# A temperature or FUV tracer? The HNC/HCN ratio in M83 on the GMC scale

Nanase Harada National Astronomical Observatory of Japan, 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan  Astronomical Science Program, Graduate
Institute for Advanced Studies, SOKENDAI, 2-21-1 Osawa, Mitaka, Tokyo
181-1855, Japan  Toshiki Saito National Astronomical Observatory of Japan,
2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Yuri Nishimura Department of
Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033,
Japan  Yoshimasa Watanabe Materials Science and Engineering, College of
Engineering, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo
135-8548, Japan  Kazushi Sakamoto Institute of Astronomy and Astrophysics,
Academia Sinica, 11F of AS/NTU Astronomy-Mathematics Building, No.1, Sec. 4,
Roosevelt Rd, Taipei 10617, Taiwan

###### Abstract

The HNC/HCN ratio is observationally known as a thermometer in Galactic
interstellar molecular clouds. A recent study has alternatively suggested that
the HNC/HCN ratio is affected by the ultraviolet (UV) field, not by the
temperature. We aim to study this ratio on the scale of giant molecular clouds
in the barred spiral galaxy M83 towards the southwestern bar end and the
central region from ALMA observations, and if possible, distinguish the above
scenarios. We compare the high (40-50 pc) resolution HNC/HCN ratios with the
star formation rate from the 3-mm continuum intensity and the molecular mass
inferred from the HCN intensities. Our results show that the HNC/HCN ratios do
not vary with the star formation rates, star formation efficiencies, or column
densities in the bar-end region. In the central region, the HNC/HCN ratios
become higher with higher star formation rates, which tend to cause higher
temperatures. This result is not consistent with the previously proposed
scenario in which the HNC/HCN ratio decreases with increasing temperature.
Spectral shapes suggest that this trend may be due to optically thick HCN and
optically thin HNC. In addition, we compare the large-scale ($\sim 200$ pc)
correlation between the dust temperature from the FIR ratio and the HNC/HCN
ratio for the southwestern bar-end region. The HNC/HCN ratio is lower when the
dust temperatures are higher. We suggest from the above results that the
HNC/HCN ratio depends on the UV radiation field that affects the interstellar
medium on the $\sim 100\,$pc scale where the column densities are low.

††facilities: ALMA, Herschel††software: astropy (Astropy Collaboration et al.,
2013, 2018), CASA (McMullin et al., 2007; CASA Team et al., 2022)

##  1 Introduction

Molecular emission is a powerful tool for diagnosing physical conditions in
star-forming regions because there are chemical formation/destruction
reactions and excitation mechanisms that are associated with these physical
conditions. Some abundances or line ratios have been proposed as particular
tracers of certain physical parameters such as temperature, density, UV field
strength, and cosmic-ray ionization rate.

The HNC/HCN line or abundance ratio is one such example. Schilke et al. (1992)
have suggested from their observations towards OMC-1 and Orion-KL that the
HNC/HCN abundance ratios decrease with the increasing temperature, probably
due to reactions whose rates become much faster at high temperatures. The
HNC/HCN ratios in dark cold cores are much higher than those in OMC-1,
providing further evidence for the temperature dependence (Hirota et al.,
1998). More recently, Hacar et al. (2020) compared the temperature obtained
from ammonia transitions with the HNC/HCN($J=$1–0) intensity ratios towards
the region including OMC-1 to OMC-4, and showed that these two quantities
indeed have good correlations. While the HNC/HCN ratio seemed to be a well-
established temperature tracer, Santa-Maria et al. (2023) recently suggested
that it is the strength of the UV radiation field rather than temperature that
changes this ratio. High temperature regions often have a UV radiation field
because the UV photons heat the gas, which also causes the low HNC/HCN ratio
in high temperature regions.

Theoretical calculations of reaction rates also pose challenges to the
reliable use of the HNC/HCN ratio as a temperature tracer. Destruction
reactions of HNC via atomic oxygen or atomic hydrogen have barriers $\gamma$,
and the reaction rates are proportional to exp$(-\gamma/T)$, where $T$ is the
gas kinetic temperature. These rates can be fast when the temperature is
comparable to $\gamma$, while they are extremely slow at low temperatures. It
has been suggested that these reactions with high barriers contribute to the
temperature dependence of the HNC/HCN abundance ratio. However, there is a
discrepancy between observationally inferred values of barriers and
theoretical ones. Observational results suggest that the barriers must be at
least a factor of several lower than those obtained by quantum calculations
(Talbi et al., 1996; Graninger et al., 2014) to fit the observed ratio.

Extragalactic observations have also revealed cases where the HNC/HCN ratio
does not necessarily correlate with the temperature. Some galactic nuclei of
(ultra-)luminous infrared galaxies that are very bright and warm have been
found to have the intensity ratios of HNC/HCN$>1$ (Aalto et al., 2002, 2007),
which the authors attribute to the infrared pumping or effects of X-rays. In a
survey of the center of the starburst galaxy NGC 253, Behrens et al. (2022)
found a high ($\sim 0.2-1$) HNC/HCN abundance ratio despite the high
temperature ($T\sim 50-300\,$K) in this region. A comparison with chemical
models suggests that a high cosmic-ray ionization rate ($\sim 10^{-12}\,$s-1)
can explain this low ratio despite the high-temperature region. 111We note
that this cosmic-ray ionization rate is about one order of magnitude higher
than the most probable value derived by Holdship et al. (2022) and two orders
of magnitude higher than the one estimated from $\gamma$-ray observations
(Phan et al., 2024) in this region. We caution the readers to note that the
cosmic-ray ionization rate can be easily overestimated when the density is
overestimated.

Can the HNC/HCN ratio be used as a temperature tracer? If so, is it still
valid for extragalactic sources in different regions of galaxies (center,
disk, etc.)? It is helpful to have such a temperature tracer in extragalactic
sources because it can be observationally expensive to conduct a large-
velocity gradient (LVG) analysis that need multiple transitions. Molecular
transitions that provide more accurate temperature values with an LVG analysis
(e.g., H2CO and NH3) are also usually much weaker.

To answer the above questions, in this paper, we analyze the HNC/HCN ratio in
the center and the bar-end regions of the nearby face-on galaxy M83 using the
high spatial resolution ($\sim 50\,$pc) data obtained from ALMA (Atacama Large
Millimeter/submillimeter Array). Even HCN observations including the disk
region of a galaxy with this spatial resolution are rare beyond the Local
Group (Sánchez-García et al., 2022). High angular-resolution observations of
HNC in the disk region are even rarer. Detection of HNC, which usually has a
weaker intensity, is possible in galactic center regions with reasonable
observing time in the (sub-)100-pc scale (Meier & Turner, 2005; Harada et al.,
2019; Eibensteiner et al., 2022). With lower spatial resolution, the HNC/HCN
ratio in a luminous infrared galaxy has been presented (Harada et al., 2018).
However, HNC observations in the disk region with an equivalent spatial
resolution are scarce. There has been a spectral scan survey of NGC 1068 that
also covers the disk region, which included HNC and HCN, but did not analyze
the HNC/HCN ratio (Nakajima et al., 2023). Our study will provide the most
comprehensive view of the HNC/HCN ratio in an extragalactic source to date.

M83 (also known as The Southern Pinwheel or NGC 5236) is one of the closest
face-on barred-spiral galaxies at the distance of $d=4.5\,$Mpc (Thim et al.,
2003). It has a moderate total star formation rate of $5.2\,M_{\odot}\,$yr-1
(Jarrett et al., 2019), a factor of a few higher than that of the Milky Way
(1.9 $M_{\odot}$ yr-1; Chomiuk & Povich, 2011). When it comes to the central
region, the star formation rate in M83 is about an order of magnitude higher
than the Galactic center (Callanan et al., 2021). The molecular gas mass to
fuel the star formation is $2.6\times 10^{9}\,M_{\odot}$, 15% of which is
concentrated in the central 1 kpc of this galaxy (Koda et al., 2023). Because
of its proximity and its face-on configuration, M83 has been the target of
studies at various wavelengths, that revealed various phases of star
formation. They include observations of young star clusters from H$\alpha$
images (Whitmore et al., 2011), supernova remnants (Long et al., 2022), and
atomic gas (Bigiel et al., 2010; Eibensteiner et al., 2023). Abundant
molecular gas and the wealth of previous studies and auxiliary data allow for
more detailed chemical analysis and comparisons with physical conditions.

This paper is organized as follows. Section 2 describes the observations and
data reduction methods, and we present velocity-integrated images, intensity
ratios, selected spectra, and comparison with far-infrared data in Section 3.
These results are discussed in Section 4. All of the above is summarized in
Section 5.

##  2 Observations and data reduction

We conduct analyses using $J=1-0$ transitions of HCN, HCO+, and HNC as well as
the 3-mm continuum in two different regions of M83, the southwestern bar-end
(SWBE) and the central region, using the ALMA data. The observed regions are
indicated in Figure 1. We also include the HCO+/HCN ratio in our analysis for
comparison, as HCO+ is another commonly observed dense gas tracer and can be
simultaneously observed with HCN.

Figure 1: Observed regions shown as magenta rectangles superimposed on a
Herschel $70\mu$m map of M83 (VNGS team, 2012).

###  2.1 M83 southwestern bar end

The data towards SWBE are taken as a part of ALMA project code 2021.1.01195.S
(PI: Harada), and consist of the 12-meter array data, as well as the Atacama
Compact Array (ACA) data (7-meter and total power). This project covers the
field of view of $94\arcsec\times 80\arcsec$ ($2.1\times 1.8\,$kpc) with a
position angle of 78 degrees. We imaged the interferometer data (12-meter and
7-meter antennae) with the PHANGS pipeline (ver. 2; Leroy et al., 2021) using
CASA (McMullin et al., 2007; CASA Team et al., 2022) version 5.6.3. After the
imaging, we used the CASA version 6.6.0. We used the total power data obtained
from the ALMA data delivery (QA2), and used the CASA task feather to combine
the interferometry data and the total power data. We convolved all the cubes
into the angular resolution of $1\farcs 9\times 1\farcs 9$ (=42 pc $\times$ 42
pc) to match the largest beam. Achieved single-channel sensitivities are 30 mK
(HCN and HCO+) and 13 mK (HNC) over 3.3 km s-1. Primary beam correction was
applied to all the cubes.

We also obtained a 3-mm continuum image at 95.8 GHz. It has an rms of
$10\,\mu$Jy beam-1 to estimate the star formation rate. Most of the 3-mm
continuum likely originates from free-free emission in HII regions and has a
direct relationship with the star formation rate. Because ALMA does not
provide the total power capability for the continuum, spatial filtering may be
an issue if the continuum emission is extended. Although we cannot check the
exact missing flux in the continuum data, we can at least compare the HCN data
with and without total power. The HCN emission is usually more extended than
the continuum emission. The missing flux of HCN is less than 10 % even if we
take the aperture of 10.7$\arcsec$, which is the beam size used in Section 3.5
to compare with lower-resolution far-infrared data.

Although the 3-mm continuum should be dominated by the free-free emission, it
may also contain contamination from the dust emission or synchrotron
radiation. We checked the continuum emission at 348.5 GHz to estimate the
contribution from the dust emission, which will be presented in our
forthcoming paper. The contamination is $\lesssim 10$ % for the region used
for our analyses in later sections. The synchrotron radiation should be
negligible because there is not many synrotron sources such as supernovae in
this region (Long et al., 2022).

###  2.2 M83 center

The HNC data are taken from the cube produced for Harada et al. (2019)
(project code: 2016.1.00164.S), and include 12-meter and 7-meter arrays with a
maximum recoverable scale (MRS) of $74\arcsec$ at 90 GHz. HCN and HCO+ data
are taken from the ALMA archive (project code 2015.1.01177: Callanan et al.,
2021), which contains only the 12-meter data with an MRS of 25$\arcsec$. These
MRSs should be enough to cover most of the emission in the central region
judging from the structure of CO(1–0) (Koda et al., 2023). Although the
CO(1–0) emission is expected to be much more extended than HCN, HCO+, and HNC,
most of the emission comes from regions within the size of 25$\arcsec$. The
data were imaged using the same way as Harada et al. (2019) using CASA ver.
5.4 and later processed with CASA ver. 6.6.0. We convolved cubes into a common
beam of $2.5\arcsec$(=55 pc), and applied primary beam correction. Single-
channel rms noise levels over 10 km s-1 are 20 mK, 17 mK, and 10 mK for HCN,
HCO+, and HNC, respectively. The continuum image has an rms of 29 $\mu$Jy
beam-1.

The 3-mm continuum (more precisely, 2.8-mm or 96.9 GHz) may also suffer from
the dust contamination in addition to the free-free emission here. By
comparing the 2.8-mm and 1.0-mm continuum presented in Harada et al. (2019),
we estimate the contamination to be less than 10 % for most emission, but can
be up to 30 % for very low-level ($<0.4\,$mJy beam-1) emission. The star
formation rate corresponding to this level of emission is
log($\dot{M}_{*}$[$M_{\odot}$ Myr-1 pc-2])$<0.5$ (see Section 3.2).

##  3 Results

###  3.1 Velocity-integrated and continuum images

####  3.1.1 SWBE

We created velocity-integrated images of HCN, HNC, and HCO+ applying masks, or
intensity thresholds, on cubes. We first convolved HCN and HCO+ images to
twice the beam size, then applied the $2\sigma$ cutoff from the convolved HCN
image to create velocity-integrated images of HCN and HNC. The $2\sigma$
cutoff from the convolved HCO+ image is used to create the HCO+ image. These
reference masks for thresholds were chosen because HNC is much fainter than
HCN while HCO+ is equally as bright as HCN. These velocity-integrated images
have different noise levels across the maps because of the cutoff we applied.

Figure 2 shows the velocity-integrated (moment 0) images of HCN(1–0) in the
upper left panel, HCO+(1–0) in the upper right panel, and HNC(1–0) on the
middle left panel. The 3-mm continuum is also shown in the middle right panel,
which should be dominated by free-free emission from the star formation at
this wavelength. These images all show distributions similar to that of
CO(1–0) reported by Koda et al. (2023), tracing the transition from the bar
region in the eastern part of the field of view to the spiral arm in the
northern part as well as the feather-like structure extending from the bar end
to the south or west. The continuum emission shows a slightly more compact and
sparse distribution than that of the molecular lines.

Figure 2: Moment 0 images of HCN (upper left), HCO+ (upper right), and HNC
(middle left) and the 3mm-continuum image (middle right) at the southwestern
bar end region of M83 and ratio maps of HCO+/HCN (lower left panel) and
HNC/HCN (lower right panel). The beam size is shown as a blue circle at the
lower right corner of each panel ($1.9\arcsec\times 1.9\arcsec$
$=42\,\mathrm{pc}\times 42\,\mathrm{pc}$). Intensity ratios are derived in the
unit of K instead of Jy beam-1.

####  3.1.2 The central region

Figure 3 shows images of HCN, HCO+, and HNC integrated intensities and 3 mm
continuum emission in the central region of M83. Similar to the images of the
SWBE region, we applied the threshold cutoff using the convolved HCN for HCN
and HNC, and then convolved HCO+ for HCO+ again using $2\sigma$. The HNC and
3-mm continuum before the beam convolution have already been presented by
Harada et al. (2019), and higher-resolution images of HCN and HCO+ by Callanan
et al. (2021). The HCN and HCO+ images show a remarkable similarity both in
low- and high-resolution images. The HNC image shows a similar distribution to
that of HCN and HCO+ as well, but has a weaker emission around the optical
nucleus (marked as position 1 in Figure 3). The 3-mm emission is more compact,
and appears only in the western part of the central region of M83.

Figure 3: Same as Figure 2, but for the central region of M83. The synthesized
beam size is $2.5\arcsec\times 2.5\arcsec$ $=55\,\mathrm{pc}\times
55\,\mathrm{pc}$.

###  3.2 Physical conditions of observed regions

To put the observed region into perspective, we have derived the dense gas
surface density ($\Sigma_{\mathrm{dense}}$) and the star formation rate
surface density ($\Sigma_{\mathrm{SFR}}$). For the dense gas surface density,
we use

$\displaystyle\Sigma_{\rm dense}=\alpha_{\mathrm{HCN}}\int T_{b}\,dv\times
cos(i)$ $\displaystyle=9.0\,\mathrm{({\it M}_{\odot}\,pc^{-2})\int
T_{b}\,dv(K\,km\,s^{-1})^{-1}},$ (1)

where $\alpha_{\rm HCN}$ is the conversion factor of $10\,M_{\odot}$ pc-2 (K
km s-1)-1 (Gao & Solomon, 2004), $\int T_{b}\,dv$ is the velocity-integrated
intensity, and $i$ is the inclination angle ($i=26^{\circ}$; Koda et al.,
2023). We derived the star formation rate surface density by first calculating
the star formation rate $\dot{M}_{*}$ within the aperture using the following
equation (e.g., Bendo et al., 2016).

$\displaystyle\dot{M}_{*}=9.49\times 10^{10}\,M_{\odot}\,{\rm yr}^{-1}g_{\rm
ff}^{-1}\left(\frac{\alpha_{B}}{\rm cm^{3}\,s^{-1}}\right)$
$\displaystyle\times\left(\frac{T_{\mathrm{e}}}{\mathrm{K}}\right)^{0.5}\left(\frac{D}{\rm
Mpc}\right)\left(\frac{f}{\rm Jy\,beam^{-1}}\right),$ (2)

where $g_{\rm ff}$ is the Gaunt factor, $\alpha_{B}$ is the effective
recombination coefficient, $T_{\rm e}$ is the electron temperature, $D$ is the
distance to the galaxy, and $f$ is the flux per beam. We assume the electron
temperature to be $T_{\rm e}=5000\,$K. The Gaunt factor is given by

$g_{\rm ff}=0.5535\,{\rm ln}\left[\left(\frac{T_{\rm
e}}{\rm\,K}\right)^{1.5}\left(\frac{\nu}{\rm
GHz}\right)^{-1}Z^{-1}\right]-1.682,$ (3)

where $\nu$ is the frequency and $Z$ is the electric charge, which can be
approximated as $\sim 1$. We approximate the effective recombination
coefficient $\alpha_{B}$ using the following formula (Michiyama et al., 2020)

$\alpha_{\mathrm{B}}=3.63\times 10^{-10}\left(\frac{T_{\rm e}}{\rm
K}\right)^{-0.79}.$ (4)

To derive the star formation rate surface density, we take

$\Sigma_{\mathrm{SFR}}(M_{\odot}\,{\rm yr}^{-1}{\rm
pc}^{-2})=\dot{M}_{*}/A\times cos(i),$ (5)

where $A$ is the aperture size in pc2.

Figure 4: The star formation rate surface density as a function of the dense
gas surface density in the SWBE region (left) and the central region (right).
Note that the star formation rate is derived from the 3-mm continuum emission
and the dense gas surface density is derived from the HCN intensity. The color
of the data point is determined by the density of the data points. Note that,
in the right panel, the star formation rate log($\dot{M}_{*}$[$M_{\odot}$
Myr-1 pc-2])$<0.5$ may contain significant contamination as discussed in
Section 2.2.

Figure 4 shows the relationship between the dense gas surface density and the
star formation surface density in the SWBE region and the central region. The
data points in the SWBE region lie close to or slightly higher than those in
the northern arm of M51 (Querejeta et al., 2019). Data points from both
regions lie roughly in the $\Sigma_{\rm SFR}-\Sigma_{\rm dense}$ relationship
in star-forming galaxies (García-Burillo et al., 2012; Usero et al., 2015;
Sánchez-García et al., 2022). It is fair to say that regions we observe have
normal star-forming conditions although the scatter is large due to the high
spatial resolution ($\sim 50\,$pc) we used (see the effect of the beam size on
the relation in Sánchez-García et al., 2022). As discussed in Section 2, the
3-mm continuum has minor contamination from the dust contribution, and caution
is needed to interpret the faint 3mm emission (i.e., low star formation rate
surface density) in this relation.

###  3.3 Intensity ratios

####  3.3.1 SWBE

The intensity ratio maps, HCO+/HCN and HNC/HCN, of the SWBE region are shown
in the lower panels of Figure 2. Only pixels above certain thresholds are
shown in the integrated images. The threshold is $7\sigma$ for HCN and HCO+,
and $5\sigma$ for HNC. Therefore, the ratios have a significance of at least
$5\sigma$ (for HCO+/HCN) and $4\sigma$ (for HNC/HCN). While the HCO+/HCN
ratios do not show locations with particularly high or low values (Figure 2
lower left), the HNC/HCN ratios have high values ($>0.6$) at the eastern and
northern part (Figure 2 lower right).

Figure 5 shows the HCO+/HCN (left panels) and HNC/HCN (right panels) ratios as
functions of the HCN intensity (top panels), the 3-mm continuum intensity
(middle panels), and the 3-mm continuum/HCN ratio (lower panels). The dense
gas surface density ($\Sigma_{\rm dense}$), the star formation surface density
($\Sigma_{\rm SFR}$), and the dense-gas star formation efficiency (SFE)
corresponding to the quantities used for the x-axes are also shown in the
second x-axes. All of the plots show constant HCO+/HCN and HNC/HCN ratios,
which seem to have no relations with the HCN intensity, the 3-mm continuum
intensity, and the 3-mm/HCN ratio. Overall, the ratios range as follows
$I(\mathrm{HCO^{+}})/I(\mathrm{HCN})=0.99\pm 0.33$ and $I({\rm HNC})/I({\rm
HCN})=0.42\pm 0.12$. Note the HCO+/HCN ratio is higher for the low HCN
intensity because the y-axis correlates with an inverse of the HCN intensity,
and this is unlikely to be a trend with a physical origin.

If the HNC/HCN ratio depends on the temperature as suggested by Hacar et al.
(2020) and other previous works, and if the temperature increases as the star
formation rate increases, then the HNC/HCN ratio should decrease as the star
formation rate increases. This is not the trend seen in the HNC/HCN ratio vs.
the 3-mm continuum intensity relationship (Figure 5 middle right). Instead,
the HNC/HCN ratio seems to be rather insensitive to the star formation rate.

While the HCO+/HCN ratio appears randomly determined by the noise, there is a
cluster of pixels with relatively high HNC/HCN ratios (0.6-0.8) where the HCN
or 3-mm continuum has high S/N, corresponding to the eastern and northern
parts identified on the ratio map.

####  3.3.2 The central region

We show ratio maps of HCO+/HCN and HNC/HCN in Figure 3 (lower panels). The
HCO+/HCN ratio (Figure 3 lower left) shows an almost constant ratio except for
the deviation caused by the low S/N regions. Meanwhile, the HNC/HCN ratio
shows higher ratios in regions where the molecular line emission is brighter.
Figure 6 shows the same quantities as Figure 5 for the central region, and the
above trend is confirmed by the relationship between the HNC/HCN ratio and the
HCN intensity (Figure 6 upper right). The HNC/HCN ratio increases with the
increasing HCN intensity. An even clearer trend is seen between the HNC/HCN
ratio and the 3-mm continuum intensity (Figure 6 middle right). A similar
trend is also seen between the HNC/HCN ratio and the 3-mm continuum/HCN ratio
(Figure 6 lower right). The ratios have means and standard deviations of
$I(\mathrm{HCO^{+}})/I(\mathrm{HCN})=0.92\pm 0.21$ and $I({\rm HNC})/I({\rm
HCN})=0.26\pm 0.11$.

We note that the discrepancy between the ALMA array configurations of the HCN
and HNC data is unlikely to be the cause of this trend. If extended emission
is missed more in HCN than in HNC due to the lack of the 7-meter array data,
then the HNC/HCN ratio would have been lower at low-intensity extended
regions. This is the opposite of our results.

One possible cause of the high HNC/HCN ratio in the high-column-density region
is the high optical depth. When there is a large column of molecular gas, the
optical depth increases. HCN is more abundant than HNC, and is more likely to
be optically thick. To investigate this possibility, we show the spectral
shapes of selected positions in Section 3.4.

Figure 5: Intensity ratios of HCO+/HCN(1–0) (left panels) and HNC/HCN(1–0)
(right panels) as a function of HCN(1–0) intensity (top panels), 3mm continuum
(middle panels), and the intensity ratio of 3mm continuum over HCN(1–0) at the
southwestern bar end region of M83. The color represents the 3mm continuum
intensity. The standard deviation and the mean of data points in each
horizontal bin are shown as red vertical and horizontal lines, respectively.

Figure 6: Same as Figure 5, but for the central region.

###  3.4 Spectral shapes

Figure 7 shows spectra from positions 1-7 shown in Figure 3. Some spectra show
different line shapes between HCN and HNC, specifically at positions 3, 5, and
possibly at 7. At these positions, HCN has either flat-top or double-peak
profiles while HNC has single-peak Gaussian-like profiles. This suggests that
HCN is optically thick compared with HNC. Meanwhile, at position 1, where the
HNC/HCN ratio is relatively low, the line profiles of HCN and HNC are similar.
This position is close to the optical nucleus (Thatte et al., 2000), and their
line widths are large. Line emission is likely to be optically thinner at this
position than others.

Note that the hyperfine structures of HCN($J=$1–0) alone cannot produce the
line profiles we see here. Compared to the strongest transition of $F=2-1$,
$F=0-1$ and $F=1-1$ have velocity shifts of $-7.1$ km s-1 and $4.9$ km s-1,
respectively. These hyperfine splittings can cause slightly wider line
profiles, but their effect should be small considering the spectral width of
our data cube, 10 km s-1. We note that, due to the large line widths (FWHM) in
our observations ($\gtrsim 40$ km s-1 in the central region, $\gtrsim 20$ km
s-1 in SWBE), we cannot check if there is any excitation anomaly among the
hyperfine splitting (e.g., ones reported towards Orion-B by Santa-Maria et
al., 2023).

Figure 7: Spectra of selected regions of HCN (green) and HNC (red) at single
points within the 2.5$\arcsec$ beam taken from positions shown in Figure 3.

###  3.5 Global variation of the intensity ratio

The FIR ratio can be a probe of dust temperature, and an increase in the dust
temperature can be caused by UV photons from a star-forming activity. We
obtained the FIR data from Herschel at $70\,\mu$m and $160\,\mu$m (Bendo et
al., 2012; VNGS team, 2012), which correspond to dust emission peaks at $\sim
40$ and 20 K, respectively. Since currently available far-IR observations only
have a coarser resolution than the ALMA data, we convolved our ALMA data into
the beam size of the 160-$\mu$m Herschel data using the CASA task imsmooth.
Since the Herschel 70-$\mu$m data also has a smaller beam ($5.6\arcsec$)
compared with the 160-$\mu$m data, we also convolved the 70-$\mu$m data to the
beam size of the 160-$\mu$m data, 10.7$\arcsec$. Figure 8 (left) shows the
HNC/HCN ratio at a $10.7\arcsec$ resolution superposed with the ratio of
70$\mu$m over $160\mu$m flux. This HNC/HCN ratio map was created by convolving
the HCN and HNC images individually to $10.7\arcsec$, and taking the ratio.
The Herschel data have already been presented by Foyle et al. (2012). The
HNC/HCN ratio tends to be high when the 70$\mu$m/$160\mu$m ratio is lower.
This is an expected result if the UV field both heats the dust and decreases
the HNC/HCN ratio. Moreover, the HNC/HCN ratio can be low even if the
70$\mu$m/$160\mu$m ratio is moderately low if it is near the high
70$\mu$m/$160\mu$m ratio region. We can interpret this trend as a global (a
few 100 pc scale) effect of the UV field on the HNC/HCN ratio.

Since the FIR data are only available in a lower resolution, it is helpful to
compare the HNC/HCN ratio with the star formation rate with the same
resolution as the FIR data. Figure 8 (right) is similar to Figure 8 (left),
but the contours are the 3-mm continuum convolved to the same resolution as
the Herschel beam. The large-scale variation of the 3-mm continuum appears
somewhat similar to that of the 70$\mu$m/$160\mu$m ratio, although the 3-mm
continuum is more concentrated around regions detected with molecules. The
region with the peak of the 70$\mu$m/$160\mu$m ratio has a low HNC/HCN ratio,
which may indicate that the global star formation rate impacts the HNC/HCN
ratio. At the same time, the HNC/HCN ratio peak at the eastern part of the map
has a moderately high star formation rate inferred from the 3mm continuum.
There does not seem to be a consistent trend between the star formation rate
and the HCN/HCN ratio even globally.

Figure 8: Color image in both panels: HNC/HCN intensity ratio map convolved to
10.7″ equivalent to the resolution of the 160$\mu$m Herschel map. Contours:
(Left) Herschel 70/160 $\mu$m ratio. The ratio is taken in the unit of MJy
sr-1. The contour levels start at 0.5, and are drawn by an increment of 0.1.
(Right) The 3-mm continuum convolved to 10.7″. The contour levels are 0.3,
0.6, 0.9, 1.2 mJy beam-1.

##  4 Discussion

###  4.1 Factors to cause variations in the HNC/HCN abundance ratio

Before discussing the implications of our results, let us summarize the
factors that may affect the abundances of HCN and HNC, and the ratio between
them.

####  4.1.1 Temperature

It was first suggested that the temperature dependence of the HNC/HCN ratio is
due to some reactions to destroy HNC with barriers:

$\mathrm{HNC+O\longrightarrow NH+CO}$ (6)

and

$\mathrm{HNC+H\longrightarrow HCN+H}.$ (7)

These reactions with barriers become very efficient above certain temperatures
because their reaction rates are proportional to exp(-$\gamma/T$), where
$\gamma$ is the reaction barrier and $T$ is the gas kinetic temperature. There
has been some debate about the values of these barriers. Quantum mechanical
calculations show that the barrier of Reaction 6 is 1100 K (Lin et al., 1992),
while that of Reaction 7 is 2000 K or 1200 K (Talbi et al., 1996; Graninger et
al., 2014). The temperature dependence of HNC/HCN seen in observations
requires much lower barriers. Hacar et al. (2020) concluded that the barriers
of 20 K and 200 K provide the best fit to the observed trends. This
discrepancy between the calculated reaction rates and observed temperature
dependence suggests that we may be missing important reactions in the network,
or that the calculated rates may not have enough accuracy, or a physical
parameter or process other than the temperature is responsible for the
observed temperature dependence of HNC/HCN.

####  4.1.2 FUV radiation

Recently, Santa-Maria et al. (2023) suggested from their observations in the
Orion B region that the interstellar radiation field may be the biggest
contributing factor to the HNC/HCN ratio rather than the temperature. This is
because the FUV radiation promotes both the formation and excitation of HCN.
There are additional formation reactions of HCN at $A_{\rm V}<4$ mag.: ${\rm
C+HNC\longrightarrow HCN+C}$ and ${\rm N+HCO\longrightarrow HCN+O}$. The
higher ionization fraction in PDRs also makes the electron excitation more
efficient. The UV radiation should of course increase the temperature, and
some relationship between the HNC/HCN ratio and the temperature is expected
without the need for low reaction barriers.

####  4.1.3 Cosmic rays

Behrens et al. (2022) studied the dependence of HNC/HCN on the cosmic-ray
ionization rate to analyze the chemistry in the starburst galaxy NGC 253.
Because the main formation pathway of HCN and HNC with high cosmic-ray
ionization rates is

$\mathrm{HCNH^{+}+e^{-}}\longrightarrow\begin{cases}\mathrm{HCN+H}\\\
\mathrm{HNC+H}\\\ \mathrm{CN+H+H}\end{cases},$ (8)

this reaction maintains the HCN/HNC abundance close to unity. The branching
ratio of the electron recombination reaction of HCNH+ is estimated to be
roughly 1/3 for each product HCN, HNC, and CN according to the KIDA
database222https://kida.astrochem-tools.org/.

###  4.2 Measured quantities and physical parameters

In the previous sections, we compared the HNC/HCN ratios with the 3-mm
continuum and the 70$\mu$m/160$\mu$m ratios. Here we connect these measurable
quantities to the physical parameters that could affect the chemistry, namely,
the temperature, UV field, and cosmic-ray ionization rates.

The 3-mm continuum emission

As mentioned above, the 3-mm continuum is considered a tracer of SFR. Although
continuum flux could contain synchrotron radiation or dust emission, there is
no obvious synchrotron source such as supernova remnants (Long et al., 2022).
Although there may be unidentified diffuse supernova remnants that cause
synchrotron radiation, we do not expect it to be more significant than for
normal star-forming galaxies, where synchrotron radiation is insignificant at
the 3-mm wavelength. We already discussed the estimate of the dust
contamination in Section 2, which tends to be insignificant.

Good spatial correlations with the temperature and SFR have been observed in
many regions. Galactic centers have higher temperatures on the GMC scale where
the star formation rates are higher (e.g., Ginsburg et al., 2016; Tanaka et
al., 2024) according to LVG analyses. An LVG analysis on the data towards the
center of M83 using the same method as Tanaka et al. (2024) shows elevated
temperatures ($\gtrsim$ a few hundred K) near regions with intense star
formation compared to the region without star formation ($\sim 100\,$K)(Kaneko
et al. in preparation). Such correlation is also seen in the spiral-arm region
of the Galaxy, but the heating is only effective on the scale of 1 pc or so
(e.g., Hacar et al., 2020; Murase et al., 2022). Of course, having a higher
number of star-forming regions within a GMC should raise the temperature on
average, but it is unclear how much the temperature is raised for a given
value of SFR in the extragalactic GMCs where the density structure within the
beam is unknown.

A high star formation rate also produces a high UV radiation field. While we
expect some spatial correlation between the star formation rate and the UV
field, the correlation between the star formation rate and the UV radiation
field may not be tight if the region has high visual extinction that allows
the attenuation of the UV photons.

The correlation between the cosmic-ray ionization rate and the 3-mm continuum
should be weak. First, the locations of supernova remnants (Long et al., 2022)
do not seem to correlate with the star formation rate on $<100\,$pc scale.
Moreover, cosmic rays penetrate high column densities, and variation among
GMCs should be small although we do expect $\sim$kpc-scale variations near the
galactic center region where supernova remnants are concentrated.

FIR intensity ratio (70$\mu$m/160$\mu$m)

We expect some spatial correlation between the UV radiation field and the FIR
intensity ratio. The UV radiation heats the dust, which increases the
$70\mu$m/$160\mu$m ratio. If the UV field also heats the gas in addition to
the dust, the gas kinetic temperature should also be high where the
$70\mu$m/$160\mu$m ratio is high. For the same reasons as the 3-mm continuum,
we do not expect a good spatial correlation between the FIR intensity ratio
and cosmic-ray ionization rates.

###  4.3 Possible scenarios

We have seen that the HNC/HCN ratio varies with the large-scale variation of
70/160$\mu$m, but not with the local star formation rates in the bar-end
region. We also found that the HNC/HCN ratio is largely determined by the
optical depth in the galactic center region. Depending on the driving force of
the HNC/HCN chemistry, we can propose the following two scenarios. For each
scenario, we add the interpretation of observed trends. The summary of this
section is also shown in Figure 9.

Figure 9: A table describing the interpretation of the observed trends.

  1. 1.

The HNC/HCN ratio changes with the temperature

SWBE $2\arcsec$ (40 pc) scale: In this case, the increase in the temperature
caused by the high star formation rate is not visible in our HNC/HCN
observations. A possible reason is that either the star formation does not
increase the temperature or that it occurs on a scale far smaller than our
beam size (i.e., parsec scale or less). Because it is hard for star formation
not to increase the temperature at all, we speculate that the heated regions
are small for the embedded star formation traced with the 3-mm continuum
emission.

SWBE $10\arcsec$ scale ($\sim 200\,$pc): There is a gas temperature increase
on a large scale as the gas flows through the bar end region, which lowers the
HNC/HCN ratio downstream. The heating source is unknown, but possible
candidates are photoelectric heating due to UV photons, shock heating, and
cosmic-ray heating. If the heating source is UV photons, it is difficult to
distinguish whether the driving force of the chemistry is temperature or UV
photons. Koda et al. (2020) found that the CO(2–1)/(1–0) ratio is higher
downstream around spiral arms, and proposed that this higher ratio is caused
by UV or cosmic-ray heating due to star formation that took place when the gas
passed through the spiral arms. This star formation causing the temperature
increase must be unobscured instead of the embedded one. Cosmic rays are
unlikely to be the main driver of chemistry in regions with high CO(2–1)/(1–0)
ratios because the cosmic rays increase the HNC/HCN ratio.

The central region: The center of M83 has a temperature of $>100\,$K according
to the LVG analysis by Kaneko et al. (in preparation). Most of the gas is
supposed to have HNC/HCN$<0.1$ if this ratio follows the relationship by Hacar
et al. (2020). We can interpret the high HNC/HCN ratio with the high cosmic-
ray ionization rate. There is still an effect of the optical depth that alters
the HNC/HCN ratio locally.

  2. 2.

The HNC/HCN ratio changes with the UV radiation field

SWBE $2\arcsec$ scale: If the HNC/HCN ratio is affected by the UV radiation
field, its effect is limited in highly obscured regions. Star-forming regions
traced with the 3mm continuum may not alter the HNC/HCN ratio because these
star-forming regions are embedded, providing little dependence of the HNC/HCN
on the star formation rate in the bar-end region on the small scale.

SWBE $10\arcsec$ scale: The global dependence of the HNC/HCN ratio on the far-
infrared ratio is caused by the UV radiation field because the UV radiation
also heats the dust.

The central region: In the galactic center region, the HNC/HCN ratio is not
very low despite the high star formation rate and high temperature because the
density is also high, and the UV radiation field can be attenuated. The high
HNC/HCN ratio in the obscured region is caused by both the lack of UV field
and the optical depth.

It is difficult to determine which scenario is correct from the observations
in the SWBE region alone, especially if the UV photons are the main heating
source. To decide which scenario is more likely, it is important to study
regions where the heating source is not UV photons, i.e., regions that are
obscured from external UV photons. The spatial distribution of the HNC/HCN
ratio in the galactic center region can give us a clue, since it generally has
high column densities judging from the fact that molecular emission and dust
continuum emission are both brighter than the bar-end region by about an order
of magnitude. For the HNC/HCN ratio to be high enough in the high-temperature
region of the M83 galactic center, cosmic-ray ionization needs to be high
according to Scenario 1, where the HNC/HCN ratio is mainly determined by the
temperature. While the cosmic-ray ionization rate is expected to be high due
to the high supernova rate (Long et al., 2022), it is unlikely to be the main
driver of the chemistry. If cosmic rays increase the HNC/HCN ratio, they
should have a stronger impact in the low-density region, because the chemistry
scales as $\zeta/n$, where $\zeta$ is the cosmic-ray ionization rate and $n$
is the density. This contradicts the observed trend in M83. The HNC/HCN ratios
are also high in high-column-density regions in the central region of NGC 253
(Behrens et al., 2022).

Even in Scenario 1, one could also argue that the HNC/HCN ratio is high in the
central region simply because of the optical depth despite the high
temperature. However, the HNC/HCN ratio is moderately high ($\sim 0.3$) even
where a line is broad and likely optically thin around the optical nucleus
(near the position 1 in Figure 3). The temperature corresponding to
$I$(HNC)/$I$(HCN)=0.3 is about 30 K according to the Hacar et al. (2020)
relation, and is too low for a galactic center. Although it appears reasonable
to exclude this case, deep maps of H13CN and an estimate of 12C/13C are
necessary for confirmation so that the optical depth in this whole region can
be derived.

It may sound unreasonable that the HNC/HCN ratio is moderately high in the
galactic center region despite the high UV field expected from the high star
formation rate if Scenario 2 is true. However, the HNC/HCN ratio is low
($\lesssim 0.2$) in low column density regions, where the UV photons can
travel without too much extinction. Near-infrared observations towards the
galactic center region reveal higher visual extinction ($A_{\mathrm{V}}\gtrsim
14$; Turner et al., 1987). Molecular regions likely have even higher visual
extinction, which would increase the HNC/HCN ratio if the HNC/HCN ratio
decreases with the UV field. For these reasons, we believe that Scenario 2 is
more plausible.

##  5 Summary

We present 40-pc or 50-pc resolution dense gas tracers (HCN, HNC, and HCO+) in
the southwestern bar-end and central regions of M83 obtained by ALMA. We focus
on the isomeric ratio of HNC and HCN, which has been previously proposed as a
temperature tracer or more recently as a UV field tracer. Here is the summary
of our findings.

  * •

The southwestern bar end and the center of M83 lie on the typical relationship
between the dense gas surface density ($\Sigma_{\mathrm{dense}}$) and the star
formation surface density ($\Sigma_{\mathrm{SFR}}$) similar to other star-
forming galaxies (e.g., M51, NGC 1068) found in the literature.

  * •

The HNC/HCN ratio has no obvious correlation with the dense gas surface
density, star formation rate, and star formation efficiency in the
southwestern bar-end region on the GMC scale ($\sim 40\,$pc).

  * •

The HNC/HCN ratio slightly increases with the dense gas surface density, star
formation rate, and star formation efficiency in the central region. This is
the opposite of what is expected if we assume that the HNC/HCN ratio decreases
with increasing temperature and that the high star-formation region raises the
kinetic temperature.

  * •

Spectra of the central region, especially regions with high HNC/HCN ratios,
show a double-peak or flat-top shape for HCN while they are closer to Gaussian
for HNC. This trend suggests that these regions are optically thick in HCN.
High optical thickness explains the high HNC/HCN ratios in high dense gas
surface density, high star-formation-rate regions.

  * •

The HNC/HCN ratio tends to be lower near the region where the ratio of
$70\mu$m/$160\mu$m luminosity is high on a large scale of $\sim 200\,$pc in
the southwestern bar-end region. The low HNC/HCN ratios tend to appear
downstream across the bar-end. This result suggests that star formation on the
bar/arm either raises the temperature or increases the UV radiation field not
on the GMC scale, but on a larger scale.

  * •

The above results suggest that the HNC/HCN ratio is likely determined by the
UV radiation field. It has a dependence on the large scale because UV photons
travel farther in low column density regions in the bar-end region. It has
little dependence on star formation rate because star formation in the bar-end
region detected by the 3-mm continuum is mostly embedded. The column density
of the galactic center region is very high, and the HNC/HCN ratio is high
despite the high star formation rate in this region. The cosmic-ray ionization
rate is likely high, but is unlikely the driver of the HNC/HCN chemistry.

Although our conclusion is that the HNC/HCN ratio is a UV field tracer, it is
necessary to have more careful analysis in regions where the main heating
source is not UV photons and where other temperature tracers are available to
confidently distinguish whether it is a temperature tracer or a UV tracer. It
is also important to note that the HNC/HCN ratio may have a temperature
dependence when the temperature is close enough to the reaction barrier of
conversion reactions from HNC to HCN (e.g., $\gtrsim$ a few 100 K in the
shocked region).

We thank the anonymous referee for the helpful comments. This paper makes use
of the following ALMA data:
ADS/JAO.ALMA#2016.1.00164.S
ADS/JAO.ALMA#2015.1.01177.S
ADS/JAO.ALMA#2021.1.01195.S.
ALMA is a partnership of ESO (representing its member states), NSF (USA) and
NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ. N.H. acknowledges support
from JSPS KAKENHI grant No. JP21K03634. Y.N. gratefully acknowledges support
from JSPS KAKENHI grant Numbers JP23K13140 and JP23K20035. K.S. thanks support
by the grants NSTC 111-2124-M-001-005- and NSTC 112-2124-M-001-014-.

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