# Molecular Outflows in $z>6$ Unobscured QSO Hosts Driven by Star Formation

Kirsty M. Butler Institut de Radioastronomie Millimétrique (IRAM), 300 rue de
la Piscine, 38400 Saint-Martin-d’Hères, France  Leiden Observatory, Leiden
University, PO Box 9513, 2300 RA Leiden, the Netherlands  Paul P. van der Werf
Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, the
Netherlands  Theodoros Topkaras  Leiden Observatory, Leiden University, PO Box
9513, 2300 RA Leiden, the Netherlands  Matus Rybak  THz Sensing Group, Faculty
of Electrical Engineering, Mathematics and Computer Science, TU Delft, The
Netherlands  Leiden Observatory, Leiden University, PO Box 9513, 2300 RA
Leiden, the Netherlands  Bram P. Venemans  Leiden Observatory, Leiden
University, PO Box 9513, 2300 RA Leiden, the Netherlands  Fabian Walter  Max-
Planck Institute for Astronomy, Konigstuhl 17, D-69117 Heidelberg, Germany
Roberto Decarli  INAF – Osservatorio di Astrofisica e Scienza dello Spazio di
Bologna, via Gobetti 93/3, I-40129, Bologna, Italy

(Accepted December 18, 2022)

###### Abstract

Feedback and outflows in galaxies that are associated with a quasar phase are
expected to be pivotal in quenching the most massive galaxies. However,
observations targeting the molecular outflow phase, which dominates both the
mass and momentum and removes the immediate fuel for star formation, are
limited in high–z QSO hosts. Massive quiescent galaxies found at $z\sim 4$ are
predicted to have already quenched star formation by $z\sim 5$ and undergone
their most intense growth at $z>6$. Here, we present two ALMA detections of
molecular outflows, traced by blue–shifted absorption of the OH 119 $\mu$m
doublet, from a sample of three $z>6$ infrared luminous QSO hosts: J2310+1855
and P183+05. OH 119 $\mu$m is also detected in emission in P183+05, and
tentatively in the third source: P036+03. Using similar assumptions as for
high–z Dusty Star–Forming Galaxy outflows, we find that our QSOs drive
molecular outflows with comparable mass outflow rates, and that are comparably
energetic except for J2310+1855’s significantly lower outflow energy flux. We
do not find evidence, nor require additional input from the central AGN to
drive the molecular outflow in J2310+1855 but can not rule out an AGN
contribution in P183+05 if a significant AGN contribution to $\rm L_{FIR}$ is
assumed and/or if the outflow covering fraction is high ($\geq 53\%$), which
evidence from the literature suggests is unlikely in these sources.
Differences observed in the blue–shifted absorption spectral properties may
instead be caused by the QSO hosts’ more compact dust continuum, limiting
observations to lower altitude and more central regions of the outflow.

High-redshift galaxies (734) — Galaxy winds (626) — AGN host galaxies (2017) —
Quasars (1319) — Stellar feedback (1602)

††facilities: ALMA††software: CASA (v4.53; McMullin et al. 2007)

—

##  1 Introduction

Feedback from star–formation and black hole activity plays a critical role in
the evolution of galaxies and galaxy populations throughout their lifetimes.
Energy and momentum injected back into the ISM through these processes
regulates galaxy growth by heating, disturbing or ejecting gas that may have
fueled future star formation. The removal of low angular momentum and metal
enriched material from the centers of galaxies via outflows is an essential
step in our understanding and abilities to reproduce observed disky galaxy
morphologies, metallicity gradients and the polluted circum–/inter galactic
medium (Governato et al., 2010; Somerville & Primack, 1999; Kereš et al.,
2009; Veilleux et al., 2005; Meyer & York, 1987; Simcoe et al., 2004;
Travascio et al., 2020).

Regulated galaxy growth implies that the most rapidly evolving galaxies must
also experience the most vigorous feedback. For massive quiescent galaxies
observed as early as $z>4$ (Straatman et al., 2014; Guarnieri et al., 2019;
Carnall et al., 2020; Valentino et al., 2020), their short but explosive
lifetimes must have been accompanied by extreme star–formation and subsequent
feedback and outflows, in order to deplete their gas reserves by this time
(Glazebrook et al., 2017; Estrada-Carpenter et al., 2020; Forrest et al.,
2020). High–z ($z>4$) dusty star–forming galaxies (DSFG) that also host an AGN
thus present the most probable progenitors of such systems, warranting an
investigation into the scale and impact of their outflows.

At low redshift, observations of the ionised and neutral phases have shown
that outflows are ubiquitous (Veilleux et al., 2005; Heckman & Thompson, 2017;
Rupke, 2018; Veilleux et al., 2020). With the advent of Herschel, observations
extended to the cooler neutral and molecular phases and revealed that the
associated denser gas that is directly associated with star formation,
dominates the mass and momentum budget of their outflows (Fluetsch et al.,
2021). The first such detections uncovered a molecular outflow in Mrk 231 via
emission in high velocity line wings of the CO molecule Feruglio et al. (2010)
and via absorption in a P–Cygni profile of the OH molecule Fischer et al.
(2010). Outflows have since been detected in various atomic and molecular
species (CO, H2O, HCN, [CII], [CI], $\mbox{\rm OH}^{+}$, OH, $\mbox{\rm
CH}^{+}$, $\mbox{\rm H}_{2}{\rm O}^{+}$, etc.), using the same techniques. At
high–z, however, high velocity line wings which typically make up only a few
percent of the total emission line flux, become difficult to detect and
disentangle, making CO an inefficient tracer. Even observations of the bright
[CII] line has detected outflows in only a handful of individual galaxies
(e.g., Fan et al. 2018; Herrera-Camus et al. 2021; Tripodi et al. 2022), and
can depend strongly on the methodology implemented Maiolino et al. (2012);
Cicone et al. (2015); Meyer et al. (2022). Stacking has helped to provide
additional detections (Gallerani et al., 2018; Ginolfi et al., 2020), but not
without some contradictory results (Bischetti et al., 2019; Novak et al.,
2020). Most convincingly, Spilker et al. (2020a) show in their Sec. 5.2 that
even high quality [CII] spectra, with comparable or higher S/N than the
stacked results mentioned, do not show evidence of high velocity wings in
sources with known molecular outflows, thus deeming [CII] as an unreliable
outflow tracer of molecular gas.

Absorption lines, on the other hand, have proven to efficiently trace the gas
intervening the observer and host galaxy in dusty high–z sources (Falgarone et
al., 2017; Indriolo et al., 2018; Spilker et al., 2020a, b; Berta et al.,
2021; Riechers et al., 2021; Butler et al., 2021; Shao et al., 2022), reliably
detecting in– and out–flowing gas when red– or blue–shifted with respect to
the host galaxies systemic velocity.

The OH molecule is the most extensively utilised of such species, with samples
in the local universe spanning both star–forming, composite and AGN dominated
systems (Sturm et al., 2011; Veilleux et al., 2013; Spoon et al., 2013; Stone
et al., 2016; Calderón et al., 2016; González-Alfonso et al., 2017).
Consistently throughout these studies, outflow properties are found to best
correlate with the AGN luminosity ${\rm L_{AGN}}$ or AGN fraction $\alpha_{\rm
AGN}$ of the host galaxy, and at best only weakly with the host galaxy’s
star–forming properties (Calderón et al., 2016). Higher ${\rm L_{AGN}}$ and
$\alpha_{\rm AGN}$ drive faster outflow velocities (Sturm et al., 2011; Spoon
et al., 2013; Stone et al., 2016) and shorter gas depletion time scales (Sturm
et al., 2011; González-Alfonso et al., 2017). Total OH absorption line EWs
strongly correlate with 9.7$\mu$m silicate absorption, a measure of
obscuration within the host galaxy (Stone et al., 2016), whilst the relative
strength of the OH emission component decreases (Spoon et al., 2013; Veilleux
et al., 2013). Furthermore, pure OH emission spectra found in some AGN
dominated systems display relatively narrow line widths, suggested to be
indicative of a stage after which the AGN has cleared the obscuring material
(Veilleux et al., 2013).

At high–z, observations targeting OH are mostly limited to starforming
galaxies (Spilker et al., 2018, 2020a, 2020b), and one tentative absorption
detection in the z = 6.13 QSO, ULAS J131911+095051 (Herrera-Camus et al.,
2020). OH absorption is detected in all of the 11 SPT sources targeted by
Spilker et al. (2020a, b), with no sources displaying OH in emission. At a
similar rate to low–z ULIRGs and QSOs, 73% display unambiguous evidence of
outflows, none of which could be detected by high velocity wings in their
corresponding [CII] spectra. Such a high detection rate indicates a typical
outflow geometry that has either a wide opening angle or is widespread. In
either case, the outflows display significant clumping unlike the smooth dust
continuum profiles of these galaxies. Covering fractions of the clumpy
outflows increase with both galaxy infrared luminosity and outflow velocity.

With no evidence and no requirement of AGN feedback needed to drive the
molecular outflows studied in the high–z DSFG sample, and with only one
tentative detection of OH absorption in a QSO at $z{>}6$, there is a clear gap
in our understanding of how and if AGN activity contributes to the ejection of
molecular outflows in the early universe. In this paper we present molecular
gas observations of the 119 $\mu$m OH doublet in three luminous $z{>}6$ QSOs
and their FIR bright host galaxies: J231038.88+185519.7 (hereafter J2310+1855,
z=6.00282), PSO J183.1124+05.0926 (hereafter P183+05, z=6.43862) and PSO
J036.5078+03.0498 (hereafter P036+03, z=6.54052).

Table 1: QSO Host Galaxy Properties From the Literature.

Name | $\rm z_{[CII]}$ |  | $\rm L_{\rm[CII]}$ | $\rm L_{\rm FIR}$ | $\rm M_{1450}$ | $\rm M_{\rm gas}$ | $\rm M_{\rm dyn}$ | $i$ | $\rm v_{\rm rot}$ | $\rm v_{\rm rot}/\sigma_{\rm V}$
---|---|---|---|---|---|---|---|---|---|---
|  | $\rm[kpc\ ^{\prime\prime-1}]$ | $\rm 10^{9}[L_{\odot}]$ | $\rm 10^{12}[L_{\odot}]$ | [mag] | $\rm 10^{10}[M_{\odot}]$ | $\rm 10^{10}[M_{\odot}]$ | [deg] | [km s-1] | [km s-1]
J2310+1855 | $6.00282^{\rm\ d}$ | 5.84 | $8.83\pm 0.44^{\rm\ c}$ | $15.0^{+0.39\rm\ e}_{-0.33}$ | $-27.75^{\rm\ d}$ | $4.4\pm 0.2^{\rm\ e}$ | $5.2^{+2.3\rm\ e}_{-3.2}$ | $25^{\rm\ e}$ | $\simeq 347^{\rm\ e}$ | $\sim 6^{\rm\ e}$
P183+05 | $6.43862^{\rm\ b}$ | 5.61 | $7.15\pm 0.32^{\rm\ b}$ | $10.53\pm 0.36^{\rm\ b}$ | $-26.99^{\rm\ d}$ | $5.0^{+27.8\rm\ a}_{-2.1}$ | $>13.0^{+7.8\rm\ a}_{-9.1}$ | $<22^{\rm\ a}$ | $>320^{\rm\ a}$ | $2.29^{\rm\ a}$
P036+03 | $6.54052^{\rm\ b}$ | 5.56 | $3.38\pm 0.09^{\rm\ b}$ | $5.77\pm 0.12^{\rm\ b}$ | $-27.28^{\rm\ d}$ | $2.8^{+15.4\rm\ a}_{-1.1}$ | $2.9^{+1.1\rm\ a}_{-0.7}$ | $21^{+5\rm\ a}_{-4}$ | $200^{+50\rm\ a}_{-30}$ | $3.21^{\rm\ a}$

Note. — Properties of the QSOs and host galaxies taken from the literature. To
obtain $\rm L_{\rm FIR}$ for J2310 we find the conversion between $\rm L_{\rm
TIR}$ and $\rm L_{\rm FIR}$ using the modified blackbody component of the
best-fit SED of Tripodi et al. (2022). This gives $\rm L_{\rm TIR}/L_{\rm
FIR}=1.6$. References: a) Neeleman et al. (2021), b) Venemans et al. (2020),
c) Wang et al. (2013), d) Mazzucchelli et al. (2017), e) Tripodi et al.
(2022).

In Sec. 2 we present the ALMA band 7 observations, reduction and imaging of
the OH 119$\mu$m line and continuum in these sources. In Sec. 3 we explore the
spectral properties of the OH line and relationship to host galaxy properties,
making comparisons to the high–z DSFG sample of Spilker et al. (2020a, b) and
low–z sample of Veilleux et al. (2013). In Sec. 4 we derive outflow
properties, consider the driving mechanisms required, as well as the possible
impact on the future of the host galaxy. In Sec. 5 we discuss the the
significance of spectral differences found between the QSO and high–z DSFG
sample and the context of the observed molecular outflows within the evolution
of the host galaxies and QSOs. In Sec. 6 we summarise our conclusions.
Throughout the paper we adopt a flat $\Lambda$CDM cosmology with $\Omega_{\rm
m}=0.307$ and ${\rm H_{0}=67.7\ km\ s^{-1}\ Mpc^{-1}}$ (Planck Collaboration
et al., 2016).

##  2 Sample, Observations and Imaging

The data presented in this paper were taken as part of the ALMA Cycle 6
project 2018.1.01790.S (P.I.: P.P. van der Werf) targeting 3 far–IR bright
QSOs: J2310+1855, first identified in the Sloan Digital Sky Survey (SDSS)
(Jiang et al., 2016), and P183+05 and P036+03, both selected as z–dropouts in
the PanSTARRS1 survey (Chambers et al., 2016) and first reported by
Mazzucchelli et al. (2017) and Venemans et al. (2015), respectively. Bañados
et al. (2019) reported the presence of a damped $\rm Ly\alpha$ absorber (DLA)
in the proximity zone of P183+05, at z=6.40392. At this redshift the OH 119
$\mu$m doublet lies just outside our frequency coverage at 340 GHz,
blue–shifted $-1400\ \mbox{\rm km\ s}^{-1}$ with respect to the systemic
velocity of P183+05’s host galaxy. All three sources have previously been
studied in resolved FIR and [CII] emission with kinematic modelling (Wang et
al., 2013; Bañados et al., 2015; Decarli et al., 2018; Feruglio et al., 2018;
Shao et al., 2019; Pensabene et al., 2020; Venemans et al., 2020; Neeleman et
al., 2021; Tripodi et al., 2022) and observed in various additional lines
(Venemans et al., 2015; Chambers et al., 2016; Jiang et al., 2016; Feruglio et
al., 2018; Li et al., 2020; Bañados et al., 2019; Tripodi et al., 2022; Shao
et al., 2022; Decarli et al., 2022). A summary of key properties taken from
the literature is shown in Tab. 1.

For each source, the ALMA band 7 receivers were tuned such that two
overlapping spectral windows of one sideband covered the OH 119 $\mu\mbox{\rm
m}$ line, with the remaining two spectral windows placed to detect the
underlying dust continuum at high S/N. All sources were observed with 43 ALMA
antennas, in good conditions. Specific details of the observations and imaging
for each source can be found in Tab. 2.

The raw data was reduced using CASA (McMullin et al., 2007) version 5.4.0-70
for J2310+1855 and CASA version 5.4.0-68 for P183+05 and P036+03. All sources
were non-interactively imaged using tclean down to a cleaning threshold of
$1\sigma$ and a robust weighting of 0.5, which was found to optimised the
signal–to–noise without losing significant spatial resolution. We separate the
data into two data cubes for each side band, with no continuum subtraction and
leave the frequency resolution equal to the channel resolution of 15.624464
MHz. The rest–frame 119 $\mu$m continuum map was created using the available
line–free channels in each source.

Table 2: ALMA Observations

|  | J2310+1855 | P183+05 | P036+03
---|---|---|---|---
R.A. | [hh:mm:ss] | 23:10:38.90 | 12:12:26.98 | 02:26:01.88
Dec. | [dd:mm:ss] | +18:55:19.82 | +05:05:33.49 | +03:02:59.39
$\rm t_{obs}$ | [min] | 34.50 | 44.28 | 39.50
Beam | [′′] | $0.56\times 0.48$ | $0.58\times 0.45$ | $0.63\times 0.44$
$\sigma_{\rm cont}$ | [$\rm\mu\rm Jy\ beam^{-1}$] | 3.31 | 0.65 | 0.99
$\Delta{\rm chan}$ | [km s-1] | 13.1 | 13.9 | 14.1
$\overline{\sigma}_{\rm chan}$ | [$\rm\mu\rm Jy\ beam^{-1}$] | 12.5 | 4.18 | 6.48

Note. — $\overline{\sigma}_{\rm chan}$ is the mean channel sensitivity, for a
channel width of $\Delta{\rm chan}$, in the sideband containing the OH
119$\mu$m doublet.

##  3 Results

###  3.1 Spectra and Spectral Fitting

Figure 1: Spectra, with resolution of 15.6 MHz, of the three QSOs in this
paper left to right: J2310+1855, P183+05 and P036+03. Top Panels: ALMA spectra
of the side band covering the OH 119 $\mu$m doublet, as a function of observed
frequency with the underling continuum included. The best fit of each spectra
are over plotted as a solid black line with individual absorption and emission
components shaded in green or blue, respectively. The residuals after
subtracting the best fits is shown at the bottom with the channel by channel
RMS shaded in grey. The rest frequencies of the OH 119 $\mu$m doublets,
assuming the redshifts in Tab. 1, are shown by the vertical dashed lines.
Bottom Panels: The same spectra with the best fit continuum subtracted, shown
as a function of velocity.

The rest frame 119 $\mu$m dust continuum is detected at high S/N and
marginally resolved in each of our sources (Fig. 2). The integrated spectra
shown in Fig. 1 are created by stacking all spaxels with a continuum level
$>8\sigma$ in the corresponding continuum map. This is done for both side
bands. The OH 119$\mu$m doublet is clearly detected in absorption in two
sources (J2310+1855 and P183+05), both blue–shifted with respect to the
systemic velocity of their respective host galaxies. OH 119$\mu$m absorption
is not found at systemic velocities in any of the sources. OH 119$\mu$m is
also detected in emission at systemic velocity in P183+05, forming a P–Cygni
profile in the spectra of this source, and tentatively detected at systemic
velocity in P036+03. This is in contrast with the sample of high–z DSFGs
studied by Spilker et al. (2020a), where OH 119$\mu$m emission was not
detected in any of the sources. We discuss this result in Sec. 5.4.

Figure 2: Maps of the three QSOs in this paper top to bottom: J2310+1855,
P183+05 and P036+03. From the left: 119 $\mu$m continuum intensity maps with
the ALMA beam shown as the white ellipse in the lower left corner. This is
followed by the OH 119 $\mu$m absorption line (J2310+1855 and P183+05) and/or
OH 119 $\mu$m emission (P183+05 and P036+03) line map. Lines are extracted
from channels within the FWHM of the higher and lower frequency doublet, for
the absorption and emission, respectively. The $8\sigma$ continuum level
contour is overplotted in white for all maps, indicating the stacking region
used to create the spectra shown in Fig. 1.

We fit each spectrum across both side bands, with a combination of one or two
double–Gaussians and an underlying linear dust continuum slope. The
corresponding spectral ranges used are 344.0-360.0 GHz, 335.5-351.0 GHz and
330.9-346.5 GHz for J2310+1855, P183+05 and P036+03, respectively. The
double–Gaussian component consists of two Gaussians of equal amplitude and
width, and placed at a fixed rest–frame separation of 4.37 GHz, as required of
the OH $\Lambda$–doublet at the redshift under consideration. The continuum
flux density and slope are left as free parameters as well as the amplitude
and width of the double–Gaussian. The frequency offset of the absorption
features in J2310+1855 and P183+05 is left as a free parameter whilst the OH
emission features in P183+05 and P036+03 are fixed at the systemic velocity of
their hosts. The resulting spectral fits are shown in Fig. 1 along with the
residual spectra. The residuals of J2310+1855 display possible excess
absorption at more blue–shifted velocities than is captured by the single
double–Gaussian fit, possibly indicating an outflow at even higher velocities.
This feature lies at the edge of the side band, however, and additional
observations extending to higher frequencies are needed to confirm an
additional outflow component. The narrow ($108\pm 22\ \mbox{\rm km\ s}^{-1}$)
line width of the tentative OH emission in P036 is comparable to that found
for the weak water vapour emission of the blended $3_{22}-3_{13}$ and
$5_{23}-4_{32}$ $\rm H_{2}O$ transitions (Bañados et al., 2015), which
similarly traces warm, dense molecular gas. The best fit parameter values and
uncertainties for each source are presented in Tab. 3. Line maps, integrated
over the FWHM, are shown in Fig. 2.

As is commonly done in the literature, we derive additional quantities of the
absorption lines from our best fit parameters in order to compare our work
with previous OH studies (Veilleux et al., 2013; Spilker et al., 2020a;
Herrera-Camus et al., 2020). These include the full width half maximum,
equivalent width (EW, equal to optical depth in the optically thin regime) and
three definitions of the absorption line velocity: $v_{50}$, $v_{84}$ and
$v_{max}$, referring to the velocities above which 50%, 84% and 98% of the
absorption lies, respectively. These values are also found in Tab. 3 and
presented in Fig. 3 as functions of FIR luminosity and EW.

Figure 3: Grid of host galaxy and best fit OH 119 $\mu$m absorption spectra
properties. This includes: $\mathbf{v_{50}}$: mean velocity,
$\mathbf{v_{84}}$: velocity above which 84% of the absorption lies,
$\mathbf{v_{max}}$: velocity above which 98% of the absorption lies, FWHM:
full width half maximum of the absorption, EW: equivalent width of the
absorption, $\mathbf{L_{IR}}$: Far Infrared luminosity of the host galaxy,
$\mathbf{\Sigma_{FIR}}$: Infrared surface brightness of the host galaxy given
by $\rm L_{FIR}/(2\pi R_{1/2,cont}^{2})$, $\mathbf{R_{cont}}$: Effective
radius of the 119$\mu$m continuum emission. We show low–z sources in grey,
including both star forming and AGN host galaxies (Veilleux et al., 2013). The
spectral properties are measurements of the total (systemic and blue shifted)
absorption lines. In green we show the high–z DSFG sample studied by Spilker
et al. (2020a, b), further separating this sample into measurements of the
total (systemic and blue shifted) absorption line (dark green
crossed–circles), just the systemic components (dark green open circles) and
just the outflowing components (light green filled). Sources with only an
outflowing component will appear as a light green dot with a dark green
outline. We display a fit to the outflow–only components in each panel
(illustrative only) with a solid line and shade the $1\sigma$ scatter, both in
light green. We include the tentative OH detection in the z = 6.13 QSO, ULAS
J131911+095051 (Herrera-Camus et al. 2020, purple triangle). J2310+1855 and
P183+05 are shown by the filled orange square and triangle, respectively.).

For comparison, Fig. 3 also shows results from previous samples of OH
absorption in star–forming and AGN hosts at both low–z (Veilleux et al., 2013;
Stone et al., 2016), and high–z (Spilker et al., 2020a; Herrera-Camus et al.,
2020). As we are specifically interested in the outflowing molecular gas we
additionally plot the outflow–only components of the high–z DSFGs studied by
Spilker et al. (2020a) (the separate components are not provided for the low–z
sample). The outflow–only components in general show stronger correlations
than the full absorption line values. Furthermore, we find that the strongest
correlation with outflow velocity is associated with $V_{50}$ and not
$V_{max}$, as is found in studies that use the total (systemic and
blue–shifted) absorption lines. The tighter relation found with $V_{max}$ for
the full absorption line may be due to the increasing fractional contribution
of the outflowing gas to the total absorption signature towards more negative
velocities of the absorption line. We provide a fit to the outflow–only
components of the DSFG sample in each panel of Fig. 3 to guide the reader’s
eye when comparing these values with the OH outflows in J2310+1855 and
P183+05. These fits are illustrative only and are not intended to imply true
physical trends in all panels.

A notable difference evident between the OH outflows in the DSFGs and those of
J2310+1855 and P183+05 is the offset to smaller FWHMs at similar $\rm L_{FIR}$
for the two QSOs. The central outflow velocities ($v_{50}$) of the two QSOs
appear on or near the DSFG $v_{50}$ vs $L_{FIR}$ trend. The narrower line
widths of the QSO outflow lines, however, cause the QSO outflows to drift
towards slower than expected velocities for more extreme velocity definitions
($v_{84}$ and $v_{max}$ vs $L_{FIR}$). This is also seen in the plots of EW vs
V.

A second, notable observation is the large EW of the OH absorption in
J2310+1855. Although less extreme in the case of P183+05, the EWs of the OH
absorption lines are relatively larger in both J2310+1855 and P183+05, than
seen in the DSFGs, given the narrower line widths.

Care should be taken when interpreting the position of ULAS J131911+095051
(Herrera-Camus et al., 2020) in Fig. 3 as these values are taken from a single
Gaussian fit. The lower frequency transition of the OH 119 $\mu$m doublet is
likely cancelled out by emission at systemic velocities, as is seen in
P183+05. Some absorption from the higher frequency transition is also likely
lost on the red side of the line, meaning a fit to this absorption feature
alone will underestimate the absorption strength and line width and will
overestimate the blue–shifted velocity offset.

###  3.2 Source Sizes

Figure 4: Radial profiles of the dust continuum (top row) and OH 119 $\mu$m
emission (bottom row) visibilities, using UV bins of width 10 $k\lambda$. Mean
values of the real visibilities in each bin are taken to fit a Gaussian or
combination of a Gaussian and point source profile to each source, which we
over plot in orange/blue along with with the $1\sigma$ uncertainty shaded also
in orange/blue. We show the individual components of the combination fit to
the continuum of P183 with dotted orange curves.

For each source we estimate the size of the 119 µm continuum emitting area.
Taking only line–free channels, the visibilities of each data set are binned
in radial uv bins. We perform the procedure for bins of uv widths of 10, 25
and 50 $k\lambda$ taking the mean value of the real visibilities in each bin.
We perform the fit on the resulting binned data using the scipy’s curve_fit
routine, adopting a scatter in the visibilities as the uncertainty. We fit the
continuum data with (1) a single Gaussian; (2) a combination of Gaussian and a
point source. A single Gaussian fit is preferred for all the sources except
P183+05. We find mean 119 µm continuum half–light radii of $0.109\pm
0.009^{\prime\prime}=637$ pc, $0.228\pm 0.008^{\prime\prime}=1280$ pc and
$0.127\pm 0.004^{\prime\prime}=707$ pc, for J2310+1855, P183+05 and P036+03,
respectively. The errors include the formal uncertainties from curve_fit and
the scatter between different uv-binnings. The results are robust with respect
to the uv bin size. All sources are marginally resolved by the beam as seen by
the distinct drop–off in continuum flux towards larger uv distances in each
source (Fig. 4).

Our measured half–light radii of J2310+1855 and P183+05 are comparable to
previous high resolution measurements of the dust continuum at 260 GHz ($\rm
R_{1/2}=0.11^{\prime\prime}\times 0.095^{\prime\prime}$, Tripodi et al. 2022)
and 158 $\mu$m ($0.225^{\prime\prime}\times 0.175^{\prime\prime}$ Venemans et
al. 2020), respectively. P036+03’s measured half–light radius is large
compared to previous high resolution measurements of
$0.095^{\prime\prime}\times 0.08^{\prime\prime}$ at 158 $\mu$m (Venemans et
al., 2020). All three QSO sizes are within the range reported for the full 27
QSO hosts studied by Venemans et al. (2020) and the high–z comparison sample
of DSFGs (Spilker et al., 2020b).

The same procedure is also applied to continuum subtracted channels within the
FWHM of the lower–frequency line of the OH emission doublet in P183+05, and in
both emission components of P036+03 (bottom row of Fig. 4). This provides an
OH 119 $\mu$m emitting radius of $0.63\pm 0.13^{\prime\prime}=3.54$ kpc for
P183+05. The OH emission is not resolved in the case of P036+03.

###  3.3 Outflow Covering Fractions and Detection Rates

A limiting factor of absorption line work is that only gas lying between the
observer and the background continuum may be detected. For some geometries,
outflowing or inflowing gas may or may not intervene the line of sight (LOS)
and background continuum given particular viewing angles. Consequently, a
non–detection does not immediately imply the absence of an out/inflow.
Likewise, when a detection is made, the observed covering fraction $\rm f_{\rm
cov}$ of the intervening gas (the fraction of the background continuum with an
absorption signature), may not be indicative of the overall $4\pi$ $\rm f_{\rm
cov}$, unless the geometry is known to be isotropic. Assumptions must
therefore be made when converting observed column densities to total,
galaxy–wide masses (see Sec. 4).

Measuring the LOS covering fraction requires resolved observations of the
intervening gas. Our observations do not resolve the structure of the outflows
detected in OH absorption in J2310+1855 and P183+05. We can, however, derive a
hard lower bound on the LOS $\rm f_{\rm cov}$ by assuming an optically thick
outflow and taking the fractional absorption depth of the OH line. This gives
$\rm f_{\rm cov}\geq$25% and 9.4% for J2310+1855 and P183+05, respectively,
which are comparable to the 5-20% fractional depths measured by Spilker et al.
(2020a) for the high–z DSFGs sample.

The spatial resolution achieved by Spilker et al. (2020a) allowed them to
detect distinct clumps in the outflowing OH absorption and measure LOS $\rm
f_{\rm cov}$ between 30-85% in their lensing reconstructions. They note that
these values are upper limits as the individual clumps remain unresolved,
accounting for (at least partially) the discrepancy between LOS $\rm f_{\rm
cov}$ and the aforementioned fractional absorption depths. They argue that the
true covering fractions are likely closer to those estimated from the peak
absorption depth as OH is expected to be highly optically thick. This has
similarly been assumed in low red–shift studies (e.g., González-Alfonso et al.
2017).

In any case, $\rm f_{\rm cov}$ measured by Spilker et al. (2020a) is typically
smaller than the outflow detection rate of 73% in their sample, interpreted by
the authors to imply that the ouflowing gas traced by OH absorption must exit
the galaxies in some ‘fortuitous geometry’, one that does not require a
special viewing angle. Spilker et al. (2020a) also find positive trends
between covering fraction, FIR luminosity and outflow velocity, further
suggesting that more luminous galaxies, capable of driving more extreme
outflows, are either more likely to drive an outflow or drive more widespread
outflows (i.e. wider opening angle/more clumps).

The detection rate of OH outflows in the four currently observed QSOs at $z>6$
is either 50% or 75%, depending on whether we include the tentative outflow
detection in the z = 6.13 QSO ULAS J131911+095051 (Herrera-Camus et al.,
2020). In the following section we use the fractional absorption depth of the
OH line to derive lower limits of the outflow properties. As we can not
measure an upper limit of the covering fraction as Spilker et al. (2020a) did
with their high spatial resolution data, we simply use an upper limit of $\rm
f_{\rm cov}$ of 100%. We caution the reader when interpreting these upper
limits, that a 100% covering fraction is likely unphysical, given the evidence
from the literature that OH traces optically thick, widespread and clumpy
outflows, thus resulting in covering fractions more comparable with that of
the fractional absorption depth.

##  4 Derived Outflow Properties

In this section we derive physical and energetic properties of the molecular
outflows observed in J2310+1855 and P183+05. To compare our outflows with
those found in the sample of high–z DSFGs studied by Spilker et al. (2020a,
b), we recalculate the outflow properties for this sample using the same
methods and assumptions adopted for J2310+1855 and P183+05. We consider only
the blue–shifted outflowing Gaussian component of the OH absorption spectra of
the DSFGs when deriving properties of the outflow and do not include the
systemic gas component. This differs from the approach of Spilker et al.
(2020b), where the outflowing component was defined as absorption seen at
velocities $<-200\ \mbox{\rm km\ s}^{-1}$ in the total (systemic and
outflowing) absorption line.

###  4.1 Outflow Mass, Mass Outflow Rate and Depletion Times

In the optically thin regime, the EW of an absorption line is equal to the
integrated optical depth. In this scenario, the EW can directly replace the
optical depth integrated over velocity, $\int\tau_{\nu}\rm dv$, when deriving
the column density of the OH119 $\mu$m , given by,

$\rm N_{OH}=\int\tau_{\nu}dv\frac{\nu^{3}g_{l}8\pi}{c^{3}A_{ul}g_{u}},$ (1)

where $\nu$ is the rest frequency of the line, $\rm g_{u}=6$ and $\rm g_{l}=4$
are the upper and lower statistical weights and $\rm A_{ul}=10^{-0.86618}\
s^{-1}$ is the Einstein coefficient of the transition. $\rm N_{OH}$ is then
converted to a total molecular hydrogen column density assuming a conversion
factor: here we assume a $\rm N_{OH}/N_{H_{2}}=1\times 10^{-7}$ from Nguyen et
al. (2018).

To convert a column density to a full outflow mass and mass outflow rate, a
geometry of the outflow must first be assumed. Our marginally resolved
observations do not allow a geometry of the outflows observed in J2310+1855
and P183+05 to be determined. We therefore assume a simple spherical thin
shell outflow geometry, commonly used elsewhere in the literature (e.g., Rupke
et al. 2005), which provides a conservative estimate of the mass and mass
outflow rate:

$\displaystyle{\rm\dot{M}_{OF}}$ $\displaystyle=$ $\displaystyle{\rm 4\pi
R_{OF}^{2}\,\mu\,m_{H_{2}}\,f_{cov}\,N_{H_{2}}\frac{V_{OF}}{R_{OF}}}={\rm\frac{M_{OF}V_{OF}}{R_{OF}}}$
(2)

where $\mu=1.36$ accounts for the universal helium fraction, R is the outflow
radius, assumed to be $R_{cont}$, V is the outflow velocity $V_{50}$ and
$f_{cov}$ is the covering fraction of the outflowing gas.

As discussed in Sec. 3.3, we can not measure $f_{cov}$ with our spatially
unresolved data. Thus, for the purpose of simply comparing our two QSOs and
with the sample of DSFGs, we derive all values of $\rm\dot{M}_{OF}$ using
$f_{cov}=1$, providing upper limits on $\rm{M}_{OF}$ and $\rm\dot{M}_{OF}$ for
the given geometry. For J2310+1855 this gives $\rm{M}_{OF}<99\times
10^{8}M_{\odot}$ and $\rm\dot{M}_{OF}<5300\ M_{\odot}yr^{-1}$ and for P183+05
$\rm{M}_{OF}<140\times 10^{8}M_{\odot}$ and $\rm\dot{M}_{OF}<5900\
M_{\odot}yr^{-1}$.

Figure 5: Mass outflow rate as a function of far infrared luminosity (bottom
axis) and star formation rate (top axis), assuming a spherical thin shell
geometry for all sources. We show the DSFGs (Spilker et al., 2020a, b) in
green assuming a covering fraction of 1 (filled) as upper limits and 0.3
(hollow) based on the average covering fractions measured for low–z star
forming–galaxies (González-Alfonso et al., 2017). We show a fit to the
$f_{cov}=1$ points with the solid green line and its $1\sigma$ spread with a
shade green region. A fit to the $f_{cov}=0.3$ points is shown by the dashed
green line. We indicate J2310+1855 and P183+05 with an orange square and
triangle, assuming a covering fraction of 1 (filled) as upper limits and at
the level of their fractional OH absorption depths, 25% and 9.4% (hollow),
respectively. The SFR=$\rm\dot{M}_{OF}$ line is shown by the grey dotted line.

Fig. 5 presents the derived values of $\rm\dot{M}_{OF}$ as a function of $\rm
L_{FIR}$ (SFR). As previously reported by Spilker et al. (2020b), the DSFGs
with larger $\rm L_{FIR}$ drive outflows with higher $\rm\dot{M}_{OF}$.
Focusing on the upper limit relations, we find J2310+1855 and P183+05 both sit
above the DSFG relation. We note however that there is only one DSFG in the
$\rm L_{FIR}$ range of the two QSO hosts, and therefore we do not view the QSO
offsets to higher $\rm\dot{M}_{OF}$ as significant. In fact if the highest
$\rm L_{FIR}$ DSFG is removed then a fit through the remaining DSFGs will
extrapolate between the two QSOs. With the assumed geometry and a $f_{cov}=1$,
we derive $\rm\dot{M}_{OF}$s greater than the SFRs in both QSOs, giving lower
limits on the gas depletion time of $\rm\tau_{OF}>8.3\ Myr$ and
$\rm\tau_{OF}>8.4\ Myr$ for J2310+1855 and P183+05, respectively. If star
formation is included and assumed to remain constant, the combined depletion
times reduce to $\rm\tau_{OF+SFR}>4.9\ Myr$ and $\rm\tau_{OF+SFR}>6.1\ Myr$
for J2310+1855 and P183+05, respectively.

González-Alfonso et al. (2017) found an average $f_{cov}$ for OH absorption in
their low–z star–forming galaxies of 0.3, which if adopted here would shift
all but one of the DSFG and both QSO $\rm\dot{M}_{OF}$s below the
$\rm\dot{M}_{OF}=SFR$ line. Whether $f_{cov}=0.3$ is a suitable covering
fraction for high–z galaxies and moreover high–z QSOs, is still yet to be
shown. As mentioned in Sec. 3.3, however, the fractional absorption depths of
the OH absorption lines provides a hard lower limit of $f_{cov}$, which in
turn can be used to derive a lower limit of $\rm{M}_{OF}$ and
$\rm\dot{M}_{OF}$. This gives $\rm{M}_{OF}>25\times 10^{8}\ M_{\odot}$ and
$\rm\dot{M}_{OF}>1300\ M_{\odot}yr^{-1}$ for J2310+1855 and
$\rm{M}_{OF}>13\times 10^{8}\ M_{\odot}$ and $\rm\dot{M}_{OF}>560\
M_{\odot}yr^{-1}$ for P183+05 This corresponds to outflow depletion timescales
of $\rm\tau_{OF}<33\ Myr$ and $\rm\tau_{OF}<90\ Myr$ and combined timescales
of $\rm\tau_{OF+SFR}<8.8\ Myr$ and $\rm\tau_{OF+SFR}<18\ Myr$ for J2310+1855
and P183+05, respectively.

###  4.2 Outflow Energetics

The energy ${\rm\dot{E}_{OF}}$ and momentum ${\rm\dot{p}_{OF}}$ flux of an
outflow can provide insight into the mechanisms needed to drive it. We derive
both these values, for J2310+1855, P183+05 and the DSFGs with the same size
and geometrical assumptions used to derive $\rm\dot{M}_{OF}$, giving

$\displaystyle{\rm\dot{E}_{OF}}$ $\displaystyle=$
$\displaystyle{\rm\frac{1}{2}\dot{M}_{OF}V_{OF}^{2}}$ (3)
$\displaystyle{\rm\dot{p}_{OF}}$ $\displaystyle=$
$\displaystyle{\rm\dot{M}_{OF}V_{OF}}.$ (4)

As in the last section, we derive these values assuming a covering fraction of
1 for all objects to compare between the DSFGs and the QSOs and again with
$\rm f_{\rm cov}=0.3$, for the DSFGs, and with the fractional absorption
depths of the two QSOs as lower limits (Fig 6). This gives limits of the
energy fluxes of $\rm 4.7\times 10^{43}\ ergs^{-1}<{\rm\dot{E}_{\rm
OF}}<19\times 10^{43}\ ergs^{-1}$ and $\rm 5.0\times 10^{44}\
ergs^{-1}<{\rm\dot{E}_{OF}}<530\times 10^{44}\ ergs^{-1}$, and of the momentum
fluxes of $\rm 28\times 10^{36}\ dyne<{\rm\dot{p}_{OF}}<110\times 10^{36}\
dyne$ and $\rm 19\times 10^{36}\ dyne<{\rm\dot{p}_{OF}}<200\times 10^{36}\
dyne$, for J2310+1855 and P183+05, respectively.

Again focusing on the upper limit relations: the DSFG sample displays a clear
positive trend for both fluxes with $L_{IR}$. The QSOs sit below and above
these relations for J2310+1855 and P183+05, respectively. J2310+1855’s
deviation below the $\rm L_{FIR}$-${\rm\dot{E}_{OF}}$ relation, however, is
particularly significant. For all sources, the energy and momentum injected by
star formation is sufficient to drive the observed outflow, even at the upper
limit values. This is perhaps surprising for J2310+1855 and P183+05, where
feedback from both star formation and the central AGN is available and may
have been expected to collectively drive a stronger outflow than star
formation alone. In Sec. 5 we discuss possible explanations for why we do not
see evidence of an AGN contribution and instead see the opposite in the case
of J2310+1855.

Figure 6: Energy (top) and momentum (bottom) flux as a function of $\rm
L_{FIR}$ (bottom axis) and SFR (top axis) derived for the comparison sample of
high–z DSFGs (Spilker et al., 2020a, b) (green) and J2310+1855 and P183+05
(orange squares and triangles, respectively). Filled symbols indicate upper
limits, assuming an outflow covering fraction of 1. Hollow symbols indicate
lower limits for J2310+1855 and P183+05, assuming a covering fraction equal to
the fractional OH absorption depth (25% and 9.4%, respectively), and values
derived assuming an average covering fraction of 0.3 (González-Alfonso et al.,
2017), for the DSFG sample. The smaller faint orange symbols indicate ranges
for J2310+1855 and P183+05 assuming a 50% AGN contribution to $\rm L_{FIR}$
(see text). We indicate regions in the top panel where the energy injected via
star formation, assuming a maximum coupling fraction to the ISM of 40% (Sharma
et al., 2014; Fielding et al., 2018), is equal to the energy flux of the
outflow (white), where an unusually high coupling fraction or AGN contribution
is required (light grey), and where an AGN is definitely required (darker
grey). We indicate regions in the bottom panel where SNe ejecta provide
sufficient momentum (white) and where radiation pressure on dust grains in an
optically thin (light grey) or thick (darker grey) outflow is needed.

###  4.3 Escape Fractions

Not all material ejected via an outflow will escape the host galaxy or the
dark matter halo’s gravitational potential. Instead some fraction of the
material will remain bound to the galaxy and may re–accrete via a galactic
fountain at a later time, unless further heating or acceleration is
experienced. Some fraction of the outflow, however, may be sufficiently
accelerated to pollute the CGM or even IGM, removing mass, momentum and metals
from the galaxy altogether. Below we attempt to estimate a possible escape
fraction of the molecular outflow in our two QSOs.

Assuming that the outflow is at a radius of $\rm R_{cont}$ and that the
outflow will not be decelerated by swept up material, or accelerated by
radiation pressure, the dynamical masses (Table 1) are enough to retain
effectively all of the outflowing molecular gas in both J2310+1855 and
P183+05.

Table 3: Measured and Derived Host Galaxy and Outflow Properties

|  | J2310+1855 | P183+05 | P036+03
---|---|---|---|---
119 $\mu$m Contintuum
$\rm R_{\rm 1/2,119\ \mu m}$ | [pc] | $637\pm 53$ | $1280\pm 45$ | $707\pm 22$
$\rm S_{\rm 119\ \mu m}$ | [mJy] | $4.73\pm 0.0016\ $ | $6.66\pm 0.0010\ $ | $5.00\pm 0.0020$
OH 119 $\mu$m Emission (systemic)
$\rm S_{\rm OH\ 119\ \mu m}$ | [Jy km s-1] | – | $0.28\pm 0.028$ | $0.12\pm 0.022$
$\sigma_{\rm Emis.}$ | [km s-1] | – | $123\pm 13$ | $45.9\pm 9.5$
$\rm FWHM_{\rm Emis}$ | [km s-1] | – | $289\pm 31$ | $108\pm 22$
OH 119 $\mu$m Absorption (outflow)
$\rm S_{\rm OH\ 119\ \mu m}$ | [Jy km s-1] | $-0.42\pm 0.04$ | $-0.19\pm 0.03$ | –
$\rm N_{\rm OH\ 119\ \mu m}$ | $[10^{15}\ \rm cm^{-2}]$ | $8.90\pm 2.1$ | $3.10\pm 0.059$ | –
$\rm EW_{\rm OF}$ | [km s-1] | $619\pm 140$ | $215\pm 4.1$ | –
$\sigma_{\rm OF}$ | [km s-1] | $140\pm 12$ | $123\pm 19$ | –
$\rm FWHM_{\rm OF}$ | [km s-1] | $330\pm 29$ | $290\pm 45$ | –
$\rm V_{\rm 50}$ | [km s-1] | $-334\pm 14$ | $-534\pm 18$ | –
$\rm V_{\rm 84}$ | [km s-1] | $-473\pm 21$ | $-656\pm 79$ | –
$\rm V_{\rm max}$ | [km s-1] | $-622\pm 85$ | $-787\pm 222$ | –
$\rm M_{\rm OF}$ | $[10^{8}\ \rm M_{\odot}]$ | $25-99$ | $13-140$ | –
$\rm\dot{\rm M}_{\rm OF}$ | $[\rm M_{\odot}\ \rm yr^{-1}]$ | $1300-5300$ | $560-5900$ | –
$\rm\dot{\rm p}_{\rm OF}$ | $[10^{35}\ \rm dyne]$ | $28-110$ | $19-200$ | –
$\rm\dot{\rm E}_{\rm OF}$ | $[10^{43}\ \rm erg\rm s^{-1}]$ | $4.7-19$ | $5.0-530$ | –
$\rm\tau_{\rm OF}$ | [Myr] | $8.3-33$ | $8.4-90$ | –
$\rm\tau_{\rm OF+SFR}$ | [Myr] | $4.9-8.8$ | $6.1-18$ | $23$

Note. — Measured properties of the 119 $\mu$m dust continuum (size and flux),
OH emission and absorption lines (with formal uncertainties from the fitting
procedure), and derived properties of the molecular outflows.

##  5 Discussion

We begin our discussion by first summarising the known properties of the
high–z DSFG sample and their molecular outflows (Spilker et al., 2020a, b).
The spatial resolution of their observations were capable of resolving several
distinct clumps in the blue–shifted OH absorption, in contrast to the
generally smooth background dust continuum. Although not capable of resolving
the clumps themselves, Spilker et al. (2020a) use optical depth arguments to
predict a substantially more clumpy structure on scales of $\sim 50$–200 pc.
The comparatively high detection rate of molecular outflows in the sample
compared with the measured covering fractions suggest a ‘fortuitous’ geometry
of the outflows, such that at least a fraction of the outflow is likely to
intervene the line of sight and background continuum, regardless of viewing
angle. Moreover, higher outflow covering fractions and higher detection rates
are found in sources with higher $\rm L_{IR}$, suggesting that more IR
luminous galaxies are capable of driving either more widespread outflows,
outflows with larger opening angles, or larger clump sizes. All three
scenarios are consistent with the observed increase in FWHM and EW of the
outflowing absorption signature towards higher $\rm L_{IR}$ (Fig. 3). Lastly,
they find that the optical depths of the outflowing clumps often peak towards
the outskirts of the background continuum, offset from the peak in continuum
emission. Whether this is the result of a clumpy expanding shell or the
removal of more easily ejected gas at lower column densities found at larger
radii, remains unclear.

###  5.1 What Drives Molecular Outflows in Unobscured QSO Hosts?

When treated under the same assumptions, the OH molecular outflows observed in
J2310+1855 and P183+05, are less or comparably energetic to those driven by
the high–z DSFGs (Fig. 6). This is despite harbouring comparable SFRs and an
additional luminous AGN.

Returning to Fig. 3, we highlight the key difference in basic host galaxy and
blue shifted absorption properties between the QSOs and the DSFG sample.
Firstly, both QSOs display narrower than expected absorption signatures for
their $\rm L_{IR}$ when compared to the DSFG sample. This may be due to a more
cohesive outflow velocity structure (i.e., sheet), fewer velocity components
contributing to the overall absorption signature (fewer clumps) or an overall
less turbulent outflow. P183+05 consistently deviates towards narrower FWHMs
from all of the DSFG relations, but does not significantly deviate in any
other way with regards to both outflow and host galaxy properties. J2310+1855,
on the other hand, deviates in three additional ways, 1) towards much higher
outflow absorption strengths (EW), 2) towards slower outflow velocities and 3)
towards a smaller dust continuum size, giving J2310+1855 the highest FIR
surface brightness of both samples. We investigate the possible effects of the
dust continuum size in Sec. 5.3.

Our upper limits on the outflow $\dot{M}_{OF}$ and energetics, assuming a
covering fraction of 100% around J2310+1855 and P183+05, provide values within
the range where the star formation in these systems is sufficient. Not only is
additional energy or momentum from an AGN simply not required to drive these
outflows, but the fact that J2310+1855 and P183+05’s do not even appear to be
boosted with respect to the DSFGs in energetics, $\dot{\rm M}_{OF}$ or
velocity, suggests that these outflows may indeed be driven by the same
mechanisms – those associated with star formation.

###  5.2 Interaction Between Central AGNs and the Surrounding ISM

At low–z, it is consistently found that higher AGN fractions and luminosities
drive faster and more energetic molecular outflows (Sturm et al., 2011; Spoon
et al., 2013; González-Alfonso et al., 2017). Outflow properties also
correlate best with AGN luminosity or AGN fraction, whilst only weakly
correlating with the star–forming properties of the host galaxy (Calderón et
al., 2016). Studies measuring 9.7$\mu$m silicate absorption, which indicates
the degree of obscuration originating in the nuclear torus and/or host galaxy
disk find strong correlations with the strength of the OH absorption
(equivalent width) (Stone et al., 2016; Veilleux et al., 2013; Spoon et al.,
2013). Together, these results suggest that not only the strength of the
radiation field, be it from star–formation or an AGN, but the obscuration and
thus ability of these energy and momentum sources to couple with the
surrounding ISM, is crucial in driving a strong molecular outflow. Indeed
González-Alfonso et al. (2017) find in their sample of 14 local Ultraluminous
Infrared Galaxies, that the highest molecular outflow velocities traced by OH
absorption are found in buried sources, where slower but more massive
expansion of the nuclear gas is found.

But how comparable are low–z AGN hosts compared with our high–z unobscured
QSOs? The entire sample studied by González-Alfonso et al. (2017) were
galaxies undergoing gas–rich mergers, and indeed AGNs found in the low–z
universe are ubiquitously inbedded in such host galaxies (Sanders & Mirabel,
1996), where AGN feedback is thought to be stochastically injected into the
chaotic surrounding ISM throughout the merging process (González-Alfonso et
al., 2017). The three $z>6$ QSOs studied in this paper, however, all display
signatures of orderly, rotationally dominated gas reservoirs (Tab. 1, Neeleman
et al. 2021; Tripodi et al. 2022), opposing a merger scenario. As unobscured
QSOs, they have already removed the obscuring material surrounding the AGN,
clearing a path through the ISM along the line of sight (note: this need not
be aligned with the host galaxy).

At high–z, the interaction between central AGNs and their host galaxies is a
matter under investigation. Rojas-Ruiz et al. (2021) found that strong
synchrotron emission extending into mm-wavelengths in the radio-loud QSO PSO
J352.4034–15.3373 contributed significantly to its FIR luminosity. This
source, however is one of the brightest radio-loud sources in the early
universe and the subsequent study of Khusanova et al. (2022), considering five
radio-loud $z>6$ QSOs, found that the SFR distribution and [CII] luminosities
of their sources were comparable with the radio-quiet population, suggesting
that radio jets to not contribute significantly to these properties.

Significant AGN contributions to the FIR luminosity via dust heating has been
measured in some high–z QSOs. Schneider et al. (2015) found an AGN
contribution between 30-70% in the $z=6.4$ QSO J1148+5251. Although chosen as
a prototype for the general population of high–z QSO, this source harbours an
X-ray luminosity twice that of J2310+1855 and has been detected in CO(17-16)
(Gallerani et al., 2014) which remains undetected in J2310+1855. Carniani et
al. (2019) inspected the CO SLEDs and FIR properties of these sources and
concluded that the differences found were likely due to different gas heating
mechanisms present, those being mechanisms associated with the central AGN for
J1148+5251 and star formation in J2310+1855. Decarli et al. (2022) similarly
find, using multi-line diagnostics and the non-detection of high-J CO
transitions, that star formation also appears to drive the molecular gas
excitation in P183+05. Duras et al. (2017) found an average AGN contribution
of 50% in their sample of 16 IR–bright QSOs. This sample was chosen to
represent an intermediate population of QSOs emerging from the heavily
obscured phase, but preceding the blue QSO phase where intervening material
has already been swept away. This again differs from the population of
unobscured, UV and FIR bright QSOs represented by our QSOs.

In a luminosity–limited sample of $z>6$ unobscured QSOs (including our
sources), no correlation is seen between quasar UV luminosity ($M_{1450}$, see
Tab. 1) and FIR luminosity (Venemans et al., 2018). This is true even in the
central regions surrounding the QSOs (Venemans et al., 2020), suggesting
little interaction between the QSOs and host galaxy ISM. Our assumption that
the SFR dominates the ${\rm L_{FIR}}$ of our sources is thus likely a good
assumption and it is perhaps also unsurprising that we do not find evidence of
a boost in the molecular outflow properties measured and derived for our
unobscured QSO hosts, compared to the DSFG sample.

In any case, we can not rule out a contribution from the AGN to the FIR
luminosity with this information alone, nor can we ignore the large
uncertainties associated with estimating this value (Venemans et al., 2018,
2020; Tripodi et al., 2022). Therefore, as an extreme case, we consider an AGN
contribution of 50% to the ${\rm L_{FIR}}$, as found for high–z BAL QSOs
(Duras et al., 2017). We expect, for the reasons stated above, that this value
is an upper limit of the AGN contribution for our unobscured sources. This
effect would move our sources left, by half, in Fig.s 5, 6 and in the left two
columns of 3, if one is to consider only the input from star formation. In
Fig. 3 (note log scales), this makes little difference to our conclusions. In
Fig.s 5 and 6, P183+05 indeed begins to appear more energetic than expected
for its SFR, if it is assumed that all the sources have an outflow covering
fraction of 100%. This moves the upper limit of the energy flux within the
‘high coupling efficiency or AGN required’ region (indicated by the smaller
faint orange symbols). We remind the reader that a covering fraction of 100%
is an extreme scenario, with the true values expected to be close to the
fractional absorption depth, which in the case of P183+05 is only 9.5%.
Assuming an AGN contribution to the FIR of 50%, a high coupling efficiency or
an AGN contribution to drive the molecular outflow seen in P183+05 is not
required unless the outflow covering fraction is $\geq 53\%$. This is higher
than all of the absorption depths measured by Spilker et al. (2020a) for
outflowing or systemic gas in their sample. Thus, whilst it is possible the
molecular outflow in P183+05 lies in the parameter space requiring either a
high coupling fraction or an AGN contribution, this would require either a
significant AGN contribution to the FIR luminosity and/or a high outflow
covering fraction ($\geq 53\%$). For reasons stated above we believe both the
condition of a significant $\rm L_{FIR}$ AGN contribution and/or high covering
fraction to move P183 into this parameter space to be unlikely, but do not
rule it out. For our other source, J2310+1855, a $\rm L_{FIR}$ 50% AGN
contribution does not display higher than expected values and does not require
a high coupling efficiency or AGN contribution even with a 100% outflow
covering fraction. In summary, an AGN contribution to the driving of the
molecular outflow in J2310+1855 is not required and is only possibly required
in P183 under particular extreme scenarios.

Recent results studying the ionised gas phase, however, have found extremely
fast outflows up to 17% the speed of light in $z\sim 6$ QSOs using CIV
absorption (Bischetti et al., 2022). Such outflows must transport enormous
amounts of energy into the circum– and intergalactic–medium from the central
engine. Included in this sample is J2310+1855, with a detected ionised gas
outflow travelling between 18500-27000 km s-1. Although clearly not associated
with the molecular outflowing gas travelling at just $\sim 300\mbox{\rm km\
s}^{-1}$, this may suggest a scenario where a combination of star formation
driven molecular outflows and AGN driven ionised outflows work in conjunction
to quench these massive active galaxies and transfer energy to atomic outflows
found at higher radii in the surrounding halos of diffuse turbulent gas (as
found in J2310+1855 in OH+ (Shao et al., 2022)). As seen in low–z studies,
molecular gas outflows dominate the mass and momentum transport of matter out
of the galaxy, whilst the warmer ionised phases dominate the kinetic energy
budget (Fluetsch et al., 2021). The molecular outflows presented here are
indeed capable of transporting large amounts of gas, providing short depletion
times on the order of Myrs predicted for these galaxies (Simpson et al., 2012;
Costa et al., 2018). As discussed in Sec. 4.3, however, a negligible fraction
of the outflowing molecular gas will escape the gravitational bind of their
host galaxy, and will be re–accreted unless additional energetic input is
provided at higher radii. Thus, whilst the molecular phase may predominantly
remove the fuel for future star formation directly from the galaxy, the
ionised phase may be responsible for keeping that material at higher radii by
efficiently injecting energy into the CGM and thus providing a scenario where
these massive gas rich galaxies can quench on short timescales.

During the QSOs’ embedded or blowout phase, however, trapped radiation from
the central engine may play a much greater role in launching molecular
outflows (Costa et al., 2018). Observing QSOs in these early stages will
therefore be crucial in our studies determining the full impact of QSOs on
their surrounding ISMs and the role they play in ejecting gas from the galaxy.

###  5.3 The Background Dust Continuum and its Effect on the Outflow
Absorption Signature

The conclusion of the previous subsection does not, however, explain the
differences in spectral properties of the OH outflows observed between our
$z>6$ QSO and the high–z DSFGs. The combination of narrower line widths and
comparable or higher EWs of the total outflow absorption may imply an increase
in outflow covering fraction or clump positions that preferentially block
brighter regions of the background dust emission. Both scenarios may be true
in the case of J2310+1855 whose small 119 $\mu$m dust size and high surface
brightness (Fig. 3) means any clumps intervening the line of sight will have
the tendency to cover brighter regions, and will block a larger fraction of
the overall surface area. For galaxy disks at higher inclinations in the
observer’s line of sight, such effects of intervening clouds are further
intensified.

Figure 7: Idealised schematic of two equally luminous disky galaxies (left and
right) seen at four different inclinations (from the top: $0^{\circ}$,
$30^{\circ}$, $60^{\circ}$ and $90^{\circ}$). We consider a clumpy outflow
ejected from the center of the galaxy, travelling radially in five angles
covering the left hand side of the disk, and vertically through a galactic
fountain trajectory. On the right we show this trajectory as a solid black
arrow. Orange circles indicate clumps that intervene the observer’s line of
site and the background continuum, and thus contribute to the absorption
signature of the outflow. Grey circles indicate when clumps do not intervene
and are invisible to the observer via absorption.

We illustrate this effect in Fig. 7, for two galaxies of equal luminosity but
different size (different surface brightness), observed at four different
inclinations. We consider the effect of the background continuum size and
inclination on the observability of foreground clumps travelling in a galactic
fountain trajectory, ejected from the center of the galaxy. We show this
trajectory for five radial directions but note that clumps may be ejected from
anywhere in the galactic plane and travel outwards in any direction. Clumps
that intervene the observer’s line of sight and background dust continuum and
are therefore observable via absorption are coloured orange. We find that for
smaller disk sizes and higher inclinations, absorption line observations
become limited to clumps at low radial distances or those lying more towards
the foreground. Individual clumps in these circumstances cover a greater
fraction of the background dust area, tend to block regions of higher surface
brightness and thus imprint a stronger absorption signature on the global
spectrum. Fewer clumps are therefore needed to absorb the same or more
background emission, limiting the number of velocity components contributing
to the velocity dispersion of the global absorption line.

Without resolving the molecular outflow we can not say for certain what the
geometry or trajectory of the outflowing gas is. Fig. 7 does, however,
illustrate that clumps at smaller scale heights are preferentially observed.
If a clump is initially ejected perpendicular from the disk (the center or
farther out), and then continues along a trajectory that deviates from this
initial direction, (such as the fountain scenario depicted in Fig. 7), the
restriction of our observations to low altitude clumps also restricts our
observations to clumps with higher perpendicular velocities. The combined
outflow velocity therefore becomes more dependent on the inclination of the
disk.

Thus, the smaller disk size of J2310+1855 may therefore cause the absorption
signature to be more sensitive to projection effects, contributing to the
offset in outflow velocity shown in the first panel of Fig.3. Neither
J2310+1855 or P183+05, however, are found to have significantly inclined disks
($25$ and $<22$ deg), and so it is not expected that projection effects play a
dominating role in the slower than expected outflow velocities. We note,
however, that Tripodi et al. (2022) found similar results for their dynamical
models of J2310+1855 for inclinations over the range of [20, 45] deg and
earlier dynamical modelling by Feruglio et al. (2018) using lower resolution
data have previously found a higher inclination of 53 deg. Tripodi et al.
(2022) discarded models with $i>30$ deg due to the gas mass exceeding the
dynamical mass, however, this cut off is dependent on the reliability and
suitability of the CO conversion factor for a high–z unobscured QSO. In the
case of P183+05, which does not display an unusually small continuum size and
has only an upper limit on the host galaxy inclination, it is unclear what
causes the smaller than expected FWHM of the absorption line and we do not
rule out simple natural variance.

Small QSO host dust sizes have been measured in a number of samples at high–z
(Ikarashi et al., 2015; D’Amato et al., 2020; Venemans et al., 2020; Stacey et
al., 2021), although evidence for an additional shallower extended component
is found in the stacking of 27 $z\geq 6$ QSO hosts (Novak et al., 2020).
Stacey et al. (2021) divided their z=1.5-2.8 QSO hosts into two categories:
those exhibiting a clumpy dust distributions, with sizes and star formation
rate densities typical of sub–mm–selected DSFGs, and those with no evidence of
clumpy features and characterised by compact ($\rm R_{eff}<1\ kpc$) sizes and
high star formation densities. The latter category is believed to indicate a
phase of dissipative contraction before becoming compact spheroids, and
describes both the QSO hosts presented in this paper and the DSFGs presented
by Spilker et al. (2020a). The optical/infrared sizes of QSO hosts at $z\sim
1.5$ (Silverman et al., 2019), place them between main sequence and quiescent
galaxies, whilst Ikarashi et al. (2015) found in their sample of $z\sim 1$–3
QSOs and starbursts, that composite sources harbour the smallest sub–mm dust
sizes. While all three of our QSO sources lie within the range of dust
continuum sizes of the DSFG comparison sample, they do lie at the extreme end
of the surface brightness. In particular, J2310+1855 exhibits a much smaller
continuum size for its infrared luminosity and the highest surface brightness
of the two samples, possibly indicating that this source is in a more advanced
stage in the transformation into a quiescent spheroidal, consistent with the
shorter depletion timescale estimated for this source. We note again that our
size estimate of P036+03 was significantly larger than previous measurements
(Venemans et al., 2020) which would instead make P036+03 our most compact
source, and possibly also further along in its dissipative collapse. This may
also provide an explanation for the absence of OH 119 $\mu$m absorption in
P036+03, as outflows from a more evolved system may have travelled farther
away from the bright central region, and a more compact background emission
decreases the total area in which an outflow may be observed. The combination
of these effects would decrease the likelihood of an outflowing component
intercepting the line of sight with the background continuum.

###  5.4 OH 119 $\mu$m Emission

OH 119 $\mu$m emission has been detected in many of the low–z galaxy samples
(Sturm et al., 2011; Veilleux et al., 2013; Spoon et al., 2013; Stone et al.,
2016; Calderón et al., 2016), and is typically associated with the presence of
an AGN. AGN fraction, and not simply AGN luminosity, was found to be key in
setting the OH 119 $\mu$m character (relative strength of emission to
absorption) (Veilleux et al., 2013; Stone et al., 2016). In the most AGN
dominated systems where OH is seen purely in emission, Veilleux et al. (2013)
notes that the line–widths remain modest, possibly indicating a phase after
which the galaxy has cleared away the obscuring molecular gas.

Deeper 9.7 $\mu$m silicate absorption (a measure of obscuration in both
nuclear torii and host galaxy disks) has been found to correlate with fainter
OH 119 $\mu$m emission and deeper OH 119 $\mu$m absorption, indicating that OH
119 $\mu$m emission is strongly affected by the geometry of the obscuring
material (Stone et al., 2016). Whilst earlier studies argued that OH 119
$\mu$m emission originates from the buried nuclear regions of galaxies (e.g.,
Spoon et al. 2013), where radiative pumping would predominantly excite the OH,
Stone et al. (2016) later showed that in some Type 2 AGNs (where the nucleus
is obscured), and where the silicate 9.7 $\mu$m line is found in absorption,
some of the OH 119 $\mu$m is still found in emission. Given the apparent
impact of obscuring material on OH 119 $\mu$m emission this may imply that the
OH 119 $\mu$m emission also originates farther out than the nucleus, such as
in the circumnuclear starburst. Here, physical conditions favor collisional
excitation over radiative pumping. Similar conclusions have emerged from a
studies measuring the relative strengths of OH transitions (e.g. in NGC 1068
Spinoglio et al. 2005) and in studies using both silicate absorption and multi
OH transition data (Runco et al., 2020).

OH 119 $\mu$m emission was not detected in any of the Spilker et al. (2020a)
high–z DSFGs, consistent with their measured subdominant AGN fractions (all
upper limits). OH 119 $\mu$m emission is likely present in the z = 6.13 QSO
ULAS J131911+095051 (Herrera-Camus et al., 2020), causing the blue–shifted
absorption observed in it’s spectra to exhibit only a single absorption peak,
due to superimposed emission and absorption of the low and high frequency
doublet transitions, respectively. A similar scenario is more clearly observed
in P183+05 of our sample. Tentative emission is also detected in a second of
our sources, P036+03, but not in that of J2310+1855, which instead displays
the strongest OH absorption. Thus, as seen at low–z, it appears the presence
of an AGN in high–z sources is also required to provide an environment in
which OH 119 $\mu$m emission may be observed. Also consistent with low–z
observations, emission line–widths appear to be modest.

All three of our QSOs are unobscured and as mentioned in our previous
discussion sections, it is suspected that the outflowing OH observed in
absorption is ejected via star formation feedback and thus likely not to have
originated from the nucleus region. It may then be expected that the gas
traced by OH 119 $\mu$m emission, is also, at least in part, located farther
out from the AGN, perhaps in a circumnuclear starburst as predicted for some
low–z galaxies (Spinoglio et al., 2005; Spoon et al., 2013; Runco et al.,
2020). Furthermore, we find in the case of P183+05, that the OH 119 $\mu$m
emission is spatially more extended than the background continuum. We can not
however determine with a single OH transition what excitation mechanism is
dominant in these sources. Future multi–line and spatially resolved OH
observations will be needed to elucidate the nature and location of these
environments.

##  6 Conclusion

We present marginally resolved ALMA band 7 observations targeting the OH 119
$\mu$m line and dust continuum in three $z>6$ QSOs: J2310+1855, P183+05 and
P036+03. We detect OH absorption in two of the sources (J2310+1855 and
P183+05), blue–shifted with respect to the host galaxy systemic velocities,
and in emission in P183+05 and tentatively P036+03, at systemic velocities. We
detail our main results below.

  * •

We compare the spectral properties of the blue–shifted OH 119 $\mu$m
absorption signatures tracing the molecular outflows in J2310+1855 and
P183+05, with those of a comparison high–z DSFG sample (Spilker et al., 2020a,
b). We find that the FWHM in both J2310+1855 and P183+05 are narrower than
expected for their host galaxy FIR luminosities, but that the equivalent width
(absorption strength) of the line is significantly larger in the case of
J2310+1855, and comparable in P183+05. This may imply a higher outflow
covering fraction or a geometry of the outflow that has a tendency to cover
brighter regions of the background dust continuum.

  * •

Assuming a spherical thin shell geometry, we derive masses, mass outflow rates
and energetics of the molecular outflows. We find that J2310+1855 and P183+05
have comparable mass outflow rates to the DSFG sample for the $\rm L_{FIR}$.
J2310+1855 is significantly offset towards lower energy flux for it’s $\rm
L_{FIR}$.

  * •

Whilst the estimated escape fractions of the molecular outflows are
negligible, we suggest that energy injected into the CGM via the fast
nuclear–driven ionised phase may (Bischetti et al., 2022) may inhibit the re-
accretion of this gas back onto the galaxy. This brings our derived depletion
times of $<1$ Myr into agreement with predictions for massive high–z QSOs
(Simpson et al., 2012; Costa et al., 2018).

  * •

We do not find any evidence, nor require any additional input from the central
AGN to drive the observed molecular outflow in J2310+1855 but can not rule out
an AGN contribution in P183+05 if the AGN contribution to $\rm L_{FIR}$ is
significant and/or the outflow covering fraction is high ($\geq 53\%$), which
we find to be an unlikely scenario for our $z>6$ unobscured QSOs (Venemans et
al., 2018, 2020). This suggests that the molecular outflows are driven
dominantly by processes associated with star–formation, as is expected of the
high–z DSFG sample.

  * •

Consequently, we suggest that the observed spectral differences of the
absorption lines are instead caused by differences in the background dust
continuum. We demonstrate with an outflow toy model (Fig. 7) that for a more
compact and/or inclined background dust continuum, observations are limited to
fewer outflowing clumps and clumps at low altitudes. This results in narrower
absorption line widths (fewer velocity components) and an increase of the
projection effects on the outflow velocity, assuming clumps move in a galactic
fountain–like trajectory. For both an increase in inclination, and more
compact dust distribution, each individual intervening clump will cover a
larger fraction of the overall dust continuum and will have the tendency to
cover regions of brighter dust continuum surface brightness. We suggest that
J2310+1855’s small dust size may make its outflow velocity more sensitive to
projection effects, contributing to its slower than expected outflow velocity.

  * •

J2310+1855’s compact dust continuum may indicate that its host galaxy is at a
more evolved stage of dissipative contraction in its transformation into a
compact spheroidal (Stacey et al., 2021). The small dust sizes measured in
other high–z QSO samples suggest that the effects of the background continuum
on the absorption line spectral properties of outflows that we find in this
paper, may be a common systematic in future, larger samples.

  * •

We detect OH 119 $\mu$m emission in P183+05, and tentatively in P036+03, in
contrast with the high–z DSFG sample where emission is not detected in any of
the sources. This is consistent with detections in low–z studies that have
found the presence of an AGN is required to provide the necessary environment
to excite the molecule.

Given the limited sample size of three in this study, and the marginally
resolved nature of our observations, we note that many of our conclusions are
speculative at this time. To concretely determine the geometry and covering
fractions of the outflowing molecular gas, spatially resolved observations are
crucial. Larger sample sizes will also be required to determine if the
differences in outflow spectral properties driven by QSO hosts, as found in
this paper, are truly caused by background dust distribution and not the
outflow itself. Similarly, larger samples of DSFGs, particularly at higher
($\rm 10^{13}\ L_{\odot}$) $\rm L_{FIR}$, are needed to constrain the trends
found in the purely star-forming sample, so as to better compare between the
two possible outflow driving mechanisms.

Lastly, in this paper we have focused on three unobscured QSOs, sources that
have already completed their blow–out phase and where energy and momentum
injected by the central black hole may efficiently escape the galaxy via the
cleared out pathway. Our results suggest that at this evolutionary phase the
interaction between QSO and host galaxy ISM is limited. Thus observations
targeting QSOs in the lead up to or during the blow–out phase may better
illuminate the role and impact QSOs play in removing cool gas from their host
galaxies.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2018.1.01790.S.
ALMA is a partnership of ESO (representing its member states), NSF (USA) and
NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ. This work benefited from
the support of the project Z-GAL ANR-AAPG2019 of the French National Research
Agency (ANR). Finally, we thank the anonymous referee for their feedback which
helped improve this paper.

## References

  * Bañados et al. (2015) Bañados, E., Decarli, R., Walter, F., et al. 2015, ApJ, 805, L8, doi: 10.1088/2041-8205/805/1/L8
  * Bañados et al. (2019) Bañados, E., Rauch, M., Decarli, R., et al. 2019, ApJ, 885, 59, doi: 10.3847/1538-4357/ab4129
  * Berta et al. (2021) Berta, S., Young, A. J., Cox, P., et al. 2021, A&A, 646, A122, doi: 10.1051/0004-6361/202039743
  * Bischetti et al. (2019) Bischetti, M., Maiolino, R., Carniani, S., et al. 2019, A&A, 630, A59, doi: 10.1051/0004-6361/201833557
  * Bischetti et al. (2022) Bischetti, M., Feruglio, C., D’Odorico, V., et al. 2022, Nature, 605, 244, doi: 10.1038/s41586-022-04608-1
  * Butler et al. (2021) Butler, K. M., van der Werf, P. P., Rybak, M., et al. 2021, ApJ, 919, 5, doi: 10.3847/1538-4357/ac0c7a
  * Calderón et al. (2016) Calderón, D., Bauer, F. E., Veilleux, S., et al. 2016, MNRAS, 460, 3052, doi: 10.1093/mnras/stw1210
  * Carnall et al. (2020) Carnall, A. C., Walker, S., McLure, R. J., et al. 2020, MNRAS, 496, 695, doi: 10.1093/mnras/staa1535
  * Carniani et al. (2019) Carniani, S., Gallerani, S., Vallini, L., et al. 2019, MNRAS, 489, 3939, doi: 10.1093/mnras/stz2410
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560.  https://arxiv.org/abs/1612.05560
  * Cicone et al. (2015) Cicone, C., Maiolino, R., Gallerani, S., et al. 2015, A&A, 574, A14, doi: 10.1051/0004-6361/201424980
  * Costa et al. (2018) Costa, T., Rosdahl, J., Sijacki, D., & Haehnelt, M. G. 2018, MNRAS, 479, 2079, doi: 10.1093/mnras/sty1514
  * D’Amato et al. (2020) D’Amato, Q., Gilli, R., Vignali, C., et al. 2020, A&A, 636, A37, doi: 10.1051/0004-6361/201936175
  * Decarli et al. (2018) Decarli, R., Walter, F., Venemans, B. P., et al. 2018, ApJ, 854, 97, doi: 10.3847/1538-4357/aaa5aa
  * Decarli et al. (2022) Decarli, R., Pensabene, A., Diax-Santos, T., et al. 2022, A&A, in press
  * Duras et al. (2017) Duras, F., Bongiorno, A., Piconcelli, E., et al. 2017, A&A, 604, A67, doi: 10.1051/0004-6361/201731052
  * Estrada-Carpenter et al. (2020) Estrada-Carpenter, V., Papovich, C., Momcheva, I., et al. 2020, ApJ, 898, 171, doi: 10.3847/1538-4357/aba004
  * Falgarone et al. (2017) Falgarone, E., Zwaan, M. A., Godard, B., et al. 2017, Nature, 548, 430, doi: 10.1038/nature23298
  * Fan et al. (2018) Fan, L., Knudsen, K. K., Fogasy, J., & Drouart, G. 2018, ApJ, 856, L5, doi: 10.3847/2041-8213/aab496
  * Feruglio et al. (2010) Feruglio, C., Maiolino, R., Piconcelli, E., et al. 2010, A&A, 518, L155, doi: 10.1051/0004-6361/201015164
  * Feruglio et al. (2018) Feruglio, C., Fiore, F., Carniani, S., et al. 2018, A&A, 619, A39, doi: 10.1051/0004-6361/201833174
  * Fielding et al. (2018) Fielding, D., Quataert, E., & Martizzi, D. 2018, MNRAS, 481, 3325, doi: 10.1093/mnras/sty2466
  * Fischer et al. (2010) Fischer, J., Sturm, E., González-Alfonso, E., et al. 2010, A&A, 518, L41, doi: 10.1051/0004-6361/201014676
  * Fluetsch et al. (2021) Fluetsch, A., Maiolino, R., Carniani, S., et al. 2021, MNRAS, 505, 5753, doi: 10.1093/mnras/stab1666
  * Forrest et al. (2020) Forrest, B., Marsan, Z. C., Annunziatella, M., et al. 2020, ApJ, 903, 47, doi: 10.3847/1538-4357/abb819
  * Gallerani et al. (2014) Gallerani, S., Ferrara, A., Neri, R., & Maiolino, R. 2014, MNRAS, 445, 2848, doi: 10.1093/mnras/stu2031
  * Gallerani et al. (2018) Gallerani, S., Pallottini, A., Feruglio, C., et al. 2018, MNRAS, 473, 1909, doi: 10.1093/mnras/stx2458
  * Ginolfi et al. (2020) Ginolfi, M., Jones, G. C., Béthermin, M., et al. 2020, A&A, 633, A90, doi: 10.1051/0004-6361/201936872
  * Glazebrook et al. (2017) Glazebrook, K., Schreiber, C., Labbé, I., et al. 2017, Nature, 544, 71, doi: 10.1038/nature21680
  * González-Alfonso et al. (2017) González-Alfonso, E., Fischer, J., Spoon, H. W. W., et al. 2017, ApJ, 836, 11, doi: 10.3847/1538-4357/836/1/11
  * Governato et al. (2010) Governato, F., Brook, C., Mayer, L., et al. 2010, Nature, 463, 203, doi: 10.1038/nature08640
  * Guarnieri et al. (2019) Guarnieri, P., Maraston, C., Thomas, D., et al. 2019, MNRAS, 483, 3060, doi: 10.1093/mnras/sty3305
  * Heckman & Thompson (2017) Heckman, T. M., & Thompson, T. A. 2017, arXiv e-prints, arXiv:1701.09062.  https://arxiv.org/abs/1701.09062
  * Herrera-Camus et al. (2020) Herrera-Camus, R., Sturm, E., Graciá-Carpio, J., et al. 2020, A&A, 633, L4, doi: 10.1051/0004-6361/201937109
  * Herrera-Camus et al. (2021) Herrera-Camus, R., Förster Schreiber, N., Genzel, R., et al. 2021, A&A, 649, A31, doi: 10.1051/0004-6361/202039704
  * Ikarashi et al. (2015) Ikarashi, S., Ivison, R. J., Caputi, K. I., et al. 2015, ApJ, 810, 133, doi: 10.1088/0004-637X/810/2/133
  * Indriolo et al. (2018) Indriolo, N., Bergin, E. A., Falgarone, E., et al. 2018, ApJ, 865, 127, doi: 10.3847/1538-4357/aad7b3
  * Jiang et al. (2016) Jiang, L., McGreer, I. D., Fan, X., et al. 2016, ApJ, 833, 222, doi: 10.3847/1538-4357/833/2/222
  * Kereš et al. (2009) Kereš, D., Katz, N., Davé, R., Fardal, M., & Weinberg, D. H. 2009, MNRAS, 396, 2332, doi: 10.1111/j.1365-2966.2009.14924.x
  * Khusanova et al. (2022) Khusanova, Y., Bañados, E., Mazzucchelli, C., et al. 2022, arXiv e-prints, arXiv:2204.08973.  https://arxiv.org/abs/2204.08973
  * Li et al. (2020) Li, J., Wang, R., Riechers, D., et al. 2020, ApJ, 889, 162, doi: 10.3847/1538-4357/ab65fa
  * Maiolino et al. (2012) Maiolino, R., Gallerani, S., Neri, R., et al. 2012, MNRAS, 425, L66, doi: 10.1111/j.1745-3933.2012.01303.x
  * Mazzucchelli et al. (2017) Mazzucchelli, C., Bañados, E., Venemans, B. P., et al. 2017, ApJ, 849, 91, doi: 10.3847/1538-4357/aa9185
  * 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 & York (1987) Meyer, D. M., & York, D. G. 1987, ApJ, 315, L5, doi: 10.1086/184851
  * Meyer et al. (2022) Meyer, R. A., Walter, F., Cicone, C., et al. 2022, arXiv e-prints, arXiv:2201.08143.  https://arxiv.org/abs/2201.08143
  * Neeleman et al. (2021) Neeleman, M., Novak, M., Venemans, B. P., et al. 2021, ApJ, 911, 141, doi: 10.3847/1538-4357/abe70f
  * Nguyen et al. (2018) Nguyen, H., Dawson, J. R., Miville-Deschênes, M. A., et al. 2018, ApJ, 862, 49, doi: 10.3847/1538-4357/aac82b
  * Novak et al. (2020) Novak, M., Venemans, B. P., Walter, F., et al. 2020, ApJ, 904, 131, doi: 10.3847/1538-4357/abc33f
  * Pensabene et al. (2020) Pensabene, A., Carniani, S., Perna, M., et al. 2020, A&A, 637, A84, doi: 10.1051/0004-6361/201936634
  * Planck Collaboration et al. (2016) Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A13, doi: 10.1051/0004-6361/201525830
  * Riechers et al. (2021) Riechers, D. A., Cooray, A., Pérez-Fournon, I., & Neri, R. 2021, ApJ, 913, 141, doi: 10.3847/1538-4357/abf6d7
  * Rojas-Ruiz et al. (2021) Rojas-Ruiz, S., Bañados, E., Neeleman, M., et al. 2021, arXiv e-prints, arXiv:2108.04257.  https://arxiv.org/abs/2108.04257
  * Runco et al. (2020) Runco, J. N., Malkan, M. A., Fernández-Ontiveros, J. A., Spinoglio, L., & Pereira-Santaella, M. 2020, ApJ, 905, 57, doi: 10.3847/1538-4357/abb8e0
  * Rupke (2018) Rupke, D. 2018, Galaxies, 6, 138, doi: 10.3390/galaxies6040138
  * Rupke et al. (2005) Rupke, D. S., Veilleux, S., & Sanders, D. B. 2005, ApJS, 160, 115, doi: 10.1086/432889
  * Sanders & Mirabel (1996) Sanders, D. B., & Mirabel, I. F. 1996, ARA&A, 34, 749, doi: 10.1146/annurev.astro.34.1.749
  * Schneider et al. (2015) Schneider, R., Bianchi, S., Valiante, R., Risaliti, G., & Salvadori, S. 2015, A&A, 579, A60, doi: 10.1051/0004-6361/201526105
  * Shao et al. (2019) Shao, Y., Wang, R., Carilli, C. L., et al. 2019, ApJ, 876, 99, doi: 10.3847/1538-4357/ab133d
  * Shao et al. (2022) Shao, Y., Wang, R., Weiss, A., et al. 2022, arXiv e-prints, arXiv:2210.11926.  https://arxiv.org/abs/2210.11926
  * Sharma et al. (2014) Sharma, P., Roy, A., Nath, B. B., & Shchekinov, Y. 2014, MNRAS, 443, 3463, doi: 10.1093/mnras/stu1307
  * Silverman et al. (2019) Silverman, J. D., Treu, T., Ding, X., et al. 2019, ApJ, 887, L5, doi: 10.3847/2041-8213/ab5851
  * Simcoe et al. (2004) Simcoe, R. A., Sargent, W. L. W., & Rauch, M. 2004, ApJ, 606, 92, doi: 10.1086/382777
  * Simpson et al. (2012) Simpson, J. M., Smail, I., Swinbank, A. M., et al. 2012, MNRAS, 426, 3201, doi: 10.1111/j.1365-2966.2012.21941.x
  * Somerville & Primack (1999) Somerville, R. S., & Primack, J. R. 1999, MNRAS, 310, 1087, doi: 10.1046/j.1365-8711.1999.03032.x
  * Spilker et al. (2018) Spilker, J. S., Aravena, M., Béthermin, M., et al. 2018, Science, 361, 1016, doi: 10.1126/science.aap8900
  * Spilker et al. (2020a) Spilker, J. S., Phadke, K. A., Aravena, M., et al. 2020a, ApJ, 905, 85, doi: 10.3847/1538-4357/abc47f
  * Spilker et al. (2020b) Spilker, J. S., Aravena, M., Phadke, K. A., et al. 2020b, ApJ, 905, 86, doi: 10.3847/1538-4357/abc4e6
  * Spinoglio et al. (2005) Spinoglio, L., Malkan, M. A., Smith, H. A., González-Alfonso, E., & Fischer, J. 2005, ApJ, 623, 123, doi: 10.1086/428495
  * Spoon et al. (2013) Spoon, H. W. W., Farrah, D., Lebouteiller, V., et al. 2013, ApJ, 775, 127, doi: 10.1088/0004-637X/775/2/127
  * Stacey et al. (2021) Stacey, H. R., McKean, J. P., Powell, D. M., et al. 2021, MNRAS, 500, 3667, doi: 10.1093/mnras/staa3433
  * Stone et al. (2016) Stone, M., Veilleux, S., Meléndez, M., et al. 2016, ApJ, 826, 111, doi: 10.3847/0004-637X/826/2/111
  * Straatman et al. (2014) Straatman, C. M. S., Labbé, I., Spitler, L. R., et al. 2014, ApJ, 783, L14, doi: 10.1088/2041-8205/783/1/L14
  * Sturm et al. (2011) Sturm, E., González-Alfonso, E., Veilleux, S., et al. 2011, ApJ, 733, L16, doi: 10.1088/2041-8205/733/1/L16
  * Travascio et al. (2020) Travascio, A., Zappacosta, L., Cantalupo, S., et al. 2020, A&A, 635, A157, doi: 10.1051/0004-6361/201936197
  * Tripodi et al. (2022) Tripodi, R., Feruglio, C., Fiore, F., et al. 2022, A&A, 665, A107, doi: 10.1051/0004-6361/202243920
  * Valentino et al. (2020) Valentino, F., Tanaka, M., Davidzon, I., et al. 2020, ApJ, 889, 93, doi: 10.3847/1538-4357/ab64dc
  * Veilleux et al. (2005) Veilleux, S., Cecil, G., & Bland-Hawthorn, J. 2005, ARA&A, 43, 769, doi: 10.1146/annurev.astro.43.072103.150610
  * Veilleux et al. (2020) Veilleux, S., Maiolino, R., Bolatto, A. D., & Aalto, S. 2020, A&A Rev., 28, 2, doi: 10.1007/s00159-019-0121-9
  * Veilleux et al. (2013) Veilleux, S., Meléndez, M., Sturm, E., et al. 2013, ApJ, 776, 27, doi: 10.1088/0004-637X/776/1/27
  * Venemans et al. (2015) Venemans, B. P., Bañados, E., Decarli, R., et al. 2015, ApJ, 801, L11, doi: 10.1088/2041-8205/801/1/L11
  * Venemans et al. (2018) Venemans, B. P., Decarli, R., Walter, F., et al. 2018, ApJ, 866, 159, doi: 10.3847/1538-4357/aadf35
  * Venemans et al. (2020) Venemans, B. P., Walter, F., Neeleman, M., et al. 2020, ApJ, 904, 130, doi: 10.3847/1538-4357/abc563
  * Wang et al. (2013) Wang, R., Wagg, J., Carilli, C. L., et al. 2013, ApJ, 773, 44, doi: 10.1088/0004-637X/773/1/44