# Gas inflows in the polar ring of NGC 4111: the birth of an AGN

Gabriel R. Hauschild Roier,1 Thaisa Storchi-Bergmann,1 Richard M. McDermid,2
Jonelle L. Walsh,3 Joanne Tan,3 Jonathan Cohn,3 Davor Krajnović,4 Jenny
Greene,5 Monica Valluri,6 Kayhan Gültekin,6 Sabine Thater,7 Glenn van de Ven,7
Karl Gebhardt,8 Nora Lützgendorf,9 Benjamin D. Boizelle,3,10 Chung-Pei Ma11
and Aaron J. Barth12

1Instituto de Física, Universidade Federal do Rio Grande do Sul, Av. Bento
Gonçalves 9500, 91501-970, Porto Alegre, RS, Brazil
2Astronomy, Astrophysics, and Astrophotonics Research Centre, Department of
Physics and Astronomy, Macquarie University, NSW 2109, Australia
3George P. and Cynthia W. Mitchell Institute for Fundamental Physics and
Astronomy, Texas A&M University, 4242 TAMU, College Station, TX 77843, USA
4Leibniz Institute for Astrophysics, Potsdam, Germany
5Department of Astrophysical Sciences, Princeton University, NJ, USA
6Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA
7Department of Astronomy, University of Vienna, Austria
8Department of Astronomy, University of Texas at Austin, USA
9European Space Agency, c/o STScI, 3700 San Martin Drive, 21218 Baltimore, MD,
USA
10Department of Physics and Astronomy, N283 ESC, Brigham Young University,
Provo, UT 84602, USA
11Department of Astronomy, UC Berkeley, USA
12Department of Physics and Astronomy, 4129 Frederick Reines Hall, University
of California, Irvine CA 92697-4575, USA
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We have used Hubble Space Telescope (HST) images, SAURON Integral Field
Spectroscopy (IFS) and adaptative optics assisted Gemini NIFS near-infrared
K-band IFS to map the stellar and gas distribution, excitation and kinematics
of the inner few kpc of the nearby edge-on S0 galaxy NGC 4111. The HST images
map its $\approx$ 450 pc diameter dusty polar ring, with an estimated gas mass
$\geq 10^{7}$ M⊙. The NIFS datacube maps the inner 110 pc radius at $\approx$
7 pc spatial resolution revealing a $\approx$ 220 pc diameter polar ring in
hot (2267$\pm 166$ K) molecular H2 1-0 S(1) gas embedded in the polar ring.
The stellar velocity field shows disk-dominated kinematics along the galaxy
plane both in the SAURON large-scale and in the NIFS nuclear-scale data. The
large-scale [O iii] $\lambda 5007$ Å velocity field shows a superposition of
two disk kinematics: one similar to that of the stars and another along the
polar ring, showing non-circular motions that seem to connect with the
velocity field of the nuclear H2 ring, whose kinematics indicate accelerated
inflow to the nucleus. The estimated mass inflow rate is enough not only to
feed an Active Galactic Nucleus (AGN) but also to trigger circumnuclear star
formation in the near future. We propose a scenario in which gas from the
polar ring, which probably originated from the capture of a dwarf galaxy, is
moving inwards and triggering an AGN, as supported by the local X-ray
emission, which seems to be the source of the H2 1-0 S(1) excitation. The fact
that we see neither near-UV nor Br$\gamma$ emission suggests that the nascent
AGN is still deeply buried under the optically thick dust of the polar ring.

###### keywords:

galaxies: active – galaxies: individual: NGC 4111 – galaxies: kinematics and
dynamics – galaxies: nucleus

††pubyear: 2022††pagerange: Gas inflows in the polar ring of NGC 4111: the
birth of an AGN–B

##  1 Introduction

Interactions between galaxies impact their evolution and that of their central
supermassive black holes (SMBHs), triggering episodes of star formation and
nuclear activity. Major mergers seem to be the dominant process of SMBH growth
at large SMBH masses ($\geq\,10^{8}$ M⊙), triggering luminous Active Galactic
Nuclei (AGN), while at lower AGN luminosities ($\leq 10^{44}$ erg s-1), the
most probable triggers are minor mergers and secular processes driving inflows
towards the nucleus such as gravitational torques in nuclear spirals and bars
(Storchi-Bergmann & Schnorr-Müller, 2019, and references therein). Minor
mergers are frequent in dense galactic environments, when massive early-type
galaxies capture gas-rich dwarf galaxies that replenishes the inner region of
the galaxy with gas, leading to episodes of renewed star formation and/or the
triggering of nuclear activity (e.g. Neistein & Netzer, 2014).

Such a minor merger may have recently happened in the nearby SO edge-on galaxy
NGC 4111, known to host an extended H I envelope (Wolfinger et al., 2013). A
member of the Ursa Major galaxy group, this galaxy lies at a distance of 15.1
Mpc (according to the NASA Extragalactic Database
(NED)111https://ned.ipac.caltech.edu/, using a $\Lambda\text{CDM}$ cosmology
with $H_{0}=67.8$ km s-1 Mpc-1, $\Omega_{m}=0.308$ and
$\Omega_{\Lambda}=0.692$) – for which 1′′ corresponds to 73.1 pc. NGC 4111 has
at least 4 companion galaxies located within 250 kpc from it, with the nearest
only 30-40 kpc away (Karachentsev et al., 2013; Pak et al., 2014; Kasparova et
al., 2016). NGC 4111 has a dust structure crossing the nucleus perpendicular
to the galaxy disk (Barth et al., 1998) associated with H I filaments, which
suggest an origin from tidal stripping of gas from a nearby or recently
captured galaxy (Verheijen & Zwaan, 2001; Verheijen, 2004; Pak et al., 2014).

Kasparova et al. (2016) showed that NGC 4111 has a flat stellar age
distribution of $\sim$ 5 Gyr across most of its disk. In the inner region,
however, with galaxy midplane distance of $\sim$ 700 pc, single stellar
population modelling reveal a more metal-rich and younger stellar population
with a characteristic 4 Gyr age. This very flattened young stellar component
could be due to a previous gas-rich minor merger.

NGC 4111 was identified as an AGN by González-Martín et al. (2009) using
Chandra X-ray data. In that work, the column density of HI and H2 were
calculated to be $4.67\times 10^{22}$ cm-2 and $37.71\times 10^{22}$ cm-2,
respectively. NGC 4111 images from Chandra show extended soft X-ray emission
and nuclear-only hard emission, with luminosities measured as
$\log(L_{\mathrm{soft}})$ = 40.9 erg s-1 (0.5 - 2.0 keV) and
$\log(L_{\mathrm{hard}})$ = 40.4 erg s-1 (2.0 - 10.0 keV). This suggests that
the source of high energy X-rays is a fairly obscured AGN which is embedded in
the dense dust ring, while the soft emission is spread across the galaxy plane
and has a maximum in the central region. This is also supported by the fact
that near-UV emission from the nucleus is not detected in HST images (Barth et
al., 1998). NGC 4111 shows 5 GHz radio emission extended by 110.4 pc$\,\times$
72.2 pc and position angle of 29$\pm$11∘ according to Nyland et al. (2016);
however, the origin of the radio emission is unclear and the nucleus of the
galaxy is classified as a LINER (Ho et al., 1997).

NGC 4111 was observed with the Gemini Near-Infrared Spectrograph (NIFS) as
part of the project “Addressing a Bias in the Relation Between Galaxies and
Their Central Black Holes" (P.I. Jonelle Walsh). While the main goal of the
project is to determine SMBH masses from the stellar kinematics in nearby
galaxies, the NIFS K-band observations of NGC 4111 revealed many lines of hot
molecular H2 gas emission in the spectra. These lines reveal peculiar
excitation and kinematics that deserve a study of its own. The goal of the
present paper is to investigate the nature of the excitation and kinematics of
the hot H2 gas emission of the inner $\approx$ 100 pc of the galaxy. In order
to do this, we also employed Hubble Space Telescope (HST) images and large
scale integral field data from the Spectrographic Areal Unit for Research on
Optical Nebulae survey (SAURON).

This paper is organised as follows. In Section 2 we present the observations
and data reduction. In Section 3, we present the measurements for the HST
(regarding the photometry), SAURON and NIFS data (regarding the emission lines
fitting and kinematics, and the stellar kinematics). In Section 4, we present
our results and discussion for all 3 instruments, so that in Section 5 we
compare these results and propose a scenario for the observational evidences
of NGC 4111. Finally, in Section 7 we present our conclusions.

##  2 Observations

As a part of GO-15323 (PI: Jonelle Walsh), we obtained HST Wide Field Camera 3
(WFC3) imaging in the F475W (see Figure 1) and F160W filters. The F160W data
were obtained using the RAPID sequence in a 2-point WFC3-IR-DITHER-LINE
pattern, with a total 53 s exposure time. The F475W data were obtained in an
ideal 4-point dither pattern using only the UVIS2-2K2C-SUB aperture, with a
total 920 s exposure time. The WFC3 data were combined into separate F475W and
F160W mosaics with the same origin and pixel scale using AstroDrizzle (Gonzaga
et al., 2012).

K-band spectroscopy of the nuclear region of NGC 4111 was obtained using the
instrument NIFS – Near-Infrared Integral Field Spectrograph (McGregor et al.,
2003), with the adaptive optics module Altair (Herriot et al., 2000; Boccas et
al., 2006) at the Gemini North Telescope on 2019 May 9. We acquired 600 s
exposures following an object-sky-object sequence, with a total on-source time
of 1 hour via the program GN-2019A-LP-8 (P.I. Jonelle Walsh). We used the
$H+K$ filter and $K$ grating centered on $2.20\,\mu$m, which provided coverage
of 1.99 $\,\mu$m - 2.40 $\,\mu$m with $R\sim 5290$. NIFS is an image slicer
with a Field-of-View (FoV) of 3${}^{\prime\prime}\times 3^{\prime\prime}$ –
corresponding to $219\times 219$ pc2 at the galaxy, sampled with pixels of
$0\aas@@fstack{\prime\prime}04\times 0\aas@@fstack{\prime\prime}1$; the
observations with the adaptative optics module Altair delivered data with a
Point-Spread Function (PSF) – as determined from the spatial profiles of
standard stars – FWHM of $0\aas@@fstack{\prime\prime}1$ corresponding to a
spatial resolution of $\approx$ 7 pc at NGC 4111. We reduced the NIFS data
using IRAF tasks (Tody, 1986, 1993) within the Gemini package v1.14, in
combination with Python scripts we developed
222https://github.com/jlwalsh12/NIFS-reduction-pipeline based on the example
NIFS processing scripts 333https://www.gemini.edu/instrumentation/nifs/data-
reduction. The main steps included sky subtraction, flat-fielding, cosmic ray
cleaning and bad pixel removal, wavelength calibration, and spatial
rectification. The galaxy spectra were telluric corrected using an A0 V star
(HD95126 or HD116405), after removal of the Br$\gamma$ absorption line and the
blackbody continuum. We constructed a temporary data cube for each galaxy
exposure and collapsed the cubes to determine the spatial offsets by means of
a two-dimensional cross-correlation. Then all six of the galaxy frames were
interpolated onto a single data cube with 0$\aas@@fstack{\prime\prime}$05 vs.
0$\aas@@fstack{\prime\prime}$05 spaxels and wavelength sampling of 2.13Å.
Finally, a rough flux calibration was carried out using the telluric-corrected
HD116405 spectrum and comparing the flux density at the isophotal wavelength
of the Two Micron All Sky Survey (2MASS) $Ks$ filter to the 2MASS magnitude
reported in the SIMBAD astronomical database (Wenger et al., 2000). This
conversion was applied to the final NGC 4111 data cube, resulting in
calibrated units of erg s-1 cm-2 Å-1. We reduced the sky frames in a similar
manner, but subtracted a 600 s master dark frame. We applied the same spatial
offsets as the ones used for the galaxy frames to produce a single sky cube
and measured the line spread function over the NIFS field-of-view from 13
strong, isolated sky lines. The sky lines spectral resolution varies over the
NIFS field-of-view, ranging from a FWHM of 3.5 to 5.9 Å, with a FWHM median
resolution of 3.9 Å.

Optical integral field spectroscopy (IFS) data were obtained with the SAURON
instrument (Bacon et al., 2001) on the William Herschel Telescope, La Palma as
part of the ATLAS${}^{\textrm{ 3D}}$ Survey (Cappellari et al., 2011). SAURON
provides a 31″$\times$41″ field of view – corresponding to 2.3 kpc$\times$3.0
kpc at the galaxy, sampled with 0.94″ square lenslets, and with a spectral
resolution of 4.2 Å FWHM ($\sigma_{\mathrm{inst}}=105$ km s-1), covering the
wavelength range 4800–5380 Å. The observations comprised the combination of
two exposures of 30 minutes, obtained on UT 2007 April 20, together with
associated calibrations. The data were reduced via standard procedures using
the dedicated XSAURON software package (Bacon et al., 2001; Emsellem et al.,
2004). The approximate seeing FWHM was 1.2″, corresponding to a spatial
resolution of $\approx$ 88 pc at the galaxy. These reduced spectral data cubes
are publicly available at www.purl.org/atlas3d.

The aforementioned data were astrometrically matched using the WCS data in the
headers, followed by a visual inspection to assure the correct relative
position of the images.

##  3 Measurements

###  3.1 HST

Figure 1: HST large scale image of NGC 4111 in the F475W filter covering a 4.8
kpc$\times$4.8 kpc region. The white dashed-line rectangle shows the
$31^{\prime\prime}\times 41^{\prime\prime}$ SAURON FoV and the smaller white
dashed-line square delimits a $6^{\prime\prime}\times 6^{\prime\prime}$ region
containing the dusty polar ring shown in the colour map of Figure 2. North is
up and East is left. Figure 2: HST F475W - F160W colour map within the inner
6${}^{\prime\prime}\times 6^{\prime\prime}$ (440$\times$440 pc2 at NGC 4111).
Overplotted in white are the contours from the H${}_{2}\lambda 2.1218\,\mu$m
emission line flux distribution (see Sec. 3.3), and in black a cross shows the
location of the peak of the stellar K-band continuum from NIFS, adopted as
corresponding to the galaxy nucleus. The white dashed lines demarcate the NIFS
FoV.

Figure 1 shows the HST F475W continuum image with the
31${}^{\prime\prime}\times 41^{\prime\prime}$ SAURON FoV delineated by a white
dashed-line rectangle. This image shows the edge-on orientation of the galaxy
and the dusty polar ring crossing the nucleus approximately perpendicular to
the disk of the galaxy. The 6${}^{\prime\prime}\times 6^{\prime\prime}$ white
dashed-line square encloses the region where the dusty polar ring is observed.

Using the F475W and the F160W images, we built the F475W - F160W colour map,
with the inner 6${}^{\prime\prime}\times 6^{\prime\prime}$ region shown in
Fig. 2. This map shows that the dusty ring has a diameter of $\approx$ 450 pc
($6\aas@@fstack{\prime\prime}3$) and a width of $\approx$ 130 pc
($1\aas@@fstack{\prime\prime}8$). The 3${}^{\prime\prime}\times
3^{\prime\prime}$ dashed white square in this figure shows the NIFS FoV, while
the white contours delineates the flux distribution in the H2(1-0) S(1)
$\lambda$ 2.1218$\,\mu$m emission line that has the shape of an off-centered
inclined ring, as shown and discussed in the following section (see Fig. 5).

###  3.2 SAURON

The SAURON optical spectra were analysed first by using Voronoi binning
(Cappellari & Copin, 2003) to increase the SNR of the spectra. We adopted a
lower threshold of SNR=40 and ran the pPXF code (Cappellari & Emsellem, 2004)
on the binned spaxels to measure the stellar kinematics. pPXF uses a stellar
spectral base to fit the absorption lines in the galaxy spectrum in order to
measure the kinematics (velocity, velocity dispersion and the $h_{3}$ and
$h_{4}$ Gauss-Hermite polynomials coefficients) in these lines. In this work,
we used the MILES stellar templates (Falcón-Barroso et al., 2011) as a base
for pPXF. Emission line properties were extracted using an implementation of
the GANDALF (Gas AND Absorption Line Fitting) software (Sarzi et al., 2017).
In this implementation, the previously-derived pPXF stellar kinematics are
fixed, and MILES SSP model templates are broadened by the corresponding LOSVD.
The template weights are permitted to vary, together with the parameters of
single Gaussian emission line components. The [O iii]$\lambda\lambda
4959,5007$ doublet is initially fitted, as this is generally the most easily
detected line without strong coincident absorption features. This fixes the
emission line kinematics for a second pass, where an H$\beta$ emission
component is also included. The fitted emission line is considered a secure
detection if it has an amplitude 4 times higher than the local noise level,
otherwise it is ignored.

###  3.3 NIFS

Figure 3: NIFS spectra in observed wavelength from 3 representative regions of
the galaxy, integrated within apertures of
0$\aas@@fstack{\prime\prime}$1$\times$0$\aas@@fstack{\prime\prime}$1: nuclear
spectrum in black; H2 ring region spectrum in red, extracted from position B
in Figure 5; spectrum from the disk of the galaxy in blue, extracted from
position C in Figure 5. The wavelengths of the H2 emission lines are marked
with dashed grey lines, along with that of the absent Br$\gamma$ line.

Sample spectra from NIFS are shown in Figure 3, integrated within
0$\aas@@fstack{\prime\prime}$1$\times$0$\aas@@fstack{\prime\prime}$1 windows,
corresponding to the nucleus (labeled X in Fig. 5) and two extranuclear
regions: one from a position over the H2 off-centered ring (labelled B in Fig.
5) and from a region beyond this ring at 1$\aas@@fstack{\prime\prime}$25 (91
pc) from the nucleus (labelled C in Fig. 5), comprising mostly light from the
stellar component of the galaxy. The spectra show absorption lines from the
stellar population, and H2 emission lines from hot molecular gas. Fig. 3
identifies the wavelengths of the H2 emission lines as well as that of the
Br$\gamma$ line, which is not present in the spectra. We note that the H2
emission is observed only along the off-centered ring above and that the
Br$\gamma$ line is absent over the whole area covered by the NIFS FoV (see
Section 4.3.2).

Figure 4: The fit of the H${}_{2}\lambda 2.1218\,\mu$m emission-line profile
at the nucleus and position B in the ring (see Fig. 5). The rest profile is
shown in black lines and the IFSCube Gauss-Hermite polynomial fit in blue
dashed lines, while the residuals are shown in red dashed lines. Figure 5:
Left: Integrated flux distribution in the molecular H2(1-0) S(1) $\lambda
2.1218\,\mu$m emission line. Right: Stellar continuum flux distribution from
the NIFS datacube, obtained by integrating the spectra within the 2.175-2.200
$\mu$m wavelength range. The cross shows the spaxel with the highest
integrated continuum flux – identified with the galaxy nucleus; the letters B
and C identify the locations from where the spectra identified in Figure 3
were extracted.

In order to measure the properties of the emitting H2 gas in the NIFS
datacube, we used the latest version (v1.1) of the software IFSCube (Ruschel-
Dutra & Oliveira, 2020) to fit the emission lines profiles with Gauss-Hermite
polynomials, within the 21180 - 21280 Å spectral window (in observed
wavelengths), which encompasses the H2 $\lambda$2.1218$\,\mu$m emission line
and a continuum region. IFSCube fits a polynomial component to the continuum
adjacent to the line, whose degree can be chosen during the fit. We opted by
the use of a linear function, that fitted well the continuum in all spaxels.
In Figure 4, we present example fits from IFSCube for two spectra extracted in
windows of $0\aas@@fstack{\prime\prime}1\times 0\aas@@fstack{\prime\prime}1$,
one from the nucleus and the other from a position along the molecular H2 ring
(position B in Fig.5), showing in black lines the spectra, in dashed blue
lines the fit and in dashed red lines the residuals. We imposed a lower
threshold for the signal-to-noise ratio (SNR) as obtained from the ratio
between the peak of the line and the noise in the continuum adjacent to the
line (standard deviation of the continuum). Spaxels with a SNR less than 2 are
regarded as noise and excluded from the fit. This same noise was used to apply
the Monte Carlo technique in order to evaluate the errors in the parameters
resulting from the fit. The left panel of Figure 5 shows the resulting flux
map of the H2 $\lambda$2.1218$\,\mu$m emission line, resembling a tilted ring
oriented approximately perpendicular to the galaxy plane. The right panel
shows the flux distribution of the stellar continuum, integrated in a window
covering the 2.175-2.200$\,\mu$m wavelength range. In Fig. 5 we also identify
the nucleus and the other locations where the spectra from Figure 3 were
extracted.

Figure 6: The fit of the stellar kinematics with pPXF was performed in the
spectral range 22950-23700Å(in observed wavelenghts). The figure shows three
representative Voronoi-binned spectra in black, from the nucleus and positions
B and C in Fig. 5, together with the fits in blue and residuals in red.

We also obtained the stellar kinematics using a similar approach to that used
for the SAURON data (see Section 3.2): first we used Voronoi binning to
increase the SNR of the spectra until it reached a lower threshold of SNR=50
in the stellar continuum and then executed pPXF with the Winge stellar
templates (Winge et al., 2009) as a base. The stellar kinematics fits at
positions X, B and C of Fig. 5, are shown, from top to bottom, in Figure 6,
where the normalized spectra are shown in black, the fit in blue and the
residuals in red.

##  4 Results and Discussion

###  4.1 Galactic scale - HST

The F475W - F160W colour map of Fig. 2 traces the obscuring structure crossing
the nuclear region seen in Fig. 1, mapping its reddening and revealing the
polar ring dust distribution which is extended perpendicular to the galaxy
plane by approximately $\approx$ 450 pc and shows the reddest colours in an
off-centered ring with a major axis of $\approx$200 pc. The NIFS FoV is
identified via the dashed white square. We have overplotted on Fig. 2,
contours from the the NIFS H${}_{2}\ \lambda 2.1218\,\mu$m flux map of Fig. 5
shown in white, while the location of the peak flux of the stellar continuum
(adopted as the galaxy nucleus) is shonw as a black cross. This figure shows
that the H2 ring is spatially associated with the off-centered ring with the
reddest colours in the polar ring that can be attributed to increased
reddening by dust. This colour map reveals that the molecular hydrogen
emission is de facto related to the dust, with both presenting similar off-
centered ring-like structure.

####  4.1.1 Cold gas mass

We have used the colour map of Fig. 2 to obtain the extinction of the region
under the assumption that the intrinsic colour of the stellar population is
that of the galaxy disk, adopted as F475W - F160W$=1.5$, according to Fig. 2,
and considering the dust obscuration as due to a foreground obscuring screen.
Figure 19 of the Appendix shows the resulting A${}_{F475W}-$AF160W extinction
map of the inner
6$\aas@@fstack{\prime\prime}$0$\times$6$\aas@@fstack{\prime\prime}$0, that has
an excess extinction at $\approx$4750 Å relative to $\approx$1.6$\,\mu$m of up
to $\sim$ 0.8 mag in the ring relative to the stellar population. This
extinction is consistent with the relatively high column density measured by
González-Martín et al. (2009) in the Chandra observations.

In our calculation, we have assumed that the dust is a foreground screen
obscuring the light from the galaxy, and we have used the extinction law from
Savage & Mathis (1979) in order to derive the extinction values $E(B-V)$ from
the A${}_{F475W}-$AF160W extinction map, with A${}_{\lambda}/E(B-V)$ values
obtained from the last column of Table 2 of Savage & Mathis (1979). Also
following Savage & Mathis (1979), we used the $E(B-V)$ values derived from the
extinction map of Fig. 19 and a gas-to-colour excess of $\langle
N(\text{H\,{i}}+\mathrm{H}_{2})/E(B-V)\rangle=5.8\times 10^{21}$ atoms cm-2
mag-1 in order to obtain a lower limit for the gas mass in each spaxel.
Multiplying by the mass of the proton and dividing by the area of each spaxel
in units of pc2, we obtain the surface gas mass distribution shown in Figure
20 of the Appendix. Adding the mass values of all spaxels, the resulting lower
limit for the cold gas mass in the 450 pc polar ring is
M${}_{\text{gas}}=9.8\times 10^{6}$ M⊙.

###  4.2 Galactic scale - SAURON

####  4.2.1 Stellar and ionised gas flux distributions

Flux distributions in the optical continuum, [O iii]$\lambda$5007 and H$\beta$
gas emission lines over the inner $\approx$20′′ of the galaxy obtained from
the SAURON observations are shown in Fig. 7. In the continuum (mapping the
optical stellar component), the flux distribution is brightest at the nucleus
decreasing almost uniformly in all directions except for a slightly more
abrupt decrease to the NW than to the SE. At faint levels there is some
extension along the galaxy plane. The flux distributions in the emission lines
are similar to that in the continuum for the highest flux levels around the
nucleus but show also more emission outwards, in particular to the SW towards
the border of the FoV.

The rightmost panel of Figure 7 shows that the line flux maps of the [O
iii]$\lambda$5007 and H$\beta$ lines from the SAURON data produce a line ratio
map with values in the range $1\leq F$[O iii]$/F(\mathrm{H\beta})\leq 3$,
increasing towards the borders of the FoV. As the SAURON data does not cover
the H$\alpha$ spectral region, we use a spectrum from this region from Ho et
al. (1995) who find [F([N ii]$\lambda 6584$)/F(H$\alpha$)$\approx$1, which
puts NGC 4111 in the LINER region of the BPT diagram (Baldwin et al., 1981;
Kewley et al., 2001; Kauffmann et al., 2003; Cid Fernandes et al., 2010), in
agreement with the classification from Nyland et al. (2016).

Figure 7: From left to right: Flux surface density distributions in the
optical continuum, [O iii]$\lambda$5007, and the line ratio map [O
iii]/H$\beta$ obtained from the SAURON data.

####  4.2.2 Stellar kinematics

Figure 8: Kinematics from SAURON data. Top: ionised gas and stellar velocity
field (centroid velocity $v$), with contour lines from the SAURON continuum
flux from Fig. 7; Bottom: gas and stellar velocity dispersion $\sigma$.

The SAURON data kinematics is shown in Fig. 8. The right panels show the
stellar kinematics on kpc scales. The top panel shows a rotation pattern with
redshifts to the SE and blueshifts to the NW.

The large-scale stellar velocity field obtained from the SAURON data was
previously analysed by Krajnović et al. (2011), who concluded that it presents
ordered and disk-like rotation, with a kinematic position angle of
$149.5\deg\pm 2.2$. The stellar velocity dispersion $\sigma_{\star}$ shown in
the bottom right panel, presents a small decrease in a linear structure,
extended by $\approx$ 800 pc crossing the galaxy bulge along the major axis of
the galaxy. This feature suggests the presence of a colder structure – as
compared to the galaxy bulge, such as a disk of stars rotating in the galaxy
plane that may have formed from recently acquired gas. Indeed, stellar
population properties measured via line-strength indices and spectral fitting
of this data by McDermid et al. (2015) reveal the presence of younger stars
than that of the surrounding bulge in this region, what is also consistent
with the stellar age of the region obtained by Kasparova et al. (2016).

####  4.2.3 Ionised gas kinematics

The [O iii] ionised gas kinematics probed by SAURON on kpc scales is shown in
the left panels of Fig. 8. The ionised gas velocity field $v$[O iii] shown in
the top panel presents a different orientation from that of the stellar
component, with redshifts to the S-SW and blueshifts to the N-NE. As compared
with the stellar velocity field, it presents a $\approx$ 50∘ shift in the
orientation of the apparent kinematic major axis from the $\approx
150^{\circ}$ (PA east of North of the redshifted side) of the stellar
kinematics, bringing the PA of the gas velocity field to $\approx$ 200∘.

Furthermore, the ionised gas velocity dispersion map shows the highest values
at various non-central locations. In particular, they seem to be observed
mostly along the minor-axis, although not exactly and with a bend towards N on
both the E and W sides of the galaxy.

####  4.2.4 Kinemetric analysis

In order to try to quantify the kinematic properties described above, we
analyse the SAURON stellar and gaseous velocity maps using kinemetry
(Krajnović et al., 2006). This method searches for the best-fitting ellipses
(specified by the position angle PA and the ellipse flattening Q) along which
the velocities can be described as a function of a cosine change in the
eccentric anomaly. Kinemetry is built on the assumption that the velocities
along the ellipses can be parameterised by $V=V_{\rm rot}\cos(\theta)$, where
$V_{\rm rot}$ is the amplitude of rotation and $\theta$ is the eccentric
anomaly.

Kinemetry performs an harmonic decomposition of velocities along ellipses and
determines the properties of the best-fitting ellipse by minimising the
Fourier coefficients in a truncated Fourier Series, summing over the odd
values of n:
$V(r,\theta)=V_{0}+\sum_{n=1}^{3}[a_{n}(r)\sin(n\theta)+b_{n}(r)\cos(n\theta)]$,
except for $b_{1}$ (from here on called $V_{\rm rot}$). $V_{0}$ is the
systemic velocity, $\theta$ is the eccentric anomaly and $a_{n}(r)$ and
$b_{n}(r)$ are the amplitudes at a given radial distance $r$. Therefore, the
products of the kinemetry analysis are the kinematic PA and flattening (Q) of
the best-fitting ellipses along a set of radii, $V_{\rm rot}$, and higher
harmonic terms that describe the variation of the velocities along the
ellipse.

The assumption behind kinemetry is that the motion of gas clouds follow
circular orbits in a thin (inclined) disk (e.g. Schoenmakers et al., 1997;
Wong et al., 2004; van de Ven & Fathi, 2010). Therefore, the dominant
kinemetry term, the one next to the $\cos(\theta)$ harmonics, is $V_{\rm
rot}=V_{\rm circ}$, which characterises the circular motions in the disk. In
case gas clouds are not moving on circular orbits (i.e. due to turbulence or
non-settled nature of the disk), the PA and Q describing the ellipse will vary
with radius. The variation of PA and Q can be related to the structural
changes of the disk, which comprises rings of different orientations and
inclinations. A further effect is the non-negligible higher harmonic
coefficients beyond $b_{1}$. A similar principle applies for the stellar
orbits in thin disks, but the majority of early-type galaxies actually show
regular disk-like kinematics (Krajnović et al., 2008, 2011).

Figure 9: Position angle (top) and rotational velocity (bottom) of the SAURON
and NIFS stellar and gas velocity maps as derived with kinemetry. Results for
the SAURON kinematics are shown with light-blue and blue squares (stars and
gas, respectively), and for the NIFS kinematics with green an lime circles
(stars and gas respectively).

As pointed out previously, the SAURON stellar velocity map of NGC 4111 was
already analysed by Krajnović et al. (2011), who concluded that the stellar
rotation is indeed ordered and disk-like. Here we repeat this analysis to
extend it to the SAURON gas to quantify how regular gas motions are. In Fig. 9
we show the variation of the position angles of best fitting ellipses, as well
as the variation of $V_{\rm rot}$. While running kinemetry on the gas velocity
maps, the flattening of the ellipses was poorly constrained. Therefore we
imposed a limit on the range of possible Q$>0.98$, making ellipses close to
circles. In this way we were still able to recover robust estimates for the PA
and $V_{\rm rot}$. Also shown in this figure are the kinemetry results from
the NIFS data, to be discussed in Sec. 4.3.5.

As pointed out above, the visual inspection of the SAURON gas velocity map
already shows (see Fig. 8), a significant difference in the orientation of gas
and stellar kinematics. This difference is now quantified by kinemetry to be
about $55\degr$ beyond the inner $\approx$ 3″. This angle for the gas
kinematics does not coincide with any of the principal axes in NGC 4111 (the
kinematic and photometric major axes have the same orientation within errors),
and, therefore, the [O iii] emission line gas is in an unstable configuration.
Not only is the gas kinematics misaligned with respect to that of the stars,
but there seems to be a continuous twisting of the kinematic position angle
towards the nucleus. This change of the gas kinematics position angle suggests
the presence of non-circular motions of gas clouds.

The pattern in the gas velocity dispersion (bottom panel of Fig. 8) with
increased values in a twisted configuration could be indication of kinematic
disturbance in the gas due to the non-circular motions. Alternatively, it
could be the result of the superposition of two kinematic components in the
gas: the first due to rotation of the gas in the galaxy disk, as for the
stars, and the second due to rotation of the gas in the polar ring.

Figure 10: Analysis of the polar motions of the SAURON ionised gas. Panel a):
the SAURON gas velocity field as in Fig. 8, with overploted ellipses used to
extract the gas motions in the equatorial plane of the galaxy. Panel b):
resulting velocity field of the gas in the equatorial plane of the galaxy.
Panel c): the velocity field representing “polar" motions of the ionised gas,
obtained by subtracting velocity field in panel b) (ordered rotation of the
gas in the equatorial plane of the galaxy) from the SAURON gas velocity field
in panel a). Panel d): ordered motion of the gas in the polar disk, obtained
using kinemetry. Panel e): SAURON gas velocity dispersion map as in Fig. 8,
but limited to the same region as in panel d), where there are data from the
polar motions. Panel f): absolute difference between the ordered motions in
the equatorial and the polar planes (panels b and d). Note that panels e) and
f) have high velocity values in the same regions, providing a qualitative
explanation for the unusual structure of the SAURON gas velocity dispersion
map. Note also that the colour bars on these panels are not the same, but
adjusted to highlight the kinematic features. On all panels grey lines
presents the isophotes of the stellar light.

We now investigate the possibility that the SAURON ionised-gas velocity field
is indeed due to the superposition of two components, one rotating in the main
galaxy (equatorial) plane and the other in the polar ring. Our goal is to
check if the features on the SAURON map of the ionised-gas velocity
dispersions are consistent with originating from a superposition of gas
motions in these two planes. Assuming that we have two gas disks, both
characterised by ordered motions, and as the location of high velocities in
each of them will be spatially offset, the expectation is that their
superposition will effectively be transposed into high velocity dispersion
values, offset from the centre, and approximately (but not exactly) along the
minor axis of the galaxy.

We used kinemetry to investigate this possibility. The first step was to
extract the ordered motions belonging to the gas disk in the equatorial plane.
To do this we used the set of best-fitting ellipses from the kinemetric
analysis of the stellar velocity field. As the stellar velocity field is very
regular, and consistent with axisymmetry (Krajnović et al., 2011), these
ellipses trace circular orbits in the equatorial plane. As Fig. 9 shows, the
orientation of these ellipses is on average 55°offset from the gas motions, as
mentioned above. We show the ellipses over-plotted on the gas velocity field
in panel a) of Fig. 10. The velocity component that is obtained in this way we
call $V_{\rm rot\\_gas}$, and show it in panel b). Under kinemetry assumptions
this component contains the motions of gas clouds in the equatorial plane and
on circular orbits.

The gas component that is not within the equatorial plane can be derived by
subtraction, $V_{\rm polar}=V_{\rm gas}-V_{\rm rot\\_gas}$, and we show it in
panel c). We tentatively call it a “polar" component as the velocity field is
aligned with the minor axis of the galaxy and the observed polar ring. The
next step is to run kinemetry on this $V_{\rm polar}$ field. On panel d) of
Fig. 10 we show the ordered motions belonging to this gas component, and call
it $V_{\rm rot\\_polar}$. This component, under assumptions of the kinemetric
analysis, represents the part of the gas that is on circular orbits in the
polar disk/ring.

As mentioned above, our goal is to check if the main features of the gas
velocity dispersion field can be reproduced by the superposition of motions in
the equatorial and polar planes. We do this by looking at the absolute
differences between the velocity fields in panels b) and d), or the difference
between the ordered motions in the two planes. The result is shown in panel f)
and should be compared with the map in panel e). The two maps are
qualitatively similar, showing high and low velocity values at the same
locations: nearly along the minor and major axes, respectively. The model
velocity dispersion map of panel f) is only good as a simplistic approximation
of the observed gas velocity dispersion in the SAURON velocity field of NGC
4111 (Fig. 8), but it highlights its consistency with the presence of two main
components in the gas. Therefore, we can conclude that the SAURON gas
kinematics is consistent with originating from two components which are
located at different planes of the galaxy.

###  4.3 Nuclear scale - NIFS

Here we discuss the results from the NIFS data, covering the inner $\approx$
110 pc radius, at a spatial resolution of $\approx$ 7 pc.

####  4.3.1 Stellar and molecular (H2) gas flux distributions

The NIFS flux distribution in the continuum is shown in the right panel of
Figure 5 integrated within the 2.175-2.200 $\mu$m wavelength range, revealing
a smooth distribution along the galaxy plane from the southeast (SE) to the
northwest (NW) of the nucleus.

The H2(1-0) S(1) line flux map, shown in the left panel of Figure 5, presents
an elongated structure running from the north-east (NE) to the south-west (SW)
resembling an inclined ring perpendicular to the galaxy plane and that seems
not to be centred at the galaxy nucleus (shown as a cross in the figure). The
diameter of the ring is $\approx$ 3′′ (210 pc), oriented perpendicular to the
galaxy plane with a projected width of $\approx 0\aas@@fstack{\prime\prime}5$
(37 pc) encircling the nucleus. The H2 flux distribution – stronger to the NW
than to the SE of the nucleus – suggests that the NW portion corresponds to
the near side of the ring.

####  4.3.2 Molecular H2 gas mass and excitation

Figure 11: Relation derived using eq. 1 from Wilman et al. (2005). The black
dot, square and diamond show, respectively, values for the lines H2 $\lambda
2.0338\,\mu$m, $\lambda 2.1218\,\mu$m and $\lambda 2.4066\,\mu$m. The red line
is a linear fit to the data, with an angular coefficient $-1/2267$ K-1.

In order to investigate the origin of the H2 emission, we first calculate its
temperature. We have looked for other emission lines and found that in some
regions of the ring, and in particular at the brightest spot to the SW, at
1$\aas@@fstack{\prime\prime}$3 (95 pc) from the nucleus, two other H2 emission
lines could be measured: H${}_{2}\lambda 2.0338\,\mu$m and H${}_{2}\lambda
2.4066\,\mu$m.

The H2 gas temperature was obtained using the relation from Wilman et al.
(2005) applied to the three emission lines above:

$\text{log}\left(\frac{F_{i}\lambda_{i}}{A_{i}g_{i}}\right)=\text{constant}-\frac{T_{i}}{T_{\mathrm{exc}}}$
(1)

where $F_{i}$ is the flux from the $i^{\mathrm{th}}$ $\mathrm{H}_{2}$ emission
line, $\lambda_{i}$ is its wavelength, $A_{i}$ is the spontaneous emission
coefficient, $g_{i}$ is the statistical weight of the upper level of the
transition and $T_{i}$ is the level energy expressed as temperature. The
expression above is valid for thermal excitation, assuming an ortho:para
abundance ratio of 3:1. From this expression we obtain
$T_{\mathrm{exc}}=2267\,\pm 166$ K for the gas as the inverse of the gradient
of the linear fit to the data, as shown in Figure 11, adopting the uncertainty
from the correlation matrix of the linear regression. $T_{\mathrm{exc}}$ is
the kinetic temperature if the $\mathrm{H}_{2}$ gas is in thermal equilibrium.

We use the flux distribution in the H${}_{2}\lambda 2.1218\,\mu$m line to
calculate the hot $\mathrm{H}_{2}$ gas mass according to the expression
(Scoville et al., 1982; Riffel et al., 2008):

$M_{\mathrm{hot\ H}_{2}}=\frac{2m_{p}\ F_{\mathrm{H}_{2}\lambda 2.1218}\ 4\pi
D^{2}}{f_{\nu=1,J=3}\ A_{S(1)}\ h\nu}$ (2)

where $m_{p}$ is the proton mass, $F_{\mathrm{H}_{2}\lambda 2.1218}$ is the
line flux, $D$ is the distance to the galaxy, $f_{\nu=1,J=3}$ is the
population fraction and $A_{S(1)}$ is the transition probability. The gas mass
is obtained in solar masses. Using T = 2267$\pm 166$ K (obtained above), the
population fraction is $f_{\nu=1,J=3}=1.22\times 10^{-2}$ and the transition
probability is $A_{S(1)}=3.47\times 10^{-7}$ s-1 (Turner et al., 1977;
Scoville et al., 1982; Riffel et al., 2008). Using these parameters, we obtain
a mass for the hot molecular gas M${}_{\mathrm{hot\ H}_{2}}=139.48\pm 4.38$
M⊙.

This mass is very small but is only be the “hot skin" of the H2 total mass,
which should be dominated by cold gas. A number of studies have compared H2
masses obtained using the cold CO molecular lines (observed at mm wavelengths)
with that of hot H2 observed in the near-IR for the nuclear regions of active
galaxies. For example, Dale et al. (2005) obtained ratios in the range
$10^{5}\leq$ M${}_{\mathrm{cold\ H}_{2}}$/M${}_{\mathrm{hot\ H}_{2}}\leq
10^{7}$, Müller Sánchez et al. (2006) in the range $10^{6}\leq$
(M${}_{\mathrm{cold\ H}_{2}}$/M${}_{\mathrm{hot\ H}_{2}})\,\leq 5\times
10^{6}$, while Mazzalay et al. (2013), compiling more data, covering a wider
range of luminosities than the previous studies have derived the following
relation:

$M_{\mathrm{cold\ H}_{2}}\approx 1174\left(\frac{L_{\mathrm{H}_{2}\lambda
2.1218}}{L_{\odot}}\right)$ (3)

where L${}_{\mathrm{H}_{2}\lambda 2.1218}$ is the luminosity of this H2 line
and the standard deviation of the scatter about the factor $\beta=1174$ is
$\approx$ 35%. Using the above expression we obtain M${}_{\mathrm{cold\
H}_{2}}\approx(1.01\pm 0.36)\times 10^{8}$ M⊙, an order of magnitude larger
than the lower limit for the cold gas mass we have obtained from the HST
colour map (Sec. 4.1).

This cold gas mass is comparable to those recently obtained by Schönell et al.
(2019) using the same instrument and methodology for a sample of 6 nearby
active galaxies, which are in the range $8\times 10^{7}$M${}_{\odot}\leq$
M${}_{\mathrm{cold\ H}_{2}}\leq 6\times 10^{8}$ M⊙.

Figure 12: Molecular hydrogen line ratio diagram H2(1-0)S(2)/H2(1-0)S(0)
versus H2(2-1)S(1)/H2(1-0)S(1) (Mouri, 1994). The gray squares are spaxels
from the H2 ring of NGC 4111. The black curve represents thermal emission
models with temperatures in the range 1000-3000 K. The red circles are the
thermal UV excitation models from Sternberg & Dalgarno (1989), the blue star
is the shock heating model from Brand et al. (1989) and the green triangles
are X-ray heating models by Draine & Woods (1990).

What physical processes heat the gas to the calculated temperature of
$\approx$ 2200 K? In order to investigate the nature of the gas excitation, we
calculated the H2(2-1)S(1)/H2(1-0)S(1) line ratio, as its value can be used to
distinguish the excitation mechanism: values of the order of 0.15$\pm$0.15 are
consistent with thermal processes and values of the order of 0.55 and larger
are caused by UV fluorescence (Mouri, 1994; Reunanen et al., 2002; Rodríguez-
Ardila et al., 2004; Storchi-Bergmann et al., 2009). For NGC 4111, we find a
mean value of 0.2 along the H2 ring, suggesting primarily thermal excitation.
The heating mechanism is believed to be the nuclear hard X-ray photons, whose
source is apparently embedded in the dusty ring (González-Martín et al.,
2009). The lack of fluorescence – that requires the presence of UV photons –
is consistent with the absence of the Br$\gamma$ recombination line in the
NIFS spectra, with the UV photons likely being extinguished by the dust
surrounding the nucleus and thus not available to ionise the neutral hydrogen.
However, the absence of Br$\gamma$ may also be explained by a lack of stellar
formation in the nuclear region – maybe due to heating of the gas by the
obscured AGN, despite the existence of available molecular gas in the region.

To further constrain the excitation mechanism, we have used the molecular
hydrogen line-ratio diagram from Mouri (1994), shown in Figure 12, where we
have plotted the ratios H2(1-0)S(2)/H2(1-0)S(0) versus H2(2-1)S(1)/H2(1-0)S(1)
from the NIFS data as grey squares for the spaxels presenting these lines.
This diagram compares line ratios that only take place in ortho H2 molecules
[the (2-1)S(1) $\lambda$2.2477$\,\mu$m and (1-0)S(1) $\lambda$2.1218$\,\mu$m
transitions] with those in para H2 molecules [the (1-0)S(2)
$\lambda$2.0338$\,\mu$m and (1-0)S(0) $\lambda$2.2235 $\,\mu$m transitions].
We included only SNR$>$2 spaxels in the plot to reduce the scattering caused
by noisy spaxels. In the figure, we also include a sequence of the thermal
models for temperatures ranging from 1000 K to 3000 K as a black curve. In
addition, we include predictions by models according to other possible
excitation mechanisms: (1) UV excitation due to fluorescence, shown as red
circles (Sternberg & Dalgarno, 1989); (2) shock excitation due to outflowing
material, e.g. from supernova remnants and/or gas winds, shown as a blue star
(Brand et al., 1989); (3) X-ray heating from AGN, shown as green triangles
(Draine & Woods, 1990). The model data used in Fig. 12 follows Mouri (1994).

The comparison between our data and the models clearly indicates thermal
excitation of H2 with temperatures of about 2000 K and higher (but lower than
3000 K), including heating by X-rays and/or shocks.

####  4.3.3 Stellar kinematics in the inner 110 pc

Figure 13: Top: NIFS stellar kinematic maps, from left to right: centroid
velocity, velocity dispersion, Gauss-Hermite moments $h_{3}$ and $h_{4}$. The
respective mean Monte Carlo errors are 4.9 km s-1, 6.8 km s-1, 0.03 and 0.06.
Bottom: As in the top panels, for the molecular gas kinematics (H${}_{2}\
\lambda 2.1218\,\mu$m), with mean errors of 17.9 km s-1, 39.5 km s-1, 0.05 and
0.04, respectively. For error maps see Fig.21 of the Appendix. The cross
indicates the location of the galaxy nucleus.

The top panels of Figure 13 show maps of the stellar kinematics, with errors
obtained using a Monte Carlo technique, with the corresponding maps shown in
Fig. 21 of the Appendix. These errors decrease outwards, with mean error
values for the centroid velocity, velocity dispersion, Gauss-Hermite moments
$h_{3}$ and $h_{4}$ of 4.9 km s-1, 6.8 km s-1, 0.03 and 0.06, respectively.

The stellar kinematics of Fig. 13 reveal a rotation pattern with blueshifts to
the NW and redshifts to the SE. A comparison of the top left panel of Fig. 13
with the top right panel of Fig. 8 shows that the NIFS stellar velocity field
within the inner 110 pc is similar to that of the SAURON kinematics at larger
scales. The $\sigma$ map shows a partial ring with radius of about 1″(73.1 pc)
with velocity dispersion values in the range 140–150 km s-1 surrounding a
small drop to about 120 km s-1 within the inner 0$\aas@@fstack{\prime\prime}$5
($\sim$37 pc), similar to the drop seen in the SAURON data at larger scales.
This indicates the presence of a dynamically cold structure, such as a disk.
Although its origin is not clear, similar structures have been associated with
young to intermediate age stellar population that retains the colder
kinematics of the gas from which it has formed and did not reach equilibrium
with the bulge velocity field of the older stars yet (Riffel et al., 2010,
2011). This would be consistent with a possible scenario in which gas from the
polar ring has been captured and is forming new stars in the center of the
galaxy.

The $h_{3}$-map shows small positive values in the blueshifted side of the
velocity field, and, similarly negative values in the redshifted side,
indicating that the velocity distribution is slightly asymmetric, showing a
"red tail" and a "blue tail" in the blueshifted and redshifted sides,
respectively. The $h_{4}$-map shows small negative values (broader than a
Gaussian) associated to higher velocity dispersion spaxels and positive
$h_{4}$ values (narrower than a Gaussian), for the spaxels with lower velocity
dispersion. From Monte Carlo simulations we obtain a mean uncertainty for the
velocity, velocity dispersion, $h_{3}$ and $h_{4}$ maps of 4.9 km s-1, 6.8 km
s-1, 0.03 and 0.06, respectively.

The measurements of the stellar velocity, velocity dispersion and the higher
Gauss-Hermite moments from the NIFS data – see the
$\sigma_{\star_{{\tt{NIFS}}}}$ map in the second panel on the upper row of
Figure 13 – will be used in a future work in order to obtain a dynamical model
and constrain the SMBH mass M∙ (together with those of other targets of our
project).

####  4.3.4 Molecular gas kinematics

The maps of the H2 gas kinematic parameters, obtained from the IFSCube fits
are shown in the bottom panels of Figure 13, while the corresponding Monte
Carlo error maps are shown in Fig. 21 of the Appendix. The mean errors in the
parameters $v$, $\sigma$, $h_{3}$ and $h_{4}$, are, respectively 17.9 km s-1,
39.5 km s-1, 0.05 and 0.04.

The H2 velocity field shows redshifts to the NW and blueshifts to the SE, thus
opposite to the observed velocities of the stellar velocity field. This
kinematics is also distinct from the [O iii] kinematics, that present
blueshifts to the S-SW and redshifts to the N-NE. Nevertheless, we point out
that the [O iii] emission line probes the ionised gas kinematics on kpc scales
and the H2 emission probes the molecular gas kinematics at 10-100 pc scales.
The velocity dispersion is roughly $\sim$70 km s-1 all along the H2 ring, with
some higher values from the NW to the NE part of the ring. The $h_{3}$-map
shows the same kind of correlation with the velocity field as shown by the
stellar kinematics maps: positive $h_{3}$ values in the blueshifted side of
the ring – a "red tail" on the profiles – and negative values for the
redshifted side of the ring – a "blue tail" on the profiles. The positive
$h_{3}$ values are nevertheless much higher than the negative values,
indicating the presence of red wings in most regions of the ring. The $h_{4}$
values are predominantly positive, presenting a similar relation to that
observed for the stellar velocity field, where negative values are in general
associated with higher velocity dispersion and positive values with lower
velocity dispersion. From Monte Carlo simulations, we obtain a mean
uncertainty for the velocity, velocity dispersion, $h_{3}$ and $h_{4}$ maps of
17.9 km s-1, 39.5 km s-1, 0.05 and 0.04, respectively, which are quite higher
than the uncertainties in the stellar kinematics. We present the Monte Carlo
error maps for the NIFS stellar and molecular gas kinematics in Figure 21 of
the Appendix.

As pointed out above, the H2 gas kinematics (bottom panels of Fig. 13) suggest
counter-rotation of the molecular ring relative to the stellar kinematics –
but the kinemetry analysis of Section 4.3.5 below reveal an angle between the
stellar and gas apparent rotation varying in the range 120∘–160∘, thus smaller
than 180∘, suggesting another interpretation. As the apparent near side of the
ring – that we hypothesise is the NW because it is brighter than the SE –
shows redshifts and the back (far) side shows blueshifts, an alternative
interpretation is that the ring of molecular gas could be falling towards the
galaxy center.

Figure 14: Channel maps of the H${}_{2}\lambda 2.1218\,\mu$m emission line,
centered at the velocities listed in the bottom left of each panel in units km
s-1. The cross indicates the location of the galaxy nucleus.

H2 Channel Maps – The higher-order moment maps of Fig. 13 indicate some
complexity in the H2 kinematics that is better illustrated via the channel
maps shown in Fig. 14, obtained with IFSCube.

In these maps, the H2(1-0) S(1) line profiles have been sliced in velocity
bins centred on velocities ranging from -165 km s-1 to 165 km s-1 with a 30 km
s-1 channel width. They show that the fastest blueshifts are observed in 3
compact regions: the smallest is just $\approx$0$\aas@@fstack{\prime\prime}$2
(15 pc) to the SE of the nucleus, the second is 0$\aas@@fstack{\prime\prime}5$
south of the nucleus and the last at 1$\aas@@fstack{\prime\prime}$3 (95 pc) to
the SW, corresponding to the brightest spot of the molecular ring (seen in the
left panel of Figure 5 marked with a blue B). In the -135 km s-1 to -75 km s-1
velocity range, the 3 aforementioned regions gradually enlarge and begin to
reveal the SE half of the annular structure. The bright spot 1′′ SW of the
nucleus seems to keep its flux up to -15 km s-1. The -75 km s-1 to 45 km s-1
channels show that the flux gradually increases to the NW of the nucleus and
fades from the SE, with only emission in a knot to the south and emission to
the SW of the nucleus still being detected. In the 75 km s-1 to 165 km s-1
range, the flux in each channel gradually diminishes, increasing again at 135
km s-1. The fastest redshifted component at 165 km s-1 is located within
$\approx 0\aas@@fstack{\prime\prime}5$ (36 pc) of the nucleus, towards the NW,
opposite to the fastest blueshifted region just to the SE of the nucleus. We
interpret this change in orientation as follows: if the NW is indeed the near
side of the ring, this velocity pattern does indicate infall towards the
center of the galaxy. We do not see indication of rotation along the ring, as,
if this were the case, we should observe the highest velocities at the SW and
NE tips of the ring, that should also be opposite to each other. We do not see
this; the highest velocities are observed to the SE and NW. The channel maps
further show that the highest velocity regions tend to be closer to the
nucleus than the lower velocity regions, suggesting an inward acceleration,
also consistent with an inflow scenario.

To further evidence the signature of inflow, we calculated the average
projected radial distance $\langle$r$\rangle$ of the H2 gas for each kinematic
channel. We present the channel velocity values as a function of these radii
in Figure 15. As expected, the mean radial distances decrease as the
velocities increase, supporting acceleration of the molecular gas towards the
nucleus in an inflow.

Figure 15: Average projected radial distance $\langle r\rangle$ for each
kinematic channel of the H2 emitting gas from Fig. 14, including the RMS
variation of the distances in each channel as a gray bar. In red (blue) we
indicate the redshifted (blueshifted) channels.

####  4.3.5 Kinemetric analysis

We have also applied kinemetry to investigate the NIFS stellar and molecular
gas kinematics, as we have done to investigate the SAURON kinematics.

The results from the kinemetry analysis for the stellar and H2 gas velocity
fields from the NIFS data – major axis $PA$ and rotation velocities $V_{rot}$
are shown, together with those for the SAURON data in the two panels of Fig.
9.

The NIFS stellar velocities rise more steeply than the SAURON velocities (as
expected given the sharper PSF of NIFS), but otherwise are fully consistent.
One other observation is worth remarking: while H2 and stellar velocities from
the NIFS data have similarly steep rise and amplitudes, molecular gas being
marginally faster (expected, e.g. Young et al., 2008), the ionised gas in the
SAURON data is significantly slower in the central region. This is a clear
indication that its clouds are neither in a thin disk configuration nor are on
circular orbits.

Figure 16: NIFS H2 kinematics (left), its kinemetry fitting (center) and the
residual between the two (right), showing evidence of non-circular components
in the velocity field.

The top panel of Fig. 9 shows that the H2 kinemetry reveals a misalignment
between the H2 and stellar kinematics of $\approx 155\degr$, indicating that,
besides the ionised gas on large scales being misaligned relative to the
stellar kinematics, the gas in the central region is also in an unstable
configuration, and that gas clouds are not moving on purely circular orbits.
We show this in the three panels of Fig. 16. The first panel shows the same H2
velocity field of Fig 13, which is followed by the kinemetric reconstruction
of a “circular" velocity map, $V_{\rm disk}$. This map is reconstructed using
the $V_{\rm rot}$ of the molecular gas (as shown in Fig 9), but assuming that
the orientation of the field is constant: we fixed it to the median value of
$305\degr$ (top panel of Fig 9). As the H2 gas shows some variation in the PA
and large values of the other harmonic coefficients, $V_{\rm disk}\neq V_{\rm
circ}$. Nevertheless, it can be used as first order approximation to gauge the
contribution of non-circular motions in the molecular gas kinematics, shown on
the residuals in the last panel of Fig. 16.

##  5 Scenario

In the present section, we use the results from the large scale gas
distribution (HST), excitation and kinematics (SAURON) as compared to those of
the nuclear scale (NIFS) to propose a scenario for the physical processes
occurring within the inner kpcs of NGC 4111.

###  5.1 Comparison between the large and nuclear scale kinematics

The stellar velocity maps of the large-scale SAURON and nuclear scale NIFS
data – characterized via kinemetry in Fig. 9 are remarkably similar: they
share the same position angle and flattening (not shown), and have minimal
residuals in higher order harmonic coefficients (also not shown).

Nevertheless, the large-scale [O iii] gas kinematics and the nuclear-scale H2
kinematics look distinct, but a closer look reveals that they seem to be
physically connected. This connection between the large-scale ionised gas and
the nuclear-scale molecular gas is suggestively shown in Figs. 17 and 18.

Fig. 17 shows a comparison between the residuals of the [O iii] and H2
velocity fields relative to the stellar velocity field. Inspection of the [O
iii] residuals within the NIFS FoV suggest blueshifts to the SE and redshifts
to the NW, as observed in the H2 residuals, suggesting that the large scale
ionised gas kinematics connect with the nuclear scale H2 gas kinematics.

We now consider the hypothesis discussed in Section 4.2.4 in which the SAURON
ionised-gas velocity field is due to the superposition of two kinematic
components, one rotating in the main galaxy (equatorial) plane and the other
in the polar ring. In the top panel of Fig. 18 we have used the results from
the kinemetry of the polar ring (Fig. 16) to obtain residuals between the
observed velocities and its reconstructed circular velocity field. The
residuals suggest the presence of a pattern in the shape of spiral arms,
outlined by the black lines in the figure. This spiral configuration is
suggestive of inflows, as observed in previous kinematic studies (e.g.
Storchi-Bergmann & Schnorr-Müller, 2019, and references therein). The small
square in the top panel shows the NIFS FoV, with the NIFS H2 velocity field
shown in the bottom panel. Although the angular resolution of the SAURON data
is much lower that that of the NIFS data, a careful inspection of the residual
velocity field of the top panel shows that, within the NIFS FoV (black square)
there is a hint of residual redshifts towards the NW and residual blueshifts
to the SE, suggesting again a connection between the large-scale ionised gas
velocity field and the nuclear scale H2 velocity field, which also shows
redshifts to the NW and blueshifts to the SE.

The above results, in which the large scale [O iii] gas kinematics seems to
connect with the nuclear scale H2 gas kinematics implies that, if we can
conclude that the H2 kinematics indicates inflow, this inflow seems to be
present also in the larger scale gas, or at least originate in the large scale
gas.

Figure 17: Comparison between the kpc-scale (SAURON) v[O iii] and the 100 pc
scale (NIFS) H2 gas velocity fields after the subtraction of the stellar
velocity field. In the left panel, the dashed square shows the FoV from the
central panel; in the central panel, the dashed square shows the NIFS FoV over
the zoomed-in velocity field of the left panel.

####  5.1.1 The Scenario

We propose the following scenario to explain the observations from the inner
$\approx$1.5 kpc radius probed by the HST and SAURON data down to the inner
$\approx$ 110-10 pc radii probed by the NIFS data. The dusty polar ring
probably originates from the capture of a dwarf galaxy by NGC 4111, consistent
with the estimated lower limit of the gas mass of $\approx$ 107 M⊙ obtained
from the extinction map of the 450 pc ring. The ionised gas seen in the SAURON
data is present in both the galaxy disk and the polar ring structures. The
increase in its velocity dispersion in the region of the polar ring can be
attributed to the superposition of two kinematic components: rotation in the
galaxy plane and orbital motion in the polar ring. This orbital motion shows a
disturbed rotation pattern, revealed by the kinemetry analysis, such that the
residual motion relative to the rotation suggests the presence of a spiral-
like structure that seems to connect with the H2 kinematics within the inner
$\approx$ 110 pc, as suggested by the two panels of Fig. 17.

Figure 18: Top: residual map between the ionised gas polar ring velocities and
its reconstructed circular velocity field from kinemetry, with the black lines
delineating an apparent spiral structure. The small square shows the
3″$\times$3″ NIFS FoV. Bottom: the NIFS H2 velocity field showing redshifts to
the NW and blueshifts to the SE that apparently connect with the residuals of
the SAURON gas kinematics.

The residual inspiral in NGC 4111, seen in Fig. 18, resembles nuclear spirals
(on 100 pc scales) associated to inward motion of gas found in previous
studies of the AGNIFS (AGN Integral Field Spectroscopy) group, such as those
in the nearby active galaxies NGC 7213 (Schnorr-Müller et al., 2014), NGC 1667
(Schnorr-Müller et al., 2017) and NGC 2110 (Diniz et al., 2019), and also the
nuclear spirals found in NGC 1097 (Davies et al., 2009; van de Ven & Fathi,
2010; Fathi et al., 2013). Other observational (e.g. Combes et al., 2014) and
theoretical (Kim & Elmegreen, 2017) studies also support the presence of
inflows along nuclear spirals in nearby active galaxies.

The H2 ring kinematics – that seems to connect with the above spirals,
suggests inward motion: assuming that the brighter NW side is the near and the
fainter SE side is the far, the blueshifts observed in the far side and
redshifts observed in the near side indicate inflows. The channel maps of Fig.
14 and the fact that the average radius of the channel maps decrease as the
velocity increases, support such inflows, suggesting, in addition, inward
acceleration.

The inflowing gas may be settling in the galaxy plane and forming new stars
there, and could be the cause of the observed sigma drop in the NIFS and
SAURON data stellar kinematics. Both $\sigma$-drop structures could be part of
the same gas-rich merger event, building the large-scale and small-scale disks
and gas structures as the merger evolves. At least part of the inflowing gas
seems to be reaching the nucleus, triggering a low-luminosity AGN that can be
observed in X-rays. This emission – possibly combined with shocks in the
region – is the source of excitation of the H2, as discussed in Section 4.3.2.

Having concluded that the observed gas kinematics indicate inflows towards the
nucleus, we have used the NIFS data to estimate the mass inflow rate and
compare it to the mass accretion rate to the obscured AGN. For this, we need
first to obtain an estimate for the SMBH mass as well as the AGN accretion
rate and Eddington ratio.

###  5.2 SMBH mass and Eddington ratio

We use the integrated $\sigma_{\star}$ value within one effective radius
$\sigma_{\star_{SAURON}}=163.3\pm 8.1$ km s-1, as previously determined from
the SAURON data by Cappellari et al. (2013) in order to estimate M∙ with the
empirical $M_{\bullet}-\sigma_{\star}$ relation from van den Bosch (2016):

$\log\left(\frac{M_{\bullet}}{M_{\odot}}\right)=(8.32\pm 0.04)+(5.35\pm
0.23)\log\left(\frac{\sigma_{\star}}{200\ \text{km s}^{-1}}\right)$ (4)

For $\sigma_{\star}=\sigma_{\star_{SAURON}}$, we obtain
M${}_{\bullet}=(7.06^{+2.62}_{-1.79})\times 10^{7}$ M⊙. This value is
consistent with a previous estimate by Nyland et al. (2016) of
M${}_{\bullet}=6.31\times 10^{7}$ M⊙, obtained with the
$M_{\bullet}-\sigma_{\star}$ relation from McConnell & Ma (2013).

The bolometric luminosity $L_{\mathrm{bol}}$ was obtained from the X-ray
luminosity in the 0.5 - 10.0 keV range (González-Martín et al., 2009),
assuming that this luminosity represents 8% of the total luminosity of the AGN
(Nemmen et al., 2006). This allows us to calculate the Eddington ratio
$L_{\mathrm{bol}}/L_{\mathrm{Edd}}=1.5^{+0.5}_{-0.4}\times 10^{-4}$ for NGC
4111, using our determined value of the SMBH mass above. The low Eddington
ratio suggests that, if there is an active nucleus in NGC 4111, as indicated
from the emitted X-rays, the accretion regime is that of a Radiatively
Inefficient Accretion Flow (RIAF).

###  5.3 Mass inflow rate and the mass accretion rate

We have estimated the mass inflow rate $\dot{m}_{\mathrm{inf}}$ using the
channel maps from Fig. 14 and the following expression:

$\dot{m}_{\mathrm{inf}}=\frac{mv}{\langle r\rangle}$ (5)

where $\langle r\rangle$ is the average radial distance of H2 in each channel
(Fig. 15), $v$ is the channel velocity and $m$ is the integrated gas mass from
each channel, determined using eq. 2 for the hot molecular gas and eq. 3 for
the cold.

One important question is: What fraction of the gas is actually inflowing? In
our previous studies cited above, as well as suggested in Figs. 16 and 18, the
residuals from rotation orbital velocity are usually observed in spiral
structures covering $\approx$10% of the observed velocity field. We have then
tentatively considered this fraction of the gas in each channel that is
actually inflowing.

We first considered only the hot phase of the gas in this calculation and
obtain a mass inflow rate of only $7.8^{+3.4}_{-1.7}\times 10^{-4}$ M⊙ yr-1.
Nevertheless, as discussed above, the hot phase of the gas is probably only
“the heated skin" of a much larger gas reservoir, dominated by the cold gas.

Considering now the cold component and that gas from all channels is
inflowing, we determine an upper limit for the mass inflow rate of
56.9${}^{+24.1}_{-12.5}$ M⊙ yr-1.

We then considered that only the 2 highest velocity channels (-165, -135, 135
and 165 km s-1) trace the inflows, with the lower velocity gas tracing gas
orbiting in the galaxy plane. The resulting mass inflow rate is
33.9${}^{+16.3}_{-7.9}$ M⊙ yr-1.

In order to obtain still another estimate, instead of using eq. 3 to estimate
the mass of cold gas, we used the value of hot molecular gas obtained with eq.
2 and the lower limit of the ratio between the cold and hot molecular gas
masses from Dale et al. (2005) of $10^{5}$. This way we obtain a lower limit
of 7.9${}^{+3.3}_{-1.7}$ M⊙ yr-1 for the mass inflow rate.

The mass accretion rate $\dot{m}_{\mathrm{acc}}$ was determined using the
expression:

$\dot{m}_{\mathrm{acc}}=\frac{L_{\mathrm{bol}}}{\eta c^{2}}$ (6)

using the previously calculated $L_{\mathrm{bol}}$ and assuming an accretion
efficiency $\eta=0.01$, justified by the low Eddington ratio for this AGN
(Nemmen et al., 2006), the resulting mass accretion rate is 0.002 M⊙ yr-1,
which supports the presesnce of a RIAF in the nucleus of NGC 4111.

The above accretion rate is larger than the mass inflow rate in hot molecular
gas, but is much lower than the estimated mass inflow rate in cold molecular
gas, that should dominate the mass of molecular gas, as previously pointed
out. This indicates that cold molecular gas could be accumulating in the
nuclear region and is enough to trigger new episodes of star formation and
stronger nuclear activity in the near future. At a mass-inflow rate of
$\approx$5–10 M⊙ yr-1, the existing cold gas reservoir of $\approx$ 108M⊙
should keep this process going for the next 107 years.

##  6 Conclusions

We have analysed galactic scale HST images of the nearby S0 polar-ring galaxy
NGC 4111 through the F475W and F160W filters together with SAURON optical IFS
of the inner 1.5 kpc radius and nuclear scale K-band Gemini NIFS AO-assisted
IFS of the inner 110 pc radius. Our main conclusions are:

  * •

The HST images reveal the dusty polar ring extending by $\sim$ 450 pc
perpendicular to the plane of the galaxy. From the colour map F475W-F160W we
obtain an extinction map and a lower limit for the cold gas mass in the ring
as M${}_{\text{gas}}=9.8\times 10^{6}$ M⊙. This mass is consistent with an
origin from a captured dwarf galaxy.

  * •

Ionised gas emission is seen in the SAURON data, with line ratio values
$1\leq$[O iii]$\lambda 4959,5007\,\AA/\mathrm{H\beta}\leq$3 supporting the
LINER classification of previous studies.

  * •

The NIFS data show a hot molecular gas ring with diameter of 220 pc – embedded
in the dusty polar ring above – with a calculated temperature of 2267$\pm$166
K and mass M${}_{\rm{hot\,H_{2}}}$=139.5$\pm$ 4.4M⊙. This hot gas mass
corresponds to an estimated cold gas mass of M${}_{\rm{cold\,H_{2}}}\approx$
108 M⊙ within the inner 110 pc (radius) which is consistent with the lower
limit for the gas mass obtained from the HST images and further suggests an
extragalactic origin for this gas.

  * •

The excitation of the hot H2 is thermal, most probably due to X-ray heating,
supporting the presence of an AGN at the nucleus. Although shocks could also
contribute to the gas excitation, the low velocity dispersion ($\sim$ 60 km
s-1) does not support a major contribution of shocks to the H2 excitation.

  * •

The large scale (1.5 kpc radius) SAURON and smaller scale (110 pc radius) NIFS
stellar velocity distributions show the same rotation pattern, as supported
also by kinemetry analysis.

  * •

Both the large and small scale stellar velocity dispersion $\sigma_{\star}$
show drops in their values along the galaxy major axis, within radii of
$\approx$ 350 pc and $\approx$ 35 pc, respectively. This is probably
associated to recent capture of gas (on both scales) that settled in a disk
and formed new stars that have still kept their colder gas kinematics as
compared to the surrounding bulge. The presence of younger stars in the region
is supported by previous studies of the stellar population.

  * •

Both the 1.5 kpc scale [O iii] and the 110 pc scale hot H2 velocity fields are
distinct from the stellar one, indicating that the gas in both ionised and
molecular phases is not in a stable configuration.

  * •

The [O iii] gas kinematics show two components: (1) rotation similar to that
of the stars in the galaxy plane; (2) disturbed rotation along the dusty polar
ring. Velocity residuals relative to the rotation component in the ring show
an spiral pattern suggestive of inflows that seem to connect to the H2
velocity field in the 110 pc ring.

  * •

The H2 velocity field in the 110 pc ring shows blueshifts in the apparent far
side and redshifts in the apparent near side, as well increasing velocity
towards the inner regions in channel maps, indicating inflows towards the
nucleus.

  * •

We have estimated the mass inflow rate towards the nucleus from the H2 channel
maps and the expected corresponding cold molecular gas mass, finding values of
5–10 M⊙ yr-1. Such values are much larger than the accretion rate to the AGN
and enough to feed new episodes of star formation within the inner few pc–100
pc considering the available gas reservoir of $\approx\,10^{8}$ M⊙.

We conclude that our data supports a scenario in which a dwarf, gas-rich
galaxy has been recently captured by NGC 4111 giving origin to its polar ring.
Part of this gas is flowing in and possibly forming new stars while another
part of it seems also to have just reached the nuclear SMBH triggering a so-
far low-luminosity AGN. This AGN is already emitting X-rays that are heating
the gas and causing thermal excitation of the H2 molecule. However, as we do
not see Br$\gamma$ in our K-band data, UV photons are not reaching the
observed gas, which suggests that either new stars have not begun to form
and/or these stars and the AGN are still buried in the dust rich environment,
supporting that the AGN has only recently been triggered.

## Acknowledgements

We thank the anonymous referee that helped us in improving our paper.

This research is based on observations obtained at the international Gemini
Observatory, a program of NSF’s NOIRLab, which is managed by the Association
of Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation. on behalf of the Gemini Observatory
partnership: the National Science Foundation (United States), National
Research Council (Canada), Agencia Nacional de Investigación y Desarrollo
(Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina),
Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and
Korea Astronomy and Space Science Institute (Republic of Korea).

This research is based on observations made with the NASA/ESA Hubble Space
Telescope obtained from the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5–26555. These observations are associated with
program GO-15323.

Research of Texas A&M has been supported by NSF grant AST-1814799.

GvdV acknowledges funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme under grant
agreement No 724857 (Consolidator Grant ArcheoDyn).

## Data Availability

The HST data used in this work is publicly available at
https://archive.stsci.edu/hst/ with project code 15323. The GEMINI data is
available online via the GEMINI archive at
https://archive.gemini.edu/searchform/, with project code GN-2019A-LP-8.
Finally, the SAURON data is available via the Isaac Newton Group archive at
http://casu.ast.cam.ac.uk/casuadc/ingarch/query identified with observation
run numbers 958460, 958461, 958462, 958463, 958464, 958465 and 958466. The
maps produced from these data can be shared on reasonable request to the
corresponding author.

## References

  * Bacon et al. (2001) Bacon R., et al., 2001, Monthly Notices of the Royal Astronomical Society, 326, 23
  * Baldwin et al. (1981) Baldwin J. A., Phillips M. M., Terlevich R., 1981, Publications of the Astronomical Society of the Pacific, 93, 5
  * Barth et al. (1998) Barth A. J., Ho L. C., Filippenko A. V., Sargent W. L. W., 1998, The Astrophysical Journal, 496, 133
  * Boccas et al. (2006) Boccas M., et al., 2006, ] 10.1117/12.670842, 6272, 62723L
  * Brand et al. (1989) Brand P. W. J. L., Toner M. P., Geballe T. R., Webster A. S., Williams P. M., Burton M. G., 1989, Monthly Notices of the Royal Astronomical Society, 236, 929
  * Cappellari & Copin (2003) Cappellari M., Copin Y., 2003, Monthly Notices of the Royal Astronomical Society, 342, 345
  * Cappellari & Emsellem (2004) Cappellari M., Emsellem E., 2004, Publications of the Astronomical Society of the Pacific, 116, 138
  * Cappellari et al. (2011) Cappellari M., et al., 2011, Monthly Notices of the Royal Astronomical Society, 413, 813
  * Cappellari et al. (2013) Cappellari M., et al., 2013, Monthly Notices of the Royal Astronomical Society, 432, 1709
  * Cid Fernandes et al. (2010) Cid Fernandes R., Stasińska G., Schlickmann M. S., Mateus A., Vale Asari N., Schoenell W., Sodré L., 2010, Monthly Notices of the Royal Astronomical Society, 403, 1036
  * Combes et al. (2014) Combes F., et al., 2014, Astronomy and Astrophysics, 565, A97
  * Dale et al. (2005) Dale D. A., Sheth K., Helou G., Regan M. W., Hüttemeister S., 2005, The Astronomical Journal, 129, 2197
  * Davies et al. (2009) Davies R. I., Maciejewski W., Hicks E. K. S., Tacconi L. J., Genzel R., Engel H., 2009, The Astrophysical Journal, 702, 114
  * Diniz et al. (2019) Diniz M. R., Riffel R. A., Storchi-Bergmann T., Riffel R., 2019, Monthly Notices of the Royal Astronomical Society, 487, 3958
  * Draine & Woods (1990) Draine B. T., Woods D. T., 1990, The Astrophysical Journal, 363, 464
  * Emsellem et al. (2004) Emsellem E., et al., 2004, Monthly Notices of the Royal Astronomical Society, 352, 721
  * Falcón-Barroso et al. (2011) Falcón-Barroso J., Sánchez-Blázquez P., Vazdekis A., Ricciardelli E., Cardiel N., Cenarro A. J., Gorgas J., Peletier R. F., 2011, Astronomy and Astrophysics, 532, A95
  * Fathi et al. (2013) Fathi K., et al., 2013, The Astrophysical Journal, 770, L27
  * Gonzaga et al. (2012) Gonzaga S., Hack W., Fruchter A., Mack J., 2012, The DrizzlePac Handbook, HST Data Handbook
  * González-Martín et al. (2009) González-Martín O., Masegosa J., Márquez I., Guainazzi M., Jiménez-Bailón E., 2009, Astronomy and Astrophysics, 506, 1107
  * Herriot et al. (2000) Herriot G., et al., 2000, ] 10.1117/12.390288, 4007, 115
  * Ho et al. (1995) Ho L. C., Filippenko A. V., Sargent W. L., 1995, The Astrophysical Journal Supplement Series, 98, 477
  * Ho et al. (1997) Ho L. C., Filippenko A. V., Sargent W. L. W., 1997, The Astrophysical Journal, 487, 568
  * Karachentsev et al. (2013) Karachentsev I. D., Nasonova O. G., Courtois H. M., 2013, Monthly Notices of the Royal Astronomical Society, 429, 2264
  * Kasparova et al. (2016) Kasparova A. V., Katkov I. Y., Chilingarian I. V., Silchenko O. K., Moiseev A. V., Borisov S. B., 2016, Monthly Notices of the Royal Astronomical Society, 460, L89
  * Kauffmann et al. (2003) Kauffmann G., et al., 2003, Monthly Notices of the Royal Astronomical Society, 346, 1055
  * Kewley et al. (2001) Kewley L. J., Dopita M. A., Sutherland R. S., Heisler C. A., Trevena J., 2001, The Astrophysical Journal, 556, 121
  * Kim & Elmegreen (2017) Kim W.-T., Elmegreen B. G., 2017, The Astrophysical Journal Letters, 841, L4
  * Krajnović et al. (2006) Krajnović D., Cappellari M., de Zeeuw P. T., Copin Y., 2006, Monthly Notices of the Royal Astronomical Society, 366, 787
  * Krajnović et al. (2008) Krajnović D., et al., 2008, Monthly Notices of the Royal Astronomical Society, 390, 93
  * Krajnović et al. (2011) Krajnović D., et al., 2011, Monthly Notices of the Royal Astronomical Society, 414, 2923
  * Mazzalay et al. (2013) Mazzalay X., et al., 2013, Monthly Notices of the Royal Astronomical Society, 428, 2389
  * McConnell & Ma (2013) McConnell N. J., Ma C.-P., 2013, The Astrophysical Journal, 764, 184
  * McDermid et al. (2015) McDermid R. M., et al., 2015, Monthly Notices of the Royal Astronomical Society, 448, 3484
  * McGregor et al. (2003) McGregor P. J., et al., 2003, ] 10.1117/12.459448, 4841, 1581
  * Mouri (1994) Mouri H., 1994, The Astrophysical Journal, 427, 777
  * Müller Sánchez et al. (2006) Müller Sánchez F., Davies R. I., Eisenhauer F., Tacconi L. J., Genzel R., Sternberg A., 2006, Astronomy and Astrophysics, 454, 481
  * Neistein & Netzer (2014) Neistein E., Netzer H., 2014, Monthly Notices of the Royal Astronomical Society, 437, 3373
  * Nemmen et al. (2006) Nemmen R. S., Storchi-Bergmann T., Yuan F., Eracleous M., Terashima Y., Wilson A. S., 2006, The Astrophysical Journal, 643, 652
  * Nyland et al. (2016) Nyland K., et al., 2016, Monthly Notices of the Royal Astronomical Society, 458, 2221
  * Pak et al. (2014) Pak M., Rey S.-C., Lisker T., Lee Y., Kim S., Sung E.-C., Jerjen H., Chung J., 2014, Monthly Notices of the Royal Astronomical Society, 445, 630
  * Reunanen et al. (2002) Reunanen J., Kotilainen J. K., Prieto M. A., 2002, Monthly Notices of the Royal Astronomical Society, 331, 154
  * Riffel et al. (2008) Riffel R. A., Storchi-Bergmann T., Winge C., McGregor P. J., Beck T., Schmitt H., 2008, Monthly Notices of the Royal Astronomical Society, 385, 1129
  * Riffel et al. (2010) Riffel R. A., Storchi-Bergmann T., Riffel R., Pastoriza M. G., 2010, The Astrophysical Journal, 713, 469
  * Riffel et al. (2011) Riffel R., Riffel R. A., Ferrari F., Storchi-Bergmann T., 2011, Monthly Notices of the Royal Astronomical Society, 416, 493
  * Rodríguez-Ardila et al. (2004) Rodríguez-Ardila A., Pastoriza M. G., Viegas S., Sigut T. A. A., Pradhan A. K., 2004, Astronomy and Astrophysics, 425, 457
  * Ruschel-Dutra & Oliveira (2020) Ruschel-Dutra D., Oliveira B. D. D., 2020, danielrd6/ifscube v1.0, doi:10.5281/ZENODO.3945237, https://zenodo.org/record/3945237
  * Sarzi et al. (2017) Sarzi M., et al., 2017, Astrophysics Source Code Library, p. ascl:1708.012
  * Savage & Mathis (1979) Savage B. D., Mathis J. S., 1979, Annual Review of Astronomy and Astrophysics, 17, 73
  * Schnorr-Müller et al. (2014) Schnorr-Müller A., Storchi-Bergmann T., Nagar N. M., Ferrari F., 2014, Monthly Notices of the Royal Astronomical Society, 438, 3322
  * Schnorr-Müller et al. (2017) Schnorr-Müller A., Storchi-Bergmann T., Ferrari F., Nagar N. M., 2017, Monthly Notices of the Royal Astronomical Society, 466, 4370
  * Schoenmakers et al. (1997) Schoenmakers R. H. M., Franx M., de Zeeuw P. T., 1997, Monthly Notices of the Royal Astronomical Society, 292, 349
  * Schönell et al. (2019) Schönell A. J., Storchi-Bergmann T., Riffel R. A., Riffel R., Bianchin M., Dahmer-Hahn L. G., Diniz M. R., Dametto N. Z., 2019, Monthly Notices of the Royal Astronomical Society, 485, 2054
  * Scoville et al. (1982) Scoville N. Z., Hall D. N. B., Ridgway S. T., Kleinmann S. G., 1982, The Astrophysical Journal, 253, 136
  * Sternberg & Dalgarno (1989) Sternberg A., Dalgarno A., 1989, The Astrophysical Journal, 338, 197
  * Storchi-Bergmann & Schnorr-Müller (2019) Storchi-Bergmann T., Schnorr-Müller A., 2019, Nature Astronomy, 3, 48
  * Storchi-Bergmann et al. (2009) Storchi-Bergmann T., McGregor P. J., Riffel R. A., Simões Lopes R., Beck T., Dopita M., 2009, Monthly Notices of the Royal Astronomical Society, 394, 1148
  * Tody (1986) Tody D., 1986, ] 10.1117/12.968154, 627, 733
  * Tody (1993) Tody D., 1993, 52, 173
  * Turner et al. (1977) Turner J., Kirby-Docken K., Dalgarno A., 1977, The Astrophysical Journal Supplement Series, 35, 281
  * Verheijen (2004) Verheijen M. A. W., 2004, ] 10.1017/S1743921304000833, pp 394–400
  * Verheijen & Zwaan (2001) Verheijen M. A. W., Zwaan M., 2001, 240, 867
  * Wenger et al. (2000) Wenger M., et al., 2000, Astronomy and Astrophysics Supplement Series, 143, 9
  * Wilman et al. (2005) Wilman R. J., Edge A. C., Johnstone R. M., 2005, Monthly Notices of the Royal Astronomical Society, 359, 755
  * Winge et al. (2009) Winge C., Riffel R. A., Storchi-Bergmann T., 2009, The Astrophysical Journal Supplement Series, 185, 186
  * Wolfinger et al. (2013) Wolfinger K., Kilborn V. A., Koribalski B. S., Minchin R. F., Boyce P. J., Disney M. J., Lang R. H., Jordan C. A., 2013, Monthly Notices of the Royal Astronomical Society, 428, 1790
  * Wong et al. (2004) Wong T., Blitz L., Bosma A., 2004, The Astrophysical Journal, 605, 183
  * Young et al. (2008) Young L. M., Bureau M., Cappellari M., 2008, The Astrophysical Journal, 676, 317
  * van de Ven & Fathi (2010) van de Ven G., Fathi K., 2010, The Astrophysical Journal, 723, 767
  * van den Bosch (2016) van den Bosch R. C. E., 2016, The Astrophysical Journal, 831, 134

##  Appendix A Extinction and gas mass distribution in the polar ring

From the colour map shown in Fig. 2, we have built the extinction map AF475W
\- AF160W shown in Fig. 19, for the inner 6″$\times$6″ (440$\times$440 pc2) of
NGC 4111, showing the reddening distribution along the dusty polar ring,
calculated as described in Sec. 4.1. The spatial correlation with the
H${}_{2}\,\lambda 2.1218\,\mu$m ring seen in the NIFS data is revealed by the
overplotted white contours from the H2 emission.

Figure 19: HST AF475W \- AF160W map of the galaxy within the inner
6${}^{\prime\prime}\times 6^{\prime\prime}$ (440$\times$440 pc2), that covers
the dusty polar ring. Overplotted in white are the contours from the
H${}_{2}\lambda 2.1218\,\mu$m emission line flux distribution obtained from
the NIFS data.

The second figure shown in this Appendix – Fig. 20, is a gas mass column
density map of the same 6″$\times$6″ (440$\times$440 pc2) region that covers
the dusty polar ring. We again show in white, contours of the
H${}_{2}\,\lambda 2.1218\,\mu$m line emission from NIFS data. This map has
been obtained from the reddening map above following the steps discussed in
Section 4.1. From this mass density map, integrating over the surface area of
each spaxel, we obtained the cold gas mass as M${}_{\text{gas}}=9.8\times
10^{6}$ M⊙.

Figure 20: Gas mass column density map from the polar ring region obtained
from the HST F475W - F160W colour map. Overplotted in white are the contours
from the H${}_{2}\lambda 2.1218\,\mu$m emission line flux distribution as
derived from the NIFS data.

##  Appendix B Error maps from the NIFS kinematics

In order to measure the intrinsic errors in the methods used for obtaining the
NIFS stellar and molecular gas kinematics, we performed the Monte Carlo
technique, perturbing the data with a Gaussian noise in every spaxel. From
this, we obtained the error maps for the stellar and molecular gas kinematics,
shown in Figure 21. Similarly to Figure 13, the top row shows the stellar
kinematics errors and the bottom panels show those for the H2 kinematics. From
left to right, the panels show the error maps of the velocity
$v_{\mathrm{err}}$, velocity dispersion $\sigma_{\mathrm{err}}$ and Gauss-
Hermite moments $h_{3\ \mathrm{err}}$ and $h_{4\ \mathrm{err}}$. From these
maps, we observe that the errors in the stellar kinematics decrease from the
center to the borders, while those for the H2 gas kinematics do not vary much.
The mean errors of each kinematic parameter (of the measurements shown in each
map, not considering the masked spaxels) are listed in Table 1.

Table 1: Mean Monte Carlo errors for each parameter of the NIFS stellar and molecular gas kinematics. Parameter |  | Mean error |
---|---|---|---
|  | Stars | Gas
$v_{\mathrm{err}}$ |  | 4.9 km s-1 | 17.9 km s-1
$\sigma_{\mathrm{err}}$ |  | 6.8 km s-1 | 39.5 km s-1
$h_{3\ \mathrm{err}}$ |  | 0.03 | 0.05
$h_{4\ \mathrm{err}}$ |  | 0.04 | 0.04
Figure 21: Monte Carlo error maps of the NIFS stellar (top panels) and
molecular gas (bottom panels) kinematics fit. From left to right, the error
maps of the velocity $v_{\mathrm{err}}$, velocity dispersion
$\sigma_{\mathrm{err}}$ and Gauss-Hermite moments $h_{3\ \mathrm{err}}$ and
$h_{4\ \mathrm{err}}$. The cross indicates the location of the galaxy nucleus.