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Rivera, G. C., Hodge, J. A., Smail, I., Swinbank, A. M., Weiß, A., Wardlow, J. L., ... 
Werf, P. P. V. D. (2018). Resolving the ISM at the peak of cosmic star formation with 
ALMA - The distribution of CO and dust continuum in z~2.5 sub-millimetre galaxies. 
The Astrophysical Journal. https://doi.org/10.3847/1538-4357/aacffa 
 
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Draft version April 20, 2018
Preprint typeset using LATEX style emulateapj v. 01/23/15
RESOLVING THE ISM AT THE PEAK OF COSMIC STAR FORMATION WITH ALMA -
THE DISTRIBUTION OF CO AND DUST CONTINUUM IN z ∼ 2.5 SUB-MILLIMETRE GALAXIES
Gabriela Calistro Rivera 1, J. A. Hodge1, Ian Smail2, A. M. Swinbank2, A. Weiß3, J. L. Wardlow2, F. Walter4, M. Rybak1,
Chian-Chou Chen5, W. N. Brandt7,8,9, K. Coppin10, E. da Cunha11, H. Dannerbauer12, 13, T. R. Greve14, A. Karim15, K. K.
Knudsen16, E. Schinnerer4, J. M. Simpson6, B. Venemans4, and P. P. van der Werf1
Draft version April 20, 2018
ABSTRACT
We use ALMA observations of four sub-millimetre galaxies (SMGs) at z ∼ 2 − 3 to investigate the spatially
resolved properties of the inter-stellar medium (ISM) at scales of 1–5 kpc (0.1–0.6′′). The velocity fields of our
sources, traced by the 12CO(J=3-2) emission, are consistent with disk rotation to first order, implying average
dynamical masses of ∼3×1011M within two half-light radii. Through a Bayesian approach we investigate
the uncertainties inherent to dynamically constraining total gas masses. We explore the covariance between
the stellar mass-to-light ratio and CO-to-H2 conversion factor, αCO, finding values of αCO = 1.1+0.8−0.7 for dark
matter fractions of 15%. We show that the resolved spatial distribution of the gas and dust continuum can be
uncorrelated to the stellar emission, challenging energy balance assumptions in global SED fitting. Through
a stacking analysis of the resolved radial profiles of the CO(3-2), stellar and dust continuum emission in SMG
samples, we find that the cool molecular gas emission in these sources (radii∼5–14 kpc) is clearlymore extended
than the rest-frame ∼250 µm dust continuum by a factor > 2. We propose that assuming a constant dust-to-gas
ratio, this apparent difference in sizes can be explained by temperature and optical-depth gradients alone. Our
results suggest that caution must be exercised when extrapolating morphological properties of dust continuum
observations to conclusions about the molecular gas phase of the ISM.
Keywords: galaxies: sub-millimeter, etc.
1. INTRODUCTION
The process of massive galaxy assembly in the Universe
has been identified to peak between 1 < z < 3, where the
majority of the stars in the present-day galaxies formed (e.g.,
calistro@strw.leidenuniv.nl
1 Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidel-
berg, Germany
1 Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Lei-
den, The Netherlands
2 Centre for Extragalactic Astronomy,Department of Physics,Durham
University, South Road, Durham DH1 3LE, UK
3 Max-Planck-Institut für Radioastronomie, Auf demHügel 69, D-53121
Bonn, Germany
4 Max–Planck Institut für Astronomie, Königstuhl 17, 69117 Heidel-
berg, Germany
5 European Southern Observatory, Karl Schwarzschild Strasse 2, Garch-
ing, Germany
6 Academia Sinica Institute of Astronomy and Astrophysics, No. 1, Sec.
4, Roosevelt Rd., Taipei 10617, Taiwan
7 Department of Astronomy & Astrophysics, 525 Davey Lab, Pennsyl-
vania State University, University Park, PA 16802, USA
8 Institute for Gravitation and the Cosmos, Pennsylvania State Univer-
sity, University Park, PA 16802, USA
9 Department of Physics, The Pennsylvania State University, University
Park, PA 16802, USA
10 Centre for Astrophysics Research, University of Hertfordshire, Hat-
field, AL10 9AB, UK
11 The Australian National University, Mt Stromlo Observatory, Cotter
Rd, Weston Creek, ACT 2611, Australia
12 Instituto deAstrofísica de Canarias (IAC), E-38205 La Laguna, Tener-
ife, Spain
13 Universidad de La Laguna, Dpto. Astrofisica, E-38206 La Laguna,
Tenerife, Spain
14 Department of Physics and Astronomy, University College London,
Gower Street, London, WC1E 6BT, UK
15 Argelander–Institute of Astronomy, Bonn University, Auf dem Hügel
71, D-53121 Bonn, Germany
16 Department of Earth and Space Sciences, Chalmers University of
Technology, Onsala Space Observatory, 439 92 Onsala, Sweden
Madau & Dickinson 2014). This star formation (SF) is likely
strongly connected to the gas content and its distribution in the
interstellar medium (ISM) and the efficiency with which this
gas is transformed into stars (e.g. Decarli et al. 2016; Scoville
et al. 2017; Tacconi et al. 2017). Gas-rich, dusty galaxies,
as submillimetre galaxies (SMGs; e.g., Blain et al. 2002)
are effective laboratories to characterize this star-forming ISM
due to their high molecular gas content (Bothwell et al. 2013)
and their bright dust continuum emission ensured by their
selection. Moreover, they appear to contribute around 20%
of the total star-formation rate density at z ∼ 2 − 3 (e.g.,
Swinbank et al. 2014) and are thus an important tracer of the
star formation occurring in massive galaxies at this epoch.
The characterization of the star-forming ISM at these high
redshifts is typically achieved through observations of the ro-
tational transitions of carbon monoxide (CO) or through deep
imaging of the Rayleigh-Jeans (RJ) tail of the dust contin-
uum emission (for reviews see, Carilli & Walter 2013; Casey
et al. 2014). However, calculations based on these ISM tracers
involve a number of assumptions about the inferred gas prop-
erties. Although CO is the most strongly emitting molecule,
it is only the second most abundant molecule in the galaxy
ISM after molecular Hydrogen, H2, and a conversion factor
(αCO) from the ground-state CO(J = 1 − 0) luminosity to H2
(e.g., Bolatto et al. 2013) is thus required to compute the
total molecular content. As a result there have been numer-
ous observational (e.g., Tacconi et al. 2008; Danielson et al.
2011;Genzel et al. 2012;Hodge et al. 2012; Bolatto et al. 2013;
Bothwell et al. 2013; Accurso et al. 2017) and theoretical (e.g.,
Narayanan et al. 2011, 2012; Lagos et al. 2012) efforts to con-
strain αCO in different galaxy populations, which represents a
significant uncertainty in total gas mass estimations.
Already in the local universe, the range of αCO values is
observed to span a factor of ∼5, and it has been shown to
ar
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 20
18
2 Calistro Rivera et al.
be a function of several galaxy properties such as gas density,
temperature, and metallicity (Bolatto et al. 2013), which likely
evolve with redshift.
Another approach to estimate galaxy gas masses is to use the
dust continuum observations as a proxy for the ISM content at
low and intermediate redshifts (e.g. Hildebrand 1983; Leroy
et al. 2011; Magdis et al. 2011; Scoville et al. 2014). Recently,
Scoville et al. (2016) combined molecular gas masses inferred
from existing CO detections and dust continuum measure-
ments in an attempt to calibrate an empirical scaling factor for
using global measurements of the Rayleigh-Jeans dust con-
tinuum (probed in the sub-mm regime) to estimate the total
ISM masses. Although they find that this calibration holds
for measurements over three orders of magnitude in infrared
luminosity and for different populations including SMGs, this
is based on significant assumptions about the properties of the
dust spectral energy distribution (SED) in addition to the un-
certainties on the αCO parameter assumed for the calibration.
To test the validity of these assumptions, observational con-
straints on the physics of the high-redshift ISM are required.
Spatially unresolved high-redshift surveys of CO and dust
continuum have begun to make progress on these tracers and
their implications for the SF picture from a global perspective.
Over 200 detections of CO line emission at high redshift have
been reported (z > 2; Carilli & Walter 2013) from both indi-
vidual sources (e.g., Genzel et al. 2012; Hodge et al. 2012;
Strandet et al. 2017) and larger statistical surveys (Ivison et al.
2011; Bothwell et al. 2013; Sharon et al. 2016; Walter et al.
2016). In addition, multiple sub-mm continuum surveys have
been conducted to characterize the dust emission and popu-
lation properties of SMGs (Hodge et al. 2013b; Karim et al.
2013; Simpson et al. 2017). Statistical studies (e.g., Both-
well et al. 2013; Sharon et al. 2016) have shed light on the
average level of excitation for SMGs, which are observed to
have large scatter at high excitation levels J ≥ 4 but behave
relatively homogeneously at J ≤ 3 with excitation ratios of
r3−1 = 0.78 ± 0.27 (Sharon et al. 2016). High-excitation CO
transitions (J ≥ 4) have thus been observed to underestimate
the gas masses, since they are biased to trace the most compact
molecular emission only. Finally, using ISM mass estimates
based on dust-continuum observations and assuming a con-
stant dust/gas ratio (e.g., Leroy et al. 2011), Genzel et al.
(2015), Scoville et al. (2017) and Tacconi et al. (2017) were
able to investigate statistically the evolution of the unresolved
star-forming ISM for SF galaxies across cosmic time.
At high resolution, significant progress with the character-
ization of the high-redshift ISM has been achieved through
the observation of gravitationally lensed sources, as part of
surveys conducted by the South Pole Telescope (SPT; e.g.,
Greve et al. 2012; Vieira et al. 2013; Spilker et al. 2016) and
Herschel (e.g. Harris et al. 2012; Wardlow et al. 2013). Lens-
ing observations, however, are sensitive to the lensing models
used to reconstruct the intrinsic morphology of the sources,
and caution must be exercised for possible differential magni-
fication biases especially when more than one ISM tracer are
observed. Only a handful of studies have characterized the
ISM on sub-galactic scales in unlensed high-redshift galax-
ies (e.g., Tacconi et al. 2008; Engel et al. 2010; Hodge et al.
2012, 2013a; Aravena et al. 2014; Decarli et al. 2016; Chen
et al. 2017), and even fewer have studied the dust-continuum
emission and gas observations on comparable scales. High-
resolution imaging is crucial for characterizing the ISM in
galaxies, since apart from providing a better morphological
description of the gas or dust continuum emission, this infor-
mation is key for estimating fundamental properties such as gas
surface density. Moreover, through dynamical modeling of the
velocity fields, one can derive dynamical mass estimates (de
Blok &Walter 2014), which reflect the total mass of baryonic
and non baryonic matter contained within the region traced
by the observed line emission, and thus constraints the sum
of stellar, gas, and dark matter masses. When complemented
with stellar mass and dark matter fraction assumptions, dy-
namical mass estimates can constrain the total mass of the gas
reservoirs (Tacconi et al. 2008; Hodge et al. 2012), and hence
the αCO parameter.
However, estimating the mass of the other components is
also complex, for example the stellar mass of a galaxy is usu-
ally inferred via SEDfitting, which suffers strong degeneracies
between the star formation history, dust reddening, luminosity-
weighted age of the stellar populations and mass-to-light ratio,
especially for highly star-forming galaxies such as SMGs (e.g.,
Hainline et al. 2011; Simpson et al. 2014, 2017). The dark
matter fraction represents a large source of uncertainty, as no
independent measurement of its mass is possible. While re-
cent spectroscopic surveys have claimed dark matter fractions
around 10–30%, (Price et al. 2016; Wuyts et al. 2016; Genzel
et al. 2017) revealing that star-forming galaxies at z > 2 ap-
pear to be heavily baryon dominated, these calculations involve
making similar uncertain assumptions about the gas fractions.
Shedding light on the impact of these uncertainties on the αCO
and gas mass estimations is thus imperative for an improved
characterization of the high-redshift ISM.
The collecting area and sensitivity of the Atacama Large
Millimeter Array (ALMA) is transforming our view of the
star-forming ISM in distant galaxies. While high-resolution
studies of the dust continuum emission in SMGs with ALMA
have shown this material appear to be mostly distributed in
compact regions (Simpson et al. 2015; Ikarashi et al. 2015;
Hodge et al. 2016), the extended sizes revealed by the few
resolved CO detections of luminous sources (Riechers et al.
2010; Hodge et al. 2012; Emonts et al. 2016; Chen et al. 2017;
Dannerbauer et al. 2017; Ginolfi et al. 2017) challenge general
assumptions of co-spatial interwoven dust and gas generally
assumed bymodels. Spatially resolved observations ofCOand
dust continuum emission for homogeneously selected samples
and modelling their interplay, e.g. through radiative transfer
approximations, may help characterize the distributions and
physics of dust and gas in the high-redshift ISM.
Here, we present high-resolution imaging of the CO emis-
sion in four SMGs from the ALESS survey (Hodge et al.
2013b; Karim et al. 2013) at sub-arcsecond resolution. We
address the following questions, which remain open in ISM
studies at high redshift: How is the molecular gas distributed
in relation to the dusty ISM and the stellar populations? What
implications do these distributions have for the assumptions
made for the dust spectral energy distributions and dust-to-gas
ratios at high redshift? How reliable are gas mass estima-
tions? What uncertainties do stellar mass estimates and dark
matter fraction assumptions introduce into the total gas mass
estimation? The paper is structured as follows: in Section 2
we describe the ALMA data reduction and the imaging of the
CO(3-2) maps. In Section 3 we present the analysis of the
kinematic properties of the CO(3-2) emission in our sources
and present the implications of these to total gas estimates. In
Section 4 we present an statistical analysis of the distributions
of gas, dust continuum and stellar emission and discuss the
physical implications of these findings. Throughout the pa-
per we adopt a Λ-CDM cosmology, consistent with the values
Resolving the ISM in z ∼ 2.5 ALESS SMGs 3
Table 1
Description of the ALMA Cycle 2 Band 3 observations and native beam properties
ALESS49.1 ALESS57.1 ALESS67.1 ALESS122.1
R.A. (J2000) 03:31:24.72 03:31:51.92 03:32:43.20 03:31:39.54
Dec. (J2000) −27 : 50 : 47.1 −27 : 53 : 27.1 −27 : 55 : 14.3 −27 : 41 : 19.7
z (opt) 2.95 2.94 2.12 2.02
z (CO(3-2)) 2.943 ± 0.001 2.943 ± 0.002 2.121 ± 0.004 2.024 ± 0.001
Natural weighted imaging
Cleaning mask radius [′′]a. 1.8 0.8 2.0 1.0
Synthesized beam FWHM [′′] 0.69 × 0.63 0.67 × 0.60 0.56 × 0.48 0.45 × 0.35
Continuum RMS [µJy beam−1] 17.6 19.5 18.2 16.3
Channel widths in final cubes [MHz] 15.6b 60.5 81.5 77.3
Channel widths in final cubes [km s−1] 54b 200 213 196
Channel RMS [µJy beam−1] 182b 148 113 131
aChosen as explained in Figure 1.
bHigher spectroscopic resolution was achieved in ALESS 49.1 as compared to the other sources, since the final cube is concatenated from two different
measurement sets. See Section 2.1 for details.
given by the Planck Collaboration et al. (2014), with ΩΛ =
0.69, Ωm = 0.31 and H0 = 67.7 km s−1Mpc−1.
2. OBSERVATIONS AND IMAGING
2.1. Target selection ALMA observations
We present ALMACycle 2 observations of the CO emission
from four SMGs, ALESS49.1, ALESS57.1, ALESS67.1 and
ALESS122.1. These sources were selected from the ALESS
survey (Hodge et al. 2013b; Karim et al. 2013): an ALMA
Cycle 0 follow-up program of 126 sources detected in the
single-dish LABOCA Extended Chandra Deep Field South
(ECDFS) Submm Survey (LESS, Weiß et al. 2009). These
four sources were selected as they are spectroscopically con-
firmed at redshifts 2.1 < z < 2.9 as the result of an ex-
tensive spectroscopic follow-up campaign (Danielson et al.
2017). Three of the four sources in our sample were de-
tected (ALESS57.1 and ALESS67.1) or marginally detected
(ALESS122.1, through stacking) in the X-rays (Wang et al.
2013), using 4 Ms Chandra observations of the CDFS re-
gion (Xue et al. 2011) and 250 ks observations in the ECDFS
(Lehmer et al. 2005). ALESS57.1 and ALESS122.1 are re-
ported as AGN candidates (Wang et al. 2013; Danielson et al.
2017), while the origin of the X-ray emission in ALESS67.1
is most probably related to star formation.
ALMA observations were taken in Cycle 2 as part of the
project 2013.1.00470.S (PI: Hodge), with a total integration
time of ∼2.5 hours in ALMA Band 3, covering the spectral
range expected for the line emission of the CO(3-2) transi-
tion at these redshifts. The sources were observed on 2015
September 4, 6 and 20, using the 12-meter array and under
good phase stability/weather conditions, with PWV at zenith
ranging between 1.56–3.03 mm. The antenna configuration
consisted of 33, 36 and 35 antennas, respectively, achieving
synthesized beam sizes that range between 0.34 – 0.67′′ ma-
jor axis FWHM with largest angular scales (LAS) between
1.9–2.9′′. The observations were calibrated based on Jupiter
as the flux-calibrator, J0334-4008 as the band-pass calibrator,
and J0334-401 as the phase calibrator.
New ALMA observations of ALESS49.1 (Wardlow et al.
2018) were taken duringCycle 4 on 2016November 12, 16 and
20 as part of the project 2016.1.00754.S (PI: Wardlow). These
observations were carried out using a total integration time of
∼ 2700 s and using the longest baselines of ∼ 650 m. With
an angular resolution of 1.1′′, these additional data increase
the signal-to-noise ratio (SNR) of our high-resolution data.
We concatenated both Cycle 2 and Cycle 4 datasets achieving
a combination of high-resolution imaging, high SNR and at
the same time reducing concerns whether we might have re-
solved out any significant flux from ALESS49.1, thanks to the
short baselines covered. An analysis of the environment of
ALESS49.1 is presented in Wardlow et al. (2018).
The ALMA data were calibrated following the ALMA
pipeline and using the CommonAstronomy Software Applica-
tion package (CASA, McMullin et al. 2007). Manual flagging
of a few corrupted time windows for ALESS57.1 was required
after an inspection of the calibration output. The imaging pro-
cess was carried out using CASA tasks (version 4.7.0). The
uv-data were Fourier transformed and deconvolved from the
point spread function using the CASA clean algorithm. After
resampling of the visibilities at different spectral resolutions to
optimize the SNR, we produced the final data cubes averaging
the visibilities to channel widths of 16, 61, 82 and 77 MHz
for ALESS49.1, 57.1, 67.1, 122.1, respectively. At the native
resolution, the rms values achieved for the final data cubes
range from 0.11-0.18 mJy beam−1 (see Table 1).
Due to the high spatial resolution of the data, it is not triv-
ial to estimate the masks on which to apply the clean task.
We adopted an iterative cleaning technique (e.g., Chen et al.
2017), in order to optimize the mask size estimation to include
possible extended low surface brightness emission. Iterative
cleaning consists of drawing concentric circular mask regions
at increasing radii and applying the clean task and line flux ex-
traction within them. Plotting the resulting line fluxes against
the corresponding circular region radii, a curve of growth is
produced (see upper right panels of Fig. 1). The expected
behaviour of the measured flux density in a curve of growth
is to continuously increase as a function of radius, reaching a
point of convergence at the maximum extent of the source. We
used the masks inferred from the iterative cleaning method to
extract the final line cubes. We explored the data for emission
at different spatial scales and surface brightness, first at the
native resolution using natural weighting, then using a Briggs
weighting with a robustness parameter 0.5, to image the CO
emission at lower SNR but slightly higher spatial resolution
and finally, by tapering the visibilities to lower resolutions
(1.5-2 × native beam size) to recover extended emission.
2.2. CO(3-2) line detections and continuum
We detect significant CO(3-2) line emission for the four
sources in our sample even from the dirty data cubes, i.e. in
the Fourier transformed visibilities prior to the beam decon-
volution (cleaning process). The CO detections are coincident
4 Calistro Rivera et al.
87.2 87.4 87.6 87.8 88.0
Frequency [GHz]
0.0000
0.0005
0.0010
0.0015
Fl
ux
de
ns
ity
[J
y]
ALESS 49.1
0.0 0.5 1.0 1.5 2.0 2.5
radii [arcsec]
0.2
0.4
0.6
0.8
1.0
Fl
ux
[J
y
km
/s
]
0 50 100 150 200
UV-distance [kλ]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Fl
ux
de
ns
ity
[m
Jy
]
FWHM: 0.66 ± 0.09 arcsec
87.0 87.5 88.0
Frequency [GHz]
−0.0005
0.0000
0.0005
0.0010
0.0015
0.0020
Fl
ux
de
ns
ity
[J
y]
ALESS 57.1
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
radii [arcsec]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Fl
ux
[J
y
km
/s
]
0 50 100 150 200 250 300
UV-distance [kλ]
−2
−1
0
1
2
3
4
5
Fl
ux
de
ns
ity
[m
Jy
]FWHM: 0.78 ± 0.13 arcsec
110.0 110.5 111.0 111.5
Frequency [GHz]
−0.001
0.000
0.001
0.002
0.003
0.004
0.005
0.006
Fl
ux
de
ns
ity
[J
y]
ALESS 67.1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
radii [arcsec]
0
1
2
3
4
Fl
ux
[J
y
km
/s
]
0 50 100 150 200 250 300
UV-distance [kλ]
−2
−1
0
1
2
3
4
5
Fl
ux
de
ns
ity
[m
Jy
]FWHM: 1.63 ± 0.18 arcsec
114.0 114.5 115.0
Frequency [GHz]
−0.001
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Fl
ux
de
ns
ity
[J
y]
ALESS 122.1
0.0 0.5 1.0 1.5 2.0 2.5
radii [arcsec]
0
1
2
3
4
5
6
7
8
Fl
ux
[J
y
km
/s
]
0 50 100 150 200 250 300
UV-distance [kλ]
−1
0
1
2
3
4
5
6
7
Fl
ux
de
ns
ity
[m
Jy
]
FWHM: 0.84 ± 0.07 arcsec
Figure 1. Analysis of the CO(3-2) data: The left panels show the CO(3-2) spectra of our sources. The spectral resolution is ∼54, 200, 213, and 116 km s−1,
for ALESS49.1, ALESS57.1, ALESS67.1 and ALESS122.1, respectively. Gaussian fits to the spectra are shown by the solid lines. For ALESS49.1 we fit a
two-component Gaussian profile and show each component as dotted lines. For ALESS67.1, we additionally show the CO spectrum extracted exclusively from
within a mask of ∼ 1” around the centroid of the main component as a black line (see Section 2.2 for more details). The right panels show two methods used to
calculate the cleaning masks and intrinsic source sizes, respectively. The first method (top right) is a curve-of-growth analysis, where the shaded area shows the
radius at convergence. This method was used to determine the size of the area used for masking the cleaning process. The second method (bottom right) is the
analysis of the visibilities (uv)-profiles, which reliably estimate intrinsic source sizes. A single Gaussian fit to the uv-data is shown by the line. The half-light
radius r1/2 from the uv-fitting method is a more robust estimate of the true size of the sources, since the curve-of-growth analysis is prone to be affected by
correlated noise. We draw hashed areas to show the FWHM from the Gaussian fit (i.e., 2 × r1/2) on the top-right panel and see that in most cases, it roughly
corresponds to the peak of the curve of growth.
Resolving the ISM in z ∼ 2.5 ALESS SMGs 5
3h31m24.6s24.7s24.8s24.9s
RA (J2000)
49"
48"
47"
46"
-27°50'45"
De
c 
(J2
00
0)
ALESS 49.1
3h31m51.9s52.0s
RA (J2000)
29"
28"
27"
-27°53'26"
De
c 
(J2
00
0)
ALESS 57.1
3h32m43.1s43.2s43.3s
RA (J2000)
16"
15"
14"
-27°55'13"
De
c 
(J2
00
0)
ALESS 67.1
3h31m39.5s39.6s
RA (J2000)
21"
20"
19"
-27°41'18"
De
c 
(J2
00
0)
ALESS 122.1
Figure 2. CO(3-2) velocity averaged contours overlaid on optical/near-IR cutouts from the available HST-WFC3 and/or ACS imaging. Resolutions of 0.4–0.6′′
are achieved through natural weighting. The contours are obtained by averaging over the velocity range corresponding to the FWHM of the Gaussian fit to the CO
spectrum. The contours in all maps show 2-10 σrms regions, where the σrms for the velocity averaged images is: (0.10 mJy beam−1) for ALESS49.1, (0.15 mJy
beam−1) for ALESS57.1, (0.11 mJy beam−1) for ALESS67.1 and (0.13 mJy beam−1) for ALESS122.1. The beam sizes are shown in the lower-left corners of
the images. The background map for ALESS49.1 represents the H160 imaging, the two-color map for ALESS57.1 uses the H160 and I814 fluxes, the background
r-g-b map for ALESS67.1 represents H160, J125,Y105 and the background map for ALESS122.1 shows the I814 imaging. The HST imaging has been corrected
for astrometric offsets using GAIA data. We see that our observations strongly detect and resolve the CO emission of these sources on scales of 3–5 kpc, finding
different morphologies in both CO and stellar emission.
6 Calistro Rivera et al.
with the expected ALMACycle 0 positions, and at frequencies
which confirm the previously reported spectroscopic redshifts
(Table 1). We identify strong line detections for all the sources
in the final line cubes constructed by applying the circular
cleaning masks described in Section 2.1. Fig. 1 show the data
as well as Gaussian profile fits to the extracted spectra. The
estimated CO(3-2) line parameters are summarized in Table 2.
We next briefly describe some important features of the line
emission of each source.
The CO spectrum of ALESS49.1 is clearly best described
by a double-peaked profile and was thus fitted using an asym-
metrical two-Gaussian model. The red and blue component
line widths are 280±40 km s−1and 390±30 km s−1(FWHM),
respectively, and are separated by 300 ± 20 km s−1.
The CO spectrum of ALESS57.1 is marginally spectroscop-
ically resolved. Nevertheless, the line width is appropriately
approximated by a Gaussian fit and the resulting values are
summarized in Table 2.
The CO line of ALESS67.1 shows a very large line width
(FWHM∼ 800 km s−1) and appears asymmetric although the
asymmetry is not statistically significant, due to the low SNR
in this source. We postulate that the CO line of ALESS67.1 is
produced by two sources of emission. This is supported by the
velocity averaged image (Fig. 2), where two spatial compo-
nents are recognizable independently in both CO (ALMA) and
optical/near-infrared (HST) imaging: one main right compo-
nent of around 1 arsec radius and a second extended emission
in the east. We thus give preference to the description of this
CO line as originating in two sources (possibly an early stage
of a merger event) and focus on the emission extracted from
the main component (1 arsec radius), which is shown as a
black line overlaid on the total line emission in Figure 1.
The CO spectrum of ALESS122.1 is the brightest in our
sample, and its line profile is well described by a single-
Gaussian fit. Table 2 lists the CO(3-2) line properties and
best-fit parameter values. A detailed description of the veloc-
ity field sampled by these CO lines will be provided in Section
3.2.1.
Continuum images were made for all the sources after ex-
cluding the channels contributing to theCO(3-2) line emission.
Using natural weighting to achieve the highest sensitivity18,
we obtained images with σrms ∼ 6 , 20, 18, 12 µJy beam−1, as
summarized in Table 1. The continuum emission is detected
in only two of the four sources in our data set: ALESS49.1
and ALESS122.1. In both cases, the naturally weighted dust
continuum emission at 3mm (rest-frame ∼850 µm) is detected
at 4-σ significance at sub-arsecond resolution (Table 2).
To test for consistency with the Cycle 0 continuum observa-
tions at 870µm (Hodge et al. 2013b), we use an extrapolation
following Sν ∝ ν2+β , where Sν is the measured flux density
and β is the dust emissivity spectral index. Adopting β = 1.5
as a reasonable assumption for dusty galaxies (Swinbank et al.
2014; Casey et al. 2014), the values extrapolated from 870µm
are consistent with our measured S3mm peak flux densities and
upper limits.
2.3. Source size estimation
High-resolution imaging reveals the detailed structure of
the gas and dust continuum emission, which is key for placing
18 The rms for ALESS49.1 is achieved using the concatenated dataset
which has a lower resolution (θbeam ∼0.7′′) than the Cycle 2 only (∼0.6′′), as
discussed in Section 2. The 88 GHz continuum emission measured from the
Cycle 4 low resolution data alone (θbeam ∼1.5′′) has a ∼ 9σ detection
constraints on the dynamical states of the sources. However,
high-resolution interferometry is less sensitive to extended,
low surface brightness emission, and thus care must be exer-
cised in the estimation of the source sizes (e.g. Emonts et al.
2016; Dannerbauer et al. 2017; Ginolfi et al. 2017). Although
the iterative cleaning method presented in Section 2.1 can pro-
vide a sense of the total source extent, it is prone to correlated
noise effects and consequently may yield uncertain results.
Moreover, iterative cleaning can only provide an (intrinsic)
source size estimate when the extent of the source is greater
than the synthesized beam. To determine the sizes indepen-
dently of these possible beam-convolution effects intrinsic to
the imaging process, we estimate the sizes directly from the
uv-data (lower right panels of Figure 1).
We extract the uv-data corresponding to the frequencies
within the FWHM of the line from the continuum-subtracted
cube, centered at the CO(3-2) observed frequency. For each
source, we then average the visibilities at different uv-distances
and plot the resulting amplitudes against them, as shown in
Fig. 1. We fit a Gaussian profile to the data and measure the
radius within which half of the light of the galaxy is contained.
We report the estimated half-light radii r1/2 in Table 2 and
adopt these values for our analysis. The half-light radii of our
sources range between 0.4–0.8′′, which correspond to 2.6–6.9
kpc at the respective redshifts, implying total physical sizes
(FWHM) of ∼ 10 kpc. In a study of the CO(3-2) emission
of a similar sample of SMGs at z ∼ 2 − 3, Tacconi et al.
(2008) find sizes ranging between 2–12 kpc. More recent
high-resolution molecular gas studies have reported similar
extents (e.g., Riechers et al. 2011; Ivison et al. 2011; Hodge
et al. 2012), suggesting that low-J transitions can show larger
extents than high-J CO emission.
Figure 2 shows the CO(3-2) emission overlaid on the stellar
emission as traced by the WFC3/IR (bands H160, J125,Y105)
and/or ACS imaging (I814) from HST (e.g., Chen et al. 2015).
We note that the astrometry in the HST-images has been cor-
rected based on the GAIA star positions, which are aligned
to the Fifth Fundamental Catalogue (FK5) (Gaia Collabora-
tion et al. 2016). With the exception of ALESS122.1, the CO
gas overlaps with the stellar distributions, although they have
slight offsets (0.1 − 0.3", 1–3 kpc offsets). The sizes of the
gas and stellar distribution in these sources are also roughly
similar. Specifically, the ratio of the HST H160 imaging (Chen
et al. 2015) to CO half-light radii of these ALESS sources
ranges between 1 and 1.5 (ALESS122.1 not included here as
no H160 is available). We will compare the extent of the dif-
ferent components in a statistical study for SMG populations
in Section 4.2. ALESS122.1 displays the striking feature that
the gas and stellar emission are completely offset. We must
point out, however, that the stellar emission in ALESS122.1 is
exclusively represented by the ACS I814 band imaging (rest-
frame 270 nm), in contrast to the other three sources which are
covered by at least one WFC3/IR band. This particular case
will be discussed in detail in Section 4.1.
Previous studies have shown that submillimeter continuum
observations of similar galaxy populations reveal very com-
pact rest-frame far-infrared-emitting regions, with median
half-light radii of only ∼ 0.7–1.6 kpc (e.g., Simpson et al.
2015; Ikarashi et al. 2015; Hodge et al. 2016; Oteo et al.
2017). This is significantly more compact than the molecular
gas emission in our sources. This difference in compactness
is similarly observed between the dust continuum and radio
emission of SMGs. Median radii of radio emitting regions
originating from SMGs have been reported to be around 2.1
Resolving the ISM in z ∼ 2.5 ALESS SMGs 7
Table 2
CO(3-2) line properties and estimated quantities.
ALESS49.1 ALESS57.1 ALESS67.1 ALESS122.1
CO(3-2) r1/2 [kpc] 2.6 ± 0.4 3.1 ± 0.5 6.9 ± 0.8 3.6 ± 0.3
FWHMCO(3−2)[km s−1] 610 ± 30 360 ± 90 720 ± 160 (500 ± 110)a 600 ± 80
Dust continuum S3 mm[µJy] 34 ± 6 54 ± 18 ≤ 54b ≤ 60b
Inclination i[degrees]c 80 ± 30 40 ± 50 50 ± 20 40 ± 20
Velocity integrated flux density ICO(3−2) [Jy km s−1] 0.89 ± 0.07 0.8 ± 0.2 3.9 ± 1.2 (1.8 ± 0.5)a 4.2 ± 0.8
Velocity integrated flux density ICO(1−0) [Jy km s−1] – – 0.44 ± 0.08 d 0.64 ± 0.07d
CO(3-2) line luminosity L′CO(3−2) [10
11 K km s−1 pc2] 0.39 ± 0.03 0.4 ± 0.1 1.0 ± 0.3 (0.5 ± 0.1)a 1.0 ± 0.2
CO(1-0) line luminosity L′CO(1−0) [10
11 K km s−1 pc2] 0.5 ± 0.2e 0.5 ± 0.2e 1.0 ± 0.2d 1.3 ± 0.2d
Molecular gas mass [1011M(αCO = 1.) ] 0.5 ± 0.2 0.5 ± 0.2 1.0 ± 0.2 1.3 ± 0.2
Mdyn(r ≤ 2r1/2) [1011 M] 1.1 ± 0.2 1.1 ± 0.5 3.6 ± 1.6 5.3 ± 1.6
Stellar mass f [1011M ] 0.4 ± 0.1 0.8 ± 0.1 2.4 ± 2.1 0.8 ± 0.5
Infrared luminosities LIR(3−2000 µm)[×1012L]f 6.8 ± 0.6 2.3 ± 2.2 5.0 ± 1.5 8.3 ± 2.5
SFR f [M yr−1 ] 700 ± 100 200 ± 200 400 ± 100 700 ± 200
a Values restricted to the main component of ALESS67.1 shown in Fig. 1. These values were used for the calculation of the dynamical masses using the disk
approximation in Section 3.3.
b3σ upper limits.
cComputed from axial ratios estimated with the CASA task imfit
dMeasured by Huynh et al. (2017).
eEstimated using r3/1 = 0.78 ± 0.27 (Sharon et al. 2016).
fAs presented by da Cunha et al. (2015)
kpc in average (e.g., Chapman et al. 2004; Biggs & Ivison
2008; Miettinen et al. 2015, 2017; Thomson 2018). Motivated
by these differences, we will explore in detail the relation be-
tween the radial profiles of the molecular gas, the dust contin-
uum emission (at rest-frame 250µm) and stellar emission in
Section 4.2.
3. DYNAMICAL CONSTRAINTS TO THE TOTAL GAS MASSES
3.1. Molecular gas masses
The masses of the CO(3-2) emitting gas in our sources
can be estimated from the observed 12CO(J=3-2) line lumi-
nosities L ′CO. These were calculated following Solomon &
Vanden Bout (2005) as L ′CO = 3.25 × 107 SCO∆v ν−2obs D2L(1 +
z)−3 K km s−1pc2; the resulting values are listed in Table 2.
Through an extrapolation from these CO masses we can cal-
culate the total molecular content of the systems (dominated
by H2), by assuming a CO line luminosity to H2 (+He) mass
conversion factor, αCO, and a brightness temperature ratio of
CO(J=3-2) to CO(J=1-0). However, the combination of spa-
tial and spectroscopic resolution of our data allow us to make
an estimate of the total gas mass independently of the above
mentioned assumptions, by estimating kinematic parameters
(Section 3.2) and using further multiwavelength information
to estimate the stellar mass contribution (Section 3.4). But
to begin with we use the classical approach to estimate the
molecular gas masses as a function of αCO.
Using the measurements of 12CO(J=1-0) by Huynh et al.
(2017) for ALESS67.1 and ALESS122.1 (see Table 2),
we calculate their brightness temperature ratio r3/1 =
LCO(3−2)/LCO(1−0), which yields r3/1 = 1.01 ± 0.36 and
r3/1 = 0.77 ± 0.19, respectively. This is consistent with pre-
vious estimates for the SMG population (Ivison et al. 2011;
Bothwell et al. 2013; Sharon et al. 2016). For ALESS49.1
and ALESS57.1 we estimate the 12CO(1-0) emission using
the excitation ratio for SMGs derived by Sharon et al. (2016),
r3/1 = 0.78±0.27, yielding L ′CO(1−0) = (0.5±0.2)×1011 K km
s−1 pc2, for both sources. The derived molecular gas masses
as a function of αCO (equivalent to αCO = 1) are reported in
Table 2.
In order to investigate possible effects of the presence of an
AGN on the molecular gas in our sample, we explore possible
correlations between galaxy properties inferred from the CO
measurements (listed in Table 2) such as the FWHM of the
CO line, the gas-to-stellar mass fraction and star formation
efficiency (SFE = SFR/Mgas) with the presence or absence
of an AGN (ALESS57.1 and ALESS122.1 are the AGN-host
candidates in our sample, see Section 2.1). We find no clear
correlation of these properties and conclude that the scales
probed by our COobservations are not affected by the presence
of an AGN, especially since we have observed the CO (J =
3 − 2) transition, which is not expected to be a tracer of AGN
excitation (Sharon et al. 2016).
3.2. CO line kinematics
Themorphological and kinematic properties of our resolved
CO images allow us to explore the nature of these star-forming
systems, whether these are in an early stage of a merger with a
chaotic structure, or whether their velocity fields are described
by an ordered rotating disk. It is important to note, however,
that these scenarios are not mutually exclusive. Observing
dynamics consistent with a rotating disk does not preclude the
galaxy from being a merging system, as the gas is collisional
and an ordered rotating disk can quickly reform after the final
coalescence stage as has been shown observationally and the-
oretically (Robertson et al. 2006; Hopkins et al. 2009, 2013;
Ueda et al. 2014).
While the few existing examples of CO detections at similar
resolution suggest a mixture of mergers and disk-like motion
(e.g., Tacconi et al. 2008; Engel et al. 2010; Hodge et al. 2012),
recent high resolution continuum imaging of SMGs has shown
that the dust continuum emission (at rest-frame 250 µm) is
mostly described by compact disk profiles (e.g. Simpson et al.
2015; Hodge et al. 2016). Here we use our high-resolution CO
observations to directly test the kinematics of these systems.
3.2.1. Position–velocity diagrams
To estimate the kinematic properties of our sources we first
investigate their position–velocity (PV) diagrams. We apply
the interactive PV Diagram Creation task from the CASA
8 Calistro Rivera et al.
Figure 3. Position–velocity (PV) diagrams for the CO(3-2) emission in our sources. The lower panels show the velocity-averaged CO images of our sources.
The arrows represent the kinematical major axis chosen for the extraction of the PV diagrams, the arrow head shows positive velocity offset, and the squares show
the origin of the PV plot. The upper panels show the corresponding resulting PV diagrams for the respective sources. Velocity gradients from the south-west to
north-east direction can be recognized in at least three sources (ALESS 67.1 may also have weak evidence), suggesting that the CO emitting material in these
sources is supported by rotation with velocity gradients of ∼300 km s−1on spatial scales of ∼ 0.2–0.7′′.
viewer to the data cubes of our sources with spectral resolu-
tion corresponding to channel widths of ∼ 100 km s−1. The
lower panel of Figure 3 show the kinematical major axis cho-
sen for the extraction of the PV diagrams overplotted as blue
arrows on the velocity-averaged CO images. The upper panels
show the resulting PV diagrams for the respective sources.
We find velocity gradients in the PV diagrams of three of
our four sources (with ALESS67.1 also showing some weak
signs), suggesting that the bulk of emission in these sources is
dominated by rotation.
The velocity gradients of ALESS49.1, ALESS57.1 show
double peaks at each side of the galactic center, although
the detailed velocity structure is ambiguous given the modest
SNR. InALESS49.1, the double-peaked spatial structure gives
rise to the double-peaked line profile observed in Figure 1.
Since both sources have the CO centered on a single optical
nucleus (as seen from their high-resolutionHST imaging), the
velocity structure suggests the presence of a disk structure or a
disk-shaped merger remnant, rather than an early stage merger.
The CO emission in ALESS67.1 and its velocity structure
appears more chaotic, which is probably accentuated by the
combination of extended emission and the lower SNRachieved
in this source. A detailed analysis of the velocity structure of
this individual source has been conducted in a complementary
study by Chen et al. (2017). They presented SINFONI Hα
observations of ALESS67.1, revealing that the extended CO
emission (including the second component to the south-east)
follows the bulk rotational motion of the rest-frame optical
Hα emission line. Kinematic modelling of both lines con-
cluded the bulk of the molecular gas in ALESS67.1 could be
described as an on-going merger, although without being able
to reject a rotating disk given the errors. It is still uncertain
whether ALESS67.1 is a multi-component system in an early
state of merging. This scenario has been discussed in Section
2.2 based on our CO and HST observations, and it has also
been supported by the analysis of its kinematics based on an-
cillary data by Chen et al. (2017). For further dynamical mass
calculations we will only consider the properties of the most
luminous component of ALESS67.1 (Table 2), and assume
that this component is well-described by a rotating disk.
ALESS122.1 is the source of highest SNR in our sample
and the velocity structure consistent with disk rotation. Due
to these reasons it was possible to analyse its velocity field
quantitatively using a rotating disk model, as will be described
in Section 3.2.2.
Although the velocity gradients may be consistent with
large-scale disk rotation as a bulk motion, we emphasize that
no conclusions can be drawn to exclude complex, disturbed
gas motions on scales smaller than the resolution limit of our
data. Based on this qualitative analysis of the PV-diagrams in
Figure 3, we will adopt the scenario of a rotating disk for our
sources for the computation of their dynamical masses. The
velocity line width (and thus an estimate of the velocity dis-
persion) and other morphological properties will be adopted
from the values listed in Table 2.
3.2.2. Kinematic Modelling
To quantitatively describe the kinematics of the molecular
gas in our sources, wemodel the data using themodelling pack-
age GalPak3D. GalPak3D is a Bayesian parametric Markov
Chain Monte Carlo fitter for three-dimensional (3D) galaxy
data that attempts to disentangle the galaxy kinematics from
resolution effects (Bouché et al. 2015). Starting from a set of
uniform priors on the disk parameters (source center, radius,
inclination, velocity dispersion, etc.), a 3D disk galaxy model
is produced and compared to the data to compute a reduced χ2ν
value, which is then minimized during the sampling process.
The reliability of the inferred kinematic parameters in Gal-
Pak3D goes approximately as δpp ∝
r1/2
rbeam
× SB1/2,obs , i.e.
the uncertainty in the inference of the parameter p is inversely
proportional to the source size to resolution ratio ( r1/2rbeam ) and
surface brightness of the source (SB1/2,obs). Given the de-
pendence of these uncertainties on the quality of the data and
due to the SNR limits in most of our sources, we were able
to apply this method only to the source with highest SNR and
resolution, ALESS122.1.
Resolving the ISM in z ∼ 2.5 ALESS SMGs 9
3h31m39.48s39.50s39.52s39.54s39.56s39.58s39.60s39.62s
RA (J2000)
DATA
3h31m39.48s39.50s39.52s39.54s39.56s39.58s39.60s39.62s
RA (J2000)
CONVOLVED MODEL
3h31m39.48s39.50s39.52s39.54s39.56s39.58s39.60s39.62s
RA (J2000)
DECONVOLVED MODEL RESIDUAL
0.4
0.2
0.0
0.2
0.4
0.6
0.8
m
Jy
/b
ea
m
200
100
0
100
200
300
km
/s
Figure 4. Modelling of the morphology and kinematics of ALESS122.1 with GalPak3D. The top row shows the zeroth-moment maps (integrated intensity) of
the observed, convolved model, deconvolved model and residual cubes. The contour lines in the top row show the 2-9 σrms levels, where σrms is the noise level
of the zeroth-moment maps. The bottom row shows the first-moment maps (intensity-weighted velocity) of the corresponding cubes, showing only regions with
fluxes > 2σrms. The color scale represents the width of the CO line in km s−1. The low-intensity levels of the residual maps show that the bulk of the emission
can be described by disk rotation. This, however, does not preclude the galaxy from being a merger, as an ordered rotating disk can be quickly ’reformed’ after
the final coalescence stage in a few dynamical times (Robertson et al. 2006; Hopkins et al. 2013)
Figure 4 shows zeroth-moment (integrated intensity)
and first-moment (intensity-weighted velocity) maps for
ALESS122.1. The four images correspond to the moment
maps of the observed data cube, the convolved model, decon-
volved model and residual (model-substracted) cubes, where
the latter three cubes are output products of GalPak3D. We
estimated the noise per pixel in the zeroth-moment map as√
N × σchan, where N is the number of channels used and
σchan is the rms noise per channel. Using this value, for the
computation of the first moment maps of the four cubes, we
masked out all pixels with SNR<2. The bottom row of Figure
4 shows the first-moment maps (intensity-weighted velocity)
of the corresponding cubes. The color scale has been chosen
to represent the velocity width of CO line of the source.
The resulting 3D model cube shows a modest agreement
with the data, with a reduced χ2ν of 1.87, which is calculated
over the total area and frequency range covered by the observed
and modelled data cubes, as represented in Figure 4. The
slightly-high reduced χ2ν value can be explained by residual
structure, which can be seen in the 0th and 1st moment maps
of the residual cubes. The model parameters obtained for
the source agree with comparable properties inferred directly
from the line profile.
The bulk of the velocity field of ALESS122.1 is consis-
tent with a rotation-dominated disk (mindful of the residual
clumps), with an inclination of i ∼ 52◦, a maximum rotational
velocity of vmax ∼ 560 km s−1, and a velocity dispersion of
σv ∼ 130 km s−1. The residual image in the right upper panel
of Figure 4 reveals few residual clumps between 2-3 σ sig-
nificance, consistent with being noise. We conclude that the
bulk of the velocity field is to a first order consistent with disk
rotation.
3.3. Dynamical Masses
The kinematic properties of a galaxy, obtained e.g. through
modelling its velocity field, can provide a reliable estimation
of the mass enclosed within the region covered by the emitting
medium. At high redshift, this is a complicated task, since
observations of molecular gas are frequently poorly spatially
resolved and the morphology of the mass distributions are thus
usually unknown. Based on the kinematic study above and the
size estimates from our analysis, we calculate the dynamical
masses assuming the bulk of the emission in our sources can
be well described by a rotating disk. The total dynamical mass
within a radius r = 2r1/2 is then given by:
Mdyn(r < 2r1/2) =
(∆vrot/2 sin (i))2 × 2r1/2
G
, (1)
where r1/2 is the half light radius estimated through uv-fitting
measured in kpc, i is the inclination of the galaxy (2) andG the
gravitational constant (e.g., Solomon & Vanden Bout 2005;
Erb et al. 2006; de Blok & Walter 2014). In the cases where
the velocity field cannot be modelled, the rotational velocity
vrot can be estimated as half the velocity width ∆VFWHM of the
line profile. For ALESS122.1 we use the parameter values
for vmax resulting from the kinematic modelling in Section
3.2.2, although both estimates provide consistent resultswithin
errors.
A large uncertainty in the estimation of the dynamical
masses is contributed by the inclination angle of the disk.
In previous dynamical-mass studies, it has been customary
to adopt a value of < sin2(i) >= 2/3 (corresponding to
i=54.7 deg), which is the average value expected for a ran-
domly oriented population of disk galaxies. However, given
our high resolution data, we have enough information to use a
simple assumption motivated by the early observation that the
apparent axis ratio is closely related to the inclination angle for
a disk. We use the relation cos2(i) = ((b/a)2 − q20)(1 − q20)−1
(Hubble 1926), where (b/a) is the axis ratio and q0 is the in-
herent thickness of the disk, assuming q0 = 0.1 (Nedyalkov
1993) . Obtaining the deconvolved axis ratios using the
CASA routine imfit, we compute the inclination angles for
10 Calistro Rivera et al.
ALESS49.1, ALESS57.1, ALESS67.1 and ALESS122.1 to
be i ∼ 80 ± 30◦, 40 ± 50◦, 50 ± 20◦ and 40 ± 20◦, respec-
tively. For ALESS122.1, where a more complex analysis
was possible in Section 3.2, we will adopt the inclination an-
gle estimated through the kinematic modelling, i ∼ 52 ± 2◦,
which is in agreement with the axis-ratio approximationwithin
the errors. Although this is an approximation and the uncer-
tainties are large, this estimation is superior to assuming the
single value of < sin2(i) >= 2/3 for all systems, since the
inclination in individual sources may anti-correlate with line
width. It is interesting to note the high inclination angle of
ALESS49.1, which is also supported by the small CO size and
double-peaked line profile. Although these profiles are not
uncommon for rotating disks and have been found in at least
40% of SMGs (Tacconi et al. 2008; Bothwell et al. 2013), the
asymmetry between the double-peaked profile suggests a non-
uniform distribution of the gas in the ’disk’, produced possibly
byminor instabilities or an unresolvedmerger of two gas disks.
The resulting dynamical masses for our sample range from
1–5×1011M(Table 2), as calculated within 2× the half-light
radii of the sources r1/2. These values are in general agree-
ment with previous measurements of the dynamical masses
of two of these sources based on other tracers (CO(J=1-0)
and Hα, Huynh et al. 2017; Chen et al. 2017). 19 This
range corresponds to masses at the high end of the aver-
age values found for other SMG samples by Ivison et al.
(2010) (2.3×1011M), Tacconi et al. (2008) (1.3×1011M),
Engel et al. (2010) (∼ 1.9 × 1011M) and slightly below
the values found for some extreme sources such as GN20
(5.4 ± 2.4 × 1011M, Hodge et al. 2012) and SMMJ131201
(9.5 ± 2.4 × 1011M, Engel et al. 2010). The uncertainties in
these values are propagated from all parameters used in their
calculation, including the inclination angles i (Table 2).
3.4. Implications on αCO and M∗/L estimates
The dynamical mass estimates discussed in Section 3.3 can
be related to the various mass components in galaxies follow-
ing:
Mdyn(r ≤ 2r1/2) = Mbaryons(r ≤ 2r1/2) + MDM(r ≤ 2r1/2),
(2)
where Mbaryons = Mgas + M∗ and MDM is the dark matter con-
tribution. Thus, given assumptions on the dark matter (DM)
content and stellar masses, the dynamical mass estimates can
be used as an independent method to constrain the total gas
masses in galaxies. Before we proceed to constrain the gas
masses using this method, we summarize the unknown pa-
rameters intrinsic to this calculation. We note that given the
scarcity of CO(J ≤ 3) gas data at high resolution, most of the
existing literature on molecular gas in high-redshift galaxies
usually assumes fixed values for unknown parameters, estimat-
ing gas masses which are thus sensitive to these assumptions
and lacking information on the inherent systematic uncertain-
ties.
19 In a study of the CO(1-0) emission, Huynh et al. (2017) found equivalent
dynamical masses of Mdyn sin i2 = (2.1 ± 1.1) and (3.2 ± 0.9) × 1011M
for ALESS122.1 and ALESS67.1, respectively. Although discrepancies were
expected given that they used optical instead of CO extensions due to the low
resolution of their CO data and assumed an inclination angle of sin2(i) = 2/3,
their result is consistent with ours given the errors. Similarly, a dynamical
study of the Hα emission in ALESS67.1 presented by Chen et al. (2017) esti-
mated a dynamical gas mass ofMdyn = (2.2±0.6)×1011M for ALESS67.1.
Although this estimation resulted from the analysis of the total source, while
our calculation used only the main component of the source, the values esti-
mated agree with our calculations within the errors.
0.1 0.2 0.3 0.4 0.5
M/LH
P(
M
/
L
H
)
0.1 0.2 0.3 0.4 0.5
M/LH
0.8
1.6
2.4
3.2
α
C
O
co
ns
t S
FH
in
st
an
t b
ur
st
0.8 1.6 2.4 3.2
αCO
P(
α
C
O
)
0.8 1.6 2.4 3.2
age[Gyr]
0.6 1.2 1.8 2.4
Mgas[10
11M¯]
DM fraction = 0%
DM fraction = 15%
DM fraction = 30%
Figure 5. One- and two-dimensional posterior probability density functions
(PDFs) of the M∗/LH and αCO parameters for the ALESS sources in this
work. The upper and lower-right panels show the one-dimensional PDFs as
histograms, where the orange, blue and black solid lines correspond to the
inference assuming dark matter contributions of 0%, 15% and 30%, respec-
tively. The galaxy age axis (upper panel, in red) equivalent to theM∗/LH axis
is computed using the relation presented by Hainline et al. (2011) for an in-
stantaneous burst SFH. The Mgas axis (lower-right panel, in red) is computed
by adopting the median LCO of our sample, < LCO >= 7.7 × 1010 K km/s
pc2. The transparent orange, blue and black vertical lines correspond to the
median values of the distributions. The lower-left panel shows the covariance
plot (two-dimensional PDF) of the parameters, were a clear correlation can
be recognized through the diagonal shape of the contours, which represent
the 25th, 50th and 75th percentiles of the sampled distribution.Two reference
lines (red) are drawn, corresponding to the average M∗/LH ratio found by
Simpson et al. (2014) for the ALESS survey as a whole, assuming a constant
SFH in contrast to an instantaneous burst SFH.
Tobeginwith, theH2 molecules that comprise the bulk of the
molecular gas reservoir in galaxies are not directly observable.
Measurements of molecular gas thus rely on CO observations,
via a conversion from the ground-state CO(1-0) luminosity
which is parametrized with the factor αCO. Indeed, high-
redshift measurements are providing increasing evidence that
the αCO values in the early universe can be lower than in solar-
metallicity galactic disks (αCO ∼ 0.8–1.0, e.g., Tacconi et al.
2008; Hodge et al. 2012; Bothwell et al. 2013).
In addition to the uncertainties in the total gas mass es-
timation, stellar mass estimates are typically obtained via
SED-fitting, which relies on assumptions regarding the star
formation history (SFH) of the stellar populations and dust
attenuation, which can be uncertain especially for starburst
systems (such as SMGs). In particular, it has been increas-
ingly observed that SED fitting of starburst systems suffers
from a degeneracy between the SFH, the mass-to-light ra-
tio (M∗/LH) and the age of the galaxy (Hainline et al. 2011;
Simpson et al. 2014). This degeneracy means that in a galaxy
with an instantaneous-burst SFH the total stellar mass would
be contained almost exclusively within young luminous stellar
Resolving the ISM in z ∼ 2.5 ALESS SMGs 11
populations, resulting in a low (M∗/LH) ∼ 0.05. Conversely,
in a galaxy of intermediate age with a constant SFH, most of
the stellar mass would be distributed in old faint populations
whose emission is outshone by the luminous newly born stars,
implying a higher mass-to-light ratio (M∗/LH ∼ 0.3). As
shown by recent resolved SED-fiting studies (Sorba & Saw-
icki 2018), this effect could underestimate total stellar masses
by factors of up to 5, especially in sources of high specific
star-formation rates such as SMGs.
Rather than adopting a single (M∗/LH ) or αCO, we can
instead parametrize the baryonic mass as:
Mbaryons = LH × M∗/LH + αCO × LCO, (3)
where LH is the rest-frame H-band luminosity corrected for
dust obscuration (here estimated by da Cunha et al. 2015) and
LCO is the CO(J=1-0) luminosity estimated in this work.
Finally, the dynamical mass of a galaxy also includes the
mass of the non-baryonic dark-matter (DM) component, which
is a source of uncertainty, as no independent measurement of
this mass fraction is available for our SMGs. Unlike ob-
servations in local disk galaxies, which have reported dark
matter fractions ( fDM) of ∼ 50% (e.g., Courteau & Dutton
2015), it has been claimed by recent spectroscopic surveys
(e.g., Price et al. 2016; Wuyts et al. 2016; Genzel et al. 2017)
that more compact star-forming disk galaxies at z > 2 appear
to be heavily baryon dominated with fDM ∼10–20%, although
these calculations involve the same unknown factors as are
used for the gas fractions. In contrast, recent simulations (e.g.
Lovell et al. 2018) have reported that the dark matter fractions
in disc-like galaxies could range up to 65% for galaxies with
stellar masses similar to SMGs (∼ 1011M).
Combining equations 2 and 3, the total mass can be ex-
pressed as:
Mdyn =
LH × (M∗/LH ) + LCO × αCO
(1 − fDM) , (4)
where the conversion factor αCO, the stellar mass-to-light ratio
(M∗/LH ) and the dark matter fraction fDM are the unknown
parameters. Given the small number of independent data
points available (one for each of our four sources), in order to
reduce the parameter space we will keep the fDM value fixed,
and discuss the effect of low and high fDM values to the other
parameters distributions later on.
Firstly, we reproduce the parameter space built up in Equa-
tion 4 by applying anMCMC technique, using the open-source
algorithm emcee (Foreman-Mackey et al. 2013) for the sam-
pling. Based on the likelihood of the measured dynamical
masses Mdyn (estimated in Section 3.3 as a function of LCO
and LH) given this model, we sample the posterior probability
density function (posterior PDF) for αCO and (M∗/LH ). It
is important to note that at this point the likelihood function
accounts only for the uncertainties in the dynamical masses
Mdyn. To account for the uncertainties in the LCO and LH
variables as well, we use a Monte Carlo approach and repeat
the inference exercise presented above for 100 iterations, each
time using values randomly chosen from within a normal dis-
tribution that corresponds to the mean and standard deviation
of our LCO and LH measurements. Finally, we average the pos-
terior PDFs gathered in these 100 iterations and obtain a final
probability distribution for the parameters which takes into ac-
count the uncertainties in the measurements of all observables
(Mdyn, LCO and LH).
Fig. 5 shows the one- and two-dimensional final posterior
PDFs of the (M∗/LH ) and αCO parameters adopting three dif-
ferent dark-matter fractions fDM = 0%, 15% and 30%. The
covariance between the parameters can be recognized in the
two-dimensional PDF (Figure 5) as an elongated ellipse in the
central countour level plot. Higher DM fractions decrease the
value ofαCO and consequentlyMgas. This trend is similarly fol-
lowed by the (M∗/LH) parameter. For aDMfraction of 15%we
find a median value of αCO = 1.1+0.8−0.7 [M/(K km s−1 pc2)−1],
while for a larger DM fraction of 30%, these values
decrease to αCO = 0.9+0.7−0.6 [M/(K km s−1 pc2)−1].
For fDM = 0 we obtain an upper limit to αCO ≤
1.4+0.9−0.9 [M/(K km s−1 pc2)−1]. For the mass-to-light ratio
parameter we find (M∗/LH) = 0.22+0.16−0.15M/L, (M∗/LH) =
0.19+0.15−0.13M/L and (M∗/LH) = 0.16+0.12−0.10M/L for DM
fractions of 0%, 15% and 30%. Using these values, the
gas reservoirs in our sources have an average gas mass of
∼ 0.9 × 1011M(DM contribution of 15%) and ∼ 0.7 ×
1011M (DM contribution of 30%), corresponding to av-
erage gas-to-total-mass fractions of 0.26% and 0.33%, respec-
tively. These sources show similar gas fractions than those
reported for typical star-forming galaxies (≤ 50%, Tacconi
et al. 2017). For comparison, Bothwell et al. (2013) presented
a study of a representative sample of SMGs at z ∼2 from pre-
dominantly CO(3-2) observations, finding mean gas masses
of (3.2 ± 2.1) × 1010Massuming αCO = 1. Since the result-
ing PDF for the M∗/LH and age parameters for our galaxies
is broad and poorly constrained, the galaxy stellar population
properties inferred through this method (∼ 0.1 − 2.0 Gyr)
easily agree with those estimated through SED-fitting by da
Cunha et al. (2015), which are also associated with large errors
(∼70%). They find the age of these galaxies range between ∼
0.04–1.22 Gyr, corresponding to M∗/LH between 0.16–0.2.
As discussed above, the values recovered for the parameters
are subject to large uncertainties due to our small sample size.
However, we note that one goal of this exercise is to shed
light upon the degeneracies among the key parameters and
large uncertainties inherent to gas mass calculations. Most
importantly, given the increasing availability of dynamical
mass measurements for high-redshift galaxies with ALMA,
we consider that this approach has potential for constraining
the molecular gas properties with more accuracy, especially
since larger sample sizes will allow the exploration of a more
detailed parameter space in the future.
4. DISTRIBUTIONS OF MOLECULAR GAS, DUST CONTINUUM
AND STELLAR EMISSION
4.1. Offset distributions of ISM tracers and stellar emission
in ALESS122.1
An interesting case among our sample is the apparently
uncorrelated distribution of dust continuum, gas and stars in
ALESS122.1 (Fig. 6). The gas and stellar emission extend
across regions of similar size, separated by ∼ 0.5′′ (∼ 5 kpc at
z = 2) as measured from their centroids, but are tightly aligned
next to each other. There is almost no overlap of gas and
stellar emission, even when considering the combined astro-
metric uncertainties (<0.1′′20). Moreover, while the gas and
stars have half-light radii r1/2 ∼ 4 kpc and are thus extended on
scales of∼10 kpc, the detected dust continuum emission (3mm
observed-frame, corresponding to ∼ 850 µm rest-frame) is
confined to a central region of ∼5 kpc, with the emission peak
20 The HST astrometric uncertainties are low since the image has been
accurately calibrated using GAIA measurements of this field.
12 Calistro Rivera et al.
Figure 6. False-color image of the molecular gas, dust continuum and stellar
emission components in ALESS122.1. The molecular gas (green) shows
the CO(3-2) emission and the dust continuum region (red) corresponds to
the 3 mm (rest-frame ∼ 850 µm) continuum detection (4-σ), both masked
at S ≥ 3σ. For clarity we overplot contours for both the CO (6, 8, 10σ)
and dust continuum emission (3, 4σ), to show that their centroids are co-
located. The stellar emission (HST-ACS F814W) is presented as the blue
region and shows a large offset from the gas and dust centroid, with almost
no overlap even when considering the combined astrometric uncertainties.
The HST astrometry in this data is accurate since the images were corrected
based on GAIA measurements. The increasing evidence of a population
of sources with misaligned stellar, dust continuum and gas emission has
important implications for energy balance assumptions in SED-fitting. We
discuss the striking difference between the observed extent of the gas and dust
continuum emission for a larger sample of sources in Section 4.2.
spatially coincident with that of the molecular gas emission.
Similar physical offsets between dust continuum, gas and stel-
lar emission, and specifically between ALMA and HST, have
been previously found in a number of high-redshift sources
(e.g., Riechers et al. 2010; Chen et al. 2015; Hodge et al.
2015; Fujimoto et al. 2017; Simpson et al. 2017). For exam-
ple, based on low-resolution 870µm continuum data (∼1.5′′),
Chen et al. (2015) reported a statistical offset with the existing
stellar component traced by HST as large as ∆p = 0.4′′ (∼ 4
kpc at z = 2) in 66% of the ALESS SMGs. Similarly, Hodge
et al. (2015) found in the z = 4 galaxy, GN20, that the FIR and
CO emission are offset by 0.6′′ (4 kpc) from the peak of the
rest-frame UV emission as traced by the HST/WFC3 F105W
image.
We consider three scenarios for explaining the mismatch of
the distributions of stellar and gas/dust continuum emission in
ALESS122.1. The first and most plausible scenario assumes
that the optical component extends to the regions of gas and
dust continuum emission, while suffering extreme extinction
in these regions. Such high-extinction scenarios have been
suggested previously in starbursts with extreme SFRs and in
cases of partial or total absence of optical counterparts (e.g.,
Walter et al. 2012; Hodge et al. 2012; Simpson et al. 2015).
This is not uncommon in sub-mm selected samples, where
optical detection rates are only ∼ 70 − 80% even with deep
data (e.g., Simpson et al. 2014).
The second scenario implies that the observed offset reflects
a physical misalignment between the gas/dust continuum dis-
tributions and that of the stellar mass. This argument has
been tested by Chen et al. (2015) for the full ALESS sample.
They tested this hypothesis by comparing the positional offsets
found in low-redshift (z < 2) to those in high redshift (z > 2)
subsamples, taking into account that at lower redshift the op-
tical photometry would probe wavelengths less affected by
obscuration. They found no statistical difference in the mea-
sured positional scatter between the low- and high-redshift
samples, implying that obscuration is not the dominant factor
for the population as a whole.
The third scenario implies that ALESS122.1 is an ongoing,
merging system comprised of two components, one of which
is a heavily obscured SMG which has no detected optical
counterpart, and the other is an optically bright galaxy in the
HST-ACS F814W imaging (which corresponds to rest-frame
∼ 3000 Å). High-resolution optical-MIR counterparts at other
wavelengths are needed in order to confirm the nature of this
source and explain the uncorrelated distributions of its physical
components.
Regardless of the underlying scenario, the significant anti-
correlation between dust continuum and optical imaging dis-
prove some assumptions which are intrinsic to multiwave-
length studies such as energy balance in SED-fitting (this has
been previously discussed by e.g., Hainline et al. 2011; Chen
et al. 2015; Hodge et al. 2016; Simpson et al. 2017; Chen et al.
2017).
4.2. Statistical analysis on the relative sizes of dust
continuum, molecular gas and stellar emission in SMGs
To gain a general understanding of the distributions of the
molecular gas, dust continuum, and stellar emission in SMGs
and how they relate, next we conduct a stacking analysis using
the CO emission measured in our sources and the available
multiwavelength data at similar resolution.
We first produced the stacked radial profiles of the CO emis-
sion of the four ALESS sources presented here. To achieve
this, we create 10× 10′′ thumbnails of our sources, align their
centers and scale them to have the same peak flux. We then
produce the radial profiles of the individual sources by radially
averaging the emission centered at the source peak, and finally,
we average the individual radial profiles in our sample (Fig-
ure 7).21 To account for the effect of outlier structures of the
individual sources, we estimate the uncertainties of the radial
profiles through bootstrapping, e.g., by creating 1000 differ-
ent average profiles, where each iteration used a randomly
resampled combination of sources.
Using the same technique, we also stack high-resolution
dust continuum emission (0.16′′ FWHM at rest-frame 250
µm) of 16 luminous ALESS sources studied by Hodge et al.
(2016). This sample of sources are representative of the
ALESS survey as a whole (ALESS median z = 2.5 ± 0.2
and LIR = (3.0 ± 0.3) × 1012L, Simpson et al. 2014; Swin-
bank et al. 2014) as they have amedian redshift of z = 2.6±0.5
and infrared luminosity of LIR = (3.6 ± 0.9) × 1012L.
Most importantly, these properties are also comparable to
those of the sample used for the CO stacked profiles (me-
dian redshift of z = 2.5 ± 0.4 and infrared luminosity of
21 We note that we investigated the difference between the approach de-
scribed above and an approach in which a stacked image is produced first and
the mean radial profile is then extracted directly from the stacked image. We
find that both methods are equivalent and result in identical average radial
profiles.
Resolving the ISM in z ∼ 2.5 ALESS SMGs 13
1 10
radius [kpc] 
10-4
10-3
10-2
10-1
100
101
Σ
co
n
t[
m
J
y
k
p
c−
2
]
Resolved radial profiles
molecular gas - CO(3-2) (this work)
dust continuum - rest-frame 250µm
stellar emission - F160W HST
1 10
radius [kpc] 
Radiative transfer model
molecular gas - CO(3-2) (this work)
dust continuum - rest-frame 250µm 10
-5
10-4
10-3
10-2
10-1
Σ
li
n
e
 [m
J
y
k
m
s−
1
k
p
c−
2
]
Figure 7. Stacked radial profiles and modelling. Left panel: one-component exponential profile fits are shown for a) the stacked CO(3-2) emission presented in
this paper (green solid line), b) the stacked high-resolution dust continuum emission at 870 µm (rest-frame ∼ 250 µm) of 16 luminous ALESS SMGs by Hodge
et al. (2016) (red solid line) and c) the stacked high-resolution H-band emission (HST) for the same 16 ALESS sources presented by Hodge et al. (2016) (blue
solid line). The profiles were normalized to have the same peak flux densities, and the error bars were obtained through bootstrapping. All exponential fits are
convolved with Gaussian functions of the size of the beam, to account for the effect of different resolutions. The data points of the dust profile at radii of >7 kpc
were discarded for the fitting, since these are evidently affected by artifacts produced by the side lobes of the beam (shown as the grey shaded area). We find that
the cool molecular gas and stellar emission are clearly more extended than the rest-frame 250 µm dust continuum by a factor of > 2. Right panel: To explain
the different sizes, we fit an extended version of the dust and line radiative transfer models of Weiß et al. (2007) to our data. The solid lines are the profiles
resulting from the best-fit radiative transfer model. The model assumes an exponentially decreasing column density distribution (Sérsic index of n = 1) and a
linear temperature gradient decreasing from the center to the outer parts of the disk. Solving the dust and line radiative transfer in several radial bins, we obtain a
exponentially decreasing gas and dust radial profile, taking into account the different beam sizes for the dust continuum and CO line observations. Assuming a
constant dust-to-gas ratio, the model is thus able to reproduce the apparent size differences between the CO(3-2) and dust continuum emission by only introducing
temperature and optical depth gradients.
LIR = (5.6± 2.2) × 1012L), although both samples have only
one source in common (ALESS67.1).
Finally, we stack high resolutionHST imaging (0.17′′ in the
H160 band) available for the same 16ALESS sources following
the procedure described above. The stacked surface brightness
profiles for the gas, dust continuum and stellar components are
shown in Fig. 7 as green, red and blue data points, respectively.
To quantify the extent and distribution of the molecular,
sub-mm and optical/near-infrared emission, first we assume
that the observed emission can be described by a exponential
profile (Sérsic profile with index n=1) convolved with a Gaus-
sian profile, which corrects for the effect of the shape of the
beam. Based on this we fit a one-dimensional exponential to
the CO and dust continuum profiles and find that they are well
described by such a model. We note that for fitting the dust
profile we discarded the data points at radius of >7 kpc, since
these are evidently affected by artifacts produced by the side
lobes of the beam (shown as the shaded area in Fig. 7)22. The
radial profile of the stellar emission results in a bad quality fit
when using an exponential, i.e. when fixing the Sérsic index
n = 1. To improve this, we leave the Sérsic index as a free
parameter and achieve a better quality fit with n = 0.8 ± 0.2,
which is consistent within the errors with the median value
found for the ALESS sample as whole (n = 1.2 ± 0.3, Chen
et al. 2015). The best-fit models consist then of exponential
profiles with radii of r = 1.7± 0.1, 3.8± 0.1 and 4.0± 2.0 kpc
for the dust continuum, CO and stellar emission respectively.
These results reveal that both the stellar (H160) and molec-
22 This issue is not relevant for CO, since the side lobes appear only at r>15
kpc
ular gas (CO(J = 3 − 2)) emission have similar sizes, but
are > 2× more extended than the dust continuum emission,
measured at rest-frame 250 µm. In addition, we note that the
estimated size of the CO(3-2) emission should be considered a
lower limit for the extent of the total molecular-mass distribu-
tion, as the ground-state transition CO(1-0) has been observed
to be even more extended than the higher J-transitions (Ivison
et al. 2011; Riechers et al. 2011).
4.3. Physical implications of the more extended molecular
gas distributions as compared to dust continuum
emission
A crucial consequence of the different scales probed by the
molecular gas, dust and stellar tracers in these galaxies (as
shown in Section 4.2) is the uncertainty in using conversion
factors between the luminosities of individual tracers. The
compactness of the dust continuum emission in SMGs has
been discussed in the literature (Simpson et al. 2015; Ikarashi
et al. 2015; Hodge et al. 2016; Barro et al. 2016; Simpson
et al. 2017), as ALMA continuum observations at high angular
resolution (0.13–0.4′′) have revealed median radii of ∼ 0.7–
1.5 kpc.
Apart from CO and optical imaging, high-resolution obser-
vations of other SF tracers such as synchrotron and free-free
emission have allowed comparison of relative sizes of dust
continuum and gas emission regions. Indeed, radio interfero-
metric observations of SMGs with the Very Large Array at 1.4
GHz (Chapman et al. 2004; Biggs & Ivison 2008), at 3 GHz
(Miettinen et al. 2015, 2017) and at 6 GHz (Thomson 2018),
have shown that dust continuum sizes appear to be 1.4–4.4
times smaller than the radio.
14 Calistro Rivera et al.
What is the origin of the significantly smaller sizes (> 2)
of the dust continuum emission in SMGs compared to other
physical components? There are three parameters that could
affect the emission of dust at larger radii: the dust-to-gas ratio,
the dust temperature and the optical depth of the dust and gas.
The small extent of the dust continuum emission at rest-frame
250 µm is likely to trace the heating of dust by star formation or
AGN, as it is confined to central compact regions, as expected
for highly star-forming systems. A decrease in optical depth
at larger radii, would similarly affect the observed sub-mm
continuum emission, as would a radially dependent dust-to-
gas ratio. Studies in the nearby Universe, however, (e.g.,
Sandstrom et al. 2013; Groves et al. 2015) suggest that no
large variations in the latter are expected across the galaxy,
making this scenario less plausible.
The different spacial extent for the rest-frame 250 µm dust
continuumemission and theCO line emission can be explained
in the context of self-consistent radiative transfer of the CO(3-
2) and dust continuum emission. Weiß et al. (2007) presented
such a model, where the line and dust continuum emission are
linked through a constant dust-to-gasmass ratio throughout the
galaxy, specifically, by connecting the gas column density NH2
to the optical depth of the dust, τdust(r) ∼ Ndust ∼ NH2 . The
different dust continuum and CO sizes can then be explained
by assuming a radially decreasing gas column density and a
radially decreasing temperature distribution T(r). Following
the radiative transfer equation, and neglecting the background
temperature, we have
S(r) ∝ T(r) · (1 − e−τ), (5)
where T(r) implies T(r) = Tdust(r) for the dust and T(r) =
Tex(r) for the molecular gas. We can expect that the long
wavelength dust continuum emission, which is optically thin
(τ  0), will be sensitive to both the column density and the
temperature gradients (Scont(r) ∝ Tdust(r)·τdust(r)), whereas the
optically thick CO line emission (τ  1) will to first order only
respond to the temperature gradient (SCO(r) ∝ Tex(r) ∼ Tkin(r)
for the low-J CO transitions, which are close to thermalisation.
This would have the effect that the dust continuum emission
becomes fainter more rapidly as a function of radius than the
gas emission.
Based on these arguments, we have used an extended version
of the dust and line radiative transfer models of Weiß et al.
(2007) to demonstrate this effect for the radial distribution of
the stacked CO(3-2) and rest-frame 250 µm dust continuum
data shown in Figure 7. In the model we use an exponentially
decreasing column density distribution (Sérsic index of n = 1)
and a linear temperature gradient from the center to the outer
parts of the disk, and we solve the dust and line radiative
transfer in several radial bins (more details on the model will
be presented in Weiß et al. (in prep)). Figure 7 shows a
fit of a exponentially decreasing gas component, taking into
account the different beam sizes for the dust continuum and
CO line observations. Given the uncertainties of the data,
the model can reproduce the different radial behaviour of the
dust continuum and the CO(3-2) line emission. From this
fit we derive an intrinsic exponential scale length of 3.4 kpc
(0.4′′) for the underlyingH2 distribution, intermediate between
the intrinsic sizes we have estimated earlier based on the de-
convolved intensity profiles for the dust and the CO(3-2) line
emission.
In this section we have proposed that assuming a unique
intrinsic distribution of dust and gas, temperature and optical
depth gradients alone could give rise to the apparent size differ-
ences observed between the CO and dust continuum emission.
If these parameters are the origin of the compactness of dust
continuum emission observed in the high-redshift Universe
(here probed at rest-frame ∼ 250 µm), caution must be ex-
ercised when extrapolating properties of high-resolution con-
tinuum observations to conclusions on the molecular phase of
the ISM. Specifically, these results advise against combining
unresolved molecular gas observations with radius estimates
from resolved dust continuum observations when calculating
key parameters such as dynamical masses. In order to em-
pirically test the assumptions placed into this model on the
temperature and optical depth gradients, high-resolution ob-
servations of the dust continuum at different frequencieswould
be necessary, as a gradient in observed sizes of the emission
regions is a direct tracer of the dust optical depth across the
SED.
5. SUMMARY
• We have presented ALMA observations of the gas and
dust of four luminous sub-millimetre galaxies at z ∼
2−3 to investigate the spatially resolved properties of the
inter-stellar medium (ISM) on scales of a few kpc. The
molecular gas in these sources, traced by the 12CO(J=3-
2) emission, is extended over FWHM∼5 –14 kpc.
• We investigated the dynamics of the molecular gas in
our sources andmodelled the kinematics of one of them,
ALESS122.1, finding that the velocity fields of three of
our four sources are consistent with disk rotation to first
order. We clarify that this scenario does not preclude
the connection of our sources tomergers as observations
of nearbymerger remnant and simulations show that gas
disks reform rapidly within <100 Myr of the peak star
formation associated with a merger.
• The resolved CO imaging provides size measurements
that allow us to derive dynamical masses for our sam-
ple. The dynamical masses found are in the range of
(1.1–5.3)×1011M, as calculated within 2× the half-
light radii of our sources, which is in agreement with
other dynamical mass estimates for SMGs.
• To provide dynamical constraints to the gas masses, we
explore the uncertainties introduced by the estimation
of stellar masses, the assumptions on the dark matter
fractions and the CO-to-H2 conversion factor αCO. Tak-
ing into account the covariance between the mass-to-
light ratio and αCO parameters, we estimate an aver-
age CO-to-H2 conversion factor of αCO = 1.1+0.8−0.7 and
αCO = 0.9+0.7−0.6 for dark matter fractions of 15% and
30% respectively, and an upper limit of αCO ≤ 1.4+0.9−0.9
for a dark matter fractions of 0%. These values imply
gas fractions of ∼30% for our sources, which are sim-
ilar to those estimated for main-sequence star-forming
galaxies and other SMGs.
• Our high resolution study allows us to investigate the
correlation between the spatial distribution of the phys-
ical components of the ISM (the dust continuum and
gas) and the stellar distributions. The sizes of gas and
stars are comparable but spatially uncorrelated, while
the rest-frame 250 µm dust continuum is significantly
more compact. The observation of the anti-correlated
distributions of the dust continuum and gas emission
Resolving the ISM in z ∼ 2.5 ALESS SMGs 15
with respect to the unobscured stellar emission may
challenge energy balance assumptions in global SED
fitting routines and suggests that caution must be exer-
cised particularly for dusty star-forming galaxies, such
as SMGs.
• To investigate this question statistically, we conduct a
stacking analysis of available high resolution ancillary
data for SMG populations of similar properties. We
find that the cool molecular gas and stellar emission are
clearly more extended than the rest-frame 250 µm dust
continuum by a factor of > 2.
• We reproduce our observations with a radiative transfer
model, finding that the different sizes are consistent
with the expected response of optically thin dust and
optically thick gas to radially decreasing optical depth
and temperature gradients, when a constant dust-to-gas
ratio is assumed. We suggest that extrapolations from
morphological properties of high-resolution continuum
observations to conclusions on the molecular phase of
the ISM should be thus treated cautiously.
ACKNOWLEDGEMENTS
We would like to thank the Allegro group in Leiden, es-
pecially Dr. Luke Maud, Dr. Erwin de Blok (Astron) and
Dr. Alison Peck for valuable help and advice at differ-
ent stages of the project. GCR acknowledge support from
the European Research Council under the European Unions
Seventh Framework Programme (FP/2007- 2013) /ERC Ad-
vanced Grant NEW-CLUSTERS-321271. JH acknowledges
support of the VIDI research programme with project num-
ber 639.042.611, which is (partly) financed by the Nether-
lands Organisation for Scientific Research (NWO). IRS ac-
knowledges support from the ERC Advanced Grant DUSTY-
GAL (321334), a Royal Society/Wolfson Merit Award and
STFC (ST/P000541/1). JLW acknowledges support of an
STFC Ernest Rutherford Fellowship (ST/P004784/1) and ad-
ditional support from STFC (ST/P000541/1). F.W and B.P.V
acknowledge funding through ERC grants "Cosmic Dawn"
and "Cosmic Gas". H.D. acknowledges financial support
from the Spanish Ministry of Economy and Competitive-
ness (MINECO) under the 2014 Ramón y Cajal program
MINECO RYC-2014-15686. This paper makes use of the fol-
lowing ALMA data: ADS/JAO.ALMA#2013.1.00470.S and
#2016.1.00754.S. ALMA is a partnership of ESO (represent-
ing its member states), NSF (USA) and NINS (Japan), to-
gether 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 research made use of astropy,
a community-developed core Python package for Astronomy
(Astropy Collaboration et al. 2013), and the open-source plot-
ting packages for PythonAPLpy (Robitaille & Bressert 2012),
and corner (Foreman-Mackey 2016).
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