11institutetext: Departamento de Física Teórica e Experimental, Universidade
Federal do Rio Grande do Norte, Natal, RN 59078-970, Brazil
11email<EMAIL_ADDRESS>22institutetext: European Southern
Observatory, Karl-Schwarzschild-Straße 2, D–85748, Garching, Germany
33institutetext: Istituto di Astrofisica e Planetologia Spaziali (INAF–IAPS),
Via Fosso del Cavaliere 100, I–00133 Roma, Italy 44institutetext: Observatoire
de Paris, LERMA, College de France, PSL University, CNRS, Sorbonne University,
F-75014 Paris, France 55institutetext: Department of Astronomy and Oskar Klein
Centre; Stockholm University; AlbaNova 106 91 Stockholm, Sweden
66institutetext: Departamento de Astronomía, Universidad de La Serena, Av.
Juan Cisternas 1200, La Serena, Chile 77institutetext: Dirección de Formación
General, Facultad de Educación y Cs. Sociales, Universidad Andres Bello, Sede
Concepción, Talcahuano, Chile 88institutetext: Núcleo de Astronomía, Facultad
de Ingeniería y Ciencias Universidad Diego Portales (UDP) Santiago de Chile
99institutetext: Dep. of Astrophysics, Astronomy & Mechanics, Faculty of
Physics, National and Kapodistrian University of Athens, Panepis-timiopolis,
Zografou 15784, Greece 1010institutetext: National Observatory of Athens,
Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing,
Penteli 15236Athens, Greece 1111institutetext: Institute of Theoretical
Astrophysics, University of Oslo, PO Box 1029, Blindern 0315, Oslo, Norway
1212institutetext: Chalmers University of Technology, Department of Earth and
Space Sciences, Onsala Space Observatory, 439 92 Onsala, Sweden
1313institutetext: National Astronomical Observatory of Japan 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan

# Molecular gas kinematics in the nuclear region of nearby Seyfert galaxies
with ALMA

A. Bewketu Belete 11 P. Andreani 22 J. A. Fernández-Ontiveros 33 E.
Hatziminaoglou 22 F. Combes 44 M. Sirressi 55 R. Slater 6677 C. Ricci 88 K.
Dasyra 991010 C. Cicone 1111 S. Aalto 1212 L. Spinoglio 33 M. Imanishi 1313 J.
R. De Medeiros 11

(Received xxx; accepted yyy)

###### Abstract

Context. The study of the distribution, morphology and kinematics of cold
molecular gas in the nuclear and circumnuclear regions of active galactic
nuclei (AGN) helps to characterise and hence to quantify the impact of the AGN
on the host galaxy over its lifetime.

Aims. We present the analysis of the molecular gas in the nuclear regions of
three Seyfert galaxies, NGC 4968, NGC 4845, and MCG-06-30-15, with the help of
ALMA observations of the CO(2-1) emission line. The aim is to determine the
kinematics of the gas in the central ($\sim$ 1 kpc) region, and thereby to
probe AGN nuclear fueling and feedback.

Methods. We use two different softwares, namely the 3D-Based Analysis of
Rotating Object via Line Observations (3DBAROLO) and DiskFit, to model the
kinematics of the gas in the molecular disc, and thereby to determine the gas
rotation and any kinematical perturbations.

Results. Circular motions dominate the kinematics of the molecular gas in the
central discs, mainly in NGC 4845 and MCG-06-30-15, however there is a clear
evidence of non-circular motions in the central ($\sim$ 1 kpc) region of NGC
4845 and NGC 4968. The strongest non-circular motion is detected in the inner
disc of NGC 4968, mainly along the minor kinematic axis, with velocity $\sim
115\,\rm{km\,s^{-1}}$. Of all DiskFit models, the bisymmetric model is found
to give the best-fit for NGC 4968 and NGC 4845, indicating that the observed
non-circular motions in the inner disc of these galaxies could be due to the
nuclear barred structure, the gas streaming in elliptical orbits aligned along
the bar. If the dynamics of NGC 4968 is modeled as a corotation pattern just
outside of the bar, the bar pattern speed turns out to be at $\Omega_{b}$ =
$52\,\rm{km\,s^{-1}\,kpc^{-1}}$ the corotation is set at 3.5 kpc and the inner
Lindblad resonance (ILR) ring at R = 300pc corresponding to the CO emission
ring. In the NGC 4968 galaxy, the torques exerted on the gas by the bar are
positive in the centre, within the gas nuclear ring, and negative outside.
This shows that the gas is transiently trapped in the inner Lindblad
resonance. The comparison of the CO intensity maps with the map of the cold
dust emission shows the absence of CO in the centre of NGC 4968 and that the
dust distribution and the CO emission in and around the centre of NGC 4845
have similar extension. The 1.2 mm ALMA continuum is peaked and compact in NGC
4968 and MCG-06-30-15, but their CO(2-1) has an extended distribution.
Allowing the CO-to-H2 conversion factor $\alpha_{CO}$ between 0.8 and 3.2,
typical of nearby galaxies of the same type, the molecular mass M(H2) is
estimated to be $\sim 3-12\times 10^{7}\leavevmode\nobreak\ {\rm M_{\odot}}$
(NGC 4968), $\sim 9-36\times 10^{7}\leavevmode\nobreak\ {\rm M_{\odot}}$ (NGC
4845), and $\sim 1-4\times 10^{7}\leavevmode\nobreak\ {\rm M_{\odot}}$
(MCG-06-30-15).

Conclusions. We conclude that the observed non-circular motions in the
molecular disc of NGC 4968 and likely that seen in NGC 4845 is due to the
presence of the bar in the nuclear region. We discuss the possibility that the
observed pattern in the kinematics be due to the presence of the AGN and this
might be the case for NGC4845. At the current spectral and spatial resolution
and sensitivity we cannot claim any strong evidence in these sources of the
long sought feedback/feeding effect due to the AGN presence.

###### Key Words.:

galaxies: active; galaxies: individual: NGC 4968, NGC 4845, MCG-06-30-15;
galaxies: ISM; galaxies: kinematics and dynamics; galaxies: nuclei; galaxies:
spiral

##  1 Introduction

Powerful active galactic nuclei (hereafter, AGNs) can drive fast outflows
which affect the properties and kinematics of the ambient gas in the nuclear
and circumnuclear regions of their host galaxies. By heating the gas, or/and
expelling it from the central regions, they may affect the star formation
histories of the host galaxy bulge (see e.g., Fluetsch et al. 2019; Oosterloo
et al. 2017; Fiore et al. 2017; Morganti et al. 2017 and references therein).
Even though the mechanisms that can produce molecular outflows are still
uncertain (Morganti et al. 2017), cold molecular gas is known as the phase
that dominates the central regions, and found to be the most massive outflow
component in AGN (see e.g., Kanekar et al. 2008; Cicone et al. 2014; Dasyra &
Combes 2011; Dasyra & Combes 2012; Morganti et al. 2015; Feruglio et al. 2010;
Rupke & Veilleux 2013; García-Burillo et al. 2015; Carniani et al. 2015; Fiore
et al. 2017; Morganti et al. 2017; Fluetsch et al. 2019), making cold
molecular gas the main tracer of AGN outflows.

Several works aim at understanding the origin of non-circular motions, outflow
driving mechanisms and the impact of AGN feedback on the interstellar medium
(ISM) by imaging and modelling the kinematics of cold molecular gas in the
central regions of AGN host galaxies. Both types of non-circular motions
(inflows and outflows) are detected in the nuclear and circumnuclear regions
of nearby star forming and AGN host galaxies. Using the ALMA observations of
dense molecular gas tracers (CO(3-2), CO(6-5), HCN(4-3), HCO+ (4-3), and
CS(7–6)) García-Burillo et al. (2014) studied the fueling and the feedback of
star formation and nuclear activity in the nearby Seyfert 2 nucleus NGC 1068.
The authors confirm the detection of molecular line and dust continuum
emissions from different regions in the source. They also indicate the
presence of both an inward radial flow in the starburst ring and the bar
region, and a massive outflow, an order of magnitude higher than the star
formation rate, in the inner region (r $\sim$ 50 pc out to r $\sim$ 400 pc),
interpreting the inward flow as the combined action of the bar and the spiral
arms, and the outflow is AGN driven. Based on the tight correlation between
the ionized gas outflow, the radio jet, and the occurrence of outward motions
in the disc the autors suggest that the outflow is likely AGN driven.
With a better spatial resolution of $\sim$4 pc towards the same galaxy,
García-Burillo et al. (2016) studied the dust emission and the distribution
and kinematics of molecular gas by using the ALMA observations of the dust
continuum at 432 $\mu$m and the CO(6–5) molecular line emission in its
circumnuclear disc. They conclude that the overall slow rotation pattern of
the disc is perturbed by strong non-circular motions and enhanced turbulence
(see also a similar work in García-Burillo et al., 2019).

Combes et al. (2014) report the ALMA observations of CO(3-2) emission in the
nuclear region of the Seyfert 1 galaxy NGC 1566. They find a conspicuous
nuclear trailing spiral, and weak non-circular motions at the periphery of the
nuclear spiral arms. Recently, by analysing the nuclear kinematics of the same
galaxy NGC 1566 via ALMA observations of the CO(2-1) emission, Slater et al.
(2019) show the presence of significant non-circular motions in the innermost
(200 pc) and along spiral arms in the central kpc. They find a molecular
outflow in the disc with velocities of $\sim 180\,\rm{km\,s^{-1}}$ in the
nucleus.

Using the ALMA observations of CO(3-2) emission around the nucleus of NGC
1433, Combes et al. (2013) find also an intense high-velocity CO emission
feature redshifted to $200\,\rm{km\,s^{-1}}$, with a blue-shifted counterpart,
at 2${}^{{}^{\prime\prime}}$ (100 pc) from the centre, interpreting the wide
component as an outflow partly driven by the central star formation, but
mainly boosted by the AGN through its radio jets. Similarly, using the ALMA
observations of the infrared-luminous merger NGC 3256, Sakamoto et al. (2014)
detect high-velocity molecular outflows from the northern and southern nucleus
with two different large velocities $>750\,\rm{km\,s^{-1}}$ and
[1000$\sim$2000] $\,\rm{km\,s^{-1}}$, respectively, interpreting the northern
outflow as a starburst-driven superwind and the southern one as an outflow
driven by a bipolar radio jet from an AGN.

In their ALMA CO(2–1) line observations with angular resolutions
0.11${}^{{}^{\prime\prime}}$-0.26${}^{{}^{\prime\prime}}$ (9-21 pc), Alonso-
Herrero et al. (2018) find strong non-circular motions in the central
(0.2${}^{{}^{\prime\prime}}$-0.3${}^{{}^{\prime\prime}}$) regions of the
nearby Seyfert galaxy NGC 5643 with velocities of up to 110 km/s, explaining
the motions as radial outflows in the nuclear disc in the absence of a nuclear
bar. Domínguez-Fernández et al. (2020) present a detailed analysis of the
kinematics and morphology of cold molecular gas in the nuclear/circumnuclear
regions of five nearby (19 - 58 Mpc) Seyfert galaxies, Mrk 1066, NGC 2273, NGC
4253, NGC 4388, NGC 7465. The authors detect CO(2-1) emission in all galaxies
with disky or circumnuclear ring like morphologies. Moreover, they find in all
galaxies, though the bulk of the gas is rotating in the plane of the galaxy,
non-circular motions in four of the galaxies (Mrk 1066, NGC 4253, NGC 4388 and
NGC 7465). They interpret the non-circular motions in NGC 4253, NGC 4388 and
NGC 7465 as streaming motions due to the presence of a large-scale bar,
whereas the non-circular motions in the nuclear regions of Mrk 1066 and NGC
4388 are outflows due to the interaction of the AGN wind with molecular gas in
the galaxy disc.

Fast and massive molecular outflows are capable to impact the nearby ISM, and
molecular mass outflow rate is shown to be well correlated with AGN bolometric
luminosity (Fiore et al., 2017). Fiore et al. (2017) also report that in AGNs
with bolometric luminosity up to $\sim$ 1046 erg s-1 the molecular mass
outflow rate dominates its ionised counterpart. Moreover, Fiore et al. (2017)
find that the molecular gas depletion timescale and the molecular gas fraction
of galaxies hosting powerful AGN driven winds are 3-10 times shorter and
smaller than those of main sequence galaxies with similar star formation rate,
stellar mass, and redshift, indicating that, at high AGN bolometric
luminosity, the reduced molecular gas fraction may be due to the destruction
of molecules by the wind, leading to a larger fraction of gas in the atomic
ionised phase.

Also using the ALMA observations of CO(2-1), Morganti et al. (2015) find that
the gas kinematics in the Seyfert 2 galaxy IC 5063 are very complex. The
authors detect fast cold molecular gas outflow with velocities up to
$650\,\rm{km\,s^{-1}}$, indicating that the outflow can be driven by the
central AGN and the radio jet. Similarly, using the CO(2-1) and CO(3-2) ALMA
observations of the nearby Seyfert 1.5 galaxy NGC 3227, Alonso-Herrero et al.
(2019) show the presence of CO clumps with complex kinematics, dominated by
non-circular motions in the central region (1′′ $\sim$73pc). Fernández-
Ontiveros et al. (2020) also show the presence of a prominent jet-driven
outflow of CO(2-1) molecular gas along the kinematic minor axis of the Seyfert
2 galaxy ESO 420-G13, at a distance of 340-600 pc from the nucleus.

Several similar works were published on constraining the kinematics/dynamics
of molecular gas in the nuclear/circumnuclear regions of star forming and AGN
host galaxies (e.g., Tadhunter et al. 2014; Ramakrishnan et al. 2019; Salak et
al. 2020; Lutz et al. 2020; Combes et al. 2019; Audibert et al. 2019; Sirressi
et al. 2019, see also review by Veilleux et al. 2020).
In this paper, we present the analysis of the CO molecular gas kinematics in
the nuclear regions of three different types of Seyfert galaxies, NGC 4968,
NGC 4845, and MCG-06-30-15, by using the ALMA observation of the bright
CO(2-1) emission line as a tracer. These galaxies are different in AGN type,
AGN luminosity, and morphology. The knowledge about the nature of cold
molecular gas kinematics and its origin in the nuclear and circumnuclear
regions of such different AGN host galaxies is essential to verify whether the
driving mechanism(s) is the same, which in turn could be used as an input to
construct a universal model that describes such physical mechanism(s).

The three galaxies belong to the TWIST sample (Fernández-Ontiveros et al.
(2020) and Fernández-Ontiveros et al, 2021 in prep) which aims at studying 41
AGN extracted from the IRAS 12$\mu m$ flux-limited sample (Rush, Spinoglio,
Malkan, 1993) located close enough (10$<$D$<$50 Mpc) to ensure a good spatial
resolution through ALMA observations and resolve the morphological structures
in the central $\sim$3$\times$3 kpc region, and being above the ”knee” of the
Seyfert galaxy luminosity function (therefore, being statistically
representative to determine the impact of the outflow and inflow mechanisms
for the bulk of the AGN population). Moreover the sample has been extensively
studied in the past 30 years and have a wealth of ancillary data from the
X-rays to the radio (Fernández-Ontiveros et al, 2021 in prep). The three
galaxies in this work extend the preliminary study of the TWIST sample
initiated in Fernández-Ontiveros et al. (2020) for ESO 420-G13. These include
one type 1 and two type 2 nuclei located at 20-40 Mpc, that sample three
different bins in X-ray luminosity. Table 1 list the properties of the three
objects under study.

To study the molecular gas kinematics we use two different softwares, namely
the 3D-Based Analysis of Rotating Object via Line Observations 3DBAROLO
111https://bbarolo.readthedocs.io/en/latest/ (Di Teodoro & Fraternali 2015)
and DiskFit (Peters et al. 2017). This paper is structured as follows. In
Section § 2 we present a brief description of the properties of the sources,
the ALMA observations and data reduction. We discuss modeling of the CO
molecular gas kinematics in § 3. The properties and kinematics of the CO
molecular gas, and the residuals in each galaxy are presented in § 4 and in §
5, § 6. We discuss the results in § 7, and the main conclusions in § 8.
We adopt a flat $\Lambda$CDM cosmology with $\Omega_{\lambda}$ = 0.7,
$\Omega_{\lambda}$ = 0.3, and $H_{0}$ = $70\,\rm{km\,s^{-1}}$ Mpc-1.

Table 1:  Physical and geometrical parameters of the galaxies. The SFR is
computed from the PAH observations (Mordini et al., 2021) and 12$\mu m$
luminosity in [${\rm log_{10}L_{\odot}}$] (from Rush, Spinoglio, Malkan,
1993). X-ray luminosity from Brighjtman & Nanda (2011)

.  NGC 4968 NGC 4845 MCG-6-30-15 AGN type S2 S2 S1.2 Redshift 0.00986 0.00411
0.008 Classification SB0 SABab Sab ${\rm\log L_{2-10keV}}$ 43.20 41.98 42.74
(erg/s) ${\rm\log L_{12\mu m}}$ 9.91 9.87 9.52 (L⊙) SFR (M⊙/yr) 4.29 - 1.82
Distance 42 Mpc 18 Mpc 37 Mpc RA 13h07m05.935s 12h58m01.187s 13h35m53.777s Dec
$-23^{o}40^{{}^{\prime}}36.23^{{}^{\prime\prime}}$
$1^{o}34^{{}^{\prime}}32.526^{{}^{\prime\prime}}$
$-34^{o}17^{{}^{\prime}}44.242^{{}^{\prime\prime}}$ INC (o) 60 73 [65-68] PA
(o) [234-256] [62-81] [115-122]

##  2 Basic galaxy properties and observations

NGC 4968 is a nearby Seyfert 2 spiral galaxy, classified as a barred Spiral
(SB0) according to the Hubble and de Vaucouleurs galaxy morphological
classification, located at a redshift of $z$ = 0.00986 (LaMassa et al. 2017;
Malkan et al. 1998), corresponding to a distance of 42 Mpc. NGC 4968 Narrow
Line Region (NLR) was imaged in the [O III] $\lambda$ 5007 and [N II]
$\lambda\lambda$ 6548, 6583 + H$\alpha$ emission lines, as well as in its
adjacent continua (centered near 5500 and 8000 Å) using HST by Ferruit et al.
(2000). From the continuum images these authors estimate a photometric major
axis P.A. of 45o and an inclination angle of 60o at radii greater than 10′′
(2.1 kpc) (Schmitt et al., 2003, see also). The NLR extends toward the south-
east side of the nucleus and the [OIII] line emission has a wedge-shaped
morphology filling the cavity inside the dusty ring. The presence of the dust
may be responsible of its morphology but the presence of a ionisation cone
projecting against the far side of the galaxy disc cannot be excluded (Ferruit
et al., 2000)
Strong et al. (2004) studied the properties of the molecular gas in NGC 4968
with single dish (15-m) millimetre observations at the ESO-SEST telescope.
They estimate the line luminosity (${\rm L_{CO}}$) and molecular mass (${\rm
M({H_{2}})}$) through observations from CO(1-0) (6.0$\times$107 K km s-1pc2
and $21.0\times 10^{7}$ M⊙, respectively), and CO(2-1) (4$\times$107 K km
s-1pc2 and $15.0\times 10^{7}$ M⊙, respectively), making use of a CO-to-H2
conversion factor, $\alpha_{\rm CO}$, of 3.47.

The galaxy NGC 4845 is a nearby Seyfert 2 with a clear starburst component
(Thomas et al., 2017), classified as an intermediate barred spiral galaxy
(SABab), at $z$ = 0.00411 located in the Virgo Southern Extension (Irwin et
al. (2015) and references therein). We adopt the Tully-Fisher distance of 18
Mpc. The inclination on the sky is almost edge-on, revealing contrasted dust
lanes on the near side, and a peanut-shape for the bulge. The galaxy contains
a bright unresolved core with a surrounding weak central disc (1.8 kpc
diameter). The radio spectrum of the core has been known to evolve with time,
which could be due to an adiabatic expansion (outflow), likely in the form of
a jet or cone (Irwin et al. 2015). Using spectral observations of NGC 4845 in
different position angles (PA = 44o, 78o, 98o, 118o, 178o), Bertola et al.
(1989) studied the kinematics of the ionised gas in the central region (r
$\leq$ 1.5 kpc) and revealed a regular but non-axisymmetric velocity field.
Based on photometry, Bertola et al. (1989) also point out the presence of a
possible slight twisting between the disc and bulge isophotes, interpreting
this as an indication of triaxial bulge in NGC 4845. This galaxy shows a
ionisation cone with an opening angle of 120o perpendicular to the
circumstellar disc of HII regions, the counter inionisation cone is faint,
likely because of exinction (Thomas et al., 2017).

The early-type Sab galaxy MCG-06-30-15 is a Seyfert 1.2 galaxy(Makarov et al.
2014) located at a distance of 37 Mpc, $z$ = 0.008 (Wu et al. 2009). This
active galaxy has a 400 pc diameter stellar kinematically distinct core (KDC)
counter-rotating with respect to the main body of the galaxy (Raimundo et al.
2017). The molecular gas, traced by the H2 2.12 $\mu$m emission is also
counter rotating with respect to the main stellar body of the galaxy, implying
that the formation of the distinct core is associated with inflow of external
gas into the centre of MCG-6-30-15 and the event that formed the counter-
rotating core is also the main mechanism providing gas for the AGN fuelling.
Moreover, this shows that external gas accretion is able to significantly
replenish the fuelling reservoir in such active galaxies. MCG-06-30-15 NLR was
imaged using HST by Ferruit et al. (2000) in the [O III] $\lambda$ 5007 and [N
II] $\lambda\lambda$ 6548, 6583 + H$\alpha$ emission lines, as well as in
their adjacent continua (centered near 5500 and 8000 Å). Ferruit et al. (2000)
estimate the photometric major axis P.A. and an inclination angle of 115o and
60o, respectively. The [O III] image reveals a nuclear extension aligned
parallel to the photometric major axis of the galaxy, which presumably
represents gas coplanar with the stellar disc (see also Schmitt et al., 2003).
Rosario et al. (2018) measure the CO(2-1) single dish flux and discuss the
properties of its molecular gas in relation to its AGN properties. These
authors estimate the line luminosity (${\rm L_{CO}}$) and molecular mass
(${\rm M({H_{2}})}$) through observations from CO(2-1) (1.3$\times$107 K km
s-1pc2 and $1.4\times 10^{7}$ M⊙, respectively) using a CO-to-H2 conversion
factor, $\alpha_{\rm CO}$, of 1.1.

###  2.1 ALMA observations and data reduction

####  2.1.1 ALMA observations

The observations of the bright CO(2-1) line at 230.5 GHz rest frequency (in
Band 6) were carried out as part of ALMA cycle 5 under project IDs
2017.1.00236.S in December 2017 and January 2018. With a spatial resolution
between 25pc and 48pc, the CO(2-1) maps are sensitive enough to detect
molecular masses as low as $\sim$ 105 M⊙ (5$\sigma$) per beam. See the summary
of ALMA observations in Table 1.

####  2.1.2 Data reduction and imaging

Data were calibrated and post-processed using the Common Astronomy Software
Applications (CASA) package (McMullin et al., 2007), applying the standard
calibration recipes provided by the ALMA Observatory. The data were calibrated
using the casa version 4.7.0 and the calibration script provided by the
observatory, while further post-processing was done using the CASA version
5.4.0. In all cases, the hogbom deconvolution algorithm was applied using
briggs weighting and a robustness value 2.0 to reconstruct the final
datacubes, optimising the value of the limiting flux threshold in each case.
The spectral datacubes for the emission lines were produced with a channel
width of $\sim 10$ and $\sim 30\,\rm{km\,s^{-1}}$ and a pixel size of about
1/5th to 1/4th of the synthesised beam size (see Table 1 for the synthesised
beam size). The emission line regions were automatically masked during the
cleaning process in the spectral cubes using the ”auto-multithresh” algorithm
in tclean.
The continuum emission was then subtracted in the spatial frequency domain -
i.e. prior to the image reconstruction - using a 1D polynomial interpolation
between the adjacent continuum channels at both sides of the respective
emission lines Continuum maps were constructed using all the continuum
channels in the four spectral windows, that is discarding the channels with
CO(2-1) emission. The masking procedure for the continuum data was run
interactively during the cleaning process.
Finally, all datacubes were corrected for the primary beam attenuation
pattern. Using the final CO(2-1) datacubes, the first three moments
corresponding to the integrated intensity map of the line, the average
velocity field and the average velocity dispersion map were computed
numerically. In order to reduce the noise in the moment maps, for each spaxel
only those channels with a signal-to-noise (S/N) above $\sim$5 the median
absolute deviation were considered, following the approach in Fernández-
Ontiveros et al. (2020).

Table 2:  ALMA CO(2-1) observation log | Target line CO(2-1) |  |  |
---|---|---|---|---
| NGC 4968 | NGC 4845 | MCG-06-30-15 |
$\nu_{rest}$ | 230.5 GHz | 230.5 GHz | 230.5 GHz |
Date | Dec 2017 | Dec 2017 | Dec 2017 |
| Jan 2018 | Jan 2018 | Jan 2018 |
Array configuration | C43-5 | C43-5 | C43-5 |
Spatial resolution | 48pc | 45pc | 25pc |
Channel width | 2.5 km s-1 | 2.5 km s-1 | 2.5 km s-1 |
Rms sensitivity | 1.4 mJy/beam | 7 mJy/beam | 0.7mJy/beam |
Synthesized beam | 0.27${}^{{}^{\prime\prime}}$x0.22${}^{{}^{\prime\prime}}$ | 0.56${}^{{}^{\prime\prime}}$x0.48${}^{{}^{\prime\prime}}$ | 0.16${}^{{}^{\prime\prime}}$x0.13${}^{{}^{\prime\prime}}$ |

##  3 Modeling the kinematics of CO(2-1) emission line

###  3.1 3D modeling of the main rotating disc

We use the CO(2-1) emission line as a tracer of the main kinematic features of
the CO gas in the nuclear region of the galaxies. To constrain the gas
kinematical perturbations we construct a 3D disc model using the 3D-Based
Analysis of Rotating Object via Line Observations (3DBAROLO) software and fit
the model to the CO (2-1) emission line datacube. This software automatically
fits 3D tilted-ring models to emission-line data cubes. The model assumes that
the emitting material at each radius is confined within a geometrically thin
disc and its kinematics are dominated by pure rotational motion (Di Teodoro &
Fraternali 2015). The model requires the geometrical parameters of the disc,
namely the centre position coordinates, the inclination angle (INC) and the
kinematic position angle (PA). When the emission peaks at the centre, like in
the case of NGC4845, the coordinates can be determined by fitting a 2D
Gaussian to the central part (where the peak emission is) of the intensity map
(see Sirressi et al. 2019), whereas for maps without a central emission peak
(the case of NGC 4968 and MCG-06-30-15) the code uses a source-finder
algorithm to identify the emission region, and then calculates the geometrical
centroid, weighted by the flux intensity. The centre positions are determined
and reported in Table 2. The INC, the angle between the normal to the disc
axis and the line of sight, can be inferred from the 0th moment map or from
the 1st moment map depending on how well these moments can be estimated. For
NGC 4845 we determine the INC parameter from the ratio of the two axes, major
and minor axes, in the 1st moment (velocity) map (see e.g. Sirressi et al.
2019). But for well resolved data (the case of NGC 4968) it is better to use
the 0th moment (intensity) map rather than the velocity field. The inclination
angle INC turns out to be 60o (NGC 4968) by fitting an ellipse to the outer
ring in the intensity map. For NGC 4845, the INC = 73o is determined from the
velocity field. For MCG-06-30-15, 3D-Barolo estimates that the INC angle
varies from 65o to 68o.
3D-Barolo measures the PA as the angle between the North and the receding half
of the major axis (= positive velocities in the velocity field), measured
counterclockwise (see Di Teodoro & Fraternali 2015). The PA varies from 234o
to 256o (NGC 4968) and from 62o to 81 o (NGC 4845). For MCG-06-30-15,
3D-Barolo estimates that the PA varies from 115o to 122o.

Using the estimated geometrical parameters and assuming a number of rings at
different radial separation we construct a disc model by using the 3D-Barolo
kinematic model and fit its emission to the continuum-subtracted ALMA CO(2-1)
line datacube. We use the ALMA CO(2-1) line datacube with a channel widths of
$10\,\rm{km\,s^{-1}}$.
The number of rings can be determined from the spatial extension of the
object. The model uses 10 rings with a radial separation of 0.217 arcsec. All
rings are placed at $N*RADSEP+RADSEP/2$, where $N$ is the number of rings and
$RADSEP$ is the radial separation in arcsec.

Since 3D-Barolo measures the noise at the spectral channel edges when it
builds the mask, to avoid the noise effect at the edges, instead of using the
continuum-subtracted ALMA CO(2-1) line datacube with velocity range =
$(-1000,990)\,\rm{km\,s^{-1}}$, we consider the central regions containing the
emission of the galaxies, reducing the velocity range of the input NGC 4968
datacube to $(-340,340)\,\rm{km\,s^{-1}}$. To construct the disc model for NGC
4968, we use 27 rings with a radial separation of 0.12 arcsec.
The velocity range of the input NGC 4845 datacube is reduced to
$(-510,240)\,\rm{km\,s^{-1}}$ and we use 22 rings with a radial separation of
0.55 arcsec. The Barolo fits for N4845 for the velocity and the velocity
dispersion are not optimal, however the results do not improve letting the
inclination angle to vary between 73 and 80 degrees.

For MCG-06-30-15, we feed the continuum subtracted line datacube to the model
without reducing its velocity range. The model is able to find the best model
reducing the residuals at minimum. This could be due to the fact that the
kinematics is purely dominated by regular rotation pattern (i.e. a simple
kinematics). A slight deviation appears between the blue and red contours in
p-v diagramme.

The Barolo fits for N4845 for the velocity and the velocity dispersion are not
optimal, however the results do not improve letting the inclination angle to
vary between 73 and 80 degrees.

The results from 3DBAROLO, the kinematic maps and $p-v$ diagrams, are given in
Figs. 1, 2 and 3 for NGC 4968, NGC 4845, and MCG-06-30-15, respectively. The
intensity maps of NGC 4968 and MCG-06-30-15 reveal the molecular gas
distribution in the nuclear regions as a ring-like morphology. The gas
distribution in the NGC 4845 appeared to have an edge-on inclination.

###  3.2 DiskFit modeling

The DiskFit software fits simple axisymmetric and non-axisymmetric non-
parametric models either to photometric images or to kinematic maps (velocity
fields) of disc galaxies. DiskFit fits an entire velocity field with a
physically motivated model. The underlying assumption is that the circular
orbit of a region of gas is affected by higher order perturbations (i.e.
”harmonics”). Physically, $m$ = 1 harmonics correspond to ”lopsided”
perturbations and $m$ = 2 harmonics correspond to bisymmetric (i.e. bar)
perturbations. The model is given by Peters et al. (2017) :

$V_{m}=V_{s}+\sin
i[V_{t}\cos(\theta)-V_{m,t}\cos(\theta_{b})\cos(\theta)-V_{m,r}(\sin
2\theta_{b})\sin(\theta)]$ (1)

where $V_{m}$ is the model (with $m$ specifying the harmonic order with $m$ =
1 or $m$ = 2 in the disc plane), $V_{s}$ is the systemic velocity, $V_{t}$ is
the mean orbital speed, $\theta$ is the angle between a point in the disc
relative to the major axis, $\theta_{b}$ is the angle between a point in the
disc relative to the bar, $V_{m,t}$ and $V_{m,r}$ are the tangential and
radial components of the non-circular motions, $\theta$ and $\theta_{b}$ are
the azimuthal angles relative to the major axis and the non-circular flow
axis, respectively, and $i$ is the disc inclination. DiskFit can also fit
radial flows (with $m$ = 0 distortions to the flow in the disc plane) and
symmetric warps in the outer disc.

DiskFit requires a flat inner disc, but it allows for a symmetric warp in the
outer disc. The disc is assumed to be flat out to a warp radius $r_{w}$,
beyond which both the ellipticity and the position angle of the line of nodes
vary in proportion to $(r-r_{w})^{2}$. In addition, DiskFit can find the best-
fitting inner warp radius $r_{w}$ and peak change in ellipticity and position
angle of the line of nodes, or it can hold any combination of these parameters
fixed. For an axisymmetric model, DiskFit estimates the circular speed for
kinematic data. For non-axisymmetric model, DiskFit provides quantitative
estimates of the non-circular flow speeds and an estimate of the mean circular
speed when run on velocity fields.

Figure 1: Upper panels: left panels (top to bottom): the $0^{th}$ (intensity),
$1^{st}$ (velocity field) and $2^{nd}$ (velocity dispersion) moment maps of
the ALMA CO(2-1) data of NGC 4968. central panels: the same as the left panels
but for the best-fit model constructed with 3DBAROLO. right panels: same as
the left panels but for the residual (data-model). A black cross marks the
centre of the galaxy. The major axis of the molecular disc is shown by a
black-dashed line in the velocity map. The yellow ellipse in the bottom-left
corner of the data velocity map shows the synthesized beam size
(0.27${}^{{}^{\prime\prime}}$x0.22${}^{{}^{\prime\prime}}$) with P.A = 245o.
North and East directions correspond to top and left, respectively. Lower
panels: : The $p-v$ diagrams extracted from the data-cube (blue solid
contours) and model-cube (red solid contours) along the major axis (top panel)
and along the minor axis (bottom panel). The contours level of both the data
and the model are at [1,2,4,8,16,32,64]*$l$, where $l$ = 0.0012. The rotation
velocity of each ring of the best-fit disc model is represented by the yellow
solid dots in the top panel.

Figure 2: The same as in Fig. 1 but for NGC 4845. The synthesized beam size
(0.56${}^{{}^{\prime\prime}}$x0.48${}^{{}^{\prime\prime}}$) is plotted in
yellow in the bottom-left corner of the data velocity map with P.A = 77o. The
contours level of both the data and the model are at [1,2,4,8,16,32,64]*$l$,
where $l$ = 0.00393635.

Figure 3: The same as in Fig. 1 but for MCG-06-30-15. The synthesized beam
size (0.16${}^{{}^{\prime\prime}}$x0.13${}^{{}^{\prime\prime}}$) is plotted in
yellow in the bottom-left corner of the model velocity map with P.A = 118o.
The contours level of both the data and the model are at
[1,2,4,8,16,32,64]*$l$, where $l$ = 0.00120941.

Different axisymmetric and non-axisymmetric DiskFit kinematic models, such as
pure rotation (flat disc), pure rotation (flat disc with warp), rotation plus
radial motion, lopsided, and bisymmetric models are shown in Figs. 4, 5, and 6
for NGC 4968, NGC 4845, and MCG-06-30-15, respectively.

##  4 The CO(2-1) residual emission

Figure 4: Diskfit results for NGC 4968. Top panels: Pure rotation DiskFit
model(flat disc). Middle panels: Rotation + radial motion DiskFit model.
Bottom panels: Bisymmetric DiskFit model. For every panel the top left figure
reports the data, the top right the model, the low left the residual obtained
subtracting the model from the data and the low right figure the dispersion.

Figure 5: DiskFit results for NGC 4845. Top panels: Pure rotation DiskFit
model (flat disk). Middle panels: Rotation + radial motion DiskFit model.
Bottom panels: Bisymmetric DiskFit model. For every panel the top left figure
reports the data, the top right the model, the low left the residual obtained
subtracting the model from the data and the low right figure the dispersion.

Figure 6: DiskFit results for MCG-06-30-15. Top panels: Pure rotation DiskFit
model (flat disc). Bottom panels: Rotation + radial motion DiskFit model. For
every panel the top left figure reports the data, the top right the model, the
low left the residual obtained subtracting the model from the data and the low
right figure the dispersion.

In the following sections, we present the properties and kinematics of the
residual (both from 3DBAROLO and DiskFit) CO molecular gas emission.

###  4.1 Residuals from 3DBAROLO

As explained in Sec. 3, 3D-Barolo makes a tilted-ring rotating disc model of
the input data, hence if there are non-circular motions, such as outflows, the
model will not be able to fully reproduce the observations. The non-circular
motions could be misinterpreted as tilted rings of the plane. Some non-
circular motions can be isolated from the rotating disc simply by subtracting
the regular rotation pattern from the observed kinematics (observation-
rotating disc model).

To see whether there are significant residuals in the CO(2-1) motions, we
calculate the residuals in the kinematic maps (see Fig. 1 for NGC 4968, Fig. 2
for NGC 4845, and Fig. 3 for MCG-06-30-15) by subtracting the 3D datacube
produced by the model from the observations (the input continuum-subtracted
CO(2-1) emission line datacube).

The 3DBAROLO model reproduces the observations of NGC 4968 relatively well
along the kinematic major axis, leaving important residuals mainly in the
north-east direction of the kinematic minor axis, as revealed by the velocity
map in Fig. 1. The residuals reach a maximum velocity of $\sim
90\,\rm{km\,s^{-1}}$, that is blueshifted to the south and south-east of the
minor axis and redshifted to the north and north-west of the minor axis with
velocity $\sim 160\,\rm{km\,s^{-1}}$. Therefore, the maximum residual velocity
is the mean of the two components as we read them from the residual datacube
$\sim$ 125 $\rm{km\,s^{-1}}$.

For NGC 4845, the model reproduces the observation reasonably well in the
kinematic major axis, leaving almost no residuals. However, the model leaves
small residuals in the nuclear region and either sides of the kinematic minor
axis (see Fig. 2). The residuals reach a maximum velocity of $\sim
60\,\rm{km\,s^{-1}}$, that is blueshifted to the north-east of the major axis,
south and south-east of the kinematic minor axis and redshifted to the north
and north-west of the minor kinematic axis with velocity $\sim$50 km s-1. The
maximum residual velocity turns out to be in this case $\sim
55\,\rm{km\,s^{-1}}$.

For MCG-06-30-15, the model reproduces well the observed CO(2-1) kinematics in
the nuclear region and along both the kinematic minor and major axes (see Fig.
3).
The residuals reach a maximum velocity of $\sim 20\,\rm{km\,s^{-1}}$, that is
blueshifted to the east direction with velocity $\sim$51 km s-1 and redshifted
to the south and south-west of the minor axis with velocity $\sim
20\,\rm{km\,s^{-1}}$. The maximum residual velocity is $\sim
35\,\rm{km\,s^{-1}}$.

Comparing these residual velocities of the gas in each galaxy with the
velocities the regular rotation shows us how important is the residual
velocity (which could be due to devation from circular motions) for each
galaxy. For NGC4968, the gas rotates at $\sim 200\,\rm{km\,s^{-1}}$ and there
is a residual of $\sim 125\,\rm{km\,s^{-1}}$, which is a large fraction of the
rotation velocity.
In NGC4845, the rotational velocity of the gas is $\sim 200\,\rm{km\,s^{-1}}$
(taking the average of the two components using the input ALMA datacube), and
a residual with velocity about $\sim 55\,\rm{km\,s^{-1}}$ is detected. In
MCG-06-30-15, the CO rotation velocity is $\sim 200\,\rm{km\,s^{-1}}$ and the
residual velocity $\sim 35\,\rm{km\,s^{-1}}$ which is small with respect to
the regular rotation velocity.

For all galaxies the residual velocities are smaller than the main rotation
velocity, indicating that the non circular kinematics very unlikely are
tracing powerful outflows (whatever the cause is stellar or AGN related). Of
all, the residual velocity of NGC4968 is larger than the other two galaxies
with respect the rotation velocity. The least residual velocity is found for
MCG, indicating that the kinematics of the gas in the central 1 kpc scale of
this galaxy is best described by circular motions.

###  4.2 Residuals from DiskFit

As shown by the kinematic maps in Figs. 4, 5, and 6 for NGC 4968, NGC 4845,
and MCG-06-30-15, respectively, different DiskFit models reproduce the
kinematics of the molecular gas as outlined by the CO(2-1) emission.
Bisymmetric DiskFit models reproduce the observation much better than pure
rotation DiskFit models for NGC 4968 and we consider this model as the best
fit. The $\chi^{2}$ reduces by $\sim$50% for the radial motion model and by
$\sim$63% for bisymmetric model with respect to its value for pure rotation
(flat disk) model, indicating that bisymmetric model is the best physical
model for the kinematics of the gas in the central region of NGC 4968. This
leads us to conclude that the residuals seen in the pure rotation models (see
Fig. 4) cannot be ascribed to additional velocity components not belonging to
the rotational kinematics. However, still there are residuals left over from
the best-fit model, mainly in the south direction of the minor kinematic axis
and west of the major axis (see Fig. 4). Also the model rotation plus radial
motion DiskFit reduces the residual observed in the pure rotation DiskFit
model (see rotation plus radial motion DiskFit model in Fig. 4, middle
panels), and indicates the presence of radial motions in the nuclear region of
this galaxy.

Similarly, for NGC 4845, pure rotation model reproduces the observation well
(see upper panels in Fig. 5), however, bisymmetric model performes slightly
better, leaving comparably smaller residuals in the kinematic minor axis (see
lower panels in Fig. 5). In this case the change in $\chi^{2}$ is small when
bisymmetric flows are included, reducing $\chi^{2}$ by $\sim$30%. We consider,
however, that the bisymmetric model is the best-fit model.

Pure rotation (flat disk) DiskFit model reproduces the observation well for
MCG-06-30-15, leaving only very small residuals (see upper panels in Fig. 6),
and this can be considered the best-fit model for this galaxy. For
MCG-06-30-15, unlike NGC 4968, incorporating a radial component into a pure
rotation DiskFit model (rotation plus radial motion model) does not reduce the
residuals observed in the pure rotation model, indicating the absence of
significant radial motions in the nuclear region of this galaxy.

##  5 Line luminosity and molecular gas mass estimates

Table 3:  Results of a Gaussian fit to the total CO(2-1) spectrum. Upper panel: best-fit parameters of the Gaussian model components shown in Fig. 7: central velocity ($\mu_{v}$)[km s-1], flux amplitude (Speak) [mJy], and velocity dispersion ($\sigma_{v}$) [km s-1]. The number in the parenthesis indicates the Gaussian components. Lower panel: Area over which the line emission is integrated on the collapsed image, the total CO(2-1)) line flux (SCO) [Jy km s-1], total CO(2-1) line luminosity ($L^{\prime}_{CO}$) [K km s-1 pc2] and molecular gas mass (M(${\rm H_{2}}$) [M⊙]. Here we report the molecular mass values corresponding to $\alpha$=0.8.  Parameters | NGC 4968 | NGC 4845 | MCG-6-30-15 |
---|---|---|---|---
$\mu_{\rm v}$(1) | -11$\pm$3 | -21$\pm$4 | 125$\pm$3 |
$\mu_{\rm v}$(2) |  | -238$\pm$4 | -8$\pm$8 |
$S_{\rm peak}$(1) | 0.71$\pm$0.01 | 4.85$\pm$0.22 | 0.26$\pm$0.03 |
$S_{\rm peak}$(2) |  | 5.38$\pm$0.22 | 0.22$\pm$0.01 |
$\sigma_{\rm v}$(1) | 258$\pm$6 | 157$\pm$10 | 67$\pm$9 |
$\sigma_{\rm v}$(2) |  | 146$\pm$9 | 171$\pm$21 |
Area | $3^{\prime\prime}\times 1.4^{\prime\prime}$ | $13^{\prime\prime}\times 3^{\prime\prime}$ | $3.4^{\prime\prime}\times 1.2^{\prime\prime}$ |
SCO(2-1) | 36 | 617 | 16 |
L${}^{\prime}_{\rm CO(2-1)}$ | $4\times 10^{7}$ | $12\times 10^{7}$ | $1.3\times 10^{7}$ |
M${}_{\rm tot}({\rm H_{2}})$ | $3\times 10^{7}$ | $9\times 10^{7}$ | $1\times 10^{7}$ |
M${}_{\rm res}({\rm H_{2}})$ | $1\times 10^{7}$ | $0.3\times 10^{7}$ | $0.07\times 10^{7}$ |

To estimate the line luminosity ${\rm L^{\prime}_{CO}}$ and the molecular gas
mass in the disc M(H2), we present the profile of the integrated CO(2-1)
emission line in Fig. 7. The line profiles are generally smooth enough to be
well fitted with a single (NGC 4968) or two (NGC 4845 and MCG-06-30-15)
Gaussian profiles. We integrate the line emission over the moment0 maps. The
results of the best fit parameters are given in Table 3 together with the size
of the region over which the line flux is estimated. This was chosen by
selecting those pixels where the S/N is larger than 3, roughly corresponding
to 10% of the maximum values. Then we derive the emission line luminosity
${\rm L^{\prime}_{CO}}$ using the relation given by Solomon & Van den Bout
(2005):

$L^{\prime}_{CO}=3.25\times 10^{7}S_{CO}\Delta\varv
v_{obs}^{-2}D_{L}^{2}(1+z)^{-3},$ (2)

where $L^{\prime}_{CO}$ is the CO line luminosity given in K km s-1 pc2,
$S_{CO}\Delta\varv$ is the velocity-integrated flux in Jy km s-1, $\nu_{obs}$
is the observed frequency in GHz; $z$ is the redshift, and $D_{L}$ is the
luminosity distance in Mpc ($D_{L}=D_{A}(1+z)^{2}$, $D_{A}$ is the angular
size distance) is the luminosity distance in Mpc. The molecular mass, ${\rm
M(H_{2})}$ is estimated using the relation (Solomon & Van den Bout (2005)):

$M(H_{2})=\alpha_{CO}L^{\prime}_{CO},$ (3)

where $\alpha_{\rm CO}$ is the CO-to-H2 conversion factor. The value of
$\alpha_{\rm CO}$ is highly uncertain, it depends on metallicity and
environment (see i.e. Bolatto A., et al, 2013) and may vary in the range
0.8-3.2. For simplicity we use here the lower value which is the average value
in active galaxies. Furthermore, strictly speaking the conversion factor
entails the CO(1-0) line luminosity, this means that in absence of similar
CO(1-0) observations an assumption on the excitation status of the molecular
gas must be made. We use the average CO spectral line distribution of
Kamenentzky et al. (2016) corresponding to the $\log({\rm L_{FIR}})$
luminosity range of 10-10.5 ${\rm\log L_{\odot}}$ to convert from the observed
${\rm L^{\prime}_{CO(2-1)}}$ to ${\rm L^{\prime}_{CO(1-0)}}$ which is used in
eq. 2. The resulting ratio is $\frac{{\rm L^{\prime}_{CO(2-1)}}}{{\rm
L^{\prime}_{CO(1-0)}}}=2/3$. For NGC4968 we use the ratio measured by Strong
et al. (2004)

The total gass mass M${}_{\rm tot}({\rm H_{2}})$ in the disc of the three
galaxies is listed in Table 3, which agrees well with the typical values for
other nearby and low-luminosity AGNs, and are in line with the claim that
Seyfert 2 galaxies do seem to possess more molecular mass than Seyfert 1
galaxies (see Strong et al. (2004) and references therein) and agree with the
single dish values published by Strong et al. (2004) for NGC4968 and
MCG-06-30-15 and by Rosario et al. (2018) for MCG-06-30-15.
Similarly, we determine the line luminosity and molecular gas mass in the
modelled disc of each galaxy. The molecular gas mass fraction in the modelled
disc of NGC 4968, NGC 4845 and MCG-06-30-15 corresponds to $\sim$69%,
$\sim$97% and $\sim$92% of the total molecular gas mass in each galaxy,
respectively.

In addition to the total molecular gas mass and the gas mass in the main
rotating disc, we also estimated the line luminosity and then the molecular
mass of the residuals for each galaxy using Eqs. 2 and 3 and listed in Table
3. The residuals are the emissions resulting from the substraction of the
modelled from the observed data cube.

Figure 7: The Gaussian fit for the profile line of NGC 4968 (top panel), of
NGC 4845 (middle panel), and of MCG-06-30-15 (bottom panel). Data are shown by
the black line, while the fitted components by the blue and green lines (see
detail in Table 3).

##  6 Gas and continuum distribution

Figure 8 shows the overlay of the collapsed CO intensity map with the map of
the continuum at the observing frequencies, derived from the flux averaged
over all the four spectral windows once neglecting the channels with the line
emission. CO emission is absent from the centre of NGC4968 and not in the
other two galaxies. Together with the kinematical analysis discussed above we
can argue that this result can be linked to the presence of the bar in the
inner part (see Fig. 10). Indeed, the torque is positive inside (meaning the
gas moves outward) and negative outside (the gas flows inward) this could be
the reason why there is no CO in the centre of NGC4968.

The continuum distribution is overall more compact than the CO emission
especially in NGC4968 and MCG-06-30-15. One may argue that some flux could be
lost because of the high resolution of these observations and the lack of
additional compact array observations. However because of the integrated CO
flux agrees with that measured with single dish observations (Strong et al.,
2004; Rosario et al., 2018), at least in NGC4968 and MCG-06-30-15, the amount
of missing flux should not be significant.

The origin of the majority of the continuum emission is very likely due to
dust. The central nucleus is expected to emit synchrotron emission from the
black hole jet or corona which may have a significant contribution to the
radiation in the millimetre range. However, the three galaxies are strong far-
IR emitters as detected by infrared satellites (see i.e. Gruppioni et al.,
2016; Cortese et al., 2014; Meléndez et al., 2014) and have a radio spectrum
typical of a central synchrotron source with a spectral index decreasing with
frequencies as $\nu\sim-0.6\div-0.8$ (radio data taken from Condon et al.
(2002); Mundell et al. (2009)), which contributes a few percent at 1 mm
wavelength.

Figure 8: Overlay of CO(2-1) contours on the 1.2 mm continuum image of NGC
4968 with 2 CO contours of 4 and 16% of maximum (top panel), of NGC 4845 with
2 CO contours of 5 and 20% of maximum (middle panel), and of MCG-06-30-15 with
2 CO contours of 5 and 20% of maximum (bottom panel). The continuum scale
(colour wedge) is in Jy/beam. The 3$\sigma$ level is 0.1 mJy, therefore 0.0001
Jy/beam in the units of the Figure for N4968, 0.5 mJ=y/beam, then 0.0005
Jy/beam for N4845 and 0.05 mJy/beam therefore 0.00005 for MCG-06-30-15.

##  7 Discussion

###  7.1 Kinematical perturbations

In addition to the kinematic maps, the comparison of the $p-v$ diagrammes of
the host galaxy disc (blue contours) with the fitted 3DBAROLO model of a
rotating disc (red contours) along the kinematic major and minor axes (see
bottom panels in Figs. 1, 2, and 3) further shows how well the model fits the
data, and helps to see the presence of any deviation from circular motions.
For NGC 4968, along the kinematic major axis, the 3DBAROLO model with the
rotating disc (red contours) fits the rotation curve of the host galaxy disc
(blue contours) relatively well, leaving only small room for additional
significant kinematical components (see the major axis in the bottom panel in
Fig. 1). The 3DBAROLO rotating disc model fits also well the observation in
the nuclear region and along the kinematic minor axis of the host galaxy disc,
however, leaving an important deviation at the end of the kinematic minor axis
(see the minor axis in the bottom panel in Fig. 1), which is in agreement with
what is observed in the corresponding velocity map in the same figure.

In NGC 4845, the 3DBAROLO model with the rotating disc fits the rotation curve
of the host galaxy disc along the kinematic major axis (see the $p-v$ diagram
in Fig. 2). Along the kinematic minor axis the 3DBAROLO model also fits
relative well the observations. However it fails around the kinematic minor
axis we see small deviations (see $p-v$ diagram in Fig. 2).

In MCG-06-30-15, the rotating disc model fits the rotation curve of the host
galaxy disc quite well both along the kinematic major and minor axes,
presenting only very small deviations (see the $p-v$ diagram in Fig. 3),
further strengthening what is observed in the corresponding kinematic map
(Fig. 3).

Deviations from circular motions could be caused by different mechanisms, such
as outflows driven by AGN or star formation. Also, it has been known that non-
circular motions of molecular gas in the nuclear regions of disc galaxies
could be due to the existence of a bar like structure, a warped circumnuclear
disc, or radial motion due to other mechanisms. For example, using lower
resolution CO(2-1) observations, Schinnerer et al. (2000) observed non-
circular motions caused by warped structure in the nuclear region
(approximately radial distances of 0.7-1") of NGC 3227. Furthermore, it has
been shown that gas inflows could be due to gravity torques from non-
axisymmetric potentials in the central regions of galaxies, such as streaming
motions along a bar (see e.g., Ruffa et al. 2019).

Indeed, the presence of residuals/deviations could be either due to some gas
components not included within the main rotating disc considered by the model
(this could be due to difference in geometry with the main rotating disc), or
there is a deviation in the kinematics of the gas from circular motion, or
both. In the galaxies of this study the observed residuals could be an
indication for the presence of deviations in the kinematics of the gas from
circular motions, as shown by the kinematic maps and corresponding $p-v$
diagrams.

Bisymmetric Diskfit model performes better in reproducing the observations
than other DiskFit models in NGC 4845 and NGC 4968, indicating that the
kinematical perturbations in these two galaxies are more likely due to a bar
pattern, whereas pure rotation model is the best-fit model for MCG-06-30-15.
Note that the bisymmetric DiskFit model describes an elliptical or a bar like
flow, and it is not surprising that bisymmetric model appears to be the best-
fit model in NGC4968 and NGC 4845, since the galaxies are shown to be barred
(see more below).

As revealed by both models, we argue that although the circular motion is the
dominant kinematics in the molecular disc of all galaxies, there is clear
evidence for the presence of non-circular motions in the nuclear regions of
NGC 4968 and NGC 4845, mainly in NGC 4968, where non-circular motions appeared
to be significant (see Sections 4.1 and 4.2). However, the smallness in the
width of the residual velocity (compared to the circular velocity) indicates
the absence of energetic feedback both from the central AGN and star formation
in the nuclear regions of the galaxies. Also, the star formation rate in all
galaxies is very small (see Table 1).

Table 1 lists too the morphological types from either NED or Hyperleda: N4968
has a strong bar and the torque analysis (see below) also confirms that. We
show in Fig. 9 a possible model for the rotation curve in the central kpc of
the galaxy, built from its various components, bulge, disc of stars and gas,
black hole and dark matter. The latter components contribute negligibly, the
dark matter is required however, to explain a flat rotation curve in the outer
parts. The bulge mass was taken from the decomposition of the red image, used
in the potential calculation, and calibrated with the rotation curve. The
black hole mass has been assumed to be 7$\times 10^{6}$ M⊙, about 0.2% of the
mass of the bulge, according to scaling relations (e.g. Kormendy & Ho 2013).
The bulge dominates the region of interest, for the observed molecular
component. Thus the mass decomposition allows the computation of the
precessing frequency $\Omega-\kappa/2$, and the determination of Lindblad
resonances. If we place the corotation just outside the bar, as it is
frequently observed in barred spirals (e.g. Buta & Combes (1996)), then the
pattern speed of the bar is $\Omega_{b}$ = $52\,\rm{km\,s^{-1}\,kpc^{-1}}$,
putting corotation at 3.5 kpc and inner Lindblad resonance (ILR) at R = 300pc,
corresponding to the CO ring.

N4845 morphology has a nice peanut shape bulge, and this is well known to be
due to a bar (e.g., Combes et al. 1990). From our analysis there is evidence
of an additional weak kinematics but we cannot argue that this is due to the
presence of the bar. Our kinematical analysis seems to confirm that unlike the
one in NGC 4968 the bar in NGC4845 is unable to change significantly the
regular rotation pattern of the molecular gas. This additional weak kinematics
(see Fig. 2 and 5) could be due to gas inflowing or outflowing the central
region but with the present data there is not firm evidence of it.

Figure 9: Top panel: A possible model for the rotation curve in the central
kpc of NGC 4948, built from its various components, bulge, disc of stars and
gas, black hole and dark matter. This latter contributes negligibly but it is
required to explain a flat rotation curve in the outer parts (see text).
Bottom panel: The precessing frequency of elongated orbits, $\Omega-\kappa/2$,
used to model the orbits in the inner region of NGC 4968. The red line is the
pattern speed of the bar (e.g. Buta & Combes (1996)).

###  7.2 Torque computation for NGC 4968

To determine whether the gas is driven outwards or inwards, a calculation of
the bar torques is necessary (e.g. Audibert et al., 2019). Through the Poisson
equation, the gravitational potential is derived from the stellar density,
assumed to be the main responsible to the gravity forces in the plane of the
galaxy, inside the central kiloparsec. The dark matter is indeed negligible in
the very centre (e.g. NGC 4968 in Fig.9). The stellar density is better traced
by the HST H-band image (F160W), since in the NIR the dust impact is minimised
(see Combes et al. (2019) for details). The HST-NIC2 image reveals a central
bulge and a stellar disc. To de-project the galaxy to face-on, we have first
isolated the bulge, assumed to be spherical, which should not be de-projected.
We then de-projected the galaxy disc with the adopted inclination angle of 60∘
and PA 250∘. The bulge was then added to the de-projected image. We assumed a
constant mass-to-luminosity ratio and calibrated it to retrieve the observed
rotation curve, modeled as shown in Fig. 9 (bottom panel). The gravitational
potential is derived from the stellar distribution, assuming a thin disc of
scale ratio $h_{z}/h_{r}$ =1/12. Both the HST-NIR and CO(2-1) de-projected
images of the galaxy have been resampled to the same pixel size of 0.03 arcsec
= 6 pc (Combes et al., 2019).

We have computed the bar gravity torques, following the method described in
(e.g. García-Burillo et al. 2005; Audibert et al. 2019). The forces are
computed at each pixel, by derivating the potential, and then the torques are
computed on the gas, taking into account the gas density at the given pixel.
The torque map is plotted in Fig. 10 together with the de-projected gas
surface density, for comparison. As shown in the top panel of the figure, the
torque map reveals the expected butterfly diagram (four-quadrant pattern) in
relation to the bar orientation (indicated by straight lines) with torques
changing sign in each quadrant. This implies that the observed non-circular
motions are well fitted by the gas flow in a bar potential.

Figure 10: Top panel: Map of the gravitational torques exerted on the gas by
the stellar potential, in the centre of NGC 4968. The map shows in each pixel
the torque derived from the HST-NIR image, multiplied by the gas surface
density. Both images have been de-projected to face-on (see text for details).
The torques change sign as expected in a four-quadrant pattern (or butterfly
diagram). The orientation of the quadrants follows the bar orientation. In
this de-projected picture, the major axis of the galaxy is oriented parallel
to the horizontal axis. Bottom panel: The de-projected image of the CO(2-1)
emission, at the same scale, and with the same orientation, for comparison.
Figure 11: The radial distribution of the average torque exerted by the
stellar bar on the gas of NGC 4968. The torque is normalised to show the
fraction of the angular momentum transferred from the gas in one
rotation–$dL/L$, estimated from the CO(2-1) de-projected map. The curve is
plotted only from a radius = 0.23 arcsec (or 46 pc), which is the largest size
of the beam.

From the torque map we compute azimuthal averages and obtain the effective
torque at each radius, per unit mass. This yields the derivative of the gas
angular momentum at this radius. To derive the relative variation of angular
momentum, we divide by the average angular momentum at this radius (from the
rotation curve). This relative variation of angular momentum in one rotation
is plotted in Fig. 11. The torque is positive in the very centre, meaning that
the gas is driven outwards to the gas ring. Outside of the ring, the torque is
negative and peaks at dL/L = -0.3 in one rotation: the gas is driven inwards,
to accumulate in the ring. In this region the gas is losing about 30% of its
angular momentum in one rotation.
The NLR dynamics does not uniquely show the presence of an outflow because it
might be affected by extinction (Ferruit et al., 2000). If an ionised outflow
were present, at least in the central region, the outward motions of the gas
(as revealed by the positive torque in the very centre) could be partly
interpreted as the interaction between the ionized outflows and the gas.
However, since the torque is negative in the outside of the ring, the outflows
could be counter balanced by inward motions.

##  8 Summary and Conclusions

We have analysed the properties and kinematics of the cold molecular gas in
the nuclear and circumnuclear regions of three Seyfert galaxies, NGC 4968, NGC
4845 and MCG-06-30-15, using ALMA observations of their CO(2-1) emission line.
We used the 3DBAROLO and DiskFit (both axisymmetric and non-axisymmetric)
softwares to model the kinematics of the molecular gas.
The main findings are summarised as follows:

  * •

The intensity maps reveale a ring-like morphology in the nuclear regions of
NGC 4968 and MCG-06-30-15, whereas the shape is edge-on in NGC 4845.

  * •

The gas kinematics in the molecular discs of NGC 4845 and MCG-06-30-15 is
dominated by pure rotational motion, but there is evidence for non circular-
motions in NGC 4968 and weakly in NGC 4845.

  * •

Unlike NGC 4845, where the deviation from circular motion is small, a
significant non circular motion are observed in NGC 4968, mainly along the
kinematic minor axis, with velocity $\sim 115\,\rm{km\,s^{-1}}$, which are
likely due to the bar.

  * •

Moreover, of all DiskFit models, the bisymmetric model is found to be the
best-fit model for NGC 4968 and NGC 4845, in agreement with the nuclear bar
origin.

  * •

Regular rotation is shown to be the dominant kinematics of the gas in the
nuclear region of MCG-06-3-15, and hence pure rotation model is the best fit
model for this galaxy.

  * •

The molecular mass, ${\rm M(H_{2}}$), in the nuclear disc is estimated to be
$\sim 3-12\times 10^{7}\leavevmode\nobreak\ {\rm M_{\odot}}$ (NGC 4968), $\sim
9-36\times 10^{7}\leavevmode\nobreak\ {\rm M_{\odot}}$ (NGC 4845), and $\sim
1-4\times 10^{7}\leavevmode\nobreak\ {\rm M_{\odot}}$ (MCG-06-30-15), allowing
the CO-to-H2 conversion factor $\alpha_{CO}$ between 0.8 and 3.2, typical of
nearby galaxies of the same type.

  * •

The molecular gas mass of the modeled disc of each galaxy corresponds to
$\sim$ 69%, $\sim$97% and $\sim$92% of the total molecular gas mass in NGC
4968, NGC 4845 and MCG-06-30-15, respectively.

  * •

For the galaxy NGC 4968, placing the corotation just outside of the bar
indicates a bar pattern speed of $\Omega_{b}$ =
$52\,\rm{km\,s^{-1}\,kpc^{-1}}$, putting corotation at 3.5 kpc and inner
Lindblad resonance (ILR) ring at R = 300pc, which corresponds to the CO ring.
The computation of the torques exerted by the stellar bar on the gas shows
that the torques are positive inside the molecular ring and negative outside,
revealing that the gas is accumulating in the inner Lindblad resonance. Thus,
the observed non-circular motions in the molecular disc of NGC 4968, could be
due to the presence of the bar in the nuclear region.

In summary, in the studied galaxies the radiative feedback or winds, seen in
the kinematics of emission lines from ionised gas (see § 2), do not
substantially alter the environments within molecular clouds that produce the
bulk of the low-excitation CO emission. We do not find any strong evidence for
gas kinematics close to the central AGN which might be univocally attributed
to the effect of the AGN. The cold, star-forming molecular gas in the centre
of the host galaxy is not strongly influenced by the presence of the AGN,
despite the fact that these AGN are luminous enough to dynamically disturb
this material.
We cannot claim any strong evidence in these sources of the long sought
feedback/feeding effect due to the coupling of mechanical energy from the
nucleus with the cold star-forming phase.

## Acknowledgements

This paper makes use of the following ALMA data:
ADS/JAO.ALMA$\\#$2017.1.00236.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. The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc. This publication has made use of data products from the
NASA/IPAC Extragalactic Database (NED). We acknowledge the usage of the
HyperLeda database (http://leda.univ-lyon1.fr). A. Bewketu Belete acknowledges
the support by the Brazilian National Council for Scientific and Technological
Development (CNPq). R.S. acknowledges the support provided by CONICYT through
FONDECYT postdoctoral research grant No. 3200909. JAFO and LS acknowledge
financial support by the Agenzia Spaziale Italiana (ASI) under the research
contract 2018-31-HH.0. Research activities of the Observational Astronomy
Board of the Federal University of Rio Grande do Norte (UFRN) are supported by
continuous grants from CNPq, CAPES and FAPERN brazilian agencies. J.R.M. and
A.B.B also acknowledge financial support from INCT INEspaço/CNPq/MCT. An
anonymous referee is warmly thanked for their comments/suggestions have
greatly improved the completeness of the paper.

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