11institutetext: Centro de Astrobiología (CAB), CSIC-INTA, Camino Bajo del
Castillo s/n, E-28692 Villanueva de la Cañada, Madrid, Spain
11email<EMAIL_ADDRESS>22institutetext: Observatorio de Madrid,
OAN-IGN, Alfonso XII, 3, E-28014 Madrid, Spain 33institutetext: Instituto de
Física Fundamental, CSIC, Calle Serrano 123, 28006 Madrid, Spain
44institutetext: Max-Planck-Institut für Extraterrestrische Physik, Postfach
1312, 85741 Garching, Germany 55institutetext: LERMA, Observatoire de Paris,
Collège de France, PSL University, CNRS, Sorbonne University, Paris, France
66institutetext: Department of Physics & Astronomy, University of Alaska
Anchorage, Anchorage, AK 99508-4664, USA 77institutetext: Instituto de
Astrofísica de Canarias, Calle Vía Láctea, s/n, 38205 La Laguna, Tenerife,
Spain 88institutetext: Departamento de Astrofísica, Universidad de La Laguna,
38206 La Laguna, Tenerife, Spain 99institutetext: Department of Physics,
University of Oxford, Oxford OX1 3RH, UK 1010institutetext: School of Physics
& Astronomy, University of Southampton, Southampton SO17 1BJ, Hampshire, UK
1111institutetext: Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA 1212institutetext: The University of Texas at San
Antonio, One UTSA Circle, San Antonio, TX 78249, USA 1313institutetext:
National Astronomical Observatory of Japan, National Institutes of Natural
Sciences (NINS), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
1414institutetext: Departamento de Física de la Tierra y Astrofísica, Fac. de
CC Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
1515institutetext: Instituto de Física de Partículas y del Cosmos IPARCOS,
Fac. CC Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
1616institutetext: INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico
Fermi 5, 50125 Firenze, Italy 1717institutetext: Department of Astronomy,
School of Science, Graduate University for Advanced Studies (SOKENDAI),
Mitaka, Tokyo 181-8588, Japan 1818institutetext: Núcleo de Astronomía de la
Facultad de Ingeniería, Universidad Diego Portales, Av. Ejército Libertador
441, Santiago, Chile 1919institutetext: Kavli Institute for Astronomy and
Astrophysics, Peking University, Beijing 100871, China

# AGN feedback in action in the molecular gas ring of the Seyfert galaxy NGC
7172

A. Alonso Herrero 11 S. García-Burillo 22 M. Pereira-Santaella 33 T. Shimizu
44 F. Combes 55 E. K. S. Hicks 66 R. Davies 44 C. Ramos Almeida 77 8 8 I.
García-Bernete 99 S. F. Hönig 1010 N. A. Levenson 1111 C. Packham 1212 13 13
E. Bellocchi 1414 15 15 L. K. Hunt 1616 M. Imanishi 1313 17 17 C. Ricci 1818
19 19 P. Roche 99

(Received 2023; accepted 2023)

We present new ALMA observations of the CO(3-2) transition and associated
$854\,\mu$m continuum at $0.06-0.3\arcsec$ resolution, together with new
VLT/SINFONI observations of NGC 7172. This is a luminous (bolometric
luminosity of $\simeq 10^{44}\,{\rm erg\,s}^{-1}$) Seyfert galaxy that belong
to the Galaxy Activity, Torus, and Outflow Survey (GATOS). The ALMA CO(3-2)
observations reveal the presence of a highly inclined cold molecular gas ring
with an approximate radius of $3-4\arcsec\simeq 540-720\,$ pc, which is likely
associated with an inner Lindblad resonance of a putative stellar bar. There
are noncircular motions in the VLT/SINFONI [Si vi]$\lambda$$1.96\,\mu$m and H2
at $2.12\,\mu$m, and ALMA CO(3-2) velocity fields. After subtracting the
stellar velocity field, we detected [Si vi] blueshifted velocities of a few
hundred ${\rm km\,s}^{-1}$ to the south of the active galactic nucleus (AGN)
position. They trace outflowing ionized gas outside the plane of the galaxy
and out to projected distances of $\simeq 200\,$pc. The CO(3-2) position-
velocity diagram along the kinematic minor axis displays noncircular motions
with observed velocities of up to $\sim 150\,{\rm km\,s}^{-1}$. Assuming that
these are taking place in the disk of the galaxy, the observed velocity signs
imply that the molecular gas ring is not only rotating but also outflowing. We
derived an integrated cold molecular gas mass outflow rate of $\sim
40\,M_{\odot}\,{\rm yr}^{-1}$ for the ring. Using the ALMA $854\,\mu$m
extended emission map, we resolved a 32 pc radius torus with a gas mass of
$8\times 10^{5}\,M_{\odot}$. These torus properties are similar to other
Seyfert galaxies in the GATOS sample. We measured a decreased cold molecular
gas concentration in the nuclear-torus region relative to the circumnuclear
region when compared to other less luminous Seyfert galaxies. We conclude that
the effects of AGN feedback in NGC 7172, which are likely caused by the AGN
wind and/or the moderate luminosity radio jet, are seen as a large-scale
outflowing molecular gas ring and accompanying redistribution of molecular gas
in the nuclear regions.

###### Key Words.:

galaxies: active – galaxies: ISM – galaxies: Seyfert – galaxies: nuclei –
galaxies: evolution

##  1 Introduction

The formation and evolution of galaxies is one of the key challenges of modern
astrophysics. State-of-the-art cosmological simulations provide the
theoretical benchmark to understand the growth of galaxies and their
supermassive black holes, and in particular, the effects of feedback (see for
instance, Sijacki et al., 2015; Dubois et al., 2016; Davé et al., 2019;
Anglés-Alcázar et al., 2021). With the new computational advances, these
simulations are able to track the gas cycle on all relevant physical scales,
from the circumgalactic medium all the way down to the sphere of influence of
supermassive black holes. One important result from these simulations is that
feedback is needed to regulate the buildup of the stellar mass in massive
galaxies. In these types of galaxies, feedback is believed to be driven by
radiation pressure from an active galactic nucleus (AGN) and mechanical energy
from radio jets (see e.g., Fabian, 2012, for a review).

Energetic multiphase (ionized, neutral, warm, and cold molecular gas) outflows
have been routinely discovered in powerful AGNs and (ultra)luminous infrared
galaxies. In strongly star-forming galaxies, the molecular outflow rates are
comparable to, or higher by a factor of few, than the ongoing star-formation
activity (Cicone et al., 2014). When an AGN is present, the outflow rates can
be strongly boosted, with more luminous AGNs driving more energetic outflows
(see, e.g., Fiore et al., 2017; Fluetsch et al., 2019). Still, at a given AGN
luminosity, the outflow rates of the ionized gas span a range of nearly two
orders of magnitude in nearby Seyfert galaxies (see Davies et al., 2020, and
references therein). Similar results are found for the molecular phase of
outflows in AGNs and ultraluminous infrared galaxies (ULIRGs), where the AGN
luminosity is found not to be the only factor driving massive outflows (see
e.g., Ramos Almeida et al., 2022; Lamperti et al., 2022, respectively). Other
factors, such as jet and/or wind inclination relative to the galaxy disks, or
gas concentration can also play a significant role.

In nearby Seyfert galaxies where the molecular and ionized gas phases were
studied together, there is evidence for positive and/or negative feedback
effects on scales of out to a few kiloparsecs caused by AGN winds, sometimes
combined with low-power radio jets (García-Burillo et al., 2014; Cresci et
al., 2015; Shimizu et al., 2019; Venturi et al., 2018, 2021; García-Bernete et
al., 2021; Gao et al., 2021). At Seyfert-like luminosities, the molecular
phase has a larger contribution to the total mass outflow rate and kinetic
power than the ionized phase (Fiore et al., 2017; Fluetsch et al., 2019). The
superb angular resolution attained with (sub)millimeter interferometry,
including the Atacama Large Millimeter/submillimeter Array (ALMA), allows for
AGN-driven cold molecular gas outflows to be probed from circumnuclear scales
of a few hundred parsecs all the way to the molecular dusty torus on tens of
parsecs. The derived molecular mass outflow rates in Seyfert galaxies range
from $\sim 1\,M_{\odot}$ yr-1 to a few tens of $M_{\odot}$ yr-1, and the
velocities are up to hundreds of km s-1 (Combes et al., 2013; García-Burillo
et al., 2014; Morganti et al., 2015; Zschaechner et al., 2016; Alonso-Herrero
et al., 2018, 2019; Audibert et al., 2019; Domínguez-Fernández et al., 2020).

The Galactic Activity, Torus, and Outflow Survey (GATOS) aims to understand
the obscuring material (torus) and the nuclear gas cycle (inflows and
outflows) in the dusty regions immediately surrounding the active nucleus of
nearby AGNs. To do so, we selected local Seyfert galaxies from the 70 month
Swift/BAT All-sky Hard X-ray Survey (Baumgartner et al., 2013). García-Burillo
et al. (2021) obtained ALMA band 7 observations of ten GATOS Seyfert galaxies
in the southern hemisphere and with distances in the 10-30 Mpc range.
Combining these Seyfert galaxies with a sample of low-luminosity AGNs (from
Combes et al., 2019), they found that galaxies with higher AGN luminosities
and/or Eddington ratios are more efficient at clearing molecular gas from the
nuclear (torus) regions. This was interpreted as the imprint on the nuclear
molecular gas distribution left by the presence of AGN winds, that is, AGN-
driven feedback. In a few GATOS Seyfert galaxies, this is confirmed by the
presence of (circum)nuclear molecular outflows (Alonso-Herrero et al., 2018,
2019; García-Burillo et al., 2019) and polar dust emission (Alonso-Herrero et
al., 2021) on these scales.

Figure 1: Seyfert galaxy NGC 7172. From top to bottom. Panel a: HST optical to
near-IR composite RGB image of NGC 7172 retrieved from ESASky4.3.0. It
combines observations from the Advanced Camera for Surveys (ACS) at 6060 and
8140 Å, and the Wide Field Camera 3 (WFC3) at $1.6\,\mu$m. The orientation of
the image is north up, east to the left. The FoV is $\simeq$2′$\times$ 2′. The
rectangle shows approximately the ALMA FoV, while the dashed lines represent
the opening angle of the southern (brighter) side of the optical ionization
cone. Image credit: ESA/Hubble & NASA, D. J. Rosario, A. Barth. Panel b: ALMA
CO(3-2) intensity map (moment 0) produced with a 3$\sigma$ clipping using the
merged configuration observations. We trimmed the original FoV to
approximately $17.6\arcsec\times 3.3\arcsec$. Both the image and the contours
are shown on a linear scale. The color bar shows the intensity scale in Jy km
s-1 per beam units. The first contour is at 0.05 Jy km s-1 per beam. The ALMA
beam (not shown) is $0.08\arcsec\times 0.07\arcsec$ ($14\,{\rm pc} \times
13\,{\rm pc}$) at PA${}_{\rm beam}=90.4^{\circ}$. Panel c: ALMA CO(3-2) mean
velocity map (moment 1) produced with a 3$\sigma$ clipping using the merged
configuration observations. The contours are the isovelocities. Panel d: ALMA
CO(3-2) mean velocity dispersion map (moment 2) produced with a 3$\sigma$
clipping using the merged configuration observations. For the last two panels
the scale bar units are ${\rm km\,s}^{-1}$.

Up until now, we investigated the ALMA properties of intermediate luminosity
Seyfert galaxies with $L_{\rm AGN}(2-10\,{\rm keV})=10^{41.4-43.5}\,{\rm
erg\,s}^{-1}$ and distances of less than 28 Mpc in the GATOS sample (Alonso-
Herrero et al., 2018, 2019; García-Burillo et al., 2021). NGC 7172 is a nearly
edge-on Sa spiral galaxy in the GATOS sample at a redshift-independent
distance of 37 Mpc (Davies et al., 2015) with an AGN bolometric luminosity of
$\sim 1.3\times 10^{44}\,$erg s-1 (Davies et al., 2015). It belongs to the
Hickson compact group HCG90, which also includes, among other galaxies, NGC
7173, NGC 7174, and NGC 7176. NGC 7172 is optically classified as a Seyfert 2
(Véron-Cetty & Véron, 2006), although Smajić et al. (2012) found evidence for
the presence of broad hydrogen recombination lines in the near-infrared (near-
IR). The nuclear region is crossed by dust lane that obscures the galaxy
nucleus in the optical but not at longer wavelengths (Smajić et al., 2012).
There is also a broader dust lane extending east-west across the galaxy that
appears to be warped at the edges (Sharples et al., 1984). Figure 1 (top
panel) shows a red-green-blue (RGB) optical to near-IR Hubble Space Telescope
(HST) image of NGC 7172 retrieved from ESASky (Baines et al., 2017; Giordano
et al., 2018), where this morphology is clearly seen. The distribution of the
prominent dust lanes to the north of the nucleus indicates this is the near
side of the galaxy. This is also in agreement with the extinction distribution
in the (circum)nuclear regions of the galaxy (Smajić et al., 2012).

Thomas et al. (2017) detected a prominent two-sided ionization cone in NGC
7172 using optical integral field unit (IFU) spectroscopy. It has a projected
opening angle of approximately $120^{\circ}$. The southern part of the cone is
brighter, which is consistent with the position of the main dust lane and with
north being the near side of the galaxy (see Fig. 1, top panel). The size on
this side of the cone is approximately $5\arcsec$, which is equivalent to a
projected physical size of 900 pc. Using spectroscopic observations with
X-shooter on the Very Large Telescope (VLT), Davies et al. (2020) derived a
velocity for the ionized gas outflow of $\sim 400\,{\rm km\,s}^{-1}$ and an
outflow rate of 0.005 M⊙ yr-1. In this work, we present new band 7 ALMA
observations of the CO(3-2) transition and the associated $854\,\mu$m
continuum of the GATOS galaxy NGC 7172. The ALMA observations were taken with
an angular resolutions of approximately 0.06″ and 0.3″, which correspond to 11
pc and 54 pc, respectively for the assumed distance. This allows us to resolve
the morphology and kinematics of the cold molecular gas of both the nuclear
and circumnuclear regions of this galaxy. This paper is organized as follows.
Section 2 presents the ALMA band 7 CO($J=3-2$) and associated continuum
observations as well as ancillary new VLT/SINFONI observations. In Sect. 3 we
discuss the overall ALMA and SINFONI morphology and kinematics, while in Sect.
4 we model the ALMA CO(3-2) kinematics. In Sect. 5, we derive the properties
of the torus of NGC 7172. Finally, in Sects. 6 and 7 we discuss the results of
this work and present our conclusions, respectively.

Figure 2: ALMA band 7 observations. Left panel: In gray scale and contours is
a zoom-in on the ALMA CO(3-2) intensity map of Fig. 1 (second panel from the
top) showing the inner part of the cold molecular gas ring. The FoV matches
that of the SINFONI observations (see Fig. 4). The gray bar shows the CO(3-2)
intensity scale in Jy km s-1 beam-1. The red contours are the band 7 continuum
map at $854\,\mu$m from the merged configuration, shown on a linear scale. The
first contour is at three times the measured continuum rms of $17\,\mu$Jy. The
continuum beam ($0.08\arcsec\times 0.06\arcsec$ at PA${}_{\rm
beam}=90.6^{\circ}$) is the blue filled ellipse in the bottom-left corner.
Right panel: The gray scale map and the red contours are the compact
configuration $854\,\mu$m continuum map, with the same FoV as in the left
panel. The contours are on a linear scale. The continuum beam
($0.34\arcsec\times 0.27\arcsec$ at PA${}_{\rm beam}=-78^{\circ}$) is the blue
filled ellipse in the bottom-left corner. Table 1: ALMA band 7 observations.

Configuration | Continuum/ | beam | PAbeam | rms
---|---|---|---|---
| Line | ($\arcsec\times\arcsec$) | (∘) |
Compact |  $854\,\mu$m | $0.34\times 0.27$ | $-78$ | 97
| CO(3-2) | $0.33\times 0.25$ | $-75$ | 2
Extended |  $854\,\mu$m | $0.07\times 0.06$ | $-88$ | 30
Merged |  $854\,\mu$m | $0.08\times 0.06$ | 91 | 17
| CO(3-2) | $0.08\times 0.07$ | 90 | 0.5
111Details of the beam sizes and PA as well as the rms of each of the
configurations used in this wok. The rms units are $\mu$Jy per beam for the
$854\,\mu$m continuum and mJy per channel and per beam for the CO(3-2)
observations.

##  2 Observations and data reduction

###  2.1 ALMA band 7

We observed the emission of the CO(3-2) and HCO+($J=4-3$) lines and their
underlying continuum emission in the circumnuclear disk (CND) of NGC 7172
using the band 7 ALMA receiver and a single pointing (project-
ID:#2019.1.00618.S; PI: A. Alonso-Herrero). Although the phase tracking center
of the galaxy was assumed to be at right ascension and declination (RA2000,
Dec2000) = (22h02m01.90s, –31o52’11.6”), the position of the AGN has
nevertheless been reassigned through a comparison with the radio coordinates
and a fit of the continuum emission, as detailed in Sects. 3.1 and 5,
respectively. The ALMA field of view (FoV) of 17$\arcsec$ corresponds to the
central 3.1 kpc region of the galaxy. We combined two sets of configurations
of the ALMA array, namely, an extended (C43-7) and a compact (C43-4)
configuration. The aim was to reach an angular resolution of
$<0\aas@@fstack{\prime\prime}07=13$ pc while keeping the largest angular scale
recovered in our maps out to $\sim 3\arcsec=540$ pc. This scale is enough to
recover a sizeable fraction of the flux inside the FoV and image with high
fidelity the torus and its connections with the CND region, which are relevant
to this work. Observations required the execution of two scheduling blocks for
the C43-7 configuration set conducted in July 2021 and one for the C43-4
conducted in October 2019, and the use of $\sim 43-44$ antennas of ALMA.

We placed four spectral windows of 1.875 GHz-bandwidth, two in the lower side
band (LSB) and two in the upper sideband (USB). This setup allowed us to
observe the CO($J=3-2$) line (345.796 GHz at rest) and the continuum emission
(344.0 GHz at rest) in the LSB bands, as well as HCO+(4-3) (356.734 GHz at
rest) and the continuum emission (358.1 GHz at rest) in the USB bands. We
calibrated the data making use of the ALMA reduction package CASA (McMullin et
al., 2007)222http//casa.nrao.edu/.

In this work we make use of the line and continuum data sets from the compact,
extended, and the merged configurations. The calibrated uv-tables of the
merged configurations were exported to
GILDAS333http://www.iram.fr/IRAMFR/GILDAS to proceed with the continuum
subtraction and imaging procedures, as detailed below. We first subtracted the
continuum from each of the spectral $(u,v)$ data sets using the GILDAS task
UV-BASELINE. We fit a baseline to the $(u,v)$ data sets through a polynomial
of degree zero masking the line emission around each transition with a range
of velocity widths $\sim 900$ km s-1 and subsequently obtained continuum-free
spectral line images for CO(3-2) and HCO+(4-3). An inspection of the HCO+ line
data cube showed no significant emission inside the ALMA FoV. The estimated
upper limit flux for this transition is $0.12\,$Jy ${\rm km\,s}^{-1}$, which
provides a CO(3-2) to HCO+(4-3) ratio of $>1.4$. The lower upper limit on the
CO-to-HCO+ ratio is consistent with the values and upper limit measured in
other GATOS Seyfert galaxies of similar Eddington ratios (García-Burillo et
al., 2021).

In the rest of this work, we restrict our analysis and discussion to the
CO(3-2) line data. We derived images of the continuum emission by averaging in
each of the two subbands centered around spectral lines those channels free of
line emission using the GILDAS tasks UV-FILTER and UV-CONT, making use of the
same velocity width masks employed by the UV-BASELINE task. The four line-free
continuum uv-tables were combined using the task UV-MERGE to obtain a genuine
continuum image of the galaxy at an average frequency range $\sim 351.1$ GHz
or $854\,\mu$m (at rest).

For the merged data set, we obtained an angular resolution $\simeq
0\aas@@fstack{\prime\prime}06-0\aas@@fstack{\prime\prime}08=11-14$ pc by
changing in the GILDAS task UV-MAP the robust parameter ($b$) to 1. The line
data cubes were binned to a common frequency resolution of 7.8 MHz (equivalent
to $\sim$6.8 km s-1 in band 7). We estimated that the flux accuracy is about
10–15$\%$, comparable to the level of uncertainty of standard ALMA
observations at the same range of frequencies. The point-source sensitivities
in the line data cubes were derived by selecting areas free from emission in
all channels. We summarize in Table 1 all the relevant parameters of the ALMA
observations. We created CO(3-2) moment maps from the merged configuration
data set using the GILDAS $\tt moment$ task with a 3$\sigma$ clipping. We show
the 0th, 1st, and 2nd moment maps in Fig. 1, while Fig. 2 show the $854\,\mu$m
continuum maps of the central region observed with the compact and merged
configurations. Additionally, in Sect. 4 we discuss the moment maps from the
compact configuration.

###  2.2 VLT/SINFONI

In this section we present new near-IR IFU spectroscopic observations obtained
with the SINFONI instrument (Eisenhauer et al., 2003; Bonnet et al., 2004) at
the VLT, as part of program 093.B-0057(B) (PI: R. Davies). NGC 7172 was
observed during the nights of 16 and 20 July 2014\. The $H+K$ grating was used
with laser guide star adaptive optics to achieve a spectral resolution
$R\simeq 1500$ over a $\simeq 3\arcsec\times 3\arcsec$ FoV. A standard
observing sequence of Object-Sky-Object was used with detector integration
times of 300 (12 exposures) and 50 seconds (6 exposures) and small dithering
between each Object exposure resulting in a total exposure time of 65 minutes.

The raw detector images were reduced with SPRED (Abuter et al., 2006), a
custom data reduction package for SINFONI developed at MPE. SPRED performs all
standard reduction steps needed to reconstruct NIR IFU cubes. We further used
the MXCOR and SKYSUB routines (Davies, 2007) to improve OH sky emission
subtraction and LAC3D, a 3D version of LACOSMIC (van Dokkum, 2001) to identify
and remove bad pixels and cosmic rays. We removed atmospheric telluric
features and flux calibrated the data based on observations of four B-type
stars. A final additional step we implemented was the correction for
differential atmospheric refraction which induces wavelength dependent spatial
offsets. The custom procedure for this is described in Lin et al. (2018).

After the data reduction, the FoV of the SINFONI images is $3.9\arcsec\times
4.2\arcsec$ with a pixel size of 0.05″. We estimated an angular resolution of
the observations of $\simeq 0.2\arcsec$ full width at half maximum (FWHM), as
measured from the $K$-band continuum image (see below) of the galaxy. For this
study, we focus on two emission lines, namely, the coronal line [Si vi] at
$1.96\,\mu$m to trace the ionized gas excited by the AGN (see, e.g., Müller-
Sánchez et al., 2011; Ramos Almeida et al., 2017; Shimizu et al., 2019) and
H2(1–0)S(1) $2.122\,\mu$m to trace the hot molecular gas emission. Before we
fit these two emission lines in the SINFONI data cube, we modeled and removed
the continuum using the Penalized Pixel Fitting tool (ppxf, see Cappellari &
Emsellem, 2004). We modeled the emission lines using a single Gaussian to
derive the flux, velocity, and velocity dispersion (corrected for instrumental
resolution) maps shown in Fig. 3.

Figure 3: VLT/SINFONI observations. From top to bottom, integrated flux (in
arbitrary units), velocity (in ${\rm km\,s}^{-1}$), and velocity dispersion
(in ${\rm km\,s}^{-1}$) maps of the H2 line at $2.12\,\mu$m (left panels) and
[Si vi]$\lambda 1.96\,\mu$m line (right panels). In the top-right panel, the
thick orange dashed lines indicate the approximate opening angle of the [O
iii]$\lambda$5007 ionization cone (Thomas et al., 2017). We note that in these
SINFONI maps, the fitted emission does not fully cover the $3.9\arcsec\times
4.2\arcsec$ FoV. The colors and the contours are on a linear scale. The (0, 0)
point in all the panels corresponds to the peak of the SINFONI line maps. The
hatched circle in the bottom-right panel shows the angular resolution (FWHM)
of the observations.

Figure 4: Comparison of the ALMA and VLT/SINFONI observations. The blue color
scale image is a zoom-in on the ALMA CO(3-2) intensity map of Fig. 1 with a
FoV matching that of the VLT/SINFONI observations (see Fig. 3). The red
contours are the H2 line at $2.12\,\mu$m (left panel) and [Si vi]$\lambda
1.96\,\mu$m (right panel), as Fig. 3. The (0, 0) position in all the panels
corresponds to the peak of the SINFONI line maps as well as the ALMA
$854\,\mu$m continuum.

Figure 5: VLT/SINFONI velocity fields of the H2 line at $2.12\,\mu$m (left
panel) and the [Si vi]$\lambda 1.96\,\mu$m line (right panel) after
subtracting the stellar velocity field fitted with ppxf. The (0, 0) position
in all the panels corresponds to the peak of the SINFONI line map. The units
of the color bars are ${\rm km\,s}^{-1}$.

##  3 Morphology and kinematics

###  3.1 ALMA CO(3-2) and $854\,\mu$m emission

Figure 1 (second panel from the top) shows the ALMA CO(3-2) intensity map
(moment 0) derived from the merged configuration data set. It maximizes the
best angular resolution with the best sensitivity of our observations. The map
displays approximately the full FoV of the observation along the RA direction.
The CO(3-2) intensity map reveals a bright circumnuclear cold molecular gas
ring with an approximate diameter of $6-8\arcsec$ or 1.1-1.4 kpc, containing
bright clumps. Beyond the ring, the CO(3-2) emission becomes more diffuse and
covers the ALMA FoV along the east-west direction. The presence of this ring
was already suspected from previous ALMA CO(2-1) images at lower angular
resolution (see Alonso-Herrero et al., 2020). For a scale reference, the top
panel of Fig. 1 displays the approximate FoV of the ALMA CO(3-2) image plotted
as a red rectangle. The CO(3-2) emission clearly traces the prominent dust
lane that crosses the (circum)nuclear region of the galaxy. In the innermost
4″, the CO(3-2) emission delineates the extinction in the ring derived from
the VLT/SINFONI near-IR continuum and the narrow components of hydrogen
recombination lines (see figure 6 of Smajić et al., 2012). The CO(3-2)
morphology detected in NGC 7172 might correspond to an inner Lindblad
resonance (ILR) and spiral arms associated to a nuclear bar. This CO(3-2)
morphology appears to be similar to that of NGC 613 (Audibert et al., 2019),
although observed at a higher inclination. In Sect. 4.3 we discuss further the
ILR.

The ALMA $854\,\mu$m high-angular resolution image from the merged
configuration data set (see Fig. 2, red contours in left panel) shows a
continuum peak lying at the center of the CO(3-2) ring. The measured
coordinates are RA =22h02m01.89s and Dec =$-$31∘52’10.49” (2000), which agree
well with those of the ALMA 1.3 mm peak emission (Alonso-Herrero et al., 2020)
and the radio emission at 8.4 GHz (Thean et al., 2000). We thus assumed that
this position corresponds to the nucleus of the galaxy, that is, it marks the
AGN position. In the cold molecular gas ring, there is another bright
$854\,\mu$m source, which is located to the southwest of the nucleus at an
approximate projected distance of $0.5\arcsec$. There is some faint continuum
emission possibly connecting the two continuum sources. Other faint continuum
peaks are also detected. Indeed, the lower angular resolution ALMA $854\,\mu$m
map from the compact configuration (Fig. 2, right panel) shows both diffuse
and compact continuum emission in the cold molecular gas ring. From ground-
based subarcsecond resolution mid-infrared (mid-IR) imaging, there is a hint
of the presence of the two bright sources detected at $854\,\mu$m, although
the mid-IR emission is dominated by the AGN (see Roche et al., 2007; Asmus et
al., 2016). The lower angular resolution Spitzer/IRAC $8\,\mu$m image (see
García-Bernete et al., 2016) reveals emission along the molecular gas ring and
again suggests the presence of mid-IR emission at an orientation of
$\sim-120^{\circ}$, likely arising from the two bright $854\,\mu$m sources
emission.

The map of the CO(3-2) mean velocity (see Fig. 1, third panel from the top)
from the merged configuration shows a rotation pattern. There are also clear
distorsions in the velocity field, which might be in part due to the presence
of an ILR in NGC 7172. However the clear departure from rotation in central
region along the minor axis of the galaxy are indicative of the presence of
radial motions. In Sect. 4, we perform a detailed modeling of the CO(3-2)
kinematics and quantify the velocity and sign of these radial motions. The
mean velocity dispersion map (see Fig. 1, bottom panel) shows a complex
structure with several regions with velocity dispersions above $100\,{\rm
km\,s}^{-1}$, whereas the most external parts of the disk probed by these
observations show lower values, down to $5-10\,{\rm km\,s}^{-1}$.

Figure 6: 3DBAROLO observed moment maps. From top to bottom, ALMA CO(3-2) maps
of the observed velocity-integrated intensity (moment 0), observed mean
velocity field (moment 1), and velocity dispersion field (moment 2), produced
with the compact configuration observations using 3DBAROLO. All the contours
are on a linear scale. The ALMA beam (not shown) is $0.34\arcsec\times
0.27\arcsec$ at PA${}_{\rm beam}=-74.9^{\circ}$. The units of the velocity and
velocity dispersion maps are km s-1. In the top panel, the star marks the
approximate location of the AGN. Figure 7: Velocity map of the 3DBAROLO
rotating disk model without a radial velocity component fitted to the ALMA
CO(3-2) observations (top) and residual velocity map (bottom). The latter was
computed by subtracting the 3DBAROLO model from the observed moment 1 map.

###  3.2 VTL/SINFONI

To compare the VLT/SINFONI and ALMA maps, we first aligned them by assuming
that the peak of the SINFONI emission line and continuum maps (the latter not
shown here) and the ALMA $854\,\mu$m continuum emission coincide. This is
justified since Smajić et al. (2012) showed that the peaks of the SINFONI
near-IR continuum maps mark the position of the nucleus of the galaxy.

The overall SINFONI H2 $2.12\,\mu$m morphology of the central $\sim
4\arcsec\times 4\arcsec$ (top-left panel of Fig. 4), which is similar to the
map from Smajić et al. (2012), shows two bright sources and diffuse emission
which extends over larger scales coincident with the CO(3-2) ring. The
brighest of the two H2 peaks arises from the nucleus, while the second peak
lies close (in projection) and to the southwest of the AGN. The comparison of
the SINFONI map with the ALMA CO(3-2) (bottom-left panel of Fig. 4) shows that
the secondary H2 peak coincides with one of the bright CO(3-2) clumps in the
ring of cold molecular gas as well as with an $854\,\mu$m continuum peak. It
is also noticeable that there is bright H2 emission at the AGN position, while
the CO(3-2) emission is fainter there, when compared to regions in the cold
molecular gas ring. Bright H2 and faint CO(3-2) emission at the AGN position
has been observed in other Seyfert galaxies, for instance, NGC 2110 (Rosario
et al., 2019). Conversely, we do not detect bright H2 emission from other
CO(3-2) clumps in the ring. Finally, the more diffuse H2 emission appears to
be filling the region of the inner rim of the CO(3-2) ring but it also extends
to the ring.

The extended emission from the SINFONI [Si vi]$\lambda 1.96\,\mu$m line map
(top right panel of Fig. 3) shows the characteristic wide-angle ionization
cone morphology, similar to that observed in the optical emission lines
(Thomas et al., 2017). It is also mostly extended to the southeast and
southwest of the AGN. Likely, the other side of the cone is obscured by the
north rim of the ring, which also marks the near side of the galaxy. The
projected size of the detected emission in this side is approximately
$1.5\arcsec\simeq 270\,$pc. This high-excitation line only traces the emission
in the cone closest to the AGN and it is generally between the broad and the
narrow line region (Müller-Sánchez et al., 2011). Indeed, the optical
ionization cone traced by the optical [O iii]$\lambda$5007 emission line is
known to be extended over much larger scales (see Thomas et al., 2017). The
second [Si vi] peak is seen close in projection to the AGN but it appears to
be slightly displaced to the east with respect to the CO(3-2) and H2 clumps in
the ring (Fig. 4).

The H2 kinematics (see Fig. 3, middle-left panel) shows a rotation pattern
with some deviations along the minor axis of te galaxy, which are similar to
those observed in the CO(3-2) mean velocity field. The [Si vi] velocity field
(see Fig. 3, middle-right panel) also shows an apparent rotation pattern,
although it can be seen that it is not exactly at the same orientation and
velocity values as that of the H2 mean velocity field (see below). The
presence of rotational + outflow motions in the coronal [Si vi] line has been
inferred in other AGNs (Müller-Sánchez et al., 2011; Ramos Almeida et al.,
2017). The velocity dispersion maps of the two lines are quite different. The
H2 line (Fig. 3, bottom-left panel) shows, except at the AGN position, a
mostly uniform distribution of with $\sigma({\rm H}_{2})\simeq 100\,{\rm
km\,s}^{-1}$. These values are slightly higher than those measured in the
central regions of other Seyfert galaxies (Hicks et al., 2009). The [Si vi]
velocity dispersion map (Fig. 3, bottom-right panel), on the other hand,
displays an interesting structure. In general, the measured values of the
velocity dispersion indicate the presence of relatively broad lines near the
AGN position with $\sigma({\rm[SiVI]})=400-600\,{\rm km\,s}^{-1}$
(FWHM$=900-1400\,{\rm km\,s}^{-1}$), which are indicative of the presence of
an ionized gas outflow (see below). The exception is the region where the AGN
wind appears to have impacted the disk of the galaxy, where the velocity
dispersions are markedly decreased.

To evaluate the presence of noncircular motions in the H2 and [Si vi] velocity
fields, we subtracted the stellar velocity field fitted with ppxf. The H2
velocity residual map shows (Fig. 5, left panel) red and blue excesses to the
northeast and southwest, respectively. If these motions are taking place in
the plane of the galaxy, they would indicate the presence of a molecular
outflow in the galaxy disk, as the near side of the galaxy is to the north.
Given the higher velocity resolution of the ALMA CO(3-2) observations, in
Sect. 4 we model the kinematics of this molecular gas transition to separate
the rotation from the noncircular motions. The [Si vi] velocity residual map
(see Fig. 5, right panel), on the other hand, displays mostly blueshifted
velocities of a few hundred ${\rm km\,s}^{-1}$ in the southern part of the
ionization cone out to $\sim 200\,$pc (in projection) from the AGN. These
noncircular motions together with the large FWHM of the lines fitted in the
same region can be interpreted as an ionized gas outflow outside the plane of
the galaxy. It likely traces the inner part of the larger scale outflow
detected in the [O iii]$\lambda$5007 emission line (Thomas et al., 2017;
Davies et al., 2020). The milder red residual velocities of the [Si vi] line
to the southwest of the AGN are associated with the brightening of the line
described above, which probably indicates that the AGN is illuminating a clump
of gas in the disk of the galaxy rather than in the ionized gas outflow
region. The redshifted velocities might indicate outflowing motions in the
disk of the galaxy.

##  4 Modeling of the ALMA CO(3-2) kinematics

In this section we model the ALMA compact configuration CO(3-2) kinematics of
NGC 7172 with the 3DBAROLO code (Di Teodoro & Fraternali, 2015). The angular
resolution of these observations (see Table 1) allows to resolve the
kinematics on physical scales of $\sim 54\,$pc. This code fits simple rotating
disk models using 3D tilted rings and can be used with a variety of emission
line data, including ALMA data cubes.

Figure 8: ALMA CO(3-2) p-v diagrams generated with 3DBAROLO along the
kinematic major (top panel) and minor (bottom panel) axes. The gray scale and
blue contours are the ALMA CO(3-2) observations, while the red contours are
the 3DBAROLO rotating disk model. The yellow dots are the fitted rotation
curve.

###  4.1 Rotating disk

3DBAROLO can fit a number of free parameters for a rotating disk model,
including the kinematic center, the systemic velocity, the disk inclination
($i$) and position angle (PA) of the kinematic major axis, the scale height of
the disk, the circular velocity, and the gas velocity dispersion ($\sigma_{\rm
gas}$). It also takes into account effects related to the beam smearing in the
definition of the best-fit model for a given spatial resolution. 3DBAROLO also
produces maps of the observed velocity-integrated intensity (moment 0), a map
of the observed mean velocity field (moment 1) and velocity dispersion field
(moment 2), as well as position-velocity (p-v) diagrams along the kinematic
major and minor axes. Before we started the fits, we trimmed the original
compact configuration data cube to the FoV with detected emission, $\sim
20.9\arcsec\times 4.6\arcsec$.

Figure 6 shows the ALMA CO(3-2) observed moment maps of NGC 7172. The
intensity, velocity, and velocity dispersion maps are similar to those in Fig.
1, considering the difference in angular resolution. The CO(3-2) mean velocity
field shows a general rotation pattern. However, some important distorsions
are readily seen in the molecular gas ring, which are accompanied by the
presence of high velocity dispersion values, especially along the east-west
direction in the disk of the galaxy. The CO(3-2) velocity dispersions show
relatively large values of up to $\sim 100\,{\rm km\,s}^{-1}$ in the ring,
whereas in the outer parts of the disk mapped with ALMA the velocity
dispersions decrease to $\sim 5\,{\rm km\,s}^{-1}$.

Figure 9:  Velocity map of the 3DBAROLO rotating disk model with a radial
velocity component and residual velocity map. Panels are the same as in Fig.
7. The star symbol shows the approximate location of the AGN.

Figure 10: ALMA CO(3-2) p-v diagrams generated with 3DBAROLO. Panels, colors,
and lines are the same as Fig. 8, but for the 3DBAROLO disk model with a
radial velocity component. The yellow dots in the top panel are the fixed
rotation curve used for this model.

For all the 3DBAROLO fits, we fixed the kinematic center at the position of
the $854\,\mu$m continuum peak (see Sect. 3.1) and used a disk Gaussian scale
height of $0.05\arcsec$ ($\simeq 10$ pc, equivalent to a 24 pc FWHM at the
assumed distance). Since NGC 7172 is seen at a high inclination (see below),
this relatively thin disk is needed to avoid mixing the different emitting
regions in our line of sight. We took a radial separation between the rings of
$0.125\arcsec$ and a total of 70 rings, thus reaching out to radial distances
of approximately $8.75\arcsec$ ($\simeq 1.6\,$kpc). Given the high inclination
of NGC 7172, we first measured it from the apparent relative size of the cold
molecular gas ring, assuming that it has a circular shape. We obtained
$i=85^{\circ}$, which we allowed to vary by a few degrees during the fit. The
observed PA of the CO(3-2) kinematics appears to be close to the east-west
direction, as found for the optical emission lines (Thomas et al., 2017). We
thus allowed our fit to vary this parameter by $10^{\circ}$. During the first
step, we fit five parameters, namely, $i$, PA, systemic velocity, circular
velocity, and $\sigma_{\rm gas}$. For the last parameter we imposed a minimum
value of $5\,{\rm km\,s}^{-1}$, as seen in the observations.

We derived a systemic velocity of 2532 km s-1 and an average value of the
inclination of $i=88^{\circ}$. Figure 7 shows the best-fit model CO(3-2) mean
velocity field (top panel) and the CO(3-2) mean velocity residuals (bottom
panel), which were computed by subtracting the model velocity from the
observed velocity field. There are velocity residuals of a few tens to $\simeq
100\,{\rm km\,s}^{-1}$, in the central region and in the outer parts of the
galaxy disk. To understand better the mean velocity residuals, we produced p-v
diagrams along the kinematic major and minor axes of the galaxy. The observed
p-v diagram along the kinematic major axis (Fig. 8, top panel, gray scale map
and blue contours) has a tilted X-shape, which is the result of beam smearing
and the ring-like structure of the highly inclined disk of NGC 7172. The
3DBAROLO rotating disk model (red contours in Fig. 8) produces a reasonably
good fit to this p-v diagram. However, the fitted rotation curve (yellow dots
in the figure) does not reach the terminal velocity at radial distances $r\sim
3-6\arcsec$ and is not well fitted in the innermost regions. Both are in part
responsible for the large velocity residuals seen in Fig. 7 (bottom panel).
Along the kinematic minor axis (Fig. 8, bottom panel), there are clear
noncircular motions in the central $2\arcsec$ that we address in the see next
section.

###  4.2 Rotating disk with radial velocity

Within the approximate inner $2\arcsec$, the minor axis p-v diagram shows
redshifted motions to the south of the AGN and blueshifted to the north (see
Fig. 8, bottom panel). Since the north is the near side of the galaxy (see the
top panel of Fig. 1), this suggests the presence of an outflow in the cold
molecular gas ring, if these motions are taking place in the plane of the
galaxy. We thus run another 3DBAROLO model including a radial velocity
($v_{\rm rad}$) component. We fixed the inclination to the average value from
the previous run and the derived systemic velocity. We also fixed the rotation
curve to agree better with the observed p-v diagram along the major axis. We
therefore left PA, $\sigma_{\rm gas}$, and $v_{\rm rad}$ as free parameters.

We show the resulting mean velocity model and velocity residual map in Fig. 9
(top and bottom panels, respectively). It is immediately clear from the
comparison with Fig. 7, that the 3DBAROLO model with the fixed rotation curve
and the radial velocity component produces a better fit to the observations.
The effect of including the latter is appreciated in the CO(3-2) p-v diagram
along the kinematic minor axis (see Fig. 10). However, even when including
radial velocities, the model does not reach the observed velocity of nearly
$+150\,{\rm km\,s}^{-1}$ to the south, close to the AGN position. The maximum
fitted radial velocities are $80-100\,{\rm km\,s}^{-1}$ (see the bottom panel
of Fig. 11), progressively decreasing to $\simeq 20-30\,{\rm km\,s}^{-1}$ out
to a radial distance of $\simeq 4.5\arcsec$. This deceleration might be due to
the AGN wind encountering large amounts of molecular gas. The bright peaks of
H2, CO(3-2), and $854\,\mu$m emission in the ring (see Sect. 3) might be
caused by this impact. Within the gas ring, the gas velocity dispersion takes
values of approximately $\sigma_{\rm gas}\simeq 10\,{\rm km\,s}^{-1}$, except
in the region with the largest radial velocity values (see the middle panel of
Fig. 11) where the gas dispersion is slightly lower. At $r>4.5\arcsec$, the
velocity dispersion goes down to the minimum value imposed in our fit
($\sigma_{\rm gas}=5\,{\rm km\,s}^{-1}$).

Figure 11: Radial profiles of the ALMA CO(3-2) median intensity (top panel),
gas velocity dispersion (middle panel), and radial velocity (bottom panel)
fitted with the 3DBAROLO model in Sect. 4.2. As explained by García-Burillo et
al. (2019), the vertical error bars in the integrated CO(3-2) emission reflect
the deviations from symmetry in the gas distribution.

Despite having included a radial velocity component in the 3DBAROLO model,
there are still some CO(3-2) mean velocity residuals in some regions of the
map (Fig. 9, bottom panel). Some are beyond the expected virial motions around
rotation of typically a few tens of ${\rm km\,s}^{-1}$. In the central
$2\arcsec$ of NGC 7172, there are two regions with moderate velocity residuals
of the order of $50\,{\rm km\,s}^{-1}$, which are redshifted to the southwest
of the AGN and blueshifted to the northeast. They appear to be coincident with
those regions where the innermost part of AGN wind, traced by the VLT/SINFONI
[Si vi] emission (see left panels of Fig. 4), impacts the inner part of the
cold molecular gas ring. Even though at the radial distances of these regions
we fit the largest values of the radial velocities (bottom panel of Fig. 11),
the residuals mean that this azimuthally averaged model cannot explain
completely the observed kinematics. In fact, these distinct velocity residuals
also define kinematically the expanding molecular ring with a diameter of
$\sim 6\arcsec$ or approximately $1.1$ kpc. The residual mean velocities are
not only confined to these regions, but there are some residuals beyond the
molecular ring, mostly to the northeast.

We note that the 3DBAROLO tool does not take into account the potential
contribution from other terms of the Fourier decomposition of noncircular
motions. These include tangental motions or higher order terms that could
improve the quality of the fit (Schoenmakers et al., 1997). The missing terms,
which can capture better the density wave streaming motions produced by a
stellar bar, are in principle more suitably accounted for by tools like
kinemetry (Krajnović et al., 2006). This is particularly clear in those cases
where the mean velocity fields provide a realistic description of the gas
motions, that is, in galaxy disks seen at favorably low inclinations444We
nevertheless note that kinemetry would be of limited use to fit the observed
mean velocity field of NGC 7172 due to its high inclination.. García-Burillo
et al. (2019) benchmarked the solutions found by 3DBAROLO against the output
provided by kinemetry for the disk of NGC 1068, which is seen at $i\simeq
41^{\circ}$, and concluded that there is an overall excellent agreement in the
sign and magnitude of the $v_{\rm rad}$ radial profiles derived by the two
modeling tools, in spite of their different working approaches.

In this context, it is worth recalling that in all realistic gas
configurations for the gas response to a stellar bar inside its corotation
(see Sect. 4.3, for a discussion of an alternative scenario), the average
value of the $v_{\rm rad}$ term should reflect prevalent inward radial motions
along the bar leading edges and down to the ILR ring. These motions are due to
the orbit crowding of precessing individual elliptical orbits (see e.g., Wong
et al., 2004; García-Burillo et al., 2014, 2019). In particular, for the case
of a spiral-like pseudo-ring formed outside and down to the ILR, gas motions
should be dominated either by inflow or, in the case of a circular ring by no-
flow at all (see e.g., Wong et al., 2004). Other orbit configurations not
contemplated in the models published by Wong et al. (2004) cannot be formally
excluded, like those related to the presence of a nuclear bar or episodic
leading gas spirals. However, there is no evidence for any of these in NGC
7172. Moreover, the fact that the sign of $<$$v_{\rm rad}$$>$$(r)$ in the
central $\simeq 700$ pc of NGC 7172 is reversed relative to the basic
theoretical expectation (i.e., no flow $<$$v_{\rm rad}>$$=0$ or inflow based
on the sign of $<$$v_{\rm rad}$$>$) suggests that there is a (true) radial
(out)flow component superposed to the usual terms that could be potentially
attributed to bar-driven noncircular motions in these regions. This is similar
to the scenario described by García-Burillo et al. (2014, 2019) for NGC 1068,
where the presence of the molecular outflow was unambiguously detected by a
clear reversal of the $s1$ term in the Fourier decomposition of the velocity
field of the gas in the inner region of the galaxy disk. Both 3DBAROLO and the
Fourier decomposition done by kinemetry capture this signature of the outflow,
that is, the sign reversal of radial motions (García-Burillo et al., 2014,
2019).

###  4.3 Signatures of an ILR in the observed CO(3-2) kinematics

In Sect. 3.1 we proposed that the conspicuous ring morphology displayed by the
CO(3–2) merged configuration emission might be explained in terms of the
canonical gas response to an ILR of a stellar bar (Buta & Combes, 1996). The
existence of a large-scale stellar bar in NGC 7172 is still debated. Based on
the modeling of the near-IR 2MASS isophotes, Menéndez-Delmestre et al. (2007)
reported the existence of a large-scale bar (PA=$96^{\circ}$ and a semi-major
axis of $a_{\rm bar}=45\arcsec\simeq 8\,$kpc), while Lin et al. (2018) did not
require one. However, the noncircular motions of the molecular gas revealed by
the CO data in the central $\simeq 1-1.5$ kpc of the galaxy disk might be
reflecting the influence on the gas kinematics of a (not yet observed) nuclear
bar located within the large-scale stellar bar. This scenario is explored in
detail in the numerical simulations of Appendix A. To explain the observed
CO(3-2) molecular ring size, the radius of this putative nuclear bar needs to
be significantly smaller, of the order of $r=2$ kpc, than that of Menéndez-
Delmestre et al. (2007).

As illustrated in Appendix A, the observed S-shape of the CO(3-2) mean
velocity field and the outflow signature along the minor axis could be
reproduced reasonably well by selecting a favorable phase angle of a nuclear
bar in the plane of the galaxy (see Figs. 16 and 17). These noncircular
motions reflect the projection of elliptical streamlines corresponding to the
$x_{\rm 1}$ orbits building the potential of the nuclear bar. In particular, a
good correspondence with the data requires that the $2$ kpc-semi-major axis
nuclear bar is seen at a moderate inclination ($i=60^{\circ}$). This is
nevertheless in stark contrast with the high value of the inclination needed
to fit the CO(3-2) kinematics with 3DBAROLO. Furthermore, in these simulations
the observed CO(3-2) morphology appears as a result of the pile-up of gas in a
highly elliptical ring at the location of a single ILR. The nuclear bar in
these simulations is a “fast” $m=2$ mode. As a result, there is little room
for $x_{\rm 2}$ orbits, which are only present when there are two distinct
ILRs. This physically possible, yet limit case, configuration has two
implications. First, the gas piles up at a highly elliptical ILR ring and,
secondly, the $x_{\rm 1}$ orbits do not precess into $x_{\rm 2}$ orbits and,
as a consequence, the formation of the canonical bar leading edges feature
—favoring the scenario described in Sect. 4.2— would be thwarted.

While the configuration described above and in Appendix A for a putative
nuclear bar is an alternative interpretation for the observations, the lack of
any direct evidence of its existence disfavors this scenario versus the AGN-
driven outflow scenario we discuss in Sect. 6.

Table 2: Nuclear and circumnuclear cold molecular gas properties.

Region | $r$ | $i$ | CO(3-2) flux | $M_{\rm gas}$
---|---|---|---|---
| (pc) | (∘) | (Jy kms-1) | ($M_{\odot}$)
Torus | 32 | 67 | 1.4 | $8.2\times 10^{5}$
Nuclear | 50 | 85 | 0.9 | $7.2\times 10^{5}$
Circumnuclear | 200 | 85 | 21 | $1.7\times 10^{7}$
Ring | 720 | 85 | 270 | $6.2\times 10^{8}$
555We used different brightness temperature ratios for the torus and the other
regions, namely, $T_{\rm B}$CO(3-2)/$T_{\rm B}$CO(1-0)$=2.9$ for the torus,
$T_{\rm B}$CO(3-2)/$T_{\rm B}$CO(1-0)$=2.0$ for the nuclear and circumnuclear
regions, and $T_{\rm B}$CO(3-2)/$T_{\rm B}$CO(1-0)$=0.7$ for the ring. See
text for details.

##  5 The torus of NGC 7172

The first ALMA detection of an AGN torus was for the Seyfert galaxy NGC 1068
(e.g., García-Burillo et al., 2016; Gallimore et al., 2016; Imanishi et al.,
2018; García-Burillo et al., 2019; Impellizzeri et al., 2019). The NGC 1068
torus is a multiphase structure with diameters in the $7-40\,$pc range,
depending on the molecular transition and the cold dust continuum. In other
nearby AGNs, ALMA high-angular resolution (typically less than $0.1\arcsec$)
observations of the cold dust and molecular gas have proven to be the most
efficient way to resolve molecular dusty tori. In the approximately twenty
detections reported so far, the tori/disks are found to be relatively large,
with diameters $20-130\,$pc, and masses in the $10^{5}-10^{7}\,M_{\odot}$
range in Seyfert galaxies (Izumi et al., 2018; Alonso-Herrero et al., 2018,
2019; García-Burillo et al., 2021) and low-luminosity AGNs (Combes et al.,
2019). Moreover, the molecular gas column densities at the AGN location appear
to be broadly correlated with the X-ray absorptions $N_{H}$, but physical
resolutions of the order of 10 pc are needed to reach the relevant scales
responsible for AGN obscuration (Alonso-Herrero et al., 2018; García-Burillo
et al., 2021).

The left panels of Fig. 12 show the observed $854\,\mu$m continuum of the
central $0.4\arcsec\times 0.4\arcsec$ (approximately $72\,{\rm pc}\times
72\,{\rm pc}$) for the observations with the highest angular resolution
(extended configuration, top panel) and the intermediate resolution (merged
configuration, bottom panel). The corresponding physical resolutions are
approximately 11 pc and 13 pc, respectively. From the comparison with the beam
of the merged configuration observations, it is immediately clear that the
continuum emission is extended. In the bottom panels of this figure we marked
the extent of the torus with a blue dashed ellipse, which traces approximately
the $3\times$rms contour (see below). The orientation of this extended
emission appears to be nearly perpendicular to the [Si vi]$\lambda 1.96\,\mu$m
emission, which indicates that it is likely tracing equatorial emission in the
dusty torus. The aspect ratio of the $854\,\mu$m emission (before the point-
source subtraction, see below) implies a torus inclination of approximately
$i_{\rm torus}=67^{\circ}$. In fact, this needs to be taken as an upper limit
because the torus is likely to have some thickness. Nevertheless, this
estimate is in good agreement within intermediate inclinations inferred from
the fitting of the infrared and X-ray emission with torus models for NGC 7172
(Ramos Almeida et al., 2009, 2011; Alonso-Herrero et al., 2011; Ichikawa et
al., 2015; Vasylenko, 2018; Tanimoto et al., 2020). The derived torus radius
is approximately $0.18\arcsec\sim 32$ pc, which is within the range observed
for other Seyfert galaxies and low-luminosity AGNs (Alonso-Herrero et al.,
2018; Combes et al., 2019; García-Burillo et al., 2021).

Nevertheless, as found in other Seyfert galaxies, it is likely that even at
$854\,\mu$m there is some contribution from synchrotron emission (Pasetto et
al., 2019; Alonso-Herrero et al., 2019; García-Burillo et al., 2019, 2021). We
followed a slightly modified version of the method described by García-Burillo
et al. (2021) to fit the unresolved emission, which is assumed to provide an
upper limit to the synchrotron emission. Briefly, we started by fitting the
extended configuration $854\,\mu$m continuum map with a point source with the
observation beam size and orientation, and an elliptical component. The
estimated unresolved flux is $520\,\mu$Jy. We then subtracted the point-source
fit from the observations. The point-source subtracted image (Fig. 12, top-
right panel) shows no emission residuals at the AGN position, that is, all the
observed emission at this angular resolution is unresolved. Next, we generated
a point source image corresponding to the beam of the merged configuration
data set, scaled it to the point source flux from the previous step, and
subtracted it from the observations.

The $854\,\mu$m point source subtracted image shows significant extended
emission at the 3 to $5\times\sigma$ levels, whereas at the AGN position there
is no residual emission (bottom-right panel of Fig. 12). The measured fluxes
are $877\,\mu$Jy for the point + extended emission and $364\,\mu$Jy after the
point source subtraction. The extended emission therefore accounts for
approximately 42% of the observed flux within $r=32\,$pc and can be associated
with cold dust emission in the torus. It is likely that the point source is
oversubtracted since in the first step we assumed that all the unresolved
emission within the 11 pc beam of the extended configuration is produced by
synchrotron emission. Higher angular resolution observations demonstrate that
at this far-IR wavelength, the synchrotron emission is confined to regions of
only a few parsecs in size (see García-Burillo et al., 2019, 2021, and 2023,
in preparation).

Figure 12: Central $0.4\arcsec\times 0.4\arcsec$ region showing the ALMA
$854\,\mu$m emission. Top panels: Observed (left panel) and point-source
subtracted (right panel) images from the extended configuration data set.
Lower panels: Same as the upper panels, but for the merged configuration. The
dashed blue ellipse marks the approximate extent of the torus. In all the
panels, the first contour is at $3\times$ rms. The gray ellipses represent the
corresponding observation beams.

We estimated the torus gas mass using the $854\,\mu$m extended emission flux
and assuming $T_{\rm dust}\simeq T_{\rm gas}=100\,$K, a dust emissivity value
of $\kappa_{\rm 351GHz}=0.0865\,{\rm m}^{2}\,{\rm kg}^{-1}$ (Klaas et al.,
2001), and a gas-to-dust ratio of 100. We obtained $M_{\rm gas}^{\rm
dust}\simeq 8.1\times 10^{5}\,M_{\odot}$. For comparison, we integrated the
CO(3-2) flux within the torus radius of 32 pc and its derived inclination (see
Table 2), using the same assumptions as in Sect. 6.1. For this estimate, we
took the brightness temperature ratio measured in the NGC 1068 torus, $T_{\rm
B}$CO(3-2)/$T_{\rm B}$CO(1-0)$=2.9$ (García-Burillo et al., 2014). We derived
a cold molecular gas in the torus of $M_{\rm gas}^{\rm CO}\simeq 8.2\times
10^{5}\,M_{\odot}$, in excellent agreement with the value estimated from the
cold dust emission. It is also within the range of torus masses inferred in
other Seyfert galaxies (García-Burillo et al., 2021). We measured an H2 column
density at the AGN position of $\log{\rm(N_{\rm H2}})=$22.34 mol cm-2, which
agrees well the observed values in other GATOS Seyfert galaxies with similar
AGN luminosities (see Fig. 19, right, from García-Burillo et al., 2021).

##  6 Discussion

In Sect. 4.2, we showed that the CO(3-2) minor axis p-v diagram (Fig. 10) goes
across significantly strong emission from the ring. Under the commonly assumed
hypothesis that the bulk of molecular gas shares a coplanar geometry, the
$v_{\rm rad}$ term is the only component of gas motions that has a nonzero
projection along the disk minor axis. If the molecular gas is following
circular orbits, for the known orientation of the galaxy, the derived sign of
the radial velocity from the global 3DBAROLO best fit to the CO(3-2) data cube
implies the presence of a prevalent outward radial component throughout the
ring region and out to $r\simeq 700$ pc in the disk. In this section, we
derive the properties of this molecular outflow, compare them with those of
the ionized outflow, and look for evidence of the impact of the outflow on
molecular gas in the nuclear regions of NGC 7172.

###  6.1 Properties of the cold molecular gas outflow

Stone et al. (2016) also found tentative evidence for the presence of a
molecular outflow in NGC 7172, using $\sim 10\arcsec$ resolution Herschel/PACS
observations of the OH $119\,\mu$m absorption feature. They measured an
approximate blueshifted velocity of $50\,{\rm km\,s}^{-1}$ of the OH feature,
which the authors considered just at the limit of their outflow detection
criterion. This value of the OH velocity is similar to the typical value of
the CO(3-2) radial velocity fit with 3DBAROLO in the molecular gas ring (see
bottom panel of Fig. 11). In the particular case of NGC 7172, the detection of
the OH outflow was probably aided by the fact that the outflow is observed
close to our line of sight.

To compute the properties of the CO(3-2) molecular outflow, we assumed a
simple shell geometry so that the mass outflow rate can be written as: ${\rm
d}M_{\rm gas}/{\rm d}t=M_{\rm gas}\times v_{\rm out}/R$ (Maiolino et al.,
2012; Lutz et al., 2020), where $M_{\rm gas}$ is the mass of molecular gas,
$v_{\rm out}$ is the outflow velocity, and $R$ is the size of the outflow
region. For a coplanar geometry for the molecular outflow, the outflow
velocity is $v_{\rm out}=v_{\rm rad}$. To derive the molecular gas mass, we
used equation 3 in Bolatto et al. (2013) with a CO-to-H2 conversion factor of
$X_{\rm CO}=2\times 10^{20}{\rm mol\,cm}^{-2}({\rm K\,km\,s}^{-1})^{-1}$. This
expression includes the helium correction. To obtain the CO(1-0) intensity, we
took a typical ratio of the brightness temperature in galaxy disks of $T_{\rm
B}$CO(3-2)/$T_{\rm B}$CO(1-0)$=0.7$ (see García-Burillo et al., 2021, and
references therein). We integrated the CO(3-2) flux in the ring (within
$R=4\arcsec\simeq 720\,$pc, see Table 2), which provides a molecular gas mass
of $M_{\rm gas}=6\times 10^{8}\,M_{\odot}$, and taking an average value of the
outflow velocity of $46\,{\rm km\,s}^{-1}$. We inferred a mass outflow rate of
$40\pm 18\,M_{\odot}\,{\rm yr}^{-1}$, assuming that the main source of
uncertainty in this calculation comes from the fitted radial velocities.

Figure 13: Molecular gas mass outflow rate versus AGN bolometric luminosity of
NGC 7172 compared with the compilation of infrared bright galaxies from Lutz
et al. (2020) except for NGC 1068 which is from García-Burillo et al. (2014),
QSO2s from Ramos Almeida et al. (2022), and local ULIRGs classified as AGNs
from Lamperti et al. (2022). For these comparison samples, we only plot
galaxies with detections in both axes.

###  6.2 Coupling between the AGN wind and the disk of the galaxy

The molecular gas mass outflow rate of NGC 7172 derived in the previous
section is large compared with the modest ionized gas mass outflow rate of
0.005 M⊙ yr-1 (Davies et al., 2020). Interestingly, even though the Seyfert
galaxies in their sample have similar AGN luminosities, NGC 7172 has one of
the lowest ionized mass outflow rates. This together with the observed scatter
of the so-called AGN-wind scaling laws might imply that AGN luminosity is not
the only physical quantity explaining the different gas phases of outflows in
active galaxies (Fluetsch et al., 2019; Davies et al., 2020). On the other
hand, our results indicate that NGC 7172 follows well the trend between
$L_{\rm AGN}$ and molecular gas mass outflow rate found by Lutz et al. (2020)
for a compilation of local infrared bright galaxies, gray points in Fig. 13.
We note however that other works, such as Ramos Almeida et al. (2022) and
Lamperti et al. (2022), do not find tight correlations between these
quantities for samples of type 2 quasars (QSO2s) and local ULIRGs classified
as AGNs, red triangles and orange squares, respectively.

In simulations of AGN winds in disk galaxies, the outflows are predicted to
escape along the path of less resistance and thus are not able to unbind
completely a molecular disk (see for instance, Faucher-Giguère & Quataert,
2012). However, outflows are predicted to be able to sweep up part of the
material in a galaxy disk, but at much lower velocities than the initial AGN
wind, which can be favored with a good geometrical coupling. An illustration
of the idea of the geometrical coupling can be found in Fig. 4 of Ramos
Almeida et al. (2022). Observationally, the scarcity of strong molecular
outflows in several Seyfert galaxies (Domínguez-Fernández et al., 2020), QSO2s
with AGN-driven winds (Ramos Almeida et al., 2022), and local ULIRGs
classified as AGNs (Lamperti et al., 2022) has been explained due to the lack
of a geometrical coupling.

The derived torus inclination of NGC 7172 is $\sim 61-67^{\circ}$ (see Sect.
5), while the molecular gas ring is seen almost edge-on (see Sect. 4). The
inclination (presumably perpendicular to the torus) and wide opening angle of
the ionization cone of NGC 7172 (Thomas et al., 2017) therefore allow for a
relatively strong geometrical coupling between the AGN wind and the galaxy
interstellar medium (ISM), thus favoring the molecular outflow in the ring.
The good spatial correspondence between the CO(3-2), near-IR H2 and continuum
$854\,\mu$m bright knot in the ring to the southwest of the AGN, and the edge
of the ionization cone traced by the VLT/SINFONI [Si vi] emission (Sect. 3 and
Figs. 2 and 4) add support to this scenario. At this particular location of
the NGC 7172 ring (also on the other side, to the northeast of the AGN), it is
likely that the impact with material in the ring caused a strong deceleration
of the AGN wind and subsequently in the outflow velocity of the molecular gas,
as seen in Fig. 11 (bottom panel). Indeed, in Davies et al. (2020) sample, NGC
7172 is among the Seyfert galaxies with the lowest velocities of the ionized
gas, thus providing further evidence to the above scenario.

###  6.3 Radio emission

A radio jet, even with low power, running through a galaxy can interact with
its ISM and entrain molecular gas in the galaxy disk. Moreover, in simulations
the geometrical coupling between radio jets and the ISM of Seyfert galaxies,
including its molecular gas phase, has been found to be an important factor
(Mukherjee et al., 2018; Talbot et al., 2022). Evidence of the interaction of
radio jets with the galaxy ISM has been observed in a few nearby Seyfert
galaxies (see, e.g., García-Burillo et al., 2014; Morganti et al., 2015;
Pereira-Santaella et al., 2022; Peralta de Arriba et al., 2023).

In this section we discuss the possibility that a low-power radio jet might be
driving, at least in part, the molecular outflow observed in NGC 7172. The
moderate angular resolution VLA 8.4 GHz observations of Morganti et al. (1999)
revealed bright nuclear emission as well as extended emission along the major
axis of the galaxy. This extended emission likely corresponds to the molecular
ring detected with our ALMA observations. Subsequent VLA observations at
subarcsecond resolution showed again nuclear point-like emission and some
faint radio emission to the northeast and southwest of the AGN with an
approximate $2\arcsec$ extent (Thean et al., 2000). The orientation of this
faint extended radio emission, especially to the southwest, resembles that of
the [Si vi] emission (see figure 8 of Smajić et al., 2012).

We estimated a jet power of $P_{\rm jet}$$\sim$$10^{43}\,{\rm erg\,s}^{-1}$
for NGC 7172, using the relation given by Bîrzan et al. (2008) and the 8.4 GHz
flux density quoted in Thean et al. (2000), assuming a power law
$f_{\nu}\propto\nu^{-1}$ to derive the 1400 MHz flux density. The kinetic
luminosity of the molecular outflow can be computed as: $L_{\rm kin}=1/2\times
dM_{\rm gas}/dt\times v_{\rm out}^{2}$ (García-Burillo et al., 2014). We
obtained $L_{\rm kin}\sim 3\times 10^{40}\,{\rm erg\,s}^{-1}$. If indeed,
there is a radio jet in NGC 7172, it could in principle provide sufficient
power to drive the molecular outflow in this galaxy. However, sensitive radio
observations at higher angular resolution are needed to confirm this.

###  6.4 Feedback in the molecular gas ring of NGC 7172

In nearby active galaxies, feedback can manifest itself in various manners,
including suppressing star formation (Gao et al., 2021), triggering star
formation (Cresci et al., 2015; Maiolino et al., 2017; Bessiere & Ramos
Almeida, 2022; Bellocchi et al., 2023), as well as redistributing the
molecular gas in galaxy disks (Alonso-Herrero et al., 2018; Shimizu et al.,
2019; García-Bernete et al., 2021; Ramos Almeida et al., 2022). In a sample of
GATOS Seyfert galaxies, García-Burillo et al. (2021) observed a clear imprint
left by the AGN wind on the molecular gas at torus and nuclear scales, with a
decreased molecular gas surface density compared to that on circumnuclear
scales ($r=200\,$pc) in Seyfert galaxies with the highest AGN luminosities
and/or Eddington ratios.

To evaluate the level of clearing of molecular gas in the torus and nuclear
regions of NGC 7172, we measured the cold molecular gas surface densities
($\Sigma$) on different scales using the CO(3-2) fluxes reported in Table 2.
We computed two cold molecular gas concentration indices defined by García-
Burillo et al. (2021), namely, Index-1=$\log\Sigma^{\rm r=50pc}_{\rm
H2}/\Sigma^{\rm r=200pc}_{\rm H2}=-0.16$ and Index-II=$\log\Sigma^{\rm
torus}_{\rm H2}/\Sigma^{\rm r=200pc}_{\rm H2}=0.25$. The main difference
between these two concentration indices in NGC 7172 is driven by the different
inclinations used for the torus and the $r=50\,$pc scales and the different
temperature brightness ratios (see Table 2). The circumnuclear $r=200\,$pc
scale does not encompass the entire ring at all. Increasing the size of the
circumnuclear region to include the ring gives a concentration index of
$\log\Sigma^{\rm r=50pc}_{\rm H2}/\Sigma^{\rm r=720pc}_{\rm H2}=-0.6$.

The comparison of the two molecular gas concentration indices of NGC 7172 with
the sample of low-luminosity AGNs and GATOS Seyfert galaxies (Fig. 18 of
García-Burillo et al., 2021) indicates that NGC 7172 follows well the observed
trends for the two physical scales of the torus and its immediate
surroundings. That is, there is a redistribution of the molecular gas in the
torus and nuclear regions of NGC 7172 when compared to other less luminous
Seyfert galaxies and AGNs. For this comparison, we used an absorption-
corrected $2-10\,$keV luminosity of $\log L({\rm 2-10keV})=42.84$ erg s-1
(Ricci et al., 2017, recalculated for the assumed distance in this work) and
an Eddington ratio of $\sim 0.02$ (Vasudevan et al., 2010).

NGC 7172 shows molecular gas concentration indices similar to NGC 3227 and NGC
4388, which also show evidence for the presence of (circum)nuclear local
outflows (Alonso-Herrero et al., 2019; Domínguez-Fernández et al., 2020;
García-Burillo et al., 2021). However, despite the clear evidence for the
presence of a large-scale (out to $r\sim 4\arcsec\sim 720\,$pc from the AGN)
outflowing ring in NGC 7172 (see Sect. 6.1), it does not seem to present an
extreme behavior in these relations. In other words, NGC 7172 does not show a
markedly strong deficiency of cold molecular gas in its nuclear regions, as
seen for instance in NGC 1068, even though both show comparable molecular gas
outflow rates. One possible explanation is that the AGN wind is more
collimated and faster in NGC 1068. Indeed, this galaxy shows an ionized gas
outflow velocity of up to $1000\,{\rm km\,s}^{-1}$ (García-Burillo et al.,
2019), which is about 2.5 times faster than that in NGC 7172 (Davies et al.,
2020). Furthermore, the velocities of the molecular gas outflow in NGC 1068
are $100-150\,{\rm km\,s}^{-1}$ (see García-Burillo et al., 2019), thus about
a factor of $2-3$ faster than those in the outflow of NGC 7172. This likely
resulted in a more efficient clearing of the molecular gas in the nuclear
region of NGC 1068 compared to NGC 7172.

We finally explore the fate of the circumnuclear molecular gas in NGC 7172
since its mass outflow rate appears to be at the high end of those observed in
other AGNs of similar luminosity (Fig. 13). On the other hand, the velocity of
the molecular outflow of NGC 7172 is modest when compared with the galaxy
circular velocity. In Appendix B we modeled the escape velocity in NGC 7172
using the 3DBAROLO rotation curve. At a radial distance of 900 pc, just
outside of the outflow region, the escape velocity is $850\,{\rm km\,s}^{-1}$,
whereas at smaller radial distances this velocity is even higher (see Fig.
18). Given that the molecular outflow is taking place mostly in the disk of
the galaxy and its velocity is low with respect to the expected escape
velocity, we can therefore conclude that in this galaxy most of the molecular
gas will not leave the galaxy, at least during this period of AGN activity.

##  7 Summary and conclusions

We presented new ALMA band 7 observations of the CO(3-2) transition and
associated $854\,\mu$m continuum, together with new VLT/SINFONI observations
of NGC 7172. This is a nearby ($d=37\,$Mpc) luminous Seyfert galaxy in the
GATOS sample with an AGN bolometric luminosity of $1.3\times 10^{44}\,{\rm
erg\,s}^{-1}$ (Davies et al., 2015). The angular resolutions of the ALMA
observations ($0.06-0.3\arcsec$) allowed us to probe regions on physical
scales of $11-56\,$pc.

The ALMA CO(3-2) intensity maps show the presence of a highly inclined
($i\simeq 85-87^{\circ}$) cold molecular gas ring with an approximate radius
of $3-4\arcsec\simeq 540-720\,$ pc, likely associated with an ILR. There is
also extended emission along the disk of the galaxy covering the FoV of the
ALMA observations along the east-west direction. This ring is also detected at
$854\,\mu$m and appears to trace the strong dust lane that crosses the
(circum)nuclear region of NGC 7172. The cold molecular gas mass of the ring is
$\simeq 6.2\times 10^{8}\,M_{\odot}$. The ALMA $854\,\mu$m continuum emission
and the VLT/SINFONI H2 at $2.12\,\mu$m and [Si vi]$\lambda 1.96\,\mu$m line
maps peak at the AGN position (see Smajić et al., 2012, for a detailed
discussion of previous SINFONI results). The CO(3-2) map, on the other hand,
shows the brightest emission in several clumps in the ring. There are also
secondary H2 and $854\,\mu$m peaks, which additionally coincide with one of
the bright CO(3-2) clumps in the ring. They all are located close to the edge
of the inner ionization cone delineated by the [Si vi] line emission.

The velocity fields of [Si vi], H2, and CO(3-2) show clear evidence for the
presence of noncircular motions. After subtraction of the stellar velocity
field, the velocities of the ionized gas, traced with the [Si
vi]$\lambda$$1.96\,\mu$m line, are blueshifted a few hundred ${\rm
km\,s}^{-1}$ in a region to the south of the AGN position. We interpreted this
as ionized gas outflowing outside the plane of the galaxy out to projected
distances of $\simeq 200\,$pc. This emission likely corresponds to the inner
part of the larger ionized gas cone and outflow detected in [O iii]. The
CO(3-2) p-v diagram along the kinematic minor axis reveals the presence of
noncircular motions of the cold molecular gas with observed velocities of up
to $\sim 150\,{\rm km\,s}^{-1}$. These are blueshifted to the north of the AGN
and redshifted to the south. Since the north side of the galaxy is the near
side, these noncircular motions imply the presence of a molecular outflow in
the plane of the galaxy.

A 3DBAROLO model of a rotating disk with a radial velocity component
reproduces reasonably well the complicated CO(3-2) kinematics observed in NGC
7172. We note that we also discussed an alternative scenario in which the
noncircular motions could be the result of a nuclear bar (see Appendix A).
However, the most plausible explanation for the observed CO(3-2) kinematics
indicates that the entire ring is not only rotating but also outflowing. The
largest values of the fitted radial velocity take place close to the AGN with
a gradual deceleration, which is probably caused by the impact of the AGN
wind, traced by the [Si vi] line, with the galaxy ISM. The integrated cold
molecular gas mass outflow rate of the ring is $\sim 40\,M_{\odot}\,{\rm
yr}^{-1}$, which is several orders of magnitude higher than that of the
ionized phase ($0.005\,M_{\odot}\,{\rm yr}^{-1}$, see Davies et al., 2020).
The wide-angle ionization cone (see Fig. 4, and also Thomas et al., 2017) of
NGC 7172 probably implies that the AGN wind is not highly collimated. As
discussed by Müller-Sánchez et al. (2011), this can result in relatively slow
outflow velocities and moderate mass outflow rates of the ionized gas phase,
as seen in NGC 7172 (Davies et al., 2020). Despite this, the geometrical
coupling between the wide-angle ionization cone (perpendicular to $i_{\rm
torus}$) and the disk of the galaxy may have favored the interaction of the
AGN wind with the surrounding ISM, thus entraining molecular gas in the galaxy
disk.

The torus of NGC 7172 is detected as extended emission in the ALMA $854\,\mu$m
map, after subtracting the unresolved emission. The latter likely has a
synchrotron origin. The derived torus radius is 32 pc and is seen at an
inclination of $i_{\rm torus}\simeq 67^{\circ}$ (lower limit), based on the
observed aspect ratio. The torus gas mass is $8\times 10^{5}\,M_{\odot}$, as
measured from the extended $854\,\mu$m emission as well as the CO(3-2)
emission. These torus properties are similar to other Seyfert galaxies in the
GATOS sample. When compared to less luminous AGNs, NGC 7172 presents decreased
CO(3-2) surface brightness on torus and nuclear scales relative to that on
circumnuclear scales. We interpreted this as evidence of redistribution of
molecular gas in the torus and nuclear region of NGC 7172 due to AGN feedback,
as observed in other luminous Seyfert galaxies.

###### Acknowledgements.

We thank the referee for some insightful comments. AA-H and SG-B acknowledge
support from grant PGC2018-094671-B-I00 funded by MCIN/AEI/
10.13039/501100011033 and by ERDF A way of making Europe. AAH also
acknowledges support from PID2021-124665NB-I00 funded by the Spanish Ministry
of Science and Innovation and the State Agency of Research
MCIN/AEI/10.13039/501100011033 PID2021-124665NB-I00 and ERDF A way of making
Europe. SGB also acknowledges support from the research project
PID2019-106027GA-C44 of the Spanish Ministerio de Ciencia e Innovación. CRA
acknowledges the projects “Feeding and feedback in active galaxies,” with
reference PID2019-106027GB-C42, funded by MICINN-AEI/10.13039/501100011033,
“Quantifying the impact of quasar feedback on galaxy evolution,” with
reference EUR2020-112266, funded by MICINN-AEI/10.13039/501100011033 and the
European Union NextGenerationEU/PRTR, and from the Consejería de Economía,
Conocimiento y Empleo del Gobierno de Canarias and the European Regional
Development Fund (ERDF) under grant “Quasar feedback and molecular gas
reservoirs,” with reference ProID2020010105, ACCISI/FEDER, UE. CR acknowledges
support from the Fondecyt Iniciacion grant 11190831 and ANID BASAL project
FB210003. EB acknowledges the María Zambrano program of the Spanish Ministerio
de Universidades funded by the Next Generation European Union and is also
partly supported by grant RTI2018-096188-B-I00 funded by
MCIN/AEI/10.13039/501100011033. This paper makes use of the following ALMA
data: ADS/JAO.ALMA#2019.1.00618.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. Based on observations collected at the European Southern Observatory
under ESO programme 093.B-0057(B). This research has made use of ESASky,
developed by the ESAC Science Data Centre (ESDC) team and maintained alongside
other ESA science mission’s archives at ESA’s European Space Astronomy Centre
(ESAC, Madrid, Spain). This research has made use of the NASA/IPAC
Extragalactic Database (NED), which is operated by the Jet Propulsion
Laboratory, California Institute of Technology, under contract with the
National Aeronautics and Space Administration. We acknowledge the usage of the
HyperLeda database (http://leda.univ-lyon1.fr). This research made use of
NumPy (Harris et al., 2020), Matplotlib (Hunter, 2007) and Astropy (Astropy
Collaboration et al., 2013, 2018).

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##  Appendix A Modelization of noncircular motions due to a central bar

This appendix describes a bar-ring model, with the nuclear bar being the
source of noncircular motions in the center, as an alternative explanation for
the observed CO(3-2) kinematics of the central regions of NGC 7172. The
central gas distribution mapped with ALMA has an extent of 3.2 kpc or
projected radius of 1.6 kpc (c.f., Fig. 1). Its morphology reveals a central
ring, with the characteristic enhancement in the northeast and southwest parts
of the ring, as shown in Fig. 2. This indicates that the ring may be a pseudo-
ring, made by the winding of the two spiral arms, elongated along the bar, and
usually observed as the dusty leading edges of the bar in spiral galaxies. The
projected radius of the ring is $\sim$ 300 pc, typical of an ILR. This central
molecular feature appears very elongated. It is likely however that the ring
and barred structure are intrinsically elongated, considering that the
inclination of the galaxy is not completely edge-on, but of the order of
$\sim$ 60∘, as noted by Hyperleda and the observed large-scale optical
morphology (Fig. 1). We then assumed this value of the inclination in the
following modelization.

Figure 14:  Circular velocity and corresponding frequencies $\Omega$,
$\Omega\pm\kappa/2$, $\Omega-\kappa/4$ of the gas model for the center of NGC
7172. The pattern speed of the nuclear bar of the N-body simulation is marked
in red.

Figure 15: Three snapshots, separated by 33 Myr, of the gas component viewed
face-on, for the NGC 7172 model.

We used N-body simulations with gas, star formation, and feedback, as
described in Combes (2008). The Poisson equation is solved with a 3D Particle-
Mesh code based on FFT, and is fully self-consistent with a live dark halo.
The gas dissipation is represented by sticky particles and a total of 240 000
particles is used. The star formation rate follows a Schmidt law, with
exponent $n=1.4$, a density threshold, and an average gas consumption time-
scale of 5 Gyr. The stellar feedback is modeled by injecting energy and gas
velocity dispersion, when the stellar mass loss is distributed through gas on
neighboring particles. The potential of the galaxy is modeled with several
components, including a stellar bulge and disk, a dark matter halo, and a gas
disk, with the parameters listed in Table 6. The shape of these components are
Miyamoto-Nagai disks and Plummer spheres, as described in Chilingarian et al.
(2010). The computed circular velocity and angular frequencies, $\Omega$,
$\Omega\pm\kappa/2$, $\Omega-\kappa/4$, are plotted in Fig. 14.

Figure 16: Moment maps of the gas model for the central regions of NGC 7172.
Left panel. Moment 0. The color scale is linear, in arbitrary units. Right
panel. Isovelocities of the gas model for the central regions of NGC 7172.
Negative velocity contours are traced by dotted lines. The spacing between
isovelocities is 30 km s-1.

Figure 17:  Computed p-v diagrams along the major axis (left) and minor axis
(right) of the gas model for the central regions of NGC 7172. For the major
axis, east is to the left, and west to the right. For the minor axis, south is
to the left, and north to the right.  Table 3: Parameters adopted for the
model.

Component | Bulge | Disk | DM-Halo | Gas
---|---|---|---|---
Mass (10${}^{9}\,$M⊙) | 11.5 | 46 | 172 | 9
Radius (kpc)a | 0.44 | 2.22 | 5.33 | 2.6
666 $a$$a$footnotetext: Characteristic radius, see text for details.

In the simulation, after 300 Myr a stellar bar has developed and gas has
accumulated at the ILR, as shown in the three snapshots of Fig. 15. The
pattern speed of the bar $\Omega_{p}$ is $\sim$ 80 km s-1 kpc-1, allowing
barely for one ILR.

The gas component at the first snapshot of Fig. 15 (top panel) is then
projected on the sky, with an inclination of 60∘, and a position angle
providing the best fit to the observations. The data are projected into a
cube, with pixel sizes of $0.16\arcsec$ and 18 km s-1. We smoothed the cube to
a beam size comparable to the compact ALMA configuration of our band 7
observations. We show the moment 0 of the cube in Fig. 16 (left panel) and the
isovelocities in Fig. 16 (right panel).

The overall morphology of the molecular ring is reproduced in this simulation,
although the model does not intend to be a fit for this peculiar galaxy. The
simulations presented here are to demonstrate that a bar and ILR ring model,
with its noncircular motions, is able to reproduce the main observed features
of the molecular gas in NGC 7172. The velocity field, with its characteristic
S-shape frequently observed in barred galaxies, indicates noncircular motions
corresponding to an apparent outflow of the molecular gas. Indeed, the near-
side of the galaxy is to the north, and far side to the south. This is deduced
from the dust morphology, and corresponds also to a trailing spiral pattern.
Along the minor axis, the velocity is negative with respect to the systemic
velocity, the gas is moving toward the observer to the north, and the reverse
to the south This apparent gas outflow is also illustrated in the p-v diagrams
of Fig. 17. The major axis is at PA=90∘, and the orientation of the cuts is
indicated in the caption. We notice that this apparent outflow is particularly
deceiving, since the gas in the simulation is in fact inflowing, due to the
gravity torques of the stellar bar.

##  Appendix B Escape velocity

In this appendix we estimate the escape velocity ($V_{\rm esc}$) as a function
of the radial distance for NGC 7172. For a particle at radius $R$, located in
a gravitational potential $\Phi(R)$, the definition of the escape velocity is
when the kinetic energy per unit mass is $V^{2}/2=-\Phi(R)$. It is assumed
that $\Phi(R)$ reaches zero in the outskirt of the potential, that is, the
virial radius of the galaxy. From the rotation curve $V_{\rm rot}$ of the
galaxy, estimated from the observed p-v diagram of Fig. 10 modeled with
3DBAROLO, we can estimate the potential, assuming in a first approximation
spherical symmetry. We can thus write $V_{\rm rot}^{2}/r={\rm d}\Phi(r)/{\rm
d}r$, and compute:

$\Phi(R)=\Phi_{0}+\int_{0}^{R}V_{\rm rot}^{2}(r)dr/r$

where $\Phi_{0}$ is then computed throughout $\Phi(R_{\rm vir})$ = 0. We have
adopted a simple rotation curve, taking a linearly increasing $V_{\rm rot}$
from 0 to $300\,{\rm km\,s}^{-1}$ up to 2.5″=0.45 kpc, and then a constant
$V_{\rm rot}$ =$300\,{\rm km\,s}^{-1}$ all the way to $r$=100″=18 kpc. After
this optical radius, we assume that the dark matter halo is dominating, with a
Navarro-French-White profile, where the dark matter density is varying as
$\rho(r)\propto r^{-3}$, and the potential becomes $\propto{\rm log}(r)/r$
from 18 kpc to $R_{\rm vir}$ =180 kpc (virial radius). At each radius $V_{\rm
esc}^{2}(R)=2|\Phi(R)|$. Figure 18 shows the derived $V_{\rm esc}$ as a
function of the radial distance. At 0.9 kpc, $V_{\rm esc}$ is already
$850\,{\rm km\,s}^{-1}$.

Figure 18: Modeled escape velocity for NGC 7172.