# ALMA-LEGUS I: The Influence of Galaxy Morphology on Molecular Cloud
Properties

Molly K. Finn Department of Astronomy, University of Virginia,
Charlottesville, VA 22904, USA  Kelsey E. Johnson Department of Astronomy,
University of Virginia, Charlottesville, VA 22904, USA  Remy Indebetouw
Department of Astronomy, University of Virginia, Charlottesville, VA 22904,
USA  National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville,
VA 22903, USA  Allison H. Costa National Radio Astronomy Observatory, 520
Edgemont Road, Charlottesville, VA 22903, USA  Angela Adamo  Department of
Astronomy, The Oskar Klein Centre, Stockholm University, SE-106 91 Stockholm,
Sweden  Alessandra Aloisi Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD 21218, USA  Lauren Bittle Independent Researcher  Daniela
Calzetti Department of Astronomy, University of Massachusetts Amherst, 710
North Pleasant Street, Amherst, MA 01003, USA  Daniel A. Dale Department of
Physics & Astronomy, University of Wyoming, Laramie, WY 82071  Clare L. Dobbs
School of Physics and Astronomy, University of Exeter, Stocker Road, Exeter,
EX4 4QL, UK  Jennifer Donovan Meyer National Radio Astronomy Observatory, 520
Edgemont Road, Charlottesville, VA 22903, USA  Bruce G. Elmegreen IBM Research
Division, T. J. Watson Research Center, 1101 Kitchawan Road, Yorktown Heights,
NY 10598, USA  Debra M. Elmegreen Department of Physics and Astronomy, Vassar
College, Poughkeepsie, NY 12604, USA  Michele Fumagalli Dipartimento di Fisica
G. Occhialini, Università degli Studi di Milano Bicocca, Piazza della Scienza
3, 20126 Milano, Italy  INAF – Osservatorio Astronomico di Trieste, via G. B.
Tiepolo 11, I-34143 Trieste, Italy  J. S. Gallagher Department of Astronomy,
University of Wisconsin-Madison
475 North Charter St., Madison, WI 53706  Department of Physics and Astronomy,
Macalester College, 1600 Grand Ave. , St. Paul, MN 55105  Kathryn Grasha
Research School of Astronomy and Astrophysics, Australian National University,
Cotter Rd., Weston ACT 2612, Australia  ARC Centre of Excellence for
Astrophysics in 3D (ASTRO-3D), Canberra ACT 2600, Australia  Visiting Fellow,
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA
02138, USA  Eva K. Grebel Astronomisches Rechen-Institut, Zentrum für
Astronomie der Universität Heidelberg, Mönchhofstr. 12–14, 69120 Heidelberg,
Germany  Robert C. Kennicutt Steward Observatory, University of Arizona,
Tucson, AZ 85719, USA  George P. and Cynthia W. Mitchell Institute for
Fundamental Physics and Astronomy, Texas A&M University, College Station, TX
77845, USA  Mark R. Krumholz Research School of Astronomy and Astrophysics,
Australian National University, Cotter Rd., Weston ACT 2612, Australia  ARC
Centre of Excellence for Astrophysics in 3D (ASTRO-3D), Canberra ACT 2600,
Australia  Janice C. Lee Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD 21218, USA  Matteo Messa Observatoire de Genéve,
Université de Genève, Versoix, Switzerland  The Oskar Klein Centre, Department
of Astronomy, Stockholm University, AlbaNova, SE-10691 Stockholm, Sweden
Preethi Nair Department of Physics and Astronomy, The University of Alabama,
Tuscaloosa, AL 35487, USA  Elena Sabbi Space Telescope Science Institute, 3700
San Martin Drive, Baltimore, MD 21218, USA  Linda J. Smith Space Telescope
Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, 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  Aida Wofford
Instituto de Astronomía, Universidad Nacional Autónoma de México, Unidad
Académica en Ensenada, Km 103 Carr. Tijuana$-$Ensenada, Ensenada, B.C., C.P.
22860, México

###### Abstract

We present a comparative study of the molecular gas in two galaxies from the
LEGUS sample: barred spiral NGC 1313 and flocculent spiral NGC 7793. These two
galaxies have similar masses, metallicities, and star formation rates, but NGC
1313 is forming significantly more massive star clusters than NGC 7793,
especially young massive clusters ($<10$ Myr, $>10^{4}$ M⊙). Using ALMA
CO(2-1) observations of the two galaxies with the same sensitivities and
resolutions of 13 pc, we directly compare the molecular gas in these two
similar galaxies to determine the physical conditions responsible for their
large disparity in cluster formation. By fitting size-linewidth relations for
the clouds in each galaxy, we find that NGC 1313 has a higher intercept than
NGC 7793, implying that its clouds have higher kinetic energies at a given
size scale. NGC 1313 also has more clouds near virial equilibrium than NGC
7793, which may be connected to its higher rate of massive cluster formation.
However, these virially bound clouds do not show a stronger correlation with
young clusters than that of the general cloud population. We find surprisingly
small differences between the distributions of molecular cloud populations in
the two galaxies, though the largest of those differences are that NGC 1313
has higher surface densities and lower free-fall times.

star formation; ALMA; spiral galaxies

††software: Pipeline-CASA51-P2-B v.40896 (Davis, 2024), CASA (v.5.1.1-5,
v.5.6.1; McMullin et al., 2007), astrodendro (Rosolowsky et al., 2008),
quickclump (Sidorin, 2017), Astropy (Astropy Collaboration et al., 2013),
Matplotlib (Hunter, 2007), NumPy (Harris et al., 2020), SciPy (Virtanen et
al., 2020),

##  1 Introduction

Figure 1: _Top:_ Hubble Space Telescope images of NGC 1313 (left) and NGC 7793
(right) using filters F814W (red), F555W (green), and F336W (blue) from the
LEGUS survey. Overplotted are the ALMA CO(2-1) observation footprints.
_Bottom:_ Positions of clusters identified in the LEGUS catalogs (methodology
described by Adamo et al. (2017)), colored by age with clusters younger than
10 Myr in cyan, 10-50 Myr in green, and 50-300 Myr in yellow, plotted overtop
the DSS2-red images. Clusters that are more massive than $10^{4}M_{\odot}$ are
outlined in red. NGC 1313 has significantly more star clusters overall than
NGC 7793, even after accounting for their differing SFRs, and especially has
more red-outlined massive star clusters, both by number and by fraction of the
total cluster mass.

At low redshifts, the majority of star formation takes place in spiral
galaxies (Brinchmann et al., 2004). This means that to understand star
formation in the local universe, we need to understand the influence of spiral
structure on the physical conditions of the molecular gas and the processes by
which that gas is converted into stars.

There have been several studies that have examined the molecular gas
properties traced by CO in nearby spiral galaxies. Some examples of these
studies include PAWS (PdBI Arcsecond Whirlpool Survey), which mapped M51 in
CO(1-0) at 40 pc resolution (Schinnerer et al., 2013), CANON (CArma and
NObeyama Nearby galaxies), which mapped the inner disks of nearby spiral
galaxies in CO(1-0) and enabled a focused study of a subsample at 62-78 pc
resolution (Donovan Meyer et al., 2013), and the barred spiral galaxy M83 was
mapped in CO(1-0) at 40 pc resolution (Koda et al., 2023). These three studies
focused primarily on galaxies with strong spiral arms rather than flocculent
spirals.

PHANGS-ALMA (Physics at High Angular resolution in Nearby Galaxies) expanded
the type of galaxies included, mapping 90 galaxies in CO(2-1) at $\sim 100$ pc
resolution (Leroy et al., 2021), including galaxies with a wide range of
morphologies. Comparing the galaxies in their sample by morphology type,
Stuber et al. (2023) found that the flocculent spirals tended to have lower
total stellar masses and star formation rates than galaxies with stronger
spiral patterns. Meanwhile Hart et al. (2017) found that in a sample of spiral
galaxies from the Sloan Digital Sky Survey, galaxies with two strong spiral
arms had similar star formation rates but higher efficiency in converting
their gas to stars than galaxies with many flocculent spiral arms. While
studies have examined how the cloud properties of spiral galaxies vary between
the disks, centers, arms, and interarm regions (e.g. Koda et al., 2009;
Rosolowsky et al., 2008; Colombo et al., 2014; Sun et al., 2018, 2020;
Rosolowsky et al., 2021; Querejeta et al., 2021; Koda et al., 2023), a more
detailed examination of how the cloud properties vary between galaxies of
different morphologies is not yet available.

Table 1: Properties of NGC 1313 and NGC 7793

Galaxy | Distancea | Metallicityb | SFRc | M${}_{*}^{d}$ | M${}_{\text{HI}}^{e}$ | M${}_{\text{mol}}^{f}$ | M${}_{\text{cluster}}^{g}$
---|---|---|---|---|---|---|---
| (Mpc) | ($12+\log(\text{O/H})$) | (M⊙/yr) | ($\times 10^{9}$ M⊙) | ($\times 10^{9}$ M⊙) | ($\times 10^{6}$ M⊙) | ($\times 10^{6}$ M⊙)
NGC 1313 | 4.6 | 8.4 | 1.15 | 2.6 | 2.1 | 7.6f | 17.3g
NGC 7793 | 3.7 | 8.52 | 0.52 | 3.2 | 0.78 | 14.0f | 6.4g

Notes: a Qing et al. (2015), Gao et al. (2016) for NGC 1313; Radburn-Smith et
al. (2011), Sabbi et al. (2018) for NGC 7793,
b Walsh & Roy (1997) and Stanghellini et al. (2015),
c Calculated by Calzetti et al. (2015) using GALEX far-UV images, dust
corrected with methods of Lee et al. (2009),
d Calculated by Calzetti et al. (2015) using extinction-corrected $B$-band
luminosities and methods of Bothwell et al. (2009),
e Calculated by Calzetti et al. (2015) using HI observations from Koribalski
et al. (2004),
f Sum of all CO(2-1) emission, multiplied by an average $X_{\text{CO}}$ and
factor of 1.4 for each galaxy as discussed in Section 5, does not cover full
galaxies due to smaller observational footprint and is likely missing flux
because 7m and TP data are not included here,
g Total mass of star clusters in LEGUS catalogs, based on methods of Adamo et
al. (2017), does not cover full galaxies.

To better understand the role of galaxy morphology on molecular gas conditions
on the scale of individual clouds and how it relates to star formation, we
present a comparative study of the molecular gas in two spiral galaxies: NGC
1313 and NGC 7793 (Figure 1). These two galaxies are included in the Legacy
ExtraGalactic UV Survey (LEGUS; Calzetti et al., 2015), a Hubble Space
Telescope (HST) Treasury Program that observed 50 nearby ($<12$ Mpc) galaxies.
As part of the LEGUS survey, they both have comprehensive catalogs of their
young star clusters and their masses and ages using the methodology described
in Adamo et al. (2017), which allows us to compare the star-forming properties
of each galaxy with the molecular gas at scales of $\sim 10$ pc.

NGC 1313 and NGC 7793 were chosen because they have many similar properties,
such as their total stellar mass ($2.6\times 10^{9}$ and $3.2\times 10^{9}$
M⊙; Calzetti et al., 2015), their overall metallicities
($12+\log(\text{O/H})=$ 8.4 and 8.52; Walsh & Roy, 1997; Stanghellini et al.,
2015), their star formation rates (SFR; 1.15 and 0.52 M⊙/yr from dust-
attenuation-corrected far-UV images; Calzetti et al., 2015), and their Hubble
type of Sd. They are also both mostly face-on with clear views of the spiral
structures in each (inclinations of $40.7\deg$ and $47.4\deg$; Calzetti et
al., 2015) and have similar distances (4.6 and 3.7 Mpc; Radburn-Smith et al.,
2011; Qing et al., 2015; Gao et al., 2016; Sabbi et al., 2018). Their main
properties are listed in Table 1.

Despite these many similarities, the two galaxies have starkly different
spiral structures, with NGC 1313 being barred with strong spiral arms and NGC
7793 being a flocculent spiral (see Figure 1). NGC 1313 also appears to be
experiencing a minor interaction (see §1.1). Based on the LEGUS cluster
catalogs, they also have strikingly different numbers of massive clusters. NGC
1313 has more than six times as many clusters that are more massive than
$10^{4}$ M⊙, despite having a SFR only 2.2 times higher than NGC 7793. NGC
1313 also has 2.7 times more neutral HI gas ($2.1\times 10^{9}$ and
$0.78\times 10^{9}$ M⊙; Calzetti et al., 2015), but only half as much
molecular gas as NGC 7793, as measured in the observational footprint
presented here (see Section 5). This makes NGC 1313 and NGC 7793 an
interesting pair of galaxies to compare to further understand how the spiral
structure of a galaxy influences the molecular gas properties and the types of
star clusters that are formed.

###  1.1 NGC 1313

NGC 1313 has an irregular morphology with a strong bar and asymmetric spiral
arms, which has historically been compared to the Large Magellanic Cloud (de
Vaucouleurs, 1963). Its irregular morphology (Sandage & Brucato, 1979) and
observations of the HI showing a loop of gas around the galaxy and a
disturbance in its velocity field in the southwest of the galaxy (Peters et
al., 1994) indicate that it is interacting with a satellite galaxy. When
measuring the galaxy’s star formation history, Larsen et al. (2007) found an
increase in recent star formation in the southwest of the galaxy, potentially
caused by this interaction. This was further confirmed by Silva-Villa & Larsen
(2012), who found that rather than undergoing a starburst across the whole
galaxy, there was only an increase in star formation in the southwestern
field. They find that the regional starburst occurred $\sim 100$ Myr ago.

Walsh & Roy (1997) found that NGC 1313 is one of the most massive galaxies
that has no gas-phase metallicity gradient across its disk. However, the more
recent study Hernandez et al. (2022) shows evidence for a metallicity gradient
based on the chemical abundances of young clusters. They also find a constant
star formation rate across the disk of NGC 1313 with the exception of the
burst in the southwest. This southwestern region where the localized starburst
is observed is just outside of the observation footprint for this study. A
difference in stellar metallicity tracing a separate population was found
throughout the disk by Tikhonov & Galazutdinova (2016), which they attribute
to a past merger with a low-mass dwarf satellite that did not gravitationally
distort the arms or central region of NGC 1313.

The star cluster population in NGC 1313 has been characterized using the LEGUS
cluster catalogs by Grasha et al. (2017b), and the sizes of these clusters
were further characterized by Ryon et al. (2017), who found that the clusters
are undergoing relaxation but appear to be gravitationally bound. Hannon et
al. (2019) studied the morphology of the H$\alpha$ around these clusters and
report clearing times for the gas of $\lesssim 1$ Myr. Messa et al. (2021)
added to the LEGUS catalogs by searching for embedded clusters identified with
Pa$\beta$ and in the near-infrared and finding that up to 60% of the star
clusters are not accounted for in the UV-optical catalogs and that gas-
clearing timescales are closer to 3-4 Myr.

###  1.2 NGC 7793

NGC 7793 is a member of the Sculptor group of galaxies and has been well-
studied due to its proximity and high Galactic latitude. It has no bar, a
small bulge with a nuclear star cluster (Kacharov et al., 2018), and a mostly
uniform distribution of small, loose spiral arms with little coherent
structure (Elmegreen et al., 2014), to the point that it has been called an
“extreme” flocculent spiral (Elmegreen & Elmegreen, 1984). It has nearby dwarf
companions, and the HI disk is warped, suggesting some level of interaction,
though they see no sign of tidal effects (Koribalski et al., 2018). It has
drawn attention for its unusual discontinuous and positive metallicity
gradient in the far outer disk (Vlajić et al., 2011) and its declining
rotation curve in the outer edges of the disk (Carignan & Puche, 1990; Dicaire
et al., 2008), although the latter could be due to a line-of-sight warp in the
disk (Bacchini et al., 2019). Studies of its stellar population have also
shown that it has a break in the disk where the surface brightness departs
from simple exponential decrease, likely caused by radial migration of the
stars (Radburn-Smith et al., 2012).

The star formation history of NGC 7793 has been studied by Sacchi et al.
(2019) and they found an inside-out growth of the galaxy, with the outer
regions undergoing a greater recent increase in star formation than the inner
region. Inside-out growth was also seen in young clumps identified in UV light
by Mondal et al. (2021), who also suggest that NGC 7793 is experiencing a
recent increase in its star formation rate. Its LEGUS-identified star clusters
were included in the same studies as NGC 1313 by Grasha et al. (2017b), Hannon
et al. (2019), and Brown & Gnedin (2021) to characterize their populations,
cluster boundedness, and gas clearing timescales. The clusters and molecular
gas were further studied by Grasha et al. (2018), finding that the younger
clusters are more spatially correlated with molecular clouds and that the
hierarchical clustering of the clouds is shared by the young clusters. Muraoka
et al. (2016) has also mapped the CO(3-2) line in NGC 7793, finding that its
emission is well-correlated with infrared tracers of star formation.

To robustly compare the properties of the molecular clouds in this pair of
galaxies, we have observed both in CO(2-1) with carefully matched spatial
resolutions of 13 pc and surface brightness sensitivities of $\sim 0.2$ K.
These observations allow us to make a direct comparison of clouds in a galaxy
with strong spiral arms and in a flocculent spiral without concern for
resolution or sensitivity effects. This paper is organized as follows: We
present the observations used in this analysis in Section 2, and the LEGUS
cluster catalogs of the two galaxies in Section 3. We then discuss the
decomposition of the CO(2-1) emission into substructures in Section 4 and the
calculation of their properties in Section 5. We examine the size-linewidth
relations of the clouds in each galaxy in Section 6, and the virialization of
the clouds in Section 7. We compare the distributions of all the measured and
derived properties in Section 8. In Section 9, we examine how the clouds and
their properties are spatially correlated with those of the clusters. We
discuss our findings in Section 10 and summarize our conclusions in Section
11.

##  2 Observations

Figure 2: CO(2-1) peak intensity maps of NGC 1313 (top) and NGC 7793 (bottom),
with beam sizes shown in the bottom left corners.

###  2.1 NGC 1313 CO(2-1)

NGC 1313 was observed by ALMA in Band 6 (project code 2015.1.00782.S; PI: K.
E. Johnson) with the 12m array. It was originally observed in Cycle 4 in 2016
but did not meet sensitivity requirements and so was observed again in Cycle 5
in 2018. The galaxy is split into two mosaics, one covering the northern arm
of the galaxy, and one covering the central region and southern arm. The
northern arm mosaic consists of 68 pointings with 1.9 minutes of integration
per pointing with a spacing of 12.9″ for a total integration time of 2.2
hours. The central mosaic consists of 104 pointings with 2.2 minutes of
integration per pointing for a total integration time of 3.75 hours, also with
a spacing of 12.9″. The largest angular scale recovered with these
observations is 7.4″, which corresponds to a spatial scale of 150 pc, much
larger than any of the clouds measured in this analysis.

The data were calibrated with the ALMA data pipeline version Pipeline-
CASA54-P1-B (Hunter et al., 2023) in CASA 5.4.0-68 using J2258-2758 for
bandpass and amplitude calibration and J2353-3037 for phase calibration. It
was imaged in CASA 6.1.1.15 with a robust parameter of 0.5, resulting in a
synthesized beam of 0.579″$\times$0.486″(12.8$\times$11.2 pc at a distance of
4.6 Mpc). In Figure 2, we show the image data after smoothing to a circular
beam size of 13 pc to match the observations of NGC 7793, which corresponds to
0.583″for NGC 7793. A summary of the resulting image is shown in Table 2.

###  2.2 NGC 7793 CO(2-1)

NGC 7793 was observed by ALMA in Band 6 during Cycle 4 in 2016 (project code
2015.1.00782.S; PI: K. E. Johnson) with the 12m array. The observations were a
mosaic of the central 180″$\times$114″ (3$\times$2 kpc) of NGC 7793. The total
integration time is 3 hours with the 12-m array with 148 pointings at 1.2
minutes of integration per pointing and a mosaic spacing of 12.9″ between
pointings. The largest angular scale recovered with these observations is
7.0″, which corresponds to a spatial scale of 125 pc, much larger than any of
the clouds measured in this analysis.

The data were calibrated with the ALMA data pipeline version 2020.1.0-40
(Hunter et al., 2023) in CASA 6.1.1.15 using J0519-4546 and J0334-4008 for
bandpass and amplitude calibration and J0303-6211 for phase calibration. It
was imaged using a Briggs weighting with a robust parameter of 2.0, resulting
in a synthesized beam size of 0.686″$\times$0.595″(12.3$\times$10.7 pc at a
distance of 3.7 Mpc). In Figure 2, we show the image data after smoothing to a
circular beam size of 13 pc to match the observations of NGC 1313, which
corresponds to 0.724″for NGC 7793. A summary of the resulting image is shown
in Table 2. These data also appeared in Grasha et al. (2018).

Table 2: ALMA 12CO(2-1) Observations Galaxy | Beam | Beam | rms | Velocity
---|---|---|---|---
| (arcsec) | (pc) | (K) | Resolution (km/s)
NGC 1313 | 0.58 | 13 | 0.15 | 1.33
NGC 7793 | 0.72 | 13 | 0.2 | 1.33

##  3 Cluster Catalogs

In addition to the CO(2-1) data, we use catalogs of star clusters and their
SED-fitted properties from the LEGUS collaboration, which used the methodology
described in Adamo et al. (2017). In this work, we use their catalog that uses
the Milky Way extinction law from Cardelli et al. (1989), averaged aperture
correction method, and Padova stellar evolutionary tracks implemented by
Yggdrasil (Zackrisson et al., 2011). We include all objects identified by
LEGUS as cluster candidates, which required that they were brighter than MV of
-6, detected above $3\sigma$ in the UBVI set of filters, and had a visual
classification of 1 or 2 (compact) or class 3 (multiply-peaked). Adamo et al.
(2017) adopt a 90% completeness limit of 5000 M⊙ for clusters with ages up to
200 Myr in NGC 602, which has a distance of 10 Mpc. However, at the distances
of NGC 1313 and NGC 7793, we expect this limit to be much lower, closer to
1000 M⊙ (Grasha et al., 2018). We represent this 1000 M⊙ limit as a vertical
line in the mass distributions shown in Figure 3.

Several studies have pointed out that a degeneracy in age and reddening during
the fitting results in many old globular clusters incorrectly being assigned
much younger ages (Turner et al., 2021; Hannon et al., 2019; Whitmore et al.,
2023). In particular, Whitmore et al. (2023) find that the majority of these
objects with incorrectly fitted ages fall above a line extending from (6, 1)
to (9, 0.1) in a plot of E(B-V) versus log(Age). They also find that these
incorrect ages primarily affect objects on the high mass end
($M>10^{4.5}M_{\odot}$). To account for these incorrect ages without biasing
our sample against high-mass objects, we remove the clusters that fall above
the E(B-V)-log(Age) line from Whitmore et al. (2023) only when comparing age
measurements between the two galaxies. This affects 76 clusters in NGC 1313
and 29 clusters in NGC 7793 (6% of the identified clusters in both galaxies).
Carefully fitting these objects with the degeneracy in mind would likely
result in many of them having ages older than 1 Gyr. We also note that there
are few enough of these objects that keeping or removing them does not
substantially alter our results.

Orozco-Duarte et al. (2022) compared the output of the LEGUS cluster catalog
for NGC 7793 with results obtained using synthetic photometry and a
stochastically sampled IMF and found masses that were on average 0.11 dex
larger and ages that were 1 Myr younger compared to the Adamo et al. (2017)
method. However, we use the original LEGUS catalogs still to maintain a
consistent method between the two galaxies.

Messa et al. (2021) also identify a significant population of embedded
clusters in NGC 1313. However, since we do not also have embedded clusters
identified in NGC 7793 to compare, we do not include those clusters in this
work.

The cluster catalogs for both galaxies were separated into east and west
portions of the map. To combine these, we identified matching pairs of
clusters in the overlap region. We then used the cluster properties from the
map that had the better fit, based on their reported quality of fit Q
parameter. We identified 67 overlapping clusters in NGC 1313 and 47 in NGC
7793. Each of these clumps has a fitted mass, age, and extinction from the
catalog.

###  3.1 Cluster Counts

Table 3: Number of cloud structures and clusters in each galaxy

|  | NGC 1313 | NGC 7793
---|---|---|---
LEGUS Clusters | All Clusters | 1201 | 467
Massive Clustersa | 333 | 53
Young, Massive Clusters${}^{a},b$ | 37 | 3
Molecular Gas Structures | Trunksc | 65 | 130
Branchesc | 82 | 187
Leavesc | 442 | 761
Clumpsd | 531 | 965
Massive Clumps${}^{a},d$ | 137 | 306

Note: aThe threshold used to define “massive” for both clumps and clusters in
this table is $M>10^{4}M_{\odot}$.
b The threshold used to define “young” for clusters is an age $<10$ Myr.
c Structures identified by astrodendro.
d Structures identified by quickclump.

NGC 1313 has $\sim 2.6$ times as many identified star clusters at all masses
as NGC 7793, with a total of 1201 clusters compared to 467 for NGC 7793.
Considering that the star formation rate in NGC 1313 is $\sim 2.2$ times
larger than that of NGC 7793, this represents a small excess in cluster
formation. We can also account for the fraction of the total SFR included in
the footprints of the LEGUS observations used to identify these clusters based
on the fraction of the GALEX far-UV light. We note that the SFR traced by UV
light is well-matched to the ages of the general cluster population, but may
be averaged over too long a timescale to be accurate for the youngest
clusters. In NGC 1313, 57% of the total SFR is included in the LEGUS
footprint, and in NGC 7793 53% is included. Assuming that the cluster
populations are well-matched to the SFR within each galaxy, NGC 1313 would
have $\sim 2110$ clusters and NGC 7793 would have $\sim 880$ clusters within
the total star forming area of each galaxy. This suggests then that NGC 1313
has $\sim 2.4$ times as many clusters than NGC 7793 in the full galaxy, still
a slight excess over the difference in total SFR.

This difference in cluster number is more extreme when we consider only the
most massive clusters with $M_{*}>10^{4}M_{\odot}$. NGC 1313 has over six
times as many massive clusters, having 333 massive clusters identified by
LEGUS where NGC 7793 has 53. Correcting for the fraction of star formation
traced by LEGUS would still leave NGC 1313 with 5.8 times more massive
clusters. Furthermore, 37 of those massive clusters are young (<10 Myr) in NGC
1313, compared to only 3 in NGC 7793. As seen in Figure 3, NGC 7793 does have
a couple of particularly massive clusters, and so we can also compare the mass
of clusters in both galaxies above the $M_{*}>10^{4}M_{\odot}$ threshold and
we find that NGC 1313 has 2.7 times as much mass in massive clusters (2.5
times the mass when including a total SFR correction), which still represents
an excess of massive cluster formation in NGC 1313 by this metric.

We also note, however, that based on the Lee et al. (2009) comparison of the
dust-corrected UV-based method of calculating SFR to measuring SFR with
H$\alpha$, we estimate that the SFR values reported in Calzetti et al. (2015)
would have $1\sigma$ uncertainties of approximately $25\%$. Calzetti et al.
(2015) do not report uncertainties on the SFR for NGC 1313 and NGC 7793
specifically, but if we take this estimated uncertainty value from Lee et al.
(2009) and propagate the error, we get a ratio of 2.2$\pm$0.8 in the SFR
between the two galaxies. In this case, the ratios reported here are not
statistically significant when considering error from counting statistics.

Overall, NGC 1313 not only has more clusters, but also has more massive
clusters than NGC 7793, despite the lower molecular gas content of NGC 1313
(as shown in Table 1 and will be discussed in Section 5). These cluster
numbers are shown in Table 3.

###  3.2 Cluster Property Distributions

We further consider how the distributions of cluster masses and ages compare
between the two galaxies by looking at histograms, Gaussian kernel density
estimations (KDEs) from scipy (Virtanen et al., 2020), and cumulative
distribution functions (CDFs). Histograms and KDEs are intuitive
representations of how the values of a parameter are distributed, but they are
also heavily affected by our choice in binning for the histogram and bandwidth
for the KDE. We use a scalar estimator bandwidth of 0.5 dex for all KDEs in
this section and Section 8 for uniformity (Scott’s rule would result in
bandwidths between 0.2 and 0.5 dex for the various distributions). CDFs are
less intuitive for understanding how values of a property are distributed, but
they are unaffected by binning and so are the most robust depiction of
property distributions. When interpreting CDFs, a line further to the right of
the plot indicates a distribution with larger values.

In Figure 3, we show the distributions of the fitted masses for both the full
cluster population and for only the youngest (<10 Myr) clusters, as well as
distributions of the fitted ages of the clusters in each galaxy. We show
histograms and KDEs in the left column and show CDFs in the right column. The
cluster masses in NGC 1313 for both the full population and especially for the
youngest clusters are skewed towards higher masses than in NGC 7793, further
emphasizing the tendency towards more massive clusters in NGC 1313. The
distribution of cluster ages in the two galaxies appears more similar, though
NGC 1313 has slightly older clusters than NGC 7793.

Figure 3: Normalized distributions of the cluster parameters for the two
galaxies, using histograms and KDEs (left) and CDFs (right). The properties
shown are the mass distribution for the full cluster population (top), the
mass distribution for only the young (<10 Myr) clusters (middle), and the age
distribution of all the clusters (bottom). The estimated mass completeness
limit of 1000 M⊙ is shown as a vertical line in the mass distributions, and
the CDFs of the mass distributions only include clusters above this mass
limit. The age distributions do not include clusters that are likely to have
incorrect ages due to the age/reddening degeneracy (Whitmore et al., 2023).

##  4 Molecular Gas Structure Decomposition

To understand the properties of individual molecular gas structures, we use
two different methods of emission decomposition to more robustly compare
physical conditions between the two galaxies. One method is to use a
dendrogram to hierarchically categorize the structures, and the other is to
identify non-overlapping clumps. These segmentation methods are described in
more detail below. Dendrograms are superior for examining the full spatial
scale of molecular clouds in the region because they are able to capture the
hierarchical nature of the gas, from large GMCs to smaller knots. However,
dendrograms count emission multiple times and so they cannot be used for any
counting statistics. We therefore use dendrograms in Sections 6 and 7 where we
want to understand the full spatial scale of the clouds and multiply-counted
emission is allowable. We use the non-overlapping clumps in Section 8, which
focuses on property distributions and so cannot include multiply-counted
emission.

###  4.1 Dendrogram Segmentation

We use the package astrodendro (Rosolowsky et al., 2008) to decompose the
structures in each galaxy into dendrograms. This results in a hierarchical
“tree” of structures that merge together at lower contour levels. The local
maxima are called “leaves” and have no further substructure, while the larger
merged structures are “branches” and “trunks”. Trunks are not bounded by any
other structures. By convention, isolated structures that have no substructure
and are also not bounded by any other structure are called leaves instead of
trunks. We use the input parameters min_value=3$\sigma$,
min_delta=2.5$\sigma$, and min_npix=2 beams, where min_value is the minimum
intensity value of an identified emission peak, min_delta is the minimum
intensity separation between structures merging, and min_npix is the minimum
number of voxels in an identified structure. The breakdown of each type of
dendrogram structure for each galaxy is shown in Table 3.

###  4.2 Clump Segmentation

We use the algorithm quickclump (Sidorin, 2017) to decompose the emission into
clumps that have no overlap. This algorithm outputs a similar style of clump
decomposition to clumpfind (Williams et al., 1995), for example. We used the
input parameters Tcutoff=4$\sigma$, dTleaf=4$\sigma$, and Npixmin=2 beams
(equal to 65 and 70 for NGC 1313 and NGC 7793, respectively). Tcutoff is the
minimum intensity included in clump assignments, dTleaf is the minimum
intensity differences for an emission peak to be considered a separate clump,
and Npixmin is the minimum number of voxels in a clump. The number of clumps
identified in each galaxy are shown in Table 3.

##  5 Calculating Cloud Properties

###  5.1 Mass

We calculate the mass of each structure using a CO-to-H2 factor,
$X_{\text{CO}}$, where $X_{\text{CO}}$ = $N_{H_{2}}$/$W_{CO}$, $N_{H_{2}}$ is
the column density of H2 in cm-2 and $W_{CO}$ is the observed brightness of CO
in K km s-1. We use the $X_{\text{CO(2-1)}}$ calibration from Gong et al.
(2020), Table 3, Equation 3b, which determines the $X_{\text{CO(2-1)}}$
conversion factor between $N_{H_{2}}$ and CO(2-1) based on the peak brightness
temperature of the clump ($T_{\text{peak}}$ in K), the beam size
($r_{\text{b}}$; 13 pc), and the metallicity ($Z$) with the equation

$X_{CO(2-1)}=(2.7\times
10^{20})T_{\text{peak}}^{-1.07+0.37\log{(r_{\text{b}})}}Z^{-0.5}r_{\text{b}}^{-0.13}.$
(1)

Using this equation, which is calibrated directly to the CO(2-1) line rather
than CO(1-0), means that we do not need to assume a ratio of CO(2-1)/CO(1-0),
which is known to vary across galaxies (Koda et al., 2012; Leroy et al.,
2022). For NGC 1313, we use an oxygen abundance of
$12+\log{\text{(O/H)}}=8.4\pm 0.1$ with no radial gradient in the galaxy
(Walsh & Roy, 1997). NGC 7793 has a measured radial gradient of
$12+\log{\text{(O/H)}}=8.572-0.054$ dex kpc${}^{-1}\times R_{\text{gal}}$
(Stanghellini et al., 2015). Using a solar oxygen abundance of
$12+\log{\text{(O/H)}}=8.69$ (Asplund et al., 2009), these abundances
correspond to metallicities of $Z=0.51Z_{\odot}$ for NGC 1313 and a range of
$Z=(0.56-0.76)Z_{\odot}$ for NGC 7793. Using the prescription from Eq. 1
results in values of $X_{\text{CO(2-1)}}=(0.69-2.56)\times 10^{20}$ cm-2/(K km
s-1) for NGC 1313 and $X_{\text{CO}}$ $=(0.64-2.65)\times 10^{20}$ cm-2/(K km
s-1) for NGC 7793.

We also consider the metallicity gradient measured for NGC 7793 by Grasha et
al. (2022), which instead finds $12+\log{\text{(O/H)}}=8.945-0.083$ dex
kpc${}^{-1}\times R_{\text{gal}}$, resulting in metallicities of
$Z=(1.14-1.79)Z_{\odot}$ and values of $X_{\text{CO(2-1)}}=(0.43-1.83)\times
10^{20}$ cm-2/(K km s-1). We find that the difference in metallicity
prescription and resulting masses does not significantly affect any of the
results in this paper and so we use the lower metallicities of Stanghellini et
al. (2015) throughout for NGC 7793. Hereafter, we refer to
$X_{\text{CO(2-1)}}$ as $X_{\text{CO}}$.

We next calculate the mass of each structure using these calibrated
$X_{\text{CO}}$ values to determine the H2 column density, then multiply by
the pixel size in cm2 and sum over all pixels to get the mass of H2. We then
multiply this M${}_{H_{2}}$ by a factor of 1.4 (which is the mean mass per
hydrogen atom and assumes all the hydrogen is molecular) to get the total mass
of the gas, $M$. We adopt a 10% error on the resulting masses due to the
standard 10% ALMA flux calibration uncertainty (Fomalont et al., 2014), which
we add in quadrature with the error from the measured rms noise (Table 2).

We also estimate a total mass of molecular gas in the observational footprint
of each galaxy, using the total CO(2-1) emission multiplied by the respective
average $X_{\text{CO}}$ measured for the clumps in each galaxy and multiplying
by a factor of 1.4 as mentioned above. We find that NGC 7793 contains nearly
twice the molecular mass as NGC 1313, with measured totals of $7.6\times
10^{6}$ M⊙ in NGC 1313 and $1.4\times 10^{7}$ M⊙ in NGC 7793. It is important
to note that our observations do not cover the whole galaxy and we do not
include 7m and total power data, so we are likely missing diffuse emission and
these values should not be considered the total molecular masses of the
galaxies. The ALMA observations do, however, cover a similar fraction of the
galaxy to the LEGUS observations that clusters are derived from.

These values of observed molecular gas mass are low compared to those measured
by PHANGS-ALMA in Leroy et al. (2021), likely due to the smaller observational
footprint and the missing diffuse gas emission since we only use the 12m array
data. The CO(2-1) emission identified to be part of a clump structure accounts
for approximately 82% of the total observed CO mass in NGC 1313 and 95% in NGC
7793, which implies that the molecular gas in NGC 1313 is more likely to be
diffuse. The fact that NGC 1313 has nearly twice the neutral HI gas as NGC
7793 (see Table 1), but about half the molecular gas, suggests that there is
an interesting difference in the balance between gas phases in these two
galaxies and a thorough accounting of the total gas mass would be interesting
for future work.

###  5.2 Velocity Dispersion

We calculate the velocity dispersion for each structure by finding the
intensity-weighted mean line profile and fitting a Gaussian, resulting in a
fitted $\sigma_{v}$. We then deconvolve this $\sigma_{v}$ with the velocity
channel width of the observations, 1.33 km s-1, converted from FWHM to
$\sigma$ with FWHM$=2.35\sigma$. The reported error in $\sigma_{v}$ comes from
the error in the fitting method, propagated through the deconvolution. After
deconvolving $\sigma_{v}$, measurements that were smaller than the channel
width return non-number values and so are dropped from the analysis. We also
remove from our analysis any structures that have a deconvolved $\sigma_{v}$
less than a tenth of the velocity resolution. Throughout this work, we also
use the term “linewidth” to refer to $\sigma_{v}$.

###  5.3 Radii

To determine the sizes of the structures, we fit ellipses to the half-power
contours and take the two axes as the HWHM of the structure. We convert these
HWHM measurements to a $\sigma_{R}$ by approximating $\sigma_{R}=$HWHM$\times
2/2.35$, then multiply $\sigma_{R}$ by 1.91 to get an “effective radius”
(Solomon et al., 1987) in each axis. We deconvolve each axis with the radius
of the beam, 6.5 pc, then take the geometric mean of the axes to get a final
$R$. The reported error in the size is determined by how non-circular the
structure is, added in quadrature with a measurement error of half a pixel
size, propagated through the deconvolution. After deconvolving the radii,
measurements that were smaller than the beam size return non-number values and
so are dropped from the analysis. We also remove from our analysis any
structures that have a reported $R$ less than a tenth of the beam size.

Of the structures that were removed because they were below the resolution
limits, there were 113 clumps and 88 dendrogram leaves in NGC 1313 and 166
clumps and 116 dendrogram leaves in NGC 7793. These removed structures account
for 4% of the total clump mass in NGC 1313 and 2% in NGC 7793.

###  5.4 Derived Quantities

From the measured mass, radius, and linewidth above, we calculate other
properties of the structures, including the surface density, $\Sigma$, the
virial parameter, $\alpha_{\text{vir}}$, the external pressure, $P_{e}$, and
the free-fall time, $t_{ff}$. The surface density is simply the total mass
divided by the structure’s area.

The virial parameter is the ratio between twice the cloud’s kinetic energy and
its gravitational energy, so that a value of one indicates that the cloud is
in virial equilibrium. While a negative total energy balance
($\alpha_{\text{vir}}$ <2) could be considered the threshold for a cloud’s
boundedness, Dib et al. (2007) demonstrate that the connection between
boundedness and gravitational collapse is much more complicated, and clouds
with a simple negative energy balance do not always collapse. By “collapse”,
we mean the process by which parts of the cloud condenses and forms stars,
while other parts of the cloud are dissipated. Furthermore, (Zweibel, 1990)
show that more careful calculations of the virial parameter that take into
account additional forces from external pressure and magnetic fields can alter
the formula for virial equilibrium by factors of more than two.

Consequently, we take a more stringent threshold for gravitational collapse of
$\alpha_{\text{vir}}$ <1\. Values greater than two suggest that the cloud is
not gravitationally bound and must either disperse or be constrained by an
external pressure, while values less than one suggest that the cloud is
dominated by gravity and will likely begin gravitational collapse. Values of
$\alpha_{\text{vir}}$ between one and two should be interpreted cautiously. We
calculate the virial parameter for each structure with the equation

$\alpha_{\text{vir}}=\frac{5\sigma_{v}^{2}R}{GM}.$ (2)

Assuming a simplified case in which the cloud is in pressure equilibrium with
the surrounding medium, the external pressure will be equal to the pressure at
the edge of cloud defined by Elmegreen (1989) with the equation

$P_{e}=\frac{3\Pi M\sigma_{v}^{2}}{4\pi R^{3}},$ (3)

where $\Pi$ is defined as the ratio of the density at the edge of the cloud to
the mean cloud density ($\rho_{e}=\Pi\langle\rho\rangle$), and here we take
$\Pi=0.5$.

The free-fall time depends only on the density of the cloud and so we
calculate it with the equation

$t_{ff}=\sqrt{\frac{3\pi}{32G\rho}}=\sqrt{\frac{\pi^{2}R^{3}}{8GM}}.$ (4)

Tables of all of these properties and their errors, for both galaxies and for
both clumps and dendrogram structures, are given in Appendix A. Given the
large number of structures, we include only the first 5 entries as a
demonstration of property values. The full tables are available as
supplementary material.

##  6 Size-Linewidth Relations

The sizes and linewidths of molecular cloud structures are expected to follow
a power law relation (Larson, 1981) of the form

$\sigma_{v}=a_{0}R^{a_{1}}.$ (5)

The intercept ($a_{0}$) and slope ($a_{1}$) of this relation have been
measured in many different environments, though the most commonly cited value
is that from Solomon et al. (1987), which found $a_{0}=1.0\pm 0.1$ and
$a_{1}=0.5\pm 0.05$ for clouds mapped in CO(1-0) in the disk of the Milky Way
at 45″ resolution, where $\sigma_{v}$ is measured in km s-1 and $R$ is
measured in pc. The units of $a_{0}$ will vary with the value of $a_{1}$, but
would be km s-1 pc-0.5 for a value of $a_{1}=0.5$. Since these units are
dependent on $a_{0}$, we report the fitted values of $a_{0}$ without units.

Since Solomon et al. (1987), other studies have measured the slope and
intercept of this relation in a variety of environments and at many
resolutions. In the Milky Way for example, Rice et al. (2016) measure clouds
with angular resolutions of 7.5’ and measure a slope of $a_{1}=0.52\pm 0.03$
and Miville-Deschênes et al. (2017) measure clouds with angular resolutions of
8.5’ and measure a slope of $a_{1}=0.63\pm 0.3$, though neither of these
studies deconvolve the sizes or linewidths with the beam and velocity channel
sizes. Faesi et al. (2016) measure clouds in the nearby spiral galaxy NGC 300
at 40 pc resolution with CO(2-1) and deconvolve their measurements, finding a
slope of $a_{1}=0.52\pm 0.2$. Steeper slopes have also been found in nearby
galaxies, such as $a_{1}=0.6\pm 0.1$ measured by Bolatto et al. (2008) across
many galaxies and with resolutions ranging from 6 to 120 pc with both CO(1-0)
and CO(2-1), or $a_{1}=0.8\pm 0.05$ measured by Wong et al. (2011) across the
Large Magellanic Cloud (LMC) at 11 pc resolution with CO(1-0). Neither of
these studies deconvolved size and linewidth measurements. Higher resolution
studies (0.1-3 pc) in the LMC with CO(2-1) have performed deconvolution and
found slopes ranging from $a_{1}=0.49$ to $a_{1}=0.78$ (Nayak et al., 2016;
Indebetouw et al., 2020; Wong et al., 2022; Finn et al., 2022). These widely
varying measurements demonstrate how resolution, molecular tracer, and the
method used to measure size and linewidth all have a large effect on the
measured slope. Consequently, we focus instead on the fitted intercept of this
relation, which still gives us information about the relative kinetic energy
of the clouds across the full range of measured size scales.

We show the radii and velocity dispersions of the dendrogram structures in
both galaxies with a fitted power law in Figure 4, where the power law is fit
with orthogonal distance regression to take into account the error in both
axes (scipy.odr;  Virtanen et al., 2020). Due to the large number of clouds,
plotting all data points results in the true distribution of points being
self-obscured. We instead represent their distribution with a 2-D Gaussian KDE
from scipy.stats, using the default Scott’s rule to determine the estimator
bandwidth.

We fit the intercept only of a power-law relation by holding the slope
constant at a fixed value of $a_{1}=0.5$. For NGC 1313, we fit a value of
$a_{0}=0.41\pm 0.01$, and for NGC 7793 we fit a value of $a_{0}=0.33\pm 0.01$
(Figure 4). The intercept of NGC 1313 is significantly higher than that of NGC
7793 by more than $3\sigma$, which suggests that NGC 1313 has more kinetic
energy in its molecular clouds than NGC 7793. We also performed this fit with
other values for the fixed slope in the power law to account for the wide
range of fitted slopes (e.g. Solomon et al., 1987; Bolatto et al., 2008; Wong
et al., 2011; Faesi et al., 2016; Nayak et al., 2016; Miville-Deschênes et
al., 2017; Indebetouw et al., 2020; Wong et al., 2022; Finn et al., 2022).
Changing the fixed slope affects the values of the fitted intercepts, but not
the conclusion that NGC 1313 has a significantly higher intercept and so more
kinetic energy.

Figure 4: Kernel density estimates of the deconvolved velocity dispersions
plotted against deconvolved radii of dendrogram structures in NGC 1313 and NGC
7793 with contours of 20%, 40%, 60%, and 80% of the maximum density. Also
shown are the fitted power laws (where we hold the slope constant at
$a_{1}=0.5$) with their respective $1\sigma$ errors shown as shaded regions.
The resulting intercepts are printed in the bottom right corner. For
comparison we show in orange the size-linewidth relation fitted in the Milky
Way by Rice et al. (2016). NGC 1313 has a higher intercept than NGC 7793 by
more than $3\sigma$, suggesting that the molecular clouds in NGC 1313 have
higher kinetic energies.

##  7 Virialization

To investigate the gravitational balance of clouds in the two galaxies, we
plot the velocity metric, $\sigma_{v}^{2}/R$, against the surface density,
$\Sigma$, of each dendrogram structure. The results are shown in Figure 5,
along with a line indicating where clouds in virial equilibrium
($\alpha_{\text{vir}}$ =1) would fall in the plot. Falling above the virial
equilibrium line indicates that the clouds are super-virial and dominated by
kinetic energy, while clouds below the line would be sub-virial and likely to
begin forming stars. Being super-virial, especially when $\alpha_{\text{vir}}$
>2, implies that the clouds are likely to disperse due to their kinetic
energy. However, the kinetic energy of clouds could also be enhanced if they
already have begun free-fall collapse, in which case they would
circumstantially fall along the line where $\alpha_{\text{vir}}$ =2 in Figure
5. The virial equilibrium line only considers the gravitational and kinetic
energies of the cloud, but external pressure or magnetic fields could also
affect the boundedness of the clouds by suppressing collapse or dispersal.
These environmental effects have been shown to be important in simulations of
GMCs in spiral galaxies (Baba et al., 2017).

Figure 5: Kernel density estimates of the velocity metric plotted against
surface density of the dendrogram structures in NGC 1313 and NGC 7793, with
contours of 20%, 40%, 60%, and 80% of the maximum density. The dashed line
shows where clouds in virial equilibrium would fall, above the line being
dominated by kinetic energy. Clouds undergoing free-fall collapse would also
have enhanced kinetic energy and fall along the dotted line. The structures in
both galaxies are mostly super-virial, though the clouds in NGC 1313 appear to
have more scatter.

Both galaxies fall mostly above the virial equilibrium line, suggesting that
they are dominated by kinetic energy. Some clouds are consistent with being in
free fall, which would enhance their observed kinetic energy. Alternatively,
excess kinetic energy could indicate that many of the clouds in these galaxies
are not gravitationally bound, or would require an external pressure to remain
bound. This is not unexpected since many studies have found a large fraction
of unbound molecular clouds in the Milky Way, nearby galaxy surveys, and
simulations (Goldsmith et al., 2008; Liszt et al., 2010; Dobbs et al., 2011;
Colombo et al., 2014; Miville-Deschênes et al., 2017; Sun et al., 2018;
Rosolowsky et al., 2021; Evans et al., 2021).

While the two galaxies generally occupy the same parameter space in Figure 5,
NGC 1313 appears to have a larger scatter and have more clouds close to virial
equilibrium. This could suggest that more of the clouds in NGC 1313 are close
to collapsing into stars and star clusters, which could drive the larger
numbers of clusters in NGC 1313 despite its fewer number of clouds. The larger
scatter of NGC 1313 clouds towards the unbound parameter space also matches
expectations of molecular clouds responding to galaxy interactions, which
cause clouds to become unbound (Pettitt et al., 2018; Nguyen et al., 2018). We
investigate the boundedness of these structures more quantitatively by
examining the spread in virial parameters, $\alpha_{\text{vir}}$, in Section
8.

##  8 Property Distribution Comparisons

We next investigate how the distributions of cloud properties compare between
the two galaxies by looking at histograms, KDEs, and CDFs of the non-
overlapping clump structures. In Figure 6, we show the distributions of the
three observed quantities (masses, radii, and linewidths) of the two galaxies.
By eye, these distributions appear very similar, with NGC 7793 having a
slightly broader distribution of masses at both the high and low mass end, and
shifted to slightly larger radii.

Figure 6: Distributions of the observed clump parameters for the two galaxies,
using histograms and KDEs (left) and CDFs (right). We see minimal difference
between the distributions except for a slightly wider mass distribution and
slightly larger radii for NGC 7793.

We see a bit more difference between the galaxies in the properties derived
from $M$, $R$, and $\sigma_{v}$. We show the distributions of the virial
parameter, surface density, external pressure, and free-fall time in Figure 7.
From these we see that NGC 1313 has more clouds at low $\alpha_{\text{vir}}$,
which we expected from Section 7, as well as higher surface densities, higher
external pressures, and lower free-fall times.

Figure 7: Distributions of the derived parameters for the two galaxies, using
histograms and KDEs (left) and CDFs (right). NGC 1313 appears to have more
clouds at low $\alpha_{\text{vir}}$, higher surface densities, higher external
pressures, and lower free-fall times than NGC 7793.

To better quantify the difference between property distributions, we consider
the two-sample version of both the Kolmogorov-Smirnoff (KS) test and the
Anderson-Darling (AD) test, where the $p$-value indicates the probability that
the two samples are pulled from the same distribution. A $p$-value of less
than 5% is generally taken to be statistically significant. The KS test is
most sensitive to the center of the distribution, while the AD test is more
sensitive to the tails. However, because there are so many samples (in this
case clouds), the comparison of every property for the two galaxies have
$p$-values less than 5%, and most are also much less than 1%. This is likely
an over-representation of how different the distributions truly are though
because the sample sizes of clouds and clusters for the galaxies is so large.
As discussed in (Lazariv & Lehmann, 2018), as the sample size becomes larger,
KS and AD tests have increasingly higher power to discern small differences in
the distributions. However, these tests do not take into account the error in
the parameters, and so at large sample sizes, these tests can discern
differences that are smaller than the error in the measurements, which we
consider unreliable.

To combat overpowered statistical tests, we take random subsamples of the
distribution for each galaxy and perform a KS and AD test, using a sample size
instead of 65. After taking 1000 random subsamples, we report the average
$p$-values for each property comparison as the bootstrapped result. We show
these results for each property in Table 4. With this bootstrapped statistic,
the only property that crosses a 5% threshold for significance for both KS and
AD tests is the distributions of cluster masses, for both the full population
and including only young clusters. This emphasizes how the cluster populations
of the two galaxies appear significantly different, but none of the cloud
properties match that level of difference.

We recommend caution when interpreting the bootstrapped KS and AD tests, since
the $p$-value of the bootstrapped test does not necessarily indicate a
statistically significant difference in the two populations. Choosing a
sufficiently large sample size causes every property to appear significantly
different between the two galaxies, and similarly a sufficiently small sample
size makes no property have a statistically significant result. Rather, we use
these results only to determine which properties show the biggest difference
between the galaxies relative to the other properties.

Table 4: Boostrapped two-sample KS and AD test results between NGC 1313 and NGC 7793 global properties Parameter | KS $p$-value | AD $p$-value
---|---|---
Cluster Mass | 0.04 | 0.02
Young Cluster Mass | 0.02 | 0.01
Cluster Age | 0.23 | 0.09
Cloud Mass | 0.46 | 0.20
Radius | 0.37 | 0.16
Linewidth | 0.46 | 0.20
Virial parameter | 0.40 | 0.18
Surface density | 0.34 | 0.15
Pressure | 0.40 | 0.18
Free-fall time | 0.20 | 0.10

These plots and tests indicate that overall, the cloud properties between the
two galaxies are not particularly different. The greater number of massive
clusters in NGC 1313 compared to NGC 7793 may be driven in part by higher
surface densities and pressures. The lower virial parameters and free-fall
times in NGC 1313 may suggest that more clouds are close to gravitational
condensation and are likely to form stars more quickly and with greater
efficiency, which could then result in more clusters being formed on this
cloud scale.

Figure 8: Gaussian KDEs of the derived dendrogram structure properties plotted
against each other for both NGC 1313 and NGC 7793, with contours of 20%, 40%,
60%, and 80% of the maximum density. The virial parameters are much less
correlated with the other three properties.

To better understand if the highest-surface density clouds in NGC 1313
represent a high-density tail of collapsing clouds, we also plot all of the
derived cloud properties against one another for both galaxies in Figure 8.
These plots show that the surface density, pressure, and free-fall time are
all closely correlated with one another, but the virial parameters are much
less correlated with all three. This matches results from Sun et al. (2022)
that $\alpha_{\text{vir}}$ shows the least correlation with other clouds
properties while most others are well-correlated, especially the surface
density (which is unsurprising since these parameters are calculated from the
same three measurements of $M$, $R$, and $\sigma_{v}$). The NGC 1313
structures with low virial parameters that may be closest to collapsing do not
have particularly high or low surface densities or free-fall times, and
slightly low external pressures. This would suggest then that the high surface
densities in NGC 1313 are not high because the clouds are collapsing, although
the higher surface density clouds also have lower free-fall times.

We note that the cloud masses found in this study have the unusual feature of
being smaller than the maximum cluster masses seen in Figure 3. For young
clusters, this difference is much smaller, with the maximum young cluster
masses in NGC 7793 well below the maximum cloud masses, while the young
cluster masses in NGC 1313 are comparable to the maximum cloud masses. This
could be an indication that the star formation efficiency is much higher in
NGC 1313 than it is in NGC 7793, which would align with recent findings by
Polak et al. (2023) that in simulations, higher mass star clusters form with a
greater efficiency than lower mass star clusters. However, even with a higher
than usual formation efficiency, we do not expect to see clusters more massive
than the most massive clouds. This observation could be in part caused by
missing flux at the largest size scales since our observations do not include
ACA 7m or TP data. It could also be an indication that cloud and cluster
masses are declining over time in the galaxies.

##  9 Property Spatial Distributions

We next look for correlations between the clouds that are more gravitationally
bound as seen in Figures 5 and 7 and the youngest of the identified clusters.
In Figure 9, we show for each galaxy the locations of the clouds that have
$\alpha_{\text{vir}}$ $<1.5$ and the youngest clusters ($<10$ Myr), as well as
the locations of all the clouds. Here we use the clump definitions rather than
the dendrogram structures for the clouds. In NGC 7793, both the clouds and the
clusters have a scattered spatial distribution, as would be expected for a
flocculent galaxy. In NGC 1313, the clouds and clusters are primarily found in
the spiral arms and the central bar, with smaller populations in the interarm
regions.

Figure 9: Locations of the youngest clusters ($<10$ Myr; cyan), all molecular
clumps (magenta), and molecular clumps with $\alpha_{\text{vir}}$ $<1.5$
(orange) in NGC 1313 (top) and NGC 7793 (bottom). The grayscale backgrounds
are the DSS2-red images.

To determine if the bound clouds are more closely associated with the young
cluster population than the general cloud population, we create density maps
of each and calculate the correlation coefficient between them. These density
maps split the area of the galaxy into cells and count the number of objects
(either clouds, bound clouds, or young clusters) in each cell. To mitigate the
effects that our chosen cell size has on the results, we repeat this process
with a variety of cell sizes ranging from 50 to 200 pixels in the ALMA maps
(5″to 20″, or 110 pc to 450 pc), as well as a variety of $\alpha_{\text{vir}}$
thresholds to determine cloud boundedness, ranging from values of 1 to 3.

In every case of cell size and $\alpha_{\text{vir}}$ threshold, the bound
clouds are not more correlated with young clusters than the rest of the cloud
population in either galaxy. Averaging over all the cell sizes and
$\alpha_{\text{vir}}$ thresholds in NGC 1313, the correlation coefficient of
the young clusters with the bound clouds is 0.24$\pm$0.06 and with the general
cloud population is 0.32$\pm$0.05. In NGC 7793, the correlation coefficients
are 0.36$\pm$0.18 and 0.44$\pm$0.13 for the bound clouds and all clouds,
respectively. This suggests that the bound clouds are not more associated with
young clusters than the general cloud population. NGC 7793 has slightly higher
correlation coefficients than NGC 1313, though this difference is not
statistically significant when we consider how the coefficients vary with
different cell sizes and $\alpha_{\text{vir}}$ thresholds. This conclusion is
the same if we consider the full cluster population as well instead of only
the youngest clusters.

We also measure the spatial correlation coefficients between the average
values of the various cloud properties and the presence of young clusters, the
average masses of young clusters, and the total mass of young clusters. We use
the same range of cell sizes as above to make maps of these properties and
compute their correlation coefficients. In both galaxies, none of the
properties show a strong correlation with any of the cluster metrics. The
largest coefficient averaged across cell sizes was 0.33 for the correlation
between cloud surface density in NGC 1313 and the density of clusters. This
further demonstrates that no individual cloud property appears uniquely
correlated to the star clusters.

Figure 10: Histograms of the distances between clusters and the centers of
their nearest molecular cloud for both the full cluster population (solid) and
the young clusters with ages <10 Myr (hatched). The young clusters appear
slightly closer to molecular clouds than the general cluster population,
though this is not a strong difference. There is a much larger difference in
the cluster-cloud distances between the two galaxies. We hypothesize this is
because the stronger spiral density waves in NGC 1313 more efficiently
separate the molecular gas from the stars.

To further characterize the connection between the molecular clouds and the
clusters, we plot histograms in Figure 10 of the distances between the
clusters and centers of their nearest molecular clouds. We do this using the
clump definitions and for both the full cluster populations as well as only
the young cluster populations with ages <10 Myr, including only clusters that
fall within the ALMA observational footprints. In this figure, we see that the
young clusters appear slightly closer to their nearest clouds than the full
cluster population for both galaxies as we would expect. This agrees with the
results of Grasha et al. (2018) in NGC 7793. This difference between the young
and old clusters’ distances to clouds is notably weaker than that found in M51
by Grasha et al. (2019). The weakness of this trend in NGC 1313 and NGC 7793
agrees with our finding little correlation between the cloud properties and
the presence of clusters. Including younger clusters that are closer to the
generation of stars being formed by the clouds would likely result in a closer
correlation.

Figure 10 shows a much larger difference in the cluster-cloud distances when
comparing the two galaxies. Both the full cluster population and the young
clusters of NGC 1313 are further from molecular clouds than those in NGC 7793.
We believe the most likely explanation for this is the morphology of NGC 1313,
where most of the molecular gas is swept up in the two large spiral arms while
the star clusters get left behind, creating large separations between the
clusters and clouds. The effect where star clusters get left behind by the
spiral arms was demonstrated in other LEGUS galaxies by Shabani et al. (2018).
This effect is much smaller in NGC 7793 where the spiral arms are weaker and
closer to each other.

##  10 Discussion

Overall, the measured cloud properties in the two galaxies are surprisingly
similar, especially given the difference in massive star cluster formation
between the two. There are slight differences in the distributions of cloud
masses, sizes, and linewidths, and these small differences compound to create
larger differences in their densities and energy balances. This suggests that
star formation variations can be driven by relatively small shifts in these
properties, at least on the size scales measured here.

The primary differences that we find between the cloud properties in the two
galaxies are that NGC 1313 has higher kinetic energies per spatial scale
(Figure 4), its clouds are closer to virial equilibrium (Figures 5 and 7), and
its clouds have higher surface densities, pressures, and shorter free-fall
times (Figure 7). These slightly more extreme properties in NGC 1313 are
likely what drive the higher rate of massive star cluster formation in the
galaxy. We also see some evidence that NGC 1313 may have higher star formation
efficiency than NGC 7793 based on the relative masses of the most massive
clouds in each galaxy to the most massive young clusters in each galaxy.

Another difference in these two galaxies is in how the different gas phases
appear to be balanced. NGC 7793 has significantly more molecular gas mass than
NGC 1313 and nearly all of that molecular mass is accounted for with
identified clouds, suggesting that NGC 1313 has more diffuse molecular gas
than NGC 7793. NGC 1313 also has more than twice the neutral hydrogen gas and
more than twice the star formation rate as NGC 7793. This suggests that the
consumption time of the gas (roughly the molecular mass divided by SFR) is
much shorter in NGC 1313 than in NGC 7793. This also mirrors the lower free-
fall times seen in Figure 7. It may be that the strong spiral density waves in
NGC 1313 are important for perturbing molecular clouds to condense and begin
star formation and then also shear these clouds apart to create greater
quantities of diffuse molecular gas. Meanwhile in NGC 7793, the clouds are
less likely to be perturbed and so can exist for a longer time in a dormant
state without collapsing or being sheared apart.

However, it is still surprising how small the differences in cloud properties
are when compared with the large difference in star formation outcomes. It is
possible that this is because the LEGUS catalog primarily observes clusters
that are optically visible and so have emerged from their natal material. It
makes sense then that the cloud properties are not closely correlated with
their presence as seen in Section 9. Messa et al. (2021) searched for embedded
clusters in NGC 1313 in the near infrared and found that up to 60% of the
clusters they identified are not accounted for in UV-optical catalogs. A
search for embedded clusters in NGC 7793 was performed by Elmegreen &
Elmegreen (2019) using Spitzer data at 8 $\mu$m wavelengths. These embedded
clusters would likely show a closer correlation with the molecular gas and its
properties.

For future study, we recommend undertaking identical searches for embedded
sources in the two galaxies so that the younger cluster populations can be
directly compared. Such a study may show that the current generation of star
clusters forming in the two galaxies are more similar than previous
generations seen in the LEGUS catalogs, which would explain the relatively
similar cloud properties. Using young, embedded clusters would also likely
reveal better insights into which cloud properties are most closely correlated
with ongoing star formation. This analysis could reveal a closer correlation
of young, embedded clusters with virially bound clouds, which we would expect
given the tendency towards collapse and the high dependence of star formation
efficiency on the boundedness of clouds (Kim et al., 2021; Evans et al.,
2022).

We also note that in Figures 1 and 9 that map the locations and ages of the
LEGUS star clusters, it is clear that in NGC 1313 especially there are
differences in the level of star formation among different regions in the
galaxy. We examine how the cloud properties of these two galaxies vary by sub-
galactic region in a follow-up study, Finn et al. (2024).

##  11 Conclusions

We present a comparison of the molecular gas of two spiral galaxies from the
LEGUS sample (Calzetti et al., 2015), NGC 1313 and NGC 7793, observed in
CO(2-1) with ALMA. These two galaxies have similar stellar masses,
metallicities, and star formation rates, yet NGC 1313 has formed significantly
more massive star clusters in the last 10 Myr than NGC 7793. With observations
of the same molecular tracer at the same physical resolution and the same
sensitivity, we compare the properties of the molecular gas to understand what
differences in gas conditions give rise to such different star formation
outcomes. Our major results are summarized below.

  * •

Comparing the clusters identified by LEGUS in the two galaxies, NGC 1313 has
significantly more massive clusters ($>10^{4}$ M⊙) and especially more young,
massive clusters (<10 Myr) than NGC 7793, even after correcting for each
galaxy’s star formation rate and the area included by LEGUS. The mass
distributions of these clusters (both the full population and only considering
the young clusters) indicate that NGC 1313 is skewed towards more massive
clusters than NGC 7793.

  * •

Despite having less star formation, NGC 7793 has significantly more molecular
gas by mass, and more identified cloud structures. This is in contrast to the
greater amount of neutral hydrogen in NGC 1313, suggesting a strong difference
in the gas phase balance in these two galaxies.

  * •

We fit the intercept of a size-linewidth power law relation, holding the slope
fixed at a value of $a_{1}=0.5$ to determine relative kinetic energies. NGC
1313 also has a significantly higher intercept than NGC 7793, suggesting that
the kinetic energy of clouds in NGC 1313 are higher than in NGC 7793.

  * •

Most of the clouds in both galaxies appear to be unbound and out of virial
equilibrium based on plots of their surface densities against their velocity
metrics. NGC 1313 has more clouds near virial equilibrium than NGC 7793.

  * •

The distributions of cloud properties between the two galaxies show minimal
differences, though the small differences in the observed masses, radii, and
linewidths appear to compound into larger differences in the derived
properties of virial parameter, surface density, pressure, and free-fall time.

  * •

NGC 1313 has lower virial parameters and free-fall times and higher surface
densities and pressures than NGC 7793. The higher surface densities of NGC
1313 are not correlated with low virial parameters, which would suggest that
they are not a power-law tail caused by clouds with enhanced surface densities
because they are collapsing.

  * •

The most gravitationally bound clouds do not appear any more spatially
correlated with young clusters than the general cloud population. We also find
that none of the average cloud properties show a strong spatial correlation
with the presence, average mass, or total mass of young star clusters. This
may be because the clusters used in this study are too old to be associated
with their natal molecular gas. Comparing the cloud properties to younger,
embedded clusters in both galaxies would be an interesting focus of future
work.

  * •

The large difference in cluster formation between the two galaxies may be
driven by perturbations from the spiral density waves in the arms of NGC 1313
causing slightly more extreme cloud properties and inducing collapse.

This material is based upon work supported by the National Science Foundation
Graduate Research Fellowship Program under Grant No. 1842490. Any opinions,
findings, and conclusions or recommendations expressed in this material are
those of the author(s) and do not necessarily reflect the views of the
National Science Foundation. KG is supported by the Australian Research
Council through the Discovery Early Career Researcher Award (DECRA) Fellowship
(project number 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.
MRK acknowledges funding from the Australian Research Council through Laureate
Fellowship LF220100020. This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2015.1.00782.S. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc. These data are associated with the HST GO Program 13364 (PI
D. Calzetti). Support for this program was provided by NASA through grants
from the Space Telescope Science Institute. Based on observations obtained
with the NASA/ESA Hubble Space Telescope, at the Space Telescope Science
Institute, which is operated by the Association of Universities or Research in
Astronomy, Inc., under NASA contract NAS5-26555. ALMA, HST (WFC3, ACS)

## References

  * Adamo et al. (2017) Adamo, A., Ryon, J. E., Messa, M., et al. 2017, ApJ, 841, 131, doi: 10.3847/1538-4357/aa7132
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481, doi: 10.1146/annurev.astro.46.060407.145222
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Baba et al. (2017) Baba, J., Morokuma-Matsui, K., & Saitoh, T. R. 2017, MNRAS, 464, 246, doi: 10.1093/mnras/stw2378
  * Bacchini et al. (2019) Bacchini, C., Fraternali, F., Iorio, G., & Pezzulli, G. 2019, A&A, 622, A64, doi: 10.1051/0004-6361/201834382
  * Bolatto et al. (2008) Bolatto, A. D., Leroy, A. K., Rosolowsky, E., Walter, F., & Blitz, L. 2008, ApJ, 686, 948, doi: 10.1086/591513
  * Bothwell et al. (2009) Bothwell, M. S., Kennicutt, R. C., & Lee, J. C. 2009, MNRAS, 400, 154, doi: 10.1111/j.1365-2966.2009.15471.x
  * Brinchmann et al. (2004) Brinchmann, J., Charlot, S., White, S. D., et al. 2004, MNRAS, 351, 1151, doi: 10.1111/j.1365-2966.2004.07881.x
  * Brown & Gnedin (2021) Brown, G., & Gnedin, O. Y. 2021, MNRAS, 508, 5935, doi: 10.1093/mnras/stab2907
  * Calzetti et al. (2015) Calzetti, D., Lee, J. C., Sabbi, E., et al. 2015, AJ, 149, doi: 10.1088/0004-6256/149/2/51
  * Cardelli et al. (1989) Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245, doi: 10.1086/167900
  * Carignan & Puche (1990) Carignan, C., & Puche, D. 1990, AJ, 100, 394, doi: 10.1086/115523
  * Colombo et al. (2014) Colombo, D., Hughes, A., Schinnerer, E., et al. 2014, ApJ, 784, doi: 10.1088/0004-637X/784/1/3
  * Davis (2024) Davis. 2024, in prep
  * de Vaucouleurs (1963) de Vaucouleurs, G. 1963, ApJ, 137, 720, doi: 10.1086/147550
  * Dib et al. (2007) Dib, S., Kim, J., Vázquez-Semadeni, E., Burkert, A., & Shadmehri, M. 2007, ApJ, 661, 262, doi: 10.1086/513708
  * Dicaire et al. (2008) Dicaire, I., Carignan, C., Amram, P., et al. 2008, AJ, 135, 2038, doi: 10.1088/0004-6256/135/6/2038
  * Dobbs et al. (2011) Dobbs, C. L., Burkert, A., & Pringle, J. E. 2011, MNRAS, 413, 2935, doi: 10.1111/j.1365-2966.2011.18371.x
  * Donovan Meyer et al. (2013) Donovan Meyer, J., Koda, J., Momose, R., et al. 2013, ApJ, 772, doi: 10.1088/0004-637X/772/2/107
  * Elmegreen (1989) Elmegreen, B. G. 1989, ApJ, 338, 178, doi: 10.1086/167192
  * Elmegreen & Elmegreen (2019) Elmegreen, B. G., & Elmegreen, D. M. 2019, ApJS, 245, 14, doi: 10.3847/1538-4365/ab4903
  * Elmegreen & Elmegreen (1984) Elmegreen, D. M., & Elmegreen, B. G. 1984, ApJS, 54, 127, doi: 10.1086/190922
  * Elmegreen et al. (2014) Elmegreen, D. M., Elmegreen, B. G., Adamo, A., et al. 2014, ApJ, 787, L15, doi: 10.1088/2041-8205/787/1/L15
  * Evans et al. (2021) Evans, Neal J., I., Heyer, M., Miville-Deschênes, M.-A., Nguyen-Luong, Q., & Merello, M. 2021, ApJ, 920, 126, doi: 10.3847/1538-4357/ac1425
  * Evans et al. (2022) Evans, N. J., Kim, J.-G., & Ostriker, E. C. 2022, ApJ, 929, L18, doi: 10.3847/2041-8213/ac6427
  * Faesi et al. (2016) Faesi, C. M., Lada, C. J., & Forbrich, J. 2016, ApJ, 821, 125, doi: 10.3847/0004-637X/821/2/125
  * Finn et al. (2022) Finn, M. K., Indebetouw, R., Johnson, K. E., et al. 2022, AJ, 164, 64, doi: 10.3847/1538-3881/ac7aa1
  * Finn et al. (2024) Finn, M. K., Johnson, K. E., Indebetouw, R., et al. 2024, ApJ
  * Fomalont et al. (2014) Fomalont, E., van Kempen, T., Kneissl, R., et al. 2014, The Messenger, 155, 19
  * Gao et al. (2016) Gao, Q., Wang, W., Liu, J.-F., & Yoachim, P. 2016, arXiv e-prints, arXiv:1602.07841, doi: 10.48550/arXiv.1602.07841
  * Goldsmith et al. (2008) Goldsmith, P. F., Heyer, M., Narayanan, G., et al. 2008, ApJ, 680, 428, doi: 10.1086/587166
  * Gong et al. (2020) Gong, M., Ostriker, E. C., Kim, C.-G., & Kim, J.-G. 2020, ApJ, 903, 142, doi: 10.3847/1538-4357/abbdab
  * Grasha et al. (2017b) Grasha, K., Elmegreen, B. G., Calzetti, D., et al. 2017b, ApJ, 842, 25, doi: 10.3847/1538-4357/aa740b
  * Grasha et al. (2018) Grasha, K., Calzetti, D., Bittle, L., et al. 2018, MNRAS, 481, 1016, doi: 10.1093/MNRAS/STY2154
  * Grasha et al. (2019) Grasha, K., Calzetti, D., Adamo, A., et al. 2019, MNRAS, 483, 4707, doi: 10.1093/mnras/sty3424
  * Grasha et al. (2022) Grasha, K., Chen, Q. H., Battisti, A. J., et al. 2022, ApJ, 929, 118, doi: 10.3847/1538-4357/ac5ab2
  * Hannon et al. (2019) Hannon, S., Lee, J. C., Whitmore, B. C., et al. 2019, MNRAS, 490, 4648, doi: 10.1093/mnras/stz2820
  * Harris et al. (2020) Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2
  * Hart et al. (2017) Hart, R. E., Bamford, S. P., Casteels, K. R. V., et al. 2017, MNRAS, 468, 1850, doi: 10.1093/mnras/stx581
  * Hernandez et al. (2022) Hernandez, S., Winch, A., Larsen, S., James, B. L., & Jones, L. 2022, AJ, 164, 89, doi: 10.3847/1538-3881/ac7ebe
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
  * Hunter et al. (2023) Hunter, T. R., Indebetouw, R., Brogan, C. L., et al. 2023, PASP, 135, 074501, doi: 10.1088/1538-3873/ace216
  * Indebetouw et al. (2020) Indebetouw, R., Wong, T., Chen, C. H. R., et al. 2020, ApJ, 888, 56, doi: 10.3847/1538-4357/ab5db7
  * Kacharov et al. (2018) Kacharov, N., Neumayer, N., Seth, A. C., et al. 2018, MNRAS, 480, 1973, doi: 10.1093/mnras/sty1985
  * Kim et al. (2021) Kim, J.-G., Ostriker, E. C., & Filippova, N. 2021, ApJ, 911, 128, doi: 10.3847/1538-4357/abe934
  * Koda et al. (2009) Koda, J., Scoville, N., Sawada, T., et al. 2009, ApJ, 700, doi: 10.1088/0004-637X/700/2/L132
  * Koda et al. (2012) Koda, J., Scoville, N., Hasegawa, T., et al. 2012, ApJ, 761, doi: 10.1088/0004-637X/761/1/41
  * Koda et al. (2023) Koda, J., Hirota, A., Egusa, F., et al. 2023, ApJ, 949, 108, doi: 10.3847/1538-4357/acc65e
  * Koribalski et al. (2004) Koribalski, B. S., Staveley-Smith, L., Kilborn, V. A., et al. 2004, AJ, 128, 16\.  http://www.atnf.csiro.au/research
  * Koribalski et al. (2018) Koribalski, B. S., Wang, J., Kamphuis, P., et al. 2018, MNRAS, 478, 1611, doi: 10.1093/mnras/sty479
  * Larsen et al. (2007) Larsen, S. S., Mora, M. D., Brodie, J. P., & Richtler, T. 2007, in Stellar Populations as Building Blocks of Galaxies, ed. A. Vazdekis & R. Peletier, Vol. 241, 435–439, doi: 10.1017/S1743921307008708
  * Larson (1981) Larson, R. B. 1981, MNRAS, 194, 809, doi: 10.1093/mnras/194.4.809
  * Lazariv & Lehmann (2018) Lazariv, T., & Lehmann, C. 2018, Goodness-of-Fit Tests for Large Datasets.  https://arxiv.org/abs/1810.09753
  * Lee et al. (2009) Lee, J. C., Gil de Paz, A., Tremonti, C., et al. 2009, ApJ, 706, 599, doi: 10.1088/0004-637X/706/1/599
  * Leroy et al. (2021) Leroy, A. K., Schinnerer, E., Hughes, A., et al. 2021, ApJS, 257, 43, doi: 10.3847/1538-4365/ac17f3
  * Leroy et al. (2022) Leroy, A. K., Rosolowsky, E., Usero, A., et al. 2022, ApJ, 927, 149, doi: 10.3847/1538-4357/ac3490
  * Liszt et al. (2010) Liszt, H. S., Pety, J., & Lucas, R. 2010, A&A, 518, A45, doi: 10.1051/0004-6361/201014510
  * McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell, 127
  * Messa et al. (2021) Messa, M., Calzetti, D., Adamo, A., et al. 2021, ApJ, 909, 121, doi: 10.3847/1538-4357/abe0b5
  * Miville-Deschênes et al. (2017) Miville-Deschênes, M.-A., Murray, N., & Lee, E. J. 2017, ApJ, 834, 57, doi: 10.3847/1538-4357/834/1/57
  * Mondal et al. (2021) Mondal, C., Subramaniam, A., George, K., et al. 2021, ApJ, 909, 203, doi: 10.3847/1538-4357/abe0b4
  * Muraoka et al. (2016) Muraoka, K., Takeda, M., Yanagitani, K., et al. 2016, PASJ, 68, 18, doi: 10.1093/pasj/psv134
  * Nayak et al. (2016) Nayak, O., Meixner, M., Indebetouw, R., et al. 2016, ApJ, 831, 32, doi: 10.3847/0004-637X/831/1/32
  * Nguyen et al. (2018) Nguyen, N. K., Pettitt, A. R., Tasker, E. J., & Okamoto, T. 2018, MNRAS, 475, 27, doi: 10.1093/mnras/stx3143
  * Orozco-Duarte et al. (2022) Orozco-Duarte, R., Wofford, A., Vidal-García, A., et al. 2022, MNRAS, 509, 522, doi: 10.1093/mnras/stab2988
  * Peters et al. (1994) Peters, W. L., Freeman, K. C., Forster, J. R., Manchester, R. N., & Ables, J. G. 1994, MNRAS, 269, 1025, doi: 10.1093/mnras/269.4.1025
  * Pettitt et al. (2018) Pettitt, A. R., Egusa, F., Dobbs, C. L., et al. 2018, MNRAS, 480, 3356, doi: 10.1093/mnras/sty2040
  * Polak et al. (2023) Polak, B., Mac Low, M.-M., Klessen, R. S., et al. 2023, arXiv e-prints, arXiv:2312.06509, doi: 10.48550/arXiv.2312.06509
  * Qing et al. (2015) Qing, G., Wang, W., Liu, J.-F., & Yoachim, P. 2015, ApJ, 799, 19, doi: 10.1088/0004-637X/799/1/19
  * Querejeta et al. (2021) Querejeta, M., Schinnerer, E., Meidt, S., et al. 2021, A&A, 656, A133, doi: 10.1051/0004-6361/202140695
  * Radburn-Smith et al. (2011) Radburn-Smith, D. J., de Jong, R. S., Seth, A. C., et al. 2011, ApJS, 195, 18, doi: 10.1088/0067-0049/195/2/18
  * Radburn-Smith et al. (2012) Radburn-Smith, D. J., Roškar, R., Debattista, V. P., et al. 2012, ApJ, 753, 138, doi: 10.1088/0004-637X/753/2/138
  * Rice et al. (2016) Rice, T. S., Goodman, A. A., Bergin, E. A., Beaumont, C., & Dame, T. M. 2016, ApJ, 822, 52, doi: 10.3847/0004-637X/822/1/52
  * Rosolowsky et al. (2021) Rosolowsky, E., Hughes, A., Leroy, A. K., et al. 2021, MNRAS, 502, 1218, doi: 10.1093/mnras/stab085
  * Rosolowsky et al. (2008) Rosolowsky, E. W., Pineda, J. E., Kauffmann, J., & Goodman, A. A. 2008, ApJ, 679, 1338, doi: 10.1086/587685
  * Ryon et al. (2017) Ryon, J. E., Gallagher, J. S., Smith, L. J., et al. 2017, ApJ, 841, 92, doi: 10.3847/1538-4357/aa719e
  * Sabbi et al. (2018) Sabbi, E., Calzetti, D., Ubeda, L., et al. 2018, ApJS, 235, 23, doi: 10.3847/1538-4365/aaa8e5
  * Sacchi et al. (2019) Sacchi, E., Cignoni, M., Aloisi, A., et al. 2019, ApJ, 878, 1, doi: 10.3847/1538-4357/ab1de1
  * Sandage & Brucato (1979) Sandage, A., & Brucato, R. 1979, AJ, 84, 472, doi: 10.1086/112440
  * Schinnerer et al. (2013) Schinnerer, E., Meidt, S. E., Pety, J., et al. 2013, ApJ, 779, doi: 10.1088/0004-637X/779/1/42
  * Shabani et al. (2018) Shabani, F., Grebel, E. K., Pasquali, A., et al. 2018, MNRAS, 478, 3590, doi: 10.1093/mnras/sty1277
  * Sidorin (2017) Sidorin, V. 2017, Quickclump: Identify clumps within a 3D FITS datacube.  http://ascl.net/1704.006
  * Silva-Villa & Larsen (2012) Silva-Villa, E., & Larsen, S. S. 2012, MNRAS, 423, 213, doi: 10.1111/j.1365-2966.2012.20797.x
  * Solomon et al. (1987) Solomon, P. M., Rivolo, A. R., Barrett, J., & Yahil, A. 1987, ApJ, 319, 730, doi: 10.1086/165493
  * Stanghellini et al. (2015) Stanghellini, L., Magrini, L., & Casasola, V. 2015, ApJ, 812, doi: 10.1088/0004-637X/812/1/39
  * Stuber et al. (2023) Stuber, S. K., Schinnerer, E., Williams, T. G., et al. 2023, A&A, 676, A113, doi: 10.1051/0004-6361/202346318
  * Sun et al. (2018) Sun, J., Leroy, A. K., Schruba, A., et al. 2018, ApJ, 860, 172, doi: 10.3847/1538-4357/aac326
  * Sun et al. (2020) Sun, J., Leroy, A. K., Schinnerer, E., et al. 2020, ApJ, 901, L8, doi: 10.3847/2041-8213/abb3be
  * Sun et al. (2022) Sun, J., Leroy, A. K., Rosolowsky, E., et al. 2022, ApJ, 164, 43, doi: 10.3847/1538-3881/ac74bd
  * Tikhonov & Galazutdinova (2016) Tikhonov, N. A., & Galazutdinova, O. A. 2016, Astronomy Letters, 42, 428, doi: 10.1134/S1063773716070082
  * Turner et al. (2021) Turner, J. A., Dale, D. A., Lee, J. C., et al. 2021, MNRAS, 502, 1366, doi: 10.1093/mnras/stab055
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2
  * Vlajić et al. (2011) Vlajić, M., Bland-Hawthorn, J., & Freeman, K. C. 2011, ApJ, 732, 7, doi: 10.1088/0004-637X/732/1/7
  * Walsh & Roy (1997) Walsh, J. R., & Roy, J. R. 1997, MNRAS, 288, 726, doi: 10.1093/mnras/288.3.726
  * Whitmore et al. (2023) Whitmore, B. C., Chandar, R., Lee, J. C., et al. 2023, MNRAS, 520, 63, doi: 10.1093/mnras/stad098
  * Williams et al. (1995) Williams, J. P., Blitz, L., & Stark, A. A. 1995, ApJ, 451, 252, doi: 10.1086/176216
  * Wong et al. (2011) Wong, T., Hughes, A., Ott, J., et al. 2011, ApJS, 197, 16, doi: 10.1088/0067-0049/197/2/16
  * Wong et al. (2022) Wong, T., Oudshoorn, L., Sofovich, E., et al. 2022, ApJ, 932, 47, doi: 10.3847/1538-4357/ac723a
  * Zackrisson et al. (2011) Zackrisson, E., Rydberg, C.-E., Schaerer, D., Östlin, G., & Tuli, M. 2011, ApJ, 740, 13, doi: 10.1088/0004-637X/740/1/13
  * Zweibel (1990) Zweibel, E. G. 1990, ApJ, 348, 186, doi: 10.1086/168226

##  Appendix A Cloud Property Tables

We include demonstrative tables of the properties derived in Section 5, where
only the first 5 entries are shown. The full tables are available as
supplementary materials with the paper. We include tables for NGC 1313
dendrogram structures (Table A) and clumps (Table A), and NGC 7793 dendrogram
structures (Table A) and clumps (Table A).

Table 5: Catalog of NGC 1313 dendrogram properties

[tabular=c|c c c c c c c c c c c c, table head=ID RA Dec $W_{CO}$
CO${}_{\text{max}}$ Mass Radius $\sigma_{v}$ $\alpha_{\text{vir}}$ $\Sigma$
log($P_{e}/k_{B}$) $t_{ff}$
(deg) (deg) (K km s-1) (K) ($\times 10^{3}$ M⊙) (pc) (km s-1) (M⊙ pc-2) (K
cm-3) (Myr)
, filter=<5] NGC1313ClumpProps_Table.dat num=, RA=, Dec=, WCO21=, errWCO21=,
COmax=max, massnew=, errmassnew=, sigvnew=, errsigvnew=, Rnew=, errRnew=,
alpha= alphaerr=, surfacedensity=, surfacedensityerr=, Pturb=, Pturberr=,
tff=, tfferr= $\pm$ max $\pm$ $\pm$ $\pm$
±$\ealph\Sig$±$\eSig\Pe$±$\ePe\tf$±$\etf$

Table 6: Catalog of NGC 1313 clump properties

[tabular=c|c c c c c c c c c c c c, table head=ID RA Dec $W_{CO}$
CO${}_{\text{max}}$ Mass Radius $\sigma_{v}$ $\alpha_{\text{vir}}$ $\Sigma$
log($P_{e}/k_{B}$) $t_{ff}$
(deg) (deg) (K km s-1) (K) ($\times 10^{3}$ M⊙) (pc) (km s-1) (M⊙ pc-2) (K
cm-3) (Myr)
, filter=<5] NGC1313ClumpProps_CL_Table.dat num=, RA=, Dec=, WCO21=,
errWCO21=, COmax=max, massnew=, errmassnew=, sigvnew=, errsigvnew=, Rnew=,
errRnew=, alpha= alphaerr=, surfacedensity=, surfacedensityerr=, Pturb=,
Pturberr=, tff=, tfferr= $\pm$ max $\pm$ $\pm$ $\pm$
±$\ealph\Sig$±$\eSig\Pe$±$\ePe\tf$±$\etf$

Table 7: Catalog of NGC 7793 dendrogram properties

[tabular=c|c c c c c c c c c c c c, table head=ID RA Dec $W_{CO}$
CO${}_{\text{max}}$ Mass Radius $\sigma_{v}$ $\alpha_{\text{vir}}$ $\Sigma$
log($P_{e}/k_{B}$) $t_{ff}$
(deg) (deg) (K km s-1) (K) ($\times 10^{3}$ M⊙) (pc) (km s-1) (M⊙ pc-2) (K
cm-3) (Myr)
, filter=<5] NGC7793ClumpProps_Table.dat num=, RA=, Dec=, WCO21=, errWCO21=,
COmax=max, massnew=, errmassnew=, sigvnew=, errsigvnew=, Rnew=, errRnew=,
alpha= alphaerr=, surfacedensity=, surfacedensityerr=, Pturb=, Pturberr=,
tff=, tfferr= $\pm$ max $\pm$ $\pm$ $\pm$
±$\ealph\Sig$±$\eSig\Pe$±$\ePe\tf$±$\etf$

Table 8: Catalog of NGC 7793 clump properties

[tabular=c|c c c c c c c c c c c c, table head=ID RA Dec $W_{CO}$
CO${}_{\text{max}}$ Mass Radius $\sigma_{v}$ $\alpha_{\text{vir}}$ $\Sigma$
log($P_{e}/k_{B}$) $t_{ff}$
(deg) (deg) (K km s-1) (K) ($\times 10^{3}$ M⊙) (pc) (km s-1) (M⊙ pc-2) (K
cm-3) (Myr)
, filter=<5] NGC7793ClumpProps_CL_Table.dat num=, RA=, Dec=, WCO21=,
errWCO21=, COmax=max, massnew=, errmassnew=, sigvnew=, errsigvnew=, Rnew=,
errRnew=, alpha= alphaerr=, surfacedensity=, surfacedensityerr=, Pturb=,
Pturberr=, tff=, tfferr= $\pm$ max $\pm$ $\pm$ $\pm$
±$\ealph\Sig$±$\eSig\Pe$±$\ePe\tf$±$\etf$