# On the Evidence for Molecular Outflows in High-redshift Dusty Star-forming
Galaxies

James Nianias Department of Physics, University of Hong Kong, Pokfulam Road,
Hong Kong  Jeremy Lim Department of Physics, University of Hong Kong, Pokfulam
Road, Hong Kong  Michael Yeung Max-Planck-Institut für extraterrestrische
Physik, Giessenbachstraße, 85748 Garching, Germany

###### Abstract

Galactic-scale outflows of molecular gas from star-forming galaxies constitute
the most direct evidence for regulation of star formation. In the early
universe ($z>4$), such outflows have recently been inferred from
gravitationally-lensed dusty star-forming galaxies (DSFGs) based on ubiquitous
detections of OH absorption extending to more blueshifted velocities than
[CII] or CO emission in spatially-integrated spectra. Because these lines are
redshifted to sub-mm wavelengths, such measurements require careful
corrections for atmospheric absorption lines, and a proper accounting of
sometimes large variations in measurement uncertainties over these lines.
Taking these factors into consideration, we re-analyze OH and [CII] data taken
with ALMA for the five sources where such data is available, of which four
were categorised as exhibiting outflows. Based on their spatially-integrated
spectra alone, we find statistically significant ($\geq 3\sigma$) OH
absorption more blueshifted than [CII] emission in only one source. By
contrast, searching channel maps for signals diluted below the detection
threshold in spatially-integrated spectra, we find evidence for a separate
kinematic component in OH absorption in all five sources in the form of: (i)
more blueshifted OH absorption than [CII] emission and/or (ii) a component in
OH absorption exhibiting a different spatio-kinematic pattern than [CII]
emission, the latter presumably tracing gas in a rotating disc. Providing a
more complete and accurate assessment of molecular outflows in
gravitationally-lensed DSFGs, we suggest methods to better assess the
precision of corrections for atmospheric absorption and to more accurately
measure the source continuum in future observations.

††software: CASA (McMullin et al., 2007), Astropy (Astropy Collaboration et
al., 2013, 2018, 2022), Matplotlib (Hunter, 2007), ESSENCE (Tsukui et al.,
2023)

tablenum SIXtablenum

##  1 INTRODUCTION

Figure 1: OH-containing bandpasses of the sources observed in S18 and S20
(coloured bands) overlaid on a representative atmospheric transmission model
(blue curve) produced in CASA (McMullin et al., 2007). Sources with high-
resolution [CII] observations are indicated in bold, while those in which S18
or S20 detect blueshifted OH absorption are indicated with asterisks. Dashed
vertical lines indicate the frequency of the higher-frequency OH line at the
respective source redshift. The broad absorption bands in the transmission
model are produced by H2O, while the narrow lines are due to O3. The
bandpasses of SPT0418-47 (green band) and SPT2319-55 (light blue band) contain
O3 atmospheric absorption lines, while the atmospheric transmission drops
steeply towards the high-frequency (low-velocity) edge of the bandpass of
SPT2132-58 (purple band).

Feedback processes related to star formation, active galactic nuclei, or both,
are thought to have regulated the formation of stars in galaxies since early
times. Without feedback, cosmological models predict galaxies to have much
larger stellar masses than are seen in the present-day universe (e.g., see
Kereš et al. 2009 and references therein). The most easily visible
manifestation of such feedback is galactic-scale outflows, a prominent example
of which can be seen in the nearby starburst galaxy M82. This outflow is
detectable in X-ray, H$\alpha$, and CO, tracing ionised, atomic, and molecular
gas, along with infrared emission tracing dust, all streaming outwards
perpendicular to the disc. Since young galaxies can exhibit more vigorous star
formation, outflows at high redshift may be even stronger (Sugahara et al.,
2019); furthermore, galaxies have lower masses in the early universe, so both
gas and dust can escape more easily from the galaxy owing to radiation
pressure and stellar winds from star-forming regions.

Unlike in nearby galaxies, galactic outflows at high redshifts are generally
not spatially resolved and are instead inferred from emission and/or
absorption line profiles. High-redshift star-forming galaxies have been shown
to exhibit spectral signatures of ubiquitous ionized/atomic outflows:
Ly$\alpha$ emission lines with peaks redshifted relative to the systemic
velocity of the host galaxy, sometimes accompanied by weaker blueshifted
peaks, are interpreted in terms of scattering of Ly$\alpha$ through partially-
or fully-ionized outflows (see reviews by Ouchi et al. 2020, Erb 2015), though
radiative transfer models are as yet unable to reproduce the observed of
different Ly$\alpha$ profiles (Gurung-López et al., 2022). A more unambiguous
indicator of outflows is the presence of blueshifted metal absorption lines
arising from partially neutral material outflowing from starburst regions
towards the observer (see Steidel et al., 2010), though such features are
difficult to detect when the stellar continuum is weak.

The apparent abundance of ionized/atomic outflows in star-forming galaxies at
high redshifts naturally raises the question of whether molecular gas also is
driven out. Molecular gas is of particular interest because it comprises the
fuel for star formation, making outflows of molecular gas the most direct
signature for feedback-regulated star formation in star-forming galaxies. At
the present time, however, high-redshift molecular outflows seen in line
emission, as inferred from broad CO line wings, have only been reported in a
small number of objects – around ten – all thought to be AGN-driven (e.g.,
review by Veilleux et al. 2020). Given the limited success in observing high-
redshift molecular outflows in line emission, observers have resorted to
searching for outflows in line absorption, since all that is required is a
sufficiently bright background continuum source such as dust emission. Spilker
et al. (2018) and Spilker et al. (2020a) (hereafter S18 and S20, respectively)
took advantage of a sample of gravitationally-lensed galaxies with
particularly bright dust continua – dusty star-forming galaxies or DSFGs – to
search for spectral signatures of outflowing molecular gas traced in OH
$119\text{\,}\mathrm{\SIUnitSymbolMicro m}$ doublet absorption. They observed
eleven of these galaxies with the Atacama Large Millimeter/submillimeter Array
(ALMA) in Band 8 (covering $385$ –
$500\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, corresponding to a redshift
range of $z\sim 4$ – 5.7 in the OH $119\text{\,}\mathrm{\SIUnitSymbolMicro m}$
doublet), and compared the resulting OH absorption spectra with archival
observations of either [CII] or CO emission from the same objects. In eight of
the eleven sources observed, they detect OH absorption blueshifted to
velocities greater than any detectable [CII] or CO emission. Interpreting the
[CII] and CO emission as tracing gas contained in the disc of the target
galaxies, they argue that the blueshifted OH absorption traces outflowing gas.
Moreover, they find no strong evidence of AGN-related emission based on mid-IR
photometry, suggesting that these outflows may be driven by feedback from
star-formation.

As was pointed out in both S18 and S20, observations in the sub-mm are
complicated by both broad and narrow atmospheric absorption features. These
features can be seen in a representative atmospheric transmission curve for
ALMA band 8, the band in which all the OH observations in S18 and S20 were
made, as plotted in Figure 1. The coloured bands in this figure indicate the
bandpasses of each target from S18 and S20. As can be seen, some of these
bandpasses coincide with large changes in atmospheric transmission, either in
the form of narrow lines due to O3 (e.g., SPT2319-55 and SPT0418-47) or broad
features across the bandpass due to H2O absorption (e.g., SPT2132-58). The
strong and sometimes rapid changes in atmospheric absorption with observing
frequency, as well as variations in time owing to changes in atmospheric
conditions and/or source elevation, have two important consequences that
obervers must consider. Firstly, although corrections are made to such changes
through measurements of atmospheric opacity towards each object observed (see
Section 2.1), it is still necessary to assess the precision of these
corrections to ensure that no residual atmospheric features remain. Secondly,
varying atmospheric transmission with frequency leads to a varying noise level
across the target spectra. While this effect is mentioned in S18, it is
crucial to explicitly compute measurement uncertainties in each channel
separately so as to assess the statistical significance of any spectral
features.

Here, we re-analyse all sources in S18 and S20 for which high-resolution [CII]
$158\text{\,}\mathrm{\SIUnitSymbolMicro m}$ observations have been made with
ALMA – five out of eleven in total, as listed in Table 1. The remaining
sources (all from S20) only have available observations in CO at angular
resolutions far too low to permit the checks described above, and are
therefore excluded from our study. To address the concerns raised above, we
check the precision of the overall bandpass calibration to define the minimum
level whereby OH absorption features can be considered genuine. In so doing,
we find that in all but one case, the bandpass is corrected to a sufficiently
high precision that any residual atmospheric effects must be well below the
noise level of the target spectra. We also determine the measurement
uncertainty in each spectral channel, necessary to assess the statistical
significance of any putative OH absorption. As a first step in searching for
outflows, we compare spatially-integrated OH and [CII] spectra in exactly the
same manner as S18 and S20 to search for OH absorption blueshifted beyond
detectable [CII] emission. Of the five sources included in our study, S18 and
S20 find such evidence for outflows in four; by contrast, with a proper
accounting of measurement uncertainties in different spectral channels, our
analysis reveals just one source in which this spectral signature is
statistically significant.

Owing to gravitational lensing, all of the sources studied are strongly
magnified into Einstein rings, allowing other diagnostics to be used for
assessing outflows. Thus, secondly, to guard against the possibility of
localised OH absorption and/or [CII] emission being diluted below the
detection threshold in the spatially-integrated spectra, we examine maps in
individual spectral channels (channel maps) for each source. We find [CII]
emission extending to more blueshifted velocities than is detectable in the
spatially-integrated spectra in two sources, highlighting a major potential
pitfall in relying on spatially-integrated spectra alone to diagnose outflows.
On the other hand, we find OH absorption extending to more blueshifted
velocities than [CII] emission not just in the source mentioned above showing
such behavior in its spatially-integrated spectrum, but also in two further
sources where the corresponding features are not detectable in their
spatially-integrated spectra. Finally, we search the channel maps for a
component in OH absorption exhibiting a different spatio-kinematic pattern
than the [CII] emission, thus providing direct evidence for a separate
kinematic component possibly tracing an outflow, finding three such examples.

In Section 2, we describe our reduction of the data taken by ALMA, focusing in
particular on how well the effects of atmospheric absorption are accounted for
in the calibration process. We stress that we follow the same steps in the
data reduction as S18 and S20, and obtain the same results within random noise
fluctuations – except now explicitly quantifying the accuracy to which
corrections in atmospheric absorption have been made in the target sources as
well as quantifying the level of noise fluctuations in each spectral channel.
In Section 3, we compare the spatially-integrated [CII] and OH spectra of each
source as well as the spatio-kinematic structure of [CII] and OH in maps of
individual spectral channels. In Section 4, we summarise the complete suite of
evidence for outflows in each source. We then discuss ramifications for the
mass outflow rates as calculated by Spilker et al. (2020b). We end our
discussion with suggestions to mitigate the difficulties in detecting weak
astronomical absorption lines in the presence of strong atmospheric absorption
lines in ALMA observations. Finally, in Section 5, we summarise our work and
offer our thoughts on how future searches of OH outflows from high-$z$
galaxies ought to be conducted.

##  2 ARCHIVAL OBSERVATIONS AND DATA REDUCTION

We obtained data for the same OH $119\text{\,}\mathrm{\SIUnitSymbolMicro m}$
observations presented in S18 and S20, along with data from ancillary
observations covering the [CII] $158\text{\,}\mathrm{\SIUnitSymbolMicro m}$
line of each target, from the ALMA archive. The OH observations were made with
one sideband containing two partially-overlapping spectral windows covering
the OH lines at the source redshift, and an alternate sideband containing two
partially-overlapping spectral windows covering only the dust continuum.
Further details of the OH observations can be found in S18 and S20. Similarly,
the [CII] observations utilised two spectral windows to cover the [CII] line
at the source redshift in one sideband, and two spectral windows to cover the
dust continuum in the other sideband. In both the OH and [CII] observations,
each spectral window is configured at its maximal possible bandwidth of
$1.875\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$. Table 1 lists the redshifts
and integration times of the observations in OH and [CII] for each source.

Table 1: Sources Source | $z$ | int. time (min)
---|---|---
|  | OH | [CII]
SPT0202-61 | 5.0180 | 43 | 54
SPT0418-47 | 4.2248 | 87 | 19
SPT0441-46 | 4.4770 | 28 | 29
SPT2132-58 | 4.7677 | 17 | 25
SPT2319-55 | 5.2943 | 30 | 21

###  2.1 Calibration

Figure 2: (a)-(b): Spectrum of the bandpass calibrator and secondary (phase)
calibrator for SPT0418-47 with neither atmospheric nor instrumental bandpass
calibration applied. Each spectrum clearly shows narrow absorption lines due
to atmospheric O3, closely matching the atmospheric transmission model in (b)
(blue curve). (c)-(d): the same spectra after atmospheric calibration but
before instrumental bandpass calibration. Both spectra cleary show residual
features around the O3 lines due to the lower spectral resolution of the
atmospheric opacity measurements. (e)-(f): the same spectra after both
atmospheric and instrumental bandpass calibration. Since the instrumental
bandpass correction is derived from this spectrum, the bandpass calibrator
spectrum in panel (e) is almost perfectly flat; however, the secondary
calibrator spectrum in panel (f) shows enhanced scatter around the O3 lines
due to higher thermal noise, residual atmospheric features, or both.

The ALMA Science Archive provides uncalibrated visibilities along with scripts
that allow users to calibrate the visibilities using the corresponding
pipeline for the ALMA cycle in which the observations were made. We calibrated
each visibility set in the same manner as reported in S18 and S20, using the
calibration script either executed by us (for SPT0418-47 and SPT2132-58) or by
the East Asia ALMA helpdesk (for the remaining sources111Although we ran the
calibration pipelines ourselves for all the sources, owing to a number of
technical issues, we had to revert to the ALMA helpdesk for calibrating the
data for some of these sources.). The only exceptions are the OH data for
SPT0441-46 and [CII] data for SPT2132-58, which we re-calibrated manually,
though excluding the data flagged in the initial automatic pipeline as for the
other sources222Our re-calibration of the OH observations of SPT0441-46 was
motivated by concerns about the high noise level found in the images made with
the original calibration; our re-calibrated data shows reduction in sidelobe
levels. For SPT2132-58, an issue in the original ALMA calibration script
manifested as a discontinuous jump in noise level between two adjacent
spectral windows.. Following subsequent self-calibration of the visibilities
(described in Section 2.2), the dust continuum maps that we produced for all
sources have morphologies and signal-to-noise ratios in close agreement with
those reported in S18 and S20; furthermore, the spatially-integrated OH
spectra also are similar to those presented in S18 and S20 within random noise
fluctuations.

Prior to calibration, the atmospheric absorption features shown in Figure 1
are imprinted on the spectra of the target as well as the calibrators. These
features are clearly visible in the uncalibrated spectra of the bandpass and
secondary calibrators (the purposes of these calibrators are described below),
examples of which are shown in Figure 2(a) for the pimary calibrator and
Figure 2(b) for the secondary calibrator used in the observations of
SPT0418-47. ALMA corrects for variable atmospheric transmission by measuring
the signal strength emitted by the atmosphere, expressed as the atmospheric
temperature $T_{atm}$, which is then used to estimate atmospheric opacity and
hence also transmission (for details see He et al. 2022). By making this
measurement as a function of both frequency (at a resolution of
$16\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$) and time (immediately before an
observation of a calibrator or the target object), the calibration pipeline
corrects for changes in the atmospheric transmission due to the changing
elevation of the target as well as varying weather conditions. Because
measurements of $T_{atm}$ are obtained at lower spectral resolution than the
calibrators and target spectra, however, residual atmospheric features remain
even after the atmospheric calibration is applied. Such residuals are most
readily apparent for relatively narrow atmospheric absorption lines that are
not spectrally resolved in the $T_{atm}$ measurements, as can be seen in
Figure 2(c) for the bandpass calibrator and Figure 2(d) for the secondary
calibrator after atmospheric calibration is applied.

The remaining gradual variation with frequency bracketed by roll-offs towards
the edges of each spectral window, most clearly apparent in Figure 2(c) and
also present in Figure 2(d), is due to the instrumental response. To correct
for this, an observation of a bright continuum source (referred to as the
bandpass calibrator, which has no known spectral lines) is conducted to derive
corrections for the instrumental spectral response; as there are residual
atmospheric features in the spectrum of the bandpass calibrator, these
features are also removed in the bandpass calibration. Figure 2(e) shows the
spectrum of the bandpass calibrator after bandpass calibration is applied: as
expected, it is perfectly flat to within the noise level. On the other hand,
the bandpass calibration does not necessarily remove (and may even exacerbate)
the residual atmospheric features in the spectrum of the secondary calibrator
and target, which are often observed at different (lower) elevations than the
bandpass calibrator and therefore suffer different (larger) degrees of
atmospheric absorption. Figure 2(f) shows the spectrum of the secondary
calibrator after bandpass calibration is applied, in which channels coinciding
with the narrow atmospheric O3 lines can be seen to exhibit enhanced scatter
owing to either residual atmospheric features or higher thermal noise in
channels with higher atmospheric opacity (or a combination thereof). This
check highlights the importance of determining the precision of the combined
atmospheric and bandpass calibration to ensure that any residual atmospheric
features are sufficiently small that they cannot significantly affect the
target spectra.

The final step in the calibration is to derive temporal variations in
amplitude and phase induced by both the atmosphere and the telescope
instrumentation on the target object. Such corrections are derived from each
scan of the secondary calibrator, and interpolated to the times of the target
scans so as to be applied to the target.

Finally, the measurement uncertainty can change quickly across the spectrum of
a given object owing to rapid changes in atmospheric transmission with
frequency. Such rapid changes in the measurement uncertainty need to be
recognised when assessing the statistical significance of any purported
spectral line features, especially when the latter coincide with narrow and
deep atmospheric absorption lines (e.g., as in the cases of SPT0418-47 and
SPT2319-55 as described in Section 3.1).

Figure 3: (a) Bandpass calibrator spectra without atmospheric or bandpass
corrections, showing the dominant imprints of changing atmospheric
transmission along with instrumental bandpass. (b) spectra of the secondary
calibrators after calibration, showing no statistically significant residual
features. (c) spatially-integrated OH spectra from each source, with grey
horizontal bars indicating the $\pm 1\sigma$ level of the continuum, blue
hatched regions indicating the velocity ranges over which we obtain the
highest signal-to-noise OH absorption blueshifted beyond the [CII] emission,
and double-headed purple arrows indicating the approximate ranges over which
S18 or S20 report blueshifted OH absorption. The $\pm 1\sigma$ error bars of
the OH spectra are shown for each channel, and can be seen to increase in size
with decreasing atmospheric transmission. (d) [CII] spectra extracted over the
same regions as OH, and binned to the same velocity resolution.

###  2.2 Self-calibration

Owing to their different sky positions and changing weather conditions, the
amplitude and phase corrections as interpolated from the secondary calibrator
may leave residual amplitude and phase errors in the calibrated data for the
target. Such residual errors can be reduced using self-calibration, which in
the cases here utilises a high-signal-to-noise continuum map of the target
itself to determine any remaining amplitude and phase corrections. In nearly
all of the observations, the spectral windows containing the OH or [CII] lines
have wide enough frequency coverage that they also permit measurements of the
continuum adjacent to the respective line profiles. We therefore selected
frequency ranges free from any OH absorption or [CII] emission, using the
spectra shown in S18 and S20 as a guide, and combined these with the
continuum-only sidebands when making continuum images. The sole exception is
the OH observations of SPT2132-58, for which S20 infer OH absorption to cover
nearly the entire bandpass, and which has no useable data in the continuum
sidebands due to low atmospheric transmission. In this case, following S20, we
used all channels in both OH-containing spectral windows to make the continuum
image; as we will show in Section 3, most of these channels do not in fact
contain statistically significant OH absorption. We then CLEANed333The images
generated are convolved with the point spread function (PSF) of the antenna
array, known as the dirty beam. CLEANing deconvolves the dirty beam from the
image and replaces it with a clean beam, a Gaussian ellipsoid fitted to the
central lobe of the PSF. the resulting continuum maps to three times the
thermal noise level444We determined the thermal noise level by making maps
with large shifts in phase center relative to the source positions. – not so
deep as to pick up noise peaks or artefacts – for self-calibration. We then
used these CLEAN continuum maps to perform phase-only self-calibration of the
target visibilities, which resulted in smaller residual phase errors and hence
significantly improved signal-to-noise in the final CLEAN continuum maps. Like
S18 and S20, we did not perform any self-calibration in amplitude, as deriving
robust amplitude corrections would require images having much higher signal-
to-noise ratios.

###  2.3 Channel maps and integrated spectra

The channel maps used in our study as presented in Section 3.2 were generated
from the self-calibrated visibilites. For each source, we CLEANed the channel
maps to $1.5$ times the thermal noise level as measured in the channel map
corresponding to the central velocity of the higher-frequency (lower-velocity)
component of the OH doublet. As a check on the quality of our CLEAN maps, we
compute the root-mean-square (rms) variation over an annulus surrouding the
source in each corresponding channel map, finding it to be only $\sim 10\%$ to
$30\%$ higher than the thermal noise level. Table 2 lists the OH channel
widths used for the individual channel maps of each source, chosen to be
approximately the same as those in S18 and S20. To make a proper comparison of
the OH and [CII] spectral profiles, we used the same widths when making [CII]
channel maps for each source. To generate continuum-subtracted [CII] channel
maps, like in S18 and S20, we performed continuum subtraction on the [CII]
visibilities in the uv-plane, fitting the continuum level using the same
channels in the [CII]-containing spectral windows as were used to make
continuum maps, i.e., channels well away from any emission. We performed
continuum subtraction in the same manner on the OH visibilities to make
continuum-subtracted OH maps; when presenting the spatially-integrated spectra
in OH, however, we retain the continuum to allow the depth in OH absorption
relative to the continuum to be computed. By comparing the OH absorption depth
to the precision in atmospheric and bandpass calibration for a particular
source, we are able to assess whether this absorption genuinely arises in the
source. Finally, we convolved the OH channel maps, continuum-subtracted [CII]
channel maps, and dust continuum maps of each target source to the smallest
possible common angular resolution (synthesised beam), which is listed in
Table 2 for each object. After convolution, the final beam sizes are only
slightly larger than the beam sizes reported in S18 and S20 for the OH
observations.

Table 2: Results from spatially-integrated spectra Source |  Channel width |  BMAJ |  BMIN |  BPA |  Outflow range |  Absorption strength |  Correction accuracy
---|---|---|---|---|---|---|---
|  ($\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$) |  ($\arcsec$) |  ($\arcsec$) |  (∘) |  ($\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$) |  ($\text{\,}\mathrm{m}\mathrm{J}\mathrm{y}\,\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$) |  ($\text{\,}\mathrm{m}\mathrm{J}\mathrm{y}\,\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$)
SPT0202-61 |  50 |  0.48 |  0.42 |  63 |  N/A |  N/A |  N/A
SPT0418-47 |  70 |  0.55 |  0.35 |  89 |  $[-525,-245]$ |  $2320\pm 980$ ($2.4\sigma$) |  890
SPT0441-46 |  75 |  0.35 |  0.26 |  79 |  $[-462,-187]$ |  $1690\pm 620$ ($2.7\sigma$) |  200
SPT2132-58 |  150 |  0.43 |  0.36 |  114 |  $[-675,-375]$ |  $2820\pm 1170$ ($2.2\sigma$) |  380
SPT2319-55 |  75 |  0.40 |  0.32 |  64 |  $[-712,-262]$ |  $2890\pm 470$ ($6.1\sigma$) |  130

As OH absorption can only arise from sightlines towards the dust continuum, we
extracted spatially-integrated OH and [CII] spectra for each source by
integrating over regions where continuum is detected above $3\sigma$ following
the same procedure as used in S18 and S20. To determine the $1\sigma$
uncertainties in individual channels of the integrated OH or [CII] spectra, we
use the Essence software package (Tsukui et al., 2023). Essence derives
uncertainties in spatially-integrated flux density using the noise
autocorrelation function, as measured from each channel map with the target
source masked out. Computing the uncertainties in this manner accounts for the
spatial correlation in the channel maps induced by both the CLEAN
(synthesised) beam as well as any residual amplitude and phase errors in the
calibration555The noise calculated this way is in close agreement with a
commonly-used approximation whereby the uncertainty in spatially-integrated
flux in each channel is taken to be the rms noise level multiplied by the
square root of the number of beams within the region of integration (to within
5 – 15%, varying from source to source and channel to channel).. The
spatially-integrated OH and [CII] spectra along with the varying $1\sigma$
uncertainties in each channel are shown in panels (c) and (d), respectively,
for each target source in Figure 3. As can be seen by comparing the OH spectra
with those of the un-corrected bandpass calibrators in panel (a) for each
source in Figure 3, the noise in each channel of the OH spectra depends on the
atmospheric transmission, such that the noise level is higher where the
atmospheric transmission is lower – and can therefore vary considerably across
the OH line profile (as is the case also in [CII] for the same reasons).

Quantifying the level of line absorption requires knowledge of the continuum
level. To estimate the continuum level and its uncertainty in the spatially-
integrated OH spectrum of all the target sources apart from SPT2132-58, we
used the same channels in the OH-containing spectral windows that were used to
generate the clean continuum map, i.e., channels well away from any
absorption. For the spatially-integrated OH spectrum of SPT2132-58, where the
continuum maps were made using the full OH-containing bandpass, we estimated
the continuum level using the channels at the low-frequency (i.e. high-
velocity) end of the bandpass. These channels are absorption-free according to
the continuum estimate provided in S20. We show the continuum levels by the
dashed grey lines and their $\pm 1\sigma$ uncertainties by the horizontal grey
bands in panel (c) for each source in Figure 3.

##  3 RESULTS AND ANALYSIS

###  3.1 Integrated spectra

In both S18 and S20, an outflow is indicated by OH absorption extending to
blueshifted velocities beyond any detectable [CII] emission in spatially-
integrated spectra. Indeed, a comparison between the OH and [CII] spectra for
all but one of the sources (SPT0202-61) shown in Figure 3 reveals systematic
offsets below the continuum level at velocities lower than the lowest velocity
at which [CII] is detected; furthermore, the nominal absorption depth in these
channels is the same as that in S18 and S20 to within measurement
uncertainties. To compute the statistical significance in the individual
cases, we integrate the OH spectrum of each source over velocities bluewards
of the lowest detectable [CII] velocity until the signal-to-noise level of
this putative absorption is maximised. The velocity ranges thus selected are
shown by hatched blue bands in panels (c) and (d) for each source in Figure 3
except SPT0202-61, for which no systematic offset below zero is appreciable
over the velocity range bluewards of the lowest detectable [CII] velocity. For
comparison, we also show the approximate velocity ranges over which S18 and
S20 report spectral signatures of OH outflows with double-headed purple
arrows. The integrated intensity of the blueshifted OH absorption and its
related measurement uncertainty, along with the velocity range over which we
perform this integration, are given for each source in Table 2.

With a now complete accounting of the measurement uncertainties across the
velocity range spanned by putative blueshifted OH absorption, we find
statistically significant ($\geq 3\sigma$) evidence for blueshifted absorption
in the spatially-integrated spectrum of only one source, SPT2319-55, at
$6.1\sigma$. The source that shows the next strongest putative blueshifted OH
absortion is SPT0441-46, at a significance level of $2.7\sigma$, followed by
SPT0418-47 at $2.4\sigma$ and SPT2132-58 at $2.2\sigma$.

Before accepting as genuine any statistically significant blueshifted OH
absorption, it is crucial to check that the calibration corrects the spectra
to a sufficiently high precision that any residual atmospheric or bandpass
features must be smaller than the depth of the putative OH absorption. To do
this, we plot the spectra of the secondary calibrators as shown in panels (b)
of Figure 3. These calibrators were observed at a similar elevation but have a
higher signal-to-noise in the continuum compared to the target sources. After
atmospheric and bandpass calibration (described in Section 2.1), none of the
secondary calibrator spectra exhibit statistically significant residual
features. Applying the same velocity ranges given in Table 2 for each target
to their respective secondary calibrator spectra, we compute $3\sigma$ upper
bounds for any residual bandpass features as a fraction of the continuum; we
can then be confident that the bandpasses of the target OH spectra have been
corrected to within the same fraction of the continuum. The upper bounds thus
derived are given in terms of integrated flux (in
$\text{\,}\mathrm{m}\mathrm{J}\mathrm{y}\,\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$)
in Table 2. Comparing the strength of the putative blueshifted absorption in
each source with the limits to the accuracy of atmospheric corrections, we
find that in most cases the former is roughly an order of magnitude higher
than the latter, indicating that imperfections in bandpass calibration cannot
be responsible for the systematic offsets below the continuum in the spectra
of most sources. The sole exception is SPT0418-47, for which the upper limit
for residual bandpass features is comparable to the $1\sigma$ uncertainty in
the blueshifted absorption, while the absorption strength itself is just
$2.4\sigma$: in this case there is a prominent atmospheric absorption line
that partially overlaps with the putative blueshifted absorption. While the
secondary calibrator spectrum does not show any statistically significant
residual feature corresponding to this line, we cannot rule out the
possibility that residual calibration errors contribute in part to the
measured absorption.

###  3.2 Channel maps

Figure 4: (a) Contours of total [CII] emission (moment 0) plotted at 10, 30,
50, 70, and 90% of the peak surface brightness (given in the box in the upper
left corner) against dust continuum from SPT0202-61 (seen as an Einstein
ring). (b) contours of total OH absorption (moment 0) plotted at $2\sigma$,
$3\sigma$, $4\sigma$, $5\sigma$, $7\sigma$, and $10\sigma$ against dust
continuum ($1\sigma$ given in the box in the upper left corner, as in the
remaining panels). (c) contours of OH absorption integrated over putative
outflow channels (blue hatched range in Figure 3) plotted at $2\sigma$,
$3\sigma$, $4\sigma$, $5\sigma$, and $7\sigma$ against dust continuum. (d) the
same contours as (c), now overlaid on [CII] emission integrated over the same
velocity range. (e) – (l) contours of individual OH velocity channel maps with
widths of $50\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$ at central
velocities as indicated in each panel plotted at $2\sigma$, $3\sigma$,
$4\sigma$, $5\sigma$, and $7\sigma$, and overlaid on [CII] emission channel
maps over the corresponding velocity ranges (colour). In all panels, magenta
crosses mark the peaks of the dust continuum as shown in panels (a) to (c),
and red arrows point to OH absorption features following a different spatio-
kinematic trend to the [CII] emission, suggesting a separate kinematic
component. Figure 5: Same as figure 4, but for SPT0418-47, with channel width
of $70\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$. White arrows in panels
(d) and (h) point to patches of OH absorption or [CII] emission diluted to
below the detection threshold in the spatially-integrated spectrum, while red
arrows in panels (l) and (j) point to OH absorption features following a
different spatio-kinematic trend to the [CII] emission, suggesting a separate
kinematic component. Figure 6: Same as Figure 4, but for SPT0441-46, with
channel width of $75\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$. White
arrows in panels (h) and (i) point to patches of OH absorption or [CII]
emission diluted to below the detection threshold in the spatially-integrated
spectrum, with panel (h) showing a patch of OH absorption blueshifted beyond
any detectable [CII] emission. Figure 7: Same as Figure 4, but for SPT2132-58,
with channel width of $150\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$. The
white arrow in panel (h) points to a patch of OH absorption blueshifted beyond
any detectable [CII] emission, which is diluted to below the detection
threshold in the spatially-integrated spectrum. Figure 8: Same as Figure 4,
but for SPT2319-55, with channel width of
$75\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$. Patches of blueshifted OH
absorption with no accompanying [CII] emission are clearly visible in channels
(h) to (e). In panels (l) to (j), red arrows indicate OH absorption features
following a different spatio-kinematic trend to the [CII] emission, suggesting
a separate kinematic component.

Relying solely on the spatially-integrated spectra shown in Figure 3 to
diagnose outflows raises two major potential pitfalls. First, the process of
spatial integration may dilute signals that are confined to localised regions
of the Einstein ring, whether they be small patches of OH absorption or of
[CII] emission. Second, the possibility that [CII] emission extends to
velocities beyond those detectable as dictated by the noise level can never be
completely ruled out, making it ambiguous whether the detection of OH
absorption more blueshifted than [CII] emission, alone, implies a kinematic
component separate from the disc. To address both these issues, we made both
OH and [CII] channel maps of each source at the same velocity resolution as
the spectra shown in Figure 3, as well maps integrated over the full velocity
ranges that we use to search for blueshifted OH (hatched blue bands in Fig.
3), using the continuum-subtracted OH and [CII] visibilities. These maps are
shown in panels (b) to (l) of Figures 4 to 8 for each source in the same order
as shown in Figure 3, where contours correspond to OH absorption, red
background to the dust continuum, and rainbow background to [CII] emission –
showing gravitationally-lensed images of each galaxy in the form of an
Einstein ring.

When analysing the channel maps, it is important to take into consideration
apparently statistically significant ($\geq 4\sigma$) patches of OH
“absorption” that are not spatially coincident with the dust continuum, as can
be seen in Figures 5(j), 6(j), and 7(f). Such features may arise due to
residual amplitude and phase errors left following calibration. We therefore
only consider as genuine those absorption patches that are not only spatially-
coincident with the dust continuum, but that are also deeper than any apparent
absorption patches that are not spatially-coincident with the dust continuum.

White arrows in the channel maps of Figures 4 to 8 indicate selected features
in either OH absorption or [CII] emission more blueshifted than are detectable
in spatially-integrated spectra. The channel maps of SPT2319-55 confirm that
its OH absorption extends to more blueshifted velocities than its [CII]
emission in the same manner as in its spatially-integrated spectrum. Moreover,
three other sources (SPT0418-47, SPT0441-46, and SPT2132-58) exhibit more
blueshifted OH absorption in channel maps than is detectable in their
spatially-integrated spectra, of which two (SPT0418-47 and SPT0441-46) also
exhibit more blueshifted [CII] emission in a corresponding comparison. In one
of these two sources (SPT0441-46), the OH absorption extends to more
blueshifted velocities than the [CII] emission, whereas in the other
(SPT0418-47), the OH absorption and [CII] emission extend to the same
blueshifted velocities albeit at different positions within the Einstein ring.
Thus, in total, three sources exhibit more blueshifted OH absorption than
[CII] emission in channel maps, compared with only one (of the same three) in
spatially-integrated spectra, demonstrating the importance of utilising
channel maps rather than relying on spatially-integrated spectra alone to
identify possible outflows.

To add to the evidence for separate kinematic components, we searched the
channel maps for features in OH absorption that show a different spatio-
kinematic pattern than [CII] emission. This approach has the additional
advantage of permitting the identification of separate kinematic components in
OH absorption even in channels with detectable [CII] emission. Before delving
into this search, we first note that a one-to-one comparison between OH
absorption and [CII] emission is complicated by the fact that the strength of
OH absorption – unlike that of the [CII] emission – depends in part on the
brightness of the background dust continuum, which can have a different
surface brightness distribution than that of the [CII] emission. Indeed,
Figures 4(a) to 8(a) show such differences in some of the target sources (e.g.
SPT0418-47 in Figure 5(a) and SPT2132-58 in Figure 7(a)), where cyan contours
indicate the integrated [CII] emission and red background the dust continuum.
Thus, we should not expect the morphology of the OH absorption to perfectly
match that of the [CII] emission in individual channels even if both lines
trace the same gas in the disc. In the channel maps of SPT2319-55, which shows
by far the strongest and the only significant blueshifted OH absorption in
spatially-integrated spectra, the OH absorption in the south of the Einstein
ring indicated by the red arrows in Figures 8(i) to 8(l) can be seen to track
the [CII] emission at velocities close to systemic where both move roughly
counter-clockwise around the Einstein ring with decreasing velocity (between
Figure 8(l) and 8(k)). At more strongly blueshifted velocities (between Figure
8(j) and 8(i)), however, the OH absorption appears to reverse this behavior
and move clockwise, whereas the [CII] emission does not. This behavior
suggests the presence of a separate kinematic component traced in OH
absorption that moreover extends to higher blueshifted velocities than gas
traced in [CII] emission contained in a rotating disc, making a strong case
for a molecular outflow in SPT2319-55.

In SPT0202-61, for which [CII] emission is detectable to even higher
blueshifted velocities than OH absorption in both spatially-integrated spectra
and channel maps, the [CII] emission at the north of the Einstein Ring as seen
in the channel maps of Figure 4 moves counter-clockwise from panels (h) to
(e). By contrast, the patch of OH absorption indicated by the red arrows moves
slightly in the opposite direction, suggesting that this feature comprises a
separate kinematic component. As this patch of OH absorption coincides with
relatively weak dust continuum, it does not appear merely as a consequence of
bright continuum.

SPT0418-47 also shows no significant OH absorption more blueshifted than any
[CII] emission in either spatially-integrated spectra or channel maps. As can
be seen in the channel maps for this source in Figure 5, the [CII] emission in
the northern portion of the Einstein ring moves clockwise starting around the
systemic velocity in panel (f) to more strongly blueshifted velocities in
panels (e) and (d). By contrast, the peak of the OH absorption – indicated by
red arrows – moves in the opposite direction, again indicating the presence of
a separate kinematic component.

##  4 DISCUSSION

###  4.1 Outflow inferences

After determining the precision of corrections for atmospheric absorption as
well as explicitly quantifying the measurement uncertainty in each spectral
channel, we find that only one of the five sources that we analysed
(SPT2319-55) shows statistically significant ($\geq 3\sigma$) evidence for OH
absorption more blueshifted than [CII] emission in its spatially-integrated
spectrum. These results constrast with those reported by S18 and S20, who
argue that four of the same five sources display OH absorption more
blueshifted than [CII] emission in spatially-integrated spectra, though
without explicitly quantifying the statistical significance of this
absorption. On the other hand, we find all five sources to exhibit evidence
for a component in OH absorption different from that in [CII] emission in
their channel maps (which were not included in the analysis of S18 and S20).

An inspection of channel maps for SPT2319-55 reveals, in addition to OH
absorption more blueshifted than [CII] emission detected in its spatially-
integrated spectrum, a component in OH absorption having a different spatio-
kinematic pattern than [CII] emission even in channels where both OH and [CII]
are detected. This source shows the strongest evidence for a molecular
outflow. Both SPT2132-58 and SPT0441-46 exhibit OH absorption more blueshifted
than [CII] emission in channel maps that is diluted below the detection
threshold in spatially-integrated spectra, thus also providing evidence for
outflows. SPT0202-61 and SPT0418-47, despite not displaying significant OH
absorption more blueshifted than [CII] emission in either spatially-integrated
spectra or channel maps, both exhibit features in OH absorption having
different spatio-kinematic patterns than [CII] emission, and therefore
evidence for separate kinematic components in OH absorption plausibly
associated with outflows.

###  4.2 Outflow properties

In Spilker et al. (2020b), the mass outflow rate for each object thought to
host an outflow is estimated using the depth of the blueshifted OH absorption.
Assuming initially the absorption to be optically thin, the OH column density
is measured from the depth of the blueshifted OH absorption integrated over
velocities more blueshifted than
$-200\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$. The total gas column
density is then computed assuming an OH abundance based on the study of a
star-forming region in our Galaxy, Sgr B2 (Goicoechea & Cernicharo, 2002).
Mass outflow rates are estimated using this column density, assuming a time-
averaged thin shell geometry (Rupke et al., 2005) with inner radius set equal
to the effective radius of the dust continuum estimated using source-plane
reconstructions of the gravitationally-lensed images of each source. To allow
for the possibility that the OH absorption is optically thick, an empirical
correction factor to the mass outflow rates is then introduced, based on
observations of 14 nearby quasars and ultra-luminous infrared galaxies
(ULIRGs) in multiple OH transitions (with P Cygni profiles or high-velocity
absorption wings) for which radiative transfer models have been made by
González-Alfonso et al. (2017). Specifically, the correction factor is based
on a correlation in this sample between mass-outflow rate and the “maximum”
blueshifted velocity of OH (defined as the velocity above which $98\%$ of
absorption takes place).

In addition, Spilker et al. (2020b) estimate alternative mass-outflow rates
based on correlations in the González-Alfonso et al. (2017) sample between
mass-outflow rate and equivalent width of blueshifted OH absorption beyond
$-100\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$, as well as equivalent
width of blueshifted OH absorption beyond
$-200\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$ multiplied by
$L_{IR}^{1/2}$, where $L_{IR}$ is the total infrared luminosity corrected for
gravitational lensing. Lastly, Spilker et al. (2020b) apply a dimensionality-
reduction technique similar to a principal component analysis to find an
empirical correlation between the measured mass-ouflow rates and combinations
of other parameters in the González-Alfonso et al. (2017) sample. We find the
same nominal depths of putative blueshifted OH absorption as those found by
S18 and S20 within measurement uncertainties. However, having now calculated
the statistical significance of these absorption features, we emphasise that
the putative mass-outflow rates – derived solely from the spatially-integrated
spectra – must have substantially higher uncertainties than presented in
Spilker et al. (2020b), in at least some cases rendering them consistent with
zero.

###  4.3 Improving observing strategies

Our analysis highlights the attention that must be paid to atmospheric
absorption features when searching at sub-mm wavelengths for spectral
signatures of high-$z$ outflows traced in absorption. Observers must not only
carefully check the results of the ALMA calibration pipeline to assess the
accuracy at which corrections for atmospheric absorption have been carried
out, but also recognize the fact that large changes in atmospheric opacity
across the bandpass lead to correspondingly large changes in the thermal noise
and hence measurement uncertainties across the observed spectra.

Observers who want to better verify that atmospheric absorption has been fully
removed by the ALMA pipeline (improving over the test made above from the
secondary calibrator) can do so by planning observations accordingly. As
observations are performed in two sidebands with one placed on the spectral
line of interest and the other normally used to measure the line-free
continuum, the latter sideband can be placed instead on a strong atmospheric
O3 line. The spectral windows in this sideband will then act as a control case
for the OH-containing spectral windows, and can be checked to see whether any
residual features associated with the atmospheric line remain after
calibration. This check, however, may not be possible in many cases owing to
restrictions on the placement of spectral windows allowed by ALMA. In such
cases, the only option left is to use the spectrum of the secondary calibrator
to ensure that the degree to which corrections to atmospheric absorption have
been made is likely smaller than the degree of absorption seen in the source
(as conducted in our work). The downside of this approach is that, in order
for this test to be effective, the secondary calibrator spectrum must be
observed at a significantly higher signal-to-noise than the target. Therefore,
a relatively large amount of observing time may need to be spent on the
secondary calibrator if the closest one to the target is relatively dim.

A separate issue that further complicates the detection of low-signal-to-noise
outflows is the estimation of the continuum level in the target spectra. As
shown above in the case of SPT2132-58, targets with broad absorption features
may have few, if any, channels to use for continuum estimation in the spectral
windows covering the OH line. In this situation, the other sideband could be
used to estimate the continuum level, as is the approach taken in S18 and S20,
but such estimates are subject to additional uncertainties introduced by the
uncertain spectral index of the target source as well as errors in bandpass
calibration. In the unfortunate case of SPT2132-58, the atmospheric
transmission in the continuum sideband (which has a fixed offset of
$12\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ with respect to the OH sideband)
is very low whether it is placed at either a lower or higher frequency than
the target bandpass (see Figure 1), so no useable continuum spectrum can be
produced at all given the restrictions on the ALMA correlator set-up.
Furthermore, the OH-containing sideband cannot be extended to cover a higher
frequency range since it is already at the maximum possible width. The only
remaining solution is to observe with two different correlator set-ups, with
one set-up being used to measure the continuum level and the other the OH
absorption. Although doubling the observing time, there may be no other choice
but to adopt this strategy in ALMA band 8 owing to deep and closely-spaced H2O
atmospheric absorption lines throughout this band (progressively less severe
in lower-frequency bands).

##  5 SUMMARY AND CONCLUSION

We re-analysed observations of the five DSFGs from S18 and S20 for which both
OH $119\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and [CII]
$158\text{\,}\mathrm{\SIUnitSymbolMicro m}$ images are available at comparable
angular resolutions with ALMA. Such observations are complicated by strong
absorption lines from the Earth’s atmosphere imprinted onto the spectra of all
targeted objects, leaving two effects that must be carefully assessed: (i)
residual atmospheric absorption even after standard bandpass calibration
procedures; and (ii) varying measurement uncertainties over the spectra owing
to varying atmospheric opacity. We therefore checked the precision to which
corrections for atmospheric (together with instrumental) effects in the
bandpass have been made, and also computed explicitly the measurement
uncertainties in each velocity channel.

Extracting spatially-integrated spectra in the same manner as S18 and S20, we
searched for OH absorption extending to more blueshifted velocities than
detectable [CII] emission – the signature used by both S18 and S20 to identify
an outflow, indicating a kinematic component different from that of the [CII]
emission attributed to the galactic disc. Over the velocity range selected to
maximise the depth of any putative blueshifted OH absorption, we found the
bandpass to have been corrected to within $\lesssim 0.3\sigma$ for all sources
except SPT0418-47, for which the bandpass is corrected to $\sim 1\sigma$. Thus
informed, we found only one source (SPT2319-55) to show statistically
significant ($\geq 3\sigma$) evidence for blueshifted OH absorption in
spatially-integrated spectra – in contrast to S18 and S20, who found four of
the five sources examined here to show unambiguous signatures of outflows,
though without explicitly quantifying the statistical significance of the
putative blueshifted OH absorption.

In spatially-integrated spectra, signals that do not span the entire source
can be diluted to below detectability, whether it be in OH absorption or [CII]
emission. To guard against this possibility, we made channel maps in both OH
absorption and [CII] emission to find signals that are even more blueshifted
than are detected in spatially-integrated spectra. Furthermore, to find
additional evidence for a separate kinematic component that can possibly arise
from an outflow, we searched for an OH component exhibiting a different
spatio-kinematic pattern than the [CII] emission. The full results for each
source are summarised below.

SPT0202-61: no OH absorption blueshifted beyond the [CII] emission in its
spatially-integrated spectrum (in agreement with S20) or in channel maps; on
the other hand, component in OH absorption having different spatio-kinematic
pattern than [CII] emission in channel maps.

SPT0418-47: tentative ($2.4\sigma$) OH absorption blueshifted beyond
detactable [CII] emission in spatially-integrated spectrum; over the velocity
range of the tentative blueshifted OH absorption, upper limit on precision of
bandpass correction corresponding to $\sim 1\sigma$ of the measurement
uncertainty, and may therefore contribute in part to this tentative absorption
feature; no OH absorption blueshifted beyond the [CII] emission in channel
maps, but a clear component in OH absorption having different spatio-kinematic
pattern than [CII] emission.

SPT0441-46: tentative ($2.7\sigma$) blueshifted OH absorption in its
spatially-integrated spectrum; significant OH absorption blueshifted beyond
any [CII] emission in channel maps.

SPT2132-58: tentative ($2.2\sigma$) blueshifted OH absorption in its
spatially-integrated spectrum; significant OH absorption blueshifted beyond
any [CII] emission in channel maps.

SPT2319-55: highly significant ($6.1\sigma$) blueshifted OH absorption its
spatially-integrated spectrum, also seen in channel maps; possible component
in OH absorption having different spatio-kinematic pattern than [CII] emission
in channel maps.

In brief, we find evidence of separate kinematic components plausibly
associated with molecular outflows in all five of the sources included in our
study.

These results highlight the potential pitfalls in relying on blueshifted OH
absorption in spatially-integrated spectra alone to infer the presence of
candidate outflows, and the importance of utilising the full spatio-kinematic
information provided by the channel maps to search for and verify candidate
outflows. Deeper follow-up observations are clearly warranted for the four
sources that we find to exhibit evidence for molecular outflows, which if
confirmed also permit a more precise determination of their outflow
properties.

Future studies should make sure – as we have – that atmospheric absorption is
fully corrected for at the level of any putative outflow absorption, and that
the varying noise level across spectral channels is properly computed. In
addition, the continuum level should be better measured where possible in
those sources where the putative OH absorption spans most of the bandpass. As
can be seen in Figure 1, two of the remaining four sources found to show signs
of outflows presented in S20 based on OH absorption more blueshifted than
detetcable CO emission (SPT0544-40 and SPT2311-54) also contain large changes
in atmospheric absorption across the OH-containing bandpasses, requiring a
proper accounting of the measurement uncertainties at the velocities of the
putative blueshifted OH absorption. We recommend that, for observations in
spectral lines, example scripts for data calibration and analysis of ALMA data
in CASA include descriptions for assessing the accuracy of bandpass
calibration and computing the measurement uncertainties in individual spectral
channels.

##  6 Acknowledgments

J. Nianias and J. Lim acknowledge support from the Research Grants Council of
Hong Kong for conducting this work under the General Research Fund 17312122.
M. Yeung acknowledges support from the Research Grants Council of Hong Kong
for conducting this work under the General Research Fund 1730451. This paper
makes use of the following ALMA data: ADS/JAO.ALMA#2018.1.00191.S,
ADS/JAO.ALMA#2016.1.01499.S. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. We acknowledge the assistance provided by the ALMA helpdesk East Asia.
We also thank the anonymous referee for their constructive feedback.

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