pm 130$
SFRs from combinations of tracers |  |
FUV + TIR |  $L_{\rm{\nu,corr}}=L_{\rm{\nu,obs}}+0.27L_{\rm{TIR}}$, $L_{\nu}-\rm{SFR}$ conversion above | $440\pm 20$
$\rm{H}\alpha$ \+ TIR |  $L_{\rm{H}\alpha,corr}=L_{\rm{H}\alpha,obs}+0.0024L_{\rm{TIR}}$, $L_{\rm{H}\alpha}-\rm{SFR}$ conversion above | $330\pm 20$
FUV + radio | $L_{\rm{FUV,corr}}=L_{\rm{FUV,obs}}+4.2\times 10^{14}L_{1.4\rm{GHz}}$ | $990\pm 80$
SFRs from SED fitting |  |
MAGPHYS |  | $690\pm 30$
BAGPIPES |  | $660\pm 60$
Table 2: The global SFR of SHiZELS-14, derived from different combinations of
SFR indicators, using a Kroupa (2002) IMF. Inferring an SFR from dust-
uncorrected fluxes at short-wavelengths yields SFRs of
$<50\rm{M_{\odot}\rm{yr}^{-1}}$. These UV or $\rm{H}\alpha$-inferred SFRs lie
well below the values derived from the TIR or radio
($\rm{SFR}=1000-2000\,\rm{M_{\odot}yr^{-1}}$). Applying either a standard dust
correction corresponding to $A_{\rm{H}\alpha}=1$ or a stellar mass dependent
dust correction provides only a modest increase in $\rm{H}\alpha$-derived SFR
($\rm{SFR}=100-200\,\rm{M_{\odot}\rm{yr}^{-1}}$). Similarly, correcting the
UV-derived SFR using the IRX-$\beta$ relation derived using HST data only
raises the SFR to $300\,\rm{M_{\odot}\rm{yr}^{-1}}$. We also estimate
$A_{\rm{H}\alpha}$ and $A_{1600}$ by scaling the $A_{V}$ derived from MAGPHYS
according to a Calzetti et al. (2000) law. This correction brings the UV-
derived SFR into better agreement with the MAGPHYS-derived SFR, however the
$\rm{H}\alpha$-derived SFR remains low, indicating additional extinction of
the $A_{\rm{H}\alpha}$ line. Including additional extinction of the
$A_{\rm{H}\alpha}$ line according to Charlot & Fall (2000) brings the
$\rm{H}\alpha$-derived SFR into line with the FIR estimate ($\rm{SFR}\sim
1000\,\rm{M_{\odot}yr^{-1}}$).

###  3.4 The inappropriateness of the $\rm{IRX}-\beta$ relation

The $\rm{IRX}-\beta$ relation (Calzetti et al., 1994; Meurer et al., 1999)
between the ratio of the FIR and UV luminosity
($\rm{IRX}=L_{\rm{FIR}}/L_{1600}$) and the spectral slope ($\beta$, where
$f_{\lambda}\propto\lambda^{\beta}$) evaluated at $1600\,\mbox{\AA}$ is a
popular method used to infer SFRs where only rest-frame UV luminosities are
available. This appears to work for samples of galaxies with relatively low
dust content (especially at very high redshift). However, individual galaxies
show a large amount of scatter around this relation, and it has been shown
that this method is not appropriate highly star-forming galaxies (e.g. Casey
et al., 2014; Chen et al., 2017; Narayanan et al., 2018), although it is
difficult to identify these based on their UV properties.
We can derive both IRX and $\beta$ for SHiZELS-14. We use the publicly
available HST $I_{814}$-band image ($\lambda_{\rm{mean}}=8100\,\mbox{\AA}$,
rest-frame $\lambda_{\rm{mean}}=2500\,\mbox{\AA}$), along with our own F606W
images ($\lambda_{\rm{mean}}=6000\,\mbox{\AA}$, rest-frame
$\lambda_{\rm{mean}}=1850\,\mbox{\AA}$), to calculate $\beta$. Adopting our
derived $\beta=-0.5\pm 0.1$, and applying the relation
$A_{1600}=4.43+1.99\beta$, we derive $A_{1600}=3.4\pm 0.2$ (lower than the
$A_{1600}$ estimated from scaling the $A_{V}$ obtained via SED fitting; see
Table 2). Correcting the global SFR inferred from the FUV flux accordingly
yields $\rm{SFR}=300^{+70}_{-50}\,M_{\odot}\rm{yr^{-1}}$. This estimate is
approximately two times lower than the SFR inferred from the SED fitting
presented in Sections 3.1 and 3.2, and three times lower than the TIR-derived
SFR in Section 3.3. We calculate IRX using the TIR luminosity derived in
Section 3.3, and the rest-frame $1851\,\mbox{\AA}$ luminosity. Globally, the
galaxy has $\log_{10}\rm{IRX}=2.09\pm 0.06$. In combination with the derived
$\beta$, this places it $\sim 0.7\pm 0.1\,\rm{dex}$ above the Meurer et al.
(1999) relation. This highlights that the galaxy has a higher TIR luminosity
than expected from the derived UV slope, or, equivalently, a much shallower UV
slope than would be expected given the radio of the global TIR luminosity to
UV luminosity. This is likely to be because the UV and FIR emission are not
co-located, as shown in Figure 1. Because of this, the UV slope is measured
from the UV emission escaping from one region of the galaxy, which is not
where most of the FIR emission arises (see also Goldader et al., 2002;
Cochrane et al., 2019). SHiZELS-14 highlights that the IRX relation does not
provide reliable estimates of the FIR emission for the most dusty galaxies, as
also argued by Chen et al. (2017).

###  3.5 Global SFR estimation

In Table 2 we present global SFR estimates from global measurements in
different wavebands, using the calibrations of Kennicutt & Evans (2012) and
assuming a Kroupa (2002) IMF. It is clear that applying standard SFR
calibrations to flux measurements that probe star formation via direct
emission at shorter wavelengths predict vastly lower SFRs than the dust-
obscured tracers. This suggests that the deficit in global SFR derived from
the dust-sensitive SFR indicators is due to the highly dusty nature of this
galaxy. In the following section, we explore the differences in the spatially-
resolved SFRs, derived at different wavelengths.

###  3.6 The lack of evidence for AGN activity

As discussed in Section 3.5, the SFRs derived from the UV, $\rm{H}\alpha$ and
FIR differ greatly. In this section, we investigate whether the presence of an
active galactic nucleus (AGN) could be a factor in this. In this scenario, the
extreme dust continuum emission towards the centre of the galaxy could be
powered by heating from a central AGN, rather than a compact region of star
formation. Since different types of AGN emit in different wavebands (see
Heckman & Best 2014 for a review, and Garn et al. 2010 for a discussion of AGN
within the HiZELS sample), identification of AGN requires a multi-wavelength
approach. Here, we use some of the key methods for AGN identification to hunt
for signs of AGN activity.

####  3.6.1 No X-ray detection

X-ray emission probes the accretion disk corona very close to a supermassive
black hole. The Chandra COSMOS-Legacy Survey (Civano et al., 2016) imaged
$2.2\,\rm{deg}^{2}$ of the COSMOS field in the wavelength range
$0.5-10\,\rm{keV}$. SHiZELS-14 lies in the central region of the COSMOS-Legacy
field, where effective exposure times are $\sim 160\,\rm{ks}$. The limiting
depths are $2.2\times 10^{-16}$, $1.5\times 10^{-15}$, and $8.9\times
10^{-16}$ $\rm{erg\,cm^{-2}\,s^{-1}}$ in the bands $0.5-2$, $2-10$, and
$0.5-10\,\rm{keV}$, respectively. At these limiting depths, SHiZELS-14 is
undetected. We derive a limit on the rest-frame hard-band $2-10\,\rm{keV}$
luminosity following Alexander et al. (2003): $L_{2-10,\rm{lim}}=4\pi
D_{L}^{2}f_{2-10,\rm{lim}}(1+z)^{\Gamma-2}$, using $\Gamma=1.9$ (Nandra &
Pounds, 1994). This gives $L_{2-10}<5.1\times 10^{43}\,\rm{erg\,s^{-1}}$.
We can predict the X-ray luminosity associated with star formation using the
$L_{2-10}$-SFR calibration proposed by Kennicutt & Evans (2012) and the SFR
measured from the other indicators. Given the SFR derived from the dust SED
fit, $950\pm 50\,\rm{M_{\odot}yr^{-1}}$, we estimate $L_{2-10}=(5.6\pm
0.3)\times 10^{42}\,\rm{erg\,s^{-1}}$. This is an order of magnitude lower
than the limit imposed by the survey depth. Therefore, the lack of an X-ray
detection is consistent with SHiZELS-14 being a star-forming galaxy.

####  3.6.2 No [NII]/$\rm{H}\alpha$ excess

The ratio of [NII]-to-$\rm{H}\alpha$ line flux reflects the hardness of the
ionising source driving the nebular emission, and hence can be used to infer
the presence of an AGN, often in combination with other line ratios (e.g.
Baldwin et al., 1981). For SHiZELS-14, there is no evidence for a strong
excess in [NII]/$\rm{H}\alpha$. For the clump nearest the peak of the rest-
frame FIR emission, [NII]/$\rm{H}\alpha=0.12$ (Swinbank et al., 2012b, clump
14a), well within the range expected for star-forming regions (e.g. Kewley et
al., 2006). Swinbank et al. (2012a) show that the [NII]/$\rm{H}\alpha$ radial
profile of SHiZELS-14 is slightly negative, in line with the rest of the
SHiZELS sample. The derived gradients reflect slightly enhanced metallicity
towards the central regions of the SHiZELS galaxies, consistent with
simulations of star-forming galaxies of similar mass and redshift (e.g. Ma et
al., 2017).

Figure 6: Maps of SFR surface density, derived for each of the four SFR
indicators using the luminosity-SFR calibrations of Kennicutt & Evans (2012)
(upper two and lower left panels) and Bell (2003) (lower right panel). Note
that dust corrections were not applied to the UV or $\rm{H}\alpha$ maps.
Pixels that have fluxes below the minimum of our $\Sigma_{\rm{SFR}}$ scale
($0.07\,\rm{M_{\odot}}\rm{yr}^{-1}\rm{kpc}^{-2}$) are coloured white to avoid
overly noisy images. We plot the maps on the same SFR scale, to compare the
SFRs directly, and show the position of the peak of the ALMA emission as a
black cross on each panel. We also overplot three concentric rings, of radii
$2\,\rm{kpc}$, $4\,\rm{kpc}$ and $6\,\rm{kpc}$. It is clear that the derived
SFRs differ across the spatial extent of the galaxy, not only in its dusty
centre. The UV map shows a ’hole’ where the rest-frame FIR emission peaks. As
shown in Figure 2, the angular resolution of the radio imaging is lower than
the other images, which causes the emission to appear more extended.

####  3.6.3 No mid-infrared excess

Obscured AGN are characterised by a strong mid-infrared (rest-frame $\sim
3-30\,\mu\rm{m}$) excess, produced by a dusty obscuring torus. Our MAGPHYS fit
(Figure 4) shows no sign of such an excess, being well-fitted by an SED
constructed without AGN templates. Fitting the SED with CIGALE, which does
allow for the inclusion of emission from AGN, provides no evidence of an AGN
($f_{\rm{AGN,\,best}}=0.001$). In addition to this, the characteristic
temperature derived from fits to the dust SED (which is well-constrained due
to the known redshift) is $32\pm 2\,\rm{K}$, well within the normal range for
star-forming galaxies. However, a single modified black body fails to fit the
shortest wavelength PACS data point, indicating non-negligible emission from
hotter dust. This could hint at some contribution to the FIR emission from an
obscured AGN, though there are numerous examples of hot dust associated with
star formation (e.g. Magnelli et al., 2014; Faisst et al., 2020).

####  3.6.4 Position on the IR-radio relation consistent with star formation

The ratio of IR to radio luminosity (e.g. Appleton et al., 2004) is frequently
employed to separate radio-loud AGN from star-forming galaxies. Following
Ivison et al. (2010), we use the following equation with the TIR luminosity
calculated in Section 3.3:

$q_{\rm{TIR}}=\log\Bigg{(}\frac{L_{\rm{TIR}}}{3.75\times
10^{12}\rm{W}}\Bigg{)}-\log\Bigg{(}\frac{L_{1.4\rm{GHz\,rest}}}{\rm{WHz^{-1}}}\Bigg{)}.$
(3)

The rest-frame $1.4\rm{GHz}$ luminosity is:

$\begin{multlined}L_{1.4\rm{GHz,\,rest}}=\frac{4\pi
D_{L}^{2}}{(1+z)^{1+\alpha}}\Bigg{(}\frac{\nu_{1.4\rm{GHz}}}{\nu_{\rm{obs}}}\Bigg{)}^{\alpha}S_{1.4\rm{GHz,\,obs}}\\\
=10^{24.54\pm
0.08}\,\rm{WHz^{-1}}.\end{multlined}L_{1.4\rm{GHz,\,rest}}=\frac{4\pi
D_{L}^{2}}{(1+z)^{1+\alpha}}\Bigg{(}\frac{\nu_{1.4\rm{GHz}}}{\nu_{\rm{obs}}}\Bigg{)}^{\alpha}S_{1.4\rm{GHz,\,obs}}\\\
=10^{24.54\pm 0.08}\,\rm{WHz^{-1}}.$ (4)

We assume a spectral index $\alpha=-0.77$, derived from the VLA $3\,\rm{GHz}$
and $1.4\,\rm{GHz}$ data. This gives $q_{\rm{TIR}}=2.28\pm 0.10$. This is
broadly in line with the distribution of $q_{\rm{TIR}}$ values for the
$250\,\micron$-selected sample of Ivison et al. (2010) (median
$q_{\rm{TIR}}=2.4$, $\sigma_{q}=0.24$; see also Algera et al. 2020). The
$q_{\rm{TIR}}$ value for SHiZELS-14 is well within $1\sigma$ of the median
relation derived for star-forming galaxies. This indicates that the radio
continuum emission is not contaminated by a compact radio core. Overall, we
find no evidence that SHiZELS-14 is host to a radio-loud AGN.

##  4 Resolved star-formation rates and dust attenuation

Figure 7: Star-formation rate surface density profiles derived using rest-
frame FUV F606W, $\rm{H}\alpha$, and rest-frame FIR flux map (scaled to the
SFR derived from fits to the dust SED; note that this assumes a constant dust
temperature across the galaxy). The profiles are centred on the peak of the
rest-frame FIR emission, shown by a black cross in Figure 6. The thick dashed
lines show the surface densities derived using Kennicutt & Evans (2012)
calibrations, with no dust corrections applied. The solid transparent lines
show the profiles derived using an $A_{\rm{H}\alpha}=3.7$ and
$A_{\rm{UV}}=4.3$, derived using $A_{V}=1.9$ from MAGPHYS, the attenuation
curve of Calzetti et al. (2000) and the preferential attenuation towards birth
clouds proposed by Charlot & Fall (2000). These corrections can bring the
profiles broadly into line at large radii, but still underestimate the star-
formation rate surface density at radii less than $\sim 2\,\rm{kpc}$, where
the rest-frame FIR emission peaks.

###  4.1 Resolved star-formation rates

In Figure 6, we present maps of SFR surface density, derived for each of the
four SFR tracers using the luminosity-SFR calibrations of Kennicutt & Evans
(2012) and Bell (2003). In order to do this, we assume that these global
calibrations are also valid on smaller spatial scales, which may not be the
case. In reality, gradients in dust temperature and opacity (e.g. Galametz et
al., 2012) may apply to the TIR model, and gradients in the reddening will
influence the $\rm{H}\alpha$ and UV maps. The radio emission is sensitive to
cosmic ray propagation and starburst age, which likely results in smoother and
more extended emission than the true SFR distribution (Thomson et al., 2019).
Making this assumption and adopting standard SFR calibrations, it is clear
from Figure 6 that the SFRs derived from the four indicators differ across the
galaxy. To investigate this more quantitatively, we derive star-formation rate
radial profiles by applying Kennicutt & Evans (2012) calibrations to the rest-
frame FUV F606W, $\rm{H}\alpha$, and TIR flux maps (see Figure 7, thick dashed
lines). The three profiles are discrepant, with the TIR-based SFR profile
increasing sharply towards the centre, and the FUV-derived profile decreasing
at radii smaller than $\sim 2\,\rm{kpc}$, in line with the ’hole’ observed at
the position of the peak of the dust continuum emission (see Figure 6).
Without any corrections for dust attenuation, the FUV and
$\rm{H}\alpha$-derived SFRs are lower than the FIR-derived SFR across the
radial extent of the galaxy. The FUV profile broadly follows the
$\rm{H}\alpha$ profile in shape, but with a different normalisation. The FUV
is most strongly attenuated by dust, and yields the lowest dust-uncorrected
SFRs across the galaxy. Thus, the discrepancy between the SFRs derived
globally cannot be attributed solely to the compact dusty centre of the
galaxy, though this is where the measurements are most discrepant. Instead,
short-wavelength light is attenuated across the galaxy.
We also show the effects of applying a dust correction. $A_{\rm{H}\alpha}$ and
$A_{\rm{UV}}$ are calculated from the MAGPHYS-derived $A_{V}$, according to
the Calzetti et al. (2000) law and a Charlot & Fall (2000) birth cloud
attenuation. These dust corrections bring the outermost regions of the FUV and
$\rm{H}\alpha$ profiles further towards agreement at radii greater than $\sim
2\,\rm{kpc}$ (see transparent solid lines). However, it is clear that the UV
and $\rm{H}\alpha$-derived SFR estimates are much lower than the TIR-derived
estimate in the centre, particularly at radii less than $\sim 2\,\rm{kpc}$.
This reflects strong central star formation and a steep gradient in dust
attenuation across the galaxy, which may be even stronger if there is a
significant gradient in either dust temperature or opacity.

Figure 8: Left: the ratio of TIR-derived SFR to $\rm{H}\alpha$-derived SFR,
assuming the luminosity-SFR calibrations of Kennicutt & Evans (2012), without
any correction for dust attenuation. The TIR-derived SFR is larger than that
derived from $\rm{H}\alpha$ across the full extent of the galaxy, but the
estimates are discrepant by a factor of $\sim 50$ in the dusty central region.
Right: the dust attenuation $A_{\rm{H}\alpha}$ derived from this ratio. Where
the $\rm{H}\alpha$ flux is below the detection limit, neither ratio nor
$A_{\rm{H}\alpha}$ value is plotted. $A_{\rm{H}\alpha}$ varies across the
galaxy, within a broad range $A_{\rm{H}\alpha}\sim 2-6$. Surveys such as
HiZELS often assume a modest global dust correction of $A_{\rm{H}\alpha}=1$,
but the dust attenuation of SHiZELS-14 derived here is well in excess of this
value. ALMA contours are overlaid on both panels in red.

###  4.2 Inferring dust attenuation using $\rm{H}\alpha$ and FIR maps

In Figure 6, we showed that the SFR surface densities derived in different
wavebands from dust-uncorrected fluxes of the dust-sensitive tracers are far
lower than the TIR measurement. We can use this to estimate the spatially-
resolved dust attenuation. In the left-hand panel of Figure 8, we present the
ratio of the $\rm{H}\alpha$-derived SFR (with no dust correction applied) to
the TIR-derived SFR. We can also use this ratio of the fluxes to estimate
$A_{\rm{H}\alpha}$ in a spatially-resolved way, as follows. Folding in a dust-
correction to the $\rm{H}\alpha$ flux, and then equating the two SFRs:

$\rm{SFR}/M_{\odot}\rm{yr}^{-1}=L_{\rm{TIR}}\times
10^{-43.41}=L_{\rm{H}\alpha}\times 10^{-41.27}\times 10^{0.4A_{\rm{H}\alpha}}$
(5)

yields an expression for $A_{\rm{H}\alpha}$:

$A_{\rm{H}\alpha}=2.5\log_{10}\Bigg{(}\frac{\rm{L_{TIR}}}{\rm{L}_{\rm{H}\alpha}}\Bigg{)}-5.35.$
(6)

Note that this method assumes that $\rm{H}\alpha$ and FIR flux are tracing
only recently formed stars, and sensitive to star formation on the same
timescales.
We plot the spatially-resolved $A_{\rm{H}\alpha}$ in the right-hand panel of
Figure 8. $A_{\rm{H}\alpha}$ substantially exceeds $1$, the canonical value
applied to global studies, across the spatial extent of the galaxy. The
derived $A_{\rm{H}\alpha}$ is larger than that derived from scaling $A_{V}$
according to the Calzetti et al. (2000) law and Charlot & Fall (2000)
prescription ($A_{\rm{H}\alpha}=3.7$) in the dustiest parts of the galaxy. In
the most dusty central region, it reaches a peak of $A_{\rm{H}\alpha}\sim 5$.
In fact, the true value is likely to be above that due to gradients in the
dust temperature and opacity.

###  4.3 Origin of the observed rest-frame UV flux

While the $\rm{H}\alpha$ emission traces broadly the same spatial extent as
the rest-frame FIR emission, the rest-frame UV emission is concentrated
towards the North East of the galaxy. Assuming that $\rm{H}\alpha$ and UV are
probing the same star formation, we can predict the observed UV flux,
$I_{\rm{obs,UV}}$, from the observed $\rm{H}\alpha$ flux,
$I_{\rm{obs,H}\alpha}$, using the $A_{\rm{H}\alpha}$ map shown in Figure 8
and:

$I_{\rm{int,H}\alpha}=I_{\rm{obs,H}\alpha}10^{0.4A_{\rm{H}\alpha}}=\frac{10^{41.27}}{10^{43.17}}\times
I_{\rm{obs,UV}}10^{0.4A_{\rm{UV}}}.$ (7)

The predicted UV flux map is highly dependent on the assumed relation between
$A_{\rm{UV}}$ and $A_{\rm{H}\alpha}$; if we account for extra attenuation
towards birth clouds according to Charlot & Fall (2000), the predicted UV flux
is slightly higher than observed, and extends towards the South West end of
the galaxy. If we use a lower $k_{\rm{H}\alpha}$ based on the continuum
$k_{\lambda}$, the flux falls below the noise level of the HST image across
the galaxy’s spatial extent.
Our modelling suggests that it is not possible to predict the observed
morphology of the rest-frame UV emission from the combination of the
$\rm{H}\alpha$ image and the $A_{\rm{H}\alpha}$ map. This may imply that the
recent star-formation (probed by $\rm{H}\alpha$) is attenuated so strongly as
to be undetectable in our F606W HST image. In this case, the UV flux that we
do observe is tracing star formation on slightly longer timescales. This
scenario is consistent with the peak of the stellar mass lying towards the
North East of the $\rm{H}\alpha$ flux (see the F140W image). Indeed,
qualitatively, we are broadly able to model the observed UV emission by
assuming that, before obscuration, the UV light traces the same region as the
optical image. If we then apply a dust attenuation map like the one shown in
Figure 8, we recover a peak of UV emission in the region that is observed. A
detailed quantitative comparison of this would require assumptions about the
relation between rest-frame UV and rest-frame optical light, which is
sensitive to the age and metallicity of the starburst.

##  5 SHiZELS-14 in the context of the sub-millimeter galaxy population

SHiZELS-14 was identified by the HiZELS survey, which uses an
$\rm{H}\alpha$-based selection and largely probes typical star-forming
galaxies, assuming typical extinction. However, it displays a number of
extreme properties including high star-formation rate, dust mass and dust
attenuation, and a TIR luminosity that places it in the ULIRG regime. In this
section, we examine SHiZELS-14 in the context of sub-millimeter galaxies at
similar redshifts.
We compare SHiZELS-14 to galaxies from the ALMA follow-up of the SCUBA-2
Cosmology Legacy Survey’s UKIDSS-UDS field (AS2UDS; Stach et al. 2018, 2019;
Dudzeviciute et al. 2020). This is drawn from a $\sim 1\,\rm{deg}^{2}$ SCUBA-2
survey. The ALMA pointings target $\sim 700$ submillimeter-luminous
($S_{870}\gtrapprox 1\rm{mJy}$) galaxies, with median redshift
$z_{\rm{phot}}=2.61\pm 0.09$ (Dudzeviciute et al., 2020). In Figure 3 (left-
hand panel), we show the distribution of dust-to-stellar mass ratio versus
total infrared luminosity for the AS2UDS SMGs from the analysis of
Dudzeviciute et al. (2020) (red circles). SHiZELS-14 lies above the average of
the galaxies in TIR luminosity, but has a fairly unremarkable dust mass-to-
stellar mass ratio. In the right-hand panel of the same figure, we show the
effective radius of the dust continuum emission along the semi-major axis
versus the total infrared luminosity for a subsample of the AS2UDS sources
with higher spatial resolution ALMA observations from Gullberg et al. (2019),
with SHiZELS-14 overplotted on the same axes. In the context of these bright
SMGs, SHiZELS-14’s TIR luminosity is not exceptional. However, it has a dust
continuum size that is larger than any of the comparison sample.
Like other SMGs, SHiZELS-14 displays a compact core of dust continuum
emission. As seen from Figure 1, it also has substantial extended emission,
which we are able to resolve due to our deep ALMA imaging. Gullberg et al.
(2019) discuss the possibility of an extended component in the AS2UDS SMGs.
For sources with SCUBA-2 flux densities brighter than $4\rm{mJy\,beam^{-1}}$
(SHiZELS-14 is in this class), the median flux recovery from the ALMA
pointings is $97^{+1}_{-2}$ per cent (Stach et al., 2019). For sources with
fainter SCUBA-2 flux densities ($2.5\leq S_{850}\leq 2.9\rm{mJy\,beam^{-1}}$),
the median flux recovery of those with ALMA detections is $88\pm 6$ per cent.
These high levels of flux recovery suggest that the rest-frame FIR emission of
the AS2UDS SMGs is genuinely very compact, and not dominated by extended
emission below the surface brightness limit of the ALMA observations. Gullberg
et al. (2019) further characterise the extended emission using a stacking
analysis. Their stacked profile is well-fitted by a two-component model,
consisting of two Sérsic profiles of effective radii $\sim 0.1^{\prime\prime}$
and $\sim 0.5^{\prime\prime}$. The extended component accounts for only $13\pm
1$ per cent of the integrated modelled emission, on average. While probing to
lower surface brightness might increase the effective radii measured
(particularly if the fainter flux is substantially more extended than the
core), the central $1-2\,\rm{kpc}$ will remain the dominant source of flux.
Smail et al. (2020) derive a statistical correction to the AS2UDS source
sizes, using a flux-weighted sum of the measured size presented by Gullberg et
al. (2019) and a $0.5^{\prime\prime}$ component with flux density
$0.5\,\rm{mJy}$. This increases their source radii by a fairly modest factor
of $1.3^{+0.25}_{-0.13}$. We apply this correction to the AS2UDS data, and
note that SHiZELS-14 remains an outlier. The $\sim 4\,\rm{kpc}$ component that
contributes only $\sim 10$ per cent of the total flux for the ASUDS SMGs is
the dominant component for SHiZELS-14, which displays an extended disk-like
structure that is well-fitted by a single two-dimensional Sérsic profile with
$R_{e}^{\rm{maj}}=4.6\,\rm{kpc}$, $n=1$ and $q=0.47$. SHiZELS-14 is genuinely
more extended than the majority of the AS2UDS SMGs, perhaps due to being a
mid-stage merger.
We also compare SHiZELS-14 to a sample of $K$-band-identified, stellar mass-
selected ($M_{*}>10^{11}M_{\odot}$), $UVJ$-classified star-forming,
intermediate redshift ($z=1.9-2.6$) galaxies studied by Tadaki et al. (2020).
Unlike the AS2UDS sources, these galaxies were not explicitly selected to be
sub-millimeter bright. For the $69$ of their sources that lie in UDS, we make
use of the same multi-wavelength parent catalogues used in Dudzeviciute et al.
(2020) for the AS2UDS galaxies, and repeat the MAGPHYS SED fitting procedure.
We also adopt the effective radii presented by Tadaki et al. (2020), obtained
via fitting in the $uv$ plane (with fixed $n=1$). Our new MAGPHYS fits and
these radii together provide the physical properties of a complementary sample
of star-forming galaxies with similar stellar masses and redshifts to
SHiZELS-14.

Figure 9: Left: dust mass-to-stellar mass ratio versus total infrared
luminosity, for the AS2UDS sub-millimeter bright galaxies (red circles;
Dudzeviciute et al. 2020), the subset of stellar mass-selected galaxies from
(Tadaki et al., 2020) that are in UDS and have size measurements, and the
three TIR-brightest SHiZELS galaxies from Cheng et al. (2020) (black).
SHiZELS-14 (black star) is well within the range of both parameters derived
for the sub-millimeter galaxy population. Dust mass and stellar mass are
derived using MAGPHYS for SHiZELS-14 and the AS2UDS and Tadaki et al. (2020)
samples. Right: effective radius (along the semi-major axis) versus total
infrared luminosity for the subsample of these galaxies targeted at higher
spatial resolution with ALMA, presented by Gullberg et al. (2019)333We have
corrected a minor error in the table presented by Gullberg et al. (2019). This
error is noted in Smail et al. (2020). The stated $R_{e}$ values for the case
of the fixed $n=1$ fit give the effective radius along the semi-minor axis,
rather than the semi-major axis. We correct these using
$R_{e,\rm{ALMA}}^{\rm{maj}}=R_{e,\rm{original}}/\rm{axial\,ratio}$., with the
small statistical correction derived by Smail et al. (2020) applied to the
source sizes. The grey line at $R_{e,\,\rm{ALMA}}=4\,\rm{kpc}$ marks the
effective radius of the faint extended component that is measured in the
stacking analysis of Gullberg et al. (2019). For both the Gullberg et al.
(2019) sample and SHiZELS-14, radii were calculated using two-dimensional
Sérsic fits (with fixed $n=1$) in the image plane. For the remaining SHiZELS
galaxies, radii were derived using a curve-of-growth analysis (Cheng et al.,
2020). For the (Tadaki et al., 2020) sample, radii were derived using Gaussian
model fits in the $uv$-plane. SHiZELS-14 has a much larger effective radius
(as measured in the rest-frame FIR) than the majority of the AS2UDS galaxies,
though several less FIR-luminous galaxies in the (Tadaki et al., 2020) sample
are similarly extended. The extended dust emission suggests that SHiZELS-14 is
caught in the mid-stages of a merger.

In line with their selection, the Tadaki et al. (2020) sample typically have
lower dust masses and TIR luminosities than the AS2UDS sample (median
$\log_{10}(L_{\rm{TIR}}/\rm{L}_{\odot})=12.5$ for the AS2UDS sample, compared
to $12.0$ for the Tadaki et al. (2020) sample), as well as lower dust
temperatures (median $T_{\rm{dust}}=40.7\,\rm{K}$ for the AS2UDS sample,
compared to $35.0\,\rm{K}$ for the Tadaki et al. (2020) sample, though see the
caveats noted in Dudzeviciute et al. (2020) regarding discrepancies between
MAGPHYS-derived dust temperatures and those inferred from modified black-body
fitting). As shown in the right-hand panel of Figure 3, the Tadaki et al.
(2020) sample occupies a different region of the $R_{e}$ versus LIR plane to
the AS2UDS galaxies. These less TIR-luminous galaxies tend to have larger
sizes (median $R_{\rm{eff,ALMA}}^{\rm{maj}}(n=1)=1.8\,\rm{kpc}$, and 11
galaxies have $R_{\rm{eff,ALMA}}^{\rm{maj}}(n=1)>3\,\rm{kpc}$). This result is
broadly consistent with the large sizes ($R_{\rm{eff,ALMA}}^{\rm{maj}}\sim
5\,\rm{kpc}$) of the broader SHiZELS sample, presented in Cheng et al. (2020);
all but one of these (SHiZELS-14) have lower TIR luminosities than the AS2UDS
sample ($\log_{10}(L_{\rm{TIR}}/\rm{L}_{\odot})<12$). The most luminous of the
Tadaki et al. (2020) sample ($\log_{10}(L_{\rm{TIR}}/\rm{L}_{\odot})\gtrapprox
12.5$) are just as compact as the AS2UDS sources.
Here, we relate the observed morphology of the dust continuum emission to the
physical processes taking place within star-forming galaxies around the peak
of cosmic star formation. As discussed by Cheng et al. (2020), the extended
dust continuum emission observed in the less-FIR luminous SHiZELS galaxies
suggests a dominant component of extended, disk-wide star formation; in
contrast, the emission from sub-millimeter selected galaxies appears to be
dominated by a compact, nuclear starburst. SHiZELS-14 is an outlier in the
sense that it has both a sub-millimeter bright compact core and very extended
emission. Tadaki et al. (2020) show that the most compact galaxies in their
sample tend to have high gas fractions (derived via $S_{870\mu\rm{m}}$), and
argue that this reflects efficient radial gas inflows. Numerical simulations
have long shown that galaxy mergers are capable of triggering tidally-driven
gas inflows (Hernquist, 1989; Barnes & Hernquist, 1991), which can cause
strong nuclear starbursts (e.g. Mihos & Hernquist, 1994, 1996; Hopkins et al.,
2013; Moreno et al., 2015). However, observations of local galaxies such as
the Antennae system demonstrate that galaxy interactions can also trigger
widespread star formation that is not limited to a compact, nuclear region
(Wang et al., 2004). More recent, high resolution simulations show that these
observations can be explained via merger-driven injections of turbulence into
the ISM: extended compression results in fragmentation into dense, star-
forming gas, and spatially extended starburst activity (Renaud et al., 2014,
2015). Renaud et al. (2015) argue that this process is particularly important
in the early and mid stages of a galaxy merger: during the first two simulated
pericenter passages, star clusters form kiloparsecs from the galactic nucleus,
with the central starburst dominating only from the beginning of the final
coalescence. This progression of star formation from extended to compact as
the merger unfolds is also consistent with observations of local galaxies (Pan
et al., 2019). The extended star formation observed in SHiZELS-14 may
therefore suggest that we are viewing the short-lived mid-stages of a merger;
this would be consistent with its complex, irregular morphology and
dispersion-dominated $\rm{H}\alpha$ kinematics. The similarly TIR-luminous but
more compact sources within the AS2UDS samples may comprise galaxies
experiencing a wider range of evolutionary stages, including some later-stage
mergers.

##  6 Conclusions

In this paper, we have presented a study of SHiZELS-14, a $z=2.24$ galaxy
originally identified by HiZELS via its $\rm{H}\alpha$ emission. SHiZELS-14
was one of the galaxies selected for high spatial resolution follow-up, due to
its proximity to a guide star (for adaptive optics observations), rather than
any special properties. However, this galaxy has some intriguing features when
resolved at high spatial resolution, particularly at long wavelengths.
The global properties of SHiZELS-14 show that it is highly star-forming. SED
fits to photometric data indicate a strong burst of star formation within
$\sim 200$ Myr of $z=2.24$ and a stellar mass of $10^{11.2\pm
0.1}\,\rm{M_{\odot}}$. Fitting the dust SED with modified black body models
yields a dust mass of $\rm{M_{\rm{dust}}}=10^{9.0\pm 0.1}\,\rm{M_{\odot}}$ and
a TIR luminosity of $\log_{10}(L_{\rm{TIR}}/\rm{L_{\odot}})=12.81\pm 0.02$.
This bright IR emission places it in the category of a ULIRG, while its strong
submillimeter detection shows it is an SMG. SHiZELS-14 lies on the $z\sim 2$
IR-radio relation expected for a star-forming galaxy and our extensive multi-
wavelength data presents no evidence of AGN activity.
FUV, $\rm{H}\alpha$, FIR and radio continuum emission are all used to infer
SFR, individually and in combination. We investigate the agreement of widely-
used SFR calibrations, globally and in a spatially-resolved manner. Without
any dust corrections, the SFRs inferred from FUV and $\rm{H}\alpha$ are $13\pm
1\,\rm{M_{\odot}}\rm{yr}^{-1}$ and $33\pm 2\,\rm{M_{\odot}}\rm{yr}^{-1}$,
respectively. The SFR inferred from the TIR emission is $950\pm
50\,\rm{M_{\odot}}\rm{yr}^{-1}$, and the radio-derived SFR is also in the
region $\sim 1000\,\rm{M_{\odot}}\rm{yr}^{-1}$. Thus, SFR inferred from short
wavelength light is orders of magnitude lower than that measured at longer
wavelengths. This suggests that SHiZELS-14 is affected by a large degree of
dust attenuation, in line with its substantial dust mass and FIR flux, and it
shares many properties with the known population of high redshift SMGs.
We present kpc-scale imaging in the rest-frame FUV and optical (from HST), at
FIR-wavelengths (from ALMA), of the $\rm{H}\alpha$ emission line (from
SINFONI, on the VLT), and of the radio continuum (from the JVLA). The range of
wavelengths probed enables us to detect both unattenuated and dust-reprocessed
emission. SHiZELS-14 shows striking, extended emission in both $\rm{H}\alpha$
and the FIR, with $\rm{H}\alpha$-derived effective radius $4.6\pm
0.4\,\rm{kpc}$ and a FIR-derived effective radius along the semi-major axis
$4.6\pm 0.2\,\rm{kpc}$ (axial ratio $q=0.47$). Unlike many SMGs studied at
similar redshifts which display compact $1-2\,\rm{kpc}$ cores, SHiZELS-14
displays an extended disk structure in the rest-frame FIR. Our deep imaging
enables us to recover directly the fainter emission across extended regions of
star formation, which are also traced by $\rm{H}\alpha$. The irregular,
extended structures and disordered $\rm{H}\alpha$ kinematics, together with
the intense burst of dusty star formation observed, likely reflects ongoing
(at $=2.24$) merger activity.
The high spatial resolution of our data enables us to study emission on kpc
scales, and compare SFRs in a spatially-resolved manner. We show that the SFR
surface density maps derived from UV, $\rm{H}\alpha$ and TIR are discrepant
across the the extent of the galaxy. Comparison of the $\rm{H}\alpha$ and TIR
maps enables us to map the dust attenuation, under the assumption of minimal
gradients in dust temperature and optical depth. We find high levels of dust
attenuation across the galaxy, with $A_{\rm{H}\alpha}\sim 2-3$ in the
outskirts, rising to $A_{\rm{H}\alpha}>5$ in the central region. This work
highlights the importance of studying galaxies at multiple wavelengths and
demonstrates the biases that can be introduced by assuming that calibrations
derived using samples of relatively dust-poor galaxies will be appropriate for
extremely dusty systems.

## Acknowledgements

We thank the anonymous reviewer for helpful suggestions that improved the
paper. RKC acknowledges funding from an STFC studentship, the Institute for
Astronomy, University of Edinburgh, and the John Harvard Distinguished Science
Fellowship. PNB is grateful for support from STFC via grant ST/R000972/1. AMS
and IRS acknowledge support from STFC (ST/T000244/1). EI acknowledges partial
support from FONDECYT through grant N∘1171710\. This work was supported by the
National Science Foundation of China (11721303, 11991052) and the National Key
R&D Program of China (2016YFA0400702). CC is supported by the National Natural
Science Foundation of China, No. 11803044, 11933003. This work is sponsored
(in part) by the Chinese Academy of Sciences (CAS), through a grant to the CAS
South America Center for Astronomy (CASSACA). DS acknowledges financial
support from Lancaster University through an Early Career Internal Grant
A100679. RKC thanks Adam Carnall for assistance with the BAGPIPES SED fitting
tool and Richard Bower for helpful discussions during the PhD viva. We thank
Jiasheng Huang for providing us with the CLAUDS image of SHiZELS-14.
This research is based on observations made with the NASA/ESA Hubble Space
Telescope obtained from the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5-26555. These observations are associated with
program 14919. This paper makes use of the following ALMA data:
ADS/JAO.ALMA2015.1.00026.S. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. This paper uses data from SINFONI, based on observations collected at
the European Organisation for Astronomical Research in the Southern Hemisphere
under ESO programme 084.B-0300. This work is based on data products from
observations made with ESO Telescopes at the La Silla Paranal Observatory
under ESO programme 179.A-2005 and on data products produced by TERAPIX and
the Cambridge Astronomy Survey Unit on behalf of the UltraVISTA consortium.
The HSC collaboration includes the astronomical communities of Japan and
Taiwan, and Princeton University. The HSC instrumentation and software were
developed by the National Astronomical Observatory of Japan (NAOJ), the Kavli
Institute for the Physics and Mathematics of the Universe (Kavli IPMU), the
University of Tokyo, the High Energy Accelerator Research Organization (KEK),
ASIAA, and Princeton University. Funding was contributed by the FIRST program
from Japanese Cabinet Office, the Ministry of Education, Culture, Sports,
Science and Technology (MEXT), the Japan Society for the Promotion of Science
(JSPS), Japan Science and Technology Agency (JST), the Toray Science
Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton University.
This work is based on observations obtained with MegaPrime/ MegaCam, a joint
project of CFHT and CEA/DAPNIA, at the CFHT which is operated by the National
Research Council (NRC) of Canada, the Institut National des Science de
l’Univers of the Centre National de la Recherche Scientifique (CNRS) of
France, and the University of Hawaii. This research uses data obtained through
the Telescope Access Program (TAP), which has been funded by the National
Astronomical Observatories, Chinese Academy of Sciences, and the Special Fund
for Astronomy from the Ministry of Finance. This work uses data products from
TERAPIX and the Canadian Astronomy Data Centre. It was carried out using
resources from Compute Canada and Canadian Advanced Network For Astrophysical
Research (CAN-FAR) infrastructure. These data were obtained and processed as
part of CLAUDS, which is a collaboration between astronomers from Canada,
France, and China described in Sawicki et al. (2019).
This research has made use of the VizieR catalogue access tool, CDS,
Strasbourg, France. The original description of the VizieR service was
published in A&AS 143, 23. The Herschel Extragalactic Legacy Project (HELP) is
a European Commission Research Executive Agency funded project under the
SP1-Cooperation, Collaborative project, Small or medium-scale focused research
project, FP7-SPACE-2013-1 scheme, Grant Agreement Number 607254.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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##  Appendix A Deriving a rest-frame FIR size from the ALMA data

In Figure 10 we show a Gaussian model fit to the $260\,\rm{GHz}$ ALMA
visibility data. The derived effective radius along the semi-major axis,
$R_{e}^{\rm{maj}}=4.5\pm 0.2\,\rm{kpc}$, is larger than is typical for SMGs,
as shown in Figure 3, but broadly in agreement with the effective radius
derived from the $\rm{H}\alpha$ image ($4.6\pm 0.4\,\rm{kpc}$; Swinbank et al.
2012a). We also fit an exponential profile ($f(r)\propto e^{-r/r_{0}}$) with
the uvmultfit tool (Martí-Vidal et al., 2014) and obtain a best-fitting scale
length $r_{0}=4.1\pm 0.2\,\rm{kpc}$.

Figure 10: $uv$-amplitude plot for the ALMA $260\,\rm{GHz}$ data. We fit a
Gaussian model with varying axis ratio in the $uv$-plane, using CASA’s
uvmodelfit task. The effective radius along the semi-major axis,
$R_{e}^{\rm{maj}}$, $4.5\pm 0.2\,\rm{kpc}$. Consistent results are obtained
using the uvmultfit tool (Martí-Vidal et al., 2014). We also fit an
exponential profile and obtain a best-fitting scale length $r_{0}=4.1\pm
0.2\,\rm{kpc}$.

##  Appendix B Detailed description of SED fitting with BAGPIPES

Figure 11: Data presented in Table 3, fitted with the BAGPIPES code (Carnall
et al., 2018), using a double power law star formation history. Error bars are
plotted on the data points, but are small. The fitting yields $\rm{SFR}=660\pm
60\,M_{\odot}/\rm{yr}$ and $\log_{10}M_{*}/M_{\odot}=11.1\pm 0.1$, in good
agreement with the estimates from MAGPHYS.

To assess the sensitivity of our derived physical parameters to our choice of
SED fitting code, we refit the photometry with another code. Our fitting makes
use of the 2016 version of the BC03 SSP templates, with a Kroupa (2002) IMF
(note that the difference between a Kroupa and Chabrier IMF is negligible).
Nebular emission is computed using the CLOUDY photoionization code (Ferland et
al., 2017), following Byler et al. (2017). CLOUDY is run using each SSP
template as the input spectrum. Dust grains are included using CLOUDY’s ‘ISM’
prescription, which implements a grain-size distribution and abundance pattern
that reproduces the observed extinction properties for the ISM of the Milky
Way. We select a Calzetti et al. (2000) dust attenuation curve. Dust emission
includes both a hot dust component from HII regions and a grey body component
from the cold, diffuse dust.
We impose a wide dust attenuation prior, $A_{v}=[0,6]$, which gives the code
the option to fit a high degree of attenuation. Following Draine & Li (2007),
we fit three parameters that affect the shape of the dust SED: $U_{\rm{min}}$,
the lower limit of the starlight intensity; $\gamma$, the fraction of stars at
$U_{\rm{min}}$; and $q_{\rm{PAH}}$, the mass fraction of polycyclic aromatic
hydrocarbons. Our priors on these parameters are broad, to allow the model the
option to fit a hot dusty galaxy: $U_{\rm{min}}=[0,25]$, $\gamma=[0,1]$, and
$q_{\rm{PAH}}=[0,10]$. We also fit $\eta$, the multiplicative factor on
$A_{V}$ for stars in birth clouds, using the range $\eta=[1,5]$. We allow
metallicity to vary in the range $Z=[0,2.5]Z_{\odot,\rm{old}}$, where
$Z_{\odot,\rm{old}}$ denotes solar models prior to Asplund et al. (2009). We
fix the redshift at $z=2.2418$, since this is known from the SINFONI spectrum.
We experiment with various star-formation history (SFH) parametrisations,
which yield very similar fits to the spectrum and consistent values for
stellar mass, $\log_{10}M_{*}/\rm{M_{\odot}}=11.1\pm 0.1$. All
parametrisations, even those allowing multiple bursts, favour a recent (at
$z=2.24$), rapid burst of star formation in which the vast majority of the
stellar mass is formed. In Figure 11, we plot a representative fit to the
photometry. This particular model uses a double power law SFH parametrisation.
The posterior estimate for the star-formation rate is $\rm{SFR}=660\pm
60\,\rm{M_{\odot}}\rm{yr}^{-1}$, and the estimated specific star-formation
rate (sSFR) is $\log_{10}(\rm{sSFR}/yr^{-1})=-8.25\pm 0.11$. Note that the SFR
is more sensitive than the stellar mass to the parametrisation of the SFH and
the data included in the fit, and averaging over multiple SFH models increases
the uncertainty on the SFR to $\sim 100\,\rm{M_{\odot}}\rm{yr}^{-1}$. The
posterior estimate for the dust attenuation in the $V$-band is $A_{v}=1.8\pm
0.1$. All of these derived physical parameters are consistent with the
estimates from MAGPHYS, which indicates that our fitting is robust to choice
of SED fitting code.

Instrument/Telescope | Filter | Measurement
---|---|---
(Survey) |  | ($\mu\rm{Jy}$)
MegaCam/CFHT | $u^{*}$ | $0.26\pm 0.04$
Suprime-Cam/Subaru | $B$ | $0.46\pm 0.03$
| $V$ | $1.01\pm 0.05$
| $r$ | $1.21\pm 0.05$
| $i_{\rm{+}}$ | $1.66\pm 0.05$
| $z_{\rm{+}}$ | $2.87\pm 0.16$
| $z_{\rm{++}}$ | $2.87\pm 0.07$
| $\rm{IA}427$ | $0.45\pm 0.08$
| $\rm{IA}464$ | $0.60\pm 0.09$
| $\rm{IA}484$ | $0.58\pm 0.08$
| $\rm{IA}505$ | $0.71\pm 0.09$
| $\rm{IA}527$ | $0.85\pm 0.06$
| $\rm{IA}574$ | $0.94\pm 0.10$
| $\rm{IA}624$ | $1.25\pm 0.08$
| $\rm{IA}679$ | $1.53\pm 0.13$
| $\rm{IA}709$ | $1.44\pm 0.09$
| $\rm{IA}738$ | $1.36\pm 0.10$
| $\rm{IA}767$ | $1.74\pm 0.12$
| $\rm{IA}827$ | $2.01\pm 0.14$
| $\rm{NB}711$ | $1.39\pm 0.16$
| $\rm{NB}816$ | $2.07\pm 0.15$
HSC/Subaru | $Y_{\rm{HSC}}$ | $3.1\pm 0.2$
VIRCAM/VISTA | $Y$ | $3.47\pm 0.07$
(UltraVISTA-DR2) | $J$ | $6.80\pm 0.10$
| $H$ | $10.64\pm 0.16$
| $K_{s}$ | $19.40\pm 0.14$
WIRCam/CFHT | $K_{\rm{sw}}$ | $19.6\pm 0.8$
| $H_{\rm{w}}$ | $10.9\pm 0.7$
Spitzer/IRAC | $3.6\,\mu\rm{m}$ | $35.1\pm 0.3$
(SPLASH) | $4.5\,\mu\rm{m}$ | $44.6\pm 0.3$
| $5.8\,\mu\rm{m}$ | $48.9\pm 3.6$
| $8\,\mu\rm{m}$ | $33.2\pm 6.1$
Spitzer/MIPS | $24\,\mu\rm{m}$ | $403\pm 17$
Herschel-HerMES/ Oliver+12 | $100\,\mu\rm{m}$ | $8.4\pm 0.9\,(\rm{mJy})$
HELP catalogue values | $160\,\mu\rm{m}$ | $20.5\pm 3.7\,(\rm{mJy})$
| $250\,\mu\rm{m}$ | $31.3\pm 2.2\,(\rm{mJy})$
| $350\,\mu\rm{m}$ | $36.5\pm 2.5\,(\rm{mJy})$
| $500\,\mu\rm{m}$ | $27.5\pm 2.7\,(\rm{mJy})$
ALMA Band 6, this paper | $260\,\rm{GHz}$ | $2.7\pm{0.2}\,(\rm{mJy})$
ALMA Band 7, Scoville+14 | $350\,\rm{GHz}$ | $4.7\pm{0.8}\,(\rm{mJy})$
SCUBA-2, Simpson+19 | $350\,\rm{GHz}$ | $5.4\pm{1.3}\,(\rm{mJy})$
JVLA, This paper | $6\,\rm{GHz}$ | $20\pm 2$
JVLA, Smolčić+17 | $3\,\rm{GHz}$ | $68\pm 4$
VLA, Schinnerer+10 | $1.4\,\rm{GHz}$ | $122\pm 13$
Table 3: Compilation of existing and new measurements of SHiZELS-14, with
source. Unless otherwise stated, the data are taken these from the tables of
Laigle et al. (2016), adopting their values calculated within a
$3^{\prime\prime}$ diameter aperture.