11institutetext: Department of Space, Earth, & Environment, Chalmers
University of Technology, Chalmersplatsen 4 412 96 Gothenburg, Sweden
11email<EMAIL_ADDRESS>22institutetext: Institut de Radioastronomie
Millimétrique (IRAM), 300 Rue de la Piscine, 38400 Saint-Martin-d’Hères,
France 33institutetext: Cosmic Dawn Center DTU Space, Technical University of
Denmark, Elektrovej 327, DK-2800 Kgs. Lyngby, Denmark

#  Exploring the environment, magnetic fields, and feedback effects of massive
high-redshift galaxies with [C ii]

K. Kade 11 K.K. Knudsen 11 W. Vlemmings 11 F. Stanley 22 B. Gullberg 33 S.
König 11

(Received July 21, 2021 / Accepted February, 2023)

###### Abstract

Context. Massive galaxies are expected to grow through different
transformative evolutionary phases. High-redshift starburst galaxies and
quasars are thought to be such phases and thus provide insight into galaxy
evolution. Several physical mechanisms are predicted to play an important role
in driving these phases; for example, interaction with companion galaxies,
active galactic nuclei feedback, and possibly magnetic fields.

Aims. Our aim is to characterize the physical properties and the environment
of the submillimeter galaxy AzTEC-3 at $z=5.3$ and the lensed quasar BRI
0952$-0115$ at $z=4.4$, and to set a limit on the polarization properties of
the two sources. We intend to place these two sources in the broader context
of galaxy evolution, specifically star formation and mass growth through
cosmic time.

Methods. We used full polarization, sub-arcsecond-resolution, ALMA band-7
observations of both BRI 0952$-0115$ and AzTEC-3. We detect [C ii]
(^2P_3/2-^2P_1/2) line emission towards both BRI 0952$-0115$ and AzTEC-3,
along with companions in each field. We present an updated gravitational
lensing model for BRI 0952$-$0115 for correction of gravitational
magnification.

Results. We present infrared luminosities, star-formation rates, and [C ii]
line to infrared luminosity ratios for each source. The [C ii] emission line
profile for both BRI 0952$-$0115 and AzTEC-3 exhibit a broad, complex
morphology, indicating the possible presence of outflows. We present evidence
of a ”gas bridge” between AzTEC-3 and a companion source. Modified blackbody
spectral energy distribution fitting is used to analyze the properties of [C
ii] detected companion sources in the field of both the submillimeter galaxy
and the quasar. We investigated the possible role of the detected companions
in outflow signatures. Using a simple dynamical mass estimate for the sources,
we suggest that both systems are undergoing minor or major mergers. No
polarization is detected for the [C ii] , placing an upper limit below that of
theoretical predictions.

Conclusions. Our results show that high-velocity wings are detected,
indicating possible signs of massive outflows; however, the presence of
companion galaxies can affect the final interpretation. Furthermore, the
results provide additional evidence in support of the hypothesis that massive
galaxies form in overdense regions, growing through minor or major mergers
with companion sources. Finally, strong, ordered magnetic fields are unlikely
to exist at the kiloparsec scale in the two studied sources.

###### Key Words.:

Galaxies: high-redshift – galaxies: evolution – galaxies: starburst –
galaxies: ISM – galaxies: interactions – galaxies: magnetic fields

##  1 Introduction

The discovery of intense starbursts ($100-1000\rm M_{\odot}$) at high redshift
demonstrates the prevalence of short, transformative phases in the evolution
of massive galaxies (e.g., Smail et al. 1997; Hughes et al. 1998; Blain et al.
1999; Casey et al. 2014). Furthermore, the discovery of the relation between
the mass of super-massive black holes (SMBHs) in the center of local massive
galaxies and the velocity dispersion of those galaxies suggests coeval
evolution between the SMBH and the host galaxy (e.g., Magorrian et al. 1998;
Ferrarese & Merritt 2000; Gebhardt et al. 2000; Häring & Rix 2004; Gültekin et
al. 2009; Beifiori et al. 2012; Kormendy & Ho 2013; Bennert et al. 2015;
Reines & Volonteri 2015). The cosmic black hole accretion rate density has
been found to follow a similar trend with redshift to that of the cosmic star-
formation rate (SFR) density, indicating that a significant part of the
evolution takes place during the first few billion years after the big bang
(e.g., Kormendy & Ho 2013 and Madau & Dickinson 2014). Thus, characterizing
the physical properties of high-redshift starburst galaxies and quasars is
essential for establishing a complete and coherent description of the
evolution of massive galaxies.

Figure 1: Hubble Space Telescope (HST)/ACS F814W (left) image of BRI0952
showing both lensed images of the quasar; Img-N and Img-S correspond to the
two images of the quasar BRI0952 and Comp-N and Comp-SW to the companion
sources. ALMA $870\,\mu$m continuum map (right) was created using line-free
channels. The contours are shown at $5,10,20,30,40,50,60,70,$ and $80\,\sigma$
levels. The synthesized beam is shown in the bottom left of the ALMA image.

Many physical mechanisms play a role in massive galaxy evolution. Galaxies are
thought to grow through two main mechanisms, namely galaxy mergers and gas
accretion from the intergalactic medium (e.g., Kereš et al. 2005; Hopkins et
al. 2008; Dekel et al. 2009; Genzel et al. 2010; Krumholz & Dekel 2010; Di
Matteo et al. 2012; Dubois et al. 2012). Additionally, the presence of a
growing SMBH, as seen in active galactic nuclei (AGNs) and quasars has been
found in theoretical modeling to provide a mechanism for regulating star
formation (e.g., Di Matteo et al. 2005; Narayanan et al. 2015; Harrison 2017).
This implies that characterizing the environment of high-redshift quasars and
starbursts, as well as understanding the role of AGN feedback, is paramount to
understanding the manner in which these galaxies evolve.

Simulations and theoretical predictions from the early universe have
demonstrated the likelihood of ubiquitous major and minor mergers occurring at
high redshift (e.g., Kaviraj et al. 2013, 2015; Fogasy et al. 2017).
Cosmological hydrodynamical simulations such as Illustris (Sijacki et al.
2015) and Horizon-AGN (Dubois et al. 2014) can shed light on the effects of
these interactions. Studies have shown that minor mergers (classified as those
with mass-ratios of ¿1:4) and the effect of companion galaxy interactions
systematically affect the SFRs and evolution of massive starbursting galaxies
(e.g., Kaviraj et al. 2015; Sparre & Springel 2016; Pearson et al. 2019;
Patton et al. 2020).

Previous studies using optical, near-infrared imaging, or Lyman-$\alpha$
emission in the environment of high-redshift starburst galaxies and quasars
have yielded conflicting results. Some of these systems show little or no
evidence of companion sources (e.g., Willott et al. 2005; Bañados et al. 2013;
Mazzucchelli et al. 2017; Yue et al. 2019), while others find overdensities
(e.g., Carilli et al. 2013; Husband et al. 2015; Fan et al. 2016). However, in
the last decade, an increasing number of companion sources around high-
redshift galaxies have been discovered with the Atacama Large
Millimeter/Submillimeter Array (ALMA), primarily using [C ii] observations
(e.g., Oteo et al. 2016; Trakhtenbrot et al. 2017; Decarli et al. 2017; Díaz-
Santos et al. 2018; Wardlow et al. 2018; Casey et al. 2019; Jones et al. 2019;
Litke et al. 2019; Neeleman et al. 2019; Fogasy et al. 2020; Venemans et al.
2020). Díaz-Santos et al. (2018) studied the hot dust-obscured galaxy 111Hot
dust-obscured galaxies are a class of high-redshift, dust-obscured, AGN-
dominated galaxies.(Hot DOG) W2246$-$0526 and found evidence of a ”gas-bridge”
structure between a companion source and the central source, suggesting
interaction-induced gas flow in the system. The system BRI 1202$-$0725 has
also been found to host multiple companions to the quasar and exhibits a
similar bridge structure (Carilli et al. 2013).

Studies of the effect of AGNs have demonstrated that galactic-scale outflows
and feedback can control star formation activity and black hole growth (e.g.,
Fabian 2012; King & Pounds 2015; Ishibashi & Fabian 2016). The extent of this
phenomena is unknown, but recent studies of both low- and high-redshift
galaxies show many of these sources exhibit outflow characteristics (e.g.,
Heckman et al. 1990; Rupke et al. 2005; Weiner et al. 2009; Banerji et al.
2011; Cicone et al. 2014; Chisholm et al. 2015; Spilker et al. 2020a) through,
for example, blueshifted absorption lines, P-Cygni line profiles, or broad
emission line components typically seen at higher absolute velocities away
from a main emission line. However, these findings become increasingly rare at
higher redshifts due to the difficulty in detecting and determining outflow
signatures in high-redshift galaxies. Although direct observations of
individual sources with outflows are still rare at $z>4$ (e.g., Maiolino et
al. 2012; Cicone et al. 2015; Spilker et al. 2020a; Butler et al. 2021),
studies using stacking of the [C ii] line have provided an alternative method
of searching for outflows in a wider variety and number of sources, though
also providing conflicting results (e.g., Gallerani et al. 2018; Decarli et
al. 2018; Bischetti et al. 2019; Stanley et al. 2019; Ginolfi et al. 2020).

The strength of the [C ii] line facilitates its ubiquitous use at high
redshift. At high redshifts, this line is shifted to the millimeter (mm) or
submillimeter (sub-mm) regime where it is observable by ground-based
facilities such as ALMA. The [CII] (^2P_3/2 $\rightarrow$ ^2P_1/2) emission is
produced primarily in photodissociation regions (PDRs) by gas exposed to
ultraviolet (UV) radiation and acts as one of the major coolants in star-
forming regions of the interstellar medium (ISM) (e.g., Stacey et al. 1991,
2010; Carilli & Walter 2013). For this reason, it has long been utilized to
study the ISM of high-redshift galaxies.

Figure 2: Moment-0 and moment-1 maps for the BRI0952 system. The top row shows
moment-0 maps of the original [C ii]  with velocity ranges for the individual
extraction shown on the image. The middle row shows the moment-0 map of the
region from which the spectra was extracted for the companions. The bottom row
shows the moment-1 maps for the sources taken from the same region the spectra
was extracted from. The contours are shown at $-3,-2,10,20,30,40,50,$ and
$60\,\sigma$ levels for BRI0952, and contours are at $-3,-2,3,4,5,6,$ and
$7\,\sigma$ levels for the companions where the respective $1\sigma$ noise
level has been taken from individual moment-0 maps due to the restrictive
velocity ranges (and thus differing noise levels). The black ellipses in the
top row correspond to the region from which the spectra was extracted. The
synthesized beam is shown in the bottom left corner of the images.

Although magnetic fields are common, their presence and role in galaxy
formation and evolution in the early Universe is still unclear. In the local
Universe, ordered magnetic fields with a strength of several $\mu$G are
revealed from synchrotron and Faraday rotation observations (e.g., Beck 2015)
in normal spiral galaxies. In local starburst galaxies, fields as high as
$\sim 20$ mG have been measured (Robishaw et al. 2008), and ordered magnetic
fields have been found using infrared (IR) dust polarization observations
(e.g., Lopez-Rodriguez et al. 2021). Exactly when these fields were generated
is unclear, but models show that a strong regular field can quickly be
generated from an initial weak seed field as a result of turbulence driven by,
for instance supernova explosions (Rieder & Teyssier 2017). Since atoms and
ions can easily be aligned by radiation and are subsequently very sensitive to
realignment under the influence of only a weak magnetic field, the strength of
the [C ii] line has led to the suggestion that [C ii] could be an excellent
tracer of magnetic fields (Yan & Lazarian 2006; Zhang et al. 2015).

In order to better constrain massive galaxy evolution at high redshift, high-
sensitivity data is required to find faint emission from companion sources and
to resolve the detailed physics ongoing within these systems. In this study,
we explored the environment, searched for magnetic-field signatures, and
examined possible outflow properties of two galaxies in the early Universe:
the quasar BRI 0952-0115 (hereafter BRI0952) at $z=4.433$ and the massive
submillimeter galaxy (SMG) AzTEC-3 at $z=5.3,$ utilizing high-resolution ALMA
band-7 [C ii] observations. These data were obtained through a proposal
designed to look for magnetic fields in the early Universe and were selected
based on their previously known extremely bright [C ii] emission. Due to the
nature of the original project, the sources were observed in full polarization
mode in an attempt to detect polarized emission from these sources.

The AzTEC-3 protocluster has been extensively studied previously and
encompasses the SMG itself (AzTEC-3) along with a quasar 13 Mpc away in
projected distance and a number of previously reported Lyman-break galaxies
(LBGs) surrounding the SMG (Capak et al. 2011; Riechers et al. 2014). BRI0952
is a gravitationally lensed quasar and has previously been studied due to its
strong [C ii] emission and lensing features (Maiolino et al. 2009; Gallerani
et al. 2012). Here, we present findings of resolved [C ii] emission in both
sources, along with an analysis of their surroundings. These findings help
shed light on the role both sources have to play in the evolution of massive
galaxies in the early Universe.

In Section 2, we describe the ALMA observations and analysis utilized in this
paper. In Section 3, we describe the results from the [C ii] line and
continuum analysis and the polarization of both AzTEC-3 and BRI0952. Section 4
provides a discussion of the properties of both sources as well as the
environment these sources reside in. Finally, we present our conclusions in
Section 5. Throughout this paper, we adopt the term ”outflows” to describe the
high-velocity flow of gas away from central regions typically associated with
energy-driven winds by central AGNs or through starburst activity. Similarly,
the term ”gas-bridge” is used to describe structures of gas connecting
components within galaxy systems thought to be caused by physical interactions
between these components. Furthermore, we utilized a flat $\Lambda$CDM
cosmology with $H_{0}$ = 70 km s-1 Mpc-1, $\Omega_{\rm M}=0.3$, and
$\Omega_{\Lambda}=0.7$.

##  2 Observations and analysis

We obtained ALMA band-7 data for BRI0952 and AzTEC-3 as part of a program
originally designed to search for magnetic field lines in the early Universe
(2018.1.01536.S, P.I. Vlemmings). The setup for both galaxies was tuned to the
[C ii] 1900.5369 GHz line, and the ”time domain mode” was used. Observation
details are listed in Table 1.

The data calibration steps were performed following the ALMA polarization
calibration scripts using CASA 5.4.0. (CASA 222http://casa.nrao.edu/ (CASA
McMullin et al. 2007)). This includes calibration of the phase, bandpass,
flux, and gain. The phase calibrators used for BRI0952 were J0948+002,
J0854+2006, and J0725-0054, and for AzTEC-3 these were J0854-2006 and
J0948+0022. The quasar J0854+2006 was used for polarization calibration. The
uncertainty on the absolute flux calibration is conservatively estimated to be
10%.

Table 1: ALMA band-7 observation details for BRI0952 and AzTEC-3. We note that these correspond to images created using a robust factor of 0.0.  Source | Date | $N_{\rm ant}$ | $\nu_{\mathrm{spw,central}}$ | Synthesized Beam | Image RMS
---|---|---|---|---|---
| [yyyy mm dd] | [GHz] | [ ${}^{\prime\prime}\times^{\prime\prime}$ ] | [mJy/beam] | [km/s]
BRI0952[CII] | 2019 04 06 | 41 | 349.8 | 0.48 $\times$ 0.35 | 0.5
BRI0952Cont |  |  | 336.0,338.0,348.0 | $0.53\times 0.41$ | 0.05
AzTEC-3 | 2019 03 22 | 48 | 301.7 | 0.80 $\times$ 0.56 | 0.2
AzTEC-3Cont |  |  | 288.0,289.9,299.9 | $0.91\times 0.65$ | 0.02
Table 2: Linear polarization $3\sigma$-limits. Source |  $P_{l,{\rm peak}}$ ([C ii] ) |  $P_{l,{\rm int}}$ ([C ii] ) | $P_{l,{\rm dust}}$
---|---|---|---
BRI0952 | $<4.8\%$ | $<0.7\%$ | $<2.7\%$
AzTEC-3 | $<2.1\%$ | $<0.2\%$ | $<2.1\%$

To analyze the Stokes-$I$ data, imaging was done using the task tclean. All
sources in the field were masked during cleaning. An initial search for line
emission was done using ”dirty” images to identify the line-free channels
available for use in continuum subtraction, which was subsequently performed
using the uvcontsub task with a polynomial fit of the order of one for both
AzTEC-3 and BRI0952 (see Figures 12 and 13). The continuum subtraction for
BRI0952 was complicated by the appearance of unexpected lines in spectral
windows adjacent to that of the [C ii] line. 333We note that the results of
this paper do not change when using other tools such as imcontsub or statcont
(Sánchez-Monge et al. 2018).

In the case of AzTEC-3, we used the frequency range of the observations up to
300 GHz due to the possible additional [C ii] wing feature seen in the
300.5-301 GHz range and the width of the [C ii] line (see Figures 7 and 12).
In the case of BRI0952, we used the frequency ranges 335.3-336.9, 347.1-347.7,
348.97-348.98, and 350.45-350.67 GHz. Line emission images were created from
the continuum-subtracted data, and continuum images were made from line-free
channels. We used Briggs weighting with a robust factor of 0.5 initially for
both AzTEC-3 and BRI0925. However, for further analysis of the companion
sources surrounding both primary targets, a robust factor of 0.0 was utilized
to increase the angular resolution of the [C ii] emission cubes; these images
were subsequently used for the analyses described in this paper. The continuum
images were created using a robust factor of 0.5. For BRI0952, the spectral
window centered on the [C ii] emission had a bandwidth of 1.8 GHz with a
spectral resolution of 31 MHz. The adjacent spectral windows had bandwidths of
2.0 GHz with spectral resolutions of 15.625 MHz. For AzTEC-3, the spectral
window centered on the [C ii] emission and the adjacent spectral windows had
bandwidths of 2.0 GHz with a spectral resolution of 31.25 MHz. Angular
resolution and sensitivity is listed in Table 1.

Polarization image cubes were created at native spectral resolutions of
$15.625$ MHz and $31.25$ MHz channels for BRI0952 and AzTEC-3, respectively,
using Briggs weighting with a robust factor of $0.5$. For BRI0952, the
resulting beam size was $0.51^{\prime\prime}\times 0.40^{\prime\prime}$ with a
position angle of $81^{\circ}$. For AzTEC-3, the mean was
$0.91^{\prime\prime}\times 0.64^{\prime\prime}$ (at $82^{\circ}$). The
different observing conditions and channel width resulted in a channel rms
noise in the Stokes Q and U maps of $0.46$ mJy beam-1 and $0.14$ mJy beam-1
for BRI0952 and AzTEC-3, respectively.

For further analysis, including spectral energy distribution (SED) fitting,
additional photometry was extracted from archival resources for both AzTEC-3
and BRI0952. Hubble Space Telescope (HST) data were extracted from the HST
archive for both sources. For AzTEC-3, we used the ACS F606W, ACS F814W, WFC3
F105W, WFC3 F125W, and WFC3 F160W bands from the following project codes:
13641 (PI Capak), 9822 (PI COSMOS24-21), and 13384 (PI Riechers). For BRI0952,
we used the WFPC2 F814W band with project code 8268 (PI Impey), cross-checked
the astrometry with the Gaia2 catalog (Gaia Collaboration et al. 2018), and
used photometry from the WISE All-Sky Data Release (Cutri & et al. 2012). We
performed an archive search for the MIPS 24$\mu$m data. We used archival data
of ALMA bands 3, 4, and 6 (2017.1.01081.S P.I. Leung and 2015.1.00388.S P.I.
Lu).

##  3 Results

###  3.1 Polarization

Our full polarization observations did not reveal any polarized emission,
neither from emission lines nor from the source continuum. In Table 2, we
indicate the $3\sigma$ upper linear polarization ($P_{l}$) limits that we
derive for both sources at the peak for the [C ii] line, both for the total
integrated line and for the continuum.

The linear polarization spectra and continuum values were extracted in a
single beam (see Section 3.1 for the size) towards the peak of the lines and
continuum, respectively. The linear polarization spectrum was produced from
the Q and U spectra using $I_{p}=\sqrt{Q^{2}+U^{2}-\sigma_{p}^{2}}$, where
$\sigma_{p}=\sqrt{\sigma_{Q}^{2}+\sigma_{U}^{2}}$ corresponds to the rms error
on the linear polarization and $\sigma_{Q,U}$ are the rms errors in Q and U,
respectively. Since we detect no polarization, the derived limits include any
potential remaining calibration uncertainty. According to ALMA specifications,
this $3\sigma$ limit corresponds to $0.1\%$. Thus, the derived upper limits on
the [C ii] lines are significantly below values that could be expected if the
level of polarization in our sources is similar to that predicted around
Galactic star-forming regions (Zhang & Yan 2018).

Figure 3: Spectra of [C ii] emission toward BRI0952 and companions. The two
companions’ line profiles are fit with a single Gaussian, which is shown in
red. The quasar’s line emission profile is fit with a single Gaussian (red)
and a double Gaussian (blue); the double Gaussian corresponding to outflow
signatures is clearly seen. The gray region represents the rms of the data in
each channel using the procedure described in Section 3.2.2.

.

Figure 4: Velocity maps of BRI0952 showing [C ii] emission across the velocity
range of the line. The velocity range is provided at the top of the images.
The gray contours are at $10,20,30,40,50,$ and $60\,\sigma$ levels from the
moment-0 map of BRI0952, which is shown in Figure 2. The black ellipses
indicate the positions and sizes of the two companions from CASA’s imfit
routine. The southern companion shows a clear velocity gradient across the
-157 to -14 km/s range. The size of the synthesized beam is shown in the
bottom left corner of the images. Figure 5: HST/WFC3 F105W (left) image of
AzTEC-3 overlaid with source positions, ALMA $850\,\mu m$ continuum map
(center), and SMG subtracted map (right). The continuum maps were created
using line-free channels. The residual map was produced following the steps
described in Section 3.3.2. The original continuum image contours are shown at
$-3,-2,5,10,20,30,40,50,60,70,$ and $80\,\sigma$ levels. The subtracted image
contours are shown at $-3,-2,3,4,5,6,$ and $7\,\sigma$ levels. Synthesized
beams are shown in the bottom left of the ALMA images. Figure 6: Moment-0 and
moment-1 maps for AzTEC-3 system. The top row shows moment-0 maps of the
original [C ii] and the central row shows the moment-0 map of the region from
which the spectra were extracted and are centered at the respective redshifts
of the sources. The bottom row shows the moment-1 maps from each using the
same region that the spectra were extracted from. The contours in the first
panel for AzTEC-3 are shown at $-3,-2,10,20,30,40,50,$ and $60\,\sigma$
levels, and the contours shown in subsequent panels are at $-3,-2,3,4,5,6,$
and $7\,\sigma$ levels where the respective $1\sigma$ noise level has been
taken from individual moment-0 maps due to the restrictive velocity ranges
(and thus differing noise levels). The black circle and ellipses in the top
row show the regions from which the spectra were extracted for each source.
The synthesized beam is shown in the bottom left of the images.

###  3.2 BRI 0952-0115

####  3.2.1 Lensing magnification

The quasar BRI0952 is lensed by a single galaxy, with the lensing source at
$z=0.632$. Although previous lensing models have been constructed for BRI0952
(Lehár et al. 2000; Eigenbrod et al. 2007; Gallerani et al. 2012; Momcheva et
al. 2015), the wing-like structures we observe in the [C ii] emission
suggested differential lensing across the apparent surface of BRI0952 (seen in
Figure 14), prompting us to create an updated lensing model using our high-
resolution data. Additionally, the presence of two companion sources in close
proximity to the quasar were also a factor as it was necessary to determine if
these represented one double-imaged object or two or more separate sources.

We determined the lensing parameters of both the source and the lens by
utilizing Visilens (Spilker et al. 2016). This code is designed specifically
to model observations of gravitationally lensed sources at radio and
millimeter wavelengths. Visilens calculates the magnification factor by
directly modeling the uv data rather than introducing bias by using images
produced from algorithms such as CASA’s CLEAN. We modeled the lens as a single
isothermal ellipsoid parameterized by its location relative to the ALMA image
phase center ($x_{L}$, $y_{L}$), the ellipticity ($e_{L}$), and position angle
of the major axis ($\phi_{L}$) in degrees east of north. We modeled the source
as a Sérsic source parameterized by position relative to the lens ($x_{S}$,
$y_{S}$), flux density, Sérsic index, half-light radius, axis-ratio, and
position angle. These parameters are then run through a Markov chain Monte
Carlo (MCMC) fitting procedure, and the best models were output using a
deviance information criterion as described in Spilker et al. (2016).

Initially, we ran Visilens on band-7 continuum data in order to determine the
best-fit parameters for the lens. Although lens parameters have been
previously reported (Lehár et al. 2000; Eigenbrod et al. 2007; Gallerani et
al. 2012; Momcheva et al. 2015), lens fitting was improved when we allowed the
parameters to vary outside of previous values. During the lens optimization,
we also allowed the source to vary in position and flux density. Once the lens
was optimized, we reran the continuum fit with fixed lens parameters but still
allowed the Sérsic source profile to vary. Similarly, for the band-7 [C ii]
emission data, we ran Visilens with the previously optimized lens parameters
on the uv line emission data while allowing the source to vary in an attempt
to increase the quality of our lensing model. The model produced by Visilens
is a good fit for our data with minimal to no residual emission, and this is
shown in Figure 14. The best-fit parameters are provided in Table 3.
Furthermore, the magnification factor produced from this model is similar to
those previously reported ($\mu\sim{3.92}\pm 1.3$).

The presence of wing-like structures across the [C ii] frequency range of our
BRI0952 observations, as seen in the [C ii] line emission map (see Figure 14,
panels 1 and 3 for observed [C ii] data and model output of Visilens),
prompted consideration of the effect of different lensing factors across the
line (i.e., differential magnification). To investigate this, we split the [C
ii] line into five bins constituting five different frequency ranges across
the line (these can be seen in Figure 14) and ran Visilens, with the source
and lens parameters as specified above, on these bins. The results of this are
shown in Figure 14. We determine that it is likely that some amount of
differential lensing across the surface of BRI0952 is occurring, and thus we
caution that conclusions drawn that correlate strength of emission with
location will be affected by this. However, we conclude that based on the low
lensing-magnification factor, this effect will not drastically change the
extent or strength of the [C ii] or continuum emission studied in this paper.

We also note that images of both the data and residuals, as seen in Figures 14
and 15 are produced by Visilens rather than by CASA. Although the imaging
process in itself is similar to the procedure that CASA performs, it lacks the
ability to change weighting schemes and does not clean images. Thus, images
produced in Visilens are dirty images with natural weighting and therefore
will look slightly different than those created by CASA. As a consequence of
this, faint sources in close proximity to BRI0952 are not clearly resolved and
distinguishable in images produced by Visilens. This is in contrast with
images produced in CASA, which are cleaned with a Briggs weighting scheme
using a robust factor of 0.0. The latter are those used throughout the
spectral analysis in this paper.

Figure 7: Spectra for the AzTEC-3 system. The red line shows the single
Gaussian fit to the data, and the blue line shows the double Gaussian fit to
the data. For AzTEC-3, the blue wing $\rm<-500\,km\,s^{-1}$ is significantly
more prominent than the red wing. We fit LBG-3 and Gal-SW with double
Gaussians to account for the additional ”bumps” in the spectra (most obvious
in LBG-3), which are likely blended flux from the SMG. The atmospheric
transmission is shown as a gray line in the top subplot for every source.

####  3.2.2 [C ii] emission

We detect [C ii] (^2P_3/2 $\rightarrow$ ^2P_1/2) line emission toward both
images of the lensed quasar BRI0952. We refer to the two images of the quasar
as the ”north” and ”south” images (names and locations shown in Figure 1). We
confirm the detection of a southern companion source (henceforth termed Comp-
SW) tentatively detected by Gallerani et al. (2012); we note that our
detection is located in the same region as that of the source reported by
Gallerani et al. (2012), but at a significantly lower signal-to-noise ratio
(S/N) and a smaller emitting region. Furthermore, we tentatively detect a
second companion (termed Comp-N) north of the top image of the quasar. Higher
resolution data and a source plane reconstruction of this system would be
required to come to a robust conclusion about the nature of this emission. For
the purposes of this paper, we treated both sources as additional companion
galaxies as the emission is not seen in our lensing model produced by
Visilens, which suggests it is not simply an affect of the lensing
magnification. We isolated our lensing model to only those velocities in which
the companions manifest and demonstrate in Figure 15 that ”residual” emission
remains in the regions of the companions, lending further weight to the
conclusion that the emission has a separate origin to that of the quasar.
Given the relatively lower S/N of Comp-N and Comp-SW in relation to BRI0952,
combined with the fact that the lensing model reproduces the flux of BRI0952
using a single Sérsic brightness distribution, we treated Comp-SW and Comp-N
as not sufficiently lensed to affect conclusions drawn in this analysis (in
effect $\rm\mu_{comp-N}=\mu_{comp-SW}=1$).

We note that including additional faint sources in the lensing analysis with
Visilens did not enable a good fit for the two companion sources; however,
given their location, they are likely to be magnified by a factor close to
$\mu\sim 1$. Furthermore, based on the close spatial proximity of Comp-SW and
Comp-N to BRI0952, we assume the emission is [C ii] and find spectroscopic
redshifts of $z_{\mathrm{Comp-SW}}=4.4323$ and $z_{\mathrm{Comp-N}}=4.432$.

To extract the spectra of BRI0952, Comp-N, and Comp-SW we defined a region
around each from which to extract the [C ii] spectra individually for each
component 444This extraction could be done through a number of different
methods; however, we find that the outcomes of these methods remain consistent
with the method employed in this paper. We also note that methods such as uv-
plane fitting introduce bias in a similar way to image-plane fitting through
base-assumptions of, e.g., a model to describe the source, boundary
conditions, and so on.. For BRI0952, we used an elliptical region of
$2.1^{\prime\prime}\times 1.45^{\prime\prime}$ encompassing $\sim 18$
beams555We define $N_{beams}=A_{extraction}/A_{beam}$., containing both Img-S
and Img-N of the quasar. For Comp-SW, we used an elliptical region of
$1.13^{\prime\prime}\times 0.57^{\prime\prime}$ encompassing $\sim 4$ beams,
and for Comp-N we used an elliptical region of $1.3^{\prime\prime}\times
0.62^{\prime\prime}$ encompassing $\sim 5$ beams. These regions are shown in
Figure 2 along with moment-0 and moment-1 maps, and extracted spectra are
shown in Figure 3. Both companions are faint compared to the emission from
BRI0952; both are $\leq 10\%$ of the flux from BRI0952 (see Figure 9). The
gray plotted rms in Figure 3 is calculated in each channel by sampling the
spectra in 25 different emission-free regions of the cube extracted from
regions the same size as those described above for each individual source.

Due to the presence of high-velocity wings at an $\sim 14\sigma$ level in the
spectra of BRI0952, we find that a double-Gaussian fit was more appropriate
(see Figure 3, top panel), yielding an improvement to the reduced $\chi^{2}$
of more than a factor of four. To investigate the impact of differential
magnification on the broad wings and attempt to determine if this feature is
simply an artifact from lensing, we calculated the ratio of the flux in the
blue and red wings of the line profile. If the ratio of the blue to red wing
is more than the error on the lensing factor, we suggest that the broad wings
could be due to differential magnification predominantly affecting one side of
the line. We define these wings to be between $\pm 500$ km/s and $1/4\times\rm
F_{peak}$, where $\rm F_{peak}$ is the peak of the flux. We find the ratio of
the red-to-blue wing to be $\sim 1.09$, which is less than the error on the
magnification factor (1.3). This suggests that while the observed broad
velocity wings may be slightly affected by lensing magnification, it is not
solely responsible for them. As an additional test, we extracted the spectra
from a region only corresponding to Img-N of BRI0952 to determine if the
double Gaussian remained a better fit to the data (shown in Figure 16).
Indeed, the broad wings remain, and a double Gaussian provides an improved fit
to the data. We further discuss the implications of this in Section 4.5.

We compare the line intensities of each component to those found by Gallerani
et al. (2012). We find that our values are lower, both for the intensity of
BRI0952 and for Comp-SW (their Comp-C). However, we note a significant
discrepancy between their decomposition and ours. Gallerani et al. (2012) find
that Comp-SW is significantly brighter than either of the individual images of
the quasar BRI0952 (here Img-N and Img-S), while we find the opposite to be
true. We attribute this to the increased spectral resolution and baseline
coverage possible with ALMA over the IRAM Plateau de Bure Interferometer
(PdBI).

The observations from Gallerani et al. (2012) were carried out with the IRAM
Plateau de Bure Interferometer with six antennas in the extended B
configuration during three observing runs and the compact C configuration
during two observing runs. They obtained a sensitivity level of 0.5 Jy km s-1
beam-1 in a 300 km s-1 channel, which corresponds to a 1$\sigma$ rms of 1.7
mJy beam-1. For comparison, our ALMA data for a similar channel width would be
$\sim 0.1$ mJy beam-1, which is about 15-17 times better in terms of
sensitivity. We note that the BRI0952 field is near equatorial, meaning that
many antennas possibly in combination with several antenna configurations are
needed to achieve a good uv-coverage in the $v$ direction. Given the higher
sensitivity combined with the improved uv coverage thanks to the larger number
of ALMA antennas, it is likely that the calibration and image reconstruction
of the ALMA data is more robust. As a further comparison between the previous
PdBI observations from Gallerani et al. (2012) and the new ALMA observations,
the spatial resolution is $1.08^{\prime\prime}\times 0.66^{\prime\prime}$ and
$0.54^{\prime\prime}\times 0.40^{\prime\prime}$, respectively, and the
absolute flux calibration is $\sim 20\%$ and $\sim 10\%$, respectively.

We used CASA’s imfit task to fit the source size for both images of the quasar
and companions. We provide [C ii] line parameters and deconvolved source sizes
in Table 5. We note that, due to the lensed nature of BRI0952, this source has
a more complex morphology than those typically handled in this way. The source
size provided from imfit is an indication of the extent of the emission in the
image plane and is not necessarily well fit by a Gaussian profile. We added an
additional 30% on the error of the spatial extent of the emission reported for
Img-S and Img-N corresponding to the uncertainty on the lensing magnification
factor.

We note the presence of a complex velocity structure between the images of the
lensed quasar and the companions. The northern companion exhibits a faint
velocity gradient, and the same is present for the south-western companion
(see Figure 4). The implications of this are further discussed in Section 4.6.

Table 3: Model lensing parameters for the foreground galaxy of BRI0952. From left to right: ($x_{L}$, $y_{L}$) is the position of the source relative to the ALMA phase center given in the first two columns, with positive values corresponding to west; M is the mass of the lens galaxy; $e_{\rm L}$ is the ellipticity; $\phi_{\rm L}$ is the position of the major axis in degrees east of north; $\gamma$ is the external tidal shear; $\phi_{\gamma}$ is the position angle of the shear, and $\mu$ is the derived lensing factor. Since the values were fixed during fitting of the source position, we do not report their respective errors. The magnification factor is taken to be the average across the line. RA | DEC | $x_{L}$ | $y_{L}$ | M | $e_{\rm L}$ | $\phi_{L}$ | $\gamma$ | $\phi_{\gamma}$ | $\mu$
---|---|---|---|---|---|---|---|---|---
$\rm[J2000]$ | [J2000] | $\rm[^{\prime\prime}]$ | $\rm[^{\prime\prime}]$ | [M⊙] |  | (deg. E of N) |  | (deg. E of N) |
09:55:00.1 | -01:30:07.1 | $0.446$ | $0.003$ | $0.619\times 10^{11}$ | 0.055 | 191 | 0.011 | 63 | $3.92\pm 1.3$

####  3.2.3 Continuum

We detect strong continuum emission toward both north and south images of
BRI0952. Using CASA’s imfit, we fit both the north and south images of the
quasar and report strong continuum emission totaling $1.96\pm 0.43$ mJy, which
is corrected for lensing. Continuum fluxes from individual images of the
quasar are provided in Table 4 and images are shown in Figure 1. We do not
detect the companion sources in continuum and report a $3\sigma$ upper limit
of $0.13$ mJy for each. Due to the non-detection of the companions in the
continuum, we defined a region corresponding to the quasar from which to
extract the continuum flux. As for the line emission, the source sizes of
BRI0952 reported in Table 4 are reported with an additional 30% error added to
account for the complex morphology and lensing uncertainties.

Since we do not detect the companions in continuum emission, we estimated
their flux using relations from their $L_{\rm{[C\,{\sc II}]}}$ to determine if
they should be detectable in our ALMA observations. We estimated their SFR’s
using the relation $\rm log(SFR)\,[M_{\odot}/yr]=1.0-7.06\times
log(L_{[CII]})\,[L_{\odot}]$ from De Looze et al. (2014) for starburst
galaxies, computed their $L_{\rm{IR}}$ using the relation in Section 4.3
(Carilli & Walter 2013), and used a modified blackbody approximation (e.g.,
Knudsen et al. 2003, Equation 2) to recover their $S_{350\rm{GHz}}$. This
results in $S_{350\rm{GHz}}=0.21$ mJy for the northern companion and
$S_{350\rm{GHz}}=0.10$ mJy for the south-western companion. This would
correspond to an $\sim 4\sigma$ detection for the northern companion and an
$\sim 2\sigma$ detection for the southern companion. Thus, in the case of the
southern companion with the current data a continuum emission detection is
unfeasible. This may also be the case for the northern companion. However, it
is also possible that without the velocity information encoded in emission
line spectra (and thus without the ability to severely isolate the frequency
or velocity range from which to attempt to extract information about the
emission from the companions), our observations are simply insufficient to
resolve any continuum emission from the companions.

####  3.2.4 SED fitting

We performed IR SED fitting and decomposition of the AGN and star formation
contributions, using DecompIR (Mullaney et al. 2011) following the methods of
(Stanley et al. 2018). We used photometry from an archival search for WISE
bands and MIPS 24 $\mu m$. We also used ALMA archival data from bands 3, 4,
and 6. We performed two sets of fits, one with only the star formation
templates and one with both AGN and star formation templates. We find that the
photometry of BRI0952 is best fit by a combination of AGN and star formation
emission in the IR. The decomposition of the IR SED allows for a calculation
of the SFR without contamination from the AGN emission, using the $L_{\rm
IR_{SF}}$ integrated from 8-1000 $\mu$m. IR luminosities are reported in Table
7 and discussed further in Section 4.2.

###  3.3 Aztec-3

####  3.3.1 [C ii] emission

We detect [C ii] (^2P_3/2 $\rightarrow$ ^2P_1/2) emission toward the SMG
AzTEC-3. We report three sources (LBG-3, Gal-S, and Gal-SW) of the same
emission in the region shown in Figure 5. LBG-3 was initially detected as an
Lyman-break galaxy with the COSMOS survey (Ilbert et al. 2009, optical ID
1447526) but was undetected in [C ii] in Riechers et al. (2014) and the
authors presented a $3\sigma$ upper limit on its [C ii] emission. An
additional companion, LBG-2 - not shown in Figure 5, was also originally
detected by COSMOS as an LBG but was also undetected in [C ii] by Riechers et
al. (2014). Similarly, we do not detect the source in [C ii] emission, and
thus do not investigate this source further. Gal-S and Gal-SW are first
detections.

The data of Riechers et al. (2014) were obtained during Cycle-0 with 16-24
antennas, with a total observing near 7000 seconds spread evenly over two
pointings. As a result, the sensitivity of the data in the region around
AzTEC-3 is lower by about a factor of two compared to the new data presented
here; however, it is important to note that the beam area of our data is
1.7$\times$ larger. We note that the $3\sigma$ limit from Riechers et al.
(2014) appears to be for a single beam, while we obtain a detection over a
more extended region corresponding to $2.8\times$ the size of beam used in
this analysis. Furthermore, we note that if converting their $3\sigma$ upper
limit to a $5\sigma$ upper limit, the resulting $I_{\rm[CII]}$ is consistent
with our detection, though it is important to keep in mind that in this
comparison we do not take into account the integration over an extended area.

We assume that the emission from the companions is [C ii] based on their close
proximity to AzTEC-3, and find a spectroscopic redshift of $z_{\rm
LBG-3}=5.284$, which is in relative agreement with the previous spectroscopic
redshift of $z=5.3$ (Riechers et al. 2014). We report spectroscopic redshifts
for the additional companions, $z_{\rm Gal-S}=5.2919$ and $z_{\rm Gal-
SW}=5.2942,$ respectively. Figure 9 shows the combined spectra of the
companions and AzTEC-3.

Table 4: Continuum fluxes for both systems. The continuum fluxes are provided for both images of BRI0952 and are corrected for lensing. However, we do not correct the sizes for lensing. We note that the error on the companions of AzTEC-3 includes an additional 10% due to the additional uncertainty introduced from the deblending process and the errors on the size of both images of BRI0952 include an additional 30% to account for lensing uncertainty. Galaxy | Region | $S_{\nu}$
---|---|---
| (${}^{\prime\prime}\times^{\prime\prime}$) | [mJy]
$\rm BRI0952_{N}$ | ([$0.35\pm 0.15]\times[0.20\pm 0.13$]) | $1.44\pm 0.4$
$\rm BRI0952_{S}$ | ([$0.31\pm 0.15]\times[0.26\pm 0.13$]) | $0.52\pm 0.14$
Comp-N | - | $<0.13$
Comp-SW | - | $<0.13$
AzTEC-3 | ([$0.38\pm 0.03]\times[0.27\pm 0.07$]) | $6.06\pm 0.13$
LBG-3 | ([$0.59\pm 0.07]\times[0.35\pm 0.07$]) | $0.19\pm 0.02$
Gal-SW | ($<0.91\times<0.66$) | $0.07\pm 0.02$
Gal-S | - | $<0.056$
ES | ([$1.09\pm 0.38]\times[0.37\pm 0.36$]) | $0.21\pm 0.05$

We followed the same procedure as described for BRI0952 and individually
extracted the spectra for the sources in this system from a region with a very
limited velocity range 666Again, similar to BRI0952; if other methods are
used, the results remain consistent with the regional spectral extraction used
here.. We used a circular region with a radius of $2.4^{\prime\prime}$ to
extract the spectra of AzTEC-3 encompassing $\sim 13$ beams. We used
elliptical regions for the following companions: $1.2^{\prime\prime}\times
1.5^{\prime\prime}$ for LBG-3 encompassing $\sim 4$ beams,
$2.6^{\prime\prime}\times 1.7^{\prime\prime}$ for Gal-S encompassing $\sim 10$
beams, and $1.3^{\prime\prime}\times 0.90^{\prime\prime}$ for Gal-SW
encompassing $\sim 3$ beams. These regions are shown in Figure 6. We were able
to minimize the source blending of the companions with AzTEC-3 since the
spectra of the companions are extracted over a very limited velocity range, as
shown in Figure 6. We calculated the rms in the same way as described in
Section 3.2.2. Additionally, we include the atmospheric transmission in the
top subplot for every source in Figure 7 to show where the atmospheric
absorption line is (shown in Figure 12), specifically in relation to the
companion spectra.

Figure 8: Velocity maps of AzTEC-3 showing [C ii] emission across the velocity
range of the line. The velocity range is provided at the top of the images.
The gray contours are at $10,20,30,40,50,$ and $60\,\sigma$ levels from the
moment-0 map of AzTEC-3, which is shown in Figure 6. The black ellipses
indicate the positions and sizes of the three companions from CASA’s imfit
routine where the dashed ellipse around Gal-SW denotes an upper-limit point
source. The ”gas-bridge” structure between AzTEC-3 and Gal-S is seen in the
velocity range of -584 to - 358 km s-1. The size of the synthesized beam is
shown in the bottom left corner of the images.

The [C ii] spectral line profile of AzTEC-3 shows the presence of high-
velocity wings at a $\sim 24\sigma$ level -and the profile is better fit with
a double Gaussian to account for this (Figure 7)- where the reduced $\chi^{2}$
is improved by more than a factor of four using a double-Gaussian fit. We note
that the blue wing is wider compared to that of the red wing, as reported in
Riechers et al. (2014). We used CASA’s imfit to determine deconvolved source
sizes. We report source sizes and Gaussian line parameters for AzTEC-3 and
companions in Table 5. The [C ii] emission from the central source is emitted
over a compact region with an extent of $4.2\pm 0.4$ kpc along the major axis,
which is consistent with the emitting region of $3.9$ kpc reported by Riechers
et al. (2014). We do not detect a strong velocity gradient, which is also in
good agreement with Riechers et al. (2014).

We note an additional feature: a possible velocity gradient between AzTEC-3
and LBG-3. We show this in Figure 8 and Figure 17. This is a tentative feature
as it only appears in a few spectral elements and could simply be emission
associated with AzTEC-3. Guaita et al. (2022) detected a bridge of
Lyman-$\alpha$ emission extending between these two components, indicating
that tidal forces could be at work between LBG-3 and AzTEC-3. The detection of
Lyman-$\alpha$ in both AzTEC-3 and LBG-3 further supports the likelihood of an
interacting system. This is further discussed in Section 4.6.

Table 5: Line parameters for the [C ii] emission lines. The distance is measured between the central source (AzTEC-3 and the northern image of BRI0952, respectively) and the surrounding sources. $I_{\rm[CII]}$ is the line intensity, and FWHM is the full width at half maximum of the lines (one entry for single-Gaussian fit and two entries for double-Gaussian fit). $A_{\rm[CII]}$ is the length of the major axis of the deconvolved source size from CASA’s imfit, we note that BRI0952 has a more complex morphology, and thus the sizes include an additional 30% error on the reported value corresponding to the uncertainty on the lensing factor. Name | R.A. | Dec. | Distance | $z_{\rm[CII]}$ | $I_{\rm[CII]}$ | $\rm FWHM_{[CII]}$ | $A_{\rm[CII]}$
---|---|---|---|---|---|---|---
| [J2000] | [J2000] |  [′′] |  |  [Jy km $\rm s^{-1}$] |  [km $\rm s^{-1}$] |  [${}^{\prime\prime}\times^{\prime\prime}$]
BRI0952 | N: 09:55:00.10 |  $-$01:30:06.61 |  | $4.433$ | $15.45\pm 1.5$ | $182\pm 5$ |  ([$0.51\pm 0.19]\times[(0.285\pm 0.12$])
| S: 09:55:00.06 |  $-$01:30:07.29 | 1.0 |  |  | $410\pm 21$ |  ([$0.36\pm 0.13]\times[0.29\pm 0.21]$])
Comp-N | 09:55:00.09 |  $-$01:30:05.89 | 0.75 | $4.432$ | $0.62\pm 0.06$ | $130\pm 10$ |  ([$0.79\pm 0.32]\times[0.23\pm 0.11$])
Comp-SW | 09:55:00.00 |  $-$01:30:08.05 | 2.2 | $4.432$ | $0.30\pm 0.04$ | $122\pm 13$ |  ([$0.76\pm 0.30]\times[0.23\pm 0.13]$])
AzTEC-3 | 10:00:20.696 | +02:35:20.35 |  | $5.2988$ | $11.34\pm 1.0$ | $320\pm 12$ |  ([$0.69\pm 0.06]\times[0.42\pm 0.10$])
|  |  |  |  |  | $660\pm 20$ |
LBG-3 | 10:00:20.766 | +02:35:21.39 | 1.5 | $5.2841$ | $0.78\pm 0.07$ | $630\pm 36$ |  ([$0.8\pm 0.02]\times[0.46\pm 0.02$])
|  |  |  |  |  | $165\pm 24$ |
Gal-S | 10:00:20.68 | +02:35:18.07 | 2.3 | $5.2919$ | $0.52\pm 0.05$ | $190\pm 10$ |  ([$0.53\pm 0.10]\times[0.41\pm 0.15$])
|  |  |  |  |  | $92\pm 23$ |
Gal-SW | 10:00:20.60 | +02:35:19.28 | 1.8 | $5.2942$ | $0.15\pm 0.01$ | $325\pm 24$ |  ([$0.36\pm 0.04]\times[0.08\pm 0.10$])

####  3.3.2 Continuum

We obtain continuum emission from imaging line-free channels in the band-7
ALMA data. Due to the lower angular resolution combined with the lack of
velocity information provided in the spectral emission, we were unable to
isolate the emission from the companions by restricting the velocity range
from which they were extracted as we did for the [C ii] emission. Hence, we
extracted the continuum flux using three different methods.

The first was to use CASA’s imfit routine on the marginally resolved continuum
image. From this we obtain a continuum flux of $6.06\pm 0.13$ mJy for AzTEC-3,
which is in good agreement with Riechers et al. (2014), $0.071\pm 0.018$ mJy
for Gal-SW, and $0.18\pm 0.023$ mJy for LBG-3.

Secondly, we used the imfit residual image with the continuum emission from
AzTEC-3 removed to obtain the continuum flux of the companions. Using this
method, we obtain a continuum flux of $0.082\pm 0.02$ mJy for Gal-SW and
$0.19\pm 0.024$ mJy for LBG-3.

Finally, we attempted to isolate the origin of the continuum flux for the
companions by creating a continuum image corresponding only to the flux from
AzTEC-3, which we were then able to subtract from the original continuum
image. To model the flux from AzTEC-3, we selected emission that was at levels
higher than $9\sigma$. This emission was then subtracted from the continuum
image. The original continuum image and the subtracted image are shown in
Figure 5. This resulted in a continuum flux of $0.06\pm 0.017$ mJy for Gal-SW
and $0.22\pm 0.025$ mJy for LBG-3. Due to the similarity of the results from
various methods, we conclude that the intrinsic value of the continuum for
each is in the range provided for the continuum for LBG-3 and Gal-SW.

We do not detect Gal-S in continuum, and we report a $3\sigma$ upper limit of
$0.05$ mJy. The companion sources are faint compared to AzTEC-3 ($\sim 3\%$
for LBG-3 and $\sim 1\%$ for Gal-SW), and their flux contribution to the
central source is negligible. Flux measurements and deconvolved source sizes
for the field are provided in Table 4, where average values are provided for
LBG-3 and Gal-SW for both continuum flux and size estimates.

We note an offset between the ALMA continuum, HST, and [C ii] emission for
LBG-3. This is shown in Figure 18. We suggest that this offset between the
three types of emission is likely linked to spatial offset between different
types of emission in this source. The offset of this emission also affects the
subtraction we performed above due to the possibility that we have in fact
subtracted some flux pertaining to LBG-3 that could be included in our model
of the emission from AzTEC-3. Thus, we suggest that the continuum flux
reported in this paper for LBG-3 be treated as a lower limit. Without
additional higher resolution data, a robust conclusion about the nature of
this offset is not possible.

We detect an additional continuum source at $\sim 10.5$ significance, referred
to extra source (ES), in the AzTEC-3 field at the position 10:00:21.066,
+02:35:16.975, which is shown in Figure 5. This source is bright across the
HST WFC3 filters, but it is undetected in [C ii] emission, indicating that it
is at a different redshift. Continuum flux measurements and source size are
provided in Table 4.

####  3.3.3 SED Fitting

We fit the SED of AzTEC-3 using photometry extracted from HST imaging
utilizing the source extraction algorithm SExtractor (Bertin & Arnouts 1996)
and our ALMA photometry (see Table 6). We matched the resolution of the HST
images to the lowest resolution filter; we note that the companion sources are
not blended with the emission from AzTEC-3 in the HST imaging. We fit the SED
using Bagpipes (Carnall et al. 2018), assuming a constant star formation
history, a Calzetti reddening law to describe the dust attenuation, and a
Chabrier initial mass function (IMF, Chabrier 2003). The mass of the central
source was allowed to vary from $10^{8}-10^{14}\rm M_{\odot,}$ and the
metallicity was allowed to vary from 0.01-1.0 $\rm Z_{\odot}$. We used the SED
fit from Bagpipes to calculate the $L_{\rm IR}$ (integrated from 8-1000
$\mu$m) of AzTEC-3, which is subsequently utilized below in determination of
the SMG’s properties.

Figure 9: [C ii] spectra for the companions of BRI0952 and AzTEC-3. The spectra of both the quasar and the SMG have been truncated so that the companion spectra are easily seen. The single- (dashed) and double- (dotted) Gaussian fits for both AzTEC-3 and BRI0952 are overplotted, along with the Gaussian fits to the companion sources. We highlight that the companions to BRI0952 are located at a very similar systemic velocity, whereas AzTEC-3’s companions are located in the blue part of the spectrum.  Table 6: Photometry for AzTEC-3 extracted from HST images using SExtractor. Filter | Magnitude
---|---
| [$\rm mag_{AB}$]
F606W | $28.89\pm 0.30$
F814W | $27.17\pm 0.10$
F105W | $24.92\pm 0.03$
F125W | $24.68\pm 0.02$
F160W | $24.52\pm 0.02$

##  4 Discussion

###  4.1 Magnetic fields

The mechanisms for the predicted polarization of the [C ii] fine structure
line has been named ground state alignment (GSA) (Yan & Lazarian 2006, 2012;
Zhang et al. 2015). GSA occurs due to the interaction of an anisotropic
radiation field with atoms or ions with fine- or hyperfine-structures. A
magnetic field induces precession, which causes the atom or ion to align with
the magnetic field. As a result, the emission or absorption of the spectral
lines becomes polarized and the polarization direction reflects the direction
of the magnetic field. The atoms align predominantly at their ground state
level. Due to the low emission and absorption rates involved in these
transitions, and hence their long life spans, already weak fields
($B>10^{-15}$ G) can cause alignment.

Predictions for the level of [C ii] polarization based on the GSA effect have
been made for [C ii] emission near galactic star-forming regions (Zhang & Yan
2018). Near the strong anisotropic radiation field produced from the regions,
[C ii] polarization up to $\sim 30\%$ could be expected. Since the radiation
field in starburst galaxies and AGN hosts are similarly energetic, comparable
levels of polarization could have been expected in early star-forming galaxies
and AGNs (Zhang & Yan 2018). Our observations do not reveal any linear
polarization of [C ii] with $3\sigma$ limits to the polarization percentages
at the peak of emission ¡5% and for the integrated emission ¡1%.

There are two possible explanations for such low or non-existent levels of
polarization. Firstly, the GSA prediction might not be relevant in conditions
where the [C ii] emission originates in the observed SMG and quasar, because
the anisotropic radiation field is not sufficient to cause significant
polarization. Alternatively, if the magnetic field is sufficiently irregular
or has a large turbulent component within our resolution elements, beam
depolarization will reduce the polarization fraction. Our angular resolution
corresponds to $\sim 3.1$ kpc and $\sim 4.7$ kpc for BRI0952 and AzTEC-3,
respectively. These scales are not significantly larger than those where
structured fields are observed in nearby galaxies (e.g., Beck 2015; Lopez-
Rodriguez et al. 2021), but if the magnetic field follows spiral arms or
warped disks, like in the case of Centaurus A (Lopez-Rodriguez 2021),
depolarization could still be large. Without a better estimate of the expected
linear polarization fraction in SMGs and around quasars, we cannot use our
limits to provide meaningful constraints on the level of depolarization, and
thus the level of structure in the magnetic field. However, unless the GSA
mechanism is much less effective than expected, it appears unlikely that a
strong ordered magnetic field exists at the kiloparsec scale in the two
sources in this paper.

###  4.2 Infrared luminosity

We obtain an $L_{\rm IR}$ estimate for AzTEC-3 by integrating our SED from
Bagpipes from 8-1000 $\mu$m of $L_{\rm IR}=(7.3\pm 0.2)\times 10^{13}\,\rm
L_{\odot}$. Although the central source is blended with surrounding
companions, we anticipate that the uncertainty caused by the companion’s IR
luminosity will be small and we do not add additional errors to the
$L_{\rm{IR}}$ of AzTEC-3. This value is consistent with that reported by Capak
et al. (2011), as they provide a wide range of possible $L_{\rm IR}$ values
ranging from $(2.2-11)\times 10^{13}\,\rm L_{\odot}$ for the 8-1000 $\mu$m
wavelength range. Riechers et al. (2014) reported a $L_{\rm FIR}$ that is a
factor of $\sim 6.5$ times lower than our reported $L_{\rm IR}$, which is
outside the range of error typically ascribed to differences between $L_{\rm
IR}$ and $L_{\rm FIR}$ 777In this analysis, we assume $L_{\rm FIR}\sim
0.75\times L_{\rm IR,}$ following Decarli et al. (2017). (Carilli & Walter
2013). We suggest that discrepancies between these two reported values, apart
from the utilized wavelength range, derive from the number of data points used
for each fit. Riechers et al. (2014) used a higher number of data points than
in our SED fitting; however, both analyses lack IR coverage, making it
difficult to obtain high levels of accuracy, and thus $L_{\rm FIR}$ or $L_{\rm
IR}$, from the SED fit.

To determine a lower limit on the IR luminosity of the companions of AzTEC-3,
we used a modified blackbody approximation (e.g., Knudsen et al. (2003),
Equation 2), assuming a temperature of 45 K and $\beta=1.7$ (typical values
for high-redshift sources; Beelen et al. 2006; Dunne et al. 2011; Carniani et
al. 2019). We utilized this approach rather than an SED fit as the SED of the
companions is poorly sampled, especially in the far-IR, and the accuracy of
sub-mm photometry is affected by the blending of the continuum emission from
the central SMG. Calculated lower limits are provided in Table 7.

A similar fit for the IR luminosity was performed for BRI0952, integrating the
SED between 8 and 1000 $\mu$m. We assume the same approximation as for
AzTEC-3: the effect of the companion sources on the SED and $L_{\rm{IR}}$ will
be negligible due to their faintness in comparison to the quasar.
Specifically, we find that the IR luminosity due to star formation is
$L_{\rm{IR_{SF}}}=(7.66\pm 2.49)\times 10^{12}\,\rm L_{\odot}$ and the IR
luminosity due to AGN is $L_{\rm{IR_{AGN}}}=(2.23\pm 0.72)\times 10^{14}\,\rm
L_{\odot}$. We note that the error on the IR luminosity comes from the
uncertainty on the lensing factor. We find that $L_{\rm{IR_{SF}}}$ is a factor
of $\sim 5$ higher than that reported by Gallerani et al. (2012). We suggest
that this is for two main reasons: (i) the methodology used for fitting -
Gallerani et al. (2012) scaled a template SED to the 870$\mu m$ continuum
flux, while our model fits based on a number of photometric values, increasing
the accuracy of the fit - and (ii) the wavelength range used in fitting (the
range 42-122 $\mu m$ is used in Gallerani et al. 2012).

Table 7: Derived properties for sources. $L_{\rm IR}$ refers to the integrated IR luminosity from 8-1000 $\mu$m for BRI0952 (using $L_{\rm{IR_{SF}}}$) and AzTEC-3 and to a modified blackbody approximation for the companion sources. $\rm SFR_{IR}$ is the SFR derived from the $L_{\rm IR}$, $\rm SFR_{[CII]}$ refers to the SFR derived from the relation given in De Looze et al. (2014) for starburst galaxies. $\dot{M}_{\rm out}$ gives the mass outflow rate, and $M_{\rm dyn}$ is the dynamical mass. Upper limits are provided for inferred properties for Gal-S, Comp-N, and Comp-SW as we do not detect these sources in continuum emission. The luminosities reported for BRI0952 are corrected for magnification.  Name | $L_{\rm[CII]}$ | $L_{\rm IR}$ | $\rm SFR_{IR}$ | $\rm SFR_{\rm[CII]}$ | $L_{\rm[CII]}/L_{\rm IR}$ | $\dot{M}_{\rm out}$ | $M_{\rm dyn,[CII]}$
---|---|---|---|---|---|---|---
| [$10^{9}$ L⊙] | [$10^{12}$ L⊙] | [M⊙ yr-1] | [M⊙ yr-1] | $10^{-3}$ | [M⊙ yr-1] | [$10^{10}$ M⊙]
BRI0952 | $2.46\pm 0.23$ | $7.66\pm 2.49$ | 770 | 247 | 0.37 | $98\pm 19$ | 0.90
Comp-N | $0.39\pm 0.04$ | ¡0.2 | ¡21 | 34 | ¡2.0 | - | 0.5
Comp-SW | $0.19\pm 0.03$ | ¡0.2 | ¡21 | 16 | ¡1.0 | - | 0.4
AzTEC-3 | $9.3\pm 0.80$ | $73.4\pm 2$ | 7340 | 809 | $0.12\pm 0.01$ | $238\pm 30$ | 6.5
LBG-3 | $0.63\pm 0.05$ | $0.40\pm 0.5$ | $40\pm 46$ | 55 | $1.6\pm 0.14$ | - | 0.95
Gal-S | $0.43\pm 0.04$ | $<0.1$ | $<12.0$ | 37 | $<3$ | - | 0.83
Gal-SW | $0.12\pm 0.01$ | $0.15\pm 0.2$ | $15\pm 23$ | 11 | $0.85\pm 0.13$ | - | 1.6

###  4.3 Star-formation rate

We calculated the SFR of BRI0952 and AzTEC-3, along with their surrounding
sources, using different methods. By assuming a Chabrier IMF we can infer the
SFR of each source via the following relation: SFR $\sim 10^{-10}L_{\rm{IR,}}$
where $L_{\rm IR}$ is given in $L_{\odot}$ (Carilli & Walter 2013). This
yields an SFR of 770 M⊙ yr-1 for the quasar BRI0952 using $L_{\rm{IR_{SF}}}$
and $\sim 7340$ M⊙ yr-1 for AzTEC-3 (significantly higher than that reported
by Riechers et al. (2014) of 1100 M⊙ yr-1).

These extremely high values are similar to those reported for other peculiar
sources in the high-redshift universe. Daddi et al. (2009) reported an SFR of
$>1000\rm M_{\odot}/yr$ in the SMGs GN20 and GN20.2 and notes that there is no
evidence of AGN activity. Similarly, SFRs of $\geq 1000$ M⊙ yr-1 have been
reported in HDF850.1 (Walter et al. 2012), AzTEC-1 (Yun et al. 2015; Sharda et
al. 2019), HFLS3 (Robson et al. 2014; Cooray et al. 2014), and BRI1202
(Carilli et al. 2013).

Following the same procedure we infer the SFRs of the companions of AzTEC-3
from the modified blackbody $L_{\rm{IR}}$ fit, reported in Table 7. The
companions exhibit significantly lower SFRs than AzTEC-3, although we assume
that these values provide a lower limit for the companions. We find comparable
SFRs to those reported for the quasar companions in Neeleman et al. (2019).

We derive SFRs through an additional method using the [C ii] -SFR relation for
starburst galaxies from De Looze et al. (2014) (provided in Section 3.2.2),
which are given in Table 7. This results in a similar distribution to the
above method, demonstrating the significant discrepancy between the SFR of the
companions and that of the central sources in both fields.

We caution that using [C ii] as a means of inferring SFR may be inaccurate as
the [C ii] emission is likely tracing other processes in addition to star
formation within the galaxies. The [C ii] emission could be tracing more
extreme processes or neutral gas (Pavesi et al. 2018) within the galaxy. If
this is the case in AzTEC-3 or BRI0952, this could also contaminate the
measurement of the SFR from the [C ii] emission. We further note the
degeneracy inherently present in determining a SFR from a galaxy’s [C ii]
luminosity due to the [C ii] versus FIR deficit, which is explored below.

###  4.4 [CII] Deficit

The [C ii] line is well known to exhibit a deficit with increasing IR
luminosity (e.g., Díaz-Santos et al. 2013; Gullberg et al. 2015; Díaz-Santos
et al. 2017; Gullberg et al. 2018; Lagache et al. 2018). This has been heavily
investigated at high redshift (e.g., Stacey et al. 2010; Wang et al. 2013;
Gullberg et al. 2015; Decarli et al. 2017; Gullberg et al. 2018; Lagache et
al. 2018; Neeleman et al. 2019), with many proposed explanations including the
physical scale of star formation, [C ii] saturation, optical depth effects,
increased dust grain charge in PDRs and the ISM, and AGN activity (Casey et
al. 2014). Some studies at high redshift have suggested that the lowest ratios
occur preferentially in AGN host galaxies (Stacey et al. 2010). This may not
be exclusively limited to [C ii] emission, as other fine structure lines such
as [O i], [O iii], [N ii], and [N iii] have been found to exhibit this deficit
as well (e.g., Graciá-Carpio et al. 2011; Decarli et al. 2012; Farrah et al.
2013). We plot the $L_{\rm[CII]}/L_{\rm{IR}}$ ratios as a function of the IR
luminosity for the sources in our sample, as well as other low- and high-
redshift galaxies in Figure 10. The ratios we find for BRI0952 and AzTEC-3 are
similar to those found in HFSL3 (Riechers et al. 2013) and the ratios reported
for two of the four quasars studied in Decarli et al. (2017).

For the companion galaxies, we also investigated the
$L_{\rm[CII]}/L_{\rm{IR}}$ ratio, though we note that the errors are very
large due to the additional uncertainty caused by the deblending of emission
from the central bright source. As the IR luminosity is seen as a lower limit
(see Section 4.2), the ratio can be treated as an upper limit. The resulting
values are consistent with those of local star-forming galaxies (Díaz-Santos
et al. 2013) and are higher than those reported for high-redshift companion
sources detected in [C ii] (e.g., Carilli et al. 2013; Decarli et al. 2017;
Neeleman et al. 2019).

A possible explanation for the ratios observed in AzTEC-3 and BRI0952 is that
of [C ii] saturation (e.g., Muñoz & Oh 2016; Gullberg et al. 2018). These
sources are both hosts to extreme star formation and, in the case of BRI0952,
AGN activity. If the temperatures in the majority of the environments in which
[C ii] is produced exceed the ground state temperature (92 K), we can expect
this line to saturate and other fine structure lines to become the primary
coolants of the ISM. If this is the case for these two sources, it could
explain the deficits observed in both. Observations of other fine structure
lines in these sources could provide further clues to the origin of the
deficit.

###  4.5 Outflows and turbulence

As shown in Sections 3.3.1 and 3.2.2, the [C ii] emission line profiles of the
bright target sources, namely BRI0952 and AzTEC-3, are better fit when
including an additional broad Gaussian function. The presence of broad, higher
velocity wings in the line profiles are often interpreted as an indication of
high-velocity outflows. We note that this need not be a unique interpretation;
however, as this is a common analysis that has been done in many previous
works (e.g., Feruglio et al. 2010; Aalto et al. 2012; Maiolino et al. 2012;
Cicone et al. 2014, 2015; Gallerani et al. 2018; Bischetti et al. 2019;
Stanley et al. 2019; Ginolfi et al. 2020). We pursue this below.

We used the luminosity of the broad component of the [C ii] line in both
AzTEC-3 and BRI0952 to infer a mass outflow rate using the equation from
Hailey-Dunsheath et al. (2010) to calculate the mass of the outflow. Similarly
to the method employed by Maiolino et al. (2012), Cicone et al. (2015), and
Stanley et al. (2019), we assumed $\mathrm{X_{C^{+}}=1.4\times 10^{-4}}$,
$T=200$ K, and $n\gg n_{\rm crit}$ \- typical values for PDRs. We estimated
the velocity of the outflow by assuming a constant outflow rate of $v_{\rm
outf}=0.5\times\mathrm{FWHM_{broad}}$ over a region with a radius of
$\mathrm{R_{out}}$, allowing us to calculate the outflow rate using
$\dot{M}_{\rm out}=M_{\rm out}\times v_{\rm out}/R_{\rm out}$.

We determined the outflow radius as the major axis of the extent of the [C ii]
emission for AzTEC-3 ($\sim 7.5$ kpc) and BRI0952 ($\sim 2.3$ kpc); for
BRI0952, this measurement was taken using the major axis through both the
image plane top and bottom images combined, and corrected for lensing
magnification 888The lensing magnification factor we utilized to correct the
extent was $\mu=3$.. We investigated alternative methods for determining the
mass outflow rate below. We find outflow rates of $\dot{M}_{\rm out}=238\pm
30\mathrm{M_{\odot}/yr}$ for AzTEC-3 and $\dot{M}_{\rm out}=98\pm
19\mathrm{M_{\odot}/yr}$ for BRI0952. Although these values are lower than
those found for other individual detections of quasar-driven outflows (assumed
to be the case for BRI0952; e.g., Feruglio et al. 2010; Sturm et al. 2011;
Cano-Díaz et al. 2012; Maiolino et al. 2012; Cicone et al. 2014; Feruglio et
al. 2015), they are in good agreement with outflow rates estimates through
stacking analyses (e.g., Gallerani et al. 2018; Stanley et al. 2019; Ginolfi
et al. 2020). The latter samples are comprised of more ‘normal’ high-redshift
sources, so the validity of the comparison is tenuous and the methodology used
is discussed at the end of this section.

As noted above, there are different methods for disentangling a potential
contribution of a high-velocity outflow to the line profile, and we note that
the velocity profile of the outflow need not be described by a single
Gaussian. As an alternative, we determined the strength of the outflow by
utilizing only the flux not accounted for in a single Gaussian fit to the [C
ii] emission; effectively subtracting the single component from the broad one.
This yields a significantly lower mass outflow rate, which we treated as a
lower limit for BRI0952 and AzTEC-3. Using this method, we find mass outflow
rates of $28\pm 8\rm M_{\odot}/yr$ for AzTEC-3 and $12\pm 4\rm M_{\odot}/yr$
for BRI0952. We attribute the discrepancy between the two methods, at least in
part, to be the effect of the companion sources on the [C ii] line emission
profile. If the emission from the central source is blended with that of the
companions, it is possible that the double-Gaussian fit (and thus the broad
complex emission line profiles) are simply an artifact caused by this
blending.

Figure 10: $L_{\rm[CII]}$/$L_{\rm IR}$ ratio as a function of $L_{\rm IR}$ for
local and high-redshift sources. Local ($z<1$) sources are taken from Díaz-
Santos et al. (2013). High-redshift sources are from De Looze et al. (2014)
and Gullberg et al. (2015). Literature results for high-redshift quasars and
companion sources are taken from Decarli et al. (2017) and Neeleman et al.
(2019) (for these we take an average of the reported $L_{\rm IR}$). We note
that we only consider the $L_{\rm[CII]}$/$L_{\rm IR}$ as an upper limit for
all companion sources. The error bar we used for BRI0952 comes from the
uncertainty on the lensing factor on $L_{\rm IR}$. The error bar on the
$L_{\rm IR}$ and hence $L_{\rm[CII]}$/$L_{\rm IR}$ ratio of AzTEC-3 is taken
to be the range of $L_{\rm IR}$ values provided by Capak et al. (2011). For
data points taken from other papers, we assumed $L_{\rm FIR}\sim 0.75\times
L_{\rm IR}$ (following Decarli et al. 2017), but added an additional
indicative error bar to the bottom left of the plot indicating the
conservative estimate $\sim 30\%$ due to this assumption (Carilli & Walter
2013).

We caution that the differential lensing of the quasar may be contributing to
the high-velocity wings. To this end, for an additional investigation into the
mass outflow rate of BRI0952 we used the spectra extracted from Img-N (as
mentioned in Section 3.2.2 and shown in Figure 3). We use a radius of
$0.35^{\prime\prime}$ ($\sim 2.38$kpc), corrected using the same lensing
factor as described above), $\rm FWHM_{broad}$ = $543$ km s-1, and $L_{[\rm
C\,{\sc II}]_{broad}}=0.22\times 10^{9}$ L⊙, resulting in an outflow of
$\dot{M}_{\rm out}=74\pm 19\,\mathrm{M_{\odot}/yr}$. The exact impact of the
gravitational lensing, and in particular differential lensing, is challenging
to estimate, and further modeling based on higher resolution and higher
sensitivity data across multiple wavelengths would be needed. We note that
systematic errors on the mass outflow rate estimates, along with the
systematic errors on other quantities used for comparison (e.g., SFR), are
likely to dominate over the effect of the differential lensing. An additional
important consideration is the origin of this broad component, which we
interpret as an outflow above; for example, we ask ourselves whether the broad
component is tracing high-velocity gas outflowing from AzTEC-3 or an
interaction between the SMG and the companion Gal-S. This is further discussed
in section 4.6.

We show the mass outflow rate estimates as a function of SFR in Figure 11,
together with similar estimates for low- and high-redshift sources. With star-
formation-rate estimates that are $\sim\rm or>1000$ M⊙ yr-1 for both BRI0952
and AzTEC-3, both sources are seen in a similar region to other results for
high-redshift galaxies. For both sources, the mass outflow rate estimates are
on the lower side of the average; however, we note that the large
uncertainties in the $\dot{M}_{\rm out}$ and SFR do not allow for additional
interpretation.

Outflows are generally studied through different probes, including both
emission from high-velocity outflows as well as absorption line studies. In
terms of high-velocity outflows, detections have been published using
different lines, including CO, [C ii], and [O iii]$\lambda\,5007$ at low and
high redshift (e.g., Cicone et al. 2014, 2015; Carniani et al. 2016; Brusa et
al. 2018). So far, only a few robust detections from single $z>4$ quasars
using [C ii] have been published (Maiolino et al. 2012; Carilli et al. 2013).
Studies using stacking analyses for larger samples of $z\sim 6$ quasars
provide conflicting results (e.g., Decarli et al. 2018; Stanley et al. 2019;
Bischetti et al. 2019), ranging from non-detection to claimed detections. In
terms of star-forming galaxies, stacking of [C ii] for $z=4-6$ galaxies in the
ALPINE survey revealed a high-velocity outflow component, finding mass outflow
rates that are consistent with our results (e.g., Ginolfi et al. 2020). The
use of broad [C ii] emission as a means of detecting outflows was called into
question by Spilker et al. (2020a) following their non-detection of broad
wings associated with a sample of dusty star-forming galaxies with clear OH
outflow absorption features. It is thus possible that the broad wings we
detect are dominated by emission from the companion sources around AzTEC-3 and
BRI0952, where the latter could also be affected by differential lensing
magnification. In addition, recent studies have reexamined previous results,
indicating the need for a broad component in the fitting of [C ii] spectra and
found these components superfluous (e.g., Meyer et al. 2022); therefore, we
caution that the true nature of the broad component cannot be confirmed as an
outflow in BRI0952 and AzTEC-3 without additional outflow tracers detected in
these galaxies.

###  4.6 Environment

The impact of the environment in which massive galaxies evolve at high-
redshift remains an open question. These two systems present extreme
situations in which to study the effects of faint companion sources in the
early universe.

The AzTEC-3 system, with the presence of multiple close companions, detected
either in [C ii] or in optical or continuum observations, provide an
exceptional laboratory to study the effect of close companions near intense
starbursts in the early Universe. There are three companion galaxies within a
projected distance of $\sim 18$ kpc from the central SMG, and an additional
system of possibly merging galaxies located at a projected distance of $\sim
95$ kpc from the central source (Riechers et al. 2014), though the latter is
not covered by our observations. We detect a bridge-like structure between the
companion galaxy Gal-S and AzTEC-3, suggesting the possible occurrence of a
gas-exchange between the two galaxies extending over $\sim 12$ kpc. This ”gas
bridge” between Gal-S and AzTEC-3 is very similar to that observed by Díaz-
Santos et al. (2018) between the Hot DOG W2246 and a companion, although only
about half as large in spatial extent. Further investigation of this requires
higher resolution ALMA data and an improved method for isolating and
subtracting the emission from the central source. As mentioned in Section 3.3,
we detect a velocity gradient between LBG-3 and AzTEC-3, indicating an
additional possible interaction. The detections of Lyman-$\alpha$ between
these two galaxies in Guaita et al. (2022) also indicate an interacting
system.

In the field of BRI0952, Comp-N and Comp-SW are detected in [C ii] with no
further sources detected out to a projected distance of 62 kpc (corresponding
to the radius of the primary beam). Also, no additional companions are seen at
other wavelengths, most notably the archival HST data. Due to the non-
detection of the companions in current HST and Herschel imaging, an analysis
of comparable level to that of AzTEC-3 is currently not feasible. We note the
possibility that one or both of Comp-N and Comp-SW could be in the process of
merging with BRI0952. If this is the case, it may suggest that we are
observing the quasar in a post-starburst state in which recent galaxy
interactions and ongoing mergers have triggered extreme star formation and AGN
activity. In order to investigate this possibility, higher-resolution data of
multiple emission lines combined with a robust source plane reconstruction
would be needed; this is beyond the scope of this paper. For the BRI0952
companion sources, we see no clear signs of gas-bridge-like structures (as
were seen for the AzTEC-3 companion galaxies). We also note that an
alternative interpretation of either of the companions Comp-N and Comp-SW
could be that they represent an extended substructure in the gas distribution.
If that is the case, it would likely indicate the presence of merger activity,
as the gravitational forces from minor or major merger interactions could
cause a more complex gas distribution (e.g., König et al. 2014; Harada et al.
2018; König et al. 2018; Young et al. 2021).

These two systems seem to be examples of long-sought-after, theorized,
typical, over-dense environments of massive sources with numerous faint
companions in the high-redshift Universe. The companion sources of both
systems contribute less than 10% to the total [C ii] emission, and even less
to the total IR luminosity between 8-1000 $\mu m$. Other systems observed in
recent years have also been found to have companion sources; however, most of
these companions have luminosities comparable to that of the central SMG or
quasar host galaxy (e.g., Clements et al. 2009; Carilli et al. 2013; Robson et
al. 2014; Fogasy et al. 2017; Trakhtenbrot et al. 2017; Wardlow et al. 2018;
Díaz-Santos et al. 2018; Neeleman et al. 2019; Fogasy et al. 2021; Bischetti
et al. 2021). The detection of faint companion sources in these two fields,
together with the results of W2246$-$0526 and BRI1202$-$0725 (Carilli et al.
2013; Díaz-Santos et al. 2018) and other such systems, are increasing the
sample enabling investigation of the role of less massive companion sources on
massive galaxy evolution.

Theoretical predictions from semi-analytical model simulations suggest that
$22\%$ of quasars should have at least one companion galaxy with stellar
masses $>10^{8}$ $\mathrm{M_{\odot}}$ (Fogasy et al. 2017). Additionally,
studies show that minor mergers, especially in the high-redshift Universe, are
common. Kaviraj et al. (2015) utilized the Horizon-AGN hydrodynamical
cosmological simulation to show that by $z\sim 1$ all massive galaxies
($>10^{10}\,\rm M_{\odot}$) have undergone a major or minor merger, and that
minor mergers (those with a mass ratio ¿ 4:1) are around $2.5\times$ more
frequent than major mergers between $1<z<4$. Their work also suggests that
major mergers are not the dominant source of star-formation enhancement at
high redshift (see Figure 5 in Kaviraj et al. 2015). This is indicative of the
need for minor mergers as fuel providers for high-redshift galaxies and is
especially important for extreme SMGs hosting maximum starbursts such as
AzTEC-3. The lack of current detections of smaller companion sources is likely
due, in part, to the long integration time required to observe them.

In order to categorize these systems as possible minor mergers (be it
progenitors or ongoing processes), we calculated the mass of the central
source using a virial mass estimator following the procedure used by Riechers
et al. (2014). We find the dynamical mass inferred from the [C ii] emission to
be $\sim 6.5\times 10^{10}$ M⊙ for AzTEC-3 and $\sim 0.90\times 10^{10}$ M⊙
for BRI0952 (lensing corrected). We used the same method to compute the masses
of the companions, reported in Table 7. In the AzTEC-3 system, we find that
the companions have dynamical masses of $\leq 4\times$ that of AzTEC-3. This
would classify these companions as minor mergers should they interact with the
central source; we already observe signs of this for AzTEC-3 and its
companions in the form of the gas bridge between these objects. These
companion sources are significantly less massive than those reported by
Neeleman et al. (2019). For the companions of BRI0952 we find the companions
have masses $\sim 1.5-2\times$ smaller than that of the quasar. These values
for the companions are closer to the values found for the quasar companions in
Neeleman et al. (2019). We note that the companion masses are likely
overestimated as we do not correct for lensing along the major axis of the
companions used for the virial mass estimates due to uncertainties in our
lensing model, and therefore the above estimate can be seen as an upper limit.

Figure 11: Mass outflow rate versus SFR for our objects and low- and high-
redshift galaxies, including stacking approaches at high redshift. The green
and orange rectangles represent the range of possible values for AzTEC-3 and
BRI0952, respectively. The low-$z$ comparison sample is taken from Fluetsch et
al. (2019), high-redshift direct observations are taken from Maiolino et al.
(2012); George et al. (2014); Feruglio et al. (2017); Brusa et al. (2018);
Herrera-Camus et al. (2019); Jones et al. (2019); Spilker et al. (2020b);
Butler et al. (2021), and high-redshift stacking averages are taken from
Gallerani et al. (2018); Bischetti et al. (2019); Ginolfi et al. (2020). For
Ginolfi et al. (2020), we plot the high-SFR sample and the median-SFR sample
in their stacking methodology as separate points. We utilized an average of
the mass outflow rates if a range is provided for an object.

The effect of the companions on massive sources remains to be seen. If these
faint companions are dynamically interacting in some manner, such as providing
gas to the central sources, this could supply the needed materials for the
extreme star formation occurring in these systems. Additionally, as suggested
by McGreer et al. (2014), the possibility of mergers occurring on a relatively
fast timescale as a short transitional phase could drastically limit our
ability to obtain high number density observations of similar systems. We
further suggest that the increased resolution now possible with ALMA will
allow for increased detections of SMG and quasar systems with numerous and
faint surrounding objects.

##  5 Conclusions

In this paper, we present observational results of [C ii] emission from
BRI0952 and AzTEC-3, along with respective companion sources. Our results lend
credibility to the paradigm of major and minor mergers in the early Universe
as progenitors for the massive galaxies we see in studies of the local
Universe. We summarize our conclusions below.

  1. 1.

We detect [C ii] emission in the lensed quasar BRI0952 at $z\sim 4.433$ and
the SMG AzTEC-3 at $z\sim 5.3$. We report serendipitous detections of [C ii]
emission from two previously unreported companion sources around BRI0952 and
new detections of [C ii] emission from three companions surrounding AzTEC-3.
These companions are each located within 3$\,{}^{\prime\prime}$ (18 kpc) of
the central source.

  2. 2.

We present a full-polarization analysis of the [C ii] emission lines for both
main targets. No polarization was detected, and upper limits are provided. The
results suggest that strong ordered magnetic fields are unlikely to exists at
the kiloparsec scale in the two studied sources, unless ground state alignment
is a less effective mechanism than expected.

  3. 3.

We constructed a new lensing model for BRI0952 using Visilens (Spilker et al.
2016), yielding a lensing magnification factor of $\mu\sim 4$ for the quasar
and insignificant lensing magnification of the two companion sources. Our
model suggests that differential lensing is occurring across the surface of
BRI0952 in both [C ii] and continuum emission. This difference is likely
insubstantial (or within errors) for our purposes, but it is important to keep
it in mind when considering the physical properties of the lensed images.

  4. 4.

The inferred SFR from the IR luminosity of both the central SMG AzTEC-3 and
the quasar BRI0952 suggest that both sources harbor starbursts of $\sim\rm
or>1000$ solar masses per year.

  5. 5.

The central SMG AzTEC-3 and a companion galaxy (Gal-S) in the field show
evidence of an interlinking gas bridge. Although we do not find a strong
velocity gradient across the central source, we suggest that this bridge may
be indicative of an ongoing gas-exchange process or merger.

  6. 6.

The [C ii] line profiles for both central sources exhibit complex broad
features indicating the possible presence of outflows. The mass outflow rates
of both BRI0952 and AzTEC-3 are similar to results for high-redshift galaxies;
any discrepancies we find are likely symptomatic of large uncertainties on
both the mass outflow rate and the SFR.

  7. 7.

The outflow features, combined with the observed gas-bridge structure between
AzTEC-3 and its southern companion (and possibly others) and velocity-
gradients between BRI0952 and companions, suggest both are interacting
systems. The extent of this interaction is unknown, but if both systems are
either entering or exiting a merger phase, this could explain the extreme star
formation events occurring in both.

Growing evidence in recent years suggests that overdense regions leading to
major and minor mergers are the progenitors of the massive galaxies we see in
the local Universe. The improved resolution possible with ALMA will allow for
the increased detection of companion galaxies in high-redshift environments,
allowing us to explore the credibility of mergers as means of creating the
extreme SFRs observed in these objects.

###### Acknowledgements.

We thank the anonymous referee for their helpful comments and insights. Kiana
Kade acknowledges support from the Nordic ALMA Regional Centre (ARC) node
based at Onsala Space Observatory. The Nordic ARC node is funded through
Swedish Research Council grant No 2017-00648. Kirsten Knudsen acknowledges
support from the Swedish Research Council and the Knut and Alice Wallenberg
Foundation. BG acknowledges support from the Carlsberg Foundation Research
Grant CF20-0644 ‘Physical pRoperties of the InterStellar Medium in Luminous
Infrared Galaxies at High redshifT: PRISMLIGHT’. Sabine König gratefully
acknowledges funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (grant
agreement No 789410). This paper makes use of the following ALMA data:
2018.1.01536.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. This paper makes use of the following HST projects: 13641 (PI Capak),
9822 (PI COSMOS24-21), and 13384 (PI Riechers), 8268 (PI Impey). Based on
observations made with the NASA/ESA Hubble Space Telescope, and obtained from
the Hubble Legacy Archive, which is a collaboration between the Space
Telescope Science Institute (STScI/NASA), the Space Telescope European
Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre
(CADC/NRC/CSA) This research made use of APLpy, an open-source plotting
package for Python (Robitaille & Bressert 2012).

## References

  * Aalto et al. (2012) Aalto, S., Garcia-Burillo, S., Muller, S., et al. 2012, A&A, 537, A44
  * Bañados et al. (2013) Bañados, E., Venemans, B., Walter, F., et al. 2013, ApJ, 773, 178
  * Banerji et al. (2011) Banerji, M., Chapman, S. C., Smail, I., et al. 2011, MNRAS, 418, 1071
  * Beck (2015) Beck, R. 2015, A&A Rev., 24, 4
  * Beelen et al. (2006) Beelen, A., Cox, P., Benford, D. J., et al. 2006, ApJ, 642, 694
  * Beifiori et al. (2012) Beifiori, A., Courteau, S., Corsini, E. M., & Zhu, Y. 2012, MNRAS, 419, 2497
  * Bennert et al. (2015) Bennert, V. N., Treu, T., Auger, M. W., et al. 2015, ApJ, 809, 20
  * Bertin & Arnouts (1996) Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393
  * Bischetti et al. (2021) Bischetti, M., Feruglio, C., Piconcelli, E., et al. 2021, A&A, 645, A33
  * Bischetti et al. (2019) Bischetti, M., Maiolino, R., Carniani, S., et al. 2019, A&A, 630, A59
  * Blain et al. (1999) Blain, A. W., Smail, I., Ivison, R. J., & Kneib, J. P. 1999, MNRAS, 302, 632
  * Brusa et al. (2018) Brusa, M., Cresci, G., Daddi, E., et al. 2018, A&A, 612, A29
  * Butler et al. (2021) Butler, K. M., van der Werf, P. P., Rybak, M., et al. 2021, arXiv e-prints, arXiv:2104.10077
  * Cano-Díaz et al. (2012) Cano-Díaz, M., Maiolino, R., Marconi, A., et al. 2012, A&A, 537, L8
  * Capak et al. (2011) Capak, P. L., Riechers, D., Scoville, N. Z., et al. 2011, Nature, 470, 233
  * Carilli et al. (2013) Carilli, C. L., Riechers, D., Walter, F., et al. 2013, ApJ, 763, 120
  * Carilli & Walter (2013) Carilli, C. L. & Walter, F. 2013, ARA&A, 51, 105
  * Carnall et al. (2018) Carnall, A. C., McLure, R. J., Dunlop, J. S., & Davé, R. 2018, MNRAS, 480, 4379
  * Carniani et al. (2019) Carniani, S., Gallerani, S., Vallini, L., et al. 2019, MNRAS, 489, 3939
  * Carniani et al. (2016) Carniani, S., Marconi, A., Maiolino, R., et al. 2016, A&A, 591, A28
  * Casey et al. (2014) Casey, C. M., Narayanan, D., & Cooray, A. 2014, Phys. Rep, 541, 45
  * Casey et al. (2019) Casey, C. M., Zavala, J. A., Aravena, M., et al. 2019, ApJ, 887, 55
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763
  * Chisholm et al. (2015) Chisholm, J., Tremonti, C. A., Leitherer, C., et al. 2015, ApJ, 811, 149
  * Cicone et al. (2015) Cicone, C., Maiolino, R., Gallerani, S., et al. 2015, A&A, 574, A14
  * Cicone et al. (2014) Cicone, C., Maiolino, R., Sturm, E., et al. 2014, A&A, 562, A21
  * Clements et al. (2009) Clements, D. L., Petitpas, G., Farrah, D., et al. 2009, ApJ, 698, L188
  * Cooray et al. (2014) Cooray, A., Calanog, J., Wardlow, J. L., et al. 2014, ApJ, 790, 40
  * Cutri & et al. (2012) Cutri, R. M. & et al. 2012, VizieR Online Data Catalog, II/311
  * Daddi et al. (2009) Daddi, E., Dannerbauer, H., Stern, D., et al. 2009, ApJ, 694, 1517
  * De Looze et al. (2014) De Looze, I., Cormier, D., Lebouteiller, V., et al. 2014, A&A, 568, A62
  * Decarli et al. (2012) Decarli, R., Walter, F., Neri, R., et al. 2012, ApJ, 752, 2
  * Decarli et al. (2017) Decarli, R., Walter, F., Venemans, B. P., et al. 2017, Nature, 545, 457
  * Decarli et al. (2018) Decarli, R., Walter, F., Venemans, B. P., et al. 2018, ApJ, 854, 97
  * Dekel et al. (2009) Dekel, A., Birnboim, Y., Engel, G., et al. 2009, Nature, 457, 451
  * Di Matteo et al. (2012) Di Matteo, T., Khandai, N., DeGraf, C., et al. 2012, ApJ, 745, L29
  * Di Matteo et al. (2005) Di Matteo, T., Springel, V., & Hernquist, L. 2005, Nature, 433, 604
  * Díaz-Santos et al. (2017) Díaz-Santos, T., Armus, L., Charmandaris, V., et al. 2017, ApJ, 846, 32
  * Díaz-Santos et al. (2013) Díaz-Santos, T., Armus, L., Charmandaris, V., et al. 2013, ApJ, 774, 68
  * Díaz-Santos et al. (2018) Díaz-Santos, T., Assef, R. J., Blain, A. W., et al. 2018, Science, 362, 1034
  * Dubois et al. (2012) Dubois, Y., Devriendt, J., Slyz, A., & Teyssier, R. 2012, MNRAS, 420, 2662
  * Dubois et al. (2014) Dubois, Y., Pichon, C., Welker, C., et al. 2014, MNRAS, 444, 1453
  * Dunne et al. (2011) Dunne, L., Gomez, H. L., da Cunha, E., et al. 2011, MNRAS, 417, 1510
  * Eigenbrod et al. (2007) Eigenbrod, A., Courbin, F., & Meylan, G. 2007, A&A, 465, 51
  * Fabian (2012) Fabian, A. C. 2012, ARA&A, 50, 455
  * Fan et al. (2016) Fan, L., Han, Y., Fang, G., et al. 2016, ApJ, 822, L32
  * Farrah et al. (2013) Farrah, D., Lebouteiller, V., Spoon, H. W. W., et al. 2013, ApJ, 776, 38
  * Ferrarese & Merritt (2000) Ferrarese, L. & Merritt, D. 2000, ApJ, 539, L9
  * Feruglio et al. (2017) Feruglio, C., Ferrara, A., Bischetti, M., et al. 2017, A&A, 608, A30
  * Feruglio et al. (2015) Feruglio, C., Fiore, F., Carniani, S., et al. 2015, A&A, 583, A99
  * Feruglio et al. (2010) Feruglio, C., Maiolino, R., Piconcelli, E., et al. 2010, A&A, 518, L155
  * Fluetsch et al. (2019) Fluetsch, A., Maiolino, R., Carniani, S., et al. 2019, MNRAS, 483, 4586
  * Fogasy et al. (2021) Fogasy, J., Knudsen, K. K., Drouart, G., & Gullberg, B. 2021, MNRAS, 501, 5973
  * Fogasy et al. (2020) Fogasy, J., Knudsen, K. K., Drouart, G., Lagos, C. D. P., & Fan, L. 2020, MNRAS, 493, 3744
  * Fogasy et al. (2017) Fogasy, J., Knudsen, K. K., Lagos, C. D. P., Drouart, G., & Gonzalez-Perez, V. 2017, A&A, 597, A123
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1
  * Gallerani et al. (2012) Gallerani, S., Neri, R., Maiolino, R., et al. 2012, A&A, 543, A114
  * Gallerani et al. (2018) Gallerani, S., Pallottini, A., Feruglio, C., et al. 2018, MNRAS, 473, 1909
  * Gebhardt et al. (2000) Gebhardt, K., Bender, R., Bower, G., et al. 2000, ApJ, 539, L13
  * Genzel et al. (2010) Genzel, R., Tacconi, L. J., Gracia-Carpio, J., et al. 2010, MNRAS, 407, 2091
  * George et al. (2014) George, R. D., Ivison, R. J., Smail, I., et al. 2014, MNRAS, 442, 1877
  * Ginolfi et al. (2020) Ginolfi, M., Jones, G. C., Béthermin, M., et al. 2020, A&A, 633, A90
  * Graciá-Carpio et al. (2011) Graciá-Carpio, J., Sturm, E., Hailey-Dunsheath, S., et al. 2011, ApJ, 728, L7
  * Guaita et al. (2022) Guaita, L., Aravena, M., Gurung-Lopez, S., et al. 2022, A&A, 660, A137
  * Gullberg et al. (2015) Gullberg, B., De Breuck, C., Vieira, J. D., et al. 2015, MNRAS, 449, 2883
  * Gullberg et al. (2018) Gullberg, B., Swinbank, A. M., Smail, I., et al. 2018, ApJ, 859, 12
  * Gültekin et al. (2009) Gültekin, K., Richstone, D. O., Gebhardt, K., et al. 2009, ApJ, 698, 198
  * Hailey-Dunsheath et al. (2010) Hailey-Dunsheath, S., Nikola, T., Stacey, G. J., et al. 2010, ApJ, 714, L162
  * Harada et al. (2018) Harada, N., Sakamoto, K., Martín, S., et al. 2018, ApJ, 855, 49
  * Häring & Rix (2004) Häring, N. & Rix, H.-W. 2004, ApJ, 604, L89
  * Harrison (2017) Harrison, C. M. 2017, Nature Astronomy, 1, 0165
  * Heckman et al. (1990) Heckman, T. M., Armus, L., & Miley, G. K. 1990, ApJS, 74, 833
  * Herrera-Camus et al. (2019) Herrera-Camus, R., Tacconi, L., Genzel, R., et al. 2019, ApJ, 871, 37
  * Hopkins et al. (2008) Hopkins, P. F., Hernquist, L., Cox, T. J., & Kereš, D. 2008, ApJS, 175, 356
  * Hughes et al. (1998) Hughes, D. H., Serjeant, S., Dunlop, J., et al. 1998, Nature, 394, 241
  * Husband et al. (2015) Husband, K., Bremer, M. N., Stanway, E. R., & Lehnert, M. D. 2015, MNRAS, 452, 2388
  * Ilbert et al. (2009) Ilbert, O., Capak, P., Salvato, M., et al. 2009, ApJ, 690, 1236
  * Ishibashi & Fabian (2016) Ishibashi, W. & Fabian, A. C. 2016, MNRAS, 463, 1291
  * Jones et al. (2019) Jones, G. C., Maiolino, R., Caselli, P., & Carniani, S. 2019, A&A, 632, L7
  * Kaviraj et al. (2013) Kaviraj, S., Cohen, S., Windhorst, R. A., et al. 2013, MNRAS, 429, L40
  * Kaviraj et al. (2015) Kaviraj, S., Devriendt, J., Dubois, Y., et al. 2015, MNRAS, 452, 2845
  * Kereš et al. (2005) Kereš, D., Katz, N., Weinberg, D. H., & Davé, R. 2005, MNRAS, 363, 2
  * King & Pounds (2015) King, A. & Pounds, K. 2015, ARA&A, 53, 115
  * Knudsen et al. (2003) Knudsen, K. K., van der Werf, P. P., & Jaffe, W. 2003, A&A, 411, 343
  * König et al. (2014) König, S., Aalto, S., Lindroos, L., et al. 2014, A&A, 569, A6
  * König et al. (2018) König, S., Aalto, S., Muller, S., et al. 2018, A&A, 615, A122
  * Kormendy & Ho (2013) Kormendy, J. & Ho, L. C. 2013, ARA&A, 51, 511
  * Krumholz & Dekel (2010) Krumholz, M. R. & Dekel, A. 2010, MNRAS, 406, 112
  * Lagache et al. (2018) Lagache, G., Cousin, M., & Chatzikos, M. 2018, A&A, 609, A130
  * Lehár et al. (2000) Lehár, J., Falco, E. E., Kochanek, C. S., et al. 2000, ApJ, 536, 584
  * Litke et al. (2019) Litke, K. C., Marrone, D. P., Spilker, J. S., et al. 2019, ApJ, 870, 80
  * Lopez-Rodriguez (2021) Lopez-Rodriguez, E. 2021, Nature Astronomy [arXiv:2104.00688]
  * Lopez-Rodriguez et al. (2021) Lopez-Rodriguez, E., Guerra, J., Asgari-Targhi, M., & Schmelz, J. T. 2021, arXiv e-prints, arXiv:2102.03362
  * Madau & Dickinson (2014) Madau, P. & Dickinson, M. 2014, ARA&A, 52, 415
  * Magorrian et al. (1998) Magorrian, J., Tremaine, S., Richstone, D., et al. 1998, AJ, 115, 2285
  * Maiolino et al. (2009) Maiolino, R., Caselli, P., Nagao, T., et al. 2009, A&A, 500, L1
  * Maiolino et al. (2012) Maiolino, R., Gallerani, S., Neri, R., et al. 2012, MNRAS, 425, L66
  * Mazzucchelli et al. (2017) Mazzucchelli, C., Bañados, E., Decarli, R., et al. 2017, ApJ, 834, 83
  * McGreer et al. (2014) McGreer, I. D., Fan, X., Strauss, M. A., et al. 2014, AJ, 148, 73
  * McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell, 127
  * Meyer et al. (2022) Meyer, R. A., Walter, F., Cicone, C., et al. 2022, ApJ, 927, 152
  * Momcheva et al. (2015) Momcheva, I. G., Williams, K. A., Cool, R. J., Keeton, C. R., & Zabludoff, A. I. 2015, ApJS, 219, 29
  * Muñoz & Oh (2016) Muñoz, J. A. & Oh, S. P. 2016, MNRAS, 463, 2085
  * Mullaney et al. (2011) Mullaney, J. R., Alexander, D. M., Goulding, A. D., & Hickox, R. C. 2011, MNRAS, 414, 1082
  * Narayanan et al. (2015) Narayanan, D., Turk, M., Feldmann, R., et al. 2015, Nature, 525, 496
  * Neeleman et al. (2019) Neeleman, M., Bañados, E., Walter, F., et al. 2019, ApJ, 882, 10
  * Oteo et al. (2016) Oteo, I., Ivison, R. J., Dunne, L., et al. 2016, ApJ, 827, 34
  * Patton et al. (2020) Patton, D. R., Wilson, K. D., Metrow, C. J., et al. 2020, MNRAS, 494, 4969
  * Pavesi et al. (2018) Pavesi, R., Riechers, D. A., Sharon, C. E., et al. 2018, ApJ, 861, 43
  * Pearson et al. (2019) Pearson, W. J., Wang, L., Alpaslan, M., et al. 2019, A&A, 631, A51
  * Reines & Volonteri (2015) Reines, A. E. & Volonteri, M. 2015, ApJ, 813, 82
  * Riechers et al. (2013) Riechers, D. A., Bradford, C. M., Clements, D. L., et al. 2013, Nature, 496, 329
  * Riechers et al. (2014) Riechers, D. A., Carilli, C. L., Capak, P. L., et al. 2014, ApJ, 796, 84
  * Rieder & Teyssier (2017) Rieder, M. & Teyssier, R. 2017, MNRAS, 471, 2674
  * Robishaw et al. (2008) Robishaw, T., Quataert, E., & Heiles, C. 2008, ApJ, 680, 981
  * Robson et al. (2014) Robson, E. I., Ivison, R. J., Smail, I., et al. 2014, ApJ, 793, 11
  * Rupke et al. (2005) Rupke, D. S., Veilleux, S., & Sanders, D. B. 2005, ApJ, 632, 751
  * Sánchez-Monge et al. (2018) Sánchez-Monge, Á., Schilke, P., Ginsburg, A., Cesaroni, R., & Schmiedeke, A. 2018, A&A, 609, A101
  * Sharda et al. (2019) Sharda, P., da Cunha, E., Federrath, C., et al. 2019, MNRAS, 487, 4305
  * Sijacki et al. (2015) Sijacki, D., Vogelsberger, M., Genel, S., et al. 2015, MNRAS, 452, 575
  * Smail et al. (1997) Smail, I., Ivison, R. J., & Blain, A. W. 1997, ApJ, 490, L5
  * Sparre & Springel (2016) Sparre, M. & Springel, V. 2016, MNRAS, 462, 2418
  * Spilker et al. (2020a) Spilker, J. S., Aravena, M., Phadke, K. A., et al. 2020a, ApJ, 905, 86
  * Spilker et al. (2020b) Spilker, J. S., Aravena, M., Phadke, K. A., et al. 2020b, ApJ, 905, 86
  * Spilker et al. (2016) Spilker, J. S., Marrone, D. P., Aravena, M., et al. 2016, ApJ, 826, 112
  * Stacey et al. (1991) Stacey, G. J., Geis, N., Genzel, R., et al. 1991, ApJ, 373, 423
  * Stacey et al. (2010) Stacey, G. J., Hailey-Dunsheath, S., Ferkinhoff, C., et al. 2010, ApJ, 724, 957
  * Stanley et al. (2018) Stanley, F., Harrison, C. M., Alexander, D. M., et al. 2018, MNRAS, 478, 3721
  * Stanley et al. (2019) Stanley, F., Jolly, J. B., König, S., & Knudsen, K. K. 2019, A&A, 631, A78
  * Sturm et al. (2011) Sturm, E., González-Alfonso, E., Veilleux, S., et al. 2011, ApJ, 733, L16
  * Trakhtenbrot et al. (2017) Trakhtenbrot, B., Lira, P., Netzer, H., et al. 2017, ApJ, 836, 8
  * Venemans et al. (2020) Venemans, B. P., Walter, F., Neeleman, M., et al. 2020, ApJ, 904, 130
  * Walter et al. (2012) Walter, F., Decarli, R., Carilli, C., et al. 2012, Nature, 486, 233
  * Wang et al. (2013) Wang, R., Wagg, J., Carilli, C. L., et al. 2013, ApJ, 773, 44
  * Wardlow et al. (2018) Wardlow, J. L., Simpson, J. M., Smail, I., et al. 2018, MNRAS, 479, 3879
  * Weiner et al. (2009) Weiner, B. J., Coil, A. L., Prochaska, J. X., et al. 2009, ApJ, 692, 187
  * Willott et al. (2005) Willott, C. J., Percival, W. J., McLure, R. J., et al. 2005, ApJ, 626, 657
  * Yan & Lazarian (2006) Yan, H. & Lazarian, A. 2006, ApJ, 653, 1292
  * Yan & Lazarian (2012) Yan, H. & Lazarian, A. 2012, J. Quant. Spec. Radiat. Transf., 113, 1409
  * Young et al. (2021) Young, L. M., Meier, D. S., Bureau, M., et al. 2021, ApJ, 909, 98
  * Yue et al. (2019) Yue, M., Fan, X., Schindler, J.-T., McGreer, I. D., & Huang, Y.-H. 2019, ApJ, 883, 141
  * Yun et al. (2015) Yun, M. S., Aretxaga, I., Gurwell, M. A., et al. 2015, MNRAS, 454, 3485
  * Zhang & Yan (2018) Zhang, H. & Yan, H. 2018, MNRAS, 475, 2415
  * Zhang et al. (2015) Zhang, H., Yan, H., & Dong, L. 2015, ApJ, 804, 142

##  Appendix A Continuum-subtracted spectra

Presented in this appendix are the figures showing the total spectra compared
with the continuum-subtracted spectra for each source (see Figures 12 and 13).

Figure 12: Pre-continuum-subtracted (top) and post-continuum-subtracted
(bottom) spectra of AzTEC-3 extracted from the same region as the spectra
(black circle shown in panel 1 of Figure 6 using a fit on the order of 1 and
encompassing frequencies up to 300GHz. The red region represents the $1\sigma$
rms of the image and the gray line represents the atmospheric transmission at
1.0 mm PVW. The possible additional [C ii] wing feature mentioned in Section 2
can be seen in the 300.5-301 GHz frequency range.  Figure 13: Pre-continuum-
subtracted (top) and post-continuum-subtracted (bottom) spectra of BRI0952
extracted from the same region as the spectra (black circle shown in panel 1
of Figure 2 using a fit on the order of 1 and encompassing frequency ranges
from $\sim 335.3-336.9$, $347.1-347.7$, $348.97-348.98,$ and $350.45-350.67$
GHz. The red region represents the $1\sigma$ rms of the image. We do not show
the atmospheric transmission as there are no relevant features in the
frequency range. We note that the spectral window of the [C ii] line has a
higher spectral resolution (see Section 2), resulting in a higher noise level
per channel compared to other spectral windows.

##  Appendix B Lensing model for BRI0952

This appendix includes the figures detailing the Visilens lensing model
results, which are given in Fig. 14.

Figure 14: Image and lens models for BRI0952 for the velocity range shown at
the top of each row. The diamond in the first three rows shows the best-fit
position of the lens. Panels from top to bottom: Row 1 shows the ALMA band-7
dirty image with contours at 4, 6, 8, 10, 12, 14, and 16 $\sigma$ levels and
the magnification value found for that bin; row 2 shows the image plane model
from Visilens with the same contour levels as row 1; row 3 shows the residuals
after the subtraction of the Visilens model, and contours are at -3, -2, -1,
1, and 2 $\sigma$ levels; row 4 shows the image plane model from Visilens, and
the red circle and point represent the critical and caustic lines; row 5 shows
the source plane model with the black dashed ellipse showing the position of
the source. All images are centered around the ALMA phase center (the (0.0,
0.0) coordinate in this case; see Table 3).

##  Appendix C Lensing model for companions to BRI0952

Appendix includes the figures detailing the Visilens lensing model results for
the companions of BRI0952, which are given in Fig. 15.

Figure 15: Image and lens models for BRI0952 isolated to the velocity range in
which Comp-N and Comp-SW manifest. The diamond in the first three rows shows
the best-fit position of the lens. Panels from top to bottom: Row 1 shows the
ALMA band-7 dirty image with contours at 3, 4, 5, 6, 8, 10, 12, 14, and 16
$\sigma$ levels and the magnification value found for that bin; row 2 shows
the image plane model from Visilens with the same contour levels as row 1 and
the residuals after the subtraction of the Visilens model, contours are at -3,
-2, 2, and 3 $\sigma$ levels; row 4 shows the image plane model from Visilens,
and the red circle and point represent the critical and caustic lines; row 5
shows the source plane model with the black dashed ellipse showing the
position of the source. All images are centered around the ALMA phase center
(the (0.0, 0.0) coordinate in this case; see Table 3).

##  Appendix D BRI0952 Img-N [C ii] spectra

Appendix includes the [C ii] spectra from Img-N of the quasar BRI0952 used in
analysis of outflow properties as described in Section 4.5.

Figure 16: [C ii] spectra extracted from Img-N of the quasar BRI0952. The
single Gaussian is plotted in red, whereas the double-Gaussian fit to the line
is plotted in blue. The wings are clearly visible, from which the outflow rate
was calculated when investigating the effect of differential magnification
described in Section 4.5.

##  Appendix E Velocity gradient of LBG-3

This appendix includes a velocity map showing the velocity gradient detected
in [C ii] between LBG-3 and AzTEC-3.

Figure 17: Velocity map of AzTEC-3 contours overlaid on HST F105W centered
around the velocities at which the slight velocity gradient between LBG-3 and
AzTEC-3 is visible. The velocity range is added to the top of the images. The
red contours are at 3, 4, 5, 6, 7, 8, 9, and 10 $\sigma$ levels.

##  Appendix F [CII] and continuum offset of LBG-3

This appendix includes figures showing the [C ii] and continuum offset for
LBG-3.

Figure 18: HST image of AzTEC-3 system with overlaid contours from the [C ii]
emission for LBG-3 (cyan) and continuum contours (white). The [C ii] contours
are shown at 3, 4, 5, and 6 $\sigma$ levels and 3, 4, 5, 6, 10, 20, and 30
$\sigma$ levels for the continuum.