# Molecular line ratio diagnostics and gas kinematics in the AGN host Seyfert
galaxy NGC 5033

Selçuk Topal1
1Yuzuncu Yil University, Department of Physics, Van, 65080, Turkey
E-mail<EMAIL_ADDRESS>
(Accepted . Received ; in original form )

###### Abstract

Multiple molecular lines are useful for studying the physical properties of
multiphase star-forming gas in different types of galaxies. We probe the
molecular gas throughout the disc of the spiral galaxy NGC 5033, hosting an
active galactic nucleus (AGN), using multiple low-$J$ CO lines [12CO(1–0, 2–1,
3–2 and 13CO(1–0, 2–1)] and dense gas tracers [HCN(1–0) and HCO+(1–0)].
Firstly, we determine the ratios of the integrated intensity maps and the
ratio of intensities in position velocity diagrams. Secondly, we obtain the
ratios of CO lines and high-density tracers at the centre; and thirdly, we
model these line ratios using a radiative transfer code. Line ratio
diagnostics reveal that the south of the gaseous disc contains cooler gas than
the northern part, and the centre hosts warmer and less tenuous gas with a
similar dense gas fraction compared to most galaxies of similar type. Our
model results mostly agree with the empirical ones in the sense that the
central region of NGC 5033 harbours warmer gas than that in the centres of
normal spirals and lenticulars without showing AGN activity. Finally, the
beam-averaged total molecular gas mass and gas surface density along the
galaxy’s major axis show a radial gradient, i.e. increasing from the outskirts
up to the central region of size $1$ kpc where there is a depression in both
gas mass and surface density.

###### keywords:

galaxies: Seyfert - galaxies: active - galaxies: ISM - ISM: molecules

††pagerange: Molecular line ratio diagnostics and gas kinematics in the AGN
host Seyfert galaxy NGC 5033-LABEL:lastpage††pubyear: 2021

##  1 Introduction

After realizing that the Milky Way was not the only ‘island universe’ in the
cosmos, our understanding of the Universe has rapidly expanded as the Universe
itself (Lemaître, 1927; Hubble, 1929; Lemaître, 1931a, b; de Vaucouleurs,
1974; Toomre, 1977; Kormendy, 1979; Kormendy & Bender, 2012). There are
different types of galaxies with a distinct appearance, luminosity, colour,
surface brightness, gas content, level of star formation (SF) and activity of
their nuclei. ‘Red and dead’ elliptical and lenticular galaxies (i.e. early-
types) suffer from a lack of molecular gas, while spirals, like our own Milky
Way, are rich in both gas and dust. The central region of galaxies play a
crucial role in the dynamics, structure and evolution of galaxies. Now we know
that almost all massive galaxies host supermassive black holes (SMBHs) at
their centre and energy feedback from central quasar-like events can affect
galaxy evolution (Kormendy & Richstone, 1995).

Seyfert galaxies, hosting active galactic nuclei (AGNs), have morphologies
similar to spiral galaxies, but with exceptionally bright star-like cores.
Their nuclei manifest powerful broad emission lines of higher excitation, and
they are subdivided into two groups called Seyfert $1$ and $2$. Studying the
ISM of such galaxies through the use of molecular emission lines allows us to
better understand SF processes in different types of galaxies.

Observation and analysis of molecular emission lines enable us to shed light
on some outstanding questions regarding SF processes and galaxy evolution.
About $200$ molecules have now been detected in the interstellar medium
(ISM)111https://zeus.ph1.uni-koeln.de/cdms/molecules. Multiple line ratio
diagnostics provide us with a great opportunity to study the physics of
molecular gas in detail. The upper level of the CO $J=1\rightarrow 0$
transition lies $\approx~{}5.5$ K above the ground state and is relatively
easy to detect in molecular clouds where the temperature is typically near
$10$ K or higher. CO is also the second most abundant molecule in the ISM
after molecular hydrogen (H2). CO, therefore, offers an indirect probe for the
physics of star-forming gas clouds where H2 is hard to observe directly.

Table 1: Basic parameters for NGC 5033

Property | Value | Ref.
---|---|---
Type | SA(s)c | a
RA (J2000) | $13^{\rm h}13^{\rm m}27.5^{\rm s}$ | a
Dec (J2000) | $36^{\rm d}35^{\rm m}38.2^{\rm s}$ | a
V⊙ (km s-1) | $875$ | a
Major diameter (arcmin) | $1.3$ | a
Minor diameter (arcmin) | $0.4$ | a
Distance (Mpc) | $14.7$ | b
Position angle (degree) | $171.8$ | b
Inclination (degree) | $66.6$ | b
Activity class of AGN | S1.8 | b
SFR ($M_{\odot}$ yr-1) | $0.12$ | c

a Nasa/Ipac Extragalactic Database (NED); b HyperLEDA (Makarov et al., 2014);
c Max Planck Institute for Astrophysics-Johns Hopkins University Data Release
8 (MPA-JHU DR8);

NGC 5033 is a nearby spiral galaxy with Seyfert $1.8$ type nucleus (Véron-
Cetty & Véron, 2006) seen at high inclination (Table 1) with a point-like
central X-ray source (Terashima et al., 1999). The galaxy is located at a
distance of about $14.7$ Mpc (HyperLEDA; Makarov et al. 2014), and is a member
of a group (Fouque et al., 1992). General properties of NGC 5033 are listed in
Table 1. We study the physics of the molecular gas in NGC 5033 using multiple
low-$J$ CO lines, i.e. 12CO(1–0), 12CO(2–1), 12CO(3–2), 13CO(1–0), and
13CO(2–1), and high-density tracers, i.e. HCN(1–0) and HCO+(1–0). The number
of molecular emission lines available to the current study and the methods
used (i.e. empirical line ratio analysis and modelling), make NGC 5033 to an
exemplary target to improve our understanding of SF in different types of
galaxies, particularly near their centre. We probe physics of the molecular
gas across the disc of the galaxy as follows. We first apply empirical line
ratio diagnostics along with the non-local thermodynamic equilibrium (non-LTE)
code RADEX (van der Tak et al., 2007) involving both CO and high density
tracers to explore the properties of the molecular gas in the galaxy.
Secondly, we study any radial variations in the integrated line intensity,
molecular gas mass and surface density throughout the galaxy’s major-axis.

Our goals are i) to constrain the physics of the central gas and its
kinematics over the disc of NGC 5033; ii) to compare our results with those of
literature studies, particularly those using similar line ratios and the same
radiative transfer code; iii) discuss possible effects of stellar feedback in
shaping the ISM at the centre of NGC 5033. The sections of this paper are
assembled in the following way. The literature data are presented in Section
2. The imaging and analysis is given in Section 3. A quantitative analysis of
the empirical line ratios through the use of RADEX is described in Section 4.
Section 5 presents the main results and further discussions. We, finally,
conclude briefly in Section 6.

Table 2: CO line data

Transition | Rest Freq. | Telescope | Beam size | Linear sizea | Reference | Info
---|---|---|---|---|---|---
| (GHz) |  | (arcsec) | (kpc) |  |
12CO(1–0) | $115.3$ | BIMA+$12$m | $6.1\times 5.4$ | $0.4$ | Helfer et al. 2003 | IM
12CO(2–1) | $230.5$ | JCMT $15$m | 22 | 1.6 | Papadopoulos & Seaquist 1998 | SP
13CO(2–1) | $220.4$
12CO(3–2) | $345.8$ | JCMT $15$m | $14.5$ | $1.0$ | Wilson et al. 2012 | RM
12CO(3–2) | $345.8$ | HHT $10$m | $22$ | $1.6$ | Mao et al. 2010 | SP

a Linear size of the beam. Information on the data aquisition method is given
in the last column; i.e. IM (interferometric map), RM (raster map), and SP
(single dish pointing), respectively.

##  2 Literature data

The literature CO data for NGC 5033 were taken from various sources. Complete
maps in 12CO(1–0) and 12CO(3–2) were taken from the Berkeley-Illinois-Maryland
Association Survey Of Nearby Galaxies survey (BIMA SONG; Helfer et al. 2003)
and the James Clerk Maxwell Telescope (JCMT) Nearby Galaxies Legacy Survey
(NGLS; Project ID MJLSN05; Wilson et al. 2012), respectively. The BIMA SONG
and JCMT maps in 12CO(1–0) and 12CO(3–2) lines cover areas of $5.7$ x $5.6$
and $5.3$ x $4.3$ arcmin2 over the galaxy, respectively. The 12CO(1–0) and
12CO(3–2) data cubes have beam sizes of $6.1$ x $5.4$ and $14.5$ x $14.5$
arcsec2, respectively. We use these data cubes to create CO integrated
intensity maps and position velocity diagrams (PVDs) with the highest
resolution possible (Section 3.2). Additional single-dish spectra of 12CO(2–1)
and 13CO(2–1) transitions were taken from Papadopoulos & Seaquist (1998) and a
12CO(3–2) spectrum was taken from the $10$m Heinrich-Hertz Telescope Survey
(Mao et al., 2010). The single-dish spectra of 12CO(2–1), 13CO(2–1), and
12CO(3–2) were obtained with the same beam size of $22$ arcsec. More details
on the data described above can be found in the associated papers. Basic
information about the literature data is listed in Table 2.

##  3 Analysis and imaging

###  3.1 Integrated line intensities and gas mass

The 12CO(2–1), 13CO(2–1) and 12CO(3–2) spectra have a beam size of $22$
arcsec, i.e. the lowest angular resolution in the CO data available for this
study, and the reported unit is main beam brightness temperature, $T_{\rm
mb}$, in Kelvin (K). However, the interferometric 12CO(1–0) data cube is in
units of Jy and has a beam size of $6.1$ x $5.4$ arcsec2. It is, therefore,
necessary to convolve the 12CO(1–0) cube to the $22$ arcsec beam and make the
unit conversion from Jy to $T_{\rm mb}$. We performed a beam convolution to
the cube using MIRIAD (Sault et al., 1995) task convol. We then estimated the
unit conversion factor of $0.19$ K/(Jy/beam) using MIRIAD task $imstat$, and
applied the conversion factor to the cube. Finally, we extracted the CO(1–0)
integrated spectrum from the area of $22$ arcsec $\times~{}22$ arcsec at the
centre of the galaxy using MIRIAD task imspect.

Figure 1: Integrated spectra of CO lines for the common beam size of $22$
arcsec. Gaussian fits are overlaid (red). Heliocentric velocity (upper left
panel) and the velocity resolution (upper left corners of each panel) are
indicated.

All of the $22$ arcsec CO spectra obtained at the centre of the NGC 5033 are
shown in Figure 1. Gaussian fits were applied to calculate the integrated line
intensities for all spectra. The MPFIT package (Markwardt, 2009) was used to
optimize the fits. The fitting parameters with the smallest absolute
$|1-\chi^{2}|$ value were considered as the best fit. The intensities
calculated for each transition are listed in Table 3. The beam-averaged total
fluxes $F$ (W m-2) per unit area and total intensities $I$ (W m-2 sr-2) were
calculated using standard expressions (Bayet et al., 2004). The values of
total intensities and total fluxes are listed in Table 3.

Table 3: $22$ arcsec beam averaged quantities at the centre of NGC 5033 Line |  $\int T_{\rm mb}$ d$v$ | Intensity | Flux | FWHM
---|---|---|---|---
|  (K km s-1) |  (W m-2 sr-1) |  (W m-2) |  (km s-1)
12CO(1–0) | $40.8\pm 2.7$ | $6.37\,\pm\,0.42\times 10^{-11}$ | $8.22\,\pm\,0.54\times 10^{-19}$ | $301.6\,\pm\,23.6$
12CO(2–1) | $45.8\pm 2.7$ | $5.72\,\pm\,0.34\times 10^{-10}$ | $7.38\,\pm\,0.43\times 10^{-18}$ | $320.5\,\pm\,16.9$
12CO(3–2) | $17.1\pm 2.7$ | $7.21\,\pm\,1.14\times 10^{-10}$ | $9.30\,\pm\,1.47\times 10^{-18}$ | $249.5\,\pm\,28.1$
13CO(2–1) | $\phantom{0}6.4\pm 0.8$ | $6.99\,\pm\,0.87\times 10^{-11}$ | $9.01\,\pm\,1.13\times 10^{-19}$ | $238.6\,\pm\,29.3$

We defined $25$ regions side by side over the major-axis so that we can probe
any changes in the physical properties of the gas as a function of radius
without selection bias (see Figure 2). Each circular region has a diameter of
$6$ arcsec, i.e. about the beam size of the 12CO(1–0) data, representing a
circular region with a diameter of $400$ pc along the major axis of the
galaxy. We first extracted the 12CO(1–0) spectra in the selected regions and
calculated the integrated intensities, as explained above. 12CO(1–0) was not
detected ($\int T_{\rm mb}$ d$v$ $<3\sigma$, where $\sigma$ is the uncertainty
in the integrated intensity) at $5$ positions in the SE of the galaxy’s major
axis (see Figure 2). For those $5$ positions, we estimated the upper limit to
the integrated intensity as $3\times\sigma_{\rm rms}\times\rm{FWHM}$, where
$\sigma_{\rm rms}$ is the noise in the spectrum at that position and FWHM is
the average Full Width at Half Maximum line width of the 12CO(1–0) spectra in
the detected positions, i.e. $40$ km s-1. The upper limit could also be
calculated as $3\times\sigma_{\rm rms}\times\delta v\times\sqrt{N}$, where
$\delta v$ is the channel width and $N$ is the number of channels across the
line. However, since BIMA 12CO(1–0) data cube has a channel width of $20$ km
s-1 and the average number of channels across the line is about $4$ for the
12CO(1–0) line profiles at the detected positions, the latter method would
give almost identical values to those estimated from the first method.

We estimated the gas mass in units of solar mass ($M_{\odot}$) in each
selected region using CO-to-H2 conversion factor ($X_{\rm CO}$), the distance
to the galaxy, and the measured 12CO(1–0) integrated red intensities. $X_{\rm
CO}$ = $2\times 10^{20}$ cm-2 (K km s-1)-1 was taken because it is a good
choice for the disc of our Galaxy (Dame et al., 2001; Abdo et al., 2010;
Bolatto et al., 2013). Studies of nearby ‘normal galaxies’ indicate similar
values (Rosolowsky et al., 2003; Bolatto et al., 2008; Donovan Meyer et al.,
2012). The discs of Seyfert galaxies show conversion factors, which are within
a factor of two consistent with the Galactic disc value (Donovan Meyer et al.,
2013). However, although it is not universal, many studies showed that $X_{\rm
CO}$ could be lower by a factor of $5$ to $10$ in the central region of
galaxies regardless of galaxy type (e.g. Sandstrom et al., 2013; Bolatto et
al., 2013). In the central region of the Seyfert galaxy NGC 1068, for example,
the conversion factor was found to be $X_{\rm CO}=0.2-0.4\times 10^{20}$ cm-2
(K km s-1)-1 (Papadopoulos & Seaquist, 1999). However, please note that the
value of the conversion factor depends on the method used (i.e. virial mass,
dust column density, spectral line modelling), resolution and metallicity
(Bolatto et al. 2013 and references therein). Such uncertainties could cause
error bars in the estimated nuclear value of $X_{\rm CO}$.

For NGC 5033 we, therefore, adopted values of $X_{\rm CO}=0.4\times 10^{20}$
cm-2 (K km s-1)-1 and $X_{\rm CO}=2\times 10^{20}$ cm-2 (K km s-1)-1 for the
central $1$ kpc (i.e. the central three red $6$ arcsec sized regions, see Fig.
2) and for the arms, respectively, where the corresponding values of
$\alpha_{\rm CO}\,\equiv\,\Sigma_{\rm H_{2}}$ / $I_{\rm 1-0}$ are
$0.6~{}M_{\odot}$(K km s-1 pc2)-1 and $3.2~{}M_{\odot}$(K km s-1 pc2)-1,
respectively (Narayanan et al., 2012). The expression used to estimate the
molecular gas mass is shown below.

$\frac{M_{{\rm H}_{2}}}{M_{\odot}}=C\,\bigg{(}\frac{I_{\rm 1-0}}{{\rm K}\,{\rm
km}\,{\rm s}^{-1}}\bigg{)}\,,$ (1)

where $I_{1-0}$ is the main beam brightness 12CO(1–0) integrated line
intensity in units of [K km s-1], and $C=1.3\times 10^{5}$ for $X_{\rm
CO}=0.4\times 10^{20}$ cm-2 (K km s-1)-1 and $C=6.6\times 10^{5}$ for $X_{\rm
CO}=2\times 10^{20}$ cm-2 (K km s-1)-1. The gas surface density, $\Sigma_{\rm
H_{2}}$, was also estimated for each selected region using $I_{\rm 1-0}$ and
$X_{\rm CO}$. The integrated 12CO(1–0) intensities, and the beam-averaged
$M_{{\rm H}_{2}}$ and $\Sigma_{\rm H_{2}}$ obtained in the selected regions
are shown in Figure 2.

On a different note, any two elements of an interferometer cannot be closer
than some minimum distance, causing the problem known as ‘missing flux’ in the
data. However, BIMA SONG data cubes for $24$ galaxies (including NGC 5033)
were created by incorporating the total flux measurement from the NRAO $12$m
telescope to achieve the flux recovery (see Helfer et al. 2003). It is
therefore important to note that the total mass estimation in the current
study is not significantly affected by missing flux.

Figure 2: Integrated intensity, beam-averaged molecular gas mass, and gas
surface density are shown in selected regions across the galaxy’s disc. The
regions along the major-axis are represented by red circles on the CO(1–0)
moment 0 map (left panel). Each red circle has a diameter of $6$ arcsec. The
variation of beam-averaged quantities as a function of distance from the
galactic centre is shown in the large middle and right panels. Zero offset
represents the galaxy centre (Table 1) in all panels. The black filled circles
in the middle and right panels represent the data for the integrated
intensity. The blue filled squares in the inserted panels $a$, and the blue
filled circles in the inserted panels $b$ represent the gas mass and surface
density, respectively. In the right panel and its inserted panels $a$ and $b$,
the southern part of the disc is to the left, while the northern part is to
the right. The data points with downward arrows show the upper limits of the
integrated intensity, i.e. $3\times\sigma_{\rm rms}\times\rm{FWHM}$ (see
Section 3.1).

###  3.2 Moment maps and position velocity diagrams (PVDs)

We obtained integrated line intensities (hereafter moment 0) and velocity maps
(hereafter moment 1) by defining a region of contiguous emission in the
12CO(1–0) and 12CO(3–2) data cubes (see Topal et al. (2016) for more details
on the procedure). Moment maps of the galaxy are shown in Figure 3.

Figure 3: Top: Moment 0 contour maps for 12CO(1–0) (left) and 12CO(3–2)
(right), respectively. The black circle in the bottom left of each panel
represents the beam sizes. Levels of integrated intensity contours on the
moment 0 maps range from $10$ to $100$ per cent of the peak intensity with an
intercept of $10$ per cent. The peak intensities in the moment 0 maps of
12CO(1–0) and 12CO(3–2) are $119.2$ K km s-1 and $13.3$ K km s-1,
respectively. The red circles centred on both images have a diameter of $22$
arcsec (i.e. lowest resolution in the adopted CO data set). Middle: Moment1
contour maps for 12CO(1–0) and 12CO(3–2). Velocity contours on the moment 1
maps are separated by $30$ km s-1. The systemic velocity of $875$ km s-1 is
shown in the top left of each panel. Bottom: The moment 0 maps (white
contours) are superimposed on an optical image of the galaxy (greyscale) taken
from the Sloan Digital Sky Survey (SDSS). East is to the left and north is up
in all panels.

We created position velocity diagrams (PVDs) by taking a slice along the
major-axis of the galaxy in the fully-calibrated and cleaned data cubes of
12CO(1–0) and 12CO(3–2) (see Figure 2, left panel). The 12CO(1–0) and
12CO(3–2) data cubes have pixel sizes of $1$ and $7.3$ arcsec, respectively.
We first rotated the cubes using the MIRIAD task $regrid$ to adjust the pixels
to a horizontal grid. We then took a slice along the major-axis of the galaxy,
averaging a total of five (for the 12CO(1–0) cube) and three (for the
12CO(3–2) cube) pixels in perpendicular direction (i.e. along the minor-axis).
The spatial resolution of each PVD was calculated using the beam major-axis
and minor-axis, the beam position angle, and the gas position angle (see Davis
et al. 2013). The PVDs are shown in Figure 4.

Figure 4: Position velocity diagrams (PVDs) of 12CO(1–0) (left) and 12CO(3–2)
(right). The rms noise (i.e. $1\sigma$) for 12CO(1–0) is $0.11$ K while the
12CO(3–2) PVD has an rms noise of $0.01$ K. Black lines on the PVDs represent
the contour levels spaced by $3\sigma$ and starting at $2\sigma$. Colour on
the contour maps starts at $2\sigma$ and $1\sigma$ for 12CO(1–0) and
12CO(3–2), respectively. The rotational velocity of the gas at $200$ km s-1 is
indicated with black horizontal dashed lines. The horizontal and vertical
lines in the lower right part of each panel indicate the spatial resolution
over the major-axis and velocity resolution, respectively.

###  3.3 Line ratios at the centre and over the disc

We first measured the ratios of the integrated line intensities at the centre.
Additional integrated line intensity ratios of 12CO(1–0) / 13CO(1–0), HCN(1–0)
/ 12CO(1–0) and HCN(1–0) / HCO+(1–0) were taken from Krips et al. (2010). All
in all, the ratios we obtained at the centre of NGC 5033 are 12CO(2–1) /
12CO(1–0) (hereafter $R_{\rm 21}$), 12CO(1–0) / 13CO(1–0) (hereafter $R_{\rm
11}$), 12CO(3–2) / 12CO(1–0) (hereafter $R_{\rm 31}$), 12CO(2–1) / 13CO(2–1)
(hereafter $R_{\rm 22}$), HCN(1–0) / 12CO(1–0) (hereafter $R_{\rm DC}$) and
finally HCN(1–0) / HCO+(1–0) (hereafter $R_{\rm DD}$). The ratios are listed
in Table 4. We then compared the ratios found at the centre of the galaxy to
those found in the centre and in the arms of other types of galaxies from the
literature (see Figure 5 and Section 5.3).

As our second approach to the line ratio analysis, we measured the ratio of
the moment 0 maps enabling us to probe the change in the $R_{\rm 31}$ ratios
across the disc of the galaxy. We then measured the ratio of the PVD
intensities (similar to Topal et al. 2016) allowing us to probe the physical
conditions throughout the gas kinematic components of the galaxy, i.e. nuclear
disc and/or inner ring (see Section 5.2). The method we used to obtain the
ratio moment 0 maps and ratio PVDs is explained below.

Before taking the ratio of the moment maps, we first convolved the 12CO(1–0)
moment 0 map to the beam size of $14.5$ arcsec, i.e. the beam size of the
12CO(3–2) data. We also applied additional corrections so that both moment 0
maps have the same pixel size and both cover the same area in the sky. The
ratio moment map is shown in Figure 6. For the PVD intensity ratios we also
made sure that the starting and ending velocities, velocity resolution and the
area in the sky were the same for both cubes. We then created the PVDs from
those identical cubes, by following the same steps explained in Section 3.2.
We finally obtained the ratio of the PVDs (see Figure 6).

##  4 Modelling

We probe the physics of the molecular gas quantitatively by performing RADEX
calculations. RADEX provides a Large Velocity Gradient (LVG) model and creates
a parameter space for a user-defined set of physical parameters. We define the
model parameters in two ways with a $\chi^{2}$ and a likelihood method.
Further details on the radiative transfer code RADEX and the best model
identification can be found below.

###  4.1 LVG code: RADEX

The input parameters for RADEX are the gas kinetic temperature $T_{\rm K}$,
hydrogen gas volume number density $n$(H2), the carbon monoxide column number
density $N$(CO), the line width of the spectrum $\Delta v$, and the intrinsic
abundance ratio, [12C] / [13C]. The radiation of the cosmic microwave
background ($T_{\rm CMB}$ = $2.73$ K) is also implemented. We considered line
widths of $300$ km/s and $250$ km/s for 12CO and 13CO, respectively. Note that
the line widths minimally affect the RADEX results (van der Tak et al., 2007).
The model grids were created as follows. Given the low-$J$ CO lines available
to this study, $T_{\rm K}$ ranges from $5$ to $20$ K with an increment of $1$
K. By doing that, we aim to sample the lower temperature regime better. Beyond
$20$ K, $T_{\rm K}$ goes up to $250$ K with an increase of $5$ K in each step.
$n$(H2) and $N$(CO) range from $10^{2}$ to $10^{7}$ cm-3, and from $10^{13}$
to $10^{21}$ cm-2, respectively, in steps of $0.25$ dex.

In our analysis, we assume that isotopic (12C / 13C) and isotopologue (12CO /
13CO) abundance ratios are not different. The [12C]/[13C] abundance ratio can
change dramatically from one galaxy to another, and even in different
locations over the same galaxy. The abundance ratio may also show a radial
gradient, i.e. the ratio increases with the distance from the Galactic centre
(e.g. Wilson & Matteucci, 1992; Milam et al., 2005; Yan et al., 2019). In our
Galaxy it ranges from $20$-$25$ near the centre (e.g. Wilson & Rood, 1994;
Müller et al., 2016; Corby et al., 2018) to $\approx 70$ near the solar circle
(e.g. Wilson & Matteucci, 1992; Milam et al., 2005). Additionally, in the far-
outer Galaxy the abundance ratio reaches $100$ with a larger error bar and
there is an inconsistency in the results obtained from the $J=1-0$ and $J=2-1$
transitions (Wouterloot & Brand, 1996). An abundance ratio of $50$ was found
in Magellanic Clouds (Wang et al., 2009). In starburst nuclei of nearby
galaxies NGC 253 and M82 the abundance ratio is [12C]/[13C] = $40-50$ (Henkel
& Mauersberger, 1993), while more recently it has been suggested to be even
higher, i.e. the lower limits for the abundance ratio are [12C]/[13C] = $81$
and [12C]/[13C] = $138$ for NGC 253 and M82, respectively (Martín et al.,
2010). In ultra-luminous infrared galaxies the ratio was found to be $90$
(Sliwa & Downes, 2017). All of these extragalactic values are higher than the
value in the centre of the Milky Way. As better representatives to NGC 5033,
in the centres of red the Seyfert galaxies NGC 1068 and NGC 4945, the
abundance ratios were found to be [12C]/[13C] = $24-62$ (with an average of
$\approx 38$) and [12C]/[13C] = $6-44$ (with an average of $\approx 17$),
respectively (Tang et al., 2019). In our model calculations, instead of taking
one single absolute value, we therefore considered a range for the abundance
ratio, i.e. from $20$ to $90$ in steps of $10$, covering almost the entire
range of the abundance ratios reported in the literature.

###  4.2 Best model identification

We applied $\chi^{2}$ and likelihood methods to identify the best model
results. $\chi^{2}$ is defined as,

$\chi^{2}\equiv\sum\limits_{i}\bigg{(}\frac{R_{i,{\rm mod}}-R_{i,{\rm
obs}}}{\Delta R_{i,{\rm obs}}}\bigg{)}^{2}\,$ (2)

where $R_{\rm mod}$ and $R_{\rm obs}$ represent modelled and observed line
ratios, respectively, while $\Delta R_{\rm obs}$ represents the uncertainty in
the observed line ratios. The best model was defined as the model with the
smallest reduced $\chi^{2}$, ($\chi_{\rm r}^{2}$ = $\chi^{2}$ / $DOF$, where
$DOF$ represents corresponding degrees of freedom, i.e. one less than the
number of line ratios). The contour map of $\Delta\chi_{\rm r}^{2}$ =
$\chi_{\rm r}^{2}$ \- $\chi_{\rm r,min}^{2}$ is shown in Figure 7.

We created the probability distribution functions (PDFs) of each model
parameter (namely $T_{\rm K}$, $n$(H2) and $N$(CO)) by following the procedure
described in Kaviraj et al. (2007). We first estimated the likelihood of each
model parameter by calculating the sum of the $e^{-\Delta\chi^{2}/2}$ (i.e.
the likelihood function) for all possible values of the other two parameters
marginalized over the other two. Assuming a uniform prior in the model
parameters and Gaussian errors lead prob($\emph{D}~{}|~{}\emph{X}$) $\propto$
$e^{-\Delta\chi^{2}/2}$, where prob($\emph{D}~{}|~{}\emph{X}$) is the
probability of the data given the model, X denotes the parameters in the model
and the $\chi^{2}$ is defined in the standard way shown above. Please see
Section 2 in Kaviraj et al. (2007) for more details on the procedure. The
PDFs, including the median with the $68$ per cent ($1\sigma$) confidence
levels around it, and the most likely model (i.e. the peak) are shown in
Figure 7.

##  5 Results and discussion

###  5.1 Intensities, gas mass and surface density

From the outskirts to the central $1$ kpc, both gas mass and surface density
increase. Although the integrated CO line intensity is the highest in the
central $1$ kpc (see Fig. 2), the inverse relation between CO integrated line
intensity and $X_{\rm CO}$ and the depression in $X_{\rm CO}$ and $\alpha_{\rm
CO}$ assumed for the central $1$ kpc region (see Section 3.1) cause a decrease
in gas mass and molecular surface density in the central region of the galaxy
(see Figure 2). Given the patchy distribution of the gas beyond an angular
galactocentric distance of $\approx 50$ arcsec in the south of the galaxy,
this causes 12CO(1–0) emission not being detected in five regions at a
$3\sigma$ level, indicated by arrows in Figure 2. However, in the north of the
disc, the true extent of the emission (see Section 3.2) does not reach beyond
$\approx 50$ arcsec. This indicates that between $50$ to $100$ arcsec from the
centre the south of the galaxy tends to a have higher surface density of
molecular gas.

###  5.2 Moment maps and PVDs

12CO(1–0) is more extended over the galaxy’s major axis compared to 12CO(3–2)
(see Figure 3). The radial extent of the 12CO(1–0) is about $60$ arcsec ($4.3$
kpc) in the NW, while it reaches to about $90$ arcsec ($6.5$ kpc) in the SE
(see Fig. 3). However, 12CO(3–2) is more centrally concentrated. It extends to
about $40$ arcsec ($2.8$ kpc) on either side. The velocity field is mostly
regular up to $\approx 50$ arcsec from the centre, and then the gas seems to
become more patchy in the SE part of the disc compared to the NW part (see
moment maps in Figure 3). This asymmetry in the south of the galaxy was also
seen in H I (Thean et al., 1997). It is interesting to see this asymmetry also
in CO, since CO is more centrally concentrated and more correlated with the
star-forming gas component. CO is, therefore, considered to be less affected
by any galaxy interactions compared to H I (Lavezzi & Dickey, 1997). Although
this is not certain, the asymmetry could be related to interactions and/or
past mergers with nearby galaxies, i.e. NGC 5002, NGC 5005 and NGC 5014 (Thean
et al., 1997).

The 12CO(1–0) and 12CO(3–2) PVDs indicate a stronger emission at the outer
edges of the disc (see Figure 4). This edge brightening is simply due to the
line of sight effect, i.e. the galaxy has a high inclination. Additionally,
the 12CO(3–2) PVD shows an increase in brightness in the north, indicating
more warmer gas there, compared to the southern part (see Figure 4). As seen
from Figure 4, at about $10$ arcsec from the centre, PVDs of both lines reach
the flat part of the rotation curve at $\approx 200$ km s-1, i.e. at the
maximum rotational velocity of the galaxy. A total dynamical mass of
$2.5\times 10^{11}$ M⊙ was estimated using H I data out to a radius of $420$
arcsec (Lavezzi & Dickey, 1997). As seen from Figure 4, the CO gas reaches the
circular velocity of $200$ km s-1 (it is $217$ km s-1 after correcting for the
inclination, see Table 1) at about $10$ arcsec from the galaxy’s centre. Using
the CO circular velocity, we calculated a dynamical mass of $8.2\times 10^{9}$
M⊙ within the central region of size $1.4$ kpc (equivalently $20$ arcsec in
diameter).

When barred galaxies are viewed close to edge-on orientation the central bar
dynamics are usually associated with characteristic X-shaped PVDs, i.e. two
kinematic components (Sellwood & Wilkinson, 1993; Kuijken & Merrifield, 1995;
Bureau & Freeman, 1999; Merrifield & Kuijken, 1999; Topal et al., 2016). As
seen from Figure 4, the PVDs of both lines reveal a rapidly rising velocity
component followed by a flat rotation curve. This indicates no evidence of a
large-scale bar in the centre of NGC 5033, but we cannot exclude that the
galaxy might host a small central bar (Thean et al., 1997; Kohno et al.,
2003b). While, because of large central line widths, integrated intensities
peak at the centre (Figure 3) when observed with $6$ or $14.5$ arcsec beams,
the PVDs (Figure 4) reveal that the CO gas in the very centre of the galaxy
shows a local minimum. This may be caused by the AGN (the $1.4$ GHz radio
continuum flux density near the centre is $126$ mJy Thean et al. 1997) or it
is simply a result of lines-of-sight not crossing tangentially a spiral arm
with comparatively strong molecular emission. Although the galaxy hosts an
AGN, Pérez-Torres & Alberdi (2007) concludes that the radio emission from the
nuclear region of the galaxy is mainly powered by starburst activity (see also
Yun et al. 2001).

Figure 5: Black filled stars represent the ratios of the integrated line
intensities (Table 4) at the centre of NGC 5033 in all panels. Red and blue
squares and circles represent the ratios in the inner ring and nuclear disc of
NGC 5866 and NGC 4710 (Topal et al., 2016), respectively, in all panels,
except panel $c$ (see the legend in the panel). The data points with arrows
indicate lower and upper limits estimated following the same approach we
performed in the current study (see Section 3.1). Starburst, Seyfert,
lenticular, peculiar and elliptical galaxies are shown by dark green, brown,
magenta, red and green filled stars, respectively (Krips et al., 2010). The
data for Seyfert galaxies in panel $c$ were taken from Papadopoulos & Seaquist
(1998). Black circles with a cross in panels $a$ and $d$ represent the GMCs in
NGC 6946 (Topal et al., 2014) and in M31 (Brouillet et al., 2005),
respectively. The light grey shaded areas in panels $a$ and $c$ show the range
for the $R_{\rm 11}$ ratios in spirals (Paglione et al., 2001), while the dark
grey shaded area in panels $a$, $b$ and $d$ show the range for $R_{\rm DC}$
ratios in spirals (Gao & Solomon, 2004). The turquoise shaded area in panel
$b$ represents the ratios for starbursts (Baan et al., 2008). The open black
square and circle in panel $b$ show the ratios in the centre of NGC 5866 and
NGC 4710, respectively (Crocker et al., 2012). The ratio of $1$ in all panels
is indicated by red dashed line.

###  5.3 Line ratios

A $22$ arcsec ($1.6$ kpc) beam typically contains many GMCs, so any physical
properties reflected by the line ratios will eventually represent average
conditions for such complexes. We assume that the source is resolved (i.e.
fills the beam) and the GMCs within the beam have the same average physical
conditions. Since higher excitation of a molecule requires a medium with
higher density and/or temperature, 12CO(3–2) indicates the existence of
slightly denser and warmer gas compared to 12CO(1–0) and 12CO(2–1).

Compared to its parent molecule 12CO, 13CO is generally optically thinner and
less abundant, i.e. allowing us to identify regions with higher column
densities. An increase in the $R_{\rm 11}$ = 12CO(1–0) / 13CO(1–0) ratio,
therefore, indicates thinner CO gas and vice-versa. To the contrary,
12CO(1–0), as it is more abundant, has a better chance for self-shielding and
can therefore better survive in a hostile interstellar environment. However,
there is evidence that a considerable fraction of CO emission could arise from
relatively diffuse and lower column density ($<10^{22}$ cm-2) molecular gas,
and a significant fraction of molecular gas could be in a non-star-forming
phase (Goldsmith et al., 2008; Heiderman et al., 2010; Krumholz et al., 2012;
Pety et al., 2013). The gas could be more diffuse due to supernova explosions,
stellar winds, intense ultraviolet (UV) radiation and associated H II regions
(e.g. Fukui et al., 2009). Such feedback processes could be different in the
arms, inter-arm regions or in the centre of a galaxy. In galaxies, centre,
arms and inter-arm regions could, therefore, have different $R_{\rm 11}$
ratios, causing fluctuations in the $R_{\rm 11}$ ratio, generally seen across
the disc of a galaxy (e.g. Topal, 2020).

Ratios between HCN to CO, i.e. $R_{\rm DC}$ = HCN(1–0) / 12CO(1–0), indicate
the portion of dense gas in the medium (i.e. the higher the $R_{\rm DC}$
ratios, the higher the dense gas fraction), while $R_{\rm DD}$ = HCN(1–0) /
HCO+(1–0), provides information on the dominant physical processes in the
environment. Supernova explosions, strong UV radiation from young massive
stars, and X-rays from AGNs, all play an important role in defining physical
properties of the ISM, and affect the molecular line ratios observed.

Although UV radiation affects the outer layers of clouds and create photo-
dissociation regions or PDRs (e.g. Hollenbach & Tielens, 1999), X-rays can
penetrate deeper into the clouds and create X-ray dissociation regions or XDRs
(e.g. Maloney et al., 1996). Based on their theoretical approach Meijerink et
al. (2007) found that when the density is $>$ $10^{5}$ cm-3 $R_{\rm DD}$ $<1$
for XDRs and $R_{\rm DD}$ $>1$ for PDRs. However at lower densities $R_{\rm
DD}$ gets higher than unity in XDRs. In galaxies with a high rate of supernova
explosions, HCO+, a molecule very sensitive to the ionization level of
molecular gas, could be enhanced with respect to HCN (i.e. $R_{\rm DD}<1$),
due to cosmic rays (CRs) produced by young supernova remnants (Dickinson et
al., 1980; Wootten, 1981; Elitzur, 1983; Joulain et al., 1998; Costagliola et
al., 2011) Please note that in the central region of active galaxies the shock
from the AGN could also produce CRs (Rachen & Biermann, 1993; Ferrari, 1998;
Achterberg et al., 2001; Berezhko, 2008; Guo & Mathews, 2011). The CRs in the
medium could ionize the H2 and produce H3+ which could react with CO to create
HCO+ (Padovani et al., 2009). In light of this information, we will discuss
the results of our line ratio diagnostics.

####  5.3.1 Ratios between CO lines

As listed in Table 4, the line ratios indicate that 12CO(2–1) is brighter than
12CO(1–0) and 12CO(3–2) at the centre of the galaxy. We compare the ratios
found at the centre of NGC 5033 to that of different types of galaxies in
Figure 5. A CO survey of about $80$ nearby spiral galaxies indicates an
average ratio of $R_{\rm 21}=0.89\pm 0.06$ (Braine et al., 1993). Similarly,
the range for $R_{\rm 21}$ ratios in nearby galaxies (including our own Milky
Way) is from $0.6$ to $1$ (Hasegawa, 1997; Leroy et al., 2009; Topal, 2020),
lower than the ratio of $1.1\pm 0.1$ we find at the centre of NGC 5033. It is
also seen in panels $b$ and $c$ of Figure 5 is that the $R_{\rm 21}$ ratio at
the centre of NGC 5033 is higher than in most of the galaxies, indicating a
relatively warm and/or dense gas component. The panel $c$ of the same figure
also indicates that NGC 5033 has a higher $R_{\rm 21}$ compared to the centre
of the spiral galaxies NGC 0628 (Topal, 2020) and NGC 2903 (Topal, 2018)
showing no AGN activity, again indicating relatively highly excited gas in the
AGN host centre of the spiral galaxy NGC 5033.

The $R_{\rm 31}$ ratios were obtained in the centre of $61$ galaxies from
different Hubble types (Mao et al., 2010). They found that the $R_{\rm 31}$
ratio ranges from $0.2$ to $2$. While the $R_{\rm 31}$ ratio in starbursts
could be as high as $2$, the central regions of normal spirals mostly have
ratios at the lower end of this range (Mao et al., 2010). We find $R_{\rm
31}=0.4\,\pm\,0.1$ at the centre of NGC 5033, which is within the range for
spirals, but higher than the ratio in the centre of NGC 0628 (i.e. $R_{\rm
31}=0.19\,\pm\,0.03$; Topal 2020) and lower than the ratio in the centre of
NGC 2903 (i.e. $R_{\rm 31}=0.83\,\pm\,0.14$; Topal 2018). This indicates that
the active centre of the spiral galaxy should have warmer and/or denser (at
least moderately) gas compared to most normal spirals, but more certainly
colder than the centre of starbursts. It is seen from Figure 5 that NGC 5033
has a relatively low $R_{\rm 11}$ ratio compared to most of the galaxies,
including the range for normal spirals (see panels $a$ and $c$), most
positions over the disc of lenticular galaxies NGC 4710 and NGC 5866 (see
panel $a$), and those located along the disc of the spiral galaxy NGC 0628
(see panel $c$). This indicates relatively less tenuous central gas in NGC
5033.

The $R_{\rm 31}$ ratio moment map and ratio PVD are shown in Figure 6. As seen
from the ratio moment map, the $R_{\rm 31}$ ratio is mostly higher in the
north of the galaxy. This could be explained by the fact that 12CO(3–2)
emission is generally fainter in the south (see Figures 3 and 4) causing lower
$R_{\rm 31}$ ratios (relatively colder and/or less dense gas) there compared
to the north where the $R_{\rm 31}$ ratio is higher (see Figure 6). The same
difference is more clearly visible in the ratio PVD maps. i.e. the ratio is
higher in the north of the galaxy (see Figure 6). To summarize: both the
moment map and the PVD indicate that the two sides of the disc have different
average excitation conditions.

Figure 6: Left: Contour map for the ratios of the 12CO(3–2) moment 0 map to
that of 12CO(1–0). Right: Contour map for the ratio of 12CO(3–2) PVD to that
of the 12CO(1–0) PVD. On both ratio maps the contour levels start from $10$
per cent of the peak value with an increment of $10$ per cent. East to the
left and north is up in both panels.

####  5.3.2 Ratios between dense gas tracers

As seen from panel $d$ of Figure 5, $R_{\rm DD}$ $>1$ in the centre of NGC
5033, while almost all starbursts (shown by green filled stars) and GMCs in
M31 (shown by black circles with a cross) have $R_{\rm DD}<1$. This indicates
that in the centre of NGC 5033, HCN could be enhanced and/or HCO+ could be
lower. Krips et al. (2008) studied the centres of $12$ active galaxies based
on HCN and HCO+ observations and found an average ratio of $R_{\rm DD}$ =
$1.1\,\pm\,0.1$ (with a median of $1.2\,\pm\,0.1$) for their sample, which is
almost half the value found at the centre of NGC 5033, i.e. $R_{\rm DD}$ =
$1.9$ (Krips et al., 2010). However, Privon et al. (2015) found a mean ratio
of $R_{\rm DD}$ = $1.84\,\pm\,0.43$ for a sample of AGN host galaxies, which
is the same as the ratio found in the centre of NGC 5033.

As our model results suggest a density range of $n$(H2)$=10^{3}-10^{4}$ cm-3
(see Table 4 and Section 5.4) and XDRs could have $R_{\rm DD}$ $>1$ in low-
density environments (see the discussion at the beginning of Section 5.3),
this indicates that the existence of XDRs rather than PDRs is a more likely
scenario for the line ratio observed in the centre of NGC 5033. Therefore, our
high $R_{\rm DD}$ ratio could be explained by the enhancement of HCN in
comparison with HCO+ through X-rays near the AGN of NGC 5033 as this is the
case in many AGN host Seyfert galaxies (e.g. Kohno et al., 2003a; Imanishi et
al., 2007; Davies et al., 2012; Privon et al., 2015).

Other supportive evidences for the high $R_{\rm DD}$ ratio observed in the
centre of NGC 5033 are the following. No supernovae have yet been found at the
centre of the galaxy (Guillochon et al., 2017). This supports the idea that
any effects of supernova explosions on the central gas complex should not
dominate potential AGN activity. Besides, the CRs created by the AGN in the
centre of NGC 5033, which could cause a considerable decrease in the $R_{\rm
DD}$ ratio, appear not to dominant over effects from X-ray radiation. The
higher $R_{\rm DD}$ ratio observed at the centre is, therefore, possibly due
to a lack of CRs, which might otherwise cause a higher abundance of HCO+ in
the medium. However, please note that, although no supernovae have yet been
detected in the centre of the galaxy and we somehow do not see the effects of
supernova in the line ratios, it is still possible for supernovae to be
invisible due to high optical depths.

Overall, the most likely scenario for the relatively high $R_{\rm DD}$ ratio
found at the centre of NGC 5033 is the existence of an AGN. Effects of X-ray
radiation may dominate in the medium, while CR and PDR chemistry may be less
important in the heart of the galaxy.

####  5.3.3 Ratios between CO to dense gas tracers

As seen from panels $a$, $b$ and $d$ of Figure 5, the active centre of NGC
5033 has an average $R_{\rm DC}$ ratio compared to other types of galaxies,
indicating a similar dense gas fraction. From the same panels, the $R_{\rm
DC}$ ratio found at the centre of NGC 5033 is similar to that seen in the
nuclear disc but higher than in the inner rings of the lenticular galaxies NGC
4710 and NGC 5866 (Topal et al., 2016). The ratio of $R_{\rm DC}$ =
$0.044\,\pm\,0.001$ found in the centre of NGC 5033 is within the range found
in the centre of the Seyfert galaxy NGC 3227 ($R_{\rm DC}$ = $0.1$ to $0.01$).
Given the AGN host nature of NGC 5033, it is plausible to assume that high
X-ray ionization rates in the central region could increase the HCN abundance
(e.g. Usero et al., 2004; Meijerink & Spaans, 2005), causing the $R_{\rm DC}$
ratio to increase. Intensity ratios of 12CO/HCO+$\,\approx\,43$ in the centre
of NGC 5033 (Krips et al., 2010) are similar to the ratios found in other
spiral galaxies, i.e. 12CO/HCO+$\,>\,25$ (Jiménez-Donaire et al., 2019).This
indicates that the effects of supernova explosions could not be dominant in
the centre of NGC 5033, as already suggested by the $R_{\rm DC}$ ratio (see
Section 5.3.2).

###  5.4 Modelling

The ISM has very complex characteristics with different temperature, density,
radiation field, and mechanical feedback. It is, therefore, only natural to
assume the existence of multiple molecular components in the gaseous ISM. In
such a complex structure, a combination of low-$J$ CO lines with a $1$D model
(such as RADEX) can only provide us with some information on relatively colder
and tenuous gas in the ISM. Transitions between higher energy levels of CO
(i.e. $J~{}\geq~{}4-3$) are necessary to probe the physical properties of a
hotter gas component with a broad range of densities. Using a complete set of
CO lines along with multiple dense gas tracers could, therefore, enable us to
model multiple gas components of the ISM and provide a better insight on
multiple phases of star-forming gas clouds (e.g. Topal et al., 2016).
Nevertheless, given the number of CO lines available to us (i.e. 12CO(1–0,
2–1, 3–2) and 13CO(1–0, 2–1)), this study still provides us with valuable
information on the physics of relatively colder and tenuous gas in the centre
of NGC 5033. In consideration of this information, we discuss our model
results as follows.

As seen from Figure 7, the $\Delta\chi_{\rm r}^{2}$ contour maps indicate that
$T_{\rm K}$ increases sharply at lower $n$(H2), and it gradually decreases as
$n$(H2) increases (i.e. the banana-shaped degeneracy, see van der Tak et al.
2007; Topal et al. 2014; Topal 2020). Single Gaussian profiles are seen in the
PDFs (see Section 4.2), except that for $T_{\rm K}$ (Fig. 7, lower left
panel), causing the best-fitting and most likely model results being in
agreement, i.e. the best-fitting model is contained within the $68$ per cent
($1\sigma$) confidence levels around the median for $n$(H2) and $N$(CO).

Figure 7: Top: $\Delta\chi_{\rm r}^{2}$ = $\chi_{\rm r}^{2}$ \- $\chi_{\rm
r,min}^{2}$ maps are shown. $\Delta\chi_{\rm r}^{2}$ is given as a function of
$T_{\rm K}$ and $n$(H2), for three values of $N$(CO) centred around the best
fit. The values of $N$(CO) are shown at the bottom of each panel, while the
value of reduced $\chi_{\rm min}^{2}$, i.e. $\chi_{\rm r,min}^{2}$, of the
best fitting model is given in the central panel and is indicated by a red
filled circle. Small red dots indicate values considered in the model
parameter space, whereas small black dots represent unused bad models (see van
der Tak et al. 2007). The contour confidence levels for $3$ degrees of freedom
are $3.5$, $8.0$, $14.2$, $22.1$ and $31.8$ for $1\sigma$ ($68\%$ probability;
the darkest greyscale), $2\sigma$, $3\sigma$, $4\sigma$ and $5\sigma$,
respectively. The $1\sigma$ confidence levels are indicated by grey lines,
while the levels higher than $1\sigma$ are shown by black lines. Bottom:
Probability distribution function (PDF) of each model parameter marginalized
over the other two (see Section 4.2). The peak (most likely) is indicated with
a dashed blue line, whereas the median and the $1\sigma$ confidence around it
are shown with a dash-dotted blue and dotted black line, respectively. The
solid red line indicates the best-fitting model in a $\chi^{2}$ sense.

According to our best model results (in a $\chi^{2}$ sense), NGC 5033 is
hosting a central molecular gas complex with physical properties as follows:
$T_{\rm K}~{}=~{}35$ K, $\log$($n$(H2))$~{}=~{}3.3$ cm-3, and
$\log$($N$(CO))$~{}=~{}19.0$ cm-2 (see Table 4). The most likely results in
agreement with the $\chi^{2}$ results except for $T_{\rm K}$ (i.e. the most
likely result indicates a higher temperature compared to the temperature
indicated by the $\chi^{2}$ method) are also listed in Table 4. We compare our
model results to those in the literature performed with the same radiative
transfer code and using low-$J$ CO lines similar to our study.

Many studies have probed the physics of the gas in the flocculent spiral
galaxy NGC 6946 (Israel & Baas, 2001; Walsh et al., 2002; Bayet et al., 2006;
Topal et al., 2014). Israel & Baas (2001) found two distinct molecular
components in the centre of NGC 6946, i.e. a warm and dense, and a hotter and
more tenuous one. Two other studies found similar gas components, i.e. a warm
($T_{\rm K}~{}=~{}40$ K) and a hotter one ($T_{\rm K}~{}=~{}130$ K), with
similar hydrogen volume number densities, i.e. $\log$($n$(H2)) $\approx 3.3$
cm-3 (Walsh et al., 2002; Bayet et al., 2006). According to our model results,
the central gas complex in NGC 5033 has the same physical properties as the
central warm gas component in NGC 6946 with similar overall temperature,
density and column density.

Table 4: Line ratios and model results from the central $22$ arcsec area.

Line ratioa | Value | Parameter | $\chi^{2}$ | Likelihood
---|---|---|---|---
$R_{\rm 21}$ | $\phantom{0}1.1\pm 0.1$ | $T_{\rm K}$ |  $35$ K |  $117^{+84}_{-74}$ K
$R_{\rm 31}$ | $\phantom{0}0.4\pm 0.1$ |  $\log$($n$(H2)) |  $3.3$ cm-3 |  $3.1^{+1.3}_{-0.4}$ cm-3
$R_{\rm 11}$ | $\phantom{0}8.3\pm 0.7$ |  $\log$($N$(CO)) |  $19.0$ cm-2 |  $19.2^{+0.3}_{-0.3}$ cm-3
$R_{\rm 22}$ | $\phantom{0}7.2\pm 1.1$ | $[^{12}\rm C]/[^{13}C]$ | $20$ |
$R_{\rm DC}$ | $\phantom{0}0.044\pm 0.001$ |  |  |
$R_{\rm DD}$ | $1.9$ |  |  |

a Integrated line intensity (K km s-1) ratios of $R_{\rm 21}$, $R_{\rm 31}$,
$R_{\rm 11}$, $R_{\rm DC}$, and $R_{\rm DD}$ stand for the ratios of 12CO(2–1)
/ 12CO(1–0), 12CO(3–2) / 12CO(1–0), 12CO(1–0) / 13CO(1–0), HCN(1–0) /
12CO(1–0), and HCN(1–0) / HCO+(1–0), respectively.

Topal et al. (2016) probed physical properties of molecular gas in the
lenticular galaxies NGC 4710 and NGC 5866 using low-$J$ CO lines, and the same
radiative transfer code. Our model results indicate that there is warmer gas
with similar $n$(H2) and $N$(CO) in the centre of NGC 5033 compared to the
centre of NGC 4710. The model results agree with the empirical results (i.e.
the results inferred directly from the observed line ratios without modelling,
see Section 5.3) in terms of temperature. However, the gas in the centre of
NGC 5866 has quite different properties compared to the centre of NGC 5033,
i.e. the gas is warmer and denser with higher column densities compared to the
central region of NGC 5033. This indicates a disagreement between the
empirical (see Section 5.3) and model results.

The physics of the star forming gas at the heart of the spiral galaxy NGC 2903
was also studied by using low-$J$ CO lines and RADEX (Topal, 2018). NGC 2903
hosts denser and colder gas in its centre (i.e. $T_{\rm K}~{}=~{}20$ K and
$\log$($n$(H2))$~{}=~{}4.2$ cm-3) with the same $N$(CO) compared to the centre
of the Seyfert galaxy NGC 5033. Additionally, various positions over the disc
of the spiral galaxy NGC 0628 were studied using an identical method to ours
(Topal, 2020). They found that the central gas complex in NGC 0628 has the
following physical properties; $T_{\rm K}~{}=~{}30$ K,
$\log$($n$(H2))$~{}=~{}2.2$ cm-3, and $\log$($N$(CO))$~{}=~{}17.7$ cm-2. These
results indicate that the gas is warmer and denser with higher $N$(CO) in the
centre of NGC 5033 compared to the centre of NGC 0628. Our model and empirical
results (see Section 5.3) are in agreement in the sense that the centre of NGC
5033 hosts warmer gas than the centres of NGC 2903, NGC 0628, and NGC 4710.

The turnover of the spectral line energy distributions, SLEDs, (hereafter
$J_{\rm max}$) provides us with valuable information on SF activity. It is
known that heavily star-forming high-$z$ or local galaxies could have $J_{\rm
max}~{}>~{}6$, while $J_{\rm max}~{}=~{}4$ in the centre of our own Milky Way
(Fixsen et al., 1999; Bayet et al., 2004; Weiß et al., 2005; Weiss et al.,
2007). As an extreme example, the heavily star-forming Orion Bar
photodissociation region in our Galaxy has $J_{\rm max}~{}=~{}13$ (Habart et
al., 2010). Topal et al. (2014) studied multiple regions over the patchy arms
of NGC 6946 and obtained SLEDs for each region studied using the RADEX code.
Similarly, Bayet et al. (2006) obtained a SLED for the centre of NGC 6946
using the same LVG code. While Topal et al. (2014) found $J_{\rm
max}~{}=~{}2-7$ (most regions have $J_{\rm max}~{}<~{}4$) across the disc of
NGC 6946, Bayet et al. (2006) found $J_{\rm max}~{}=~{}6$ at the centre of NGC
6946 (see Fig. 8).

As shown in Figure 8, based on the best-fitting model $J_{\rm max}~{}=~{}4$
for the centre of NGC 5033, higher than that in most regions over the disc of
NGC 6946, but lower compared to the centre of NGC 6946 where $J_{\rm
max}~{}=~{}6$ (see Fig. 8.) This indicates a higher (lower) activity at the
heart of NGC 5033 compared to the spiral arms (the centre) of NGC 6946.
However, the number of lines available to construct the SLED could also affect
the location of the turnover. A CO ladder with more lines could, therefore,
lead to a higher $J_{\rm max}$. The ISM has a complex multiphase structure,
and divergence could be present in the SLED beyond $J~{}>~{}4-3$ (Papadopoulos
et al., 2014). Any information from a single turnover representing the whole
SLED will, therefore, provide average physical properties of such gas
complexes. The turnover based on the low-$J$ transitions, consequently, offers
physical properties averaged over relatively colder and tenuous gas
components.

Figure 8: CO SLEDs. The total intensity is shown as a function of the upper
energy level of CO transitions up to $J$ = $15-14$. The solid red line shows
the best-fitting model, while the blue diamonds with error bars represent the
observations for NGC 5033. SLEDs obtained in the centre (Bayet et al., 2006)
and along the arms of NGC 6946 (Topal et al., 2014) are shown by solid brown
and solid black lines, respectively, for comparison.

##  6 Conclusion

We probed the physics and kinematics of the molecular gas in the AGN host
(Seyfert 1.8) spiral galaxy NGC 5033 using multiple low-$J$ CO lines [i.e.
12CO(1–0, 2–1, 3–2) and 13CO(1–0, 2–1)] and high-density tracers [i.e.
HCN(1–0) and HCO+(1–0)]. We also applied a radiative transfer code and
obtained the best model results by comparing the modelled and the empirical
line ratios. Our main conclusions are summarized below.

  * •

12CO(1–0) is more extended over the galaxy’s disc compared to the other CO
lines available to this study. At the centre of the galaxy 12CO(2–1) is the
brightest among the CO transitions analysed by the current study. CO shows
higher excitation (in terms of $3-2/1-0$ line ratios) northeast than southwest
of the nuclear region. 12CO(1–0) gas extends further to the SE than to the NW
from the centre, indicating an asymmetry in gas distribution. Previously
published H I data confirm this asymmetry. Although determining the reason
behind this asymmetry is not within the scope of the current study, we can
still speculate that it could be related to past or ongoing interaction with
nearby galaxies, i.e. NGC 5002, NGC 5005 and NGC 5014.

  * •

The CO(1–0) integrated intensity shows a radial gradient, i.e. decreasing with
the distance from the galactic centre. H2 mass and gas surface density also
decrease beyond $1$ kpc from the galactic centre. However, within the central
$1$ kpc there is a decrease in H2 mass and gas surface density because of the
assumed depression in $X_{\rm CO}$, the conversion factor between H2 column
density and 12CO(1–0) integrated intensity. Position velocity diagrams (PVDs)
reveal a central rapidly rising velocity component (possibly no large-scale
bar). The integrated line intensity ratio of the moment 0 maps and the
corresponding ratios of the PVDs indicate that the gas on either side of the
disc has a different temperature, i.e. the gas is colder in the south.

  * •

Line ratio diagnostics suggest that the centre of the spiral galaxy NGC 5033,
hosting an AGN, harbours warmer and less tenuous gas with similarly dense gas
fraction (i.e. similar $R_{\rm DC}$) with respect to the centres and the arms
of most galaxies (including spirals, lenticulars and Seyferts). However, the
gas in NGC 5033 is colder compared to starbursts. The $R_{\rm DD}$ = HCN(1–0)
/ HCO+(1–0) $>1$ ratio may be caused by the AGN, so the X-ray radiation in the
medium could be the reason for this ratio, while CRs and PDRs seem to be less
likely or at least not the primary driver of the ISM at the heart of the
galaxy.

  * •

Our best model results (in a $\chi^{2}$ sense) mostly agree with the most
likely model results, except for $T_{\rm K}$ since $T_{\rm K}$ results from
the likelihood method are more uncertain (the likelihood method also indicates
a higher temperature). The best model results for the centre of NGC 5033 are
as follows: $T_{\rm K}=35$ K, $\log$($n$(H2)$)=3.3$ cm-3, and
$\log$($N$(CO)$)=19.0$ cm-2. We compared our results to similar studies in the
literature which used almost identical CO lines and the same radiative
transfer code. The centre of the spiral galaxy NGC 5033 with its AGN hosts
very similar gas to the warm gas component in the centre of the spiral galaxy
NGC 6946. The gas is warmer in the centre of NGC 5033 compared to the centre
of the spiral galaxies NGC 0628 and NGC 2903. However, the gas is denser with
higher $N$(CO) compared to NGC 0628 and less dense with the same $N$(CO)
compared to that in the centre of NGC 2903. Our model results suggest warmer
gas with similar densities compared to the centre of the lenticular galaxy NGC
4710. However, the central gas in NGC 5033 is colder and/or less dense with
lower $N$(CO) compared to the centre of the dusty lenticular galaxy NGC 5866.
Our empirical and model results are in agreement in the sense that both
methods suggest the existence of warmer gas in the centre of NGC 5033 compared
to most spirals and lenticulars, including the spirals NGC 0628 and NGC 2903
and the lenticular galaxy NGC 4710. The SLED turnover, i.e. $J_{\rm max}$, for
the centre of NGC 5033 occurs at a higher (lower) transition compared to most
regions over the disc (the centre) of NGC 6946, indicating a relatively higher
(lower) SF activity in the centre of NGC 5033 with respect to the disc (the
centre) of NGC 6946.

## Acknowledgements

ST would like to thank the anonymous referee for his/her insightful comments
and suggestions. ST thanks Timothy A. Davis for insightful discussions on gas
kinematics in galaxies. ST thanks Sugata Kaviraj for providing the code used
to estimate the probability distribution function. The James Clerk Maxwell
Telescope is operated by the East Asian Observatory on behalf of The National
Astronomical Observatory of Japan; Academia Sinica Institute of Astronomy and
Astrophysics; the Korea Astronomy and Space Science Institute; Center for
Astronomical Mega-Science (as well as the National Key R&D Program of China
with No. 2017YFA0402700). Additional funding support is provided by the
Science and Technology Facilities Council of the United Kingdom and
participating universities in the United Kingdom and Canada. We acknowledge
the usage of the HyperLEDA database (http://leda.univ-lyon1.fr).

## Data availability

The data underlying this article will be shared on a reasonable request to the
corresponding author.

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