# PHANGS-JWST First Results: Stellar Feedback-Driven Excitation and
Dissociation of Molecular Gas in the Starburst Ring of NGC 1365?

Daizhong Liu Max-Planck-Institut für Extraterrestrische Physik (MPE),
Giessenbachstr. 1, D-85748 Garching, Germany  Eva Schinnerer Max-Planck-
Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany  Yixian
Cao Max-Planck-Institut für Extraterrestrische Physik (MPE), Giessenbachstr.
1, D-85748 Garching, Germany  Adam Leroy Department of Astronomy, The Ohio
State University, 140 West 18th Ave, Columbus, OH 43210, USA  Antonio Usero
Observatorio Astronómico Nacional (IGN), C/Alfonso XII, 3, E-28014 Madrid,
Spain  Erik Rosolowsky Department of Physics, University of Alberta, Edmonton,
AB T6G 2E1, Canada  Eric Emsellem European Southern Observatory, Karl-
Schwarzschild-Straße 2, 85748 Garching, Germany  Univ Lyon, Univ Lyon1, ENS de
Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, F-69230 Saint-
Genis-Laval France  J. M. Diederik Kruijssen Cosmic Origins Of Life (COOL)
Research DAO, coolresearch.io  Mélanie Chevance Universität Heidelberg,
Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-
Str 2, D-69120 Heidelberg, Germany  Cosmic Origins Of Life (COOL) Research
DAO, coolresearch.io  Simon C. O. Glover Universität Heidelberg, Zentrum für
Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str 2,
D-69120 Heidelberg, Germany  Mattia C. Sormani Universität Heidelberg, Zentrum
für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str 2,
D-69120 Heidelberg, Germany  Alberto D. Bolatto Department of Astronomy and
Joint Space-Science Institute, University of Maryland, College Park, MD 20742,
USA  Jiayi Sun Department of Physics and Astronomy, McMaster University, 1280
Main Street West, Hamilton, ON L8S 4M1, Canada  Canadian Institute for
Theoretical Astrophysics (CITA), University of Toronto, 60 St George Street,
Toronto, ON M5S 3H8, Canada  Sophia K. Stuber Max-Planck-Institut für
Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany  Yu-Hsuan Teng Center
for Astrophysics and Space Sciences, Department of Physics, University of
California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA  Frank
Bigiel Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71,
53121 Bonn, Germany  Ivana Bešlić Argelander-Institut für Astronomie,
Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany  Kathryn Grasha
Research School of Astronomy and Astrophysics, Australian National University,
Canberra, ACT 2611, Australia  ARC Centre of Excellence for All Sky
Astrophysics in 3 Dimensions (ASTRO 3D), Australia  Jonathan D. Henshaw
Astrophysics Research Institute, Liverpool John Moores University, 146
Brownlow Hill, Liverpool L3 5RF, UK  Max-Planck-Institut für Astronomie,
Königstuhl 17, D-69117 Heidelberg, Germany  Ashley. T. Barnes Argelander-
Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn,
Germany  Jakob S. den Brok Argelander-Institut für Astronomie, Universität
Bonn, Auf dem Hügel 71, 53121 Bonn, Germany  Toshiki Saito National
Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588,
Japan  Daniel A. Dale Department of Physics and Astronomy, University of
Wyoming, Laramie, WY 82071, USA  Elizabeth J. Watkins Astronomisches Rechen-
Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstraße
12-14, 69120 Heidelberg, Germany  Hsi-An Pan Department of Physics, Tamkang
University, No.151, Yingzhuan Road, Tamsui District, New Taipei City 251301,
Taiwan  Ralf S. Klessen Universität Heidelberg, Zentrum für Astronomie,
Institut für Theoretische Astrophysik, Albert-Ueberle-Str 2, D-69120
Heidelberg, Germany  Universität Heidelberg, Interdisziplinäres Zentrum für
Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, D-69120 Heidelberg,
Germany  Gagandeep S. Anand Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD 21218, USA  Sinan Deger The Oskar Klein Centre for
Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova,
Stockholm, SE-106 91, Sweden  Oleg V. Egorov Astronomisches Rechen-Institut,
Zentrum für Astronomie der Universität Heidelberg, Mönchhofstraße 12-14, 69120
Heidelberg, Germany  Christopher M. Faesi University of Massachusetts-Amherst,
710 North Pleasant Street, Amherst, MA 01003, USA  Hamid Hassani Department of
Physics, University of Alberta, Edmonton, Alberta, T6G 2E1, Canada  Kirsten L.
Larson AURA for the European Space Agency (ESA), Space Telescope Science
Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA  Janice C. Lee
Gemini Observatory/NSF’s NOIRLab, 950 N. Cherry Avenue, Tucson, AZ 85719, USA;
Caltech/IPAC, California Institute of Technology, Pasadena, CA 91125, USA
Laura A. Lopez Department of Astronomy, The Ohio State University, 140 West
18th Ave, Columbus, OH 43210, USA  Center for Cosmology and Astroparticle
Physics, 191 West Woodruff Avenue, Columbus, OH 43210, USA  Flatiron
Institute, Center for Computational Astrophysics, NY 10010, USA  Jérôme Pety
IRAM, 300 rue de la Piscine, 38400 Saint Martin d’Hères, France  LERMA,
Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités,
75014 Paris  Karin Sandstrom Center for Astrophysics and Space Sciences,
Department of Physics, University of California, San Diego, 9500 Gilman Drive,
La Jolla, CA 92093, USA  David A. Thilker Department of Physics and Astronomy,
The Johns Hopkins University, Baltimore, MD 21218, USA  Bradley C. Whitmore
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA  Thomas G. Williams Sub-department of Astrophysics, Department of Physics,
University of Oxford, Keble Road, Oxford OX1 3RH, UK  Max-Planck-Institut für
Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany

(Accepted December 7, 2022)

###### Abstract

We compare embedded young massive star clusters (YMCs) to (sub-)millimeter
line observations tracing the excitation and dissociation of molecular gas in
the starburst ring of NGC 1365. This galaxy hosts one of the strongest nuclear
starbursts and richest populations of YMCs within 20 Mpc. Here we combine
near-/mid-IR PHANGS-JWST imaging with new ALMA multi-$J$ CO(1–0, 2–1 and 4–3)
and [C i](1–0) mapping, which we use to trace CO excitation via
${R_{42}}=I_{\mathrm{CO}\,(4\textnormal{--}3)}/I_{\mathrm{CO}\,(2\textnormal{--}1)}$
and
${R_{21}}=I_{\mathrm{CO}\,(2\textnormal{--}1)}/I_{\mathrm{CO}\,(1\textnormal{--}0)}$
and dissociation via
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}=I_{[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)}/I_{\mathrm{CO}\,(2\textnormal{--}1)}$
at 330 pc resolution. We find that the gas flowing into the starburst ring
from northeast to southwest appears strongly affected by stellar feedback,
showing decreased excitation (lower ${R_{42}}$) and increased signatures of
dissociation (higher ${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$) in the
downstream regions. There, radiative transfer modelling suggests that the
molecular gas density decreases and temperature and
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ abundance ratio increase. We compare
${R_{42}}$ and ${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ with local
conditions across the regions and find that both correlate with near-IR 2
${\mu\mathrm{m}}$ emission tracing the YMCs and with both PAH (11.3
${\mu\mathrm{m}}$) and dust continuum (21 ${\mu\mathrm{m}}$) emission. In
general, ${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ exhibits $\sim 0.1$ dex
tighter correlations than ${R_{42}}$, suggesting C i to be a more sensitive
tracer of changing physical conditions in the NGC 1365 starburst than CO(4–3).
Our results are consistent with a scenario where gas flows into the two arm
regions along the bar, becomes condensed/shocked, forms YMCs, and then these
YMCs heat and dissociate the gas.

galaxies: ISM — galaxies: star formation — ISM: molecules — ISM: atoms

††journal: ApJL††software: Astropy (Astropy Collaboration et al., 2013, 2018,
2022), CASA software (CASA Team et al., 2022), Matplotlib (Hunter, 2007),
MICHI2 (Liu et al., 2021; Liu, 2020), PHANGS-ALMA pipeline (Leroy et al.,
2021b), Photutils (Bradley et al., 2020), RADEX (van der Tak et al., 2007),
Scipy (Virtanen et al., 2020), spectral_cube (Ginsburg et al., 2019)

##  1 Introduction

The interplay between star formation and the interstellar medium (ISM) is a
key topic in our understanding of galaxy evolution. Star formation happens in
cold molecular gas (e.g., review by Kennicutt & Evans, 2012) and then young
massive stars (often found in young massive clusters, or YMCs) drive energetic
winds and radiation that may heat up or destroy giant molecular clouds (GMCs),
a process known as stellar feedback (e.g., see reviews by Chevance et al.
2020, 2022). An active galactic nucleus (AGN), if present, can also have a
significant impact on the host galaxy’s ISM and star formation, known as the
AGN feedback (see e.g. the reviews by Cicone et al. 2018; Harrison et al.
2018). Across the universe, much star formation occurs in gas-rich, turbulent,
and high surface density regions (e.g., Tacconi et al., 2020). To understand
how feedback processes operate in such intense environments, the local
starburst galaxy population, and especially starbursting galaxy centers,
represent key targets where we can observe the physical state of the molecular
gas and the impact of stellar feedback in the greatest detail.

Thanks to high resolution optical (e.g., LEGUS: Calzetti et al. 2015; PHANGS-
HST: Lee et al. 2022; PHANGS-MUSE: Emsellem et al. 2022; MAD: Erroz-Ferrer et
al. 2019; TIMER: Gadotti et al. 2019) and mm-wave imaging (e.g., NUGA: Combes
et al. 2019; PHANGS-ALMA: Leroy et al. 2021a; GATOS: García-Burillo et al.
2021), we have made great strides in understanding the interplay of molecular
gas, star formation, and stellar feedback in normal galaxy disks (e.g.,
feedback timescales: Grasha et al. 2018; Kruijssen et al. 2019; Chevance et
al. 2020; Kim et al. 2022; Pan et al. 2022, pressure and turbulence: Sun et
al. 2020; Barnes et al. 2021, 2022; outflows of AGNs: Audibert et al. 2019;
García-Burillo et al. 2021; Saito et al. 2022a, b; to name a few). However,
the nuclear starbursts, which contain a significant to dominant fraction of
host galaxy’s star formation and especially the most massive
($M_{\star}\gtrsim 10^{6}\;\mathrm{M_{\odot}}$) YMCs, are still far from being
well understood.

NGC 1365 among the most actively star-forming local galaxies
($\mathrm{SFR}=16.9\;\mathrm{M_{\odot}\,yr^{-1}}$; Leroy et al. 2021a) and
hosts the richest populations of YMCs in the local $\sim 20$ Mpc Universe
(Kristen et al., 1997; Galliano et al., 2008; Whitmore et al., subm.). At a
distance of $19.57\pm 0.78$ Mpc (Anand et al. 2021a, b; $1^{\prime\prime}=95$
pc), its nuclear starbursting ring ($R\sim 1.8$ kpc; Schinnerer et al. subm.)
is fed by gas flowing inward along bar lanes of its well-known 17 kpc-long
stellar bar (Lindblad, 1999). An optical/radio/X-ray AGN is also well-known at
its center (e.g., Veron et al. 1980; Turner et al. 1993; Morganti et al. 1999;
Fazeli et al. 2019). Based on the first data of PHANGS-JWST (Lee et al.
subm.), 37 $M_{\star}\gtrsim 10^{6}\;\mathrm{M_{\odot}}$ and
$\mathrm{age}\lesssim 10\;\mathrm{Myr}$ YMCs are found within the central
$\sim 3\,\mathrm{kpc}\times 2.5\,\mathrm{kpc}$ area (Whitmore et al., subm.),
more numerous than in any other galaxy within $\sim 20$ Mpc.

In this work, we utilize the first PHANGS-JWST mid-IR imaging along with new
and archival ALMA multi-$J$ (1–0, 2–1 and 4–3) CO and [C i](1–0) line mapping
to assess how tracers of CO excitation, dissociation, and other molecular gas
properties relate to the location and likely evolution of embedded YMCs in
this rich inner region of NGC 1365.

The spectral line energy distribution (SLED) of CO is a powerful tool to
constrain gas temperature and density (e.g., Goldreich & Kwan 1974; Israel et
al. 1995; Bayet et al. 2004, 2006; Papadopoulos et al. 2007, 2010; Greve et
al. 2014; Zhang et al. 2014; Liu et al. 2015; Rosenberg et al. 2015; Israel et
al. 2015; Kamenetzky et al. 2014, 2016, 2017). The CO(4–3) transition has more
than an order of magnitude higher critical density and upper level energy
($E_{u=4}/k_{\mathrm{B}}=55.32\ \mathrm{K}$, $n_{\mathrm{crit.}}\sim 4\times
10^{4}\ \mathrm{cm^{-3}}$; Meijerink et al. 2007) than the ground 1–0
transition ($E_{u=1}/k_{\mathrm{B}}=5.53\ \mathrm{K}$, $n_{\mathrm{crit.}}\sim
3\times 10^{3}\ \mathrm{cm^{-3}}$) 111Although practically these lines can be
moderately excited and detectable even at lower densities (e.g., Scoville
2013; Shirley 2015).. Therefore, a higher ${R_{41}}\equiv
I_{\mathrm{CO}\,(4\textnormal{--}3)}/I_{\mathrm{CO}\,(1\textnormal{--}0)}$
line ratio generally means a higher density and temperature of gas, but the
actual shape of CO SLED (e.g., traced by both a mid-$J$ ratio ${R_{42}}\equiv
I_{\mathrm{CO}\,(4\textnormal{--}3)}/I_{\mathrm{CO}\,(2\textnormal{--}1)}$ and
a low-$J$ ratio ${R_{21}}\equiv
I_{\mathrm{CO}\,(2\textnormal{--}1)}/I_{\mathrm{CO}\,(1\textnormal{--}0)}$) is
important to distinguish the effects of changing density, temperature and
other ISM properties (e.g., turbulent line width) that may relate to the
stellar feedback.

Meanwhile, the C i offers an additional potential diagnostic on the feedback
affecting the dissociation of CO. C i originates from a thin dissociation
layer in photon-dominated regions (PDRs; Langer 1976; de Jong et al. 1980;
Tielens & Hollenbach 1985a, b; Hollenbach et al. 1991) exposed to the UV
radiation of H ii regions (Hollenbach & Tielens 1997; Kaufman et al. 1999;
Wolfire et al. 2022). Cosmic rays and X-rays from YMCs and AGN, known as the
cosmic-ray dominated regions (CRDR; Papadopoulos 2010; Papadopoulos et al.
2011, 2018) and X-ray dominated regions (XDR; Maloney et al. 1996; Meijerink &
Spaans 2005; Meijerink et al. 2007; Wolfire et al. 2022), respectively, can
drastically increase C i abundances and lead to a high C i/CO line ratio
(${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$; Israel et al. 2015; Salak et al.
2019; Izumi et al. 2020).

Because embedded YMCs and AGN exert intense radiative and mechanical feedback,
they should in principle have a strong effect on the surrounding gas, which
should manifest as observable variations in the CO SLED and the C i/CO ratios.
However, isolating the effects of this feedback is challenging due to the lack
of high-resolution, multi-$J$ CO and C i observations and high-resolution,
sensitivity mid-IR imaging in the past. Therefore, in this Letter, we use the
new JWST+ALMA data and present the first multi-$J$ CO and C i \+ embedded YMC
study to trace the molecular gas properties and feedback in the bar-fed
central starbursting environment in NGC 1365.

##  2 Observations & Data

###  2.1 JWST observations

Full descriptions of the PHANGS-JWST observations (Program ID: 02107; PI: J.
Lee) are given by Lee et al. (subm.). We provide a brief summary of the
observations and processing used for NGC 1365 here. The galaxy was observed
during two NIRCam and four MIRI visits. The resulting NIRCam mosaic covers the
central $\sim 4.6^{\prime}\times 2.9^{\prime}$ ($26.2\times 16.5$ kpc) and the
MIRI mosaic covers $\sim 3.8^{\prime}\times 2.6^{\prime}$ ($21.6\times 14.8$
kpc). The NIRCam F200W, F300M and F360M filters cover primarily the stellar
continuum. The MIRI F1000W and F2100W filters primarily cover dust continuum
imaging. In addition, the NIRCam F335M and MIRI F770W and F1130W filters
recover mostly emission associated with Polycyclic Aromatic Hydrogen (PAH)
bands in addition to an underlying stellar and dust continuum. Hereafter we
refer to the bands by their corresponding wavelengths: 2 ${\mu\mathrm{m}}$ for
F200W, 11.3 ${\mu\mathrm{m}}$ for F1130W, and 21 ${\mu\mathrm{m}}$ for F2100W.

We use PHANGS-JWST internal release versions “v0p4p2” for NIRCam and “v0p5”
for MIRI. Lee et al. (subm.) describe the data reduction used for these first
results, including modifications to the default JWST pipeline 222https://jwst-
pipeline.readthedocs.io parameters, our customized $1/f$ noise reduction
(destriping) and background subtraction for the NIRCam images, the subtraction
of MIRI “off” images, and how we set the absolute background level in the MIRI
images.

JWST’s high sensitivity results in saturation of pixels on top of the AGN and
the brightest star-forming complexes. In this work, because we convolve the
JWST images to the $3.5^{\prime\prime}$ resolution of CO(4–3) and [C i](1–0)
lines, the saturation of brightest emission needs to be fixed. Here we use a
point spread function (PSF) curve-of-growth analysis to match the unsaturated
outskirts of each bright saturated spot, i.e., the center of NGC 1365 (where
the AGN is located) and the three bright star-forming complexes to the north.

Next, these images are PSF-matched to our common resolution of
$3.5^{\prime\prime}$ corresponding to the ALMA CO(4–3) beam in this work. We
use the WebbPSF software to generate the PSFs and the photutils software to
create convolution kernels (with fine-tuned TopHatWindow). The images are then
resampled with the reprojection software in Python to the same world
coordinate system and pixel scale.

Fig. 1: ALMA and JWST images of NGC 1365. Left column (a, d, g): Native-
resolution ($0.3^{\prime\prime}$) ALMA CO(2-1) integrated intensity (mom0),
line-of-sight velocity (mom1) and velocity dispersion (mom2); see also
Schinnerer et al. (subm.). Middle column (b, e, h): JWST stellar continuum
dominated NIRCam 2 $\mu\mathrm{m}$, PAH-dominated MIRI 11.3 $\mu\mathrm{m}$,
and dust continuum dominated MIRI 21 $\mu\mathrm{m}$, all at native
resolutions; see also Whitmore et al. (subm.). Right column (c, f, i): Ratio
maps in logarithmic scale for
${R_{21}}=I_{\mathrm{CO}\,(2\textnormal{--}1)}/I_{\mathrm{CO}\,(1\textnormal{--}0)}$,
${R_{42}}=I_{\mathrm{CO}\,(4\textnormal{--}3)}/I_{\mathrm{CO}\,(2\textnormal{--}1)}$
and
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}=I_{[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)}/I_{\mathrm{CO}\,(2\textnormal{--}1)}$
at the common resolution of $3.5^{\prime\prime}$ (beam is shown in bottom
left). Same contours of $I_{\mathrm{CO}\,(2\textnormal{--}1)}$ at 400, 1000,
1500, 2000 and 3000 $\mathrm{K\,km\,s^{-1}}$ are shown in all panels. Four
regions mentioned in this work are highlighted in panel a). The cone in panel
d) represents the known ionized gas outflow with a half-opening angle
$50^{\circ}$, cone axis inclination $35^{\circ}$ and PA $126^{\circ}$ (Hjelm &
Lindblad 1996; see also Sandqvist et al. 1995; Lindblad 1999; Venturi et al.
2018; Gao et al. 2021) and the white line indicates the disk kinematic major
axis at PA $220^{\circ}$ (Jorsater & van Moorsel 1995; Lindblad 1999).

###  2.2 ALMA observations of CO(1–0), (2–1) and (4–3), and [C i](1–0)

We have obtained new ALMA ACA (7m) Band 8 observations (program
2019.1.01635.S, PI: D. Liu) that map the CO(4–3) and [C i](1–0) from the inner
part of NGC 1365. The CO(4–3) observations at 458.53 GHz cover the inner
$75^{\prime\prime}\times 22^{\prime\prime}$ ($7.3\times 2.1$ kpc2) using a
19-pointing mosaic and on-source integration time of $\sim 1$ hour and had
$T_{\mathrm{sys}}\sim 550$ K. The [C i](1–0) observations at 489.48 GHz
covered the same area using a 23-pointing mosaic and an on-source integration
time of $\sim 8$ hours with $T_{\mathrm{sys}}\sim 500\text{--}1000$ K. The raw
data were reduced using the standard ALMA calibration pipeline with CASA
software (CASA Team et al., 2022).

We also reduced archival ALMA 12m+7m observations of CO(1–0) (2015.1.01135.S,
PI: F. Egusa; 2017.1.00129.S, PI: K. Morokuma), 12m+7m observations of CO(2–1)
(2013.1.01161.S, PI: K. Sakamoto), including the CO(1–0) and (2–1) total power
(TP) data.

After running the ALMA pipeline, we imaged and processed our data into data
cubes using the PHANGS–ALMA pipeline
333https://github.com/akleroy/phangs_imaging_scripts (Leroy et al., 2021b).
Then we used the spectral_cube444spectral-cube.readthedocs.io software to
convolve our cubes to the common beam of $3.5^{\prime\prime}$ matching the
coarsest C i data.

The native resolution of the CO(1–0) and (2–1) data are $2.4^{\prime\prime}$
and $0.31^{\prime\prime}$. Based on the arrays used, these images have maximum
recoverable scales (MRS) of $\sim 80^{\prime\prime}$ and $40^{\prime\prime}$,
respectively. Our CO(4–3) and [C i](1–0) data have
$3.4\text{--}3.5^{\prime\prime}$ beams and $15\text{--}20^{\prime\prime}$
MRSs. For CO(1–0) and (2–1) the short-spacing is corrected with the
PHANGS–ALMA pipeline using their total power data, however, other lines lack
the short-spacing correction. We considered using the archival 12m-only ALMA
CO(3–2) data for this galaxy but found that its poor $u-v$ coverage made it
not useful in the analysis presented.

We expect only a minor percentage of missing flux for our CO(4–3) and [C
i](1–0) data (e.g., $\lesssim 25\%$). Indeed, our total CO(4–3) line
luminosity within a radius $\sim 14^{\prime\prime}$ is $5.3\times 10^{8}\
\mathrm{K\,km\,s^{-1}\,pc^{2}}$, which is more than half of the total Herschel
SPIRE FTS CO(4–3) luminosity within a $\sim 43^{\prime\prime}$ beam
($7.3\times 10^{9}\pm 1.2\times 10^{7}\ \mathrm{K\,km\,s^{-1}\,pc^{2}}$; Liu
et al. 2015; scaled to the same distance). Simulations of visibilities
mimicking similar ACA Band 8 observations also reveal that the missing flux is
minimal at relatively bright line emission spots ($\lesssim 10\%$; D. Liu et
al. submitted).

We collapsed the data cubes into moment maps using the PHANGS-ALMA imaging and
post-processing pipeline. We specifically focus on the “strict,” high-
confidence mask, which is constructed using a watershed algorithm with
relatively high clipping values (Rosolowsky & Leroy 2006; Rosolowsky et al.
2021) and so expected to include only significant detections. We build a
single common strict mask by combining the individual masks for CO(1–0),
CO(2–1), CO(4–3) and $[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)$,
then we extracted moment maps for each line therein. The error maps are also
measured from the data cube, then computed for moment maps following the
standard procedures implemented in the PHANGS–ALMA pipeline. In our final
moment-0 maps, the S/N is 5–200 for CO(4–3), 5–100 for
$[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)$, and much higher (20–250)
for CO(1–0) and CO(2–1). We create line ratio maps from every pair or lines at
the best common resolution of $3.5^{\prime\prime}$ and use them to compute
correlations and CO SLEDs.

###  2.3 Auxiliary data products and complementary information

We use the YMC catalog from Whitmore et al. (subm., this Issue) to determine
the locations where CO and C i line fluxes are extracted and studied. It
contains 37 YMCs with HST or JWST photometry derived masses $M_{\star}\sim
1\times 10^{6}\ \text{--}\ 2\times 10^{7}\ \mathrm{M_{\odot}}$ and ages $\sim
1\ \text{--}\ 8\ \mathrm{Myr}$.

We use the CO(2–1) line-of-sight decomposition and orbital time information
from Schinnerer et al. (subm., this Issue) for discussions relating to line
velocity dispersion. Schinnerer et al. (subm.) present the
$0.3^{\prime\prime}$-resolution CO(2–1) data and decomposition of each line-
of-sight spectrum into multiple Gaussian components with the ScousePy software
(Henshaw et al., 2016, 2019). They find that multiple velocity components
exists in the system, and individual components have a typical line width
$\sigma\sim 19\ \mathrm{km\,s^{-1}}$. We use this value as the microturbulent
line width $\sigma$ for our later radiative transfer calculation. They derive
a dynamical timescale $t_{\mathrm{dyn}}\sim 20\ \mathrm{Myr}$ at
$R=5^{\prime\prime}\approx 475\,\mathrm{pc}$, which is roughly the radius of
the dynamically cold inner gas disk in this starburst ring system. This time
scale is used as a context for discussion in this work.

##  3 Results & Discussion

###  3.1 Spatial and kinematic structure

In Fig. 1 we present the ALMA and JWST data at their native resolution ($\sim
6$ pc at 2 $\mu\mathrm{m}$, $\sim 30$ pc for CO(2–1) and $\sim 60$ pc at 21
$\mu\mathrm{m}$) and the multi-$J$ CO and C i ratio maps at their common
resolution of $3.5^{\prime\prime}$ ($\sim 330$ pc). We define
${R_{21}}=I_{\mathrm{CO}\,(2\textnormal{--}1)}/I_{\mathrm{CO}\,(1\textnormal{--}0)}$
to trace the low-$J$ CO excitation,
${R_{42}}=I_{\mathrm{CO}\,(4\textnormal{--}3)}/I_{\mathrm{CO}\,(2\textnormal{--}1)}$
for the mid-$J$ excitation, and
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}=I_{[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)}/I_{\mathrm{CO}\,(2\textnormal{--}1)}$
as a tentative tracer of CO dissociation.

We also label four regions in this study to facilitate the later discussion:
i) the “Northern Arm”, which is where the gas flows in from northeast along
the bar; ii) the “Mid-Southwest” region, which is the downstream location of
the gas coming from the Northern Arm (and we call the Northern Arm the
upstream of the Mid-Southwest region); iii) the “Southern Arm”, similar to the
Northern Arm, is the location of gas flowing in from the southeast along the
bar; iv) the “Mid-East” region, considered as the downstream of the Southern
Arm. The Northern Arm and Mid-Southwest both belong to the “northern bar lane”
as defined in Schinnerer et al. (subm.), and the Southern Arm and Mid-East
correspond to the “southern bar lane” therein. The Northern Arm alone is also
emphasized as the “region 1” in Whitmore et al. (subm.).

The CO emission mostly arises from the prominent starburst ring, oriented from
northeast to southwest, but exhibits a highly asymmetric distribution within
this ring. The 2 $\mu\mathrm{m}$ stellar emission, which is much less affected
by dust attenuation than HST optical images, reveals a more symmetric
distribution than CO. We show the azimuthal profiles of the CO, 2
$\mu\mathrm{m}$, 11.3 $\mu\mathrm{m}$ and 21 $\mu\mathrm{m}$ emission along
the starburst ring in Fig. 2. These profiles are measured from the radially-
averaged emission at each azimuthal angle $\theta$ using a common annulus at
our working resolution of $3.5^{\prime\prime}$. Here, $\theta=0^{\circ}$
corresponds to the receding side of major kinematic axis with PA of
$220^{\circ}$, and $\theta=180^{\circ}$ ($-180^{\circ}$) to the approaching
side. All azimuthal profiles show a peak at $\theta_{\mathrm{max}}\sim
150^{\circ}$, corresponding to the Northern Arm region. The 2 $\mu\mathrm{m}$
profile shows the least azimuthal variation of about 50% (with a maxima-to-
minima ratio of 1.9), whereas the other three profiles show large variations
$\sim 80\%\text{--}95\%$, with a maxima-to-minima ratio of 8.5, 6.0 and 19.4,
for CO, 11.3 $\mu\mathrm{m}$ and 21 $\mu\mathrm{m}$ respectively.

The Northern Arm peak ($\theta\sim 150^{\circ}$) in the azimuthal profiles
mainly consists of three extremely massive star clusters, YMC 29, 33 and 28,
corresponding to Galliano et al. (2005, 2008) mid-IR ID M4, M5 and M6, and
Sandqvist et al. (1995) radio 20 cm/6 cm ID D, E and G, respectively.

Fig. 2: Panels a)–d) are the CO(2–1) line integrated intensity, 2
$\mu\mathrm{m}$, 11.3 $\mu\mathrm{m}$ and 21 $\mu\mathrm{m}$ images, PSF-
matched to our $3.5^{\prime\prime}$ resolution. A common annulus is shown in
all panels with radius $=0.9\pm 0.2$ kpc, inclination $40^{\circ}$ and PA
$220^{\circ}$ (white solid line Lindblad, 1999). Panels e)–f) show the
normalized azimuthal profiles of the four upper panels and ${R_{42}}$,
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ and ${R_{21}}$ line ratios as a
function of azimuthal angle $\theta$ measured from the PA of the receding side
of kinematic major axis. Dark green, light green, dark red and light red
shading represents the Northern Arm, Mid-Southwest, Southern Arm and the Mid-
East regions, respectively.

In Fig. 3 we show the distribution of YMCs on the HST RGB and JWST 2
$\mu\mathrm{m}$ image and indicate the dust lanes by two pairs of curved
arrows. The CO(2–1) emission contours broadly match the dust lanes in the
Northern and Southern Arm regions but appear to be narrow at the edge of dust
lanes. Such dust lanes in barred galaxies are usually seen as a result of
dissipative processes in the gaseous component, and the widely accepted view
is that they delineate shocks in the interstellar gas (e.g., see reviews by
Sellwood & Wilkinson 1993; Buta & Combes 1996; Lindblad 1999; see also Pastras
et al. 2022 for detailed simulations).

In addition to the gas and dust lanes, we also highlight in Fig. 3 the YMCs
younger than $\sim 3$ Myr and more attenuated than $A_{V}\sim 8$ magnitude
with cyan squares and yellow stars, respectively. The majority of the most
massive, young and attenuated YMCs sit in the Mid-Southwest and Mid-East
regions.

The multi-$J$ CO and C i line ratio maps exhibit a significant asymmetry as
well. The Northern Arm region shows a factor of 1.5–2$\times$ higher
excitation and dissociation than other regions, as traced by $R_{42}$ and
$R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$. In particular, the $R_{42}$ and
$R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$ peaks coincide with the YMC ID 29 in
the Northern Arm, which also corresponds to the mid-IR source M4 in Galliano
et al. (2005, 2008). It has the highest CO excitation (${R_{42}}\sim 0.51\pm
0.01$, ${R_{21}}\sim 0.92\pm 0.01$) and shows the most signs of dissociation
(${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}\sim 0.17$). The distributions of
low-$J$ excitation, $R_{21}$, mid-$J$ excitation $R_{42}$, and our
photodissociation tracer $R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$ also appear
distinct from one another. $R_{21}$ shows a more symmetric, smooth
distribution than the other two line ratios. The $\log{R_{21}}$ is above
$-0.1$ in most regions, indicating that CO(2–1) is almost thermalized in the
regions we study. The $R_{42}$ and $R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$
ratios have much larger dynamical ranges, and both peak in the Northern Arm.
However, $R_{42}$ is depressed whereas
$R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$ is enhanced in the Mid-Southwest
region, and their trends are the opposite in the Southern Arm region.

The molecular gas has complex, rapidly-changing kinematics in these regions.
Panels (d) and (g) in Fig. 1 show the line-of-sight velocity and line velocity
dispersion maps. The Northern and Southern Arm regions correspond to locations
where molecular gas flows inward along the bar. The dissipative gas flow in
such a strong bar potential can trigger shocks at the leading edge of the bar,
appearing as dust lanes following the orbital skeleton (e.g., Athanassoula
1992; Sellwood & Wilkinson 1993; Buta & Combes 1996; Lindblad 1999; Sellwood &
Masters 2022; Pastras et al. 2022; see also Fig. 1 of Maciejewski et al.
2002). In the Southern Arm, the enhanced $R_{42}$, non-enhanced
$R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$, lack of YMCs and elevated velocity
dispersion $\sigma\sim 50\ \mathrm{km\,s^{-1}}$ (Fig. 1 g) may suggest a
scenario where shocks triggered at the edge of dust lanes are compressing the
gas and hence highly-exciting the mid-$J$ CO, but not leading to significant
CO dissociation or higher C i abundance in this region. However, in other
cases, e.g., the Northern Arm, when the gas is so dense and even fragments to
trigger intensive star formation and hence stellar feedback, the effect of
shocks can be mixed with the stellar feedback effect. Future observations of
shock tracers like SiO or HNCO for less destructive shocks (e.g. Usero et al.,
2006; García-Burillo et al., 2010; Meier et al., 2015; Kelly et al., 2017)
will be the key to shed light on this shock scenario.

In the panel (d) of Fig. 1 we also highlight the well-known ionized gas
outflow (Phillips et al., 1983; Hjelm & Lindblad, 1996; Lindblad, 1999;
Sandqvist et al., 1995; Sakamoto et al., 2007; Lena et al., 2016; Venturi et
al., 2018; Gao et al., 2021). We do not find a high ${R_{42}}$ nor enhanced
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ peaking at the center and extending
along the outflow cone, unlike the cases of known C i molecular outflows in
AGN host galaxies (e.g., Saito et al. 2022a, b; with
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}\sim 1$). This agrees with Schinnerer
et al. (subm.) who find no evidence for the ionized outflow to intersect the
molecular gas disk, and with Combes et al. (2019) who find that this region
lacks a molecular gas outflow (and instead shows evidence for inflow).

Fig. 3: YMCs (Whitmore et al., subm.) overlaid on HST RGB (F814W/F555W/F438W)
image (top) and JWST F200W (2 $\mu\mathrm{m}$) image (bottom). All YMCs are
shown as red circles. Symbol sizes from smallest to largest indicate masses
from $\sim 10^{6.0}\;\mathrm{M}_{\odot}$ to $\sim
10^{7.1}\;\mathrm{M}_{\odot}$. Cyan squares are YMCs with an age less than
$\sim 3$ Myrs, and yellow stars are YMCs with an attenuation $A_{V}>8$
magnitude. We show these YMCs for the context of the discussion in Sect. 3.1
of this work. See Whitmore et al. (subm.) for the original and detailed study
of these YMCs.  Fig. 4: Left panels: CO(2–1) and 2 ${\mu\mathrm{m}}$ zoom-in
images of the Northern Arm, Mid-Southwest, Mid-East and Southern Arm regions
(from top to bottom). Hexagons indicate YMCs identified by Whitmore et al.
(subm.) (with numbers indicating their ID from that paper), YMC-free CO peaks
(labelled “CO.N1–N2” and“CO.S1–S3” in Northern and Southern regions,
respectively, visually identified from this work), and the galaxy center. The
“M2”–“M6” labels indicate YMCs that have a mid-IR counterpart from Galliano et
al. (2005). The “J” label indicates that YMC 3 has a radio counterpart from
Sandqvist et al. (1995). All images have the same field of view of
$10^{\prime\prime}$ ($\sim 950$ pc) and color scaling as in Fig. 1. Hexagons
have the same diameter of $3.5^{\prime\prime}$ ($\sim 330$ pc). The black
arrows at left indicate the up-to-down-stream directions. Right panels: CO and
C i SLEDs of the hexagons centered at YMCs or YMC-free CO peaks in the
corresponding upper/lower four left image panels. Hexagons and SLEDs are
color-coded by their $R_{42}$ (see the bottom color bar). Solid and dotted
lines represent up- and downstream regions, respectively. The Center’s CO SLED
is shown as the dashed line in the lower panel. These CO and C i SLEDs are
used for the radiative transfer modeling fitting in Sect. 3.2 with gas
properties reported in Table 2.

###  3.2 Zoom-in views and CO and C i excitation

We examine the aforementioned regions in more detail in Fig. 4. We first draw
hexagonal apertures centered on bright YMCs (Whitmore et al., subm.), CO peaks
that do not coincide with a YMC (based on Fig. 4, hereafter YMC-free CO peaks,
labeled as CO.N1/N2 and CO.S1/S2/S3 for those in the Northern and Southern
Arms, respectively), and the galaxy center, each with a 330 pc diameter. Then,
we take the pixel value at the hexagon center from the
$3.5^{\prime\prime}$-resolution moment-0 map for each line, and show their
normalized CO and C i SLED in the right panels of Fig. 4. The hexagons in the
left panels are then color-coded by their mid-$J$ excitation ${R_{42}}$. In
this way we can clearly see how gas in the apertures is excited.

The most (mid-$J$) excited aperture is YMC 29 (M4) coinciding with the
brightest CO peak in the Northern Arm, with ${R_{42}}=0.50\pm 0.01$ (and
${R_{21}}=0.92\pm 0.01$, ${R_{41}}=0.46\pm 0.01$). Its stellar age is
estimated as $\sim 3$ Myr (with a $\sim 0.4$–0.6 dex uncertainty; Whitmore et
al. subm.). The least (mid-$J$) excited aperture we analyzed is YMC 12 (M3) in
the Mid-Southwest region, with ${R_{42}}=0.24\pm 0.02$. However, its low-$J$
excitation is still quite high, with ${R_{21}}=\ 0.98\pm 0.02$. It is also
very young, with a stellar age $\sim 3$ Myr (with a similarly large
uncertainty; Whitmore et al. subm.). Other YMCs and YMC-free CO peaks have
${R_{42}}$ values in-between these two extreme cases.

Based on the motion of gas along the dust lanes and starburst ring (Figs.
1–3), the Northern Arm is upstream of the Mid-Southwest region, and the
Southern Arm is upstream of the Mid-East region. Gas enters the system first
via the Northern/Southern Arms then moves to the Mid-Southwest/Mid-East
regions, forming the starburst ring. Along the Northern Arm, gas moves from
the less-excited CO.N2 location to the highly-excited CO.N1 position. Then, in
about a quarter of the orbital time, e.g., $\sim 5$ Myr, the gas will arrive
in the Mid-Southwest region, where the CO excitation is decreasing again. It
is expected that gas will move from the Mid-Southwest region towards the
Southern Arm and possibly trigger collision and compression. Similarly,
starting from the Southern Arm, the gas moves from CO.S3 to CO.S2 and CO.S1
positions, then circles to the Mid-East region, and heads towards the Norther
Arm. The youngest YMCs are found in these possibly colliding areas, i.e., YMC
3 (J) and YMC 28 (M6, G), which both have an age $\sim 1$ Myr and are
highlighted as yellow stars in Fig. 3. 555This gas colliding scenario is
similar to the hypothesis of the formation of the youngest super star cluster
RCW 38 in the Milky Way (Fukui et al., 2016).

Fig. 5: Non-LTE LVG model fitting results for CO and C i SLEDs in hexagon
apertures (see Fig. 4) in the Northern Arm to Mid-Southwest regions (upper
panels) and Southern Arm to Mid-East regions (lower panels), respectively. The
$x$-axis is the azimuthal angle starting clockwise from the PA $=220^{\circ}$
direction, same as in Fig. 2. Dark/light green and red shadings indicate the
$\theta$ range of the corresponding regions. The $y$-axes show (from left to
right) gas volume density ($\mathrm{log}\,n_{\mathrm{H_{2}}}$), kinetic
temperature ($T_{\mathrm{kin}}$) and the
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ abundance ratio. Hexagon IDs are
indicated at the top of the left panels at their corresponding $\theta$. Error
bars are the $\pm 1\sigma$ uncertainty from the fitting (based on MICHI2; Liu
et al. 2021; see also Appendix A). We discuss the trends of decreasing
$\mathrm{log}\,n_{\mathrm{H_{2}}}$ and increasing $T_{\mathrm{kin}}$ and
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ from the upstream (dark green/red,
left part of each panel) to the downstream regions (light green/red, right
part of each panel) in Sect. 3.2.

To obtain a quantitative description of the gas excitation and
photodissociation along the starburst ring, we perform a non-local
thermodynamic (non-LTE) large velocity gradient (LVG) radiative transfer
modeling of the CO and C i SLEDs for the YMC apertures and CO peaks to
evaluate the gas density and temperature and
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ abundance ratio. We use the MICHI2
Monte Carlo fitting tool (Liu et al. 2021), with templates generated by the
RADEX software (van der Tak et al., 2007) with a grid of gas kinetic
temperature $T_{\mathrm{kin}}\sim 5\textit{--}200\ \mathrm{K}$, H2 volume
density ($\log n_{\mathrm{H_{2}}}/\mathrm{cm^{-3}}=2.0\text{--}5.0$),
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ abundance ratio 0.05–3.0, and a
fixed line turbulence FWHM ${\Delta v}=45\ \mathrm{km\,s^{-1}}$ (matching the
average CO line width of $\sigma\sim 19\ \mathrm{km\,s^{-1}}$ inferred at 30
pc resolution; Schinnerer et al. subm.; and Fig. 1), as well as a free beam
filling factor 666A fixed CO abundance per velocity gradient
$\mathrm{[CO/H_{2}]/(\mathrm{d}v/\mathrm{d}r)}=10^{-5}\
\mathrm{km^{-1}\,s\,pc}$ is also adopted (e.g. Curran et al. 2001; Weiß et al.
2007; Zhang et al. 2014; Liu et al. 2021). This leads to a non-independent CO
column density $N_{\mathrm{CO}}=\mathrm{[CO/H_{2}]}\times
n_{\mathrm{H_{2}}}\times{\Delta v}/(\mathrm{d}v/\mathrm{d}r)$ that has
reasonable values from our fitting ($\log N_{\mathrm{CO}}/\mathrm{cm^{-2}}\sim
17.5\text{--}18.7$).. We show examples of our LVG fitting to the most and
least excited YMC apertures, YMC 29 (M4) and YMC 12 (M3), respectively, in
Appendix A. We find $\log(n_{\mathrm{H_{2}}}/\mathrm{cm^{-3}})\sim
3.50^{+0.09}_{-0.11}$ and $\sim 2.80^{+0.27}_{-0.20}$, and
$T_{\mathrm{kin}}\sim 25^{+8}_{-2}$ K and $\sim 90^{+113}_{-51}$ K,
respectively. Table 2 reports the best-fit parameters and 1-$\sigma$
uncertainties for all apertures.

In Fig. 5 we present the LVG fitting results for all apertures whose CO plus C
i SLEDs are shown in Fig. 4. The fitted $\mathrm{log}\,n_{\mathrm{H_{2}}}$,
$T_{\mathrm{kin}}$ and $[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ are plotted
as functions of azimuthal angle $\theta$ (see Fig. 2). In the upper panels of
Fig. 5, $\theta$ ranges from $\sim 160^{\circ}$ to $\sim 10^{\circ}$, in
clockwise direction tracking the gas movement from the Northern Arm (dark
green shading) to the Mid-Southwest region (light green shading). Similarly,
in the lower panels of Fig. 5, $\theta$ spans $\sim 0^{\circ}$ to
$\sim-150^{\circ}$, in clockwise direction from the Southern Arm (dark red
shading) to the Mid-East region (light red shading). We find tentative trends
that $\mathrm{log}\,n_{\mathrm{H_{2}}}$ is lower, $T_{\mathrm{kin}}$ is higher
and $[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ is higher downstream the gas
flow. The $[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ ratio increases up to
$\sim 1.4$ at the Mid-Southwest YMC 13, YMC 12 (M3) and YMC 10 locations. Such
a high C i abundance relative to CO is likely due to the strong radiation
field created by the YMCs in a relatively diffuse molecular gas.

Therefore, we propose a scenario where gas arriving from the dust lanes is
piled up, compressed and shocked at the Arm regions, and YMCs are formed; then
gas and YMCs travel to the downstream region during about a quarter of the
orbital period (a few Myrs); the gas may continue forming stars (clusters) on
the way, but must undergo strong stellar feedback, so that it is heated and C
i-enriched upon its arrival in the Mid-Southwest/Mid-East regions, as our LVG
fitting results suggest.

We caution that the above picture still needs higher-resolution observational
supports. The trends are only significant in the Northern Arm to Mid-Southwest
side ($T_{\mathrm{kin}}$ increases from below $50$ K to above $100$ K and
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ increases by a factor of two). The
other side of the starburst ring from Southern Arm to Mid-East region indeed
has much weaker temperature and $[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$
variations. The variations of $n_{\mathrm{H}_{2}}$, $T_{\mathrm{kin}}$ and
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ along the ring are also highly non-
monotonous. We note that the environment in this starburst ring system is
highly dynamic and stochastic. The density of the inflow cold gas feeding the
starburst ring likely has an impact on how much the stellar feedback can
affect the natal molecular gas. The Southern Arm gas density is much higher
than that of the Northern Arm from our fitting, in line with the gas in the
Southern Arm/Mid East regions being more shielded and less affected by the
stellar feedback.

Finally, although the galaxy center hosts a Seyfert 1.5 AGN and a prominent [O
iii] ionized gas outflow (Phillips et al. 1983; Lindblad 1999; Sandqvist et
al. 1995; Hjelm & Lindblad 1996; Venturi et al. 2018; Sakamoto et al. 2007;
Gao et al. 2021), it shows only moderately excited CO and C i. As shown in the
next section, the center’s line ratios tracing CO excitation and dissociation
are consistent with other regions when correlating these line ratios with mid-
IR emission. At our resolution, we do not find any evidence of an extreme XDR
such as a highly-excited CO SLED as seen in, e.g., Mrk 231 (van der Werf et
al. 2010), NGC 1068 (Spinoglio et al. 2012), and other local ultra-luminous IR
galaxies whose global ${R_{41}}$ are highly-excited or even close to being
thermalized ($\sim 0.85\text{--}1.1$; see also Rangwala et al. 2011; Meijerink
et al. 2013; Kamenetzky et al. 2014, 2016, 2017; Glenn et al. 2015; Liu et al.
2015; Rosenberg et al. 2015; Lu et al. 2017). We observe
$I_{[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)}/I_{\mathrm{CO}\,(1\textnormal{--}0)}=0.10$
and
$I_{[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)}/I_{\mathrm{CO}\,(2\textnormal{--}1)}=0.11$
in NGC 1365’s center at 330 pc-resolution. The fitted
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ is $0.25^{+0.23}_{-0.01}$ (Table 2).
These line ratios and abundance ratio are much lower than those measured in
the more powerful AGNs in NGC 7469 (Izumi et al., 2020) and NGC 1068 (Saito et
al., 2022a, b), which have
$I_{[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)}/I_{\mathrm{CO}\,(1\textnormal{--}0)}\sim
0.5\text{--}1$ and $[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}\gtrsim 1$.

Fig. 6: Panels a) to f): $R_{42}$ in red and $R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$ in blue as functions of six variables at 330 pc resolution across the inner part of NGC 1365: a) CO(1–0) line-integrated intensity, b) velocity dispersion, c) $R_{21}$ line ratio, d) 2 ${\mu\mathrm{m}}$, e) 11.3 ${\mu\mathrm{m}}$, and f) 21 ${\mu\mathrm{m}}$ emission. Dashed lines are the best-fit trends and legends show the Spearman rank correlation coefficients, which are also reported in Table 1. Each inset upper panel shows the rms distribution of the data after subtracting the best-fit trend in bins of the horizontal-axis variable.  | $\log_{10}I_{[\mathrm{C}\tt{I}](1\text{--}0)}/I_{\mathrm{CO}(2\text{--}1)}$ | $\log_{10}I_{\mathrm{CO}(4\text{--}3)}/I_{\mathrm{CO}(2\text{--}1)}$
---|---|---
$x$ variable | $N$ | $A$ | $\rho$ | $P_{0}$ | rms | $N$ | $A$ | $\rho$ | $P_{0}$ | rms
1) $\log_{10}I_{\mathrm{CO}(1\text{--}0)}$ | $0.38$ | $-1.94$ | $0.65$ | $<0.001$ |  $0.16$ | $0.61$ | $-2.13$ | $0.74$ | $<0.001$ | $0.25$
2) $\sigma_{\mathrm{CO}(2\text{--}1),\;30\,\mathrm{pc}}$ | $0.00$ | $-1.00$ | $0.48$ | $<0.001$ |  $0.19$ | $0.01$ | $-0.65$ | $0.60$ | $<0.001$ | $0.28$
3) $\log_{10}(I_{\mathrm{CO}(2\text{--}1)}/I_{\mathrm{CO}(1\text{--}0)})$ | $1.38$ | $-0.82$ | $0.37$ | $0.001$ |  $0.18$ | $0.50$ | $-0.42$ | $0.21$ | $0.064$ | $0.30$
4) $\log_{10}I_{\mathrm{2\mu\mathrm{m}}}$ | $0.25$ | $-1.29$ | $0.79$ | $<0.001$ |  $0.15$ | $0.20$ | $-0.75$ | $0.67$ | $<0.001$ | $0.27$
5) $\log_{10}I_{\mathrm{11.3\mu\mathrm{m}}}$ | $0.26$ | $-1.56$ | $0.84$ | $<0.001$ |  $0.12$ | $0.16$ | $-0.83$ | $0.67$ | $<0.001$ | $0.26$
6) $\log_{10}I_{\mathrm{21\mu\mathrm{m}}}$ | $0.18$ | $-1.41$ | $0.83$ | $<0.001$ |  $0.13$ | $0.13$ | $-0.78$ | $0.70$ | $<0.001$ | $0.25$
Table 1: Best-fit slope $N$ and intercept $A$ of the $y=N\cdot x+A$ lines
shown in Fig. 6, where $y$ is one of the
$\log_{10}{R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}\equiv\log_{10}(I_{\mathrm{[C{\tt{I}}](1\text{--}0)}}/I_{\mathrm{CO(2\text{--}1)}})$
and
$\log_{10}{R_{42}}\equiv\log_{10}(I_{\mathrm{CO(4\text{--}3)}}/I_{\mathrm{CO(2\text{--}1)}})$
line ratios, and $x$ is one of the variables to correlate with: 1) the CO(1–0)
integrated intensity $\log_{10}I_{\mathrm{CO(1\text{--}0)}}$; 2) the high-
resolution ($\sim 30$ pc) CO(2–1) moment-2 map, convolved to the
$3.5^{\prime\prime}$ ($\sim 330$ pc) resolution
$\sigma_{\mathrm{CO(2\text{--}1)},\;30\,\mathrm{pc}}$; 3) the low-$J$ CO line
ratio $\log_{10}(I_{\mathrm{CO(2\text{--}1)}}/I_{\mathrm{CO(1\text{--}0)}})$;
4) the stellar continuum dominated 2 $\mu\mathrm{m}$ emission
$\log_{10}I_{\mathrm{2\mu\mathrm{m}}}$; 5) the PAH dominated 11.3
$\mu\mathrm{m}$ emission $\log_{10}I_{\mathrm{11.3\mu\mathrm{m}}}$; and 6) the
dust continuum dominated 21 $\mu\mathrm{m}$ emission
$\log_{10}I_{\mathrm{21\mu\mathrm{m}}}$. For each of
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ and ${R_{42}}$, we list five
fitting result parameters: the best-fit slope $N$, the intercept $A$, the
Spearman correlation coefficient $\rho$, the null hypothesis probability
$P_{0}$, and the rms scatter of data points after subtracting the best-fit
line. See Sect. 3.3 for details.

###  3.3 Correlations of CO and C i line ratios

We investigate what star formation and ISM properties correlate with the CO
and C i line ratios in Fig. 6. We examine CO(1–0) line-integrated intensity
($I_{\mathrm{CO}\,(1\textnormal{--}0)}$), molecular gas velocity dispersion
($\sigma_{\mathrm{CO(2\text{--}1),\,30~{}pc}}$ 777For the molecular gas
velocity dispersion, we use the native resolution CO(2–1) equivalent width
(ew) map (Schinnerer et al., subm.) then compute the average in apertures with
size equaling the common resolution, so as to trace the velocity dispersion at
$\sim 30$ pc.), $R_{21}$, 21 ${\mu\mathrm{m}}$, PAH-dominated 11.3
${\mu\mathrm{m}}$, and stellar continuum dominated 2 ${\mu\mathrm{m}}$
intensities, all at PSF-matched $3.5^{\prime\prime}$ ($\sim 330$ pc)
resolution and sampled in independent resolution units (by binning in hexagons
with diameter equaling the beam FWHM $3.5^{\prime\prime}$ then taking the
aperture center value). For each pair of variables, we perform a linear
fitting in log-log space with the scipy.optimize.curve_fit code, including
errors on the line ratio propagated the original moment and uncertainty maps
(Sect. 2.2). We obtain a best-fit slope $N$ and intercept $A$ for each fit and
calculate the rms of the data points around the best-fitting line. We also
calculate the Spearman correlation coefficient, $\rho$, and null hypothesis
probability, $P_{0}$, using the pingouin code. The resulting parameters are
summarized in Table 1.

The properties that correlate the most strongly with $R_{42}$ and
$R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$ are the PAH-dominated 11.3
${\mu\mathrm{m}}$, the dust continuum dominated 21 ${\mu\mathrm{m}}$ and the
stellar dominated 2 ${\mu\mathrm{m}}$ emission, with $\rho>0.7$. The
$I_{\mathrm{CO}\,(1\textnormal{--}0)}$ is the next strongly correlated
variable. The velocity dispersion,
$\sigma_{\mathrm{CO(2\text{--}1),\,30~{}pc}}$, and ${R_{21}}$ show weak or no
correlation, with $\rho\lesssim 0.3$.

For each scatter plot panel in Fig. 6, we show the rms distribution of the
data in bins of the horizontal-axis variable. In all cases (except for
${R_{21}}$, panel $c$) the rms is higher at lower $x$-axis values. For all
variables except $I_{\mathrm{CO}\,(1\textnormal{--}0)}$ (panel $a$), $R_{42}$
and $R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$ tend to lie below the fitted line
at the faint end. In regions with low CO intensities, the CO(4–3) line can
still be as highly excited as CO-brightest regions, despite a factor of $\sim
10$ weaker CO(1–0) emission. This may be surprising if the CO(1–0) emission
indeed indicates lower gas surface density and perhaps volume density, but
these regions might also simply show low CO(1–0) at 330 pc resolution because
of a low area filling fraction. Obtaining higher-resolution high-$J$ CO and C
i observations is critical to understanding the scenarios in the future.

In panel $b)$ of Fig. 6, we find no correlations of ${R_{42}}$ or
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ versus $\sigma_{\mathrm{CO}}$, with
slope $\sim 0$. This indicates that CO excitation and C i enrichment correlate
more strongly with radiation properties than with gas dynamics in this
starburst ring. Indeed, in Fig. 1 (g), we find a peak
$\sigma_{\mathrm{CO}}\sim 50\;\mathrm{km\,s^{-1}}$ at the Southern Arm,
whereas the Northern Arm with the strongest star formation and most numerous
YMCs has nearly half that value, i.e., $\sigma_{\mathrm{CO}}\sim
20\text{--}30\;\mathrm{km\,s^{-1}}$. Schinnerer et al. (subm.) find that the
CO emission in this system is usually composed of multiple (e.g. 2–4) line-of-
sight velocity components, with individual component having a similar line
width $\sigma\sim 19\;\mathrm{km\,s^{-1}}$. Therefore, this geometry effect
may well blend out any $\sigma_{\mathrm{CO}}$ versus line ratios trends in
this study.

In panel $c)$ of Fig. 6, the poor correlation between $R_{21}$ and $R_{42}$ at
our $\sim 330$ pc resolution indicates that the low-$J$ and mid-$J$ CO SLED
shapes are largely decoupled. ${R_{21}}$ is mostly saturated/thermalized in
environments like the center of NGC 1365. It is therefore necessary to obtain
higher-$J$ CO lines to trace the CO excitation.

The stellar dominated 2 $\mu\mathrm{m}$, PAH-dominated 11.3 $\mu\mathrm{m}$,
and warm dust continuum dominated 21 $\mu\mathrm{m}$ emission all show tight,
positive correlations with the line ratios as seen in panels $d)$ to $f)$ of
Fig. 6. These correlations are robust (i.e., tighter than about 0.2 dex) in
the range of $10\lesssim
I_{2\,{\mu\mathrm{m}}}/[\mathrm{MJy\,sr^{-1}}]\lesssim 80$, $20\lesssim
I_{11.3\,{\mu\mathrm{m}}}/[\mathrm{MJy\,sr^{-1}}]\lesssim 1000$, and
$20\lesssim I_{21\,{\mu\mathrm{m}}}/[\mathrm{MJy\,sr^{-1}}]\lesssim 2000$,
respectively. The 2 $\mu\mathrm{m}$ correlation has the smallest valid range,
only less than a decade, whereas the dust correlations are valid over nearly
two decades. The galaxy center and its surrounding apertures are outliers in
the line ratio versus $I_{2\,{\mu\mathrm{m}}}$ plot even at our $\sim 330$ pc
resolution, but not for the line ratios versus PAH or dust continuum. We
caution that the statistics is based on only one starburst ring system at a
coarse resolution. Larger-sample studies will be critical to deeper
understanding of the statistics.

Comparing the trends in $R_{42}$ to those in
$R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$, we find similar correlations
relating each line ratio to the other variables. The trends with
$R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}$ do tend to be tighter, with scatter
about $\sim 0.05$–0.1 dex smaller than we find for $R_{42}$. This likely
relates to the fact that $[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)$
has a $>30\times$ lower critical density and $2\times$ lower upper level
energy temperature ($E_{u}$) than CO(4–3) (e.g., Crocker et al., 2019, Table
3). This makes $[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)$ more
sensitive to the temperature and low-density part of the medium, which is
substantially affected by the stellar feedback from embedded star formation
traced by the YMCs, PAH emission, and warm dust continuum.

##  4 Summary

In this Letter we use multi-$J$ CO and C i line ratios to trace the CO
excitation and dissociation and infer molecular gas temperature, density and
feedback under the impact of YMCs in the bar-fed starbursting ring of NGC
1365. The mid-$J$ CO SLED up to CO(4–3), and the
$[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)$ line, together with the
distribution of young ($<10\ \mathrm{Myr}$), massive ($M_{\star}\gtrsim
10^{6}\ \mathrm{M_{\odot}}$) star clusters revealed by JWST allow us to infer
how the molecular gas properties are impacted by stellar feedback from YMCs as
the gas enters and circulates in the starburst ring. We summarize our findings
below.

  * •

The Northern and Southern Arms have a high molecular gas density, relatively
low temperature and $[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ abundance ratio,
with observed line ratios ${R_{21}}\sim 0.8\text{--}1$, ${R_{42}}\sim
0.45\text{--}0.51$ and ${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}\sim
0.1\text{--}0.2$. These are in line with the scenario where the Northern and
Southern Arm regions are the locations where molecular gas flows into the
starburst ring along the bar and dust lanes. Bar-induced shocks may play a key
role in affecting the gas there, but further observational support is needed.

  * •

The molecular gas in the Mid-Southwest region seems largely impacted by the
stellar feedback (i.e., low ${R_{42}}$ but high ${R_{21}}$ and
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$), exhibiting a low gas density
($\log(n_{\mathrm{H}_{2}}/\mathrm{cm^{-3}})\sim 2.9$), high temperature ($\sim
100$ K) and enhanced $[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ abundance ratio
($\gtrsim 1$) compared to the upstream Northern Arm
($\log(n_{\mathrm{H}_{2}}/\mathrm{cm^{-3}})\sim 3.4$, $T_{\mathrm{kin}}\sim
40$ K and $[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}\sim 0.7$) as inferred from
our LVG fitting.

  * •

The molecular gas in the Mid-East region exhibits both a high ${R_{42}}$ and
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$, possibly due to its much higher
density than that of the Mid-Southwest region and thus less impacted by the
stellar feedback. Our LVG fitting infer that there is only a moderate decrease
in gas density ($\log(n_{\mathrm{H}_{2}}/\mathrm{cm^{-3}})\sim 3.4$) or weak
increase in temperature ($\sim 25$ K) and
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ ($\sim 0.5$) compared to the
upstream Southern Arm region ($\log(n_{\mathrm{H}_{2}}/\mathrm{cm^{-3}})\sim
4.0$, $T_{\mathrm{kin}}\sim 15$ K and
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}\sim 0.2$).

  * •

Through a correlation analysis, we find that the mid-$J$ CO excitation
${R_{42}}$ or the CO dissociation tracer
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ does not obviously correlate with
the low-$J$ CO excitation ${R_{21}}$, likely because the ${R_{21}}$ shows high
ratios and appears nearly thermalized across the whole region. We also find
little correlation between the line ratios and the apparent CO line velocity
dispersion, implying that the complex gas dynamics does not affect the CO
excitation and photodissociation in the starburst ring.

  * •

We find tightest correlations between ${R_{42}}$ or
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ and the mid-IR PAH-dominated 11.3
$\mu\mathrm{m}$ and dust continuum dominated 21 $\mu\mathrm{m}$ emission
($\rho\sim 0.67$–0.84, $\mathrm{rms}\sim 0.12$–0.27 dex). The stellar
continuum dominated 2 $\mu\mathrm{m}$ emission correlates with ${R_{42}}$ and
${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ well too ($\rho\sim 0.67$–0.79,
$\mathrm{rms}\sim 0.15$–0.27 dex) but the very center does not follow the
trend.

  * •

The ${R_{\mathrm{C}\text{\sc{i}}\mathrm{CO}}}$ correlations with mid-IR
dust/PAH and near-IR stellar emission properties are in general slightly
tighter ($\sim 0.1$ higher in $\rho$) and less scattered ($\sim-0.5$ dex
smaller rms) than those of ${R_{42}}$. This may relate to the significantly
lower critical density of $[\mathrm{C}\,{\text{\sc{i}}}]\,(1\textnormal{--}0)$
than $\mathrm{CO}\,(4\textnormal{--}3)$ and to CO dissociation which make C i
more sensitive to the mid-IR traced bulk of star-forming gas and stellar
feedback.

  * •

Despite hosting an Seyfert 1.5 AGN and having an ionized gas outflow, NGC
1365’s central $\sim 330$ pc area (our resolution unit) exhibits only moderate
CO excitation and C i/CO line ratio comparable to or even less highly excited
than other regions that we studied.

##  Appendix A LVG model fitting

We illustrate our Monte Carlo LVG model fitting in Fig. A.1. We first use
RADEX (van der Tak et al., 2007) with the Leiden Atomic and Molecular Database
(Schöier et al., 2005) to build a library of LVG models with the parameter
grids as described in Sect. 3.2. Then, we use the MICHI2 code (Liu et al.,
2021) to run Monte Carlo fitting and obtain the $1/\chi^{2}$ posterior
distribution for each parameter (following the statistical criterion of $\pm
1\sigma$ in Press et al. 1992). Blue squares with error bars are the CO and C
i line fluxes to be fitted, and black to gray dots are model data points with
different reduced $\chi^{2}$. Our free model parameters are
$\mathrm{log}\,n_{\mathrm{H_{2}}}$, $T_{\mathrm{kin}}$,
$[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$, and normalization (beam filling
factor). Their $1/\chi^{2}$ distributions and the $\pm 1\sigma$ ranges are
shown in the lower panels. All fitting results are presented in Table 2.

Fig. A.1: Upper row: the CO and C i SLED of YMC 29 (M4, the most excited YMC aperture in the Northern Arm; left panel) and that of YMC 12 (M3, the least excited YMC aperture in the Mid-Southwest region; right panel). Observed line fluxes are shown as blue squares with error bars. Black to gray solid circles are fitted points from a series of fitting within $1\sigma$ with an increasing $\chi^{2}$ (and reduced $\chi^{2}$, $\chi_{r}^{2}$). Bottom panels: corresponding $1/\chi^{2}$ distributions of model fitting parameters $T_{\mathrm{kin}}$, $\mathrm{log}\,n_{\mathrm{H_{2}}}$, $\log N_{\mathrm{H_{2}}}$ (non-independent) and $[\mathrm{C}{\text{\sc{i}}/\mathrm{CO}]}$ from the MICHI2 code. Yellow shading indicates the $\pm 1\sigma$ parameter range.  Aperture | RA (J2000) | DEC (J2000) | $\log n_{\mathrm{H_{2}}}/\mathrm{cm^{-3}}$ | $\log N_{\mathrm{H_{2}}}/\mathrm{cm^{-2}}$ | $T_{\mathrm{kin}}/\mathrm{K}$ | $[\mathrm{C}\text{\sc{i}}/\mathrm{CO}]$
---|---|---|---|---|---|---
Northern Arm |  |  |  |  |  |
CO.N2 | $53.40340917$ | $-36.13729972$ | $3.20_{-0.12}^{+0.25}$ | $22.44_{-0.12}^{+0.26}$ | $25.0_{-11.2}^{+8.0}$ | $0.60_{-0.25}^{+0.13}$
36 | $53.40311543$ | $-36.13715197$ | $2.70_{-0.02}^{+0.35}$ | $21.94_{-0.01}^{+0.36}$ | $155.0_{-110.0}^{+12.9}$ | $1.00_{-0.31}^{+0.09}$
35 | $53.40306629$ | $-36.13749402$ | $3.30_{-0.26}^{+0.09}$ | $22.54_{-0.25}^{+0.06}$ | $25.0_{-2.3}^{+24.7}$ | $0.60_{-0.03}^{+0.40}$
33,M5 | $53.40251420$ | $-36.13768031$ | $3.30_{-0.13}^{+0.09}$ | $22.54_{-0.16}^{+0.06}$ | $35.0_{-3.4}^{+13.0}$ | $0.80_{-0.08}^{+0.16}$
30 | $53.40098220$ | $-36.13841668$ | $3.30_{-0.17}^{+0.09}$ | $22.54_{-0.16}^{+0.06}$ | $35.0_{-3.4}^{+18.0}$ | $0.70_{-0.04}^{+0.29}$
29,M4 | $53.40170236$ | $-36.13843398$ | $3.50_{-0.11}^{+0.09}$ | $22.74_{-0.16}^{+0.07}$ | $25.0_{-2.3}^{+8.0}$ | $0.50_{-0.02}^{+0.23}$
28,M6 | $53.40318107$ | $-36.13847524$ | $3.60_{-0.25}^{+0.09}$ | $22.84_{-0.20}^{+0.07}$ | $15.0_{-1.2}^{+12.9}$ | $0.30_{-0.03}^{+0.36}$
25 | $53.40092801$ | $-36.13910029$ | $3.40_{-0.08}^{+0.10}$ | $22.64_{-0.09}^{+0.04}$ | $20.0_{-3.1}^{+2.9}$ | $0.40_{-0.04}^{+0.02}$
CO.N1 | $53.40132208$ | $-36.13871556$ | $3.40_{-0.05}^{+0.14}$ | $22.64_{-0.06}^{+0.17}$ | $30.0_{-10.2}^{+3.0}$ | $0.60_{-0.20}^{+0.06}$
Mid-Southwest Region |  |  |  |  |  |
22 | $53.40046102$ | $-36.13984982$ | $3.30_{-0.03}^{+0.02}$ | $22.54_{-0.06}^{+0.01}$ | $20.0_{-3.1}^{+2.9}$ | $0.45_{-0.03}^{+0.03}$
19 | $53.39952417$ | $-36.14009082$ | $2.60_{-0.01}^{+0.85}$ | $21.84_{+0.00}^{+0.87}$ | $195.0_{-180.0}^{+7.9}$ | $1.00_{-0.70}^{+0.09}$
12,M3 | $53.39955255$ | $-36.14112108$ | $2.80_{-0.20}^{+0.27}$ | $22.04_{-0.20}^{+0.30}$ | $90.0_{-50.6}^{+112.9}$ | $1.00_{-0.25}^{+0.31}$
11 | $53.39977124$ | $-36.14112797$ | $2.70_{-0.02}^{+0.35}$ | $21.94_{-0.01}^{+0.36}$ | $175.0_{-125.8}^{+17.9}$ | $1.25_{-0.35}^{+0.12}$
9 | $53.40018429$ | $-36.14131523$ | $2.70_{-0.02}^{+0.39}$ | $21.94_{-0.08}^{+0.36}$ | $180.0_{-130.8}^{+17.9}$ | $1.25_{-0.41}^{+0.15}$
7,M2 | $53.39987072$ | $-36.14183303$ | $3.10_{-0.42}^{+0.09}$ | $22.34_{-0.41}^{+0.06}$ | $35.0_{-3.4}^{+157.9}$ | $0.70_{-0.07}^{+0.58}$
5 | $53.40033806$ | $-36.14207205$ | $3.30_{-0.26}^{+0.04}$ | $22.54_{-0.30}^{+0.06}$ | $20.0_{-0.2}^{+17.4}$ | $0.40_{-0.01}^{+0.30}$
3,J | $53.40069177$ | $-36.14212741$ | $3.40_{-0.08}^{+0.05}$ | $22.64_{-0.09}^{+0.04}$ | $15.0_{-4.0}^{+4.9}$ | $0.30_{-0.03}^{+0.03}$
Mid-East Region |  |  |  |  |  |
23 | $53.40337423$ | $-36.13956883$ | $3.30_{-0.04}^{+0.35}$ | $22.54_{-0.03}^{+0.36}$ | $30.0_{-16.1}^{+3.0}$ | $0.60_{-0.36}^{+0.06}$
21 | $53.40333174$ | $-36.13986047$ | $3.40_{-0.10}^{+0.14}$ | $22.64_{-0.06}^{+0.17}$ | $25.0_{-5.2}^{+2.9}$ | $0.45_{-0.12}^{+0.14}$
18 | $53.40339461$ | $-36.14021144$ | $3.60_{-0.25}^{+0.05}$ | $22.84_{-0.20}^{+0.07}$ | $15.0_{-1.2}^{+12.9}$ | $0.25_{-0.03}^{+0.23}$
16 | $53.40291154$ | $-36.14045529$ | $3.40_{-0.05}^{+0.14}$ | $22.64_{-0.06}^{+0.17}$ | $25.0_{-5.2}^{+4.7}$ | $0.45_{-0.15}^{+0.05}$
15 | $53.40321229$ | $-36.14061030$ | $3.50_{-0.06}^{+0.14}$ | $22.74_{-0.05}^{+0.16}$ | $20.0_{-5.0}^{+4.7}$ | $0.30_{-0.10}^{+0.05}$
13 | $53.40293504$ | $-36.14082502$ | $3.50_{-0.11}^{+0.09}$ | $22.74_{-0.10}^{+0.07}$ | $20.0_{-3.2}^{+7.9}$ | $0.30_{+0.00}^{+0.18}$
10 | $53.40283403$ | $-36.14127466$ | $3.60_{-0.23}^{+0.05}$ | $22.84_{-0.25}^{+0.07}$ | $15.0_{-1.2}^{+14.7}$ | $0.20_{+0.00}^{+0.30}$
Southern Arm |  |  |  |  |  |
1 | $53.40028097$ | $-36.14257775$ | $3.50_{-0.05}^{+0.05}$ | $22.74_{-0.06}^{+0.00}$ | $15.0_{-1.1}^{+4.9}$ | $0.25_{-0.01}^{+0.02}$
2 | $53.39989135$ | $-36.14257526$ | $3.50_{-0.11}^{+0.04}$ | $22.74_{-0.10}^{+0.07}$ | $15.0_{-1.2}^{+7.9}$ | $0.25_{-0.01}^{+0.13}$
CO.S1 | $53.39917000$ | $-36.14308806$ | $4.10_{-0.01}^{+0.04}$ | $23.34_{-0.01}^{+0.06}$ | $10.0_{-2.0}^{+3.9}$ | $0.05_{-0.02}^{+0.01}$
CO.S2 | $53.39845708$ | $-36.14325417$ | $4.00_{-0.05}^{+0.05}$ | $23.24_{-0.04}^{+0.03}$ | $10.0_{-2.0}^{+1.0}$ | $0.05_{-0.02}^{+0.01}$
CO.S3 | $53.39761333$ | $-36.14309889$ | $3.50_{-0.09}^{+0.05}$ | $22.74_{-0.06}^{+0.00}$ | $15.0_{-1.1}^{+4.9}$ | $0.15_{-0.03}^{+0.03}$
Center |  |  |  |  |  |
Center | $53.40154167$ | $-36.14041694$ | $3.50_{-0.24}^{+0.04}$ | $22.74_{-0.23}^{+0.07}$ | $15.0_{-1.2}^{+12.9}$ | $0.25_{-0.01}^{+0.23}$
Table 2: Results of MICHI2 LVG fitting to the CO and C i SLED of YMC, CO peak
and galaxy center apertures. YMC IDs and R.A. and Declination coordinates are
from Whitmore et al. (subm.). See description of the fitting in Sect. 3.2. See
also Fig. 5 for the illustration of the fitted parameters along the starburst
ring.

## Acknowledgments

We thank the anonymous referee for very helpful comments. This work was
carried out as part of the PHANGS collaboration. This work is based on
observations made with the NASA/ESA/CSA JWST and NASA/ESA Hubble Space
Telescopes. The data were obtained from the Mikulski Archive for Space
Telescopes at the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5-03127 for JWST and NASA contract NAS 5-26555 for HST. The JWST
observations are associated with program 2107, and those from HST with program
15454.

Some of the data presented in this paper were obtained from the Mikulski
Archive for Space Telescopes (MAST) at the Space Telescope Science Institute.
The specific observations analyzed can be accessed via:
http://dx.doi.org/10.17909/9bdf-jn24 (catalog PHANGS-JWST observations),
https://doi.org/10.17909/t9-r08f-dq31 (catalog PHANGS-HST image products) and
https://doi.org/10.17909/jray-9798 (catalog PHANGS-HST catalog products).

This Letter makes use of the following ALMA data: ADS/JAO.ALMA#2019.1.01635.S,
ADS/JAO.ALMA#2013.1.01161.S, ADS/JAO.ALMA#2015.1.01135.S,
ADS/JAO.ALMA#2017.1.00129.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.

AKL gratefully acknowledges support by grants 1653300 and 2205628 from the
National Science Foundation, by award JWST-GO-02107.009-A, and by a Humboldt
Research Award from the Alexander von Humboldt Foundation. AU acknowledges
support from the Spanish grants PGC2018-094671-B-I00, funded by
MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, and
PID2019-108765GB-I00, funded by MCIN/AEI/10.13039/501100011033. ER
acknowledges the support of the Natural Sciences and Engineering Research
Council of Canada (NSERC), funding reference number RGPIN-2022-03499. JMDK
gratefully acknowledges funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme via the
ERC Starting Grant MUSTANG (grant agreement number 714907). COOL Research DAO
is a Decentralized Autonomous Organization supporting research in astrophysics
aimed at uncovering our cosmic origins. MC gratefully acknowledges funding
from the DFG through an Emmy Noether Research Group (grant number CH2137/1-1).
SCOG, RSK, EJW acknowledge funding provided by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID
138713538 – SFB 881 (“The Milky Way System”, subprojects A1, B1, B2, B8, and
P2). JS acknowledges support by the Natural Sciences and Engineering Research
Council of Canada (NSERC) through a Canadian Institute for Theoretical
Astrophysics (CITA) National Fellowship. FB and JdB would like to acknowledge
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (grant agreement
No.726384/Empire). KG is supported by the Australian Research Council through
the Discovery Early Career Researcher Award (DECRA) Fellowship DE220100766
funded by the Australian Government. KG is supported by the Australian
Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions
(ASTRO 3D), through project number CE170100013. HAP acknowledges support by
the National Science and Technology Council of Taiwan under grant
110-2112-M-032-020-MY3. RSK acknowledges financial support from the European
Research Council via the ERC Synergy Grant “ECOGAL” (project ID 855130), from
the Heidelberg Cluster of Excellence (EXC 2181 - 390900948) “STRUCTURES”,
funded by the German Excellence Strategy, and from the German Ministry for
Economic Affairs and Climate Action in project “MAINN” (funding ID 50OO2206).
SD is supported by funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (grant
agreement no. 101018897 CosmicExplorer). OE gratefully acknowledge funding
from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in
the form of an Emmy Noether Research Group (grant number KR4598/2-1, PI
Kreckel). JP acknowledges support by the DAOISM grant ANR-21-CE31-0010 and by
the Programme National “Physique et Chimie du Milieu Interstellaire” (PCMI) of
CNRS/INSU with INC/INP, co-funded by CEA and CNES. TGW acknowledges funding
from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement No. 694343). SKS
acknowledges financial support from the German Research Foundation (DFG) via
Sino-German research grant SCHI 536/11-1.

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