# The Environments of CO Cores and Star Formation in the Dwarf Irregular
Galaxy WLM

Haylee N. Archer School of Earth and Space Exploration
Arizona State University
Tempe, AZ 85287 USA  Lowell Observatory
1400 W Mars Hill Rd
Flagstaff, AZ 86001 USA  Deidre A. Hunter Lowell Observatory
1400 W Mars Hill Rd
Flagstaff, AZ 86001 USA  Bruce G. Elmegreen IBM T. J. Watson Research Center
1101 Kitchawan Road
Yorktown Heights, NY 10598 USA  Phil Cigan George Mason University
4400 University Dr.
Fairfax, VA 22030-4444, USA  Rolf A. Jansen School of Earth and Space
Exploration
Arizona State University
Tempe, AZ 85287 USA  Rogier A. Windhorst School of Earth and Space Exploration
Arizona State University
Tempe, AZ 85287 USA  Leslie K. Hunt INAF, Osservatorio Astrofisico di Arcetri
Largo E Fermi 5
50125 Firenze Italy  Monica Rubio Departamento de Astronomía
Universidad de Chile
Casilla 36-D, 8320000 Santiago, Chile

(Received October 7, 2021; Revised January 10, 2022; Accepted January 23,
2022)

###### Abstract

The low metallicities of dwarf irregular galaxies (dIrr) greatly influence the
formation and structure of molecular clouds. These clouds, which consist
primarily of H2, are typically traced by CO, but low metallicity galaxies are
found to have little CO despite ongoing star formation. In order to probe the
conditions necessary for CO core formation in dwarf galaxies, we have used the
catalog of Rubio et al. (2022, in preparation) for CO cores in WLM, a Local
Group dwarf with an oxygen abundance that is 13% of solar. Here we aim to
characterize the galactic environments in which these 57 CO cores formed. We
grouped the cores together based on proximity to each other and strong FUV
emission, examining properties of the star forming region enveloping the cores
and the surrounding environment where the cores formed. We find that high H i
surface density does not necessarily correspond to higher total CO mass, but
regions with higher CO mass have higher H i surface densities. We also find
the cores in star forming regions spanning a wide range of ages show no
correlation between age and CO core mass, suggesting that the small size of
the cores is not due to fragmentation of the clouds with age. The presence of
CO cores in a variety of different local environments, along with the similar
properties between star forming regions with and without CO cores, leads us to
conclude that there are no obvious environmental characteristics that drive
the formation of these CO cores.

††journal: AJ††facilities: ALMA, VLA, GALEX, Lowell
Observatory:1.1m††software: IRAF (Tody, 1986), SExtractor (Bertin & Arnouts,
1996)

##  1 Introduction

Wolf-Lundmark-Melotte (WLM) is a Local Group, dwarf irregular (dIrr) galaxy at
a distance of $985\pm 33$ kiloparsecs (kpc) (Leaman et al., 2012). Like other
dwarf galaxies, the mass and metallicity of WLM are low, with a total stellar
mass of $1.62\times 10^{7}M_{\odot}$ (Zhang et al., 2012) and metallicity of
12$+$log(O/H)$=$7.8 (Lee et al., 2005). WLM is an isolated galaxy, and the
large spatial distances between it and both the Milky Way and M31 indicate a
low probability of past interaction with either (Teyssier et al., 2012; Albers
et al., 2019). The low mass, low metallicity, distance, and isolation of WLM
make it an ideal laboratory for understanding star formation in undisturbed
dwarf galaxies.

Star formation in galaxies is believed to be mostly regulated by molecular gas
found in giant molecular clouds (GMCs) in the interstellar medium (ISM)
(Kennicutt, 1998; McKee & Ostriker, 2007). The most abundant species in these
molecular clouds is molecular hydrogen (H2), which is nearly impossible to
observe in the typical conditions of the cold ISM because it does not possess
a permanent dipole moment and thus no dipolar rotational transitions (Bolatto
et al., 2013). As such, H2 is traced using indirect methods, the most common
of which is through the measurement of low rotational lines of carbon monoxide
(CO). Despite being much less abundant than H2 in molecular clouds, CO is
easily excited even in the cold ISM.

Many low-metallicity dwarf galaxies are found to have little CO despite
ongoing star formation (Elmegreen et al., 1980a), which disputes the standard
model of star formation in CO-rich molecular clouds. If the small amount of
detected CO is translated to the total H2 of the cloud using the standard
conversion factor, $X_{CO}$, of more massive galaxies, the high inferred star
formation efficiency of the dwarfs would make them outliers on the Schmidt-
Kennicutt relation (Kennicutt, 1998; Madden & Cormier, 2019). Elmegreen (1989)
finds that the increase in CO formation time at lower metallicity could result
in the disruption and dissociation of H2 before CO can form anywhere but in
the cores of larger clouds. This longer CO formation time is partly because
lower metallicity also corresponds to lower dust abundance, which allows far-
ultraviolet (FUV) photons to photodissociate CO molecules in the molecular
cloud and leave behind smaller CO cores (Elmegreen et al., 1980b; Taylor et
al., 1998; Schruba et al., 2012). H2 is self-shielded from the FUV photons and
can survive in the photodissociation region (PDR). This H2 gas that is not
traced by the CO cores is referred to as “dark” gas (Wolfire et al., 2010).
There is strong evidence that the observed lack of CO at low metallicities is
a natural consequence of the lower carbon and oxygen abundances as metallicity
decreases, with the result that the H2 is primarily associated with the so-
called CO-dark molecular gas (Wolfire et al., 2010; Planck Collaboration et
al., 2011; Pineda et al., 2014; Cormier et al., 2017).

Following the discovery by Elmegreen et al. (2013) of CO(3–2) in two star
forming regions of WLM using the APEX telescope, Rubio et al. (2015) used
pointed CO(1–0) of these regions with the the Atacama Large Millimeter Array
(ALMA) to map 10 CO cores for the first time at an oxygen abundance that is
13% of the solar value (Lee et al., 2005; Asplund et al., 2009). The PDR
region as traced by the C ii observations surrounding six of the discovered
cores is five times wider than the cluster of cores. This indicates that
molecular cloud structure at lower metallicities consists of thicker H2 shells
and smaller CO cores compared to those seen in the Milky Way (Rubio et al.,
2015; Cigan et al., 2016). An FUV image of the region with that PDR and the
six detected CO cores overlaid as contours is shown in Figure 1. Rubio et al.
(2022, in preparation) has since mapped most of the star forming area of WLM
with pointed ALMA CO(2–1) observations and detected an additional 47 cores.

Figure 1: FUV image of a WLM star forming region (region 1 in this paper, as
in Figures 3–6) overlaid with the PDR indicated by [C ii]$\lambda$158 $\mu$m
contours (red) of $2.5\times 10^{-19}$ and $4.6\times 10^{-19}$ W m-2 pix-1,
for pixels of 3$\farcs$13 per side, from Cigan et al. (2016) and 6 CO core
contours (green) from Rubio et al. (2015).

This paper seeks to characterize the galactic environments in which these star
forming CO cores formed in WLM to determine (1) if the CO cores have the same
properties in different local environments, (2) if areas where CO has formed
have different properties from star forming regions without detected CO, (3)
the nature of the stellar populations surrounding the molecular clouds, and
(4) the relationship between CO and star formation. The paper is organized as
follows. In Section 2 we introduce our multi-wavelength data and describe our
region selection and definitions of their environment, along with our methods
for determining the region age, stellar mass surface density, and CO-dark gas.
We present our results in Section 3 and discuss our findings in Section 4.

Figure 2: $V$ band image of WLM showing the ALMA field of view (FOV) from
Rubio et al. (2015) (smaller magenta squares) and Rubio et al. (2022, in
preparation) (larger magenta rectangle). The orientation of the image is such
that North is up and East is to the left. Colorbar values can be converted
from counts in one pixel (DN/pixel) to Johnson magnitudes with the equation:
$V_{Johnson}=0.0157(B-V)_{Johnson}-2.5\log V_{counts}+29.41$.

##  2 Data

Two star-forming regions of WLM were imaged in CO(1–0) with ALMA in Cycle 1 by
Rubio et al. (2015) where 10 CO cores were detected with an average radius of
2 pc and average virial mass of $2\times 10^{3}$ $M_{\odot}$. Another 47 CO
cores were discovered in WLM from Cycle 6 ALMA CO(2–1) observations over much
of the star-forming area of the galaxy, which included one of the two regions
observed in Cycle 1 (Rubio et al., 2022, in preparation). The beam size of
these observations were $0\farcs 6\times 0\farcs 5$. These two resulting
catalogues provide characteristics of the CO cores including locations, virial
masses, and surfaces densities. We use the sum of the virial masses of the
individual CO cores for each region ($M_{\textnormal{\scriptsize{CO}},vir}$)
and the median surface density of the individual CO cores in each region
($\Sigma_{\scriptsize{\textnormal{CO}}}$) to examine any relationships with
other star forming and environmental properties. Figure 2 shows the $V$ band
image of WLM overlaid with an outline of the total field of view observed by
Rubio et al. (2015) and Rubio et al. (2022, in preparation).

UBV images of WLM came from observations using the Lowell Observatory Hall
1.07-m Telescope. Further information on the acquisition and reduction of
these images are described by Hunter & Elmegreen (2006). H i surface density
($\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$) maps and H i
surface density radial profiles were acquired by Hunter et al. (2012) with the
Very Large Array (VLA111The VLA, now the Karl G. Jansky Very Large Array, is a
facility of the National Radio Astronomy Observatory. The National Radio
Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc.
Observations were made during the transition from the Very Large Array to the
Karl G. Jansky Very Large Array.) for the Local Irregulars That Trace
Luminosity Extremes, The H i Nearby Galaxy Survey (LITTLE THINGS), a multi-
wavelength survey of 37 nearby dIrr galaxies and 4 nearby Blue Compact Dwarf
(BCD) galaxies. The authors created robust-weighted and natural-weighted H i
maps, and we chose to use the robust-weighted maps due to the higher
resolution ($6\arcsec$). The FUV and near-ultraviolet (NUV) images came from
the NASA Galaxy Evolution Explorer (GALEX222GALEX was operated for NASA by the
California Institute of Technology under NASA contract NAS5-98034.) satellite
(Martin et al., 2005) GR4/5 pipeline, and were further reduced by Zhang et al.
(2012). We also used stellar mass surface density ($\Sigma_{*}$) and pressure
maps created by Hunter et al. (2018). The stellar mass surface density image
was determined on a pixel-by-pixel basis based on $B-V$ (Herrmann et al.,
2016), and the pressure map was calculated with the equation

$\textnormal{P}=2.934\times
10^{-55}\times\Sigma_{gas}(\Sigma_{gas}+(\frac{\sigma_{gas}}{\sigma_{*}})\Sigma_{*})\textnormal{
[g/(s${}^{2}$ cm)]}$ (1)

where $\Sigma$ is a surface density and $\sigma$ is a velocity dispersion
(Elmegreen, 1989). The $\Sigma_{gas}$ in the pressure map comes from the
robust-weighted H i map from Hunter et al. (2012). Further details on the
creation of these images are described by Hunter et al. (2018). To gain
insight into the formation of the CO cores, we used the pressure, H i surface
density, and stellar mass surface density data to characterize the regions
within which the CO cores formed and the environment surrounding the regions.
We also used the UBV, FUV, and NUV data for determining ages of the young
stars in the star-forming regions of the CO cores.

###  2.1 Regions

We grouped the CO cores into regions based on apparent proximity to FUV knots
and each other. The size and clustering of region 1 was chosen using both the
ALMA mapped CO cores of Rubio et al. (2015) and their [C ii]$\lambda$158
micron image from the Herschel Space Observatory indicating the PDR that
surrounds those cores (Figure 1). The other regions were chosen by eye based
on the following criteria: 1) apparent distance to nearby FUV emission within
the plane of the galaxy and 2) apparent distance to other CO cores, with the
size of the region determined by grouping CO cores that appeared to be closest
to the same FUV knots. We then used SExtractor (Bertin & Arnouts, 1996) with a
detection and analysis threshold of 3 sigma, a minimum of 10 pixels above the
threshold for detection, and a background mesh and filter size of 50 and 7
respectively to objectively identify the brighter FUV knots. We then computed
the distances between the center of the CO cores and the center of the
detected FUV sources to determine how far each CO core in a region is from its
closest detected FUV knot.

Figure 3: FUV image of WLM showing the ALMA FOV of region 1 from Rubio et al.
(2015) (smaller magenta square) and of the Rubio et al. (2022, in preparation)
survey (larger magenta rectangle), regions and annuli defined here (blue
circles for regions with CO cores and red dashed circles for the regions
without CO cores), and the CO cores (tiny green circles). Colorbar values can
be converted from counts to calibrated AB magnitudes with the equation:
FUV${}_{AB}=-2.5$log${}_{10}($FUV${}_{counts})+18.82.$ Figure 4: As in Figure
3, but for stellar mass surface density. The colorbar values are in units of
$M_{\odot}$ pc-2.  Figure 5: As in Figure 3, but for H i, with a beam size of
$7\farcs 6\times 5\farcs 1$. The colorbar values can be multiplied by 0.231 to
convert from J bm-1 m s-1 to $M_{\odot}$ pc-2 (see §2.2). Figure 6: As in
Figure 3, but for pressure with a beam size of $7\farcs 6\times 5\farcs 1$.
The pressure is dominated by the gas, as is evident from a comparison with
Figure 5. The colorbar values are in units of g s-2 cm-1.

We attempted to cluster the CO cores using the clustering algorithm DBSCAN
(Density-Based Spatial Clustering of Applications with Noise) (Ester et al.,
1996). We found that we could not reproduce the known clustering in region 1
with this algorithm. Depending on the parameters chosen, the algorithm would
either include most CO cores across the galaxy in the same cluster or leave
each core as an outlier.

Instead, we grouped the cores into 22 regions, several of which only include
one CO core. Four additional regions (regions 23, 24, 25, and 26) were
selected as regions including strong FUV emission without any CO cores. These
regions were used as comparisons to the regions containing CO cores. The
regions, along with the CO cores and ALMA FOV from both Rubio et al. (2015)
and Rubio et al. (2022, in preparation), are overlaid and labeled on the FUV,
stellar mass surface density, H i surface density, and pressure maps in
Figures 3, 4, 5, and 6, respectively. We list the region IDs, coordinates, and
sizes in Table 1.

###  2.2 Environments

Each region consists of a circular inner region representing the CO cores and
the star-forming region in which they currently sit, along with an outer
annulus which represents the projected environment in which the star-forming
region formed. We will refer to the star forming regions as the _inner
regions_ and the surrounding environments as the _annuli_. For region 1, we
chose the inner region to be about the size of the PDR. The outer annuli
widths used in measuring the environmental characteristics ranged from 3.7 to
14.2 arcseconds depending on the location of the CO cores in the galaxy and
their surrounding to minimize contamination from other regions. The annuli are
also overlaid on the FUV, stellar mass surface density, H i surface density,
and presssure maps in Figures 3, 4, 5, and 6, respectively and can be found in
Table 1.

We used the Image Reduction and Analysis Facility (IRAF) (Tody, 1986) routine
Apphot to measure the fluxes in the H i surface density, stellar mass surface
density, pressure map, $U$, $B$, $V$, FUV, and NUV images. We found the
average pixel value for each inner region and the modal pixel value each outer
annulus. The modal pixel value was chosen for the annulus to minimize
contamination from the environmental annulus overlapping other regions. We
converted the pixel values for the UBV images to Johnson magnitudes for each
region and the FUV and NUV image values for each region to AB magnitudes. We
also converted the H i surface density values from Jy$\cdot$m beam-1 s-1 to
$M_{\odot}$ pc-2 using the equation

$M_{HI}=235.6\ D^{2}\sum_{i}S_{i}\Delta V$ (2)

where $D$ is the distance to the object in Mpc, $S_{i}$ is the flux in Jy,
$\Delta V$ is the velocity resolution in m s-1, and $M_{HI}$ is in units of
$M_{\odot}$ (Brinks, private communication). The Robust-weighted H i moment 0
map ($S_{i}\Delta V$) is in units of Jy$\cdot$m beam-1 s-1 per pixel, so we
divide this by the number of pixels per beam

$M_{HI}=235.6\ D^{2}\sum_{i}S_{i}\Delta V\ \times\frac{pixel\ size^{2}}{1.13\
\Delta\alpha\Delta\delta}=208.5\ D^{2}\sum_{i}S_{i}\Delta V\
\times\frac{pixel\ size^{2}}{\Delta\alpha\Delta\delta}$ (3)

where the distance to WLM is 1 Mpc, the pixel size is 1$\farcs$5 and
$\Delta\alpha$ and $\Delta\delta$ are the beam semi-major and semi-minor axis,
which are 7$\farcs$6 and 5$\farcs$1 respectively. This makes the MHI in one
pixel

$M_{HI}=12.21\ S[Jy/beam\cdot m/s/pixel]\ M_{\odot}.$ (4)

One pixel is 52.93 pc2, so the H i surface density becomes

$\Sigma_{HI}=0.231\ S[Jy/beam\cdot m/s/pixel]\ \ M_{\odot}/pc^{2}.$ (5)

The stellar mass density and pressure map images were already in units of
$M_{\odot}$ pc-2 and g s-2 cm-1 respectively. We list the center coordinates,
radius of star forming region, and width of annulus of each region, along with
the background subtracted and extinction corrected colors described in §2.3
for each inner region can be found in Table 1, while the inner region H i
surface densities and stellar mass surface densities can be found in Table 2.
The extinction corrected colors, H i surface densities, stellar mass surface
densities, and pressures for each region’s corresponding annulus can be found
in Table 3. The quantities are averaged over regions or annuli that are larger
than the 6″ resolution of the H i and pressure maps except for a few annuli
widths, as can be seen in Table 1.

Table 1: Region centers & background subtracted photometry of star forming
regions

|  |  | Inner | Annulus |  |  |  |  |
---|---|---|---|---|---|---|---|---|---
| RA | Dec | Radius | Width | FUV | FUV $-$ NUV | $V$ | $U-B$ | $B-V$
Region | (J2000) | (J2000) | (″) | (″) | (mag) | (mag) | (mag) | (mag) | (mag)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
1 | 0:02:01.7 | –15:27:53.0 | 23.4 | 10.2 | 22.61 $\pm$ 0.01 | –0.32 $\pm$ 0.01 | 23.88 $\pm$ 0.06 | –0.32 $\pm$ 0.14 | –0.17 $\pm$ 0.08
2 | 0:01:57.0 | –15:26:55.5 | 25.0 | 10.0 | 23.27 $\pm$ 0.01 | –0.01 $\pm$ 0.01 | 23.66 $\pm$ 0.04 | –0.51 $\pm$ 0.09 | –0.06 $\pm$ 0.06
3 | 0:01:55.8 | –15:27:16.2 |  8.2 |  4.4 | 23.35 $\pm$ 0.01 | 0.23 $\pm$ 0.01 | 23.60 $\pm$ 0.04 | –0.45 $\pm$ 0.09 | –0.11 $\pm$ 0.05
4 | 0:01:55.1 | –15:27:27.5 |  5.9 |  4.3 | 24.54 $\pm$ 0.01 | 0.10 $\pm$ 0.01 | 25.41 $\pm$ 0.10 | –0.78 $\pm$ 0.29 | –0.41 $\pm$ 0.12
5 | 0:01:55.1 | –15:27:37.3 |  5.9 |  4.3 | 24.73 $\pm$ 0.01 | 0.10 $\pm$ 0.01 | 24.72 $\pm$ 0.07 | –0.20 $\pm$ 0.20 | 0.16 $\pm$ 0.10
6 | 0:01:54.2 | –15:27:08.3 |  5.9 |  4.3 | 22.70 $\pm$ 0.01 | –0.08 $\pm$ 0.01 | 23.84 $\pm$ 0.08 | 0.73 $\pm$ 0.29 | –0.30 $\pm$ 0.11
7 | 0:01:52.5 | –15:27:08.9 |  5.9 |  4.3 | 23.88 $\pm$ 0.01 | –0.56 $\pm$ 0.01 | 26.77 $\pm$ 0.18 | –0.62 $\pm$ 0.23 | –1.11 $\pm$ 0.20
8 | 0:01:59.6 | –15:27:16.7 |  5.9 |  4.3 | 17.04 $\pm$ 0.01 | –0.22 $\pm$ 0.01 | 21.69 $\pm$ 0.08 | –0.09 $\pm$ 0.33 | –0.01 $\pm$ 0.13
9 | 0:01:59.5 | –15:27:27.7 |  7.6 |  5.2 | 22.73 $\pm$ 0.01 | –0.51 $\pm$ 0.01 | 23.97 $\pm$ 0.06 | –0.46 $\pm$ 0.14 | –0.18 $\pm$ 0.08
10 | 0:01:59.4 | –15:28:56.2 |  9.1 |  7.8 | 23.62 $\pm$ 0.01 | –0.27 $\pm$ 0.01 | 24.70 $\pm$ 0.07 | –0.55 $\pm$ 0.14 | –0.18 $\pm$ 0.09
11 | 0:01:56.0 | –15:28:45.4 |  6.1 |  4.9 | 25.34 $\pm$ 0.01 | 0.56 $\pm$ 0.01 | 24.69 $\pm$ 0.07 | –0.80 $\pm$ 0.14 | –0.04 $\pm$ 0.09
12 | 0:01:56.1 | –15:28:37.8 | 11.0 |  9.2 | 22.17 $\pm$ 0.01 | –0.24 $\pm$ 0.01 | 23.20 $\pm$ 0.04 | –0.55 $\pm$ 0.08 | –0.08 $\pm$ 0.05
13 | 0:01:53.8 | –15:28:43.8 | 11.5 | 11.3 | 24.00 $\pm$ 0.01 | 0.19 $\pm$ 0.01 | 23.48 $\pm$ 0.04 | –0.07 $\pm$ 0.11 | 0.05 $\pm$ 0.05
14 | 0:01:55.3 | –15:29:18.1 |  9.4 |  6.8 | 25.22 $\pm$ 0.01 | –0.68 $\pm$ 0.01 | 26.15 $\pm$ 0.14 | –1.15 $\pm$ 0.22 | –0.31 $\pm$ 0.18
15 | 0:01:56.4 | –15:29:24.1 |  9.4 |  6.8 | 22.68 $\pm$ 0.01 | –0.05 $\pm$ 0.01 | 23.29 $\pm$ 0.04 | –0.53 $\pm$ 0.10 | 0.19 $\pm$ 0.05
16 | 0:01:53.6 | –15:27:27.4 | 10.0 | 10.0 | 23.13 $\pm$ 0.01 | –0.09 $\pm$ 0.01 | 23.19 $\pm$ 0.04 | –0.49 $\pm$ 0.09 | 0.16 $\pm$ 0.05
17 | 0:01:54.7 | –15:26:25.8 |  8.0 |  6.0 | 24.60 $\pm$ 0.01 | –0.01 $\pm$ 0.01 | 24.75 $\pm$ 0.07 | –0.03 $\pm$ 0.18 | –0.12 $\pm$ 0.09
18 | 0:01:58.5 | –15:27:55.5 |  9.4 |  6.8 | 19.77 $\pm$ 0.01 |  $\cdots$ 11NUV background counts were higher than measured inside the region. | 22.80 $\pm$ 0.11 | 0.53 $\pm$ 0.36 | –0.31 $\pm$ 0.18
19 | 0:01:59.4 | –15:28:29.5 |  9.4 |  6.8 | 23.20 $\pm$ 0.01 | –0.18 $\pm$ 0.01 | 23.99 $\pm$ 0.06 | –0.20 $\pm$ 0.16 | 0.05 $\pm$ 0.08
20 | 0:01:53.2 | –15:28:11.4 |  9.4 |  6.8 | 17.90 $\pm$ 0.01 | –0.47 $\pm$ 0.01 | 21.81 $\pm$ 0.05 | –0.23 $\pm$ 0.19 | 0.07 $\pm$ 0.08
21 | 0:02:00.2 | –15:29:17.9 |  9.4 |  6.8 | 24.66 $\pm$ 0.01 | –0.35 $\pm$ 0.01 | 25.28 $\pm$ 0.09 | –0.07 $\pm$ 0.21 | –0.29 $\pm$ 0.12
22 | 0:01:59.4 | –15:29:36.7 |  9.4 |  6.8 |  $\cdots$ 22FUV background counts were higher than measured inside the region. |  $\cdots$ 22FUV background counts were higher than measured inside the region. | 23.98 $\pm$ 0.08 | 1.06 $\pm$ 0.37 | –0.28 $\pm$ 0.12
23 | 0:01:54.5 | –15:26:54.4 | 16.0 | 14.2 | 23.08 $\pm$ 0.01 | –0.27 $\pm$ 0.01 | 24.11 $\pm$ 0.06 | –0.71 $\pm$ 0.13 | –0.12 $\pm$ 0.08
24 | 0:01:57.8 | –15:27:36.7 |  7.4 |  4.0 | 24.90 $\pm$ 0.01 | –0.07 $\pm$ 0.01 | 28.97 $\pm$ 0.50 | –4.94 $\pm$ 0.25 | 1.45 $\pm$ 0.55
25 | 0:01:56.3 | –15:27:59.8 |  9.6 |  5.3 | 22.48 $\pm$ 0.01 | –0.08 $\pm$ 0.01 | 22.97 $\pm$ 0.04 | –0.18 $\pm$ 0.14 | –0.08 $\pm$ 0.06
26 | 0:01:53.7 | –15:29:25.4 |  8.1 |  3.7 | 20.62 $\pm$ 0.01 | –0.40 $\pm$ 0.01 | 23.58 $\pm$ 0.06 | –0.06 $\pm$ 0.23 | –0.23 $\pm$ 0.11

Note. — Magnitudes and colors are background subtracted and corrected for
Galactic foreground and internal extinction.

Table 2: Characteristics of star forming regions

|  |  |  |  |  |  |  | Log Age
---|---|---|---|---|---|---|---|---
| $\Sigma_{*\tiny{\textnormal{,SF}}}$ | $\Sigma_{\tiny{\textnormal{H}\,\textnormal{\sc{i},SF}}}$ |  $\Sigma_{\tiny{\textnormal{H}\,\textnormal{\sc{i},SF}}}-\Sigma_{\tiny{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,rad}}}$ 11Average star forming region $\Sigma_{\tiny{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$ above radial average $\Sigma_{\tiny{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,rad}}}$. Uncertainties are carried over from the $\Sigma_{\tiny{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$ of the region. |  $M_{\tiny{\textrm{CO, }vir}}$ 22Sum of CO core virial masses given by Rubio et al. (2015) and Rubio et al. (2022, in preparation) |  $\Sigma_{\tiny{\textrm{CO}}}$ 33Rubio et al. (2015) and Rubio et al. (2022, in preparation) calculated the $\Sigma_{\tiny{\textrm{CO}}}$ of the individual CO cores from their $M_{\tiny{\textrm{CO},vir}}$. For each ensemble of individual $\Sigma_{\tiny{\textrm{CO}}}$ in a given region, we adopt the median $\Sigma_{\tiny{\textrm{CO}}}$ value. The $\Sigma_{\tiny{\textrm{CO}}}$ $\pm$ uncertainties represent the range of $\Sigma_{\tiny{\textrm{CO}}}$ for each region containing multiple CO cores. |  $M_{\tiny{Dark\textrm{ H}_{2}}}$/$M_{\tiny{MC}}$ 44Percentage of original total molecular cloud mass in dark H2. | $E(B\\!-\\!V)$ | (Chabrier IMF)
Region | ($M_{\odot}\textrm{ pc}^{-2}$) | ($M_{\odot}\textrm{ pc}^{-2}$) | ($M_{\odot}\textrm{ pc}^{-2}$) | ($M_{\odot}$) | ($M_{\odot}\textrm{ pc}^{-2}$) | (%) | (Chabrier IMF) | (years)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
1 | $0.06^{+0.74}_{-0.00}$ | 21.33$\pm$0.01 | 15.30$\pm$0.01 | 21700$\pm$6440 | $106.4^{+421.6}_{-67.6}$ | $82.1^{+17.2}_{-0.0}$ | 0.21 | $6.62^{+1.19}_{-0.02}$
2 | $0.91^{+0.03}_{-0.39}$ | 24.05$\pm$0.01 | 17.96$\pm$0.01 | 33900$\pm$5260 | $106.7^{+682.5}_{-80.0}$ | $98.4^{+0.8}_{-0.0}$ | 0.06 | $7.74^{+0.02}_{-0.42}$
3 | $1.18^{+0.24}_{-0.19}$ | 21.91$\pm$0.01 | 16.13$\pm$0.01 | 4300$\pm$2550 | $101.4^{+54.1}_{-54.1}$ | $98.5^{+0.9}_{-0.0}$ | 0.06 | $7.91^{+0.15}_{-0.15}$
4 | $0.56^{+0.05}_{-0.21}$ | 20.11$\pm$0.01 | 14.54$\pm$0.01 | 1790$\pm$888 | $74.3^{+50.8}_{-50.8}$ | $97.5^{+1.4}_{-0.0}$ | 0.06 | $8.56^{+0.05}_{-0.30}$
5 | $0.55^{+0.16}_{-0.21}$ | 19.63$\pm$0.01 | 14.61$\pm$0.01 | 4160$\pm$2000 | $145.1^{+105.8}_{-106.0}$ | $94.2^{+3.6}_{-0.0}$ | 0.08 | $8.16^{+0.20}_{-0.40}$
6 | $1.46^{+0.39}_{-0.29}$ | 16.15$\pm$0.01 | 11.63$\pm$0.01 | 2140$\pm$1130 | $61.5^{+0}_{-0}$ | $98.9^{+0.7}_{-0.0}$ | 0.42 | $8.26^{+0.20}_{-0.15}$
7 | $0.02^{+0.00}_{-0.01}$ | 16.90$\pm$0.01 | 13.80$\pm$0.01 | 571$\pm$1050 | $32.70^{+0}_{-0}$ | $71.4^{+14.3}_{-17.1}$ | 0.06 | $6.40^{+0.10}_{-0.00}$
8 | $2.05^{+2.60}_{-0.00}$ | 18.61$\pm$0.01 | 15.26$\pm$0.01 | 2800$\pm$1960 | $121.1^{+61.1}_{-61.1}$ | $98.9^{+0.8}_{-0.0}$ | 1.10 | $7.10^{+0.53}_{-0.08}$
9 | $0.06^{+0.00}_{-0.01}$ | 20.45$\pm$0.01 | 16.73$\pm$0.01 | 16800$\pm$2170 | $138.4^{+56.1}_{-77.6}$ | $0.0^{+38.7}_{-0.0}$ | 0.20 | $6.50^{+0.02}_{-0.00}$
10 | $0.03^{+0.02}_{-0.00}$ | 15.48$\pm$0.01 | 11.32$\pm$0.01 | 3050$\pm$1900 | $100.3^{+34.7}_{-34.7}$ | $67.1^{+23.7}_{-0.0}$ | 0.06 | $6.64^{+0.02}_{-0.12}$
11 | $0.21^{+0.46}_{-0.02}$ | 17.44$\pm$0.01 | 12.70$\pm$0.01 | 935$\pm$586 | $114.6^{+0}_{-0}$ | $96.8^{+0.2}_{-0.0}$ | 0.06 | $7.34^{+0.92}_{-0.16}$
12 | $0.11^{+0.01}_{-0.00}$ | 15.62$\pm$0.01 | 10.70$\pm$0.01 | 6010$\pm$1820 | $85.4^{+31.5}_{-31.5}$ | $87.7^{+6.6}_{-0.0}$ | 0.08 | $6.62^{+0.00}_{-0.02}$
13 | $2.05^{+0.33}_{-0.18}$ | 14.92$\pm$0.01 | 11.63$\pm$0.01 | 3960$\pm$2330 | $146.9^{+3.1}_{-6.1}$ | $99.6^{+0.2}_{-0.0}$ | 0.06 | $8.26^{+0.15}_{-0.05}$
14 | $0.03^{+0.00}_{-0.01}$ | 19.05$\pm$0.01 | 15.58$\pm$0.01 | 701$\pm$565 | $33.3^{+0}_{-0}$ | $92.2^{+3.9}_{-0.0}$ | 0.08 | $6.40^{+0.06}_{-0.00}$
15 | $1.03^{+0.00}_{-0.01}$ | 22.03$\pm$0.01 | 18.16$\pm$0.01 | 10100$\pm$5020 | $182.5^{+232.9}_{-97.6}$ | $97.0^{+1.6}_{-0.0}$ | 0.11 | $7.59^{+0.06}_{-0.15}$
16 | $1.17^{+0.08}_{-0.25}$ | 17.84$\pm$0.01 | 13.09$\pm$0.01 | 543$\pm$1130 | $34.6^{+0}_{-0}$ | $99.9^{+0.1}_{-0.0}$ | 0.08 | $7.63^{+0.05}_{-0.17}$
17 | $0.46^{+0.12}_{-0.05}$ | 21.02$\pm$0.01 | 16.13$\pm$0.01 | 1760$\pm$2780 | $64.4^{+0}_{-0}$ | $98.4^{+1.0}_{-0.0}$ | 0.06 | $8.01^{+0.20}_{-0.10}$
18 | $0.60^{+0.19}_{-0.05}$ | 12.71$\pm$0.01 |  8.51$\pm$0.01 | 469$\pm$1090 | $30.3^{+0}_{-0}$ | $99.8^{+0.3}_{-0.0}$ | 1.03 | $6.40^{+0.72}_{-0.00}$
19 | $0.73^{+0.14}_{-0.05}$ | 20.98$\pm$0.01 | 17.09$\pm$0.01 | 1020$\pm$1680 | $102.4^{+0}_{-0}$ | $99.6^{+0.2}_{-0.0}$ | 0.16 | $8.01^{+0.20}_{-0.10}$
20 | $0.47^{+0.66}_{-0.00}$ | 12.78$\pm$0.01 |  9.69$\pm$0.01 | 518$\pm$1010 | $146.5^{+0}_{-0}$ | $99.7^{+0.3}_{-0.0}$ | 0.81 | $6.50^{+0.48}_{-0.02}$
21 | $0.25^{+0.01}_{-0.23}$ | 24.15$\pm$0.01 | 19.58$\pm$0.01 | 447$\pm$634 | $43.8^{+0}_{-0}$ | $99.5^{+0.3}_{-3.7}$ | 0.06 | $7.91^{+0.05}_{-1.29}$
22 | $2.68^{+0.00}_{-0.00}$ | 26.71$\pm$0.01 | 22.06$\pm$0.01 |  665$\pm$1000 | $94^{+0}_{-0}$ | $99.9^{+0.0}_{-0.0}$ | 0.43 | $8.71^{+0.00}_{-0.00}$
23 | $0.09^{+0.02}_{-0.00}$ | 18.73$\pm$0.01 | 13.02$\pm$0.01 | 0 | 0 | 100 | 0.17 | $6.76^{+0.08}_{-0.04}$
24 | $0.002^{+0.000}_{-0.000}$ | 15.22$\pm$0.01 | 10.54$\pm$0.01 | 0 | 0 | 100 | 0.06 | $6.40^{+0.00}_{-0.00}$
25 | $2.32^{+1.43}_{-0.00}$ |  7.52$\pm$0.01 |  1.67$\pm$0.01 | 0 | 0 | 100 | 0.30 | $8.01^{+0.40}_{-0.15}$
26 | $0.08^{+1.42}_{-0.00}$ | 15.64$\pm$0.01 | 12.86$\pm$0.01 | 0 | 0 | 100 | 0.51 | $6.62^{+1.49}_{-1.19}$

Table 3: Colors and characteristics of environments

|  |  |  |  |  |  | Pressure |  | Log Age
---|---|---|---|---|---|---|---|---|---
| FUV | FUV $-$ NUV | $V$ | $U-B$ | $B-V$ | $\Sigma_{*\tiny{\textnormal{,env}}}$ | ($\times 10^{-12}$) | $\Sigma_{\tiny{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$ | (Chabrier IMF)
Region | (mag) | (mag) | (mag) | (mag) | (mag) | ($M_{\odot}\textrm{ pc}^{-2}$) | (g s-2 cm-1) | ($M_{\odot}\textrm{ pc}^{-2}$) | (years)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
1 | 24.87$\pm$0.01 |  0.58$\pm$0.01 | 22.86$\pm$0.03 | –0.04$\pm$0.10 | 0.36$\pm$0.04 | 10.30$\pm$0.28 | 3.86$\pm$4.29 | 19.50$\pm$0.01 | $8.81^{+0.00}_{-0.05}$
2 | 24.43$\pm$0.01 |  0.26$\pm$0.01 | 22.65$\pm$0.03 | 0.09$\pm$0.09 | 0.37$\pm$0.04 | 12.02$\pm$0.29 | 5.66$\pm$4.67 | 21.22$\pm$0.01 | $8.61^{+0.05}_{-0.15}$
3 | 23.69$\pm$0.01 |  0.01$\pm$0.01 | 22.52$\pm$0.03 | –0.08$\pm$0.08 | 0.28$\pm$0.04 | 12.38$\pm$0.28 | 5.68$\pm$4.02 | 18.27$\pm$0.01 | $8.31^{+0.05}_{-0.20}$
4 | 23.84$\pm$0.01 |  0.03$\pm$0.01 | 22.87$\pm$0.03 | –0.17$\pm$0.09 | 0.32$\pm$0.04 |  9.10$\pm$0.25 | 5.33$\pm$4.80 | 21.81$\pm$0.01 | $8.16^{+0.05}_{-0.20}$
5 | 24.09$\pm$0.01 | –0.02$\pm$0.01 | 23.10$\pm$0.03 | 0.04$\pm$0.11 | 0.31$\pm$0.05 |  8.79$\pm$0.27 | 4.78$\pm$4.17 | 18.92$\pm$0.01 | $8.36^{+0.05}_{-0.20}$
6 | 24.16$\pm$0.01 |  0.18$\pm$0.01 | 23.00$\pm$0.03 | –0.002$\pm$0.10 | 0.33$\pm$0.05 |  8.25$\pm$0.24 | 3.59$\pm$3.67 | 16.66$\pm$0.01 | $8.46^{+0.00}_{-0.05}$
7 | 24.74$\pm$0.01 |  0.29$\pm$0.01 | 23.31$\pm$0.04 | 0.06$\pm$0.12 | 0.30$\pm$0.05 |  5.89$\pm$0.19 | 2.81$\pm$3.42 | 15.56$\pm$0.01 | $8.61^{+0.05}_{-0.10}$
8 | 23.85$\pm$0.01 |  0.15$\pm$0.01 | 22.46$\pm$0.02 | 0.08$\pm$0.08 | 0.25$\pm$0.04 | 13.83$\pm$0.31 | 5.56$\pm$4.19 | 19.05$\pm$0.01 | $8.46^{+0.00}_{-0.05}$
9 | 23.94$\pm$0.01 |  0.31$\pm$0.01 | 22.45$\pm$0.02 | 0.02$\pm$0.08 | 0.35$\pm$0.04 | 13.65$\pm$0.31 | 5.07$\pm$4.13 | 18.78$\pm$0.01 | $8.61^{+0.05}_{-0.10}$
10 | 24.44$\pm$0.01 |  0.09$\pm$0.01 | 22.87$\pm$0.03 | –0.02$\pm$0.10 | 0.36$\pm$0.04 | 10.11$\pm$0.27 | 4.38$\pm$3.94 | 17.90$\pm$0.01 | $8.41^{+0.05}_{-0.05}$
11 | 24.53$\pm$0.01 |  0.04$\pm$0.01 | 22.87$\pm$0.03 | –0.03$\pm$0.10 | 0.50$\pm$0.05 |  8.68$\pm$0.23 | 3.65$\pm$4.08 | 18.56$\pm$0.01 | $8.41^{+0.05}_{-0.05}$
12 | 24.18$\pm$0.01 |  0.18$\pm$0.01 | 22.88$\pm$0.03 | –0.09$\pm$0.09 | 0.31$\pm$0.04 |  7.67$\pm$0.21 | 2.48$\pm$3.01 | 13.71$\pm$0.01 | $8.41^{+0.05}_{-0.05}$
13 | 23.12$\pm$0.01 | –0.08$\pm$0.01 | 23.05$\pm$0.03 | –0.36$\pm$0.08 | 0.18$\pm$0.05 |  5.04$\pm$0.15 | 1.93$\pm$2.75 | 12.50$\pm$0.01 | $7.72^{+0.09}_{-0.02}$
14 | 23.77$\pm$0.01 |  0.14$\pm$0.01 | 23.01$\pm$0.03 | –0.14$\pm$0.09 | 0.22$\pm$0.05 |  6.98$\pm$0.20 | 3.39$\pm$4.16 | 18.89$\pm$0.01 | $8.31^{+0.10}_{-0.10}$
15 | 24.91$\pm$0.01 |  0.14$\pm$0.01 | 23.01$\pm$0.03 | –0.21$\pm$0.09 | 0.28$\pm$0.05 |  7.64$\pm$0.22 | 4.97$\pm$4.58 | 20.80$\pm$0.01 | $8.31^{+0.10}_{-0.10}$
16 | 24.48$\pm$0.01 |  0.19$\pm$0.01 | 23.25$\pm$0.04 | –0.15$\pm$0.11 | 0.36$\pm$0.05 |  6.40$\pm$0.20 | 2.86$\pm$3.21 | 14.61$\pm$0.01 | $8.41^{+0.05}_{-0.05}$
17 | 25.51$\pm$0.01 |  0.11$\pm$0.01 | 23.13$\pm$0.03 | 0.18$\pm$0.12 | 0.49$\pm$0.05 |  9.24$\pm$0.28 | 4.97$\pm$4.39 | 19.97$\pm$0.01 | $8.46^{+0.00}_{-0.00}$
18 | 24.46$\pm$0.01 |  0.39$\pm$0.01 | 22.60$\pm$0.03 | 0.19$\pm$0.09 | 0.41$\pm$0.04 | 13.33$\pm$0.32 | 2.96$\pm$2.84 | 12.90$\pm$0.01 | $8.71^{+0.05}_{-0.05}$
19 | 23.96$\pm$0.01 |  0.19$\pm$0.01 | 22.71$\pm$0.03 | –0.06$\pm$0.09 | 0.32$\pm$0.04 | 10.54$\pm$0.26 | 4.48$\pm$4.00 | 18.17$\pm$0.01 | $8.41^{+0.05}_{-0.05}$
20 | 25.33$\pm$0.01 |  0.37$\pm$0.01 | 23.63$\pm$0.04 | 0.11$\pm$0.14 | 0.38$\pm$0.06 |  6.18$\pm$0.24 | 1.71$\pm$2.55 | 11.58$\pm$0.01 | $8.66^{+0.10}_{-0.00}$
21 | 24.83$\pm$0.01 |  0.37$\pm$0.01 | 22.99$\pm$0.03 | 0.004$\pm$0.10 | 0.41$\pm$0.05 |  8.66$\pm$0.25 | 7.54$\pm$5.09 | 23.11$\pm$0.01 | $8.66^{+0.05}_{-0.05}$
22 | 23.89$\pm$0.01 |  0.09$\pm$0.01 | 22.92$\pm$0.03 | –0.17$\pm$0.09 | 0.28$\pm$0.04 |  7.92$\pm$0.22 | 7.25$\pm$5.33 | 24.21$\pm$0.01 | $8.31^{+0.05}_{-0.20}$
23 | 24.64$\pm$0.01 |  0.36$\pm$0.01 | 22.98$\pm$0.03 | 0.22$\pm$0.11 | 0.39$\pm$0.05 |  8.74$\pm$0.30 | 3.40$\pm$4.36 | 19.81$\pm$0.01 | $8.71^{+0.00}_{-0.05}$
24 | 20.79$\pm$0.01 |  0.12$\pm$0.01 | 22.57$\pm$0.03 | 0.10$\pm$0.09 | 0.36$\pm$0.04 | 11.89$\pm$0.21 | 4.35$\pm$3.60 | 16.37$\pm$0.01 | $8.46^{+0.00}_{-0.05}$
25 | 21.02$\pm$0.01 |  0.29$\pm$0.01 | 22.89$\pm$0.03 | –0.07$\pm$0.09 | 0.31$\pm$0.04 | 10.03$\pm$0.27 | 3.77$\pm$3.71 | 16.84$\pm$0.01 | $8.51^{+0.10}_{-0.00}$
26 | 21.83$\pm$0.01 |  0.45$\pm$0.01 | 21.57$\pm$0.03 | 0.10$\pm$0.09 | 0.36$\pm$0.04 |  4.68$\pm$0.12 | 2.79$\pm$3.36 | 15.26$\pm$0.01 | $8.76^{+0.00}_{-0.05}$

Note. — Magnitudes and colors have been corrected for extinction.

###  2.3 Age

To calculate the age of each inner region, we used the colors in the region
and iterated on reddening to find the best fit with cluster evolutionary
models. First, to determine the region colors, we subtracted the background
stellar disk from each region. To do so, we subtracted the mode of the pixel
values of the outer annulus, measured using Apphot, from the average pixel
value in the inner region. We chose to use the mode of the surroundings rather
than the average in order minimize contamination from other star-forming
regions (partially) sampled by the annulus.

Figure 7: Left: Histogram of ages of the environment where CO cores formed
(blue) and environment surrounding the star forming regions without any CO
cores (red). Right: Histogram of ages of star forming regions with CO cores
(blue) and the star forming regions without any CO cores (red). Ages were
computed using the Chabrier IMF.

To find the extinction toward each region, we computed FUV $-$ NUV, $U-B$, and
$B-V$ colors using a series of $E(B\\!-\\!V)$ values ranging from 0.06–1.5 in
steps of 0.01. The lower $E(B\\!-\\!V)$ limit of 0.06 was selected from adding
the Milky Way foreground reddening and a minimal (0.05 mag) internal reddening
for stars (Schlafly & Finkbeiner, 2011; Cardelli et al., 1989). We used an
upper limit $E(B\\!-\\!V)$ of 1.5 in our model search as it is higher than the
estimates of reddening necessary to form CO molecules in the Milky Way (Glover
& Clark, 2012; Lee et al., 2018).

We then compared the background-subtracted FUV $-$ NUV, $U-B$, and $B-V$
colors to evolutionary stellar population synthesis models from GALEXEV
(Bruzual & Charlot, 2003). The single stellar population (SSP) models used
were computed using the Bertelli et al. (1994) Padova evolutionary tracks with
a metallicity of 0.004, as this was closest of the models to the WLM
metallicity of $\sim$0.003. We compared models computed using both the
Chabrier (2003) initial mass function (IMF) and the Salpeter (1955) IMF with
the aforementioned evolutionary tracks and metallicity. We then compared the
observed and modeled FUV $-$ NUV, $U-B$, and $B-V$ colors to find the age that
corresponded to the closest fit for each $E(B\\!-\\!V)$ value. For each
region, we adopt the combination of age and $E(B\\!-\\!V)$ that minimizes the
residuals between observed and modeled colors. Using this extinction, we then
compared the FUV $-$ NUV, $U-B$, and $B-V$ colors with their respective upper
and lower uncertainty limits and the model colors, and selected these as the
worst case scenario upper and lower age uncertainties of that region. Both
IMFs produced similar results, so we report only $E(B\\!-\\!V)$ and ages
calculated using the Chabrier IMF in Table 2. Figure 7 shows a histogram of
the ages of the inner regions.

Grasha et al. (2018, 2019) find a strong correlation between the age of star
clusters and distance from their GMCs, with the age distribution increasing as
the cluster-GMC distance increases. For star forming regions that contained
multiple FUV knots, we used the method described above to explore the ages of
the individual knots compared to the age we computed for the entire region. We
selected the photometry aperture size for each knot based on the FUV and $V$
images to encompass as much as was likely to be part of the same star forming
knot. We used a larger aperture size around multiple knots that could not be
individually resolved. For each star forming region, the individual knots have
the same or similar ages as that of the entire region. For example, individual
knots in region 1 range from 3.2 to 4.4 Myr, with 10 out of 13 regions having
the same age as we calculated for the entire region – 4.2 Myr. Similarly, the
average $E(B\\!-\\!V)$ of the individual knots in region 1 is 0.23, while that
of the entire region is 0.21. Figure 8 shows the star forming regions with
multiple knots and the photometry apertures we selected for the individual
knots in each region. We note that the ages and reddening of the knots are
sensitive to aperture size and background subtraction selection due to the
crowding of knots within the regions.

Figure 8: FUV image of star forming regions (blue solid or red dashed
circles), star forming knots (red circles), and CO cores (green circles) for
which we compared the average of the ages of the individual knots to the
calculated age of the entire region. We find that the individual knot ages are
the same or similar to the age of the region comprising the knots.  Figure 9:
The age of the inner region plotted against the average distance of the CO
cores in that region to its nearest FUV knot in parsecs. Age error bars that
appear one-sided are the result of the upper or lower color uncertainties
finding the same age in the model. Regions 18 and 22 are marked with an
($\times$) as the age was determined from UBV alone. Figure 10: Comparison of
(_a_) inferred ages, log(age), and (_b_) color excesses, $E(B\\!-\\!V)$, of
the inner regions, computed using either background subtracted fluxes (method
1; horizontal axes) or background subtracted colors (method 2; vertical axes).
Age error bars that appear one-sided are the result of the upper or lower
color uncertainties finding the same age in the model. The gray line
represents where both methods return the same age or $E(B\\!-\\!V)$. Regions
18 and 22 are marked with an ($\times$) as the age from the background flux
subtraction was determined from UBV alone. The regions without CO (regions 23,
24, 25, and 26) are marked with a red star ($\star$).

The projected distance from the CO core to the nearest FUV knot in regions 22
and especially 18 is greater than for most other regions (Figure 9) and the
NUV or FUV background measured in their annuli exceeded the corresponding
average of their inner region. One reason for this may be that the inner star
forming region actually extends into the annulus we adopted for the
environment. This prevented us from placing meaningful constraints on the FUV
$-$ NUV colors of these regions. We see in Figure 9 that there are possibly
two relationships showing the age of a region increasing with distance from
its nearest FUV knot (one above log(age) $\simeq$ 7.25 and one below), but
there is no clear explanation for why the regions would separate into these
two sequences. As such, only the $U-B$ and $B-V$ colors were used in the age
calculation for these two regions. We mark these regions with an ($\times$)
when showing the region ages (Figures 15 and 20). We also examined subtracting
the background colors instead of the background fluxes to find the color
excess before iterating on reddening, which allowed us to use the FUV $-$ NUV,
$U-B$, and $B-V$ colors in the age calculation of all regions. We compare the
two methods in Figure 10, where we see a trade-off between the extinction and
the age. Subtracting the background colors typically finds regions to have
lower $E(B\\!-\\!V)$ extinction and higher ages compared to subtracting the
background fluxes. We chose to use the ages computed with the background flux
subtracted photometry throughout this analysis in order to avoid unphysically
old ages for star forming regions.

To account for the stochastic effects of red supergiants (RSGs), which could
skew the colors of small young clusters (Krumholz et al., 2015), we looked at
the location of catalogued RSGs in WLM from Levesque & Massey (2012). We found
three RSGs in four regions (regions 11, 12, 18, and 20), with one RSG located
in the overlap of regions 11 and 12. The ages of regions 11, 12, 18, and 20
are rather young at 22, 4, 2, and 3 Myr respectively. With the age of these
regions well within the range of all other regions, it is not clear that RSGs
have made a noticeable impact on our age calculations.

To find the age of the annulus representing the environment where the star-
forming region formed, we did not subtract any background since the age we
were measuring was that of the background disk surrounding each region.
Likewise, we only computed our measured FUV $-$ NUV, $U-B$, and $B-V$ colors
with the $E(B\\!-\\!V)$ of 0.068 since the annuli are not likely to be heavily
reddened. As for the inner regions, our measured colors were fit to the BC03
model colors for each region, where we selected the best fit as the age for
that region. Table 3 contains the age of each annulus computed with the
Chabrier IMF, and Figure 7 shows a histogram of the annuli ages.

###  2.4 Stellar mass surface density

After finding the age of the inner region using BC03, we took the ratio
between the $V$ flux corresponding to the model age of each region and
measured the integrated $V$ flux, which was corrected for the extinction we
determined from the colors. This ratio was used to scale the model mass and
find the mass of young stars ($M_{*,\scriptsize{\textnormal{SF}}}$) for each
inner region.

The young star mass was then divided by the area of each region in parsecs to
find the corresponding average $\Sigma_{*}$ in $M_{\odot}$ pc-2. We note that
this method of determining the stellar mass surface density does not take into
account the dispersal of stars over time. The model $V$ values corresponding
to the upper and lower age uncertainties for each region were used for the
model $V$ uncertainties, which were used to compute the uncertainties for the
$M_{*}$ and $\Sigma_{*}$ for each region. These stellar mass surface densities
and uncertainties for the star forming regions can be found in Table 2. Since
the ages were used in calculating the $\Sigma_{*}$ of the inner regions,
regions 18 and 22, where the ages were calculated from UBV alone, have their
$\Sigma_{*}$ marked with an ($\times$) in relevant figures.

###  2.5 CO-dark H2 gas

We also wanted to examine any potential relationship of CO-dark H2 gas with
the small CO cores. In order to find the percentage of the original molecular
cloud mass $M_{MC}$ in CO-dark H2 ($M_{\scriptsize{Dark\textrm{
H}_{2}}}$/$M_{\scriptsize{MC}}$), we assumed that the percentage of the
original total molecular cloud gas that was converted into stars was roughly
2% (Krumholz et al., 2012). We used $M_{*}$ and 2% efficiency to find the
total molecular cloud gas mass for each inner region. Then, given that the
molecular gas mass of the cloud is a combination of the CO-dark gas mass and
the mass contained in CO cores, we found the percentage of the molecular cloud
that is CO and that is CO-dark. For region 1, we also looked at how much the
mass of carbon in the PDR contributes to the mass of the molecular cloud. The
[C ii]$\lambda$158 $\mu$m flux measurements from Cigan et al. (2016)
correspond to $40-170M_{\odot}$ of free carbon atoms. As this is only
$0.03-0.14$% of the original total mass of the molecular cloud, we choose to
ignore it in our analysis. We note that the $M_{MC}$ is the original mass of
the molecular cloud, which would break up and dissociate with time. Without
information on the status of the cloud itself, our estimates do not take into
account the current structure of the molecular cloud. The uncertainties in the
CO-dark H2 mass were found by computing the dark H2 mass percentage using the
uncertainties in the $M_{*}$ for each region as previously described, although
the uncertainty is most likely dominated by the assumption of a star formation
efficiency. The $M_{\scriptsize{Dark\textrm{ H}_{2}}}$/$M_{\scriptsize{MC}}$
and associated uncertainties can be found in Table 2. Since the $M_{*}$ for
each region is determined by the $V$ value corresponding to the model age
found, regions 18 and 22, for which their age was calculated from UBV alone,
have their dark H2 mass denoted with an ($\times$) in relevant figures.

In summary, the star forming region properties include the H i surface density
($\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$),
stellar mass surface density ($\Sigma_{*\scriptsize{\textnormal{,SF}}}$), sum
of individual CO core virial masses in a region
($M_{\textnormal{\scriptsize{CO}},vir}$), median individual CO core surface
density ($\Sigma_{\scriptsize{\textnormal{CO}}}$) in a region, stellar age,
and dark molecular hydrogen to original molecular cloud mass ratio
($M_{\scriptsize{Dark\textrm{ H}_{2}}}$/$M_{\scriptsize{MC}}$). The
environmental properties include the H i surface density
($\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$),
pressure, stellar mass, and age. In Section 3 we compare and contrast these
properties.

##  3 Results

###  3.1 Characteristics of star-forming regions

Figure 11: Histograms of properties of inner regions where CO cores currently
sit (blue) and the inner regions without any CO cores (red). Left: Average
stellar mass surface density. Center: Average H i surface density. Right:
Difference between the average
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
and the corresponding azimuthally-averaged radial profile
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,rad}}}$
at the region
($\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i},SF}}}-\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,rad}}}$).

In Figure 11 we plot histograms for the star-forming region properties of
stellar mass surface density $\Sigma_{*\scriptsize{\textnormal{,SF}}}$ and H i
surface density
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$.
We also plot a histogram of the difference between the average
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
and the corresponding azimuthally-averaged radial profile
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,rad}}}$
at the region
($\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i},SF}}}-\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,rad}}}$).
While the regions without CO cores typically have
$\Sigma_{*\scriptsize{\textnormal{,SF}}}$,
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$,
and
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i},SF}}}-\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,rad}}}$
values within the range of values for the regions with CO, the
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
and
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i},SF}}}-\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,rad}}}$
tend to fall at lower end of that range.

####  3.1.1 CO core mass and surface density

Figure 12: H i surface density of each inner region versus the total mass of
CO cores of that region, where the H i uncertainties are smaller than the size
of the plot markers. We find that a higher H i surface density is found in
regions with a higher total CO core mass (regions 1, 2, 9, and 15), while a
high H i surface density does not necessarily correspond to a higher total CO
core mass (regions 3, 4, 17, 19, 21, and 22).  Figure 13: Left: Stellar mass
surface density of each inner region plotted against the total mass of CO
cores of that region. The regions without CO cores (region 23, 24, 25, and 26)
are marked with a red star ($\star$) and have a total
$M_{\textnormal{\scriptsize{CO}},vir}$ of zero, but have been placed at a
total $M_{\textnormal{\scriptsize{CO}},vir}$ of $1.2\times 10^{2}\ M_{\odot}$
to show their corresponding $\Sigma_{*}$. Right: Percentage of original total
molecular cloud mass that is dark H2 gas of each inner region plotted against
the total mass of CO cores in that region. We do not show the
$M_{\scriptsize{Dark\textrm{ H}_{2}}}$/$M_{\scriptsize{MC}}$ against the total
$M_{\textnormal{\scriptsize{CO}},vir}$ of regions without detected CO as they
all have a total $M_{\textnormal{\scriptsize{CO}},vir}$ of zero and thus a
dark H2 mass percentage of 100%. Region 9 is displayed with arrow marker to
indicate that the actual dark H2 mass ratio value is $0\%$ but has been
shifted up to better show the distribution of the dark H2 mass ratios of the
other regions. The correct dark H2 mass percentages are listed in Table 2.
Regions 18 and 22 are marked with an ($\times$) as the stellar mass surface
density and dark H2 were determined from UBV alone.  Figure 14: Left: Stellar
mass surface density of each inner region plotted against the median
individual CO core surface density of that region. Regions 18 and 22 are
marked with an ($\times$) as the stellar mass surface density was determined
from UBV alone. Right: H i surface density of each inner region plotted
against the median individual CO core surface density of that region, where
the H i uncertainties are smaller than the size of the plot markers. The
x-axis error bars are not uncertainties, but instead represent the range of CO
core surface densities for that region, with some being smaller than the size
of the marker, especially if the region only has one CO core. The regions
without CO cores (region 23, 24, 25, and 26) are marked with a red star
($\star$) and have a CO core surface density of zero.  Figure 15: Left:
Stellar mass surface density of each inner region plotted against the age of
that region. Center: ratio (%) of dark H2 mass to original total molecular
cloud mass of each inner region plotted against the age of that region. Region
9 is displayed with an arrow marker to indicate that the actual dark H2 mass
ratio value is 0% but has been shifted up to better show the distribution of
the dark H2 mass ratios of the other regions. Right: H i surface density of
each inner region plotted against the age of that region, where the H i
uncertainties are smaller than the size of the plot markers. Age error bars
that appear one-sided are the result of the upper or lower color uncertainties
finding the same age in the model. Regions 18 and 22 are marked with an
($\times$) as the age and stellar mass were determined from UBV alone. The
regions without CO (region 23, 24, 25, and 26) are marked with a red star
($\star$) and are assumed to have a dark H2 mass percentage of 100%. Neither
the stellar mass surface densities nor dark H2 mass percentages take into
account the current structure of the molecular cloud, which would break up and
dissociate with time.

Next, we look at whether the sum of individual CO virial masses,
$M_{\textnormal{\scriptsize{CO}},vir}$, and median surface density,
$\Sigma_{\scriptsize{\textnormal{CO}}}$, of the individual CO cores in a
region have any relationship with the star forming region where they now sit.
To do this, we plot the
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$,
$\Sigma_{*\scriptsize{\textnormal{,SF}}}$, and $M_{\scriptsize{Dark\textrm{
H}_{2}}}$/$M_{\scriptsize{MC}}$ against the total mass of the CO cores in each
region. In Figure 12 we see that regions with a higher total
$M_{\textnormal{\scriptsize{CO}},vir}$ also show a higher
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
(regions 1, 2, 9, and 15), while a region with a higher
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
does not necessarily correspond to a higher total
$M_{\textnormal{\scriptsize{CO}},vir}$ (regions 3, 4, 17, 19, 21, and 22). The
correlation between higher $M_{\textnormal{\scriptsize{CO}},vir}$ and
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
suggests that considerable amounts of H i are needed to create large
quantities of molecules, and that large molecular clouds are difficult or
impossible to make at low
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$. Figure 13 shows
$\Sigma_{*}$ and $M_{\scriptsize{Dark\textrm{ H}_{2}}}$/$M_{\scriptsize{MC}}$
plotted against the total $M_{\textnormal{\scriptsize{CO}},vir}$ of each
region, where we see no relationship in either.

In Figure 14 we plot $\Sigma_{*\scriptsize{\textnormal{,SF}}}$ and
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
with the median individual $\Sigma_{\scriptsize{\textnormal{CO}}}$ in each
region. Here, the error bars given for the
$\Sigma_{\scriptsize{\textnormal{CO}}}$ are the minimum and maximum
$\Sigma_{\scriptsize{\textnormal{CO}}}$ in that region for regions with more
than one CO core. We do not find any relation between the
$\Sigma_{\scriptsize{\textnormal{CO}}}$ in a region and the
$\Sigma_{*\scriptsize{\textnormal{,SF}}}$ or
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
of that region.

####  3.1.2 Age

In Figure 15 we plot the $\Sigma_{*\scriptsize{\textnormal{,SF}}}$,
$M_{\scriptsize{Dark\textrm{ H}_{2}}}$/$M_{\scriptsize{MC}}$, and
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
against the age of the region to examine any relationships between the star
forming region properties and the age of the regions where we find CO cores.
We find that both the $\Sigma_{*\scriptsize{\textnormal{,SF}}}$ and
$M_{\scriptsize{Dark\textrm{ H}_{2}}}$/$M_{\scriptsize{MC}}$ appear to
increase with age. Both quantities are computed from the age of the region but
do not take into account the disruption of the molecular cloud by stars with
time, which may affect any apparent correlation seen between the
$\Sigma_{*\scriptsize{\textnormal{,SF}}}$, $M_{\scriptsize{Dark\textrm{
H}_{2}}}$/$M_{\scriptsize{MC}}$, and age.

####  3.1.3 Dark H2 mass to total molecular cloud mass ratio

In Figure 16 we plot the $\Sigma_{*\scriptsize{\textnormal{,SF}}}$ and
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$
of the inner region against the percentage of the original molecular cloud
mass that is in dark H2 to determine if the amount of CO-dark H2 where we find
CO cores correlates to other star forming region properties. We find that most
regions have a dark H2 mass that is between 90 and 100% of the original total
molecular cloud mass, and that higher $M_{\scriptsize{Dark\textrm{
H}_{2}}}$/$M_{\scriptsize{MC}}$ tends to corresponds to higher
$\Sigma_{*\scriptsize{\textnormal{,SF}}}$. Both of these quantities are
derived from the age of the region, while neither take into account dispersal
of the molecular cloud over time which may affect any apparent correlation.
The HI surface density of the inner regions varies independently of the
percentage of dark gas in the molecular cloud.

Figure 16: Left: Stellar mass surface density of each inner region plotted
against the ratio of dark H2 mass to total molecular cloud mass of that
region. Right: H i surface density of each inner region plotted against the
ratio of dark H2 mass to total molecular cloud mass of that region, where the
H i uncertainties are smaller than the size of the plot markers. Region 9 is
displayed with a left-pointing arrow marker to indicate that the actual dark
H2 mass ratio value is 0% but has been shifted right to better show the
distribution of the other dark H2 mass ratios. Regions 18 and 22 are marked
with an ($\times$) as the stellar mass surface density and dark H2 were
determined from UBV alone. The regions without CO (region 23, 24, 25, and 26)
are marked with a red star ($\star$) and are assumed to have a dark H2 mass
percentage of 100%. Neither the original molecular cloud mass nor the
$\Sigma_{*\scriptsize{\textnormal{,SF}}}$ account for the dispersal of the
molecular cloud over time, which may affect any correlation seen between the
two quantities. The correct stellar mass surface densities and dark H2 mass
percentages are listed in Table 2.  Figure 17: Histogram of average stellar
mass surface density (left), pressure (center), and H i surface density
(right) of annuli representing the environment where CO cores formed (blue)
and the annuli of the star forming regions without any CO cores (red).

###  3.2 Environments of star-forming regions

To compare the environment where CO cores formed against regions where we do
not detect any CO cores, we plot histograms for the environmental properties
of $\Sigma_{*\scriptsize{\textnormal{,env}}}$, pressure, and
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$
for the outer annulus of all 26 regions. We again find that the annuli
surrounding the star forming regions with CO cores fall within the same range
of environmental property values as the annuli surrounding regions where no CO
cores reside. These histograms are shown in Figure 17.

####  3.2.1 CO core mass and surface density

Figure 18: Stellar mass surface density (left), pressure (center), and H i
surface density (right) of each annulus plotted against the log of the total
CO core mass of that region. H i uncertainties are smaller than the size of
the plot markers. The regions without CO cores (regions 23, 24, 25, and 26)
are marked with a red star ($\star$) and have a total
$M_{\textnormal{\scriptsize{CO}},vir}$ of zero, but have been placed at a
$M_{\textnormal{\scriptsize{CO}},vir}$ of $1.2\times 10^{2}\ M_{\odot}$ to
show their corresponding $\Sigma_{*\scriptsize{\textnormal{,env}}}$, pressure,
and
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$.
Figure 19: Stellar mass surface density (left), pressure (center), and H i
surface density (right) of each annulus plotted against the median individual
CO core surface density of that region. H i uncertainties are smaller than the
size of the plot markers. The x-axis error bars are not uncertainties, but
instead represent the range of CO core surface densities for that region, with
some being smaller than the size of the marker. The regions without CO cores
(regions 23, 24, 25, and 26) are marked with a red star ($\star$) and have a
CO core surface density of zero.  Figure 20: Left column: Stellar mass surface
density (top), pressure (center), and H i surface density (bottom) of each
annulus plotted against the age of that annulus. Right column: Stellar mass
surface density (top), pressure (center), and H i surface density (bottom) of
each annulus plotted against the age of the corresponding inner region. The
age of inner regions spans a much larger range than the age of the annuli,
however most star forming regions are less than 100 Myr while the ages of the
environment are mostly older than 100 Myr. The H i uncertainties are smaller
than the size of the plot markers. Age error bars that appear one-sided are
the result of the upper or lower color uncertainties finding the same age in
the model. Regions 18 and 22 are marked with an ($\times$) as the age and
stellar mass were determined from UBV alone. The regions without CO (regions
23, 24, 25, and 26) are marked with a red star ($\star$).

Another way of examining the environment where the CO cores formed is to look
at the relationship between the sum of individual CO core virial masses
$M_{\textnormal{\scriptsize{CO}},vir}$ of a region with the corresponding
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$,
pressure, and $\Sigma_{*\scriptsize{\textnormal{,env}}}$ of the annulus of
that region. We show these in Figure 18. We find that regions with a higher
total $M_{\textnormal{\scriptsize{CO}},vir}$ tend to have a higher
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$,
as we found in the star forming regions themselves, while again showing that a
higher H i does not necessarily lead to a higher total
$M_{\textnormal{\scriptsize{CO}},vir}$. This correlation between the
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$ and total
$M_{\textnormal{\scriptsize{CO}},vir}$ is not as pronounced in the annuli as
the inner regions. The three regions with highest
$M_{\textnormal{\scriptsize{CO}},vir}$ also have relatively high
$\Sigma_{*\scriptsize{\textnormal{,env}}}$, but we find no relationship
between the total $M_{\textnormal{\scriptsize{CO}},vir}$ and the pressure. We
also compare the pressure,
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$,
and $\Sigma_{*\scriptsize{\textnormal{,env}}}$ of the annuli with the median
individual $\Sigma_{\scriptsize{\textnormal{CO}}}$ of the regions in Figure 19
and find no relationship.

####  3.2.2 Age

To examine any relationships between the environmental properties and the age
of both the environment where the CO cores formed and the star forming region
where we now find the CO cores, we plot the environmental pressure,
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$,
and $\Sigma_{*\scriptsize{\textnormal{,env}}}$ against the age of the annuli
and the age of the inner region in Figure 20. Not surprisingly we find that
the age of the annuli are older than inner regions. The annuli ages of the
regions fall between $\sim$50 and 650 Myr, with most around 250 Myr. The age
of inner regions spans a much larger range between $\sim$2 and 500 Myr, with
most regions less than 100 My. We do not find any correlation between the
environment where the CO cores formed and either the current age of that
environment or the age of the star-forming region in which the CO cores sit.

####  3.2.3 Dark H2 mass to original total molecular cloud mass ratio

Figure 21: Stellar mass surface density (left), pressure (center), and H i
surface density of each annulus plotted against the dark H2 mass to original
total molecular cloud mass ratio of that region. H i uncertainties are smaller
than the size of the plot markers. Region 9 is displayed with a left-pointing
arrow marker to indicate that the actual dark H2 mass ratio is 0% but has been
shifted right to better show the distribution of the other dark H2 mass
ratios. The total molecular cloud mass is the original mass of the cloud and
does not take into account the dissociation of the cloud over time. Regions 18
and 22 are marked with an ($\times$) as the dark H2 were determined from the
stellar mass that was derived from UBV alone. The regions without CO (regions
23, 24, 25, and 26) are marked with a red star ($\star$) and assumed to have a
dark H2 mass percentage of 100%.

In Figure 21 we plot the $\Sigma_{*\scriptsize{\textnormal{,env}}}$, pressure,
and
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$
of the annulus of each region against the $M_{\scriptsize{Dark\textrm{
H}_{2}}}$/$M_{\scriptsize{MC}}$ for that region to determine if the amount of
CO-dark H2 in the star forming regions where the CO cores sit have any
relationship with the environmental properties where the CO cores formed. We
find no correlations between the percentage of original molecular cloud mass
in dark H2 and the $\Sigma_{*\scriptsize{\textnormal{,env}}}$, pressure, or
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$
of the annuli where the CO cores formed.

###  3.3 Summary of results

Rubio et al. (2015) and Rubio et al. (2022, in preparation) discovered CO
cores in the dIrr galaxy WLM, which has a metallicity 13% of solar. The
detection of this CO is important for understanding star formation in the most
numerous type of galaxy, as CO is used to trace the molecular hydrogen thought
to be responsible for star formation. This study is aimed at understanding the
environments in which these small CO cores form at low mass and metallicities.
In this work, we have examined the properties of CO-detected regions in WLM
and explored relationships between the CO and the environments where they
formed and the star-forming regions where they currently reside. We grouped
the cores into 22 regions based on proximity to FUV knots, along with four
regions containing FUV emission that don’t have any detected CO cores.

We looked at the $\Sigma_{*\scriptsize{\textnormal{,SF}}}$,
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,SF}}}$,
total $M_{\textnormal{\scriptsize{CO}},vir}$, median individual
$\Sigma_{\scriptsize{\textnormal{CO}}}$, age, and $M_{\scriptsize{Dark\textrm{
H}_{2}}}$/$M_{\scriptsize{MC}}$ of the star forming regions and the
$\Sigma_{*\scriptsize{\textnormal{,env}}}$, pressure,
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}\,\textnormal{,env}}}$,
and age of the environments measured in annuli around the star-forming
regions. We do not see any difference between the star forming region
properties where we find CO cores and the star forming region properties where
we do not find CO cores, nor do we see a difference between environmental
region properties where we find CO cores and environmental region properties
where we do not. We do not see any correlations among the star forming region
properties or environmental region properties except between the
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$ and total
$M_{\textnormal{\scriptsize{CO}},vir}$ and, to a lesser extent, the pressure
and total $M_{\textnormal{\scriptsize{CO}},vir}$. We find that regions with a
higher total $M_{\textnormal{\scriptsize{CO}},vir}$ have higher H i surface
densities, and this relationship is more pronounced in the star forming
regions than in the surrounding environment.

Figure 22: Spitzer 8 $\mu$m image of WLM showing the regions defined here
(larger blue and red dashed circles) and the CO cores (tiny green circles).
Colorbar values are in units of MJy sr-1.

##  4 Discussion and Conclusions

Regions 1, 2, 9, and 15 have the highest number of CO cores (6, 17, 4, and 3
cores respectively) and, as expected, the highest total
$M_{\textnormal{\scriptsize{CO}},vir}$ of the regions. We calculate the amount
of dark H2 in a region using the assumption that 2% of the total molecular gas
(dark H2 plus $M_{\textnormal{\scriptsize{CO}},vir}$) is turned into stars,
and find that the percentage of CO-dark H2 of regions 1, 2, and 15 agree with
that of the other regions. Region 9, however, has a
$M_{\scriptsize{Dark\textrm{ H}_{2}}}$/$M_{\scriptsize{MC}}$ of 0%. The total
$M_{\textnormal{\scriptsize{CO}},vir}$ of the region is higher than what the
total molecular cloud gas mass is expected to be with a 2% star formation
efficiency. One possible reason for this is embedded star formation. To look
for potential embedded star formation, we show the regions and their CO cores
overlaid on the Spitzer 8 $\mu$m image of WLM in Figure 22. Here we see 8
$\mu$m peaks near several CO cores, including those in region 9. This may
suggest that region 9 has yet to convert 2% of its molecular gas to stars.

Figure 23: Ratio of young stellar mass to observed CO virial mass in the inner
region ($M_{\ast}$/$M_{\textnormal{\scriptsize{CO}},vir}$) against the age of
the inner region. The gray dashed line at
$M_{\ast}$/$M_{\textnormal{\scriptsize{CO}},vir}$$=2\%$ shows where
$M_{\ast}$/$M_{\textnormal{\scriptsize{CO}},vir}$ is equal to the star
formation efficiency of 2%.

In Figure 23 we plot the ratio of the young stellar mass to the observed CO
virial mass ($M_{\ast}$/$M_{\textnormal{\scriptsize{CO}},vir}$) of the inner
regions against the age of the inner regions. Because we made the assumption
that $M_{\ast}=0.02(M_{CO,vir}+M_{Dark\ H_{2}})$, we mark with a gray dashed
line where the $M_{\ast}$/$M_{\textnormal{\scriptsize{CO}},vir}$ is 2% to
examine what the excess mass above our estimated star formation efficiency is
in dark CO. For young regions (1, 7, 10, 11, 14) we find that the excess of
$M_{\ast}$/$M_{\textnormal{\scriptsize{CO}},vir}$ above 2% is

$\left(1+\frac{M_{Dark\ H_{2}}}{M_{CO,vir}}\right)\approx 5,$ (6)

which yields

$\frac{M_{Dark\ H_{2}}}{M_{CO,vir}}\approx 4.$ (7)

This value agrees with that found in larger scale regions in recent papers
(Hunter et al., 2019, 2021). When the ratio
$M_{\ast}$/$M_{\textnormal{\scriptsize{CO}},vir}$ is much larger than $\sim$4,
as we see it is for mostly old regions, the molecular gas has likely been
destroyed. We see this transition at an age of about 5 Myr which is reasonable
for the time it takes for young star formation to break apart its GMC
(Williams et al., 2000; Kim et al., 2018; Kruijssen et al., 2019).

Looking at the scale of the whole galaxy, we see in Figure 5 a ridge or shell
surrounding a depression of H i. Star formation, shown in Figure 3, is found
within and along the ridge as well as further into the hole. A possible
scenario is that past star formation within the hole pushed the H i gas
outward and created the ridge we see today (Heiles, 1979; Meaburn, 1980;
Hunter et al., 2001; Kepley et al., 2007). However, we would then expect to
see an age gradient, with the oldest regions closer to the center of the hole,
but in fact we do not see any systematic pattern of ages.

The wide range of ages for our star forming regions and their lack of
correlation with total $M_{\textnormal{\scriptsize{CO}},vir}$ also suggests
that the extremely small size of the individual CO cores is not due only to
fragmentation of aging clouds. Instead, tiny CO cores are all that can be
formed in a galaxy with this gas density and metallicity without some galaxy-
scale compression.

Hunter et al. (2001) find star formation is located where
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$ is locally higher
in the dIrr galaxy NGC 2366 which, like WLM, has a ring of H i surrounding
most of the star formation in the galaxy. In Figure 11 we see that star
forming regions with CO cores have an average
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$ higher than the
radial average by amounts of 8-22 $M_{\odot}$, which is consistent with the
need for a higher $\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$
than the average in dIrrs to form stars. This, along with the relationship
between higher $\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$ and
higher total $M_{\textnormal{\scriptsize{CO}},vir}$ suggests that
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$ may play a role in
the formation of these CO cores. However, the presence of star forming regions
with lower $M_{\textnormal{\scriptsize{CO}},vir}$ along this H i ridge
suggests that a higher
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$ does not guarantee
their formation. We also find star forming regions with CO cores that are not
on this high density H i ridge, which we would not expect to see if higher
$\Sigma_{\scriptsize{\textnormal{H}\,\textnormal{\sc{i}}}}$ or pressure were
needed to form CO cores. This could mean that the ridge of H i that we see is
actually a “bubble” that we are only seeing in two dimensions. Additionally,
there are portions of the H i ridge without any star formation associated with
it, particularly to the southeast, that do not show any obvious difference
from the rest of the ridge. This portion of the ridge may contain CO cores,
but was not surveyed due to lack of time. However, the area surveyed is still
representative of the star forming area of the galaxy. The presence of CO
cores in a variety of different local environments, along with the similar
properties between star forming regions containing CO cores and those without
CO cores, leads us to conclude that we do not find clear characteristics to
form star forming regions with CO cores.

We are grateful for funding for this work, which was provided by the National
Science Foundation through grant AST-1907492 to D.H. M.R. wishes to
acknowledge support from ANID(CHILE) through FONDECYT grant No1190684. This
paper makes use of the following ALMA data: ADS/JAO.ALMA#2012.1.00208.S and
ADS/JAO.ALMA#2018.1.00337.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. The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc. Lowell Observatory sits at the base of mountains sacred to
tribes throughout the region. We honor their past, present, and future
generations, who have lived here for millennia and will forever call this
place home.

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