# Neutral atomic and molecular clouds and star formation in the outer Carina
arm

Geumsook Park (박금숙) Korea Astronomy and Space Science Institute, 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  Research
Institute of Natural Sciences, Chungnam National University 99 Daehak-ro,
Yuseong-gu, Daejeon 34134, Republic of Korea  Bon-Chul Koo Department of
Physics and Astronomy, Seoul National University, Seoul 08861, Republic of
Korea  Research Institute of Basic Sciences, Seoul National University, Seoul
08826, Republic of Korea  Kee-Tae Kim Korea Astronomy and Space Science
Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea
Bruce Elmegreen IBM Thomas J. Watson Research Center, Yorktown Heights, New
York 10598, USA

###### Abstract

We present a comprehensive investigation of H i (super)clouds, molecular
clouds (MCs), and star formation in the Carina spiral arm of the outer Galaxy.
Utilizing HI4PI and CfA CO survey data, we identify H i clouds and MCs based
on the ($l$, $v_{\mathrm{LSR}}$) locations of the Carina arm. We analyzed 26 H
i clouds and 48 MCs. Most of the identified H i clouds are superclouds, with
masses exceeding $10^{6}~{}\mathrm{M_{\odot}}$. We find that 15 of these
superclouds have associated MC(s) with $M_{\mathrm{HI}}\gtrsim
10^{6}~{}\mathrm{M_{\odot}}$ and $\Sigma_{\mathrm{HI+H_{2}}}\gtrsim$ 50
$\mathrm{M_{\odot}}\rm pc^{-2}$. Our virial equilibrium analysis suggests that
these CO-bright H i clouds are gravitationally bound or marginally bound. We
report an anti-correlation between molecular mass fractions and Galactocentric
distances, and a correlation with total gas surface densities. Nine CO-bright
H i superclouds are associated with H ii regions, indicating ongoing star
formation. We confirm the regular spacing of H i superclouds along the spiral
arm, which is likely due to some underlying physical process, such as
gravitational instabilities. We observe a strong spatial correlation between H
ii regions and MCs, with some offsets between MCs and local H i column density
peaks. Our study reveals that in the context of H i superclouds, the star
formation rate surface density is independent of H i and total gas surface
densities but positively correlates with molecular gas surface density. This
finding is consistent with both extragalactic studies of the resolved
Kennicutt-Schmidt relation and local giant molecular clouds study of Lada et
al. (2013), emphasizing the crucial role of molecular gas in regulating star
formation processes.

††software:  ASTROML (VanderPlas et al., 2012; Ivezić et al., 2014), The IDL
Astronomy User’s Library (Landsman, 1993)

mj

##  1 Introduction

Stars form within the densest regions of molecular clouds, which are
predominately found within giant H i clouds, known as H i superclouds
(Grabelsky et al., 1987; Elmegreen & Elmegreen, 1987; Lada et al., 1988). Star
complexes, the largest scale of star-forming regions in galaxies, form within
giant molecular clouds (GMCs) inside H i superclouds (Elmegreen, 2004).
Therefore, the formation of H i superclouds marks the onset of star formation.
Understanding the properties of H i superclouds is essential for comprehending
global star formation properties in galaxies.

Fukui & Kawamura (2010) reviewed the importance of studying the association
between GMCs and H i gas in understanding the formation and evolution of GMCs.
They summarized the finding that while GMCs often form in H i filaments,
intense H i is not always associated with CO gas. However, the GMC-H i
association has not been well established in the Milky Way, leaving room for
further investigation. This connection suggests a strong interplay between the
atomic and molecular phases of the interstellar medium, which is crucial for
understanding star formation processes.

H i superclouds typically exhibit masses ranging from $10^{6}$ to
$10^{7}~{}\mathrm{M_{\odot}}$ and sizes up to approximately 1 kpc, as reported
by various studies such as those by Elmegreen & Elmegreen (1987) and
Engargiola et al. (2003). The regular distribution of these superclouds along
the spiral arms of galaxies, including the Milky Way, has been well-
established through H i observations (e.g., McGee & Milton, 1964; Elmegreen &
Elmegreen, 1983; Boulanger & Viallefond, 1992). McGee & Milton (1964)
conducted an early study that demonstrated a series of H i superclouds can be
observed in the Carina spiral arm in the fourth quadrant of the Milky Way.

According to Grabelsky et al. (1987), there is good agreement between
distributions of H i superclouds and molecular clouds (MCs) in spiral arms.
However, previous H i surveys with low angular resolution limited the ability
to reveal detailed structures of H i superclouds in both space and velocity.
The recent all-sky H i $4\pi$ (HI4PI) survey (HI4PI Collaboration et al.,
2016) provides a significantly improved angular resolution, offering 3 to 8
times better resolution compared to previous surveys. In this paper, we aim to
identify and analyze H i superclouds and GMCs in the longitude range from 288°
to 340° at positive velocities, corresponding to the outer Carina arm.

The outer Carina arm is a favorite subject for research because it does not
have kinematic distance ambiguity, which reduces the likelihood of being
influenced by outer spiral arms. Despite this advantage, the outer Carina arm
has received limited attention since the 1980s. In this study, we use the
locations ($l$, $v_{\mathrm{LSR}}$) of the outer Carina arm as determined by
Koo et al. (2017, hereafter referred to as Paper I) to extract H i emission
associated with the spiral arm. Paper I traced the spiral arms in the outer
Galaxy using the LAB H i data with a beam size of 30′–36′ full-width at half-
maximum (FWHM) (Kalberla et al., 2005). The study identified four spiral arms,
including the Sagittarius-Carina, Perseus, Outer, and Scutum-Centaurus arms,
using a combination of local peak intensities and radial velocities integrated
along latitudes. Through the use of ($l$, $v_{\mathrm{LSR}}$) diagrams of
local peak intensities integrated along latitudes, Paper I clearly defined the
four spiral arms and prominent interarm features.

Many previous studies have explored the relationships between gas and star
formation on both local and extragalactic scales. For example, Bigiel et al.
(2008) demonstrated that the star formation rate surface density correlates
well with molecular gas surface density but shows little or no correlation
with atomic gas surface density in nearby spiral galaxies. Furthermore, Lada
et al. (2013) found that star formation rates in local GMCs are independent of
total gas surface density, emphasizing the importance of molecular gas in star
formation. These results highlight the importance of understanding the
properties and distribution of H i superclouds in relation to molecular gas
and star-forming regions.

In this paper, we present a comprehensive study of the outer Carina arm,
focusing on H i clouds and their relationships with MCs and star-forming
regions. Section 2 provides brief descriptions of H i and ${}^{12}\textrm{CO}$
(hereafter CO) survey data used in this study. In Section 3, we outline the
process of identifying H i clouds and MCs in the outer Carina arm and
determining their physical parameters, such as velocity, distance, and mass.
We also examine the spatial distribution and virial equilibrium of the H i
superclouds identified in this study. Section 4 compares the properties of H i
clouds and molecular clouds in the outer Carina arm. In Section 5, we compare
the properties of star-forming regions with the two cloud components and
analyze the star formation rates in the H i superclouds. Finally, in Section
6, we summarize our results and draw our conclusions.

##  2 Data

###  2.1 H i Data from the HI4PI Survey

In order to obtain images with a higher angular resolution, we utilize the
HI4PI survey (HI4PI Collaboration et al., 2016). This survey combines the
Effelsbeg-Bonn H i Survey (EBHIS) observed with the 100 m Effelsberg radio
telescope in the northern hemisphere (Kerp et al., 2011; Winkel et al., 2016),
and the Galactic All-Sky Survey (GASS) collected with the 64 m Parkes
telescope in the southern hemisphere (McClure-Griffiths et al., 2009; Kalberla
et al., 2010; Kalberla & Haud, 2015). The HI4PI survey has an angular
resolution of 16$\farcm$2 FWHM and a velocity channel width of 1.29
$\mathrm{km\,s^{-1}}$, with a brightness temperature noise level of $\sim 43$
mK.

During the analysis, we encountered a false absorption-like feature around
($l$, $b$) $\sim(291.5\arcdeg,-0.5\arcdeg)$ when comparing with other data,
such as SGPS data (Parkes multibeam data) (McClure-Griffiths et al., 2005). To
address this issue, the erroneous pixels were replaced with the SGPS data. The
SGPS data were rebinned and interpolated to match the grid coordinates of the
HI4PI data. Additionally, the reprocessed SGPS data were multiplied by 0.956
to account for the slightly different brightness temperature levels, which
were obtained by averaging brightness temperature ratios from four neighboring
peaks.

###  2.2 CO Data from the CfA Survey

We use the composite Galactic CO survey data of Dame et al. (2001). The survey
is comprised of several large-scale, unbiased surveys using the CfA 1.2 m
telescope in the northern hemisphere (with an angular resolution of
8$\farcm$4) and CfA-Chile 1.2 m telescope in the southern hemisphere (with an
angular resolution of 8$\farcm$8). The composite CO survey data are grid
sampled with a sampling interval of 7$\farcm$5 and a velocity width of 1.3
$\mathrm{km\,s^{-1}}$. The data for the Galactic 4th quadrant, that are used
in this study, provide a main beam temperature noise level of $\sim 0.17$ K.
To obtain a CO cube with the same angular resolution as the H i data, we
employed Gaussian smoothing with a kernel size of 13$\farcm$8 FWHM. Throughout
this paper, we utilized the smoothed CO data with an angular resolution of
16$\farcm$2 FWHM for all images and analysis.

##  3 Atomic and molecular clouds in the outer Carina arm

###  3.1 Cloud Identification

In Paper I, we presented systemic LSR velocity information along the outer
Carina arm. Figure 1 depicts three $b$-integrated ($l$, $v_{\mathrm{LSR}}$)
diagrams of H i local peak intensities as well as ordinary H i and CO
emissions. The zigzagging solid lines in the figure denote the locations of
the outer Carina arm, which were traced in Paper I. A majority of the emission
features associated with the outer Carina arm appear to be distributed between
two thick dotted lines, approximately $25~{}\mathrm{km\,s^{-1}}$ in width. The
spiral arm exhibits clear visible clumpy structures in both H i and CO
emissions.

Figure 1:  ($l$, $v_{\mathrm{LSR}}$) diagrams with the locations of the outer
Carina arm. The outer Carina arm traces obtained by Paper I are overlaid with
a zigzagging solid line in each panel. Top: $b$-integrated local peak
intensities in H i ($=\sum_{b=-10\arcdeg}^{b=+30\arcdeg}T_{\rm
b,max}(l,b,v_{\mathrm{LSR}})$) from the LAB H i data used in Paper I. Contour
levels are 20, 40, 60, and 80 K. Middle: $b$-averaged H i intensities from
$b=-2\arcdeg$ to +1° from the HI4PI data. Contour levels are 30, 40, 50, 60,
70, and 80 K. Bottom: Similar to the middle panel, but showing the CfA CO
data. Contour levels are 0.1 and 0.5 K. All three images are displayed on a
square-root scale. Two thick dotted lines spaced approximately
$25~{}\mathrm{km\,s^{-1}}$ apart indicate the velocity range from which the
$v$-integrated maps in Figure 2(a) are obtained. Two thin dotted lines at
$l>332\arcdeg$ aid in locating an interval of $\pm 8~{}\mathrm{km\,s^{-1}}$
from the solid line mentioned in Sections 3.1.2. A horizon (black or white)
line is included to indicate where $v_{\mathrm{LSR}}=0~{}\mathrm{km\,s^{-1}}$.

Due to the ubiquitous nature of H i emission, particularly in the Galactic
plane, identifying three-dimensional clumps from cube data is challenging.
Therefore, our clump identification procedure involved two main steps. In the
first step, we determine the projected ($l$, $b$) area from a $v$-integrated
image (as discussed in Section 3.1.1). In the second step, we use Gaussian
decomposition to measure the mean velocity component(s) of each cloud from the
area-averaged spectra (as explained in Section 3.1.2). Although the CO PPV
cube is less complex than the H i cube, we employ this method to define MCs
for consistency.111In this study, the identification of clouds is based on the
$v$-integrated map and does not take into account the three-dimensional CO
distribution. As a result, multiple components along a line of sight may be
merged into a single identified MC.

####  3.1.1 Step I: Spatial Identification

To identify clumpy structures of the arm, we begin by creating a
$v$-integrated ($l$, $b$) diagram using data within a width of approximately
$25~{}\mathrm{km\,s^{-1}}$ centered at the outer Carina arm traces depicted in
Figure 1. The resulting ($l$, $b$) diagrams in H i and CO, presented in Figure
2(a), exhibit clumpy structures along Galactic longitudes similar to those
shown in earlier studies, such as Figure 6a of McGee & Milton (1964) or Figure
15 of Grabelsky et al. (1987), albeit at a higher resolution. To identify H i
clouds and MCs from Figure 2(a), we employ the IDL/CLUMPFIND algorithm
(Williams et al., 1994). This algorithm works by contouring an input image
from the highest level to the lowest one. The outcome, such as the number and
size of clouds, depends sensitively on the input contour levels. To obtain
appropriate levels of the $v$-integrated intensity, we conduct empirical
attempts and determine the following: (1210, 1260, 1320, 1430, 1700, 1810,
1850) $\mathrm{K\,km\,s^{-1}}$ for H i and (2.5, 4.5, 7, 10, 15, 20)
$\mathrm{K\,km\,s^{-1}}$ for CO. The minimum of the H i contour levels
corresponds to $N_{\mathrm{HI}}\simeq 2.2\times 10^{21}~{}\mathrm{cm^{-2}}$,
assuming the line to be optically thin, while the minimum CO threshold is
comparable to $N_{\mathrm{H_{2}}}\simeq 5\times 10^{20}~{}\mathrm{cm^{-2}}$.
We identify twenty-nine H i clouds and forty-nine MCs along the outer Carina
arm, spanning from $l=288\arcdeg$ to 340° (see Figure 2(b)). While defining
MCs, we try to delineate clumpy structures as individual objects as much as
possible, which differs slightly from the identification of H i clouds.

(a) $v$-integrated H i and CO maps of the outer Carina arm

(b) H i and CO maps of the outer Carina arm with cloud identification

Figure 2:  ($l$, $b$) maps of the outer Carina arm in H i and CO. These maps
are obtained by integrating spectra within a range of about
$25~{}\mathrm{km\,s^{-1}}$ centered around the outer Carina arm traces in
Figure 1. The top panels show a $v$-integrated HI4PI H i map on a square-root
scale, with a range of 100 to 2600 $\mathrm{K\,km\,s^{-1}}$. The bottom panels
show $v$-integrated CfA CO map on the same scale, with a range of 0 to 20
$\mathrm{K\,km\,s^{-1}}$. Figure 2(b) is the same as Figure 2(a), but with
contours and labels indicating H i and CO clouds identified in this study. A
contour in the top panel indicates the lowest H i level of 1210
$\mathrm{K\,km\,s^{-1}}$ described in Section 3.1.1, while a contour in the
bottom panel is drawn at the lowest CO level of 2.5 $\mathrm{K\,km\,s^{-1}}$
described in Section 3.1.1. Best-fit ellipses are drawn to aid in locating the
H i clouds in Figure 2(b), and, in its bottom panel, the colors of circles are
the same as those of associated H i clouds. The colors of the circles indicate
whether they are matched with MCs, and the floating numbers correspond to
those assigned to the H i clouds or MCs. Three H i clouds, H4, H9, and H22,
and one MC of M34 are excluded from further analysis and discussion (see
Section 3.1.1 for details).

Some H i clouds were found to have abnormal, discontinuous pixels included in
the clumpfind-result area. These pixels were manually removed. Additionally,
two H i clouds, H2, and H5, were obtained by combining two or three clumpfind-
pieces, as they appeared to be connected with each other. On the other hand,
we observed that for three H i clouds, H4, H9, and H22, their latitudinal
intensity distributions suggest that the identified area is not a significant
contributor within the given longitude range. These clouds may be part of a
larger cloudy structure. Therefore, we have excluded them from further
analysis and discussion, despite the inferred parameters presented in Table 1.
As a result, this paper focuses on twenty-six H i clouds.

The process of identifying H i clouds involves defining bright areas against
widely-extended diffuse H i emission. On the other hand, the identification of
MCs takes into account most of the detectable CO emissions from the given
survey data. Almost all of the identified MCs listed in this paper are likely
to be associated with the H i clouds mentioned herein. A few MCs located at
$l\sim 288\arcdeg$ to 289° are not included in this paper, as they are
associated with other H i emission features that are not explored here.
Additionally, we limit the minimum pixel number of MCs to 5, which corresponds
to a circle area with a radius of approximately $9\farcm 5$.

We examined the presence and overlap of MCs within the identified H i cloud
areas and determined the possible association between MCs and H i clouds. Our
analysis revealed that 16 cataloged H i clouds are associated with MCs. Among
the CO-bright H i clouds, six are matched with single MCs, while ten are
matched with two or more MCs. We also found that H9 is associated with the
relevant MC (M34), although it was excluded from the statistical analysis.
Furthermore, M34 was also excluded from further analysis, resulting in a total
of 48 MCs that will be discussed in this paper.

####  3.1.2 Step II: Gaussian Decomposition

In order to understand the kinematic characteristics of clouds, we attempt to
isolate the cloud velocity component(s) using multiple Gaussian fitting from a
velocity profile averaged within the identified cloud area in ($l$, $b$)
space. However, this task is challenging, particularly for H i profiles, due
to contamination by different arm or interarm components. This complexity
results in a mixing of many velocities, making it difficult to determine the
number of features present. To efficiently and accurately extract the velocity
component(s) of the H i cloud, we obtain an area-averaged velocity profile
from a specific region within the cloud. The cloud area is determined using
the CLUMPFIND process, which clips at the minimum velocity-integrated
intensity, 1210 $\mathrm{K\,km\,s^{-1}}$. We then fit the area-averaged
velocity profile to a Gaussian Mixture Model (GMM) using the
sklearn.mixture.GaussianMixture function in python.222An example of a one-
dimensional GMM can be found at
https://www.astroml.org/book_figures/chapter4/fig_GMM_1D.html.  This
algorithm, which is an unsupervised learning algorithm for clustering, is
advantageous in that it does not require an initial setting of the number of
Gaussian components and their parameters. In situations where a profile
exhibits complexity, the resulting best-fit values can differ based on the
value of the “random_state” parameter, which controls the random seed for
initialization. To mitigate this, we performed 100 iterations with
random_state values ranging from 0 to 99, and utilized a value of tol (= 1e-5;
the convergence threshold) larger than the default threshold, as determined by
manual inspection, The average parameters and their standard deviations were
computed. 333Out of the identified H i clouds, convergence issues were
encountered in some iterations of the GMM fitting for eight of them.
Consequently, statistical values were derived from the iterations that
achieved successful convergence and those that did not were excluded from the
calculation. Smaller standard deviation values suggest that the decomposition
results converge to a specific case with greater clarity. Conversely, larger
standard deviation values indicate that the profile for a given velocity range
may have multiple possible solutions.

The kinematic selection of the decomposed Gaussian components is based on
their central velocities, which are compared to the mean velocity of the outer
Carina arm traces with the longitude range of each cloud. We accept Gaussian
components that fall within a velocity range of $\pm
12.5~{}\mathrm{km\,s^{-1}}$ for $l\leq 332\arcdeg$ and $\pm
8~{}\mathrm{km\,s^{-1}}$ for $l>332\arcdeg$. The narrower velocity range for
the latter is chosen because the corresponding H i emission features, as seen
in the position-velocity diagram (see Figure 1), are distributed over a
relatively narrower velocity range than in the former case.

On the other hand, the CO emission features appear to be relatively isolated
and exhibit almost no extended diffuse emission feature. We performed a
decomposition process of the velocity component(s) for the CO data, similar to
that described above for the H i data, but with the additional criterion that
only those Gaussian components with peaks that are $3\times T_{\mathrm{rms}}$
or higher were retained. $T_{\mathrm{rms}}$ is the noise level, which was
determined from regions where no astronomical signal is present.

###  3.2 Derivation of Physical Parameters

####  3.2.1 Position and Size

The central position ($l_{\mathrm{c}}$, $b_{\mathrm{c}}$) of each cloud is
determined by fitting a best-fit ellipse to Galactic coordinates within the
clumpfind-result area using the IDL procedure MPFITELLIPSE (Markwardt, 2009).
This fitting also calculates the semi-major/minor axes ($r_{\mathrm{major}}$
and $r_{\mathrm{minor}}$, respectively). For H i clouds, a position angle (PA)
is a free-fitting parameter, whereas it is set to be 0 for MCs. The presented
PA in this paper is a counter-clockwise rotation angle measured from the
$+b$-axis. The best-fit ellipses represent about 50% of the clumpfind-result
area on average. In estimating other parameters, such as column density and
mass, we use a geometrical mean radius ($r_{\mathrm{geo}}$), which is defined
as the radius of an imaginary circle with the same clumpfind-result area ($A$)
as given by Equation 1.

$r_{\mathrm{geo}}=\sqrt{A/\pi}.$ (1)

####  3.2.2 Central Velocity and Velocity Dispersion

The central velocity ($v_{\mathrm{c}}$) and velocity dispersion
($\sigma_{\mathrm{v}}$) of each cloud are estimated through Gaussian
decomposition of the area-averaged velocity ($\overline{T}(v)$) profile, as
described in Section 3.1.2. These parameters are intensity-weighted and
computed as follows:

$v_{\mathrm{c}}=\frac{\sum_{v}v\,\mathcal{G}(v)dv}{\sum_{v}\mathcal{G}(v)dv},$
(2)
$\sigma_{\mathrm{v}}=\sqrt{\frac{\sum_{v}(v-v_{\mathrm{c}})^{2}\,\mathcal{G}(v)dv}{\sum_{v}\mathcal{G}(v)dv}},$
(3)

where
$\mathcal{G}(v)(=\sum_{\mathrm{clouds}}\overline{T}(v)_{\mathrm{Gauss}})$
represents the sum of Gaussian components that are identified as being
associated with each cloud, also explained in Section 3.1.2.

####  3.2.3 Distance

Based on the derived central velocity, we calculate the kinematic distance to
each cloud by employing the flat Galactic rotation model of Reid & Dame
(2016), which updates the model presented in Reid et al. (2014). The model
provides the Sun’s distance to the Galactic center as $\mathrm{R_{0}}=8.34$
kpc and the Sun’s rotational speed as $\mathrm{\Theta_{0}}=240$
$\mathrm{km\,s^{-1}}$.

####  3.2.4 Mass and Surface Density

The mass of each H i cloud is determined using the expression:

$M_{\mathrm{HI}}=N_{\mathrm{HI}}\times\pi r_{\mathrm{geo,HI}}^{2}\times
m_{\mathrm{H}}\times 1.36,$ (4)

where $r_{\mathrm{geo,HI}}$ is the geometrical mean radius of the H i cloud as
defined earlier, $m_{\mathrm{H}}$ is the mass of a hydrogen atom, and 1.36 is
mean atomic mass per H atom (Allen, 1973).

The H i column density ($N_{\mathrm{HI}}$) is calculated under the assumption
of a constant spin temperature ($T_{\mathrm{s}}$), following Levine et al.
(2006), where $T_{\mathrm{s}}$ is assumed to be 155 K. The calculation is
based on the area-averaged velocity profile, from which the portion associated
with a given cloud is extracted. The equation for $N_{\mathrm{HI}}$ is given
by:

$N_{\mathrm{HI}}=1.82\times 10^{18}\
\sum_{v}-T_{\mathrm{s}}\mathrm{ln}\left(1-\frac{\mathcal{G}(v)}{T_{\mathrm{s}}}\right)dv.$
(5)

Similarly, the mass of each MC ($M_{\mathrm{H_{2}}}$), which represents the
total mass of molecular hydrogen, is calculated using the following equation:

$M_{\mathrm{H_{2}}}=X_{\mathrm{CO}}\times\sum_{v}\mathcal{G}(v)dv\times\pi
r_{\mathrm{geo,CO}}^{2}\times m_{\mathrm{H}}\times 2.72,$ (6)

where $X_{\mathrm{CO}}$ is the CO-to-$\mathrm{H_{2}}$ conversion factor of
$2\times 10^{20}$ $(\mathrm{K\,km\,s^{-1}})^{-1}\,\mathrm{cm^{-2}}$ (Bolatto
et al., 2013), and 2.72 is the mean atomic mass per H2 molecule.

Although CO is commonly used as a tracer of molecular hydrogen gas, it is
known that molecular gas exists without being detected by CO lines. This
phenomenon has been observed (e.g., Grenier et al., 2005; Abdo et al., 2010;
Planck Collaboration et al., 2011a, b) and theoretically predicted (e.g., van
Dishoeck & Black, 1988; Wolfire et al., 2010). To address this issue,
alternative tracers such as OH, $\textrm{HCO}^{+}$, and $\textrm{C}^{+}$ lines
have been utilized in many observational studies (e.g., Liszt & Lucas, 1996;
Lucas & Liszt, 1996; Tang et al., 2017; Park et al., 2018). Studies by Pineda
et al. (2013) have revealed the existence of CO-dark molecular gas, which is
warm and diffuse, extends over a wider range of Galactocentric distance
($R_{\mathrm{GC}}$) than the cold and dense molecular gas traced by
${}^{12}\textrm{CO}$ and ${}^{13}\textrm{CO}$. The contribution of CO-dark
molecular gas increases with increasing $R_{\mathrm{GC}}$, resulting in an
increase in the $X_{\mathrm{CO}}$ conversion factor as well. From the relation
between $X_{\mathrm{CO}}$ and $R_{\mathrm{GC}}$ presented in Figure 20 of
Pineda et al. (2013), it is evident that $X_{\mathrm{CO}}$ increases by a
factor of approximately 1.5 to 2.5 in the $R_{\mathrm{GC}}$ range of (9, 11)
kpc. For this study, we have adopted the conventional $X_{\mathrm{CO}}$, which
means that the resulting $M_{\mathrm{H_{2}}}$ values may represent a lower
limit of the actual total molecular cloud mass.

####  3.2.5 Basic Properties

Tables 1 and 2 provide the physical parameters of the 29 H i clouds and 49 MCs
identified in this study. The geometrical mean radii of 26 H i clouds, except
H4, H9, and H22, range from 74 pc to 318 pc with a mean value of 187 pc. The H
i cloud mass ranges from $4.2\times 10^{5}~{}\mathrm{M_{\odot}}$ to $2.0\times
10^{7}~{}\mathrm{M_{\odot}}$, with most clouds (23 of 26) being more massive
than $10^{6}~{}\mathrm{M_{\odot}}$. The mean H i cloud mass is calculated to
be $5.9\times 10^{6}~{}\mathrm{M_{\odot}}$. According to the classification of
Elmegreen & Elmegreen (1987, hereafter, EE87), clouds with a mass greater than
$\sim 10^{6}~{}\mathrm{M_{\odot}}$ are referred to as H i superclouds, and
most clouds in this study can be classified as such.

Table 1: H i Superclouds in the Carina Arm ($288\arcdeg\lesssim l\lesssim
340\arcdeg$)

|  $l_{\mathrm{c}}$**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter.  |  $b_{\mathrm{c}}$**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter.  |  $r_{\mathrm{major}}$**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter.  |  $r_{\mathrm{minor}}$**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter.  | PA**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter.  | $r_{\mathrm{geo}}$ |  $v_{\mathrm{c}}$††The standard deviation of the outputs from 100 iterations.  |  $\sigma_{\mathrm{v}}$ † | $d$ | $R_{\mathrm{GC}}$ | $r_{\mathrm{geo}}$ |  $\Sigma_{\mathrm{HI}}$††The standard deviation of the outputs from 100 iterations.  |  $M_{\mathrm{HI}}$ ‡
---|---|---|---|---|---|---|---|---|---|---|---|---|---
#HI | (°) | (°) | (°) | (°) | (°) | (°) | ($\mathrm{km\,s^{-1}}$) | ($\mathrm{km\,s^{-1}}$) | (kpc) | (kpc) | (pc) | ($\mathrm{M_{\odot}}\rm pc^{-2}$) | ($\mathrm{M_{\odot}}$)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14)
0H1 | 289.34 (0.01) |  $-$0.95 (0.01) | 1.03 (0.01) | 0.98 (0.01) | 8 (9) | 1.43 |  $+$19.3 (2.4) | 8.2 (1.2) | 7.4 | 9.1 | 184 | 67.4 (14.5) | 7.2e+6 (1.6e+6)
0H2 | 291.58 (0.01) |  $-$0.56 (0.01) | 0.98 (0.01) | 0.90 (0.01) | 111 (10) | 1.30 |  $+$24.9 (2.3) | 8.4 (1.3) | 8.3 | 9.4 | 189 | 54.0 (9.2) | 6.0e+6 (1.0e+6)
0H3 | 293.95 (0.01) |  $-$0.74 (0.01) | 0.94 (0.01) | 0.85 (0.01) | 96 (7) | 1.27 |  $+$24.7 (1.7) | 8.0 (1.0) | 8.9 | 9.4 | 197 | 58.4 (9.7) | 7.1e+6 (1.2e+6)
0H4 | 295.23 (0.02) |  $-$2.06 (0.01) | 0.57 (0.01) | 0.35 (0.01) | 95 (3) | 0.62 |  $+$22.0 (2.1) | 8.2 (1.2) | 8.9 | 9.3 | 96 | 42.1 (7.7) | 1.2e+6 (2.2e+5)
0H5 | 296.47 (0.01) |  $-$0.92 (0.01) | 0.97 (0.01) | 0.83 (0.01) | 104 (3) | 1.29 |  $+$22.3 (1.6) | 8.6 (0.9) | 9.3 | 9.3 | 209 | 64.8 (8.7) | 8.9e+6 (1.2e+6)
0H6 | 299.11 (0.02) |  $-$0.08 (0.01) | 1.02 (0.01) | 0.62 (0.01) | 85 (1) | 1.18 |  $+$24.4 (2.4) | 8.4 (1.1) | 10.0 | 9.4 | 205 | 53.8 (8.7) | 7.1e+6 (1.1e+6)
0H7 | 303.29 (0.02) |  $-$0.66 (0.01) | 1.49 (0.01) | 0.82 (0.01) | 89 (1) | 1.60 |  $+$29.4 (2.1) | 8.0 (1.1) | 11.4 | 9.8 | 318 | 61.9 (11.9) | 2.0e+7 (3.8e+6)
0H8 | 306.53 (0.01) |  $-$1.68 (0.02) | 0.36 (0.02) | 0.16 (0.01) | 179 (3) | 0.34 |  $+$33.6 (1.3) | 8.2 (1.0) | 12.5 | 10.1 |  074 | 44.7 (6.2) | 7.7e+5 (1.1e+5)
0H9 | 306.86 (0.01) |  $-$0.55 (0.01) | 0.17 (0.01) | 0.14 (0.01) | 163 (27) | 0.23 |  $+$34.2 (2.1) | 9.1 (1.2) | 12.6 | 10.1 |  050 | 44.5 (8.2) | 3.4e+5 (6.2e+4)
H10 | 308.06 (0.01) |  $-$0.71 (0.01) | 0.69 (0.01) | 0.56 (0.01) | 15 (5) | 0.91 |  $+$31.7 (2.8) | 7.3 (1.2) | 12.7 | 10.0 | 202 | 42.2 (10.5) | 5.4e+6 (1.3e+6)
H11 | 311.07 (0.02) |  $-$0.57 (0.01) | 1.10 (0.01) | 0.68 (0.01) | 89 (1) | 1.28 |  $+$33.1 (2.9) | 8.6 (1.3) | 13.5 | 10.2 | 303 | 61.2 (15.3) | 1.8e+7 (4.5e+6)
H12 | 313.31 (0.02) |  $-$0.27 (0.01) | 0.74 (0.01) | 0.49 (0.01) | 92 (2) | 0.80 |  $+$32.8 (2.1) | 12.5 (5.9)0 | 14.0 | 10.2 | 195 | 46.8 (9.9) | 5.6e+6 (1.2e+6)
H13 | 314.89 (0.02) |  $-$0.62 (0.01) | 0.52 (0.02) | 0.35 (0.01) | 94 (4) | 0.57 |  $+$36.2 (2.0) | 8.6 (1.2) | 14.7 | 10.6 | 145 | 47.3 (9.4) | 3.1e+6 (6.2e+5)
H14 | 316.15 (0.01) |  $-$0.68 (0.02) | 0.42 (0.02) | 0.31 (0.01) | 5 (5) | 0.46 |  $+$34.8 (1.9) | 8.8 (1.5) | 14.8 | 10.5 | 120 | 43.8 (9.4) | 2.0e+6 (4.3e+5)
H15 | 317.83 (0.02) |  $-$0.64 (0.01) | 1.07 (0.01) | 0.54 (0.01) | 91 (1) | 1.13 |  $+$35.8 (3.0) | 8.0 (1.3) | 15.3 | 10.7 | 301 | 51.1 (11.8) | 1.5e+7 (3.5e+6)
H16 | 321.23 (0.02) |  $-$0.44 (0.01) | 0.84 (0.01) | 0.52 (0.01) | 89 (2) | 0.94 |  $+$29.1 (2.5) | 10.0 (3.4)0 | 15.4 | 10.3 | 251 | 47.4 (9.1) | 9.4e+6 (1.8e+6)
H17 | 323.04 (0.02) |  $-$0.71 (0.01) | 0.33 (0.01) | 0.22 (0.01) | 89 (6) | 0.36 |  $+$24.7 (1.7) | 7.5 (0.9) | 15.4 | 10.0 |  097 | 40.0 (7.1) | 1.2e+6 (2.1e+5)
H18 | 324.60 (0.01) |  $-$0.43 (0.01) | 0.59 (0.01) | 0.50 (0.01) | 83 (7) | 0.77 |  $+$25.9 (2.2) | 8.3 (1.3) | 15.8 | 10.2 | 213 | 46.6 (11.0) | 6.6e+6 (1.6e+6)
H19 | 325.91 (0.01) |  $-$0.58 (0.01) | 0.44 (0.01) | 0.43 (0.01) | 66 (131) | 0.63 |  $+$27.7 (2.4) | 8.1 (1.4) | 16.3 | 10.5 | 178 | 45.2 (10.2) | 4.5e+6 (1.0e+6)
H20 | 328.32 (0.02) |  $-$0.56 (0.01) | 0.42 (0.01) | 0.24 (0.01) | 88 (3) | 0.47 |  $+$32.0 (1.9) | 7.5 (0.9) | 17.4 | 11.2 | 142 | 39.1 (7.9) | 2.5e+6 (5.1e+5)
H21 | 329.71 (0.02) |  $-$0.62 (0.01) | 0.61 (0.02) | 0.32 (0.01) | 95 (2) | 0.60 |  $+$30.9 (1.6) | 10.2 (3.0)0 | 17.5 | 11.2 | 182 | 42.7 (7.2) | 4.5e+6 (7.6e+5)
H22 | 331.13 (0.03) |  $-$0.83 (0.01) | 0.39 (0.02) | 0.16 (0.01) | 85 (4) | 0.34 |  $+$29.9 (2.3) | 10.1 (3.0)0 | 17.8 | 11.2 | 105 | 44.4 (10.9) | 1.5e+6 (3.7e+5)
H23 | 332.67 (0.01) |  $-$0.21 (0.02) | 0.22 (0.01) | 0.15 (0.01) | 172 (9) | 0.27 |  $+$20.7 (2.1) | 6.7 (1.1) | 16.9 | 10.3 |  080 | 21.3 (5.2) | 4.2e+5 (1.0e+5)
H24 | 333.77 (0.02) |  $-$0.45 (0.01) | 0.25 (0.01) | 0.16 (0.01) | 87 (8) | 0.29 |  $+$20.6 (2.5) | 7.4 (2.8) | 17.1 | 10.3 |  086 | 26.7 (7.9) | 6.3e+5 (1.9e+5)
H25 | 334.81 (0.01) |  $-$0.79 (0.02) | 0.41 (0.01) | 0.35 (0.01) | 158 (12) | 0.54 |  $+$19.1 (1.8) | 6.1 (0.9) | 17.1 | 10.2 | 162 | 29.2 (7.2) | 2.4e+6 (5.9e+5)
H26 | 335.92 (0.02) |  $-$0.62 (0.01) | 0.53 (0.01) | 0.40 (0.01) | 109 (6) | 0.66 |  $+$19.5 (1.2) | 6.1 (1.0) | 17.4 | 10.4 | 201 | 28.7 (6.4) | 3.6e+6 (8.1e+5)
H27 | 337.49 (0.02) |  $-$0.71 (0.01) | 0.60 (0.01) | 0.33 (0.01) | 93 (2) | 0.66 |  $+$20.6 (2.2) | 6.3 (1.3) | 17.9 | 10.7 | 206 | 27.6 (8.8) | 3.7e+6 (1.2e+6)
H28 | 338.96 (0.01) |  $-$0.62 (0.01) | 0.44 (0.01) | 0.40 (0.01) | 169 (12) | 0.60 |  $+$21.8 (1.6) | 6.0 (1.3) | 18.5 | 11.1 | 193 | 34.1 (9.3) | 4.0e+6 (1.1e+6)
H29 | 340.12 (0.02) |  $-$0.62 (0.01) | 0.53 (0.01) | 0.39 (0.01) | 100 (4) | 0.67 |  $+$22.3 (1.7) | 5.7 (0.5) | 18.9 | 11.4 | 220 | 33.0 (6.2) | 5.0e+6 (9.4e+5)

Note. — (1) Number assigned to a H i cloud; (2–3) central position in Galactic
coordinates; (4–6) semi-major/minor axes and position angle (PA) of a best-fit
ellipse; (7) angular geometrical mean radius; (8) intensity-weighted mean LSR
velocity; (9) intensity-weighted velocity dispersion; (10) Heliocentric
distance; (11) Galactocentric distance; (12) linear geometrical mean radius;
(13) surface density; (14) H i cloud mass.

Table 2: Molecular Clouds in the Carina Arm ($288\arcdeg\lesssim l\lesssim
340\arcdeg$)

|  |  $l_{\mathrm{c}}$**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter but is replaced by the symbol ‘***’ if it is too large (larger than 180°).  |  $b_{\mathrm{c}}$**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter but is replaced by the symbol ‘***’ if it is too large (larger than 180°).  |  $r_{\mathrm{major}}$**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter but is replaced by the symbol ‘***’ if it is too large (larger than 180°).  |  $r_{\mathrm{minor}}$**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter but is replaced by the symbol ‘***’ if it is too large (larger than 180°).  | PA**These parameters were derived by an ellipse-fitting. The value in parentheses is $1\sigma$ uncertainty of each derived ellipse parameter but is replaced by the symbol ‘***’ if it is too large (larger than 180°).  | $r_{\mathrm{geo}}$ |  $v_{\mathrm{c}}$††The standard deviation of the outputs from 100 iterations.  |  $\sigma_{\mathrm{v}}$††The standard deviation of the outputs from 100 iterations.  | $d$ | $R_{\mathrm{GC}}$ | $r_{\mathrm{geo}}$ |  $\Sigma_{\mathrm{H_{2}}}$††The standard deviation of the outputs from 100 iterations.  |  $M_{\mathrm{H_{2}}}$‡‡The given uncertainty considers only that of the surface density (relevant to integral of decomposed Gaussian components), not including that of distance.
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
#CO | #HI | (°) | (°) | (°) | (°) | (°) | (°) | ($\mathrm{km\,s^{-1}}$) | ($\mathrm{km\,s^{-1}}$) | (kpc) | (kpc) | (pc) | ($\mathrm{M_{\odot}}\rm pc^{-2}$) | ($\mathrm{M_{\odot}}$)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15)
0M1 |  0H1 | 288.93 (0.02) |  $-$0.48 (0.02) | 0.47 (0.02) | 0.42 (0.02) | 29 (29) | 0.62 |  $+$21.1 (0.3) | 7.2 (0.5) | 7.4 | 9.2 | 80 | 80.9 (1.7) | 1.6e+6 (3.3e+4)
0M2 |  0H1 | 289.07 (0.04) |  $-$1.36 (0.03) | 0.39 (0.04) | 0.29 (0.03) | 37 (40) | 0.37 |  $+$21.4 (0.7) | 6.9 (0.9) | 7.5 | 9.2 | 49 | 28.8 (1.7) | 2.2e+5 (1.3e+4)
0M3 |  0H1 | 289.37 (0.02) |  $+$0.24 (0.02) | 0.26 (0.02) | 0.19 (0.01) | 174 (10) | 0.32 |  $+$19.8 (1.6) | 4.3 (1.8) | 7.4 | 9.1 | 42 | 19.0 (4.5) | 1.0e+5 (2.4e+4)
0M4 |  0H1 | 289.66 (0.02) |  $-$1.29 (0.03) | 0.26 (0.02) | 0.15 (0.01) | 100 (13) | 0.28 |  $+$19.3 (0.6) | 9.5 (0.5) | 7.4 | 9.1 | 36 | 41.8 (1.9) | 1.7e+5 (7.8e+3)
0M5 |  0H1 | 289.87 (0.02) |  $-$0.76 (0.02) | 0.33 (0.02) | 0.31 (0.02) | 126 (36) | 0.43 |  $+$17.8 (1.8) | 6.6 (0.8) | 7.3 | 9.0 | 55 | 38.9 (7.2) | 3.7e+5 (6.8e+4)
0M6 |  0H1 | 290.09 (0.02) |  $-$1.40 (0.02) | 0.21 (0.02) | 0.17 (0.02) | 79 (25) | 0.28 |  $+$15.2 (1.6) | 6.1 (1.4) | 7.2 | 8.9 | 35 | 24.4 (3.1) | 9.6e+4 (1.2e+4)
0M7 |  0H2 | 290.55 (0.03) |  $-$0.23 (0.02) | 0.33 (0.02) | 0.25 (0.02) | 97 (32) | 0.40 |  $+$22.9 (1.5) | 7.7 (0.9) | 7.9 | 9.3 | 55 | 26.8 (3.3) | 2.5e+5 (3.0e+4)
0M8 |  0H2 | 290.85 (0.02) |  $-$0.88 (0.02) | 0.29 (0.02) | 0.27 (0.01) | 41 (***) | 0.39 |  $+$22.4 (2.2) | 7.7 (1.6) | 8.0 | 9.3 | 55 | 19.7 (3.1) | 1.9e+5 (3.0e+4)
0M9 |  0H2 | 291.25 (0.02) |  $-$0.22 (0.03) | 0.27 (0.02) | 0.24 (0.02) | 155 (21) | 0.32 |  $+$20.9 (1.9) | 7.5 (1.9) | 7.9 | 9.2 | 43 | 16.0 (3.5) | 9.5e+4 (2.0e+4)
M10 |  0H2 | 291.78 (0.02) |  $-$0.72 (0.03) | 0.37 (0.02) | 0.33 (0.01) | 27 (60) | 0.46 |  $+$22.2 (0.3) | 8.0 (0.3) | 8.2 | 9.3 | 66 | 38.8 (0.8) | 5.3e+5 (1.1e+4)
M11 |  0H2 | 292.07 (0.02) |  $-$0.14 (0.02) | 0.23 (0.02) | 0.22 (0.02) | 110 (39) | 0.33 |  $+$24.4 ($<$0.1) | 5.5 ($<$0.1) | 8.4 | 9.4 | 48 | 18.0 ($<$0.1) | 1.3e+5 (1.0e+2)
M12 |  0H2 | 292.50 (0.02) |  $+$0.14 (0.02) | 0.21 (0.02) | 0.18 (0.01) | 77 (18) | 0.27 |  $+$19.7 (0.5) | 2.7 (0.5) | 8.1 | 9.1 | 39 | 13.0 (1.0) | 6.1e+4 (4.4e+3)
M13 |  0H3 | 293.69 (0.02) |  $+$0.12 (0.03) | 0.17 (0.04) | 0.06 (0.03) | 68 (28) | 0.17 |  $+$25.5 (0.1) | 2.7 ($<$0.1) | 8.9 | 9.4 | 27 | 15.9 (0.2) | 3.6e+4 (5.2e+2)
M14 |  0H3 | 293.81 (0.03) |  $-$0.77 (0.03) | 0.31 (0.02) | 0.30 (0.02) | 82 (52) | 0.39 |  $+$29.5 (0.2) | 5.4 (0.2) | 9.2 | 9.6 | 63 | 41.1 (1.7) | 5.1e+5 (2.1e+4)
M15 |  0H3 | 293.81 (0.04) |  $-$1.77 (0.02) | 0.28 (0.04) | 0.12 (0.02) | 23 (163) | 0.24 |  $+$21.4 (0.1) | 2.6 (0.1) | 8.6 | 9.2 | 37 | 16.2 (0.2) | 6.9e+4 (1.0e+3)
M16 |  0H3 | 294.43 (0.02) |  $-$0.96 (0.03) | 0.22 (0.03) | 0.19 (0.03) | 180 (14) | 0.29 |  $+$28.6 (0.9) | 9.9 (1.6) | 9.3 | 9.6 | 47 | 27.0 (3.0) | 1.9e+5 (2.1e+4)
M17 |  0H3 | 294.55 (0.03) |  $-$1.33 (0.02) | 0.21 (0.02) | 0.16 (0.02) | 113 (55) | 0.26 |  $+$23.3 ($<$0.1) | 3.0 ($<$0.1) | 8.9 | 9.3 | 41 | 17.5 (0.2) | 9.2e+4 (1.2e+3)
M18 |  0H3 | 295.15 (0.02) |  $-$0.77 (0.02) | 0.24 (0.02) | 0.19 (0.01) | 106 (19) | 0.31 |  $+$24.3 (2.3) | 7.7 (1.5) | 9.1 | 9.4 | 49 | 29.1 (5.6) | 2.2e+5 (4.2e+4)
M19 |  0H5 | 296.04 (0.03) |  $-$0.20 (0.03) | 0.17 (0.02) | 0.16 (0.04) | 83 (6) | 0.21 |  $+$15.4 (1.6) | 3.9 (0.9) | 8.6 | 9.0 | 32 | 15.8 (1.6) | 5.0e+4 (5.0e+3)
M20 |  0H5 | 296.34 (0.03) |  $-$1.03 (0.03) | 0.39 (0.03) | 0.37 (0.03) | 80 (145) | 0.49 |  $+$21.9 (2.2) | 6.5 (2.2) | 9.2 | 9.3 | 78 | 18.3 ($<$0.1) | 3.5e+5 (5.8e$-$1)
M21 |  0H5 | 297.02 (0.02) |  $-$1.50 (0.02) | 0.47 (0.02) | 0.31 (0.01) | 119 (***) | 0.54 |  $+$21.7 ($<$0.1) | 5.3 ($<$0.1) | 9.3 | 9.3 | 88 | 23.5 ($<$0.1) | 5.7e+5 (9.8e+1)
M22 |  0H5 | 297.34 (0.02) |  $-$0.70 (0.02) | 0.30 (0.02) | 0.25 (0.02) | 176 (9) | 0.40 |  $+$23.4 (0.3) | 7.0 (0.2) | 9.5 | 9.4 | 66 | 53.8 (1.2) | 7.4e+5 (1.6e+4)
M23 |  0H5 | 297.56 (0.02) |  $-$0.14 (0.02) | 0.28 (0.02) | 0.26 (0.01) | 98 (8) | 0.40 |  $+$19.5 (0.2) | 5.2 (0.1) | 9.3 | 9.2 | 65 | 56.3 (1.3) | 7.4e+5 (1.7e+4)
M24 |  0H6 | 298.15 (0.03) |  $-$0.99 (0.02) | 0.34 (0.02) | 0.25 (0.02) | 132 (***) | 0.38 |  $+$23.0 (0.1) | 6.0 (0.1) | 9.7 | 9.4 | 64 | 21.2 (0.1) | 2.5e+5 (1.5e+3)
M25 |  0H6 | 298.22 (0.02) |  $-$0.40 (0.02) | 0.26 (0.02) | 0.23 (0.02) | 84 (31) | 0.36 |  $+$24.5 ($<$0.1) | 7.8 ($<$0.1) | 9.8 | 9.4 | 62 | 47.9 ($<$0.1) | 6.4e+5 (1.7e+2)
M26 |  0H6 | 298.84 (0.02) |  $+$0.11 (0.02) | 0.28 (0.02) | 0.28 (0.02) | 52 (***) | 0.41 |  $+$23.8 (0.2) | 5.5 (0.2) | 9.9 | 9.4 | 70 | 45.3 (0.9) | 7.0e+5 (1.4e+4)
M27 |  0H6 | 299.05 (0.03) |  $-$0.57 (0.02) | 0.36 (0.03) | 0.24 (0.02) | 90 (63) | 0.41 |  $+$25.0 (0.2) | 6.7 (0.1) | 10.1 | 9.5 | 71 | 40.1 (0.9) | 6.4e+5 (1.4e+4)
M28 |  0H6 | 299.60 (0.02) |  $-$0.08 (0.03) | 0.42 (0.02) | 0.29 (0.01) | 83 (5) | 0.46 |  $+$23.3 ($<$0.1) | 7.7 ($<$0.1) | 10.1 | 9.4 | 81 | 28.4 ($<$0.1) | 5.8e+5 (8.1e+2)
M29 |  0H6 | 300.20 (0.03) |  $-$0.33 (0.03) | 0.33 (0.02) | 0.29 (0.02) | 86 (16) | 0.42 |  $+$30.6 ($<$0.1) | 4.9 ($<$0.1) | 10.8 | 9.8 | 79 | 28.7 ($<$0.1) | 5.6e+5 (2.8e+2)
M30 |  0H7 | 301.84 (0.02) |  $-$0.07 (0.02) | 0.30 (0.02) | 0.24 (0.02) | 174 (13) | 0.37 |  $+$23.9 (0.1) | 4.0 (0.1) | 10.6 | 9.4 | 69 | 24.0 (0.5) | 3.4e+5 (7.3e+3)
M31 |  0H7 | 302.26 (0.03) |  $-$0.78 (0.02) | 0.56 (0.02) | 0.31 (0.01) | 77 (7) | 0.58 |  $+$30.5 ($<$0.1) | 4.7 ($<$0.1) | 11.3 | 9.8 | 115 | 47.7 (0.4) | 2.0e+6 (1.8e+4)
M32 |  0H7 | 303.49 (0.02) |  $-$0.65 (0.02) | 0.39 (0.02) | 0.37 (0.02) | 93 (18) | 0.54 |  $+$27.9 ($<$0.1) | 6.0 ($<$0.1) | 11.3 | 9.7 | 106 | 37.7 ($<$0.1) | 1.3e+6 (1.4e+3)
M33 |  0H7 | 304.29 (0.03) |  $-$0.34 (0.03) | 0.52 (0.02) | 0.51 (0.02) | 2 (8) | 0.67 |  $+$29.5 (0.1) | 5.6 (0.2 ) | 11.6 | 9.8 | 136 | 31.9 (1.0) | 1.9e+6 (6.1e+4)
M34 |  0H9 | 306.84 (0.02) |  $-$0.41 (0.02) | 0.27 (0.02) | 0.19 (0.01) | 114 (37) | 0.32 |  $+$24.8 (0.1) | 3.2 (0.1) | 11.9 | 9.6 | 67 | 26.2 (0.6) | 3.7e+5 (8.4e+3)
M35 | H10 | 307.54 (0.02) |  $-$0.79 (0.02) | 0.33 (0.02) | 0.21 (0.01) | 0 (32) | 0.39 |  $+$32.7 (0.1) | 3.8 ($<$0.1) | 12.7 | 10.1 | 86 | 27.9 (0.4) | 6.4e+5 (9.0e+3)
M36 | H10 | 308.14 (0.02) |  $-$0.50 (0.02) | 0.26 (0.02) | 0.22 (0.02) | 135 (62) | 0.35 |  $+$32.1 (0.1) | 6.6 ($<$0.1) | 12.7 | 10.0 | 77 | 31.8 (0.2) | 5.9e+5 (4.1e+3)
M37 | H10 | 308.23 (0.03) |  $-$0.99 (0.02) | 0.36 (0.03) | 0.20 (0.02) | 0 (10) | 0.38 |  $+$37.2 (0.3) | 4.0 (0.9) | 13.2 | 10.4 | 87 | 19.7 (3.5) | 4.7e+5 (8.4e+4)
M38 | H11 | 310.73 (0.02) |  $-$0.47 (0.02) | 0.45 (0.02) | 0.42 (0.02) | 92 (7) | 0.63 |  $+$28.2 (0.7) | 7.9 (0.6) | 13.0 | 9.9 | 142 | 41.9 (4.8) | 2.7e+6 (3.1e+5)
M39 | H11 | 311.74 (0.02) |  $-$0.34 (0.02) | 0.44 (0.02) | 0.42 (0.01) | 171 (***) | 0.62 |  $+$28.6 (0.5) | 9.2 (1.2) | 13.3 | 9.9 | 144 | 57.5 (4.4) | 3.7e+6 (2.8e+5)
M40 | H12 | 313.23 (0.02) |  $-$0.28 (0.03) | 0.33 (0.02) | 0.21 (0.01) | 93 (2) | 0.37 |  $+$43.0 ($<$0.1) | 3.9 ($<$0.1) | 14.9 | 11.0 | 95 | 29.3 (0.2) | 8.4e+5 (5.1e+3)
M41 | H12 | 313.93 (0.03) |  $-$0.14 (0.03) | 0.26 (0.03) | 0.24 (0.02) | 77 (149) | 0.32 |  $+$32.6 ($<$0.1) | 6.0 ($<$0.1) | 14.1 | 10.3 | 80 | 21.0 (0.1) | 4.2e+5 (2.5e+3)
M42 | H15 | 317.49 (0.04) |  $-$0.51 (0.01) | 0.53 (0.04) | 0.14 (0.01) | 90 (8) | 0.40 |  $+$30.1 (0.2) | 5.8 (0.2) | 14.7 | 10.2 | 102 | 22.3 (1.2) | 7.3e+5 (4.1e+4)
M43 | H15 | 317.90 (0.03) |  $-$0.13 (0.03) | 0.23 (0.03) | 0.21 (0.02) | 180 (14) | 0.27 |  $+$23.7 (4.3) | 8.0 (1.9) | 14.2 | 9.8 | 68 | 34.4 (11) | 5.0e+5 (1.7e+5)
M44 | H15 | 318.78 (0.03) |  $-$0.44 (0.02) | 0.37 (0.02) | 0.23 (0.01) | 163 (38) | 0.39 |  $+$35.1 ($<$0.1) | 4.1 ($<$0.1) | 15.5 | 10.7 | 104 | 19.4 (0.3) | 6.6e+5 (8.6e+3)
0M45§§This MC is on the edge of the H i cloud when overlaying the $v$-integrated CO map onto the $v$-integrated H i map.  | H16 | 320.49 (0.04) |  $-$0.39 (0.04) | 0.22 (0.03) | 0.18 (0.05) | 167 (19) | 0.27 |  $+$22.7 (1.1) | 4.8 (2.2) | 14.7 | 9.8 | 70 | 17.4 (6.7) | 2.7e+5 (1.0e+5)
0M46§§This MC is on the edge of the H i cloud when overlaying the $v$-integrated CO map onto the $v$-integrated H i map.  | H17 | 322.63 (0.02) |  $-$0.72 (0.04) | 0.22 (0.03) | 0.10 (0.02) | 89 (62) | 0.21 |  $+$19.0 (0.9) | 6.2 (0.5) | 14.8 | 9.6 | 55 | 20.2 (2.2) | 1.9e+5 (2.1e+4)
0M47§§This MC is on the edge of the H i cloud when overlaying the $v$-integrated CO map onto the $v$-integrated H i map.  | H19 | 325.81 (0.02) |  $-$0.12 (0.03) | 0.24 (0.02) | 0.20 (0.02) | 86 (14) | 0.29 |  $+$29.2 (0.8) | 5.0 (1.0) | 16.4 | 10.6 | 83 | 20.8 (2.1) | 4.5e+5 (4.4e+4)
0M48§§This MC is on the edge of the H i cloud when overlaying the $v$-integrated CO map onto the $v$-integrated H i map.  | H20 | 328.44 (0.02) |  $-$0.12 (0.03) | 0.17 (0.04) | 0.06 (0.03) | 175 (16) | 0.17 |  $+$31.0 ($<$0.1) | 3.2 ($<$0.1) | 17.3 | 11.0 | 52 | 23.7 ($<$0.1) | 2.0e+5 (8.2e+0)
M49 | H28 | 339.23 (0.06) |  $-$0.69 (0.02) | 0.28 (0.08) | 0.06 (0.04) | 95 (7) | 0.17 |  $+$23.4 (1.4) | 7.5 (1.2) | 18.9 | 11.5 | 57 | 17.6 (2.2) | 1.8e+5 (2.2e+4)

‡‡footnotetext: The given uncertainty considers only that of the surface
density (relevant to the integral of decomposed Gaussian components), not
including that of distance.

Note. — (1) Number assigned to a MC; (2) Number of associated H i cloud; (3–4)
central position in Galactic coordinates; (5–7) semi-major/minor axes and PA
of a best-fit ellipse; (8) angular geometrical mean radius; (9) intensity-
weighted mean LSR velocity; (10) intensity-weighted velocity dispersion; (11)
Heliocentric distance; (12) Galactocentric distance; (13) linear geometrical
mean radius; (14) surface density; (15) $\mathrm{H_{2}}$ mass.

It is noteworthy that all CO-bright H i clouds observed in this study have
masses greater than $1\times 10^{6}~{}\mathrm{M_{\odot}}$, with the majority
exceeding $5\times 10^{6}~{}\mathrm{M_{\odot}}$. These clouds also exhibit H i
surface densities of $\Sigma_{\mathrm{HI}}\gtrsim$ 34 $\mathrm{M_{\odot}}\rm
pc^{-2}$, while some CO-dark H i clouds have H i surface densities ranging
from 34 $\mathrm{M_{\odot}}\rm pc^{-2}$ to 47 $\mathrm{M_{\odot}}\rm pc^{-2}$.
In addition, with respect to the surface density of total gas (see Equation
13), the majority of CO-bright H i clouds have values of
$\Sigma_{\mathrm{HI+H_{2}}}\gtrsim$ 50 $\mathrm{M_{\odot}}\rm pc^{-2}$, while
the minimum value for the H i clouds in this study is 21.3
$\mathrm{M_{\odot}}\rm pc^{-2}$.

Observational studies of extragalaxies and the Milky Way suggest that a
minimum H i surface density of $\sim 10~{}\mathrm{M_{\odot}}\,{\rm pc^{-2}}$
at solar metallicity is required for $\mathrm{H_{2}}$ formation (e.g., Wong &
Blitz, 2002; Bigiel et al., 2008; Lee et al., 2012b, 2015). The Analytical
study by Krumholz et al. (2009) has shown that $\mathrm{H_{2}}$ formation is
closely related to metallicity and total gas surface density. Based on the
Galactic metallicity gradient shown in (Pedicelli et al., 2009) and the fact
that our H i clouds are located at $R_{\mathrm{GC}}\sim$ 9–11 kpc, a rough
estimate suggests that the metallicity has decreased to about 0.8 times the
solar value, while the most extreme case indicated in their Figure 3 suggests
a value of about 0.3 times the solar value. For the 11 out of 26 H i clouds in
our sample that do not show detectable CO emission according to our criteria,
the absence of CO may be due to the need for higher H i surface densities
resulting from their lower metallicity, although the possibility of CO
emission with column densities below our detection limit cannot be entirely
excluded.

However, it should be noted that the previous studies of the minimum H i
surface density required for $\mathrm{H_{2}}$ formation were derived from
pixel-to-pixel analysis, while this study is based on the total area of each
cloud. Therefore, a direct comparison between the two values should be made
with caution.

The average geometrical mean radius of 48 MCs, excluding M34, is 70 pc, and
their $M_{\mathrm{H_{2}}}$ ranges from $3.6\times 10^{4}~{}\mathrm{M_{\odot}}$
to $3.7\times 10^{6}~{}\mathrm{M_{\odot}}$, with a mean value of $6.0\times
10^{5}~{}\mathrm{M_{\odot}}$. Of the 48 MCs, 41 have $M_{\mathrm{H_{2}}}$
values that equal or exceed $10^{5}~{}\mathrm{M_{\odot}}$, which implies that
either giant molecular clouds or groups of MCs, namely, molecular cloud
complexes.

In terms of H i clouds, we investigated the relationship between
$R_{\mathrm{GC}}$ and mass or radius using the Spearman’s rank correlation
test, which examines if two variables are monotonically related. We found a
weak negative correlation between $R_{\mathrm{GC}}$ and the H i mass of H i
clouds (Spearman’s correlation coefficient ($\rho$) = $-0.36$ and p-value =
0.071). This means that as $R_{\mathrm{GC}}$ increases, the H i mass tends to
decrease. However, the correlation is not statistically significant, so it is
unclear whether the two variables have a real relationship. On the other hand,
we found that there is a strong negative correlation between $R_{\mathrm{GC}}$
and $\mathrm{H_{2}}$ mass assigned to the corresponding H i clouds
($\rho=-0.52$ and p-value = 0.048). This means that as $R_{\mathrm{GC}}$
increases, the $\mathrm{H_{2}}$ mass tends to decrease. The p-value is very
small, so the correlation is statistically significant. Finally, we found that
there is no correlation between $R_{\mathrm{GC}}$ and $r_{\mathrm{geo}}$ of
the H i clouds ($\rho=-0.085$ and p-value = 0.68). This means that there is no
clear relationship between the two variables.

###  3.3 Spatial Distribution of H i Superclouds

Most of the identified H i superclouds and MCs are below $b=0\arcdeg$. The
mean deviation from $b=0\arcdeg$ is $\Delta b\simeq-0\fdg 6$, corresponding to
a linear distance of $-110$ pc in the $R_{\mathrm{GC}}$ range of $\sim 9$ kpc
to $\sim 11$ kpc, based on the distances provided in Tables 1 and 2. This
spatial distribution is likely due to the warped Galactic plane (Burton, 1988;
Levine et al., 2006; Koo et al., 2017). Generally, the MCs appear to be
situated within their corresponding H i superclouds, although their
integrated-intensity peak positions often differ (see Section 4.1 for
details).

The spatial distribution of the 26 H i clouds is illustrated in a face-on view
in Figure 3. Even a cursory glance shows that the clouds are regularly
distributed. The average separation between cloud ($i$) and its immediate
neighboring clouds ($i-1$ and $i+1$) can be determined using the cosine law,
which is given by the following equation:

$Separation=0.5\,\sqrt{d_{i+1}^{2}+d_{i-1}^{2}–2\,d_{i+1}\,d_{i-1}\,cos(\Delta
l)},$ (7)

where $\Delta l=l_{i+1}-l_{i-1}$.

Figure 3:  Schematic face-on view of the H i clouds analyzed in this paper.
Circles indicate clouds of mass $\geq 5\times 10^{6}~{}\mathrm{M_{\odot}}$ (in
red) or $<5\times 10^{6}~{}\mathrm{M_{\odot}}$ (in orange). The size of each
circle corresponds to the geometrical mean radius listed in Table 1. The brown
curve denotes the (Sagittarius-)Carina arm spiral model, as derived by Paper
I. The filled ellipse located near the Galactic center represents the central
bar, as reported by (Wegg et al., 2015).

The left-hand panel of Figure 4 presents a histogram depicting this average
spacing between adjacent H i clouds along the Carina arm, covering a distance
of approximately 20 kpc. The bin size used for this analysis is
$0.012\,\mathrm{R_{0}}$, which is equivalent to 100 pc, assuming
$\mathrm{R_{0}}=$ 8.34 kpc. The yellow histogram indicates the distribution of
all H i clouds, which displays a prominent peak at $0.084\,\mathrm{R_{0}}$
($\sim 700$ pc). On the other hand, the red histogram, which represents
neighboring H i superclouds with $M_{\mathrm{HI}}\geq 5\times
10^{6}~{}\mathrm{M_{\odot}}$, shows a peak at $0.144\,\mathrm{R_{0}}$ ($\sim
1.2$ kpc).

Figure 4:  Histogram of the distribution of spacings between neighboring H i
clouds (left), and the ratio of the separation to filament diameter (right).
The filament diameter is determined as the cloud minor axis
($2r_{\mathrm{minor}}$). The yellow sticks with left diagonals represent all
twenty-six H i clouds, while the red sticks with right diagonals represent
massive clouds with $M_{\mathrm{HI}}\geq 5\times 10^{6}~{}\mathrm{M_{\odot}}$.
The bin size is $0.012\,\mathrm{R_{0}}$, which corresponds to around 100 pc.
The separation of 3.3 kpc between the last two massive clouds (H18 and H29)
with $M_{\mathrm{HI}}\geq 5\times 10^{6}~{}\mathrm{M_{\odot}}$ is not included
in this plot.

The separation between H i superclouds along the Carina arm has been
investigated in previous studies (e.g., Efremov, 1998, 2009), which
corroborate our finding. It is worth noting that EE87 reported a spacing of
approximately 1500 pc between H i superclouds in the first quadrant. Although
this value is somewhat larger than ours, it will be still comparable,
considering the use of different assumptions, such as the Sun’s location and
the Galactic rotation model.

Regular segmentation in the spiral arms of nearby galaxies (Elmegreen &
Elmegreen, 1983) has been observed recently in M31 (Efremov, 2010), M100
(Elmegreen et al., 2018), 15 other spirals (Elmegreen & Elmegreen, 2019), and
3 more (Gusev et al., 2022). It has been attributed to gravitational or
combined gravitational and magnetic (Parker-Jeans) instabilities in compressed
spiral-arm gas (e.g, Elmegreen, 1979, 1982; Kim et al., 2002; Dobbs, 2008;
Renaud et al., 2013; Lee & Hong, 2011; Inoue & Yoshida, 2019) or wiggle
instabilities (Wada & Koda, 2004; Mandowara et al., 2022). The three-
dimensional MHD simulation conducted by Lee & Hong (2011) demonstrated that
when a perturbation wavelength greater than the Jeans critical wavelength acts
on a self-gravitating disk of magnetized isothermal gas, the cooperation of
the Parker and Jeans instabilities suppresses convection and generates a
dense, large-scale structure of mass and size corresponding to the observed H
i superclouds.

We introduce the concept of the ratio of lengths as an indicator of filament
regularity and the underlying instability processes. The ratio of lengths,
predicted to be around 3.9 in Elmegreen et al. (2018), represents the ratio of
separation to the effective filament diameter for a non-magnetic cylinder,
derived using equation 4.2 of Nagasawa (1987). While our observations do not
directly measure the effective diameter or exhibit all the ideal conditions
assumed in the theoretical derivation, the essence lies in capturing the
regularity of the clouds and the presence of an instability mechanism rather
than random cloud agglomeration. Building upon this understanding, we have
considered an alternative approach to assess the regularity of the clouds by
focusing on the ratio of separation to the minor axis. We believe the minor
axis, being a representative measure of the filament diameter, offers a closer
approximation to the relevant diameter compared to the major axis. The right-
hand panel of Figure 4 shows a histogram of the ratio of separation to cloud
minor axis. The peak is at a ratio of around 3.

In addition, the relative separation difference (RSD), defined as the
difference between two adjacent separations divided by their average, provides
further insight into the regularity of cloud spacing along the filament. As
described in Elmegreen et al. (2018), the relative difference in the
separations between three adjacent clumps, i.e., $i-1$, $i$, and $i+1$, is

$RSD=2\,(S_{i,i-1}-S_{i,i+1})/(S_{i,i-1}+S_{i,i+1}).$ (8)

Here, $S$ is the separation between two adjacent clouds and not the average
separation between a cloud and its neighbors, as in equation 7. This RSD
quantifies the deviation from equally spaced separations along the filament.
This value ranges from 0 to a maximum value of 2, where a value of 0 indicates
equally spaced separations and a larger value signifies a deviation from equal
spacing. A peak in the histogram of these RSDs at a small value would indicate
a higher level of regularity in cloud spacing, providing further evidence for
the presence of instability that shapes the filamentary structures.

The RSD histogram is shown in Figure 5. The RSD peaks at $\sim 0.35$. Although
the observed clouds may not exhibit the same level of regularity as seen in
other cases, such as the well-studied M100 (Elmegreen et al., 2018), this does
not diminish the significance of our findings. We can confidently state that
the ratio of separation to the minor axis closely aligns with theoretical
expectations, and the modest regularity observed in the RSD histogram suggests
the involvement of a gravity-driven process in shaping these structures.

Figure 5:  Histogram of the relative separation difference between clouds.

Figure 6 shows a theoretical distribution of separation and RSD for $N=10^{6}$
points randomly placed on a line. The placement is made by assigning the point
position to be a random number uniformly distributed between 0 and 1. These
positions are then ordered by increasing value and their separations
determined. To account for the trend of decreasing average separation with
increasing $N$, the separations are multiplied by $N$; then the average is 1,
and the separations range from 0 to some large number up to $N$. The
separation distribution on the left of Figure 6 peaks at 0.5 with a dip toward
zero separation because it is increasingly unlikely for two points to be much
closer than the average separation. The RSD distribution on the right has a
slowly decreasing trend toward a value of 2. This maximum occurs when all the
points are at one end of the line and one point is at the other end, making
$S_{i,i-1}=0$ and $S_{i,i+1}=1$.

Figure 6: Theoretical model for the separation distribution (left) and the
distribution of relative separation differences (right) for points uniformly
distributed on a line. The units of separation in the theoretical distribution
are arbitrary. The theoretical relative separation difference is non-zero
above 1.1 where the observed distribution has no examples, suggesting that the
observed distribution is not random. A selection effect related to cloud
blending could prevent these high values.

Figure 5 should be compared to Figure 6 (right) because both are on relative
scales. The theoretical result has 26% of the separation differences larger
than 1.1 whereas the observations have none. The average RSD from theory is
0.75.

We consider the Kolmogorov–Smirnov test to determine how likely it is that the
observed RSD comes from the same model as the random distribution. This test
uses the normalized cumulative distributions. For the RSD, this cumulative
distribution (not shown) reaches unity at the maximum difference of $\sim
1.1$, from Figure 5. At this same value, the cumulative distribution for the
theoretical case equals only 0.55. The difference is 0.45, which we take to be
the Kolmogorov–Smirnov statistic when considering the hypothesis that the
observed and theoretical distributions are from the same model. This statistic
should be compared with $c(\alpha)\left[(N_{\rm clouds}+N)/(N_{\rm
clouds}N)\right]^{0.5}$ for number of clouds in Figure 5 equal to $N_{\rm
clouds}=26$ and $N=10^{6}$ in the model. Here
$c(\alpha)=\left[-0.5\ln(\alpha/2)\right]^{0.5}$ for level $1-\alpha$ at which
the hypothesis is rejected. Setting $0.45=c(\alpha)/\left(N_{\rm
clouds}\right)^{0.5}$ for $N>>N_{\rm clouds}$, we derive $\alpha=5.3\times
10^{-5}$, meaning that the hypothesis the observed distribution is from the
same model as the random distribution is rejected at a confidence level of
99.995%.

The lack of RSDs larger than 1.1 in the observations could be the result of a
selection effect, where clouds that are too close to each other are called a
single cloud. If we consider two nearby clouds at a separation $a$ with
another cloud a distance $b$ from one of them, then the RSD is $2(b-a)/(b+a)$.
Setting this less than 1.1 as in the observed limit gives $a>0.29b$. If the
minimum separation between two adjacent clouds is never less than $0.29$ times
their near-neighbor distance, we can explain the lack of high values. This
type of selection effect is possible because the mean separation is $\sim 700$
pc from Figure 4 (left) and 0.29 times this is $\sim 200$ pc, which is
comparable to the average major axis length of the H i clouds, $\sim 300$ pc.
Thus, the upper limit in Figure 5 could be because “touching” clouds have
become confused with single clouds, eliminating the short spacings.

###  3.4 Virial Equilibrium

Determining whether H i superclouds or MCs are gravitationally bound is a
fundamental question in understanding star formation. To examine the degree of
self-gravitational bounding, one can compare the one-dimensional virial
theorem velocity dispersion ($v_{\textrm{VT}}$) to the measured velocity
dispersion ($\sigma_{\mathrm{v}}$) of the H i cloud. Assuming a spherical
cloud with an isothermal mass distribution, the virial dispersion is given by

$v_{\textrm{VT}}^{2}=\frac{GM}{4R},$ (9)

where $M$ and $R$ are the total mass and the radius of the complex,
respectively (EE87). The factor $\beta$ in Equation 18 of EE87 indicates the
ratio of magnetic to turbulent pressures, and they adopted $\beta=1$ based on
the understanding that magnetism plays an important role in contributing to
cloud support (see Appendix A in Elmegreen & Clemens, 1985). We adopt this
value, resulting in the constant in the denominator of Equation 9 being 4. $M$
is the sum of $M_{\mathrm{HI}}$ in Table 1 and $M_{\mathrm{H_{2}}}$ in Table
2, and $R$ is the geometrical mean radius of the H i cloud in Table 1. If a
cloud is in virial equilibrium, the velocity ratio
$v_{\textrm{VT}}/\sigma_{\mathrm{v}}=1$ or virial parameter (defined as
$\alpha_{\mathrm{vir}}$ $=4R\sigma_{\mathrm{v}}^{2}/GM$) is equal to 1.

Figure 7 displays the velocity ratio as a function of the total cloud mass for
the 26 H i clouds identified in this study. The total cloud mass
($M_{\mathrm{HI+H_{2}}}$) is defined as

$M_{\mathrm{HI+H_{2}}}=M_{\mathrm{HI}}+M_{\mathrm{H_{2},all}},$ (10)

where $M_{\mathrm{H_{2},all}}$ is the sum of masses of MCs associated with an
H i cloud. The velocity ratios fall in the range of approximately 0.3–1.5,
which is close to unity, indicating that some of the clouds may be
gravitationally bound. For reference, if we assume a uniform density profile
for the cloud in Equation 9, the constant 4 changes to 5, which results in a
slightly downward of the data points shown in this figure. Comparison of CO-
bright and CO-dark H i clouds reveals that CO-dark clouds generally have lower
total gas mass, but the velocity ratio shows no significant difference between
the two types of clouds in the mass range where both types coexist. Moreover,
the velocity ratio appears to increase with increasing total gas mass, with
lower-mass clouds having lower velocity ratios and higher-mass clouds having
higher velocity ratios. Most of the CO-bright H i clouds have velocity ratios
$\gtrsim 0.7$ ($\alpha_{\mathrm{vir}}\lesssim 2$), suggesting that they are
gravitationally bound or marginally bound. Conversely, we infer that clouds
with velocity ratios $\lesssim 0.5$ ($\alpha_{\mathrm{vir}}\gtrsim 4$) are
likely to be gravitationally unbound and will either expand or dissipate in
the absence of confinement from external pressure.

Figure 7:  Relationship between the total cloud mass ($M_{\mathrm{HI+H_{2}}}$)
and the velocity ratio ($v_{\mathrm{VT}}/\sigma_{\mathrm{v}}$). Filled circles
represent CO-bright H i clouds, while unfilled circles indicate other H i
clouds. The lines mark the loci for virial parameters
($\alpha_{\mathrm{vir}}$) of 0.5, 1, 2, and 4.

In addition to examining the virial equilibrium of the H i clouds, we further
investigate the relationship between the critical velocity dispersion
($\sigma_{v,\mathrm{crit}}$) and the observed velocity dispersion
($\sigma_{\mathrm{v}}$). The critical velocity dispersion is denoted as the
minimum velocity dispersion required for achieving equilibrium within
filamentary structure (e.g., Ostriker, 1964; Inutsuka & Miyama, 1992;
Chandrasekhar & Fermi, 1953; Stodólkiewicz, 1963; Nagasawa, 1987; Fiege &
Pudritz, 2000). It provides a measure of the velocity dispersion necessary for
self-gravitational stability of the spiral arm H i to determine whether it
might have collapsed into the observed clouds from a more uniform filamentary
structure in the long spiral shock.

In the context of our study, we consider the critical velocity dispersion as a
key parameter for assessing the gravitational stability of the H i in the
spiral arm before it formed the observed superclouds. The critical velocity
dispersion is determined based on the equilibrium mass ($\mu$) per unit
length.

$\sigma_{v,\mathrm{crit}}^{2}=G\mu/2.$ (11)

We estimate $\mu$ as the total gas mass ($M_{\mathrm{HI+H_{2}}}$) divided by
the spacing between the clouds which is derived using Equation 7. This
approach allows us to identify the minimum velocity dispersion required to
maintain a state of equilibrium within the Carina arm.

Figure 8 presents a scatter plot of $\sigma_{v,\mathrm{crit}}$ versus the
$\sigma_{\mathrm{v}}$ for the H i clouds analyzed in this work. The
corresponding histograms illustrate the distributions of the critical and
observed velocity dispersions. Notably, the observed velocity dispersions,
calculated from brightness temperature-weighted measurements, exhibit a
relatively constant behavior. The critical dispersion averages around 4 km
s-1. If the observed clouds formed by gravitational instabilities in a
previously more uniform spiral arm gas, then the velocity dispersion in this
gas had to be less than or equal to $\sim 4$ km s-1 for this process to be
rapid. Such a decrease is expected theoretically (Cowie, 1981; Dobbs et al.,
2008) and there are indications of a low dispersion for the cool component H i
in observations of spiral galaxies by Ianjamasimanana et al. (2012). The
higher observed velocity dispersions in present-day H i clouds suggest the
presence of additional energy sources, such as gravitational energy from their
formation or young stellar feedback after stars appeared.

Figure 8:  Scatter plot of critical velocity dispersion
($\sigma_{v,\mathrm{crit}}$) and observed velocity dispersion
($\sigma_{\mathrm{v}}$), with histograms of each. The left histogram displays
the distribution of $\sigma_{v,\mathrm{crit}},$ while the right histogram
shows the distribution of $\sigma_{\mathrm{v}}$. In the histograms, the yellow
sticks with left diagonals represent all H i clouds, whereas the red sticks
with right diagonals represent massive clouds with $M_{\mathrm{HI}}\geq
5\times 10^{6}~{}\mathrm{M_{\odot}}$. The bin size for both histograms is set
to 0.5 $\mathrm{km\,s^{-1}}$.

##  4 H i Superclouds and Molecular clouds

###  4.1 Spatial Relation between H i Superclouds and MCs

The formation of molecular clouds from H i gas is a complex process that can
be driven by a combination of physical processes, such as turbulent
compression and fragmentation (which create density fluctuations), radiative
compression (which triggers thermal instability), gravitational instability
(which enhances self-gravity), and magnetic instability (which can contribute
to cloud collapse and fragmentation) (e.g., Kwan & Valdes, 1987; Elmegreen,
1996; Hennebelle & Pérault, 2000; Ostriker & Kim, 2004; Dobbs et al., 2014).
While the classical understanding of the spatial distribution of H i and
molecular gas is a layered structure with a giant molecular cloud surrounded
by atomic gas (Blitz, 1993), the resulting spatial distribution of molecular
clouds relative to their parent H i clouds is expected to depend on a variety
of factors, including the specific physical conditions of the gas and the
relative importance of these formation mechanisms. However, the ubiquity of H
i gas in the Galactic disk and the difficulty in determining its exact
kinematic distance along the line of sight makes it challenging to establish a
definitive association between H i and molecular clouds and to provide
observational insight. Nevertheless, it is worthwhile to investigate the
spatial distribution of H i superclouds and MCs, particularly in the outer
Carina arm, which is relatively well-identified.

A simple question arises as to whether the detected MCs are centered on the
associated H i superclouds or matched with local H i emission peaks.
Extragalactic observational studies of the spatial distribution and kinematics
of molecular clouds relative to their associated H i gas have been conducted
using a variety of tracers, such as CO and H i emission (e.g., Wong et al.,
2009; Tosaki et al., 2011). It is found that CO emission was typically
associated with high-intensity H i gas, but not all regions of high H i
intensity were found to have CO emission.

Figure 9 displays a position-velocity diagram of H i and CO emission features,
which is averaged over latitudes. The H i cloud emission features defined in
this work are generally visible within the gray contour of 30 K (see Section
3.1.1 and Figure 1 for details). The CO emission features, displayed with
bright gray contours, are commonly placed in the velocity range where the H i
cloud features are visible, although some small and weak CO emission features
at $l\gtrsim 320\arcdeg$ do not appear in this averaged diagram. Extended, an
arc-like feature in H i emission is observed at $l\sim$ 296° to 300° and
$v_{\mathrm{LSR}}\sim$ 35 to 60 $\mathrm{km\,s^{-1}}$, which appear as a ring-
like structure when lower velocity H i gas is included. However, this feature
is not within the scope of this study. This may indicate activity such as a
supershell or chimney, and is very likely to be related to GSH 298$-$01$+$35,
proposed as a chimney structure, identified by McClure-Griffiths et al.
(2002). A detailed 3D kinematic analysis would provide further insight into
the structures of the H i and molecular gas.

Figure 9:  $b$-averaged ($l$, $v_{\mathrm{LSR}}$) H i map, overlaid with CO
contours and star-forming regions. The integrated latitude range for the map
is from -2° to $+1$°. The background image with a thin, dark gray contour
represents H i, and the contour level is set at 30 K. CO contours, displayed
as thick, bright gray lines, indicate levels of 0.1, 0.2, 0.3, 0.4, and 0.5 K.
WMAP sources, likely related to the outer Carina arm, are marked with thick,
blue pluses, whereas thin, orange pluses represent those that are unlikely to
be related. Similarly, thick, magenta crosses represent WISE H ii regions with
a single measured velocity, likely associated with the outer Carina arm, while
thin, brown crosses indicate those that are unlikely to be related.

Figure 10 presents a comparison of the H i and CO emission features in a
position-position diagram. The figure shows the ratio of column densities
between $\mathrm{H_{2}}$ column density($N_{\mathrm{H_{2}}}$) and H i column
density ($N_{\mathrm{HI}}$) obtained by using Figure 2(a). The column density
ratio, $2N_{\mathrm{H_{2}}}/N_{\mathrm{HI}}$, is beneficial for studies of
molecular clouds and star formation, as it reflects the degree of molecular
gas enrichment in a given region, which refers to the proportion of molecular
gas present relative to atomic gas. This parameter is important for
understanding the conditions necessary for star formation. The color image
displays the column density ratio with contours indicating $N_{\mathrm{HI}}$
from 2.2 to 4.8 $\times 10^{21}~{}\textrm{cm}^{-2}$ for the top panel, and
$N_{\mathrm{H_{2}}}$ from 5 to 60 $\times 10^{20}~{}\textrm{cm}^{-2}$ for the
bottom panel. The column density ratios were calculated only where
$N_{\mathrm{H_{2}}}$ is greater than or equal to $5\times
10^{20}~{}\textrm{cm}^{-2}$, which is equal to the minimum limit for the
identification of MCs in the work. The $v$-integrated positions of all CO
emissions of the identified MCs are equal to where column density ratios are
expressed. The column density ratios displayed in this figure range from
approximately 0.2 to 3.2, with the highest value observed at M31 in
association with H7.

Figure 10:  Ratio map of $\mathrm{H_{2}}$ column density
($N_{\mathrm{H_{2}}}$) to H i column density ($N_{\mathrm{HI}}$), specifically
$2N_{\mathrm{H_{2}}}/N_{\mathrm{HI}}$, overlaid with the H i column density
contours (top) or $\mathrm{H_{2}}$ column density contours (bottom). The white
areas in both the top and bottom panels indicate regions where
$N_{\mathrm{H_{2}}}<5\times 10^{20}~{}\mathrm{cm}^{-2}$, which corresponds to
the minimum threshold for MC identification, and have been masked. We also
masked the area of $l>291\arcdeg$ and $b<-2\arcdeg$ or $b>0.8\arcdeg$. Some
weak CO emission features are visible in the region, but their validity is
uncertain as they were obtained by different surveys with relatively low
sensitivity and a large sampling value. The contours are color-graded from
gray to black to indicate increasing levels. In the top panel, the
$N_{\mathrm{HI}}$ levels are 2.2, 2.7, 3.0, 3.3, 3.7, 4.0, 4.2, 4.4, 4.6,
$4.8\times 10^{21}~{}\mathrm{cm}^{-2}$. In the bottom panel, the
$N_{\mathrm{H_{2}}}$ levels are 5, 10, 15, 30, 40, 50, $60\times
10^{20}~{}\mathrm{cm}^{-2}$. The star-forming regions, which are likely
related to the outer Carina arm, are represented by magenta circles and blue
pluses for WMAP sources and WISE H ii regions, respectively, as shown in
Figure 9. The size of each circle for the WMAP sources corresponds to their
respective effective radii.

The minimum value for H i column density used to identify H i clouds in this
study may provide insight into areas where $\mathrm{H_{2}}$ formation occurs
more efficiently through self-shielding. Numerous previous studies have
demonstrated that the saturation of H i column density at $\approx
10^{21}\mathrm{cm}^{-2}$ in the correlation between H i column density and
tracers of total gas column density, such as infrared surface brightness and
optical reddening, indicates the presence of $\mathrm{H_{2}}$ (e.g., Reach et
al., 1994; Meyerdierks & Heithausen, 1996; Barriault et al., 2010; Liszt,
2014; Park et al., 2018). However, it is important to note that the conversion
from atomic to molecular gas can also be influenced by other factors, such as
metallicity (Bolatto et al., 2013, and references therein).

Most of the MCs appear to be spatially associated within the corresponding H i
superclouds, but a majority of them are not situated in the central regions of
these superclouds. Notably, many peaks in CO emission appear somewhat distant
from the nearby H i emission peaks. It should be noted that some MCs (e.g.,
H47 at $l\simeq 326\arcdeg$ and H48 at $l\simeq 328\arcdeg$) are found to be
situated at or beyond the periphery of the relevant H i supercloud. Although
the cloud boundary, particularly for H i superclouds, was arbitrarily
delineated based on bright, dense regions, the physical associations of the
aforementioned cases may be less clear than those of other cases. Nonetheless,
we have included those MCs in the catalog.

As seen in the bottom panel in Figure 10, $N_{\mathrm{H_{2}}}$ is positively
correlated with the column density ratio. That is, the CO emissions peak in
regions with high column density ratios, indicating that the conversion of H i
to $\mathrm{H_{2}}$ is more efficient in those regions. This may be due to
certain physical conditions that favor the formation of molecular gas, such as
high gas density or low gas temperature. However, as seen in the top panel in
Figure 10, the correlation between column density ratios and local H i peaks
seems lacking. This may be due to various factors. One possible explanation is
that the conversion of H i to $\mathrm{H_{2}}$ is not solely determined by the
local H i column density but also by other physical conditions such as gas
density, temperature, radiation field, and turbulence or magnetic fields. In
regions where the physical conditions are favorable for forming molecular gas,
the conversion may be more efficient even if the local $N_{\mathrm{HI}}$ is
not high. On the other hand, in regions where the physical conditions are
unfavorable, the conversion may be less efficient even if the local
$N_{\mathrm{HI}}$ is high. It is possible that triggered molecular cloud
formation could play a role in the lack of correlation between the column
density ratios and local H i peaks. When molecular clouds form due to external
triggering mechanisms, such as shock compression or radiation from massive
stars, the conversion from H i to $\mathrm{H_{2}}$ can happen more efficiently
in certain regions that are influenced by these triggering mechanisms (e.g.,
Ballesteros-Paredes et al., 1999; Hartmann et al., 2001; Inoue & Inutsuka,
2009; Inutsuka et al., 2015). This can lead to molecular gas being present in
regions with lower H i column densities or in regions where the H i gas has
been dispersed or compressed by the triggering event.

Figure 11 presents a quantitative comparison between the positions of H i
clouds and MCs. The left group of three panels shows the projected distances
on the sky in angular scale, with an adopted angular bin size of 8′, which is
approximately half of the angular resolution of the data used. The right group
of three panels displays the distances computed using the heliocentric
distance of the corresponding H i cloud provided in Table 1, presented in
linear scale with an arbitrarily selected linear bin size of 25 pc. According
to the cloud definition method in this paper, the emission peaks of MCs (${\rm
MC_{P}}$) are typically located at or near the centers of the MCs (${\rm
MC_{C}}$), given the angular resolution (panel (b)). In contrast, the local
emission peaks of H i clouds (${\rm HC_{LP}}$) are not always situated at
their centers (${\rm HC_{C}}$) (panel (a)), and some clouds even exhibit
multiple peaks (e.g., H7 and H11). When comparing ${\rm MC_{P}}$ with ${\rm
HC_{C}}$, we observe that most ${\rm MC_{P}}$ are significantly distant from
${\rm HC_{C}}$ (green in panel (c)). Additionally, we identified the nearest H
i peak for a given MC and labeled it as ${\rm HC_{NP,MC}}$, then measured the
distance between them (yellow in panel (c)). The distribution of ${\rm
MC_{P}}$–${\rm HC_{NP,MC}}$ exhibits a relatively stronger correlation than
that of the ${\rm MC_{P}}$–${\rm HC_{C}}$ and displays two prominent peaks
with a valley around the mean mutual distances of $\sim 23\arcmin$.
Specifically, 17 pairs on the left side of the distribution exhibit a strong
positional correspondence or marginal overlap, while the remaining 31 pairs
show a clear positional discrepancy.

Figure 11:  Histogram of the mutual distances between different positions,
including: (a) the local emission peaks of H i clouds (${\rm HC_{LP}}$) and
the geometric centers of the H i clouds (${\rm HC_{C}}$) (${\rm
HC_{LP}}$–${\rm HC_{C}}$), (b) the emission peaks of MCs (${\rm MC_{P}}$) and
the geometric centers of the MCs (${\rm MC_{C}}$) (${\rm MC_{P}}$–${\rm
MC_{C}}$), and (c) the emission peaks of MCs (${\rm MC_{P}}$) and either the
geometric centers of MC-related H i clouds (${\rm HC_{C}}$) (${\rm
MC_{P}}$–(${\rm HC_{C}}$; green with right diagonals) or the local emission
peaks of H i clouds nearest the MCs (${\rm HC_{NP,MC}}$) (${\rm MC_{P}}$–${\rm
HC_{NP,MC}}$; yellow with left diagonals). The left group of four panels shows
the distances projected in the sky in angular scale, and the right group shows
the distances calculated assuming the heliocentric distance of relevant H i
cloud, provided in Table 1, in linear scale. These result in the minimum
values, which are not the actual separation in 3D. The emission peaks were
derived from $v_{\mathrm{LSR}}$-integrated maps (e.g., Figure 2(a)). For the
left panels, we chose a bin size is 8′, which is approximately half of the
angular resolution of the data used. The right panels, on the other hand, were
binned with an arbitrary bin size of 25 pc. A vertical dotted line marks the
mean value of each case (the parentheses refer to the right panel): (a) 18′
(68 pc), (b) 6′ (16 pc), (c) 23′ (72 pc); 40′ (122 pc). The two mean values
for the left and right panels do not correspond directly to each other since
the distances to the H i clouds are different.

###  4.2 Molecular Mass Fraction of H i Superclouds

In Figure 12, we present two distributions showing the molecular mass fraction
as a function of Galactocentric distance (left panel) or total gas surface
density (right panel) of H i superclouds. The molecular mass
fraction,$f_{\mathrm{H_{2}}}$, is defined as

$f_{\mathrm{H_{2}}}=\frac{M_{\mathrm{H_{2},all}}}{M_{\mathrm{HI}}+M_{\mathrm{H_{2},all}}}.$
(12)

The total gas surface density, $\Sigma_{\mathrm{HI+H_{2}}}$, is defined as

$\Sigma_{\mathrm{HI+H_{2}}}=\frac{M_{\mathrm{HI}}+M_{\mathrm{H_{2},all}}}{A_{\mathrm{HI}}},$
(13)

where $A_{\mathrm{HI}}$ is the area of a H i supercloud (see Section 3.2.1).

Figure 12:  Relation of the molecular mass fractions ($f_{\mathrm{H_{2}}}$)
and the total gas surface densities ($\Sigma_{\mathrm{HI+H_{2}}}$) of H i
superclouds (left) or their Galactocentric distances (right). Filled symbols
indicate H i superclouds associated with H ii region(s), while unfilled
symbols represent H i superclouds without H ii region(s).

As anticipated, a larger mass of an H i cloud is generally associated with a
larger mass of an MC. The relation between $f_{\mathrm{H_{2}}}$ and
$\Sigma_{\mathrm{HI+H_{2}}}$ exhibits a clear positive correlation. In regions
where the $\Sigma_{\mathrm{HI+H_{2}}}$ is higher, there is generally a higher
pressure environment, which facilitates the conversion of atomic gas into
molecular gas. The positive correlation between $f_{\mathrm{H_{2}}}$ and
$\Sigma_{\mathrm{HI+H_{2}}}$ can be understood within the context of
interconnection processes that drive the conversion of atomic hydrogen into
molecular hydrogen and ultimately lead to star formation.

Furthermore, previous studies, such as Elmegreen & Elmegreen (1987), have
observed a trend where the value of $f_{\mathrm{H_{2}}}$ decreases as the
Galactocentric distance increases. In our study, we observe this trend in the
outer Carina arm clouds spanning $l=288\arcdeg$ to $340\arcdeg$, which extends
over the Galactocentric distance range of $R_{\mathrm{GC}}\sim$ 9–11 kpc. We
find that the decrease in $f_{\mathrm{H_{2}}}$ smoothly declines with
increasing $R_{\mathrm{GC}}$, with few deviations. Additionally, the majority
of H i superclouds with $f_{\mathrm{H_{2}}}>0.1$ or
$\Sigma_{\mathrm{HI+H_{2}}}\gtrsim$ $60~{}\mathrm{M_{\odot}}\mathrm{pc^{-2}}$
exhibit evidence of star-forming activity, as indicated by the presence of H
ii region(s). The $f_{\mathrm{H_{2}}}$ values of H i superclouds between
$R_{\mathrm{GC}}\sim$ 9–10 kpc exhibit a relatively wide distribution ranging
from $\sim 0.1$ to 0.3, suggesting that variations in $f_{\mathrm{H_{2}}}$ may
be influenced by local environmental factors or other processes affecting the
conversion of atomic to molecular gas. For example, higher gas densities in
some H i superclouds might lead to increased molecular mass fractions and
consequently promote star formation. In contrast, the range of 0.1–0.3 at
$R_{\mathrm{GC}}\sim$ 9–10 kpc is somewhat larger than the
$f_{\mathrm{H_{2}}}$ values ($<0.1$) of solar-neighboring H i superclouds
reported by Elmegreen & Elmegreen (1987), It is worth noting, however, that
the mean $f_{\mathrm{H_{2}}}$ value over the entire gas disk, integrated over
$b$ from $-30\arcdeg$ to $+30\arcdeg$, at the solar radius is 0.1–0.2, while
it increases to $\sim$ 0.5 at the Galactic midplane when integrated over
$b=-1\fdg 5$ to $+1\fdg 5$ (Koda et al., 2016). This observation underscores
the importance of considering the relationship between molecular mass
fraction, gas surface density, and the presence of H ii regions in
understanding star formation processes within these superclouds.

##  5 Star Formation

###  5.1 Spatial Relation of H ii regions with H i Superclouds and MCs

The presence of H ii regions is a strong indicator of the existence of high-
mass star-forming regions. To investigate the relationship between H i
superclouds and H ii regions in the outer Carina arm, We overlaid the H ii
regions, obtained from the H i catalog, in the outer Galaxy onto $b$-averaged
($l$, $v$) or $v$-integrated ($l$, $b$) diagrams of Figures 9 and 10. We used
star-forming regions including those cataloged by Lee et al. (2012a) using
Wilkinson Microwave Anisotropy Probe (WMAP) data and the H ii regions
identified in the outer Galaxy from the all-sky Wide-field Infrared Survey
Explorer (WISE) survey (Anderson et al., 2014)444We used Version 2.0.
Specifically, we focused on H ii regions with a single observed velocity. In
Figure 9, the associations of two objects, namely WISE H ii regions and WMAP
sources, with the outer Carina arm are indicated through different symbols and
line thicknesses. The associations are determined based on a simple comparison
of observed LSR velocities. WISE H ii regions are represented by pluses,
marked in blue or orange, with varying line thickness. The thicker blue pluses
correspond to likely associations with the outer Carina arm, while the thinner
orange pluses indicate likely no association. Similarly, WMAP sources are
depicted as crosses in magenta or brown, with different line thicknesses. The
magenta crosses with thicker lines indicate likely associations, while the
thinner brown crosses do not exhibit a clear association. Figure 10
specifically highlights the blue pluses for WISE H ii regions and marks WMAP
sources likely related to the outer Carina arm with magenta circles. The
circle size of each WMAP source represents its effective radius. Most of the H
ii regions appear to be associated with the outer Carina arm, suggesting a
clear positional correlation between the three components: H i superclouds,
GMCs, H ii regions.

Upon closer examination, we found that eleven H i superclouds (H1–3, H5–7,
H10–11, H15, H18, and H25) are associated with WISE H ii regions, indicating
ongoing high-mass star formation. However, we were unable to detect any CO
emission, which is commonly used as a tracer of molecular gas, associated with
two of them (H18 and H25). This could imply that either the molecular gas in
these regions is not abundant enough to be traced by CO emission or that the
CO emission is too weak to be detected with our current observations.

The spatial distribution of star-forming regions relative to their associated
H i supercloud is also not centralized. However, these regions are typically
located within the range of the H i supercloud and distributed closer to the
CO emission peaks. This is a natural phenomenon as stars form in dense regions
of MCs. Murray & Rahman (2010) proposed that the WMAP sources are bubbles
generated by massive star clusters, representing the extended low-density H ii
regions previously described by Mezger (1978). Furthermore, they found that
classical giant H ii regions are distributed in the bubble walls, which can be
explained by triggered star formation. H7 provides a good example of such a
scenario, where a WMAP source is located in the center of H7, which exhibits
low $N_{\mathrm{HI}}$ and $N_{\mathrm{H_{2}}}$. Several WISE H ii regions are
located near the effective radius boundary of the WMAP source and are closer
to the CO emission peaks. Based on these facts, we propose that the earlier
star formation at the cloud center produced the WMAP bubble, which then
triggered the next star formation event in the WISE H ii regions.
Additionally, it is likely that the atomic and molecular gases in the cloud
center were blown away during this process.

The results of the comparison between the centers of WISE H ii regions and
${\rm MC_{P}}$, ${\rm HC_{C}}$, or ${\rm HC_{NP,MC}}$ are shown in Figure 13.
The mean mutual distances increase from ${\rm MC_{P}}$ to ${\rm HC_{NP,MC}}$,
and their distributions exhibit some differences (red, yellow, and green,
respectively). We found that the degree of correlation with the central
positions of the H ii regions follows the order of ${\rm HC_{NP,MC}}$ $<{\rm
HC_{C}}$ $<{\rm MC_{P}}$. Notably, the distribution of H ii region–${\rm
MC_{P}}$ is positively skewed by numerous pairs with lower values than their
mean, suggesting a strong positional correspondence or marginal overlap for
many pairs. These results indicate that H ii regions are more closely related
to emission peaks of MCs than those of H i clouds. This is consistent with the
fact that stars form within the densest cores within MCs, and the ionizing
radiation from young massive stars creates H ii regions within or near the
MCs. On the other hand, as stars form and evolve, stellar feedback, such as
radiation pressure, stellar winds, and supernova explosions, can remove the
surrounding gas and dust, potentially influencing the correlation between the
central positions of H ii regions and emission peaks of MCs. However, our
angular resolution might not be high enough to resolve the detailed effects of
stellar feedback, especially for targets at distances over 7 kpc. Also, there
is a limitation in the examination of correlation in 2D space integrated along
velocity. Despite these limitations, our findings are in line with the general
understanding that H ii regions are more closely related to MCs than large,
diffuse H ii clouds. The fact that 67 out of 106 pairs ($\sim 63\%$) in the H
ii region–${\rm MC_{P}}$ distribution show good matching supports the notion
that H ii regions and MCs are physically associated with each other.

Figure 13:  Histogram similar to Figure 11, but for the mutual distances
between different positions, the centers of WISE H ii regions and either ${\rm
MC_{P}}$ (H ii region–${\rm MC_{P}}$; red filled) or ${\rm HC_{C}}$ (H ii
region–${\rm HC_{C}}$; green with right diagonals) or ${\rm HC_{NP,MC}}$ (H ii
region–${\rm HC_{NP,MC}}$; yellow with left diagonals). Vertical dotted lines
mark mean values of 16′ (47 pc); 21′ (66 pc); 37′ (112 pc), with the values in
parentheses corresponding to those for the right panel.

###  5.2 Star Formation Rate

The star formation rate (SFR) in the Galactic star-forming regions has been
extensively studied in the literature, often using free-free emission flux
measured from WMAP (Murray & Rahman, 2010; Lee et al., 2012a). In this work,
we use physical information of star-forming complexes(SFCs) cataloged by Lee
et al. (2012a). We match seven SFCs to six H i superclouds, and their catalog
numbers are listed in Table 3. We derive SFRs from the total ionizing photon
luminosity ($Q$) using the following equations, which are similar to Equations
(3), (9)–(10) of Lee et al.:

$\frac{\rm SFR}{(\mathrm{M_{\odot}}\,\mathrm{yr}^{-1})}=4.1\times
10^{-54}\,Q,$ (14) $\frac{Q}{(s^{-1})}=1.34\times
10^{26}\times\left(\frac{4\pi d^{2}F_{\nu}}{\mathrm{erg\,s^{-1}}}\right)\times
1.37,$ (15)

where 1.37 is a correction factor accounting for the absorption of ionizing
photons by dust grains, and the term of $4\pi d^{2}F_{\nu}$ describes the
specific free-free luminosity at 94 GHz of a given H ii region, which is
calculated with the 94 GHz free-free flux cataloged in Table 1 of Lee et al.
and its recalculated distance. The distances were derived using the velocities
given in Lee et al. and the flat Galactic rotation model adopted in this work.
Table 3 lists $Q$, SFR, and surface densities of SFR, molecular gas, and total
gas ($\Sigma_{\mathrm{SFR}}$, $\Sigma_{\mathrm{H_{2}}}$, and
$\Sigma_{\mathrm{HI+H_{2}}}$) derived for a given H i supercloud. The surface
densities are based on the area of a matched H i supercloud, e.g.,
$\mathrm{SFR}\times\mathrm{A}_{\mathrm{HI}}^{-1}$ as similar to Equation 13.

Table 3: Star Formation Properties of H i Superclouds  | $Q$ | SFR |  $\Sigma_{\mathrm{SFR}}$aaAll surface densities are based on the area of a matched H i supercloud. |  $\Sigma_{\mathrm{H_{2}}}$aaAll surface densities are based on the area of a matched H i supercloud. |  $\Sigma_{\mathrm{HI+H_{2}}}$aaAll surface densities are based on the area of a matched H i supercloud. |
---|---|---|---|---|---|---
#HI | (s-1) | ($\mathrm{M_{\odot}}\mathrm{yr}^{-1}$) | ($\mathrm{M_{\odot}}\mathrm{pc}^{-2}\mathrm{Myr}^{-1}$) | ($\mathrm{M_{\odot}}\mathrm{pc}^{-2}$) | ($\mathrm{M_{\odot}}\mathrm{pc}^{-2}$) | Lee SFCbbSFC(s) cataloged in Lee et al. (2012a) which is/are matched to a given H i supercloud.
0H1 | 1.3e+51 | 5.4e-03 | 1.050 | 24.0 | 91.7 | 167
0H3 | 4.6e+50 | 1.9e-03 | 0.016 |  09.2 | 67.4 | 171
0H5 | 2.4e+51 | 9.9e-03 | 0.071 | 17.9 | 82.7 | 172, 173
0H6 | 4.3e+51 | 1.8e-02 | 0.134 | 25.5 | 79.3 | 174
0H7 | 4.4e+51 | 1.8e-02 | 0.057 | 17.4 | 80.4 | 181
H11 | 1.2e+51 | 4.9e-03 | 0.017 | 22.2 | 84.6 | 192

The empirical relationship well-known as the Kennicutt-Schimidt (K-S) law
(Schmidt, 1959; Kennicutt, 1989, 1998) describes a power-law relation between
gas surface density and SFR surface density. The original K-S relation uses
the total gas surface density, which includes both atomic and molecular gas.
It appears still prominent in the global galaxy scale, that is, disk-averaged
(Kennicutt & Evans, 2012, reference therein). However, in some cases,
variations of the K-S relation focus on molecular gas only, as molecular gas
is more directly related to star formation. For example, Bigiel et al. (2008)
studied the relationship between $\Sigma_{\mathrm{SFR}}$ and
$\Sigma_{\mathrm{HI}}$ or $\Sigma_{\mathrm{H_{2}}}$ at sub-kpc scales within
nearby spiral galaxies. They found that $\Sigma_{\mathrm{SFR}}$ correlates
well with $\Sigma_{\mathrm{H_{2}}}$, but shows little or no correlation with
$\Sigma_{\mathrm{HI}}$. Similar results known as the resolved K-S relation
have been reported by other extragalactic studies (e.g., Leroy et al., 2008;
Schruba et al., 2011; Williams et al., 2018).

Figure 14 presents the relation between the SFR surface density
($\Sigma_{\mathrm{SFR}}$) and the surface densities of H i
($\Sigma_{\mathrm{HI}}$), H ii ($\Sigma_{\mathrm{H_{2}}}$), or total gas
($\Sigma_{\mathrm{HI+H_{2}}}$) in H i superclouds (referred to as
$\Sigma_{\mathrm{SFR}}$–$\Sigma_{\mathrm{HI}}$,
$\Sigma_{\mathrm{SFR}}$–$\Sigma_{\mathrm{H_{2}}}$, and
$\Sigma_{\mathrm{SFR}}$–$\Sigma_{\mathrm{HI+H_{2}}}$, respectively). As shown
in the previous studies, We also find that $\Sigma_{\mathrm{SFR}}$ appears
independent of $\Sigma_{\mathrm{HI}}$ and $\Sigma_{\mathrm{HI+H_{2}}}$ in H i
superclouds. The correlations are weak, with $\rho$ of $-0.029$ and p-value of
0.96 for both. Although our findings are limited to a very small number of
samples, they are still meaningful to compare to others. Since the H i
component dominates the total gas content for our H i superclouds, the
$\Sigma_{\mathrm{SFR}}$–$\Sigma_{\mathrm{HI+H_{2}}}$ relation follows the
$\Sigma_{\mathrm{SFR}}$–$\Sigma_{\mathrm{HI}}$ trend closely. Our finding of
no-correlation in $\Sigma_{\mathrm{SFR}}$–$\Sigma_{\mathrm{HI}}$ and
$\Sigma_{\mathrm{SFR}}$–$\Sigma_{\mathrm{HI+H_{2}}}$ is consistent with those
obtained by Lada et al. (2013) for local GMCs in the Milky Way. They explained
their findings as a characteristic of constant gas surface density for
Galactic GMCs (e.g., Lombardi et al., 2010; Heyer et al., 2009), which might
also be acceptable to our result of H i superclouds.

Figure 14:  Relation between the SFR surface density ($\Sigma_{\mathrm{SFR}}$)
and the surface densities of H i ($\Sigma_{\mathrm{HI}}$; left),
$\mathrm{H_{2}}$ ($\Sigma_{\mathrm{H_{2}}}$; middle), or total gas
($\Sigma_{\mathrm{HI+H_{2}}}$; right) in six H i superclouds. All surface
densities in this plot were calculated based on the area of a matched H i
supercloud. In the middle panel, the best single power-law fit with a power-
law index of $n\simeq 1.3$ is marked with a dotted line.

On the other hand, we do observe a positive correlation between
$\Sigma_{\mathrm{SFR}}$ and $\Sigma_{\mathrm{H_{2}}}$, similar to the resolved
K-S relation, although this correlation can be less clear due to a small
number of data points. Spearman’s rank correlation coefficient of 0.54 and
p-value of 0.27 also indicate a moderate positive correlation. The power-law
index of $\sim 1.3$ we found is in good agreement with the well-known value of
$\sim 1.4$ for the global K-S relation Kennicutt (1998). This consistency
implies that the star formation process in our study region follows a similar
scaling relation as observed on global scales in other galaxies. Our results
are also consistent with the findings of Bigiel et al. (2008) and Leroy et al.
(2013), who demonstrated that molecular gas plays a dominant role in
regulating star formation across a wide range of spatial scales and
environments. This reinforces the importance of molecular gas in regulating
star formation and provides additional support for the K-S relation as a
fundamental scaling law governing the conversions of gas into stars.

##  6 Summary

In this study, we investigated H i clouds, MCs, and star formation in the
Carina spiral arm of the outer Galaxy.

Using HI4PI survey and CfA CO survey data, we identified H i clouds and MCs
based on ($l$, $v_{\mathrm{LSR}}$) locations of the Carina arm obtained from
Paper I. We derived physical parameters, including size, mass, and distance,
for 29 H i clouds and 49 MCs, but conducted further analysis on 26 H i clouds
and 48 MCs (see Section 3.1.1).

Most of the identified H i clouds are more massive than
$10^{6}~{}\mathrm{M_{\odot}}$ and are referred to as H i superclouds. Fifteen
of the 26 H i clouds have associated MC(s) with masses exceeding
$10^{6}~{}\mathrm{M_{\odot}}$ with $\Sigma_{\mathrm{HI+H_{2}}}\gtrsim$ 50
$\mathrm{M_{\odot}}\rm pc^{-2}$. Our virial equilibrium analysis suggests that
these CO-bright H i clouds are gravitationally bound or marginally bound.

We also found an anti-correlation between molecular mass fractions and
Galactocentric distances, as well as a correlation between molecular mass
fractions and total gas surface densities. Among the CO-bright H i
superclouds, nine are associated with H ii regions, indicating ongoing star
formation. The star-forming H i superclouds have molecular mass fractions
larger than 0.1, although some H i superclouds that meet this criterion do not
match with H ii regions.

Consistent with previous studies, we showed that H i superclouds are regularly
spaced along the spiral arm, with a typical spacing of $0.084\,\mathrm{R_{0}}$
($\sim 700$ pc); this could be partly a selection effect from blending at
short spacings. The presence of a peak in the ratio of separation to the minor
axis, which closely aligns with the theoretical expectation of 3.9, suggests
that the observed regular spacing is not a result of chance but rather an
outcome of an underlying physical process. We observed a strong spatial
correlation between H ii regions and molecular clouds, with some offsets
between molecular clouds and local H i column density peaks.

Lastly, we examined the relationship between the SFR surface density and
surface densities of H i, $\mathrm{H_{2}}$, and total gas. In agreement with
extragalactic studies of the resolved K-S relation and local GMCs study by
Lada et al. (2013), our results indicate that $\Sigma_{\mathrm{SFR}}$ is
independent of $\Sigma_{\mathrm{HI}}$ and $\Sigma_{\mathrm{HI+H_{2}}}$, but
show a positive correlation with $\Sigma_{\mathrm{H_{2}}}$ with a power-law
index of $\sim 1.3$. This consistency with the well-established value of $\sim
1.4$ for the global K-S relation highlights the significant role molecular gas
plays in controlling star formation and lends further credence to the K-S
relation as a key scaling law that governs the transformation of gas into
stars.

G.P. was supported by the National Research Foundation of Korea through grants
NRF-2020R1A6A3A01100208 and RS-2023-00242652. This work was partly supported
by the Korea Astronomy and Space Science Institute grant funded by the Korea
government(MSIT) (Project No. 2022-1-840-05).

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