# Distributions and Physical Properties of Molecular Clouds in the Third
Galactic Quadrant: $l=[\,219\fdg 75,~{}229\fdg 75\,]$ and $b=[\,-5\fdg
25,~{}5\fdg 25\,]$

Yiwei Dong  Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, People’s Republic of China  School of Astronomy and Space Science,
University of Science and Technology of China, Hefei 230026, People’s Republic
of China  Yan Sun Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, People’s Republic of China  Ye Xu Purple Mountain Observatory,
Chinese Academy of Sciences, Nanjing 210023, People’s Republic of China
School of Astronomy and Space Science, University of Science and Technology of
China, Hefei 230026, People’s Republic of China  Zehao Lin  Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210023, People’s Republic of
China  School of Astronomy and Space Science, University of Science and
Technology of China, Hefei 230026, People’s Republic of China  Shuaibo Bian
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023,
People’s Republic of China  School of Astronomy and Space Science, University
of Science and Technology of China, Hefei 230026, People’s Republic of China
Chaojie Hao  Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, People’s Republic of China  School of Astronomy and Space Science,
University of Science and Technology of China, Hefei 230026, People’s Republic
of China  Dejian Liu  Purple Mountain Observatory, Chinese Academy of
Sciences, Nanjing 210023, People’s Republic of China  School of Astronomy and
Space Science, University of Science and Technology of China, Hefei 230026,
People’s Republic of China  Yingjie Li Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210023, People’s Republic of China  Ji Yang
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023,
People’s Republic of China  Yang Su Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210023, People’s Republic of China  Xin Zhou
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023,
People’s Republic of China  Shaobo Zhang Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210023, People’s Republic of China  Qing-Zeng Yan
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023,
People’s Republic of China  Zhiwei Chen Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210023, People’s Republic of China

###### Abstract

We present the results of an unbiased 12CO/13CO/C18O ($J=1$–0) survey in a
portion of the third Galactic quadrant (TGQ): $219\fdg 75\leqslant l\leqslant
229\fdg 75$ and $-5\fdg 25\leqslant b\leqslant 5\fdg 25$. The high-resolution
and high-sensitivity data sets help to unravel the distributions and physical
properties of the molecular clouds (MCs) in the mapped area. In the LSR
velocity range from $\sim$$-1$ to $\sim$$85~{}\rm km\,s^{-1}$, the molecular
material successfully traces the Local, Perseus, and Outer arms. In the TGQ,
the Outer arm appears to be more prominent than that in the second Galactic
quadrant (SGQ), but the Perseus arm is not as conspicuous as that in the SGQ.
A total of 1,502 12CO, 570 13CO, and 53 C18O molecular structures are
identified, spanning over $\sim$2 and $\sim$6 orders of magnitude in size and
mass, respectively. Tight mass–radius correlations and virial parameter–mass
anticorrelations are observable. Yet, it seems that no clear correlations
between velocity dispersion and effective radius can be found over the full
dynamic range. The vertical distribution of the MCs renders evident pictures
of the Galactic warp and flare.

Interstellar molecules (849) — CO line emission (262) — Molecular clouds
(1072) — Spiral arms (1559)

††software: GILDAS/CLASS (Pety, 2005), Astropy (Astropy Collaboration et al.,
2013, 2018), matplotlib-v3.4.3666https://doi.org/10.5281/zenodo.5194481
(Hunter, 2007), NumPy (Harris et al., 2020)

##  1 Introduction

Table 1: CO Surveys of the TGQ

Telescope | Transitions | Sky | Beam | Velocity | RMS | Reference
---|---|---|---|---|---|---
| ($J=1$–0) | Coverage | Size | Resolution | Noise |
|  |  |  | ($\rm km\,s^{-1}$) | ($T\rm_{MB}$)(K) |
CfA 1.2 m |  12CO | All Galactic plane | $8\farcm 8$ | 1.3 | 0.1–0.4 | (1)
|  |  $194\degree\leqslant l\leqslant 270\degree$, |  |  |  | (2)
|  | $-4\degree\leqslant b\leqslant 1\degree$ |  |  |  |
NANTEN 4 m |  12CO |  $220\degree\leqslant l\leqslant 60\degree$, | $2\farcm 6$ | 0.65 | 0.4 | (3)
|  | $|b|\leqslant 10\degree$ |  |  |  |
Nagoya 4 m |  13CO |  $208\degree\leqslant l\leqslant 230\degree$, | $2\farcm 7$ | 0.1 | 0.5 | (4)
|  | $-20\degree\leqslant b\leqslant 10\degree$ |  |  |  |
Mopra 22 m |  12CO/13CO/ |  $l\sim 224\fdg 4$, |  $\sim$$38\arcsec$ |  $\sim$0.1 | 0.3–0.9 | (5)
| C18O/C17O | $b\sim-0\fdg 6$ |  |  |  |
Nobeyama 45 m |  12CO/13CO/ |  $10\degree\leqslant l\leqslant 50\degree$; $198\degree\leqslant l\leqslant 236\degree$, |  $\sim$$14\arcsec$ |  $\sim$1.3 | 0.6/0.3aa0.6 K for 12CO, and 0.3 K for 13CO and C18O. | (6)
| C18O | $|b|\leqslant 1\degree$ |  |  |  |
ARO 12 m |  12CO/13CO |  $220\degree<l<240\degree$, |  $\sim$$55\arcsec$ | 0.26/0.65bb0.26 and 0.65 $\rm km\,s^{-1}$ for two backend filter banks, respectively.  | 0.3–1.3 | (7)
|  | $-2\fdg 5<b<0\degree$ |  |  |  |
PMO 13.7-m |  12CO/13CO/ |  $10\degree\lesssim l\lesssim 230\degree$, |  $\sim$$50\arcsec$ |  $\sim$0.16 | 0.5/0.3ccThe present work. 0.5 K for 12CO, and 0.3 K for 13CO and C18O. | (8)
| C18O | $|b|\leqslant 5\fdg 25$ |  |  |  |

References. — (1) Dame et al. (1987, 2001); (2) May et al. (1993, 1997); (3)
Mizuno & Fukui (2004); (4) Kim et al. (2004); (5) Olmi et al. (2016); (6)
Umemoto et al. (2017); (7) Benedettini et al. (2020, 2021); and (8) Su et al.
(2019).

CO has been the most commonly used tracer of the molecular gas since its first
detection (Wilson et al., 1970), and numerous CO line surveys have been
conducted over the decades (Heyer & Dame, 2015, and references therein).
Unlike the first quadrant of the Galaxy, the third Galactic quadrant (TGQ) has
neither been extensively observed nor widely discussed. Table 1 summarizes the
CO surveys of the TGQ. Using the CfA 1.2 m survey data, Rice et al. (2016) and
Miville-Deschênes et al. (2017) produced their individual all-Galaxy molecular
cloud (MC) catalogs by applying different cloud detection algorithms.
Combining the 12CO data of Mizuno & Fukui (2004) with Herschel data, Elia et
al. (2013) studied the star formation activity in the TGQ. More recently,
Benedettini et al. (2020, 2021) have studied the large-scale molecular
material distributions and properties in this region by using the Forgotten
Quadrant Survey’s 12CO and 13CO (1–0) line data, which were conducted by the
Arizona Radio Observatory (ARO) $12\rm~{}m$ antenna. Although our knowledge of
the molecular interstellar medium has improved, new data, with the combination
of multitracers, high-sensitivity, high-resolution, and wide Galactic
coverage, can offer more accurate and comprehensive insights into the TGQ.

Such data are currently being provided by the ongoing Milky Way Imaging Scroll
Painting (MWISP) project, an unbiased large-scale 12CO, 13CO, and C18O
($J=1$–0) survey conducted by the Purple Mountain Observatory (PMO) 13.7 m
telescope (Su et al., 2019). To date, the Galactic range of $l=[\,219\fdg
75,~{}229\fdg 75\,]$ and $b=[\,-5\fdg 25,~{}5\fdg 25\,]$ (hereafter, the G220
region) has been fully mapped by the MWISP project. This study aims to
investigate the essential information of the spatial distribution and physical
properties of MCs in the G220 region. The entire G220 region covers a total of
105 deg2, which contains several well-separated spiral arm features (the
Local, Perseus, and Outer arms) along the line of sight. The high-quality
MWISP data can provide a more comprehensive cloud sample than previous
studies, especially for the Outer arm. Therefore, we can expect to reveal new
features of the molecular gas distribution within this region.

In this paper, we present the results of the MWISP 12CO/13CO/C18O ($J=1$–0)
survey toward the G220 region ($J=1$–0 may be omitted hereafter, for
simplicity). In Section 2, we summarize the observations, data reduction, and
cloud identification. In Section 3.1, we present the large-scale structures
traced by 12CO, 13CO, and C18O data. Estimates of and statistics for the
physical properties are exhibited from Sections 3.2 to 3.4. Section 3.5
describes five particular MCs. Spatial distributions of the MCs are shown in
Section 4. A summary can be found in Section 5.

##  2 Data

###  2.1 Observations and Data Reduction

Figure 1: Left: histograms of the rms noise levels ($\sigma$) for 12CO (blue),
13CO (green), and C18O (red). The median values of $\sigma$ and the total
number of pixels are marked in the top right corner. Right: cumulative
distributions of $\sigma$.

The observations were conducted from 2016 December to 2021 April by using the
PMO $13.7~{}\rm m$ millimeter-wavelength telescope in Delingha, China. The
telescope, with a half-power beam width of $\sim$$50\arcsec$ at
$115\rm~{}GHz$, operates with a $3\times 3$ multibeam sideband separation
receiver named the Superconducting Spectroscopic Array Receiver (Yang et al.,
2008; Shan et al., 2012). The backend of the receiver system comprises 18 fast
Fourier transform spectrometers, each configured with $1\rm~{}GHz$ bandwidth
and 16,384 spectral channels, which yield a velocity coverage of
$\sim$2,600$\rm~{}km\,s^{-1}$, and yield velocity resolutions of
$0.159\rm~{}km\,s^{-1}$ at $115\rm~{}GHz$ and $0.166\rm~{}km\,s^{-1}$ at
$110\rm~{}GHz$. The 12CO line is observed at the upper sideband, while the
13CO and C18O lines are observed at the lower sideband simultaneously.

The G220 region is divided into 420 small tiles for the on-the-fly (OTF)
mapping, each with a size of $30\arcmin\times 30\arcmin$. The CLASS software
from the GILDAS package111https://www.iram.fr/IRAMFR/GILDAS (Pety, 2005) is
used for data reduction. The OTF data are resampled into $30\arcsec\times
30\arcsec$ pixels and converted to three-dimensional (3D) FITS cubes after a
first-order baseline is applied to the spectra. The velocity channels are not
smoothed. The data in the FITS cubes are on the main-beam brightness
temperature ($T_{\rm MB}$) scale, which is converted from the antenna
temperature ($T^{\ast}_{\rm A}$) with the typical beam efficiencies of
$\sim$0.51 for 13CO and C18O and $\sim$0.46 for 12CO (see the status report of
the telescope)222http://www.radioast.nsdc.cn/mwisp.php. Adding the 420 tiles
together, we create the final large mosaic, which contains 1,514,461 spectra
for each CO isotopolog. Please also refer to Su et al. (2019) for more details
about the observations and data reduction. Figure 1 shows the normalized
distributions of rms noise levels for 12CO (blue), 13CO (green), and C18O
(red). The median rms noise values are $\sim$$0.50\rm~{}K$ for 12CO at a
channel width of $\sim$$0.16\rm~{}km\,s^{-1}$, and $\sim$$0.24\rm~{}K$ for
13CO and C18O at a channel width of $\sim$$0.17\rm~{}km\,s^{-1}$.

###  2.2 Cloud Identification and Bad Channel Cleaning

An MC is popularly defined as a set of contiguous voxels in the position-
position-velocity (PPV) space, with the brightness temperatures above a
threshold (Heyer & Dame, 2015). Based on this definition, we employ an
approach developed by Yan et al. (2020) to identify the molecular structures
from the 12CO, 13CO, and C18O data. Note that the identified 12CO structures
are often referred to as 12CO clouds or MCs. The technique is based on the
density-based spatial clustering of applications with noise (DBSCAN)
algorithm333https://scikit-
learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html (Ester et al.,
1996), which contains three free parameters: $\epsilon$ and MinPts define the
connection property of the voxels in the PPV space, while $T_{\rm cutoff}$
defines the boundary isosurface of the structures (Yan et al., 2020). A
judicious option is $\epsilon=1$, $\rm MinPts=4$, and $T_{\rm
cutoff}=2\sigma$, ensuring most of the significant emission being identified
without omitting the faint but real signals. Yan et al. (2020) also recommend
the usage of post-selection criteria to exclude the noise and bad channel
contamination as much as possible. A sample will be rejected from the raw
catalog if it does not meet the following criteria: (1) number of voxels
$\geqslant 16$; (2) peak main-beam brightness temperature $\geqslant 5\sigma$;
(3) projection area contains more than one compact $2\times 2$ pixels
($1\arcmin\times 1\arcmin$ area); and (4) the number of velocity channels
$\geqslant 3$.

We then apply the DBSCAN signal identification results to mask the raw data
cubes. However, we see that the bad channels centered at $\sim$$34~{}\rm
km\,s^{-1}$ with a typical width of four to five channels (see Figure A1 in
Appendix A) cannot be completely excluded by the post-selection criteria.
Therefore, we visually inspect all identified structures based on their
spatial and velocity features in the PPV space. Fortunately, we find that the
bad channels contaminate only three real MCs (MWISP G224.153$+$1.211, MWISP
G223.784$+$2.950, and MWISP G224.097$+$2.290, marked as the red circles in
Figures 2, 3, and A1), while the majority of the bad channels simply produce
spurious samples that contain only bad channels without the presence of real
signal and show no signs of hierarchical structures. To get rid of the effects
of these bad channels, we further exclude the spurious samples to make the
final catalog (see Table B1 in Appendix B), and ignore the three contaminated
12CO clouds as well as their associated 13CO structure (MWISP
G224.166$+$1.218) when estimating physical properties.

Table 2: Number of Samples

Layer | Emission | Full | Flawed | Sliced | Counted
---|---|---|---|---|---
Name | Line | Sample | Sample | Sample | Sample
Local Arm |  12CO | 830 | 0 | 6 | 824
|  13CO | 419 | 0 | 1 | 418
| C18O | 48 | 0 | 0 | 48
Perseus Arm |  12CO | 404 | 3 | 6 | 395
|  13CO | 112 | 1 | 0 | 111
| C18O | 5 | 0 | 0 | 5
Outer Arm |  12CO | 268 | 0 | 4 | 264
|  13CO | 39 | 0 | 1 | 38

Note. — “Full Sample” in Column 3 includes all confident samples in our
catalog. Column 4, “Flawed Sample”, gives the number of samples contaminated
by the bad channels (see Section 2.2). Note that one of the contaminated 12CO
clouds contains a 13CO structure that is also treated as a contaminated
sample. Column 5, “Sliced Sample”, lists the number of samples that touch the
mapped borders. These structures are truncated by the edges of the G220
region, leaving less than half of the complete molecular structures. By
subtracting Columns 4 and 5 from Column 3, we get Column 6 (“Counted Sample”),
the number of samples that are used for the analysis of physical properties
(see Sections 3.3.2, 3.3.3 and 3.4).

Figure 2: Longitude–velocity (left) and latitude–velocity (right) maps of the
“cleaned” CO emission, integrated over a Galactic latitude range from $-5\fdg
25$ to $5\fdg 25$ and a Galactic longitude range from $219\fdg 75$ to $229\fdg
75$, respectively. The maps only contain emission from the samples in our
catalog. Mask “B,” “G,” and “R” indicate the regions where 12CO, 13CO, and
C18O emission exists, respectively. The three contaminated MCs are marked as
the red circles. The dashed lines sketch out the boundaries of each velocity
layer.

##  3 Results

###  3.1 Large-scale Structures Traced by ${}^{12}{\rm CO}$, ${}^{13}{\rm
CO}$, and ${\rm C}^{18}{\rm O}$

The number of samples is listed in Table 2. In total, we detected 1,502 12CO,
570 13CO, and 53 C18O molecular structures. One can see that the number of the
12CO structures of the Local arm is more than twice that of the Perseus arm
and more than three times that of the Outer arm. Figure 2 displays the
“cleaned” $l$–$v$ and $b$–$v$ diagrams, i.e., only containing emission from
the confident molecular structures identified by this study. Following Sun et
al. (2020), we define the mask “B,” “G,” and “R” regions as the regions where
12CO, 13CO, and C18O emission exists, respectively. Note that the mask “R”
region contains 12CO and 13CO emission, and the mask “G” region contains 12CO
emission as well. According to this definition, the red mask “R” region in
Figure 2 is included in the green mask “G” region, and the latter is further
included in the blue mask “B” region.

We find that the molecular gas emission is located in the LSR velocity
($v\rm_{\scriptscriptstyle LSR}$) range from $\sim$$-1$ to $\sim$$85~{}\rm
km\,s^{-1}$ in Figure 2. The dashed lines are defined as the boundaries that
have the same velocity separation to the adjacent arm centers (refer to Figure
3 of Reid et al., 2019). It is intriguing that the new high-quality MWISP data
successfully trace not only the two nearby spiral arms, but also the distant
Outer arm. However, from the $b$–$v$ map, it seems that our current Galactic
latitude coverage is still very limited in revealing a complete view of the
Local arm. Also note that we do not subdivide the interarm regions since their
contribution to the total emission is quite small.

The mask maps of integrated intensity of the whole G220 region and the three
arm features therein are shown in Figure 3, where the mask “B,” “G,” and “R”
regions are defined the same as in Figure 2. We see that both 12CO and 13CO
emission are detected in all velocity layers, while C18O emission is only
present in the two more nearby spiral arms at our current sensitivities. The
decrease in flux completeness with the increasing distance may largely account
for the nondetection of C18O emission in the Outer arm.

Figure 3: Mask regions of the entire G220 region (top-left) and the Local
(top-right), Perseus (bottom-left), and Outer (bottom-right) arms. The
definitions of the mask “B,” “G,” and “R” regions are the same as in Figure 2.
The red circles and rectangles mark the structures that are contaminated by
bad channels and touch the borders of the G220 region, respectively. These
structures will be ignored in the statistical analysis.  Table 3: Layers and
Mask Regions

Layer | Mask | Pixel | Pixel
---|---|---|---
Name | Region | Number | Percentage
Local Arm | B | 244,729 | 16.2$\%$
| G | 83,004 | 5.5$\%$
| R | 4,176 | 0.3$\%$
Perseus Arm | B | 41,999 | 2.8$\%$
| G | 8,712 | 0.6$\%$
| R | 123 | 0.008%
Outer Arm | B | 13,066 | 0.9$\%$
| G | 1,071 | 0.07$\%$

Note. — Pixel percentage is defined as the ratio of the pixel number in each
mask region to the total number of pixels in the G220 region, i.e., 1,514,461.

The pixel numbers and pixel percentages (the ratios of pixel numbers to the
total pixel number in the entire map, i.e., 1,514,461) of the mask regions are
listed in Table 3. Obviously, only a small fraction ($\lesssim$16.2%) of the
mapped pixels show CO emission, and the pixel percentages decrease rapidly
from the nearest arm to the farthest arm. However, CO emission seems to occupy
most of the mapped area in the inner Galaxy, e.g., in the Galactic longitude
of $l=[25\fdg 8$, $49\fdg 7$] (see Figure 6 of Su et al., 2019). In the second
Galactic quadrant (SGQ), Du et al. (2017) and Sun et al. (2020) also reported
pixel percentages of $\lesssim$26.2% and $\lesssim$35.7% in the G140 region
($139\fdg 75\leqslant l\leqslant 149\fdg 25$) and the G130 region ($129\fdg
75\leqslant l\leqslant 140\fdg 25$), respectively. Since all of these studies
used the MWISP survey data with uniform quality and employed very similar
statistical methods, the differences strongly imply that, on average, the
molecular gas becomes sparser when moving from the inner to the outer Galaxy.
In addition, as expected, the number of pixels in the mask “B” region is the
largest, while that in the mask “R” region is the smallest in each spiral arm
layer.

Figure 4: The velocity distribution of 12CO in the Local arm. The dashed lines
indicate the boundaries of the six regions where different distances were
adopted. The cold clumps (empty circles) of the Planck Collaboration et al.
(2016) and the 13CO clouds (filled circles) of Kim et al. (2004) are used as
references for determining the distances in the six regions.

###  3.2 Distances to MCs

The distances to the MCs in the outer Galactic plane are widely determined by
assuming a rotation curve, the so-called kinematic method. However, this
method is limited by large uncertainties for nearby clouds. Therefore, for the
MCs in the Local arm, we adopt the distances from the literature that are
mainly determined by the dust extinction and photometric methods. These
methods generally provide more reliable distance measurements than the
kinematic method. The Planck Collaboration et al. (2016) estimated the
distances of the cold clumps (the empty circles in Figure 4) using the
extinction method. Kim et al. (2004) zonally determined the distances of the
13CO clouds (the filled circles in Figure 4) in the Canis Major region.
Accordingly, the Local arm can be divided into six regions by the dashed lines
in Figure 4. For simplicity, we assign a constant distance for the MCs within
each region. The adopted distance and the number of MCs in each region are
given in Table 3.2. Region 1 is tentatively further subdivided into two cases:
a distance of $\rm 0.2~{}kpc$ is adopted for the relatively nearby clouds with
low $v\rm_{\scriptscriptstyle LSR}$ (the uncertainty-weighted average distance
of the cold clumps in this region; Planck Collaboration et al., 2016), and a
distance of $\rm 2~{}kpc$ is adopted for the relatively distant clouds with
high $v\rm_{\scriptscriptstyle LSR}$ (Montillaud et al., 2015). Also using the
uncertainty-weighted average method, the distances to the MCs in regions 2, 5,
and 6 are determined as 0.6, 0.3, and $\rm 0.7~{}kpc$, respectively. Referring
to Kim et al. (2004), we assign 1 and $\rm 1.15~{}kpc$ (the photometric
distance to the CMa OB1 stellar association; Clariá, 1974) to the MCs in
regions 3 and 4, respectively.

Considering that very few references are available, we derive the kinematic
distances for the MCs in the Perseus and Outer arms. The universal rotation
curve of Persic et al. (1996, two-parameter version) and parameter values from
Reid et al. (2019, model fit A5) are adopted here. In the G220 region, MWISP
G229.573$+$0.146 is the only MC with high-accuracy distance measurements (a
parallax distance of $4.59^{+0.27}_{-0.24}\rm~{}kpc$ is measured by Choi et
al., 2014, and a kinematic distance of $\sim$$4.9\rm~{}kpc$ is obtained and
adopted by us). However, the arm assignment for MWISP G229.573$+$0.146 remains
controversial. In this study, we still follow the results of Reid et al.
(2019) to assign this source to the Perseus arm. And it is worth noting that,
more recently, Xu et al. (2023) considered this source to belong to the Outer
arm.

Table 4: Regions and Distances in the Local Arm

Region | 1 | 2 | 3 | 4 | 5 | 6
---|---|---|---|---|---|---
Reference | (1) | (2) | (1) | (3) | (3) | (1) | (1)
Dist. (kpc)aaHeliocentric distance to each region. | 0.2 | 2 | 0.6 | 1 | 1.15 | 0.3 | 0.7
$\\#$ of CloudsbbNumber of 12CO clouds in each region. | 118 | 19 | 136 | 92 | 335 | 60 | 70

References. — (1) Planck Collaboration et al. (2016); (2) Montillaud et al.
(2015); and (3) Kim et al. (2004).

Table 5: Statistics of Excitation Temperatures, H2 Column Densities, Masses,
and Areas

Layer | Mask | $T_{\rm ex}~{}\left(\rm K\right)$ | $\log\\!\left[N_{\rm H_{2}}~{}\left(\rm{cm}^{-2}\right)\right]$ | Mass | Area
---|---|---|---|---|---
Name | Region | Min. | Max. | Med. | Avg. | S.D. | Min. | Max. | Med. | Avg. | S.D. | ($M_{\odot}$) | (pc2)
Local Arm | B | 3.7 | 36.5 | 5.9 | 6.9 | 3.03 | 19.4 | 22.3 | 20.8 | 20.7 | 0.59 |  $1.5\times 10^{5}$ | 5,242
| G | 3.9 | 36.5 | 9.1 | 9.9 | 3.47 | 19.4 | 22.7 | 20.8 | 20.8 | 0.62 |  $7.1\times 10^{4}$ | 2,020
| R | 6.1 | 32.9 | 12.8 | 14.9 | 5.31 | 20.5 | 22.7 | 21.4 | 21.4 | 0.45 |  $1.0\times 10^{4}$ | 111
Perseus Arm | B | 3.6 | 31.8 | 5.2 | 6.0 | 2.45 | 19.4 | 22.2 | 20.5 | 20.5 | 0.55 |  $1.7\times 10^{5}$ | 11,245
| G | 3.9 | 31.8 | 8.5 | 9.5 | 3.46 | 19.5 | 22.5 | 20.6 | 20.7 | 0.62 |  $6.5\times 10^{4}$ | 2,247
| R | 8.6 | 28.9 | 11.0 | 14.6 | 5.48 | 20.6 | 22.1 | 21.3 | 21.3 | 0.37 |  $2.0\times 10^{3}$ | 30
Outer Arm | B | 3.7 | 10.9 | 4.9 | 5.1 | 0.94 | 19.4 | 21.6 | 20.3 | 20.3 | 0.45 |  $8.3\times 10^{4}$ | 11,911
| G | 4.1 | 10.7 | 6.6 | 6.7 | 1.07 | 19.6 | 21.6 | 20.4 | 20.4 | 0.43 |  $7.6\times 10^{3}$ | 948

Note. — “Min.”, “Max.”, “Med.”, “Avg.”, and “S.D.” are the abbreviations for
minimum, maximum, median, average, and standard deviation.

###  3.3 Statistics of Physical Properties

The derivation of the physical properties using the 12CO, 13CO, and C18O lines
is described in detail in Appendix C. We remind the reader that the
calculation of $T_{\rm ex}$ is based on the assumption that the beam-filling
factor is equal to unity. However, the actual values are often less than unity
for the majority of MCs. Using the simulation results of Yan et al. (2021,
Equation 9 therein), the median filling factors of the 12CO structures in the
Local, Perseus, and Outer arms are estimated to be about 0.66, 0.65, and 0.64,
respectively. Hence, the excitation temperatures derived in this study
represent the lower limits.

We should also note that $N{\rm{}_{H_{2}}}$ traced by the 12CO alone is
obtained using the X-factor method, while those traced by 13CO and C18O are
derived using the LTE method. We know that $X_{\rm CO}$ may vary in changing
environments, and early works suggest that $X_{\rm CO}$ increases from the
Galactic center to the outer disk, due to the decreasing metallicity (Brand &
Wouterloot, 1995; Sodroski et al., 1995; Strong et al., 2004). Applying the
method of Barnes et al. (2015, 2018) to the 12CO clouds harboring 13CO
structures, we estimate the mean values of $X\rm_{CO}$ to be about 1.4, 1.6,
and 2.2 $\times 10^{20}~{}\rm cm^{-2}\left(K~{}km/s\right)^{-1}$ for the
Local, Perseus, and Outer arms, respectively. These values do not
significantly deviate from $X_{\rm CO}=2.0\times 10^{20}~{}\rm
cm^{-2}\left(K~{}km/s\right)^{-1}$ (Bolatto et al., 2013), so the commonly
used value is assumed throughout this study.

####  3.3.1 Image-based Statistics$\rm\,:$ $T_{\rm ex}$, $N{\rm{}_{H_{2}}}$

The pixel-by-pixel statistics of the excitation temperatures ($T_{\rm ex}$)
and H2 column densities ($N{\rm{}_{H_{2}}}$) are listed in Table 5 and plotted
as histograms in Figure 5. We find that the excitation temperatures and H2
column densities in the mask “B,” “G,” and “R” regions increase progressively.
In addition, the two nearby arms show very similar $T_{\rm ex}$ and
$N{\rm{}_{H_{2}}}$ values, while they show higher $T_{\rm ex}$ and
$N{\rm{}_{H_{2}}}$ values than the Outer arm. The different levels of beam
dilution effects may partially contribute to this trend. When comparing to
other Galactic environments, we find that the values for both properties in
the G220 region are lower than those in the G130 region (Sun et al., 2020),
suggesting the relatively low-excitation and low-density environment in the
G220 region.

Furthermore, we notice the bimodal distributions of the excitation
temperatures in the mask “R” regions in both the Local arm and the Perseus
arm, and the lower peaks appear to dominate the distributions. For the Local
arm, the two components are regarded to be contributed by two types of MCs.
The “cold” component with a peak at $T_{\rm ex}\sim 12\rm~{}K$ is contributed
by quiescent clouds or clouds in the early stages of star formation, while the
“warm” component with a peak at $T_{\rm ex}\sim 22\rm~{}K$ is related to MCs
containing active star-forming activity (Lin et al., 2021). For the Perseus
arm, the two components may also be due to two different types of MCs.

####  3.3.2 Sample-Based Statistics

The physical properties of the 12CO, 13CO, and C18O structures within the
three spiral arms are presented and compared in this section, including the
velocity dispersion ($\sigma_{v}$), effective radius ($R\rm_{eff}$), mass
($M$), mass surface density ($\Sigma$), and virial parameter
($\alpha\rm_{vir}$). Please refer to Appendix C for their definitions. Figure
6 exhibits the histograms of their distributions. The numbers of structures
are labeled in the top panels. The median values for each property are also
labeled in each panel. Note that the scale range of the x-axis is fixed for
each property of the 12CO and 13CO structures due to their similar dynamic
ranges, while it is wider than that for the C18O structures. Generally
speaking, the outskirts of an individual MC are traced by 12CO, the moderately
dense structures are traced by 13CO, and the most dense structures are traced
by C18O. At our current sensitivities, the vast majority of the 12CO clouds do
not harbor 13CO and C18O structures. And most of the 13CO structures do not
harbor C18O structures either (see Section 3.3.3 for details). Therefore, the
physical properties derived by the three isotopologs may have different
distributions. Besides, plots of the mean and median values of the physical
properties at different Galactocentric radii are displayed in Figure D1 in
Appendix D.

The velocity dispersions in Figure 6 show narrow distributions that span over
$\sim$0.1–2.2$~{}\rm km\,s^{-1}$, $\sim$0.1–2.0$~{}\rm km\,s^{-1}$, and
$\sim$0.1–0.9$~{}\rm km\,s^{-1}$ for the 12CO, 13CO, and C18O structures,
respectively. For each individual CO isotopolog, the median values of
$\sigma_{v}$ appear to be the same across the Galactic disk (around $\sim$0.4,
0.3, and 0.3$~{}\rm km\,s^{-1}$ for the 12CO, 13CO, and C18O structures,
respectively). For the 12CO structures, the median value of $\sigma_{v}$ is
much lower than those shown by the data from the CfA survey (e.g., $\sim$ 2.8
$\rm km\,s^{-1}$; Miville-Deschênes et al. 2017) and from the MWISP survey
with different decomposition algorithms (e.g., $\sim$ 1.1 $\rm km\,s^{-1}$; Ma
et al. 2021). However, it is similar to those shown by Sun et al. (2021) from
their results for the MWISP data with the same DBSCAN cloud decomposition
method. Note that the velocity resolution of the data, the cloud decomposition
algorithm, and the local environment of the interstellar medium may all affect
the statistics of $\sigma_{v}$.

Figure 5: Histograms of the excitation temperatures (left) and H2 column
densities (right). Top to bottom: histograms of the Local, Perseus, and the
Outer arms. The mask “B,” “G,” and “R” regions are colored in blue, green, and
red, respectively. The vertical dashed lines in the corresponding colors
indicate the median values.  Figure 6: Histograms of the derived physical
properties of the 12CO (left), 13CO (center) and C18O (right) structures.
Distributions for the structures in the whole G220 region and the Local,
Perseus, and Outer arms are shown in black, gray, orange, and blue histograms,
respectively. Top to bottom: histograms of the velocity dispersion, effective
radius, mass, mass surface density, and virial parameter. The median values
are labeled in each panel. The total numbers of molecular structures included
in the statistics are marked in the top panels. The vertical dashed lines in
the bottom panels denote the loci of $\alpha\rm_{vir}=2$.  Figure 7:
Histograms of $\mathbf{A}^{13}_{12}$ (top-left), $\mathbf{A}^{18}_{12}$ (top-
right), $\mathbf{M}^{13}_{12}$ (bottom-left), and $\mathbf{M}^{18}_{12}$
(bottom-right) of MCs in the whole G220 region (black) and the Local (gray),
Perseus (orange), and Outer (blue) arms. Please refer to Section 3.3.3 for the
definitions of the area and mass ratios. The total numbers of structures
included in the statistics and the median values for the ratios are marked.

The cloud sizes and masses of our sample span about 2 and 6 orders of
magnitude, respectively. As expected, the dynamic ranges of $R\rm_{eff}$ and
$M$, visible in Figure 6, show the highest, medium, and lowest values for the
12CO, 13CO, and C18O structures, respectively. Due to the improved sensitivity
and resolution of the MWISP data, we detect a large number of small and/or
faint structures with subparsec radii and subsolar masses that were largely
missed or identified as parts of the large MCs in previous studies. The
relatively small and/or faint 12CO and 13CO structures typically do not
contain C18O structures, possibly due to the C18O structures suffering more
severe beam dilution effects. When compared to the median values that are
based on the CfA data within the G220 region, such as Miville-Deschênes et al.
(2017, $\sim$17 pc and $\sim$$5\times 10^{3}~{}M_{\odot}$) and Rice et al.
(2016, $\sim$17 pc and $\sim$$8\times 10^{3}~{}M_{\odot}$), our 12CO samples
show the much smaller median values for both $R\rm_{eff}$ and $M$. However,
our 12CO samples again show similar median $R\rm_{eff}$ and $M$ values to
those of Sun et al. (2021, see Tables 6 and 7 therein).

In the entire G220 region, the total masses of the 12CO, 13CO, and C18O
structures are $4.0\times 10^{5}$, $1.4\times 10^{5}$, and $1.2\times
10^{4}~{}M_{\odot}$, respectively (listed in Column 13 of Table 5). The Local,
Perseus, and Outer arms account for $\sim$$38\%$, $\sim$$41\%$, and
$\sim$$21\%$ of the total 12CO-traced mass in the G220 region, respectively.
It seems that the two nearby spiral arms contribute a similar portion of the
total molecular gas mass and are more prominent than the Outer arm.
Nevertheless, the Perseus arm is much more prominent than the other arms in
the G130 region (Sun et al., 2020), with the Local, Perseus, and Outer arms
accounting for $\sim$20%, $\sim$70%, and $\sim$10% of the total 12CO-traced
mass, respectively. Besides, both our 12CO- and 13CO-traced masses in the
Outer arm are two times larger than those of the G130 region. These trends
follow the scenario traced by the young stellar population (Carraro et al.,
2005; Moitinho et al., 2006; Vázquez et al., 2008) and H I gas (Koo et al.,
2017)—the Perseus arm becomes less prominent, while the Outer arm seems to
grow, not lessen, from the SGQ to the TGQ.

The mass surface densities of the structures traced by different CO
isotopologs vary greatly—by $\sim$2 orders of magnitude. As expected, the 12CO
structures tracing the relatively diffuse portion of the MCs have the smallest
median values of $\Sigma$, while the C18O structures tracing the relatively
dense portion of the MCs have the largest median values of $\Sigma$. For each
individual CO isotopolog, the median values of $\Sigma$ are almost constant
across different Galactocentric radii (around $\sim$4.6, 5.6, and
53.2$~{}M_{\odot}\,\rm pc^{-2}$ for 12CO, 13CO, and C18O structures,
respectively). The nearly constant median value of $\Sigma\approx
5~{}M_{\odot}\,\rm pc^{-2}$ for 12CO clouds at $R_{\rm GC}\gtrsim 10\rm~{}kpc$
is also reported in previous studies (e.g., Miville-Deschênes et al., 2017;
Sun et al., 2021).

Figure 8: Relations between physical properties of the molecular structures
traced by different CO isotopologs. Top row: most 12CO structures are plotted
as small dots; those containing 13CO structures are plotted as bigger dots in
darker colors; and those further containing C18O structures are enclosed in
black squares. Middle row: similar to the top panels, but for 13CO structures.
Bottom row: for C18O structures. Left column: mass vs. effective radius
diagram. The yellow shadings, $M(r)\leqslant 870\,M_{\odot}\left(R/\rm
pc\right)^{1.33}$, highlight the regions where the clouds fail to form high-
mass stars (Kauffmann et al., 2010a, b, 2013; Kauffmann & Pillai, 2010). The
solid red lines are the empirical lower limit of the surface density required
for massive star formation ($\Sigma=0.05~{}\rm g\,cm^{-2}$, Urquhart et al.,
2013a, b). Middle column: velocity dispersion vs. effective radius plot. The
first Larson relation revealed by the data from Solomon et al. (1987) is also
drawn with the cyan line for comparison. Right column: virial parameter as a
function of mass. The pink shadings indicate the regions of
$\alpha\rm_{vir}<2$. The black solid, black dashed, and green solid lines
delineate the log–log linear least-squares fitting relations between the
physical properties of the 12CO, 13CO, and C18O structures, respectively. The
fitting results are also annotated in each graph, with the Pearson correlation
coefficients marked in parentheses.

The virial parameter describes the balance between the kinetic and
gravitational energies of the MCs. The vertical dashed lines in the last row
of Figure 6 demarcate the gravitationally bound structures
($\alpha\rm_{vir}<2$) from the unbound structures ($\alpha\rm_{vir}\geqslant
2$; Kauffmann et al. 2013). We find that only a very small fraction of 12CO
structures appear to be bound, with the percentages of $\sim$$0.5\%$,
$\sim$$4.1\%$, and $\sim$$8.0\%$ for the Local, Perseus, and Outer arms,
respectively. And there are $\sim$$3.1\%$, $\sim$$32.4\%$, and $\sim$$42.1\%$
gravitationally bound 13CO structures in the Local, Perseus, and Outer arms,
respectively. Unlike the 12CO and 13CO structures, the C18O structures are
more likely to be bound, i.e., $\sim$$86.8\%$ of the C18O structures in the
entire G220 region have $\alpha\rm_{vir}<$2\. In addition, the median
$\alpha\rm_{vir}$ values in the Perseus and Outer arms are much lower than
those in the Local arm. This seems to be a consequence of the increasing
detection limit. In the more distant arms, we miss smaller structures that
tend to have relatively high $\alpha\rm_{vir}$ values (as shown in Section
3.4).

####  3.3.3 Dense Gas Fraction

In the entire G220 region, there are 216 12CO clouds ($\sim$15%) containing
13CO dense structures and 11 12CO clouds ($\sim$0.7%) containing C18O dense
structures. The proportion of $\sim$15% is consistent with that measured by
the MWISP survey in the SGQ (Yuan et al., 2022). Besides, the proportions for
12CO clouds harboring 13CO dense structures are similar across the Galactic
disk, with $\sim$14%, $\sim$16%, and $\sim$14% in the Local, Perseus, and
Outer arms, respectively. One can see that typically only a small fraction of
12CO clouds harbor 13CO and/or C18O dense structures. To understand the
contributions of the dense structures to the MCs, we define the area ratios as
follows: $\mathbf{A}^{13}_{12}\equiv
A\left({\rm{}^{13}CO}\right)/A\left({\rm{}^{12}CO}\right)$ and
$\mathbf{A}^{18}_{12}\equiv A\left({\rm
C^{18}O}\right)/A\left({\rm{}^{12}CO}\right)$ where
$A\left(\rm{}^{12}CO\right)$, $A\left(\rm{}^{13}CO\right)$, and $A\left(\rm
C^{18}O\right)$ are the area of the 12CO cloud and the total areas of the 13CO
and C18O dense structures within each 12CO cloud, respectively. Similarly, we
define the mass ratios as $\mathbf{M}^{13}_{12}\equiv
M\left({\rm{}^{13}CO}\right)/M\left({\rm{}^{12}CO}\right)$ and
$\mathbf{M}^{18}_{12}\equiv M\left({\rm
C^{18}O}\right)/M\left({\rm{}^{12}CO}\right)$ where
$M\left(\rm{}^{12}CO\right)$, $M\left(\rm{}^{13}CO\right)$, and $M\left(\rm
C^{18}O\right)$ are the mass of the 12CO cloud and the total masses of the
13CO and C18O dense structures within each 12CO cloud, respectively.

The histograms of the ratios are plotted in Figure 7. The area ratios
$\mathbf{A}^{13}_{12}$ and $\mathbf{A}^{18}_{12}$ span ranges from $\sim$1.2%
to 80% and from $\sim$0.9% to 5.9%, respectively. The distributions of the
mass ratios are similar to the area ratios, ranging from $\sim$0.3% to 76.6%
and from $\sim$1.6% to 12.3% for $\mathbf{M}^{13}_{12}$ and
$\mathbf{M}^{18}_{12}$, respectively. Yuan et al. (2022) reported a sharp
upper limit of $\mathbf{A}^{13}_{12}=70\%$, and it is notable that, in
general, our $\mathbf{A}^{13}_{12}$ values are indeed below this upper limit.
Moreover, we see that the median values (labeled in each panel) of
$\mathbf{A}^{18}_{12}$ and $\mathbf{M}^{18}_{12}$ are quite small, suggesting
that the C18O dense structures typically occupy only a very small fraction of
areas and masses in MCs.

###  3.4 Relations between Physical Properties

Figure 8 shows the relations between the physical properties of the 12CO (top
panels), 13CO (center panels), and C18O (bottom panels) structures. One can
see that the 12CO clouds that contain 13CO and/or C18O dense structures and
the 13CO structures that contain C18O dense structures generally have the
largest sizes and masses and the most turbulent velocity dispersions. The
log–log linear least-squares fitting results are labeled in the diagrams, with
the Pearson correlation coefficients marked in parentheses.

A power-law relation between mass and radius, $M\propto R^{2}$, is available
from Larson (1981), indicating the clouds having a nearly constant surface
density. Kauffmann et al. (2010a, b) treated the exponent of the $M$–$R$
relation as a proxy for how column density varies with radius. The left panels
of Figure 8 show the strong correlations (Pearson correlation coefficients
$r\gtrsim 0.95$) between $\log(M)$ and $\log(R\rm_{eff})$ for the 12CO, 13CO,
and C18O structures, with the exponents $\beta=2.15$, 2.35, and 2.34,
respectively. We find that the $\beta$ values fitted from the 13CO, and C18O
structures are very close to those measured by the Galactic Ring Survey (GRS)
survey (Roman-Duval et al., 2010), while those fitted from the 12CO structures
are closer to Larson’s results.

Table 6: Basic Properties of Peculiar MCs Name |  | $v\rm_{\scriptscriptstyle LSR}$ | $\sigma_{v}$ |  |  |  |  |  |  |  |  | Dist. | $R\rm_{eff}$ | MassaaRefers to the molecular mass traced by 12CO. |  | $\alpha\rm_{vir}$ | $\mathbf{A}^{13}_{12}$ | $\mathbf{M}^{13}_{12}$ | $\mathbf{A}^{18}_{12}$ | $\mathbf{M}^{18}_{12}$ | Arm |  |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | ($\rm km\,s^{-1}$) | ($\rm km\,s^{-1}$) |  |  |  |  |  |  |  |  | (kpc) | (pc) | ($M_{\odot}$) |  |  | (%) | (%) | (%) | (%) |  |  |
MWISP G220.634$-$1.916 |  | 11.7 | 2.22 |  |  |  |  |  |  |  |  | 1.0 | 9.7 | $8.3\times 10^{3}$ |  | 6.7 | 52.8 | 42.7 | 1.8 | 4.0 | Local |  |
MWISP G221.775$-$3.007 |  | 12.9 | 1.05 |  |  |  |  |  |  |  |  | 1.0 | 11.3 | $1.0\times 10^{4}$ |  | 1.4 | 44.5 | 37.7 | 0.9 | 1.6 | Local |  |
MWISP G224.440$-$1.069 |  | 16.3 | 1.91 |  |  |  |  |  |  |  |  | 1.1 | 27.9 | $1.0\times 10^{5}$ |  | 1.1 | 50.5 | 52.7 | 3.9 | 9.1 | Local |  |
MWISP G221.921$-$2.121 |  | 39.3 | 1.19 |  |  |  |  |  |  |  |  | 3.7 | 21.4 | $6.5\times 10^{4}$ |  | 0.5 | 58.6 | 67.3 | 0.9 | 1.6 | Perseus |  |
MWISP G223.736$-$2.027 |  | 63.0 | 0.88 |  |  |  |  |  |  |  |  | 6.6 | 11.2 | $4.7\times 10^{3}$ |  | 2.2 | 22.3 | 18.8 |  $\cdots$ |  $\cdots$ | Outer |  |

The $M$–$R$ diagrams can also be used to investigate the possible high-mass
star forming sites. The yellow shadings in Figure 8 represent the region where
clouds are not massive enough to form high-mass stars, i.e., $M(r)\leqslant
870\,M_{\odot}\left(R/\rm pc\right)^{1.33}$ (Kauffmann et al., 2010a, b, 2013;
Kauffmann & Pillai, 2010). The solid red lines trace the empirical minimum
threshold required for massive star formation—surface density equal to
$0.05~{}\rm g\,cm^{-2}$ (Urquhart et al., 2013a, b). We find that none of our
structures reaches the threshold of Urquhart et al. (2013a, b), and only two
12CO clouds (MWISP G224.440$-$1.069 and MWISP G221.921$-$2.121; see Figure 9)
together with two 13CO structures (MWISP G223.939$-$1.895 and MWISP
G221.954$-$2.090) lie above the border of Kauffmann et al. (2010a, b, 2013)
and Kauffmann & Pillai (2010). We also find that the two 13CO structures match
the two 12CO clouds, respectively, which are the most massive MCs
($\gtrsim$$6\times 10^{4}~{}M_{\odot}$) in the G220 region. The scarcity of
high-mass star formation is consistent with the literature, i.e., no 6.7 GHz
methanol maser has been detected in the G220 region (according to the MaserDB
database;444https://maserdb.net Ladeyschikov et al., 2019).

The velocity dispersion–size relation of the form $\sigma_{v}\propto R^{0.5}$
is well known as the first Larson relation (the cyan line in Figure 8; Larson,
1981; Solomon et al., 1987; Heyer & Brunt, 2004). The middle panels of Figure
8 render the moderate correlations between $\log(\sigma_{v})$ and
$\log(R\rm_{eff})$ with the Pearson correlation coefficients $r=0.44$, 0.54,
and 0.67 for the 12CO, 13CO, and C18O structures, respectively. We find that
the exponents traced by the 12CO and 13CO structures in the TGQ ($\beta=0.17$
and 0.25, respectively) are comparable with those observed by the MWISP survey
in the SGQ (Li et al., 2020; Ma et al., 2021). However, these $\beta$ values
are much shallower than the Larson relation. The shallow
$\sigma_{v}$–$R\rm_{eff}$ relations may be due to the fact that the small
clouds deviates from the Larson relation. Similar to Benedettini et al.
(2020), we again perform least-squares fits to the 12CO clouds at two
different scales. For those with radius $R_{\rm eff}\geqslant 2\rm~{}pc$, the
best fit gives $\beta=0.55$ (and $r=0.55$), which is in good agreement with
the Larson relation, whereas the best fit for those with $R_{\rm
eff}<2\rm~{}pc$ is flatter ($\beta=0.11$ and $r=0.25$), which deviates
significantly from the Larson relation. These are basically consistent with
the results of Benedettini et al. (2020).

Figure 9: Integrated intensity maps and spectra of the MCs MWISP
G220.634$-$1.916, G221.775$-$3.007, G224.440$-$1.069, G223.736$-$2.027, and
G221.921$-$2.121. The 12CO, 13CO, and C18O lines are drawn in blue, green, and
red, respectively. The integrated intensity maps are shown in a square-root
scale to clearly visualize the faint parts of the MCs, and the color bars
represent integrated intensity in units of $\rm K~{}km\,s^{-1}$. The spectra
shown in each plot, with the y-axis on the $T_{\rm MB}$ scale, are averaged
over a $90\arcsec\times 90\arcsec$ ($3\times 3$ pixels) region selected around
the brightest pixel of each MC. The magenta crosses denote the 22 GHz H2O
masers detected toward the star formation regions (Han et al., 1998;
Valdettaro et al., 2001; Sunada et al., 2007; Urquhart et al., 2011). The H II
regions from Blitz et al. (1982) and the WISE catalog (Anderson et al., 2014)
are marked as green and yellow circles, respectively.  Figure 10: Molecular
gas distributions along the Galactic longitude (upper panels) and the Galactic
latitude (lower panels), integrated over a Galactic latitude range from
$-5\fdg 25$ to $5\fdg 25$ and a Galactic longitude range from $219\fdg 75$ to
$229\fdg 75$, respectively. The mass distributions of the whole G220 region
and the Local, Perseus, and Outer arms are shown in black, gray, orange, and
blue histograms, respectively. And the mass distributions traced by 12CO,
13CO, and C18O are exhibited in the left, middle, and right panels,
respectively.

For pressure-confined objects (i.e., $\alpha\rm_{vir}\gg 1$), Bertoldi & McKee
(1992) predicted a theoretical power-law correlation between virial parameters
and masses with an exponent equal to $-\text@frac{2}{3}$. In Figure 8 (right
panels), anticorrelations over a broad mass range can be seen. We notice that
the correlations for the 12CO and 13CO structures are well defined
($r\sim-0.8$), while the correlation for C18O structures is just modest
($r=-0.39$). The exponents for 12CO and 13CO structures ($=-0.36$ and $-0.35$,
respectively) are similar to that reported by Kauffmann et al. (2013) from
their analysis of the GRS data (Roman-Duval et al., 2010). These
anticorrelation trends reflect a scenario in which more massive clouds are
more gravitationally bound and therefore less stable—more likely to collapse
without the additional support, such as from a strong magnetic field
(Kauffmann et al., 2013). Moreover, the masses in the bound 12CO, 13CO, and
C18O structures account for $\sim$54.1%, $\sim$82.4%, and $\sim$96.8% of the
total 12CO, 13CO, and C18O masses, respectively. These mass proportions for
the bound structures are much higher than the number proportions (see Section
3.3.2). We can then conclude that, despite their small numbers,
gravitationally bound molecular structures hold most of the molecular masses.

###  3.5 Massive MCs Presentation

The high-sensitivity and high-resolution MWISP 12CO, 13CO, and C18O data
provide an excellent opportunity to observe the elaborate morphologies of the
MCs. In this section, we present five peculiar MCs that show filamentary
structures and represent the most massive MCs in the three spiral arms. Their
basic properties are tabulated in Table 6. Interestingly, the dense gas
fractions in these clouds are generally higher than the typical values marked
in Figure 7 for each arm component. Their integrated intensity maps and
spectra are shown in Figure 9, with 12CO, 13CO, and C18O drawn in blue, green,
and red, respectively. In each image, we also mark the associated 22 GHz H2O
maser sources, by using the MaserDB database (Ladeyschikov et al., 2019), and
the associated H II regions, by referring to Blitz et al. (1982) and the Wide-
Field Infrared Survey Explorer (WISE) catalog of Galactic H II regions
v2.2555http://astro.phys.wvu.edu/wise/ (Anderson et al., 2014, hereafter, the
WISE catalog). The following descriptions of the MCs are in the order of the
maps in Figure 9.

MWISP G220.634$-$1.916. This cloud has the largest velocity dispersion
($\sim$$2.2\rm~{}km\,s^{-1}$) in the G220 region. The optically thick 12CO
spectral line around the emission peak exhibits an obvious red asymmetric
structure. We find a that 22 GHz H2O maser (Han et al., 1998) and two H II
regions (Blitz et al., 1982) are associated with this cloud.

MWISP G221.775$-$3.007. The optically thick 12CO molecular line around the
emission peak shows a significant red asymmetric structure.

MWISP G224.440$-$1.069. This cloud is the most massive MC, accounting for
$\sim$26%, $\sim$38%, and $\sim$76% of the total 12CO, 13CO, and C18O traced
masses in the entire G220 region, respectively. It traces the CMa OB1 complex,
which has been studied in detail by the previous works, such as Kim et al.
(2004), Elia et al. (2013), and Lin et al. (2021). A total of seven 22 GHz H2O
masers (e.g., Sunada et al., 2007; Urquhart et al., 2011) and three H II
regions (according to the WISE catalog) are associated with this cloud.

MWISP G223.736$-$2.027. It does not contain any C18O dense structures. This
source shows the typical filamentary structure even at a distance of $\sim$6.6
kpc. None of the known 22 GHz H2O masers and H II regions are associated with
this cloud.

MWISP G221.921$-$2.121. This is the second most massive MC in the G220 region.
A 22 GHz H2O maser has been detected toward it (e.g., Valdettaro et al.,
2001). Two H II regions from the WISE catalog and one H II region from Blitz
et al. (1982) are associated with this cloud.

Figure 11: Left: locations of the MCs projected on the Galactic plane. The
plan view of the Milky Way (Reid et al., 2019) is overlaid. The straight
dashed lines denote the directions of the Galactic longitude $l=180\degree$,
$210\degree$, $240\degree$, and $270\degree$. The Sun (red Sun symbol) is at
(0, 8.15) kpc. The solid gray, orange, and blue curved lines trace the centers
(and the dotted curved lines indicate the widths enclosing $90\%$ of the high-
mass star-forming regions of Reid et al. 2019) of the Local, Perseus, and
Outer arms, respectively. Right: distribution of the $\it z$-scale height vs.
the Galactocentric radius $R\rm_{GC}$. The Galactic plane ($z=0$) is drawn
with the dashed line. The Sun (red Sun symbol) is at ($8.15\rm~{}kpc$,
$5.5\rm~{}pc$). The red crosses indicate the centers of $R\rm_{GC}$ and $\it
z$ of the three arms, whose values are also marked. The red bars denote the
thicknesses of the arms, with their values noted on the side. In both panels,
the lightest, medium, and darkest filled circles represent the 12CO, 13CO, and
C18O structures, respectively. The symbol size is proportional to
$\log\left(M\right)$. The proportions of the three CO isotopologs are
different for the convenience of presentation.

##  4 3D Distributions in the Milky Way

In order to understand the mass distributions, we calculate the total
molecular mass within every $0.5\degree$ of the Galactic longitude and
latitude, respectively. The mass distributions along the $l$ (upper panels)
and $b$ (lower panels) directions are depicted in Figure 10, with those traced
by 12CO, 13CO, and C18O plotted in the left, center, and right panels,
respectively.

We notice that in each individual spiral arm, the distribution peaks of the
masses traced by 12CO, 13CO, and C18O are approximately at the same $l$ and
$b$. Along the $l$ direction, most of the molecular masses are distributed in
the range of $l<225\degree$. The mass distributions in the Local arm are
concentrated at $l\sim 224\degree$, while those in the Perseus arm are
concentrated at $l\sim 222\degree$. And there is no significant mass peak
along the $l$ direction in the Outer arm. This suggests that the molecular gas
is unevenly distributed along the Local and Perseus arms, but appears to be
more evenly distributed along the Outer arm. After close examination, we find
that the distribution peaks of the Local and Perseus arms correspond to the
aforementioned massive MCs MWISP G224.440$-$1.069 and MWISP G221.921$-$2.121
(Figure 9), respectively. Along the $b$ direction, the majority of the
molecular gases are distributed in the range of $b<0\degree$. According to the
13CO maps of Kim et al. (2004), the Local arm in the G220 region extends to at
least $b\sim-10\degree$, therefore it is important to note that our data do
not actually cover the entire Local arm (also mentioned in Section 3.1).
However, the Perseus and Outer arms seem to be almost completely mapped. The
masses of the Perseus arm are concentrated at $b\sim-2\degree$. The Outer arm
has no significant distribution peak along the $b$ direction either.

The face-on and vertical distributions of the MCs are displayed in Figure 11,
with the circle sizes proportional to $\log\left(M\right)$. In both maps, the
Outer arm traced by the molecular gas appears prominently in this Galactic
range for the first time, although it has been well described by other spiral
arm tracers (Carraro et al., 2005; Moitinho et al., 2006; Vázquez et al.,
2008; Koo et al., 2017). Furthermore, we find that the spiral arms traced by
MCs are different from the arm model of Reid et al. (2019) in the face-on map.
The discrepancy may be attributed to both the uncertainty of the kinematic
distances and the bias of very few maser targets in the arm model. Along the
$z$-direction, the MCs seem to be asymmetrically distributed. The minimum $z$
of the MCs reaches $\sim$$-600\rm~{}pc$, while the maximum $z$ only reaches
$\sim$$400\rm~{}pc$. A substantial proportion ($\sim$$75\%$) of the molecular
structures fall below the Galactic plane. In addition, we see that the dynamic
ranges of the MCs’ $z$-scale heights are increasing with the Galactocentric
radius $R_{\rm GC}$. These reveal evident pictures of the Galactic disk
warping and flaring (Burke, 1957; Kerr, 1957; Westerhout, 1957; Burton, 1988;
Wouterloot et al., 1990) in the G220 region.

To better quantify the warp and flare of the molecular gas disk, we derive the
arm ($R_{\rm GC}$, $z$) centers by the mass-weighted average of the MCs’
$R_{\rm GC}$ and $z$-scale height, and we derive the arm thicknesses by the
mass-weighted standard deviation of the MCs’ $z$-scale height. The center
positions are drawn as red crosses, and the thicknesses are marked with red
bars in Figure 11. The derived ($R_{\rm GC}$, $z$) centers of the Local,
Perseus, and Outer arms are located at about (9, $-$23), (11, $-$90), and (14,
$-$162) in units of (kpc, pc), respectively. The thicknesses of the Local,
Perseus, and Outer arms are about 48, $201$, and $457$ pc, respectively. The
Outer arm is more than twice as thick as the Perseus arm. Obviously, both the
vertical displacements and thicknesses of the spiral arms are increasing with
$R_{\rm GC}$. These results are consistent with those traced by other spiral
arm tracers in the same Galactic longitude range, such as H I and stellar
emission (e.g., Gum et al., 1960; Russeil, 2003).

##  5 Summary

Using the high-quality MWISP data, we conducted a large-scale 12CO, 13CO, and
C18O ($J=1$–0) survey in the G220 region, i.e., $l=[\,219\fdg 75,~{}229\fdg
75\,]$ and $b=[\,-5\fdg 25,~{}5\fdg 25\,]$ (105 deg2 in total), and obtained
1,514,461 spectra for each CO isotopolog. According to the $l$–$v$ maps, the
entire G220 region is divided into the Local, Perseus, and Outer arms that are
discussed. Our main results can be summarized as follows.

  1. 1.

We identified a total of 1,502 12CO, 570 13CO, and 53 C18O molecular
structures by using the DBSCAN algorithm. There are 216 12CO structures
containing 13CO dense structures and 11 12CO structures containing C18O dense
structures.

  2. 2.

The G220 region is generally in the low-excitation and low-density phase. The
total masses of the 12CO, 13CO, and C18O structures are estimated to be
$4.0\times 10^{5}$, $1.4\times 10^{5}$, and $1.2\times 10^{4}~{}M_{\odot}$,
respectively. The Local, Perseus, and Outer arms account for $\sim$$38\%$,
$\sim$$41\%$, and $\sim$$21\%$ of the total 12CO-traced mass in the G220
region, respectively. Comparing to the SGQ (Sun et al., 2020), we notice that
in the TGQ, the Outer arm appears to be more conspicuous, while the Perseus
arm is less prominent.

  3. 3.

Our survey resolves the molecular structures at different scales, i.e., with
the effective radii of $\sim$0.04–$27.9\rm~{}pc$ and masses of
$\sim$$10^{-2}$–$10^{5}~{}M_{\odot}$. The vast majority of the 12CO and 13CO
structures appear to be gravitationally unbound ($\alpha\rm_{vir}\geqslant
2$), while the C18O structures are more likely to be bound
($\alpha\rm_{vir}<2$).

  4. 4.

Strong $M$–$R\rm_{eff}$ correlations and tight $\alpha\rm_{vir}$–$M$
anticorrelations are observable. However, the correlations between
$\sigma_{v}$ and $R\rm_{eff}$ appear to be not obvious over the full dynamic
range.

  5. 5.

For the Local, Perseus, and Outer arms, the derived arm $(R_{\rm GC},~{}z)$
centers are about (9, $-$23), (11, $-$90), and (14, $-$162) in units of (kpc,
pc), and the derived arm thicknesses are about 48, $201$, and $457\rm~{}pc$,
respectively. Both the vertical displacements and thicknesses of the spiral
arms are increasing with the Galactocentric radius.

This research has made use of the data from the Milky Way Imaging Scroll
Painting (MWISP) project, which is a multiline survey in 12CO/13CO/C18O along
the northern Galactic plane with the PMO $13.7\rm~{}m$ telescope. We are very
grateful to all members of the MWISP working group, particularly the staff
members at the PMO $13.7\rm~{}m$ telescope, for their long-term support. MWISP
was sponsored by the National Key R&D Program of China with grant
2017YFA0402701 and the CAS Key Research Program of Frontier Sciences with
grant QYZDJ-SSW-SLH047. Y.S. acknowledges support by the Youth Innovation
Promotion Association, CAS (Y2022085), and the “Light of West China” Program
(No. xbzg-zdsys-202212). J.Y. is supported by the National Natural Science
Foundation of China through grant 12041305. PMO $13.7\rm~{}m$ telescope ,
SAOImage DS9 (Joye & Mandel, 2003).

Table B1: Physical Properties of Molecular Structures

Index | Name | $v\rm_{\scriptscriptstyle LSR}$ | $\sigma_{v}$ |  |  |  |  | $W\rm_{CO}$ | $T_{\rm peak}$ | Dist. | $R\rm_{eff}$ | Area | Mass | $\Sigma$ | $M_{\rm vir}$ | $\alpha\rm_{vir}$ | Arm | Flag | Matching
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | ($\rm km\,s^{-1}$) | ($\rm km\,s^{-1}$) |  |  |  |  | ($\rm K~{}km\,s^{-1}$) | (K) | (kpc) | (pc) | (pc2) | ($M_{\odot}$) | ($M_{\odot}\rm~{}pc^{-2}$) | ($M_{\odot}$) |  |  |  |  12CO cloud
4 | MWISP G220.634$-$1.916 | 11.66 | 2.22 |  |  |  |  | 6.4 | 27.5 | 1.00 |  | 294.8 | $8.3\times 10^{3}$ | 28.1 | $5.6\times 10^{4}$ |  6.7 | Loc | 12 |  $\cdots$
892 | MWISP G222.927$+$0.922 | 31.31 | 0.31 |  |  |  |  | 2.3 | 9.2 | 2.84 |  | 8.9 | $8.7\times 10^{1}$ | 9.8 | $1.8\times 10^{2}$ |  2.1 | Per | 12 |  $\cdots$
1282 | MWISP G223.302$-$0.333 | 53.71 | 0.40 |  |  |  |  | 2.1 | 5.8 | 5.33 |  | 60.7 | $5.6\times 10^{2}$ | 9.2 | $8.0\times 10^{2}$ |  1.4 | Out | 12 |  $\cdots$
1640 | MWISP G220.312$-$1.740 | 13.80 | 0.53 |  |  |  |  | 1.1 | 3.6 | 1.00 |  | 6.2 | $8.8\times 10^{1}$ | 14.2 | $4.7\times 10^{2}$ |  5.3 | Loc | 13 | 4
1975 | MWISP G221.954$-$2.090 | 39.59 | 0.87 |  |  |  |  | 2.8 | 9.1 | 3.73 |  | 661.7 | $4.1\times 10^{4}$ | 61.2 | $1.3\times 10^{4}$ |  0.3 | Per | 13 | 953
2061 | MWISP G227.939$-$0.138 | 66.08 | 0.36 |  |  |  |  | 0.6 | 1.4 | 6.59 |  | 19.3 | $1.6\times 10^{2}$ | 8.4 | $3.5\times 10^{2}$ |  2.1 | Out | 13 | 1421
2068 | MWISP G229.744$+$0.117 | 70.29 | 0.33 |  |  |  |  | 0.6 | 1.8 | 6.99 |  | 30.0 | $2.7\times 10^{2}$ | 9.1 | $3.7\times 10^{2}$ |  1.4 | Out | 13 | 1468
2077 | MWISP G220.677$-$1.866 | 12.28 | 0.40 |  |  |  |  | 0.5 | 2.2 | 1.00 |  | 1.9 | $1.2\times 10^{2}$ | 65.0 | $1.4\times 10^{2}$ |  1.1 | Loc | 18 | 4
2125 | MWISP G229.578$+$0.153 | 52.90 | 0.60 |  |  |  |  | 0.5 | 1.1 | 4.92 |  | 8.2 | $5.3\times 10^{2}$ | 64.1 | $6.3\times 10^{2}$ |  1.2 | Per | 18 | 1204

Note. — Column (1): index of the source. Column (2): source name given by the
MWISP project and the Galactic coordinates of the cloud centroid. Columns
(3)–(4): LSR velocity and velocity dispersion. Column (5): average integrated
intensity across the area of the structure. Column (6): peak main-beam
temperature. Columns (7)–(13): heliocentric distance, effective radius, area,
mass, mass surface density, virial mass, and virial parameter. Column (14):
spiral arm layer. Column (15): flag—“12”, “13”, and “18” denote samples traced
(and their physical properties estimated) by the 12CO, 13CO, and C18O lines,
respectively. Column (16): index of the matching 12CO cloud for the 13CO and
C18O structures. Only a small portion of the catalog is shown here, and a
machine-readable version of the full table is published at Science Data Bank:
https://doi.org/10.57760/sciencedb.07765 (Dong et al., 2023).

##  Appendix A Data with the bad channels

The $l$–$v$ map of the “uncleaned” 12CO emission is shown in Figure A1. The
integration ranges are $-5\fdg 25\leqslant b\leqslant 5\fdg 25$. The map
includes the spurious signals caused by $\sim$$34~{}\rm km\,s^{-1}$ bad
channels.

Figure A1: Longitude–velocity map of the “uncleaned” 12CO emission, integrated
over a Galactic latitude range from $-5\fdg 25$ to $5\fdg 25$. The three MCs
in red circles are contaminated by the bad channels.

##  Appendix B Properties of Molecular Structures

The physical properties of the 12CO, 13CO, and C18O molecular structures are
summarized in Table B1.

##  Appendix C Derivation of Physical Properties

This appendix presents the equations used to estimate the physical properties.

###  C.1 Excitation Temperature

Assuming that the 12CO line is optically thick and that the beam-filling
factors are near unity, the excitation temperature in each pixel of the MC can
be expressed as (e.g., Bourke et al., 1997)

$T_{\rm
ex}=\frac{5.532}{\ln\left[\,1+5.532/\left(T\rm_{MB,pk}\\!\left({}^{12}CO\right)+0.819\right)\,\right]},$
(C1)

where $T{\rm{}_{MB,pk}\\!\left({}^{12}CO\right)}$ is the peak main-beam
brightness temperature of 12CO.

Figure D1: Physical properties of the 12CO (blue), 13CO (green), and C18O
(red) structures as a function of the Galactocentric radius. Histograms and
triangles indicate the mean and median values of physical properties in the
$R\rm_{GC}$ bins of 1 kpc width, respectively, and vertical lines correspond
to the standard deviations around the mean values. From top to bottom:
velocity dispersion, effective radius, mass, mass surface density, and virial
parameter. Note that the y-axis is logarithmically scaled for the physical
properties whose mean or median values span more than $\sim$2 orders of
magnitude along $R\rm_{GC}$.

###  C.2 $\rm H_{2}$ Column Density

The H2 column density for the 12CO clouds can be estimated by simply
multiplying the integrated intensities of 12CO ($\int
T{\rm{}_{MB}\\!\left({}^{12}CO\right)}\,dv$) by the commonly used CO-to-H2
conversion factor $X_{\rm CO}=2.0\times 10^{20}~{}\rm
cm^{-2}\left(K~{}km/s\right)^{-1}$ (Bolatto et al., 2013). For the 13CO and
C18O structures, the H2 column density can be derived using the LTE method,
which is based on the assumption of the equal excitation temperatures for
12CO, 13CO, and C18O in the LTE conditions.

Firstly, the optical depths of the 13CO and C18O lines in each pixel of the
molecular structure are given by

$\displaystyle\tau\\!\left(\rm{}^{13}CO\right)=-\ln\\!$
$\displaystyle\left[1-\frac{T{\rm{}_{MB,pk}\\!\left({}^{13}CO\right)}}{5.29}\right.$
$\displaystyle\left.\times\left(\frac{1}{e^{5.29/T_{\rm
ex}}-1}-0.164\right)^{-1}\right]$ (C2)

and

$\displaystyle\tau\\!\left(\rm C^{18}O\right)=-\ln\\!$
$\displaystyle\left[1-\frac{T{\rm{}_{MB,pk}\\!\left(C^{18}O\right)}}{5.27}\right.$
$\displaystyle\left.\times\left(\frac{1}{e^{5.27/T_{\rm
ex}}-1}-0.166\right)^{-1}\right],$ (C3)

where $T\rm_{MB,pk}\\!\left({}^{13}CO\right)$ and
$T\rm_{MB,pk}\\!\left(C^{18}O\right)$ are the peak main-beam brightness
temperatures of 13CO and C18O, respectively. In general, the C18O line is
optically thin. For the 13CO line, we find that the median, 5th percentiles,
and 95th percentile values of $\tau\\!\left(\rm{}^{13}CO\right)$ are
$\sim$0.27, 0.12, and 0.67, respectively. This suggests that the 13CO line can
be considered optically thin for almost all pixels of our 13CO structures.
Then, the 13CO and C18O column densities in each pixel of the molecular
structure can thus be expressed as (Bourke et al., 1997; Pineda et al., 2010)

$\displaystyle N_{\rm{}^{13}CO}=2.$ $\displaystyle
42\times{10}^{14}\times\frac{\tau\\!\left(\rm{}^{13}CO\right)}{1-e^{-\tau\\!\left(\rm{}^{13}CO\right)}}$
$\displaystyle\times\frac{1+0.88/T_{\rm ex}}{1-e^{-5.29/T_{\rm
ex}}}\int\\!T_{\rm MB}\\!\left(\rm{}^{13}CO\right)\,dv$ (C4)

and

$\displaystyle N_{\rm C^{18}O}=2.$ $\displaystyle
54\times{10}^{14}\times\frac{\tau\\!\left(\rm
C^{18}O\right)}{1-e^{-\tau\\!\left(\rm C^{18}O\right)}}$
$\displaystyle\times\frac{1+0.88/T_{\rm ex}}{1-e^{-5.27/T_{\rm
ex}}}\int\\!T_{\rm MB}\\!\left(\rm C^{18}O\right)\,dv.$ (C5)

Finally, the isotope ratios of $\left[\rm{}^{12}C/^{13}C\right]=6.21\it
R\rm_{GC}+18.71$ ($R_{\rm GC}$ is the Galactocentric radius in units of kpc;
Milam et al., 2005) and $\left[\rm{}^{16}O/^{18}O\right]=560$ (Wilson & Rood,
1994) and an abundance ratio of $\left[\rm H_{2}/^{12}C\right]=1.1\times
10^{4}$ (Frerking et al., 1982) are adopted to convert the 13CO and C18O
column densities to H2 column densities.

###  C.3 Mass, Mass Surface Density, Effective Radius, Velocity Dispersion,
and Virial Parameter

The mass of the molecular structure is estimated as $M=2\mu
m_{\scriptscriptstyle\rm H}a^{2}d^{2}\sum\nolimits_{i}N_{\rm H_{2}}$, where
$\mu=1.36$ is the mean atomic weight, taking the contribution of helium and
metals into account, $m\rm{}_{H}$ is the mass of a hydrogen atom,
$a=30\arcsec$ is the angular size of a pixel, and $d$ is the heliocentric
distance.

The mass surface density, in units of $M_{\odot}~{}\rm pc^{-2}$, is simply
calculated by $\Sigma=M/\left(A\times d^{2}\right)$, where $A=a^{\rm 2}\times
N_{\rm pixel}$ is the angular area (projected area) of the molecular
structure.

Assuming that the cloud is spherical, the effective radius can thus be
expressed as $R_{\rm eff}=d\,\sqrt{\frac{A}{\pi}-\frac{\theta^{2}_{\rm
MB}}{4}}$ (Ladd et al., 1994), where $\theta_{\rm MB}\sim 50\arcsec$ is the
beam size.

The velocity dispersion ($\sigma_{v}$) of the molecular structure is defined
as the $T\rm_{MB}$-weighted second moment within the PPV voxels of the
structure. Then, the line width of the molecular structure is estimated as
$\Delta v=\sqrt{8\ln 2}\times\sigma_{v}$.

The virial mass can be calculated by $M_{\rm vir}=210\times R_{\rm
eff}\times\left(\Delta v\right)^{2}$ (MacLaren et al., 1988), where $R_{\rm
eff}$ is in units of pc, $\Delta v$ is in units of $\rm km\,s^{-1}$, and the
derived $M_{\rm vir}$ is in units of $M_{\odot}$. Then, the virial parameter
is defined as $\alpha_{\rm vir}=M_{\rm vir}/M$.

##  Appendix D Physical Properties at different Galactocentric radii

This appendix presents the mean and median values of physical properties as a
function of the Galactocentric radius.

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