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arXiv:1503.08720v1 [astro-ph.GA] 30 Mar 2015
Mon. Not. R. Astron. Soc. 000, 1–11 (2014) Printed 2 April 2015 (MN L
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Revealing the complex nature of the strong gravitationally
lensed system H-ATLAS J090311.6+003906 using ALMA
S. Dye1⋆, C. Furlanetto1,2, A. M. Swinbank3, C. Vlahakis4,5, J. W. Nightingale1, L.
Dunne6,7, S. A. Eales8, Ian Smail3, I. Oteo-G´omez7,9, T. Hunter10, M. Negrello11,
H. Dannerbauer12, R. J. Ivison7,9, R. Gavazzi13, A. Cooray14, P. van der Werf15
1School of Physics and Astronomy, Nottingham University, University Park, Nottingham, NG7 2RD, UK
2CAPES Foundation, Ministry of Education of Brazil, Bras´ılia/DF, 70040-020, Brazil
3Centre for Extragalactic Astronomy, Durham University, South Road, Durham DH1 3LE, UK
4Joint ALMA Observatory, Alonso de C´ordova 3107, Vitacura, Santiago, Chile
5European Southern Observatory, Alonso de C´ordova 3107, Vitacura, Santiago, Chile
6Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand
7Institute for Astronomy, Royal Observatory Edinburgh, Blackford Hill, Edinburgh, EH9 3HJ, UK.
8School of Physics and Astronomy, Cardiff University, Queen’s Buildings, The Parade, Cardiff, CF24 3AA, UK
9European Southern Observatory, Karl-Schwarzschild-Str. 2, Garching, Germany
10National Radio Astronomy Observatory, 520 Edgemont Rd, Charlottesville, VA, 22903, USA
11INAF, Osservatorio Astronomico di Padova, Vicolo Osservatorio 5, I-35122 Padova, Italy
12Universit¨at Wien, Institut f¨ur Astrophysik, T¨urkenschanzstrasse 17, 1180 Wien, Austria
13Institut d’Astrophysique de Paris, UMR7095 CNRS-Universit´e Pierre et Marie Curie, 98bis bd Arago, F-75014 Paris, France
14Astronomy Department, California Institute of Technology, MC 249-17, 1200 East California Boulevard, Pasadena, CA 91125, USA
15Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 RA Leiden, The Netherlands
ABSTRACT
We have modelled Atacama Large Millimeter/sub-millimeter Array (ALMA) long
baseline imaging of the strong gravitational lens system H-ATLAS J090311.6+003906
(SDP.81). We have reconstructed the distribution of continuum emission in the
z= 3.042 source and we have determined its kinematic properties by reconstructing
CO line emission. The continuum imaging reveals a highly non-uniform distribution
of dust with clumps on scales of ∼200 pc. In contrast, the CO line emission shows
a relatively smooth velocity field which resembles disk-like dynamics. Modelling the
velocity field as a rotating disk indicates an inclination angle of (40 ±5)◦, imply-
ing an intrinsic asymptotic rotation velocity of 320 kms−1and a dynamical mass of
3.5×1010 M⊙within 1.5 kpc. We obtain similar estimates of the total molecular gas
mass of 2.7×1010 M⊙and 1.4×1010 M⊙from the dust continuum emission and CO
emission respectively. Our new reconstruction of the lensed HST near-infrared emis-
sion shows two objects that appear to be interacting, with the rotating disk of gas and
dust revealed by ALMA distinctly offset from the near-infrared emission. The clumpy
nature of the dust and the low value of the Toomre parameter of Q∼0.2 we measure
suggest that the disk is in a state of collapse. From our dynamical measurements,
we estimate that the disk is unstable on scales from ∼50 pc (the Jeans length) to
∼700 pc (the scale on which the disk should be stabilized by shear). This agrees well
with the sizes of the clumps that we observe. We estimate that stars are forming in
the disk at a rate of 500 M⊙/yr, and that the star-formation efficiency in the disk
is ∼65 times greater than in typical low-redshift galaxies. Our findings add to the
growing body of evidence that the most infra-red luminous, dust obscured galaxies in
the high redshift Universe represent a population of merger induced starbursts.
Key words: gravitational lensing - galaxies: structure
⋆E-mail: simon.dye@nottingham.ac.uk
1 INTRODUCTION
Our understanding of high redshift sub-millimetre (submm)
bright galaxies (SMGs) has grown immensely since their
c
2014 RAS
2S. Dye et al.
discovery nearly two decades ago (Smail et al. 1997;
Hughes et al. 1998; Barger et al. 1998). The fact that ap-
proximately half of the total energy output from stars within
the observable history of the Universe has been absorbed by
dust and re-emitted at submm wavelengths (Puget et al.
1996; Fixsen et al. 1998) and that SMGs represent the most
active sites of dusty star formation at high redshifts, indi-
cates that their role in early galaxy formation is an impor-
tant one.
Morphological and kinematical measurements of SMGs
have led many studies to conclude that they are a more en-
ergetic version of more local ultra-luminous infrared galax-
ies (ULIRGs; e.g. Engel et al. 2010; Swinbank et al. 2010;
Alaghband-Zadeh et al. 2012; Rowlands et al. 2014). How-
ever, observations have been limited by the low imaging reso-
lution typically offered by submm facilities, forcing detailed
investigations to turn to other wavelengths which permit
higher resolution. With strong attenuation over ultraviolet
to near-infrared wavelengths, where imaging technology has
benefitted from a longer period of development, this has
proven challenging. Hence, a reliance has traditionally been
made on correlations with other wavelengths which often
only result in indirect diagnostics of the internal energetics
of the physical processes at work in these galaxies.
A powerful diagnostic which gives unique insight
into the star formation processes in galaxies in gen-
eral is measurement of molecular gas (see for example
Papadopoulos et al. 2014, and references therein). In par-
ticular, in the more extreme environments of ULIRG and
SMG interiors where strong feedback from star-formation
and shock-heating of molecular gas by supernovae are dom-
inant processes, star formation models can be put through
the most rigorous of tests (e.g. Papadopoulos et al. 2011).
In this way, examination of the quantity and kinematical
properties of molecular gas provides a direct probe of the
mode of star formation. Following this approach, some stud-
ies have concluded that star formation mechanisms in early
systems are distinctly different from those seen in more lo-
cal systems (e.g. Bournaud & Elmegreen 2009; Jones et al.
2010).
A detailed study to measure the properties of star
formation in distant SMGs requires two key ingredients.
Firstly, observations must be carried out at submm wave-
lengths, where most of the bolometric luminosity is emit-
ted, to allow emission from the dust enshrouded molecular
gas to be detected. Secondly, the observations must be of
sufficient angular resolution to isolate the dynamics of the
∼200 pc gravitationally unstable regions usually found in
their star-forming disks (Downes & Salomonv 1998).
To provide a sample of suitable SMGs for such inves-
tigation, the large area surveys carried out recently by the
Herschel Space Observatory, such as the Herschel Astrophys-
ical Terahertz Large Area Survey (H-ATLAS; Eales et al.
2010) and the Herschel Extragalactic Multi-tiered Extra-
galactic Survey (Oliver et al. 2012) along with the survey
at millimetre wavelengths carried out at the South Pole Tele-
scope (Carlstrom et al. 2011; Vieira et al. 2013) now pro-
vide a bountiful supply of high redshift dusty star bursts for
detailed study. Obtaining the required high resolution imag-
ing in the submm is now made possible using the Atacama
Large Millimetre/sub-millimetre Array (ALMA).
A particularly compelling use of ALMA for these pur-
poses is to target strongly lensed SMGs. The submm
has long been suspected to harbour a rich seam of
strongly lensed galaxies due to a high magnification
bias resulting from their steep number counts (Blain
1996; Negrello et al. 2007). Thanks to the aforemen-
tioned mm/submm surveys, such suspicions have now
been verified (Vieira et al. 2010; Negrello et al. 2010;
Hezaveh & Holder 2011; Wardlow et al. 2013). The intrin-
sic flux and spatial magnifications by factors of ∼10 −30
inherent in strongly lensed systems therefore combine with
the use of ALMA to provide the highest possible resolution
and signal-to-noise imaging of SMGs currently achievable by
a considerable margin.
In this paper, we report our analysis of the recently re-
leased ALMA science verification observations of the strong
lens system H-ATLAS J090311.6+003906 (SDP.81), one of
the first five strongly lensed submm sources detected in the
H-ATLAS data (Negrello et al. 2010). The system was sub-
sequently followed up in the near-infrared using the Hubble
Space Telescope (HST; see Negrello et al. 2014, for details
of these observations; N14 hereafter). Lens modelling of the
system by Dye et al. (2014, D14 hereafter) showed that the
observed Einstein ring can be explained by a single compo-
nent of emission in the source plane. The purpose of this
paper is to exploit the high resolution ALMA imaging of
the highly magnified lensed source to determine its physical
properties. One of our key questions is how the rest-frame
optical source emission reconstructed by D14 relates to the
reconstructed submm emission detected by ALMA.
The layout of this paper is as follows: Section 2 out-
lines the data. In Section 3 we describe the modelling pro-
cedure used to obtain the results which are given in Sec-
tion 4. We discuss our findings in Section 5 and summarise
the major results of this work in Section 6. Throughout
this paper, we assume the following cosmological param-
eters; H0= 67 k m s−1Mpc−1, Ωm= 0.32, ΩΛ= 0.68
(Planck Collaboration 2014).
2 DATA
2.1 ALMA data
ALMA Science Verification data on SDP.81 were taken from
the ALMA Science Portal1(ASP). We give an overview
of those data here, although more details can be found in
ALMA Partnership, Vlahakis et al. (2015).
SDP.81 was observed in October 2014 as part of
ALMA’s Long Baseline Campaign, using between 22 and
36 12 m-diameter antennas and ALMA’s band 4, 6 & 7 re-
ceivers. The band 4 observations had the fewest total num-
ber of antennas (a maximum of 27 compared to a maximum
of 36 in the other bands), although the 21-23 element long
baseline configuration was similar in all three bands.
Four 1.875 GHz bandwidth spectral windows were used,
over a total bandwidth of 7.5GHz. In each observing band,
one or two spectral windows covered a spectral line, with
the remaining spectral windows used for continuum. The
band 4, 6 and 7 data include the redshifted CO(5-4) (vrest =
1http://www.almascience.org
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2014 RAS, MNRAS 000, 1–11
Reconstruction of H-ATLAS J090311.6+003906 using ALMA 3
576.267 GHz), CO(8-7) (vrest = 921.799 GHz), and CO(10-
9) (vrest = 1151.985 GHz) lines, respectively, as well as rest
frame 250 µm, 320 µm and 500 µm continuum. The band 6
data also include the redshifted low-excitation water line
H2O (202 −111) (vrest = 987.927 GHz; Eup = 101 K) but
we leave analysis of this feature for future work (see Section
6).
The calibration and imaging of the data is described in
the scripts provided on the ASP. These were carried out us-
ing the Common Astronomy Software Application package
(CASA2; McMullin et al. 2007). A robust=1 weighting of the
visibilities was used. Line-free channels were used to sub-
tract the continuum emission from the CO data. The CO
line data were imaged using rest frequencies correspond-
ing to z= 3.042 and were uv-tapered to a resolution of
∼170 mas (1000 kλ), since the high-resolution CO data has
relatively low signal-to noise. In the case of H2O, the data
were uv-tapered to 200 kλ(providing an angular resolution
of ∼0.9′′) in order to achieve a reasonable detection. The
resulting RMS noise levels are 0.20 mJy and 0.15 mJy per
21 kms−1channel for CO(5-4) and CO(8-7) respectively.
We also carried out our own independent imaging of
the calibrated visibility data supplied via the ASP. We at-
tempted a variety of different tapers and cleaning parame-
ters but found the ASP data to be already optimal for our
purposes. We note also that in this paper we have used the
band 4 image cube later staged on the ASP on March 2nd
2015 with correctly subtracted continuum.
For the purposes of our lens modelling, we binned the
band 6 and band 7 continuum images from a pixel scale
of 0.005′′ to a pixel scale of 0.01′′. This not only increases
modelling efficiency, but also lessens image pixel covariance
(see Section 3). In the modelling, we assumed the synthe-
sised beam sizes prescribed in the ALMA data themselves;
155×121 mas and 169×117 mas for CO(5-4) and CO(8-7),
respectively.
The panels on the left in Figure 1 show the ALMA band
6 and band 7 continuum images.
2.2 Near-IR data
We have re-analysed the Hubble Space Telescope (HST)
imaging3of SDP.81 modelled by D14. We have applied our
modelling to the deeper F160W image which has a total
exposure time of 4418 s. The image was reduced using the
IRAF MultiDrizzle package resulting in an image resam-
pled to a pixel scale of 0.064′′.
We have post-processed the data in two different ways.
Firstly, we applied a small astrometric correction to ensure
accurate alignment with the ALMA data. We used the Sloan
Digital Sky Survey data release 10 (Ahn et al. 2014) to
identify stars in the region covered by the HST image and
tied the resulting stellar catalogue to the two Micron All
Sky Survey (Skrutskie et al. 2006). This catalogue then in-
dicated a small astrometric offset of ∼0.1′′ from the HST
image which we then corrected the HST astrometry with
accordingly.
2http://casa.nrao.edu
3The HST imaging was acquired with the Wide Field Camera 3
(WFC3) in Cycle 18 under proposal 12194 (PI Negrello).
Secondly, we carried out an independent removal of the
lens galaxy light prior to lens modelling using the GALFIT
software (Peng et al. 2002). In doing so, we have revealed
additional structure in the F160W data to the south of the
lens. Since this influences our new interpretation of the char-
acteristics of the lensed source, we include this additional
structure in our lens modelling with a larger image plane to
encompass it (see section 4.2 for more details).
In the lens modelling of the F160W data, we used a
point spread function created by the TinyTim software pack-
age (Krist 1993). The upper left panel of Figure 2 shows the
reprocessed F160W data with the band 6 continuum over-
laid as contours.
3 LENS MODELLING
We carried out our lens modelling in the image plane rather
than the uv plane. The disadvantage of this approach is that
we do not directly model the pure interferometric visibilities,
but their modulated Fourier transform instead. A side effect
of this is that image pixels are correlated by the beam which
biases image plane modelling if the uncertainties do not take
the covariance of image pixels into account. However, in the
case of the ALMA data modelled in this paper, the beam size
is comparable to the image pixel scale and so this covariance
is relatively low. The covariance is lowered even further by
our use of the 2 ×2 pixel binned version of the band 6 and
band 7 science verification continuum image data. Further-
more, the ALMA data have a very high coverage of the uv
plane which significantly reduces errors in the image plane.
Any bias resulting from ignoring covariance in the im-
age plane will affect the overall normalisation of the figure of
merit. Whilst this effect will be small in the current ALMA
data, this will still prevent a fair comparison between differ-
ent lens model parameterisations in principle. However, for a
fixed parameterisation such as that used in the present work,
the relative difference in the figure of merit between differ-
ent sets of parameter values remains unaffected. In this way,
a reliable best fit lens model can still be found and hence
image plane covariance is not a concern in this regard.
We have verified that these assumptions are valid with
the ALMA data analysed in this paper using the following
procedure. Firstly, as we discuss below, we located the best
fit lens model by application of the semi-linear method in the
image plane to the 2 ×2 binned version of the band 7 contin-
uum image. We then transformed the best fit model lensed
image to the uv plane by using MIRIAD uvmodel to produce
a simulated visibility dataset for the same uv coverage as in
the ALMA dataset. Using the ALMA visibilities, their un-
certainties and the model visibilities, we computed χ2. We
then varied different lens model parameters, stepping away
from the set which provide the best fit in the image plane,
generating new images each time and transforming to the
uv plane to measure how χ2varied. We found that although
there is a slight offset in parameter space between the im-
age plane minimum-χ2and the uv plane minimum-χ2, this
is within the parameter uncertainties.
There are two main advantages to working in the im-
age plane. The first is that the image can be masked to limit
calculation of the goodness of fit to those parts of the image
where there is detected emission from the lensed source. This
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2014 RAS, MNRAS 000, 1–11
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continuum source
200 pc
band 7 model continuum
band 6 observed continuum band 6
continuum source
200 pc
band 6 model continuum
band 7 observed continuum band 7
Figure 1. Reconstruction of the band 6 (top row) and band 7 (bottom row) continuum image. We show the observed image (left), the
model image of the reconstructed source (middle) and the reconstructed source (right) for both bands. The white line in the source shows
the position of the caustic.
gives a considerably more sensitive figure of merit for the
fitting than working in the uv plane where modelling neces-
sarily fits to visibilities that largely describe extended areas
of background sky. The second is of particular relevance to
the ALMA dataset under analysis in this paper; modelling
in the image plane is vastly more efficient than working di-
rectly with the extremely large visibility dataset which has
to be trimmed in Fourier space anyway to ensure that the
modelling process is feasible (e.g. Rybak et al. 2015).
3.1 Lens modelling procedure
We used the latest implementation of the semi-linear in-
version method (Warren & Dye 2003) as described by
Nightingale & Dye (2015). The crux of the method is the
manner in which the source plane discretisation adapts to
the magnification produced by a given set of lens model
parameters. By introducing a random element to the dis-
cretisation and by ensuring that the discretisation maps ex-
clusively back to only those areas in the image within the
mask, the method eradicates biases in lens model parameter
estimation. Crucially, the method removes a significant bias
in the inferred value of the logarithmic slope of power-law
mass density profiles which occurs when semi-linear inver-
sion is used with a fixed source plane size and/or a fixed
source plane pixellisation (see Nightingale & Dye 2015, for
more details).
We have also used simultaneous reconstruction of multi-
ple source planes from multiple images as described in D14.
We attempted a variety of different combinations of data,
but found that there were no clear improvements on lens
model constraints beyond using a dual reconstruction of the
ALMA band 6 and band 7 continuum image data.
For our lens model, we adopted a single smooth power-
law profile with a volume mass density of the form ρ∝
r−α. In utilising this profile, it is assumed that the power-
law slope, α, is scale invariant. This assumption appears
to be reasonable on the scales probed by strong lensing as
demonstrated by a lack of any trend in slope with the ratio of
Einstein radius to effective radius (Koopmans et al. 2006;
Ruff et al. 2011).
The corresponding projected mass density profile used
to calculate lens deflection angles is therefore the elliptical
power-law profile introduced by Kassiola & Kovner (1993)
with a surface mass density, κ, given by
κ=κ0(˜r/1kpc)1−α.(1)
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2014 RAS, MNRAS 000, 1–11
Reconstruction of H-ATLAS J090311.6+003906 using ALMA 5
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RA (J2000)
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RA (J2000)
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RA (J2000)
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4 kpc 800 pc
Figure 2. Source reconstruction of the HST F160W data. Panels show the observed image (left; black ellipse masks out residual noise
left from lens galaxy light subtraction and the inset panel shows the lensed image of the reconstructed source), the full scale of the
reconstructed source that fits the tidal debris-like emission seen in the observed image (middle) and a zoomed-in section of the source
overlaid with band 6 continuum contours (right).
Here, κ0is the normalisation surface mass density (the spe-
cial case of α= 2 corresponds to the singular isothermal
ellipsoid, SIE). The radius ˜ris the elliptical radius defined
by ˜r2=x′2+y′2/ǫ2where ǫis the lens elongation defined as
the ratio of the semi-major to semi-minor axes. Three fur-
ther parameters define the lens mass profile: the orientation
of the semi-major axis measured in a counter-clockwise sense
from north, θ, and the coordinates of the centre of the lens
in the image plane, (xc, yc). Finally, following the findings of
D14, we include an external shear component which is de-
scribed by the shear strength γand orientation θγmeasured
counter-clockwise from north.
As this paper is concerned primarily with the properties
of the lensed source, we have not considered more compli-
cated lens models. For example, one possibility is to model
the lens using a cored density profile. Whilst there is contin-
uum emission detected at the centre of the ring where a core
would be expected to produce an image, our measurements
of the spectral index indicate that this emission cannot be
entirely from the background source. Similarly, the high res-
olution and high signal-to-noise submm images may provide
a perfect test-bed for lens mass profiles including substruc-
ture. Nevertheless, we leave more detailed lens modelling for
future study.
4 RESULTS
4.1 Lens model
Table 1 lists the most probable lens model parameters
identified by marginalising over the Bayesian evidence (see
Nightingale & Dye 2015, for more details). The parameters
are consistent with those obtained by D14 from modelling
solely the HST data. They are also in agreement with the
parameters obtained by Rybak et al. (2015) who performed
uv modelling of the same ALMA data we have analysed in
the present work. This provides further strength to our argu-
ment concerning the viability of lens modelling in the image
plane in this case.
Lens parameter Value
κ0(0.86 ±0.04) ×1010M⊙kpc−2
ǫ1.25 ±0.04
θ13◦±2◦
α2.01 ±0.05
γ0.04 ±0.01
θγ−4◦±3◦
Table 1. Most probable lens model parameters. The quantities
are the lens mass normalisation, κ0, the elongation of the lens
mass profile, ǫ, the orientation of the semi-major axis of the
lens measured counter-clockwise from north, θ, the density pro-
file slope, α, the strength of the external shear component, γand
the orientation of the shear θγmeasured counter-clockwise from
north.
We also note that the ring is remarkably well fit if we
force a slope of α= 2 and zero external shear, corresponding
to a pure SIE model. In this case, the best fit elongation
increases to ǫ≃1.4 but the model has a lower evidence
(with ∆χ2≃20) than the most probable model.
4.2 Source morphology
Figure 1 shows the lensed source reconstructed from the
ALMA band 6 and band 7 continuum images. In the figure,
we show the source reconstructed on a regular grid for pur-
poses of illustration, although the adaptive source pixellisa-
tion scheme was used in the lens modelling. We also show a
zoomed-in section of the image of the source to demonstrate
the quality of the fit.
The source continuum emission shows that the distribu-
tion of dust is very irregular with many small scale clumps.
The morphology is broadly similar between both bands, al-
though the ratio of the band 7 flux to the band 6 flux varies
slightly across the source, most likely due to varying dust
temperature. Rybak et al. (2015) also show that the star
formation rate varies considerably across the source.
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2014 RAS, MNRAS 000, 1–11
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0.02 0.180.10 0.140.06(Jy/beam.km/s)
11s.5611s.5711s.58RA (J2000)
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Dec (J2000)
Dec (J2000)
400 pc 400 pc
Figure 3. Zeroth moment CO map for C0(5-4) (left) and CO(8-7) (right) emission in the source. In both maps, the band 6 continuum
emission is shown by the white contours and the F160W emission is shown by the yellow contours.
Turning to the F160W data, Figure 2 shows our recon-
struction performed using the best fit lens model obtained by
simultaneously fitting to the band 6 and band 7 continuum
data. As is immediately apparent from a direct comparison
of the observed lensed images, there is a very distinct offset
between the submm emission and the near-IR (rest frame
blue) emission. The additional structure revealed in our re-
processing of the F160W data is reconstructed in the source
plane as shown in the lower two panels of Figure 2. The
lower right panel reveals the dominant near-IR component
which gives rise to the bulk of the light seen in the ring.
This matches that reconstructed by D14, although a tail of
emission to the south is now apparent. In the larger scale
reconstruction shown in the lower left panel, it appears that
this tail is only part of a larger extent of near-IR emission.
In addition, to the north of the ring, there is another single
component which, in the image plane, gives rise to the arclet
seen to the north of the ring. We have measured the F110W-
F160W colour of these additional components, drawing on
the shallower F110W data described in N14, and find that
it is consistent with the colour of the main arc seen in the
HST data.
We find total magnification factors of 16.0±0.7 and
15.8±0.7 for the band 7 continuum and band 6 continuum
reconstructed sources respectively. For the F160W source,
we find a total magnification factor of 4.5±0.3 for the en-
tire source as shown in the lower left panel of Figure 2. For
the dominant component seen in the F160W source, shown
in the lower right panel of Figure 2, we measure a magnifi-
cation factor of 10.2±0.5, consistent with the magnification
measured by D14 for this part of the source.
4.3 CO emission and source kinematics
We used our best fit lens model to reconstruct the distribu-
tion of flux in the source plane for each slice of the image
data cubes released as part of the ALMA science verifica-
tion data. Our reconstruction was able to detect significant
CO(5-4) and CO(8-7) emission in the reconstructed band
4 and 6 cubes respectively. We were unable to detect any
significant CO(10-9) emission in the reconstructed band 7
cube.
Figure 3 shows the zeroth moment map of the CO line
emission. These were made using CASA immoments, stack-
ing over channels 31 to 61 inclusive (rest-frame velocities
from -370 kms−1to 260 kms−1) for CO(5-4) and channels
30 to 60 inclusive (rest-frame velocities from -391 kms−1to
239 kms−1) for CO(8-7). Our modelling yields total magnifi-
cation factors of 13.7±0.6 for the CO(5-4) flux and 13.1±0.6
for the CO(8-7) flux.
For comparison, in the zeroth moment maps we also
show the the band 6 continuum reconstructed source (white
contours) and the F160W source (yellow contours). It is im-
mediately apparent from these plots that while the CO(5-4)
emission follows the continuum emission, there is a signifi-
cant offset between the more highly excited CO(8-7) emis-
sion and the continuum. Furthermore, the CO(8-7) map
shows more extended emission, linking the submm and near-
IR emission regions.
Using CASA immoments to generate a first moment map
to obtain the velocity field in each reconstructed CO cube,
we also found a relatively smooth variation in velocity across
the source (see Figure 4). The velocity field in each cube has
the hallmarks of disk rotation and hence we fitted rotation
curves assuming rotation of a disk (see Section 4.3.1). Sim-
ilar application of CASA immoments to generate the second
moment map, shows a velocity dispersion which peaks in
the dynamical centre of the source but also has strong peaks
throughout.
4.3.1 Dynamical modelling
To model the velocity field of the CO(8-7) and CO(5-4) and
so estimate the disk inclination and asymptotic rotational
velocity, we fitted a two dimensional model whose velocity
field is described by a combination of stars and gas such that
v2=v2
D+v2
Hwhere the subscripts denote the disk and
dark matter halo respectively (we ignore any contribution
of Hito the rotational velocity). For the disk, we assumed
that the surface density follows a Freeman profile (Freeman
c
2014 RAS, MNRAS 000, 1–11
Reconstruction of H-ATLAS J090311.6+003906 using ALMA 7
Figure 5. Rotation curves of the lensed source from CO(5-4)
and CO(8-7) emission. The data points show the observed line
of sight velocity extracted from a 0.4 kpc wide slit running along
the major kinematic axis and the line shows the best dynamical
model fit.
1970). For the halo, we assumed the Berkert (1995) density
profile which incorporates a core of size r0and converges to
the Navarro, Frenk & White (1996, NFW) profile at large
radii. For suitable values of r0, the Berkert profile can mimic
the NFW or an isothermal profile over the limited region of
galaxy mapped by the rotation curves.
This mass model has three free parameters: the disk
mass, the core radius of the dark matter halo and the central
core density. To fit the two-dimensional velocity fields, we
constructed a two-dimensional kinematic model with these
three parameters, but we also we allowed the [x/y] centre
of the disk, the position angle (PA) and the disk inclination
to be additional free parameters. We constrained the [x/y]
dynamical centre to be within 0.5 kpc of the band 7 contin-
uum centroid and then fitted the two dimensional dynamics
using an MCMC code.
The best-fit kinematic maps and velocity residuals are
shown in Figure 4. The best fit disk inclination is (40 ±
5)◦. Assuming that the observed velocity field is indeed due
to disk rotation, then the observed maximum line of sight
rotational velocity of 210 kms−1corresponds to an intrinsic
asymptotic velocity of 320 kms−1.
Figure 5 shows the one dimensional rotation curves ex-
tracted from a 0.4 kpc wide strip running along the major
kinematic axis identified from the dynamical models for the
CO(8-7) and CO(5-4) emission. For these rotation curves,
we defined the velocity zero point using the dynamical cen-
tre of the galaxy. The error bars for the velocities are derived
from the formal 1σuncertainty in the velocity arising from
the Gaussian profile fits to the CO emission. We note that
the data have not been folded about the zero velocity, so
that the degree of symmetry can be assessed.
The rotation curves imply a mass within 1.5kpc of
3.5×1010 M⊙with only a small contribution from the halo
within this radius. Comparing the significantly lower maxi-
mum velocity dispersion of ∼90 kms−1with this rotational
velocity suggests, under the assumption of a disk, that a
correction for asymmetric drift need not be applied to the
10 100 1000
Wavelength (µm)
0.1
1
10
Flux (mJy)
Figure 6. Rest-frame de-magnified best fit SED to the band
6 and 7 continuum source fluxes and to the fluxes from table
2 in N14 (but de-magnified using our derived continuum source
magnification factor). The dashed curves show the hot (99 K) and
cold (48 K) SED components.
inferred dynamical mass. If we assume that all of the mass
lies within the exponential disk component, this corresponds
to a surface mass density of 5030 M⊙pc−2. This is a typical
value for high redshift SMGs (see Figure 6 in Ivison et al.
2013).
Using this surface mass density and the observed ve-
locity dispersion in the disk, the resulting Toomre stability
value is Q≃0.2 which indicates a collapsing disk. Such
low values of Qare observed in early merger systems before
feedback can restore equilibrium in the disk (see Hopkins
2012).
4.4 Other intrinsic source properties
4.4.1 Dust mass and total dust luminosity
We have measured the dust mass of the lensed source by
fitting a two-component spectral energy distribution (SED)
model to a combination of our measured band 6 and band 7
continuum fluxes and also the source fluxes presented in N14
but de-magnified by our average continuum magnification
factor of 15.9. The SED model allows the dust temperature,
emissivity index, β, and optical depth at 100 µm, τ100 , to
vary in the fitting. We used a dust mass opacity coefficient
equivalent to κ850µm= 0.077 m2kg−1to be consistent with
the fitting in N14.
Figure 6 shows the best fit SED model which has an
effective dust temp erature of 51 K, an emissivity index of
β= 2.5 and an optical depth of τ100 = 6.5, yielding a dust
mass of 1.8×108M⊙after de-magnifying by our average
continuum magnification factor. The fit favours both a hot
and cold dust component with temp eratures of 99 K and
48 K resp ectively.
If we fix the emissivity index to β= 2.0, we obtain a
lower optical depth of τ100 = 3 and a lower temperature of
46 K but all optically thick fits, with or without fitting to the
160µm flux returned a dust mass in the range (1.8−2.1) ×
108M⊙. A second colder dust temperature component (10–
c
2014 RAS, MNRAS 000, 1–11
8S. Dye et al.
Figure 4. Observed, modelled and residual velocity fields (left, middle-left and middle-right respectively) and observed line of sight
velocity dispersion (right). The top row corresponds to the CO(8-7) line emission and the bottom row corresponds to the CO(5-4). The
white line in the left-most panels shows the principle axis of the best-fit disk model and the dashed black line shows that of the stacked
CO emission. The white ellipse in the middle-left panels shows the extent of the disk used in the dynamical modelling.
40 K) was allowed in the fitting but was not favoured by the
data.
Assuming a typical gas to dust ratio of 150 (for exam-
ple Dunne et al. 2000; Draine et al. 2007; Coretese et al.
2012; Sandstrom et al. 2013; Swinbank et al. 2014) there-
fore gives a total molecular gas mass of 2.7×1010 M⊙. In
making these calculations, we have of course neglected any
effects of differential magnification which could bias the in-
ferred dust temperature and/or emissivity index.
From integrating the best-fit SED between 8 and
1000 µm, we estimate that the total far-infrared emission
is 5.0×1013 L⊙, which agrees well with the value of 5.4×
1013 L⊙given in N14. Our estimate of the average contin-
uum magnification factor of 15.9 implies that the intrinsic
far-infrared luminosity is 3.1×1012 L⊙.
4.4.2 CO(1-0) gas
We have derived an estimate of the CO(1-0) luminosity
of the gas in the lensed source using the CO(1-0) spec-
trum from Valtchanov et al. (2011). To do this, we used
our CO(5-4) source plane velocity and magnification map
to estimate the magnification as a function of velocity in
the source plane. By transforming the CO(1-0) SED to ve-
locity space, we then de-magnified the SED flux at each ve-
locity with the corresponding magnification factor from our
magnification-velocity relation. Figure 7 shows the magni-
fied and de-magnified SEDs.
Using the de-magnified SED, we determined a CO(1-0)
flux of 34 ±5 mJy k ms−1which corresponds to a luminosity
of L′
CO = (1.4±0.3) ×1010 K km s−1pc2. The errors take
into account a number of uncertainties: 1) There appears
to be more CO(1-0) emission at higher and lower velocities
than we see in our CO(5-4) data and so in our velocity-
magnification relationship, we assumed a fixed magnifica-
tion of 3 in these extremes; 2) The measure of de-magnified
flux is sensitive to the binning of the CO(1-0) spectrum and
velocity-magnification mapping; 3) We have determined the
de-magnified flux assuming the CO(1-0) emission exactly
follows the CO(5-4) emission. The flux changes by ∼15% if
we assume the CO(1-0) emission is more evenly distributed
in the source plane.
To estimate the total mass of molecular gas in the
source, we used the CO luminosity to molecular gas mass
conversion factor from Bothwell et al. (2013) of αCO = 1
appropriate for compact starbursts similar to ULIRGS in
local universe. This gives a total molecular gas mass in the
source of (1.4±0.2)×1010 M⊙which compares with the value
of 2.7×1010 M⊙we obtained by scaling from the dust mass.
Using the dynamical mass as an estimate of total mass, this
corresponds to a molecular gas fraction of 30% in the source.
Conversely, if we assume that the source is gas dominated,
then this provides an upper limit of αCO <
∼3.
c
2014 RAS, MNRAS 000, 1–11
Reconstruction of H-ATLAS J090311.6+003906 using ALMA 9
−600 −400 0−200 200 400
Velocity (km/s)
Flux (mJy)
0 0.02 0.04 0.06 0.08
0 400200−400−600 −200
Figure 7. The de-magnified CO(1-0) spectrum in velocity space.
The inset panel shows the lensed SED from Valtchanov et al.
(2011) with our estimated magnification factor as a function of
velocity overlaid in red.
5 DISCUSSION
The offset between the reconstructed rest-frame optical
source emission detected by HST/WFC3 and the recon-
structed submm source from the ALMA data is strik-
ing. D14 found good alignment between the rest-frame
optical emission and the submm source reconstructed by
Bussmann et al. (2013), although this latter study used
imaging acquired with The Submillimeter Array (SMA)
with a beam width approximately two orders of magni-
tude larger than the ALMA image data analysed in the
present work. The anti-correlation seen between the rest-
frame optical and submm emission is not unique; the con-
figuration in SDP.81 is similar to the offset between the opti-
cal and submm emission seen in the z=4.05 SMG GN20 (see
Daddi et al. 2009; Hodge et al. 2015). However, occurrence
of such large offsets is not common. For example, in a sur-
vey of 126 SMGs carried out using ALMA (see Hodge et al.
2013), only two sources, ALESS88.11 and ALESS92.2 ex-
hibit a similar configuration (Chen et al. 2015).
There are a number of scenarios which could explain the
observed configuration of the lensed source. The three most
likely ones are: 1) The submm and optical components are
simply two different sources which are closely aligned on the
sky but well separated along the line of sight; 2) The submm
and optical emission originates from the same source and
we observe a total lack of optical emission from the submm
region due to very strong dust absorption; 3) The optical and
submm components are two separate systems undergoing a
merger.
The first scenario is challenging to verify, not least
because of the large effective radius of the lens in the
optical/near-infrared compared to the Einstein radius for
the optical source. Photon noise from the lens light thus
dominates the already faint optical source which will hinder
attempts to measure its redshift, either spectroscopically or
photometrically. This scenario also draws into question the
structure of optical source and the nature of the apparent
tidal debris to the south and the component to the north.
The second scenario could arise as a result of a strong
dust lane in a disk galaxy. There are many examples of
ULIRGs in the local Universe where strong absorption by
dust lanes result in a delineation between optical and submm
emission. In the case of SDP.81, it may be that a wide and
thick dust lane is located at the eastern edge of the disk,
which, because of its inclination, provides a much higher
column density of dust toward regions in the source which
emit optically. On the assumption that the optical absorp-
tion efficiency factor of a dust grain is inversely proportional
to wavelength, which is true in Mie theory if the grain size is
much less than the wavelength, our estimate of the optical
depth at 100 µm (see Section 4.4.1) implies that the opti-
cal depth in the optical waveband is ∼1000. Therefore, we
would not expect to see much starlight from within the disk
of gas and dust.
The third scenario is suggested by the presence of the
northern rest-frame optical component and the apparent
tidal debris seen to the south. A tempting interpretation
of this is that the northern component is a second galaxy
which has passed through the larger, strongly lensed sys-
tem, causing the tidal debris observed and enhancing the
star formation rate and dust mass. Although the velocity
field appears to be quite regular, the low Toomre Q param-
eter we have measured (Q≃0.2) suggests a collapsing disk.
Also, there are several strong peaks in the velocity dispersion
map which may still point towards some level of interaction
and there are filaments in the CO(8-7) emission (but not
the less excited CO(5-4) emission) which extend up to the
optical region.
In our attempts to search for more hints as to the na-
ture of the source, we also carefully searched through all
channels in the band 6 and 7 ALMA data cubes, looking for
CO emission from the northern and southern optical com-
ponents. Such emission might indicate an association with
the source or provide additional kinematic information. We
could not find any significant emission from the northern or
southern optical components in either of the cubes.
Whatever the connection between the rotating disk
of gas and dust revealed by ALMA and the HST near-
infrared sources, we can draw some conclusions about the
properties of the star formation in the disk. We have es-
timated the star-formation rate in the disk from the in-
trinsic far-infrared luminosity, which is the method sug-
gested by Kennicutt & Evans (2012) for estimating the
star-formation rate in a highly obscured galaxy. From the
relationship between star-formation rate and far-infrared lu-
minosity given in Kennicutt & Evans, we estimate that the
star-formation rate in this object is ∼470 M⊙/yr.
Although it is well-known that high-redshift galaxies are
very clumpy and irregular in broad-band optical/UV images
(Cowie, Hu & Songalia 1995), it has always been an open
question whether the clumpiness is the result of the star
formation occurring in clumps or whether it is the result of
patchy dust obscuration. In the case of this object, both the
reconstructed CO and dust emission are clumpy on the scale
of the point spread function in the reconstructed images,
∼200 pc. The CO lines are high-excitation lines, so that we
cannot rule out the possibility that the clumpiness is the re-
sult of a variation in the excitation rather than a variation in
c
2014 RAS, MNRAS 000, 1–11
10 S. Dye et al.
the distribution of the gas. There is also the recent sugges-
tion that a clumpy CO distribution in high-redshift galax-
ies might be the result of the destruction of CO molecules
by cosmic rays (Bisbas, Papadopoulos & Viti 2015). How-
ever, neither of these two caveats apply to the dust emission;
dust grains are robust and found in all phases of the inter-
stellar medium, and the emission from the dust depends
only very weakly on the intensity of the interstellar radia-
tion field. Therefore, the clumpiness of the dust is strong
evidence that the distribution of gas in this object is truly
extremely clumpy. The low value of the Toomre Q param-
eter and the very irregular distribution of gas are exactly
what one would expect if sections of the disk are collapsing
to form stars. From the rotation curve and the velocity dis-
persion, we estimate that the disk is unstable over the scale
range ∼50 pc to ∼700 pc, the lower limit being the Jeans
length and the upper limit being the scale on which the disk
should be stabilized by shear. This agrees well with the sizes
of the clumps observed.
Finally, we have estimated the efficiency of the star-
formation process in this galaxy. Using the dust mass as
a tracer of the total mass of gas, Rowlands et al. (2014)
and Santini et al. (2014) have found evidence that the
star-formation efficiency (star-formation rate/gas mass) are
higher in high-redshift galaxies than in galaxies in the local
Universe. Rowlands et al. (2014) give relationships between
the star-formation rate and dust mass for local galaxies and
for high-redshift SMGs. Using our measurement of the dust
mass, we have used these relationships to estimate that, if
SDP.81 were a galaxy in the local Universe, it should be
forming stars at a rate of 7.2 M⊙/yr, and if it were a typical
SMG, it should be forming stars at a rate of 58 M⊙/year.
Thus the star-formation efficiency in SDP.81 is ∼65 times
greater than in the nearby Universe and significantly greater
than that of a typical SMG.
6 SUMMARY
We have used the exceptional angular resolution of ALMA
to reconstruct a detailed map of the submm emission and
dynamics in the lensed source in SDP.81. Our modelling of
the reprocessed HST data has revealed an offset of ∼1.5 kp c
between the submm and rest-frame optical centroids in the
source. The submm continuum emission in the source is
magnified by a total magnification factor of 15.9±0.7 which
compares to the magnification of the rest-frame optical emis-
sion of 10.2±0.5 which mainly lies outside of the source
plane caustic. Similarly, the CO(5-4) and CO(8-7) emission
is magnified by the total magnification factors 13.7±0.6 and
13.1±0.6 respectively.
Our reconstruction of the source kinematics from the
CO emission reveals a relatively smooth velocity gradient
across the source and suggests regular disk-like rotation. We
have carried out dynamical modelling of the observed line
of sight velocities and find that the data are best fit by a
disk inclined at an angle of (40 ±5)◦to the line of sight with
an asymptotic rotational line of sight velocity of 210kms−1.
Accounting for the disk inclination, this corresponds to an
intrinsic asymptotic velocity of 320 kms−1. Our dynamical
modelling returns a low Toomre Q-parameter of Q≃0.2.
We have combined our measurements of the dust con-
tinuum flux from the ALMA data with photometry of the
lensed source given in Negrello et al. (2014) to fit a mod-
ified black body SED. This indicates a total dust mass of
1.8×108M⊙after de-magnifying by our average continuum
magnification factor. Assuming a typical gas to dust ratio
of 150 gives total molecular gas mass of 2.7×1010 M⊙. We
have also estimated the total molecular gas mass from the
de-magnified CO(1-0) spectrum of the lensed source from
Valtchanov et al. (2011). This gives a total CO luminosity
of L′
CO = (1.4±0.3) ×1010 K km s−1pc2which, assuming
a gas mass conversion factor of unity, typical for ULIRGs
in the local Universe, gives a total molecular gas mass of
(1.4±0.2) ×1010 M⊙.
One observable we have not discussed in this work
is the low-excitation water line H2O (202 −111) (vrest =
987.927 GHz (Eup = 101 K)) which can be seen in the band
6 data. We have attempted to reconstruct the distribution
of this line in the source plane using our most probable lens
model, but this has proven too weak to locate easily. We
have therefore left analysis of this feature for future study.
To summarise, the nature of SDP.81 is somewhat per-
plexing! Although the observational evidence we have assim-
ilated in this paper is suggestive of a galaxy merger, we can-
not rule out other possibilities. Pending further analysis of
additional observational data, the source evades our full un-
derstanding. Nevertheless, this work has demonstrated the
complexity we can begin to expect in high redshift SMGs
when they are studied at the high angular resolution now
made possible by ALMA’s incredible long baseline imaging
capability.
ACKNOWLEDGEMENTS
SD acknowledges financial support from the Midland
Physics Alliance and STFC. CF acknowledges funding
from CAPES (proc. 12203-1). MN acknowledges financial
support by PRIN-INAF 2012 project Looking into the
dust-obscured phase of galaxy formation through cosmic
zoom lenses in the H-ATLAS’. IRS acknowledges support
from STFC (ST/L00075X/1), the ERC Advanced Investi-
gator programme DUSTYGAL 321334 and a Royal Soci-
ety/Wolfson Merit Award. This paper makes use of the fol-
lowing ALMA data: ADS/JAO.ALMA#2011.0.00016.SV.
ALMA is a partnership of ESO (representing its member
states), NSF (USA) and NINS (Japan), together with NRC
(Canada), NSC 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. The work in this paper is based on observations
made with the NASA/ESA Hubble Space Telescope under
the HST programme #12194.
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2014 RAS, MNRAS 000, 1–11
Reconstruction of H-ATLAS J090311.6+003906 using ALMA 11
Source property Value
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Disk inclination (40 ±5)◦
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